Section 3F, IRIX 6.5

1555 pages.

abort(3F) [p_man/cat3/f90] ABORT - Requests abort with traceback
abort(3F) [p_man/cat3/ftn] abort - terminate Fortran program
abs(3F) abs, iabs, dabs, qabs, cabs, zabs, cqabs, iiabs, jiabs - FORTRAN absolute value
acos(3F) acos, dacos, qacos, acosd, dacosd, qacosd - FORTRAN arccosine intrinsic function
aint(3F) aint, dint, qint, iint, jint, iidint, jidint, iiqint, jiqint, kiqint - FORTRAN integer part intrinsic function
alarm(3F) alarm - execute a subroutine after a specified time
amax(3F) idamax, isamax, izamax, icamax - BLAS Maximum index functions
asin(3F) asin, dasin, qasin, asind, dasind, qasind - FORTRAN arcsine intrinsic function
asnctl(3F) ASNCTL - Controls function of ASSIGN, ASNFILE, ASNUNIT, and ASNRM routines
asnqfile(3F) ASNQFILE, ASNQUNIT - Returns the assign options currently in effect for a file name or unit number
assign(3F) ASSIGN, ASNUNIT, ASNFILE, ASNRM - Provides library interface to assign processing
asum(3F) dasum, sasum, dzasum, scasum - BLAS level ONE L1 norm functions.
atan(3F) atan, datan, qatan, atand, datand, qatand - FORTRAN arctangent intrinsic function
atan2(3F) atan2, datan2, qatan2, atan2d, datan2d, qatan2d - FORTRAN arctangent intrinsic function
axpy(3F) daxpy, saxpy, zaxpy, caxpy - BLAS level ONE axpy subroutines
BAKVEC(3F) BAKVEC, SBAKVEC - EISPACK routine. This subroutine forms the eigenvectors of a NONSYMMETRIC TRIDIAGONAL matrix by back transforming those of the corresponding symmetric matrix determined by FIGI.
BALANC(3F) BALANC, SBALANC - EISPACK routine. This subroutine balances a REAL matrix and isolates eigenvalues whenever possible.
BALBAK(3F) BALBAK, SBALBAK - EISPACK rotuine. This subroutine forms the eigenvectors of a REAL GENERAL matrix by back transforming those of the corresponding balanced matrix determined by BALANC.
BANDR(3F) BANDR, SBANDR - EISPACK routine. This subroutine reduces a REAL SYMMETRIC BAND matrix to a symmetric tridiagonal matrix using and optionally accumulating orthogonal similarity transformations.
BANDV(3F) BANDV, SBANDV - EISPACK routine. This subroutine finds those eigenvectors of a REAL SYMMETRIC BAND matrix corresponding to specified eigenvalues, using inverse iteration. The subroutine may also be used to solve systems of linear equations with a symmetric or non-symmetric band coefficient matrix.
BISECT(3F) BISECT, SBISECT - EISPACK routine. This subroutine finds those eigenvalues of a TRIDIAGONAL SYMMETRIC matrix which lie in a specified interval, using bisection.
blas(3F) BLAS - Basic Linear Algebra Subprograms
bool(3F) bool: iand, kiand, and, iior, ior, or, jior, kior, inot, jnot, knot, not, iieor, jieor, kieor, ieor, xor, iishft, jishft, kishft, ishft, lshift, rshift, iishftc, jishftc, kishftc, ishftc, iibits, jibits, kibits, ibits, iibset, jibset, kibset, ibset, bitest, bjtest, bktest, btest, iibclr, jibclr, kibclr, ibclr, mvbits - FORTRAN bitwise boolean functions
BQR(3F) BQR, SBQR - EISPACK routine. This subroutine finds the eigenvalue of smallest (usually) magnitude of a REAL SYMMETRIC BAND matrix using the QR algorithm with shifts of origin. Consecutive calls can be made to find further eigenvalues.
CBABK2(3F) CBABK2, SCBABK2 - EISPACK routine. This subroutine forms the eigenvectors of a COMPLEX GENERAL matrix by back transforming those of the corresponding balanced matrix determined by CBAL.
CBAL(3F) CBAL, SCBAL - EISPACK routine. This subroutine is a complex version of BALANCE.
cbdsqr(3F) CBDSQR - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
CCHDC(3F) CCHDC - CCHDC computes the Cholesky decomposition of a positive definite matrix. A pivoting option allows the user to estimate the condition of a positive definite matrix or determine the rank of a positive semidefinite matrix.
CCHDD(3F) CCHDD - CCHDD downdates an augmented Cholesky decomposition or the triangular factor of an augmented QR decomposition. Specifically, given an upper triangular matrix R of order P, a row vector X, a column vector Z, and a scalar Y, CCHDD determines a unitary matrix U and a scalar ZETA such that
CCHEX(3F) CCHEX - CCHEX updates the Cholesky factorization
CCHUD(3F) CCHUD - CCHUD updates an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. Specifically, given an upper triangular matrix R of order P, a row vector X, a column vector Z, and a scalar Y, CCHUD determines a unitary matrix U and a scalar ZETA such that
CDIV(3F) CDIV, SCDIV - EISPACK auxiliary routine.
CFFT2(3F) CFFT2 - Calculate a complex-to-complex Fourier synthesis/analysis.
cfftm1d(3F) cfftm1d, zfftm1d - Multiple 1D, complex-to-complex, Fast Fourier Transforms.
cfftm1di(3F) cfftm1di, zfftm1di - initialize the coefficient array for complex-to- complex Multiple 1D FFT modules.
CG(3F) CG, SCG - EISPACK routine. This subroutine calls the recommended sequence of subroutines from the eigensystem subroutine package (EISPACK) to find the eigenvalues and eigenvectors (if desired) of a COMPLEX GENERAL matrix.
cgbbrd(3F) CGBBRD - reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation
CGBCO(3F) CGBCO - CGBCO factors a complex band matrix by Gaussian elimination and estimates the condition of the matrix.
cgbcon(3F) CGBCON - estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm,
CGBDI(3F) CGBDI - CGBDI computes the determinant of a band matrix using the factors computed by CGBCO or CGBFA. If the inverse is needed, use CGBSL N times.
cgbequ(3F) CGBEQU - compute row and column scalings intended to equilibrate an M- by-N band matrix A and reduce its condition number
CGBFA(3F) CGBFA - CGBFA factors a complex band matrix by elimination.
cgbrfs(3F) CGBRFS - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
CGBSL(3F) CGBSL - CGBSL solves the complex band system A * X = B or CTRANS(A) * X = B using the factors computed by CGBCO or CGBFA.
cgbsv(3F) CGBSV - compute the solution to a complex system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices
cgbsvx(3F) CGBSVX - use the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
cgbtf2(3F) CGBTF2 - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges
cgbtrf(3F) CGBTRF - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges
cgbtrs(3F) CGBTRS - solve a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general band matrix A using the LU factorization computed by CGBTRF
cgebak(3F) CGEBAK - form the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by CGEBAL
cgebal(3F) CGEBAL - balance a general complex matrix A
cgebd2(3F) CGEBD2 - reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation
cgebrd(3F) CGEBRD - reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation
CGECO(3F) CGECO - CGECO factors a complex matrix by Gaussian elimination and estimates the condition of the matrix.
cgecon(3F) CGECON - estimate the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by CGETRF
CGEDI(3F) CGEDI - CGEDI computes the determinant and inverse of a matrix using the factors computed by CGECO or CGEFA.
cgeequ(3F) CGEEQU - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number
cgees(3F) CGEES - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z
cgeesx(3F) CGEESX - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z
cgeev(3F) CGEEV - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
cgeevx(3F) CGEEVX - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
CGEFA(3F) CGEFA - CGEFA factors a complex matrix by Gaussian elimination.
cgegs(3F) CGEGS - compute for a pair of N-by-N complex nonsymmetric matrices A,
cgegv(3F) CGEGV - compute for a pair of N-by-N complex nonsymmetric matrices A and B, the generalized eigenvalues (alpha, beta), and optionally,
cgehd2(3F) CGEHD2 - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation
cgehrd(3F) CGEHRD - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation
cgelq2(3F) CGELQ2 - compute an LQ factorization of a complex m by n matrix A
cgelqf(3F) CGELQF - compute an LQ factorization of a complex M-by-N matrix A
cgels(3F) CGELS - solve overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A
cgelss(3F) CGELSS - compute the minimum norm solution to a complex linear least squares problem
cgelsx(3F) CGELSX - compute the minimum-norm solution to a complex linear least squares problem
cgeql2(3F) CGEQL2 - compute a QL factorization of a complex m by n matrix A
cgeqlf(3F) CGEQLF - compute a QL factorization of a complex M-by-N matrix A
cgeqpf(3F) CGEQPF - compute a QR factorization with column pivoting of a complex M- by-N matrix A
cgeqr2(3F) CGEQR2 - compute a QR factorization of a complex m by n matrix A
cgeqrf(3F) CGEQRF - compute a QR factorization of a complex M-by-N matrix A
cgerfs(3F) CGERFS - improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution
cgerq2(3F) CGERQ2 - compute an RQ factorization of a complex m by n matrix A
cgerqf(3F) CGERQF - compute an RQ factorization of a complex M-by-N matrix A
CGESL(3F) CGESL - CGESL solves the complex system A * X = B or CTRANS(A) * X = B using the factors computed by CGECO or CGEFA.
cgesv(3F) CGESV - compute the solution to a complex system of linear equations A * X = B,
cgesvd(3F) CGESVD - compute the singular value decomposition (SVD) of a complex M- by-N matrix A, optionally computing the left and/or right singular vectors
cgesvx(3F) CGESVX - use the LU factorization to compute the solution to a complex system of linear equations A * X = B,
cgetf2(3F) CGETF2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges
cgetrf(3F) CGETRF - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges
cgetri(3F) CGETRI - compute the inverse of a matrix using the LU factorization computed by CGETRF
cgetrs(3F) CGETRS - solve a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general N-by-N matrix A using the LU factorization computed by CGETRF
cggbak(3F) CGGBAK - form the right or left eigenvectors of a complex generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by CGGBAL
cggbal(3F) CGGBAL - balance a pair of general complex matrices (A,B)
cggglm(3F) CGGGLM - solve a general Gauss-Markov linear model (GLM) problem
cgghrd(3F) CGGHRD - reduce a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, where A is a general matrix and B is upper triangular
cgglse(3F) CGGLSE - solve the linear equality-constrained least squares (LSE) problem
cggqrf(3F) CGGQRF - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B
cggrqf(3F) CGGRQF - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B
cggsvd(3F) CGGSVD - compute the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B
cggsvp(3F) CGGSVP - compute unitary matrices U, V and Q such that N-K-L K L U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0
cgtcon(3F) CGTCON - estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF
cgtrfs(3F) CGTRFS - improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution
CGTSL(3F) CGTSL - CGTSL given a general tridiagonal matrix and a right hand side will find the solution.
cgtsv(3F) CGTSV - solve the equation A*X = B,
cgtsvx(3F) CGTSVX - use the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
cgttrf(3F) CGTTRF - compute an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges
cgttrs(3F) CGTTRS - solve one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B,
CH(3F) CH, SCH - EISPACK routine. This subroutine calls the recommended sequence of subroutines from the eigensystem subroutine package (EISPACK) to find the eigenvalues and eigenvectors (if desired) of a COMPLEX HERMITIAN matrix.
chbev(3F) CHBEV - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
chbevd(3F) CHBEVD - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
chbevx(3F) CHBEVX - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
chbgst(3F) CHBGST - reduce a complex Hermitian-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,
chbgv(3F) CHBGV - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x
chbtrd(3F) CHBTRD - reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
checon(3F) CHECON - estimate the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF
cheev(3F) CHEEV - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
cheevd(3F) CHEEVD - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
cheevx(3F) CHEEVX - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
chegs2(3F) CHEGS2 - reduce a complex Hermitian-definite generalized eigenproblem to standard form
chegst(3F) CHEGST - reduce a complex Hermitian-definite generalized eigenproblem to standard form
chegv(3F) CHEGV - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
cherfs(3F) CHERFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution
chesv(3F) CHESV - compute the solution to a complex system of linear equations A * X = B,
chesvx(3F) CHESVX - use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A * X = B,
chetd2(3F) CHETD2 - reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
chetf2(3F) CHETF2 - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
chetrd(3F) CHETRD - reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
chetrf(3F) CHETRF - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
chetri(3F) CHETRI - compute the inverse of a complex Hermitian indefinite matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF
chetrs(3F) CHETRS - solve a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF
chgeqz(3F) CHGEQZ - implement a single-shift version of the QZ method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the equation det( A - w(i) B ) = 0 If JOB='S', then the pair (A,B) is simultaneously reduced to Schur form (i.e., A and B are both upper triangular) by applying one unitary tranformation (usually called Q) on the left and another (usually called Z) on the right
CHICO(3F) CHICO - CHICO factors a complex Hermitian matrix by elimination with symmetric pivoting and estimates the condition of the matrix.
CHIDI(3F) CHIDI - CHIDI computes the determinant, inertia and inverse of a complex Hermitian matrix using the factors from CHIFA.
CHIFA(3F) CHIFA - CHIFA factors a complex Hermitian matrix by elimination with symmetric pivoting.
CHISL(3F) CHISL - CHISL solves the complex Hermitian system A * X = B using the factors computed by CHIFA.
chmod(3F) chmod - change mode of a file
CHPCO(3F) CHPCO - CHPCO factors a complex Hermitian matrix stored in packed form by elimination with symmetric pivoting and estimates the condition of the matrix.
chpcon(3F) CHPCON - estimate the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF
CHPDI(3F) CHPDI - CHPDI computes the determinant, inertia and inverse of a complex Hermitian matrix using the factors from CHPFA, where the matrix is stored in packed form.
chpev(3F) CHPEV - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage
chpevd(3F) CHPEVD - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
chpevx(3F) CHPEVX - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
CHPFA(3F) CHPFA - CHPFA factors a complex Hermitian matrix stored in packed form by elimination with symmetric pivoting.
chpgst(3F) CHPGST - reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage
chpgv(3F) CHPGV - compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
chprfs(3F) CHPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and backward error estimates for the solution
CHPSL(3F) CHPSL - CHISL solves the complex Hermitian system A * X = B using the factors computed by CHPFA.
chpsv(3F) CHPSV - compute the solution to a complex system of linear equations A * X = B,
chpsvx(3F) CHPSVX - use the diagonal pivoting factorization A = U*D*U**H or A = L*D*L**H to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices
chptrd(3F) CHPTRD - reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation
chptrf(3F) CHPTRF - compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method
chptri(3F) CHPTRI - compute the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF
chptrs(3F) CHPTRS - solve a system of linear equations A*X = B with a complex Hermitian matrix A stored in packed format using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF
chsein(3F) CHSEIN - use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H
chseqr(3F) CHSEQR - compute the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors
CINVIT(3F) CINVIT, SCINVIT - EISPACK routine. This subroutine finds those eigenvectors of A COMPLEX UPPER Hessenberg matrix corresponding to specified eigenvalues, using inverse iteration.
clabrd(3F) CLABRD - reduce the first NB rows and columns of a complex general m by n matrix A to upper or lower real bidiagonal form by a unitary transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A
clacgv(3F) CLACGV - conjugate a complex vector of length N
clacon(3F) CLACON - estimate the 1-norm of a square, complex matrix A
clacpy(3F) CLACPY - copie all or part of a two-dimensional matrix A to another matrix B
clacrm(3F) CLACRM - perform a very simple matrix-matrix multiplication
clacrt(3F) CLACRT - applie a plane rotation, where the cos and sin (C and S) are complex and the vectors CX and CY are complex
cladiv(3F) CLADIV - := X / Y, where X and Y are complex
claed0(3F) CLAED0 - the divide and conquer method, CLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix
claed7(3F) CLAED7 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
claed8(3F) CLAED8 - merge the two sets of eigenvalues together into a single sorted set
claein(3F) CLAEIN - use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H
claesy(3F) CLAESY - compute the eigendecomposition of a 2-by-2 symmetric matrix ( ( A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger than some threshold value
claev2(3F) CLAEV2 - compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ]
clags2(3F) CLAGS2 - compute 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q = V'*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = ( CSV SNV ),
clagtm(3F) CLAGTM - perform a matrix-vector product of the form B := alpha * A * X + beta * B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1
clahef(3F) CLAHEF - compute a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
clahqr(3F) CLAHQR - i an auxiliary routine called by CHSEQR to update the eigenvalues and Schur decomposition already computed by CHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI
clahrd(3F) CLAHRD - reduce the first NB columns of a complex general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero
claic1(3F) CLAIC1 - applie one step of incremental condition estimation in its simplest version
clangb(3F) CLANGB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals
clange(3F) CLANGE - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex matrix A
clangt(3F) CLANGT - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex tridiagonal matrix A
clanhb(3F) CLANHB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n hermitian band matrix A, with k super-diagonals
clanhe(3F) CLANHE - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A
clanhp(3F) CLANHP - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A, supplied in packed form
clanhs(3F) CLANHS - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
clanht(3F) CLANHT - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix A
clansb(3F) CLANSB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals
clansp(3F) CLANSP - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A, supplied in packed form
clansy(3F) CLANSY - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A
clantb(3F) CLANTB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals
clantp(3F) CLANTP - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
clantr(3F) CLANTR - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A
clapll(3F) CLAPLL - two column vectors X and Y, let A = ( X Y )
clapmt(3F) CLAPMT - rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N
claqgb(3F) CLAQGB - equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C
claqge(3F) CLAQGE - equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
claqhb(3F) CLAQHB - equilibrate a symmetric band matrix A using the scaling factors in the vector S
claqhe(3F) CLAQHE - equilibrate a Hermitian matrix A using the scaling factors in the vector S
claqhp(3F) CLAQHP - equilibrate a Hermitian matrix A using the scaling factors in the vector S
claqsb(3F) CLAQSB - equilibrate a symmetric band matrix A using the scaling factors in the vector S
claqsp(3F) CLAQSP - equilibrate a symmetric matrix A using the scaling factors in the vector S
claqsy(3F) CLAQSY - equilibrate a symmetric matrix A using the scaling factors in the vector S
clar2v(3F) CLAR2V - applie a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices,
clarf(3F) CLARF - applie a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right
clarfb(3F) CLARFB - applie a complex block reflector H or its transpose H' to a complex M-by-N matrix C, from either the left or the right
clarfg(3F) CLARFG - generate a complex elementary reflector H of order n, such that H' * ( alpha ) = ( beta ), H' * H = I
clarft(3F) CLARFT - form the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors
clarfx(3F) CLARFX - applie a complex elementary reflector H to a complex m by n matrix C, from either the left or the right
clargv(3F) CLARGV - generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y
clarnv(3F) CLARNV - return a vector of n random complex numbers from a uniform or normal distribution
clartg(3F) CLARTG - generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ]
clartv(3F) CLARTV - applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y
clascl(3F) CLASCL - multiplie the M by N complex matrix A by the real scalar CTO/CFROM
claset(3F) CLASET - initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals
clasr(3F) CLASR - perform the transformation A := P*A, when SIDE = 'L' or 'l' ( Left-hand side ) A := A*P', when SIDE = 'R' or 'r' ( Right-hand side ) where A is an m by n complex matrix and P is an orthogonal matrix,
classq(3F) CLASSQ - return the values scl and ssq such that ( scl**2 )*ssq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
claswp(3F) CLASWP - perform a series of row interchanges on the matrix A
clasyf(3F) CLASYF - compute a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
clatbs(3F) CLATBS - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
clatps(3F) CLATPS - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
clatrd(3F) CLATRD - reduce NB rows and columns of a complex Hermitian matrix A to Hermitian tridiagonal form by a unitary similarity transformation Q' * A * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A
clatrs(3F) CLATRS - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
clatzm(3F) CLATZM - applie a Householder matrix generated by CTZRQF to a matrix
clauu2(3F) CLAUU2 - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
clauum(3F) CLAUUM - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
COMBAK(3F) COMBAK, SCOMBAK - EISPACK routine. This subroutine forms the eigenvectors of a COMPLEX GENERAL matrix by back transforming those of the corresponding upper Hessenberg matrix determined by COMHES.
COMHES(3F) COMHES, SCOMHES - EISPACK routine. Given a COMPLEX GENERAL matrix, this subroutine reduces a submatrix situated in rows and columns LOW through IGH to upper Hessenberg form by stabilized elementary similarity transformations.
COMLR(3F) COMLR, SCOMLR - EISPACK routine. This subroutine finds the eigenvalues of a COMPLEX UPPER Hessenberg matrix by the modified LR method.
COMLR2(3F) COMLR2, SCOMLR2 - EISPACK routine. This subroutine finds the eigenvalues and eigenvectors of a COMPLEX UPPER Hessenberg matrix by the modified LR method. The eigenvectors of a COMPLEX GENERAL matrix can also be found if COMHES has been used to reduce this general matrix to Hessenberg form.
COMQR(3F) COMQR, SCOMQR - EISPACK routine. This subroutine finds the eigenvalues of a COMPLEX upper Hessenberg matrix by the QR method.
COMQR2(3F) COMQR2, SCOMQR2 - EISPACK routine. This subroutine finds the eigenvalues and eigenvectors of a COMPLEX UPPER Hessenberg matrix by the QR method. The eigenvectors of a COMPLEX GENERAL matrix can also be found if CORTH has been used to reduce this general matrix to Hessenberg form.
conjg(3F) conjg, dconjg, qconjg - FORTRAN complex conjugate intrinsic function
conv(3F) conv, libconv, convolution, correlation - Convolution and Correlation Library
copy(3F) dcopy, scopy, zcopy, ccopy - BLAS level ONE copy subroutines
cor1d(3F) SCOR1D, DCOR1D, CCOR1D, ZCOR1D - 1D Correlation in the time domain.
cor2d(3F) SCOR2D, DCOR2D, CCOR2D, ZCOR2D - 2D Correlation in the space domain.
corm1d(3F) SCORM1D, DCORM1D, CCORM1D, ZCORM1D - N 1D convolutions in the time domain.
CORTB(3F) CORTB, SCORTB - EISPACK routine. This subroutine forms the eigenvectors of a COMPLEX GENERAL matrix by back transforming those of the corresponding upper Hessenberg matrix determined by CORTH.
CORTH(3F) CORTH, SCORTH - EISPACK routine. Given a COMPLEX GENERAL matrix, this subroutine reduces a submatrix situated in rows and columns LOW through IGH to upper Hessenberg form by unitary similarity transformations.
cos(3F) cos, dcos, qcos, ccos, zcos, cqcos, cosd, dcosd, qcosd - FORTRAN cosine intrinsic function
cosh(3F) cosh, dcosh, qcosh - FORTRAN hyperbolic cosine intrinsic function
CPBCO(3F) CPBCO - CPBCO factors a complex Hermitian positive definite matrix stored in band form and estimates the condition of the matrix.
cpbcon(3F) CPBCON - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRF
CPBDI(3F) CPBDI - CPBDI computes the determinant of a complex Hermitian positive definite band matrix using the factors computed by CPBCO or CPBFA. If the inverse is needed, use CPBSL N times.
cpbequ(3F) CPBEQU - compute row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the two-norm)
CPBFA(3F) CPBFA - CPBFA factors a complex Hermitian positive definite matrix stored in band form.
cpbrfs(3F) CPBRFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward error estimates for the solution
CPBSL(3F) CPBSL - CPBSL solves the complex Hermitian positive definite band system A*X = B using the factors computed by CPBCO or CPBFA.
cpbstf(3F) CPBSTF - compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A
cpbsv(3F) CPBSV - compute the solution to a complex system of linear equations A * X = B,
cpbsvx(3F) CPBSVX - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B,
cpbtf2(3F) CPBTF2 - compute the Cholesky factorization of a complex Hermitian positive definite band matrix A
cpbtrf(3F) CPBTRF - compute the Cholesky factorization of a complex Hermitian positive definite band matrix A
cpbtrs(3F) CPBTRS - solve a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRF
CPOCO(3F) CPOCO - CPOCO factors a complex Hermitian positive definite matrix and estimates the condition of the matrix.
cpocon(3F) CPOCON - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF
CPODI(3F) CPODI - CPODI computes the determinant and inverse of a certain complex Hermitian positive definite matrix (see below) using the factors computed by CPOCO, CPOFA or CQRDC.
cpoequ(3F) CPOEQU - compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm)
CPOFA(3F) CPOFA - CPOFA factors a complex Hermitian positive definite matrix.
cporfs(3F) CPORFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite,
CPOSL(3F) CPOSL - CPOSL solves the COMPLEX Hermitian positive definite system A * X = B using the factors computed by CPOCO or CPOFA.
cposv(3F) CPOSV - compute the solution to a complex system of linear equations A * X = B,
cposvx(3F) CPOSVX - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B,
cpotf2(3F) CPOTF2 - compute the Cholesky factorization of a complex Hermitian positive definite matrix A
cpotrf(3F) CPOTRF - compute the Cholesky factorization of a complex Hermitian positive definite matrix A
cpotri(3F) CPOTRI - compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF
cpotrs(3F) CPOTRS - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF
CPPCO(3F) CPPCO - CPPCO factors a complex Hermitian positive definite matrix stored in packed form and estimates the condition of the matrix.
cppcon(3F) CPPCON - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF
CPPDI(3F) CPPDI - CPPDI computes the determinant and inverse of a complex Hermitian positive definite matrix using the factors computed by CPPCO or CPPFA .
cppequ(3F) CPPEQU - compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
CPPFA(3F) CPPFA - CPPFA factors a complex Hermitian positive definite matrix stored in packed form.
cpprfs(3F) CPPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution
CPPSL(3F) CPPSL - CPPSL solves the complex Hermitian positive definite system A * X = B using the factors computed by CPPCO or CPPFA.
cppsv(3F) CPPSV - compute the solution to a complex system of linear equations A * X = B,
cppsvx(3F) CPPSVX - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B,
cpptrf(3F) CPPTRF - compute the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format
cpptri(3F) CPPTRI - compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF
cpptrs(3F) CPPTRS - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF
cprod1d(3F) cprod1d, zprod1d - Compute the product of a 1D Fourier transform with a 1D filter.
cprod2d(3F) cprod2d, zprod2d - Compute the product of a 2D Fourier transforms with a 2D filter.
cprod3d(3F) cprod3d, zprod3d - Compute the product of a 3D Fourier transforms with a 3D filter.
cprodm1d(3F) cprodm1d, zprodm1d - Compute the product of Multiple 1D Fourier transforms with Multiple 1D filters.
cptcon(3F) CPTCON - compute the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by CPTTRF
cpteqr(3F) CPTEQR - compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF and then calling CBDSQR to compute the singular values of the bidiagonal factor
cptrfs(3F) CPTRFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
CPTSL(3F) CPTSL - CPTSL given a positive definite tridiagonal matrix and a right hand side will find the solution.
cptsv(3F) CPTSV - compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices
cptsvx(3F) CPTSVX - use the factorization A = L*D*L**H to compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix and X and B are N-by-NRHS matrices
cpttrf(3F) CPTTRF - compute the factorization of a complex Hermitian positive definite tridiagonal matrix A
cpttrs(3F) CPTTRS - solve a system of linear equations A * X = B with a Hermitian positive definite tridiagonal matrix A using the factorization A = U**H*D*U or A = L*D*L**H computed by CPTTRF
CQRDC(3F) CQRDC - CQRDC uses Householder transformations to compute the QR factorization of an N by P matrix X. Column pivoting based on the 2- norms of the reduced columns may be performed at the users option.
CQRSL(3F) CQRSL - CQRSL applies the output of CQRDC to compute coordinate transformations, projections, and least squares solutions. For K .LE. MIN(N,P), let XK be the matrix
CRFFT2(3F) CRFFT2 - Calculate a complex-to-real Fourier synthesis/analysis.
cry2mips(3F) CRY2MIPS, MIPS2CRY - Converts Fortran data types between Cray Fortran data types and MIPS IEEE Fortran data types
cscal1d(3F) cscal1d, zscal1d - scales a 1D real sequence.
cscal2d(3F) cscal2d, zscal2d - scales a 2D complex sequence.
cscal3d(3F) cscal3d, zscal3d - scales a 3D complex sequence.
cscalm1d(3F) cscalm1d, zscalm1d - scales Multiple 1D complex sequences.
csfft1du(3F) csfft1du, zdfft1du - 1D, Complex to Real, Inverse Fast Fourier Transforms.
csfft2du(3F) csfft2du, zdfft2du - 2D, Complex-to-Real, Inverse Fast Fourier Transforms.
csfft3du(3F) csfft3du, zdfft3du - 3D, Complex to Real, Inverse Fast Fourier Transforms.
csfftm1du(3F) csfftm1du, zdfftm1du - Multiple 1D, Complex to Real, Inverse Fast Fourier Transforms.
CSICO(3F) CSICO - CSICO factors a complex symmetric matrix by elimination with symmetric pivoting and estimates the condition of the matrix.
CSIDI(3F) CSIDI - CSIDI computes the determinant and inverse of a complex symmetric matrix using the factors from CSIFA.
CSIFA(3F) CSIFA - CSIFA factors a complex symmetric matrix by elimination with symmetric pivoting.
CSISL(3F) CSISL - CSISL solves the complex symmetric system A * X = B using the factors computed by CSIFA.
CSPCO(3F) CSPCO - CSPCO factors a complex symmetric matrix stored in packed form by elimination with symmetric pivoting and estimates the condition of the matrix.
cspcon(3F) CSPCON - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF
CSPDI(3F) CSPDI - CSPDI computes the determinant and inverse of a complex symmetric matrix using the factors from CSPFA, where the matrix is stored in packed form.
CSPFA(3F) CSPFA - CSPFA factors a complex symmetric matrix stored in packed form by elimination with symmetric pivoting.
cspr(3F) CSPR - perform the symmetric rank 1 operation A := alpha*x*conjg( x' ) + A,
csprfs(3F) CSPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution
CSPSL(3F) CSPSL - CSISL solves the complex symmetric system A * X = B using the factors computed by CSPFA.
cspsv(3F) CSPSV - compute the solution to a complex system of linear equations A * X = B,
cspsvx(3F) CSPSVX - use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices
csptrf(3F) CSPTRF - compute the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method
csptri(3F) CSPTRI - compute the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF
csptrs(3F) CSPTRS - solve a system of linear equations A*X = B with a complex symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF
CSROOT(3F) CSROOT, SCSROOT - EISPACK auxiliary routine.
CSROT(3F) CSROT - CSROT applies the complex Givens rotation
csrscl(3F) CSRSCL - multiplie an n-element complex vector x by the real scalar 1/a
cstedc(3F) CSTEDC - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
cstein(3F) CSTEIN - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration
csteqr(3F) CSTEQR - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method
CSVDC(3F) CSVDC - CSVDC is a subroutine to reduce a complex NxP matrix X by unitary transformations U and V to diagonal form. The diagonal elements S(I) are the singular values of X. The columns of U are the corresponding left singular vectors, and the columns of V the right singular vectors.
csycon(3F) CSYCON - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF
csyr(3F) CSYR - perform the symmetric rank 1 operation A := alpha*x*( x' ) + A,
csyrfs(3F) CSYRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution
csysv(3F) CSYSV - compute the solution to a complex system of linear equations A * X = B,
csysvx(3F) CSYSVX - use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A * X = B,
csytf2(3F) CSYTF2 - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
csytrf(3F) CSYTRF - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
csytri(3F) CSYTRI - compute the inverse of a complex symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF
csytrs(3F) CSYTRS - solve a system of linear equations A*X = B with a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF
ctbcon(3F) CTBCON - estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm
ctbrfs(3F) CTBRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
ctbtrs(3F) CTBTRS - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,
ctgevc(3F) CTGEVC - compute some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B)
ctgsja(3F) CTGSJA - compute the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) matrices A and B
ctpcon(3F) CTPCON - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm
ctprfs(3F) CTPRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix
ctptri(3F) CTPTRI - compute the inverse of a complex upper or lower triangular matrix A stored in packed format
ctptrs(3F) CTPTRS - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,
CTRCO(3F) CTRCO - CTRCO estimates the condition of a complex triangular matrix.
ctrcon(3F) CTRCON - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
CTRDI(3F) CTRDI - CTRDI computes the determinant and inverse of a complex triangular matrix.
ctrevc(3F) CTREVC - compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T
ctrexc(3F) CTREXC - reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that the diagonal element of T with row index IFST is moved to row ILST
ctrrfs(3F) CTRRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
ctrsen(3F) CTRSEN - reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace
CTRSL(3F) CTRSL - CTRSL solves systems of the form
ctrsna(3F) CTRSNA - estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q*T*Q**H with Q unitary)
ctrsyl(3F) CTRSYL - solve the complex Sylvester matrix equation
ctrti2(3F) CTRTI2 - compute the inverse of a complex upper or lower triangular matrix
ctrtri(3F) CTRTRI - compute the inverse of a complex upper or lower triangular matrix A
ctrtrs(3F) CTRTRS - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,
ctzrqf(3F) CTZRQF - reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations
cung2l(3F) CUNG2L - generate an m by n complex matrix Q with orthonormal columns,
cung2r(3F) CUNG2R - generate an m by n complex matrix Q with orthonormal columns,
cungbr(3F) CUNGBR - generate one of the complex unitary matrices Q or P**H determined by CGEBRD when reducing a complex matrix A to bidiagonal form
cunghr(3F) CUNGHR - generate a complex unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by CGEHRD
cungl2(3F) CUNGL2 - generate an m-by-n complex matrix Q with orthonormal rows,
cunglq(3F) CUNGLQ - generate an M-by-N complex matrix Q with orthonormal rows,
cungql(3F) CUNGQL - generate an M-by-N complex matrix Q with orthonormal columns,
cungqr(3F) CUNGQR - generate an M-by-N complex matrix Q with orthonormal columns,
cungr2(3F) CUNGR2 - generate an m by n complex matrix Q with orthonormal rows,
cungrq(3F) CUNGRQ - generate an M-by-N complex matrix Q with orthonormal rows,
cungtr(3F) CUNGTR - generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by CHETRD
cunm2l(3F) CUNM2L - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',
cunm2r(3F) CUNM2R - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',
cunmbr(3F) CUNMBR - VECT = 'Q', CUNMBR overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
cunmhr(3F) CUNMHR - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
cunml2(3F) CUNML2 - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',
cunmlq(3F) CUNMLQ - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
cunmql(3F) CUNMQL - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
cunmqr(3F) CUNMQR - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
cunmr2(3F) CUNMR2 - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',
cunmrq(3F) CUNMRQ - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
cunmtr(3F) CUNMTR - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
cupgtr(3F) CUPGTR - generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by CHPTRD using packed storage
cupmtr(3F) CUPMTR - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dbdsqr(3F) DBDSQR - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
DCHDC(3F) DCHDC - DCHDC computes the Cholesky decomposition of a positive definite matrix. A pivoting option allows the user to estimate the condition of a positive definite matrix or determine the rank of a positive semidefinite matrix.
DCHDD(3F) DCHDD - DCHDD downdates an augmented Cholesky decomposition or the triangular factor of an augmented QR decomposition. Specifically, given an upper triangular matrix R of order P, a row vector X, a column vector Z, and a scalar Y, DCHDD determines an orthogonal matrix U and a scalar ZETA such that
DCHEX(3F) DCHEX - DCHEX updates the Cholesky factorization
DCHUD(3F) DCHUD - DCHUD updates an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. Specifically, given an upper triangular matrix R of order P, a row vector X, a column vector Z, and a scalar Y, DCHUD determines a untiary matrix U and a scalar ZETA such that
ddisna(3F) DDISNA - compute the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general m-by-n matrix
dgbbrd(3F) DGBBRD - reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation
DGBCO(3F) DGBCO - DGBCO factors a double precision band matrix by Gaussian elimination and estimates the condition of the matrix.
dgbcon(3F) DGBCON - estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm,
DGBDI(3F) DGBDI - DGBDI computes the determinant of a band matrix using the factors computed by DGBCO or DGBFA. If the inverse is needed, use DGBSL N times.
dgbequ(3F) DGBEQU - compute row and column scalings intended to equilibrate an M- by-N band matrix A and reduce its condition number
DGBFA(3F) DGBFA - DGBFA factors a double precision band matrix by elimination.
dgbrfs(3F) DGBRFS - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
DGBSL(3F) DGBSL - DGBSL solves the double precision band system A * X = B or TRANS(A) * X = B using the factors computed by DGBCO or DGBFA.
dgbsv(3F) DGBSV - compute the solution to a real system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices
dgbsvx(3F) DGBSVX - use the LU factorization to compute the solution to a real system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
dgbtf2(3F) DGBTF2 - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges
dgbtrf(3F) DGBTRF - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges
dgbtrs(3F) DGBTRS - solve a system of linear equations A * X = B or A' * X = B with a general band matrix A using the LU factorization computed by DGBTRF
dgebak(3F) DGEBAK - form the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by DGEBAL
dgebal(3F) DGEBAL - balance a general real matrix A
dgebd2(3F) DGEBD2 - reduce a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation
dgebrd(3F) DGEBRD - reduce a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation
DGECO(3F) DGECO - DGECO factors a double precision matrix by Gaussian elimination and estimates the condition of the matrix.
dgecon(3F) DGECON - estimate the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by DGETRF
DGEDI(3F) DGEDI - DGEDI computes the determinant and inverse of a matrix using the factors computed by DGECO or DGEFA.
dgeequ(3F) DGEEQU - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number
dgees(3F) DGEES - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z
dgeesx(3F) DGEESX - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z
dgeev(3F) DGEEV - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
dgeevx(3F) DGEEVX - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
DGEFA(3F) DGEFA - DGEFA factors a double precision matrix by Gaussian elimination.
dgegs(3F) DGEGS - compute for a pair of N-by-N real nonsymmetric matrices A, B
dgegv(3F) DGEGV - compute for a pair of n-by-n real nonsymmetric matrices A and B, the generalized eigenvalues (alphar +/- alphai*i, beta), and optionally, the left and/or right generalized eigenvectors (VL and VR)
dgehd2(3F) DGEHD2 - reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation
dgehrd(3F) DGEHRD - reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation
dgelq2(3F) DGELQ2 - compute an LQ factorization of a real m by n matrix A
dgelqf(3F) DGELQF - compute an LQ factorization of a real M-by-N matrix A
dgels(3F) DGELS - solve overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A
dgelss(3F) DGELSS - compute the minimum norm solution to a real linear least squares problem
dgelsx(3F) DGELSX - compute the minimum-norm solution to a real linear least squares problem
dgeql2(3F) DGEQL2 - compute a QL factorization of a real m by n matrix A
dgeqlf(3F) DGEQLF - compute a QL factorization of a real M-by-N matrix A
dgeqpf(3F) DGEQPF - compute a QR factorization with column pivoting of a real M-by-N matrix A
dgeqr2(3F) DGEQR2 - compute a QR factorization of a real m by n matrix A
dgeqrf(3F) DGEQRF - compute a QR factorization of a real M-by-N matrix A
dgerfs(3F) DGERFS - improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution
dgerq2(3F) DGERQ2 - compute an RQ factorization of a real m by n matrix A
dgerqf(3F) DGERQF - compute an RQ factorization of a real M-by-N matrix A
DGESL(3F) DGESL - DGESL solves the double precision system A * X = B or TRANS(A) * X = B using the factors computed by DGECO or DGEFA.
dgesv(3F) DGESV - compute the solution to a real system of linear equations A * X = B,
dgesvd(3F) DGESVD - compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors
dgesvx(3F) DGESVX - use the LU factorization to compute the solution to a real system of linear equations A * X = B,
dgetf2(3F) DGETF2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges
dgetrf(3F) DGETRF - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges
dgetri(3F) DGETRI - compute the inverse of a matrix using the LU factorization computed by DGETRF
dgetrs(3F) DGETRS - solve a system of linear equations A * X = B or A' * X = B with a general N-by-N matrix A using the LU factorization computed by DGETRF
dggbak(3F) DGGBAK - form the right or left eigenvectors of a real generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by DGGBAL
dggbal(3F) DGGBAL - balance a pair of general real matrices (A,B)
dggglm(3F) DGGGLM - solve a general Gauss-Markov linear model (GLM) problem
dgghrd(3F) DGGHRD - reduce a pair of real matrices (A,B) to generalized upper Hessenberg form using orthogonal transformations, where A is a general matrix and B is upper triangular
dgglse(3F) DGGLSE - solve the linear equality-constrained least squares (LSE) problem
dggqrf(3F) DGGQRF - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B
dggrqf(3F) DGGRQF - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B
dggsvd(3F) DGGSVD - compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B
dggsvp(3F) DGGSVP - compute orthogonal matrices U, V and Q such that N-K-L K L U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0
dgtcon(3F) DGTCON - estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by DGTTRF
dgtrfs(3F) DGTRFS - improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution
DGTSL(3F) DGTSL - DGTSL given a general tridiagonal matrix and a right hand side will find the solution.
dgtsv(3F) DGTSV - solve the equation A*X = B,
dgtsvx(3F) DGTSVX - use the LU factorization to compute the solution to a real system of linear equations A * X = B or A**T * X = B,
dgttrf(3F) DGTTRF - compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges
dgttrs(3F) DGTTRS - solve one of the systems of equations A*X = B or A'*X = B,
dhgeqz(3F) DHGEQZ - implement a single-/double-shift version of the QZ method for finding the generalized eigenvalues w(j)=(ALPHAR(j) + i*ALPHAI(j))/BETAR(j) of the equation det( A - w(i) B ) = 0 In addition, the pair A,B may be reduced to generalized Schur form
dhsein(3F) DHSEIN - use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H
dhseqr(3F) DHSEQR - compute the eigenvalues of a real upper Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**T, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors
dim(3F) dim, ddim, qdim, idim, iidim, jidim - FORTRAN positive difference intrinsic functions
dlabad(3F) DLABAD - take as input the values computed by SLAMCH for underflow and overflow, and returns the square root of each of these values if the log of LARGE is sufficiently large
dlabrd(3F) DLABRD - reduce the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A
dlacon(3F) DLACON - estimate the 1-norm of a square, real matrix A
dlacpy(3F) DLACPY - copie all or part of a two-dimensional matrix A to another matrix B
dladiv(3F) DLADIV - perform complex division in real arithmetic a + i*b p + i*q = --------- c + i*d The algorithm is due to Robert L
dlae2(3F) DLAE2 - compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]
dlaebz(3F) DLAEBZ - contain the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix T less than or equal to its argument w
dlaed0(3F) DLAED0 - compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
dlaed1(3F) DLAED1 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
dlaed2(3F) DLAED2 - merge the two sets of eigenvalues together into a single sorted set
dlaed3(3F) DLAED3 - find the roots of the secular equation, as defined by the values in D, W, and RHO, between KSTART and KSTOP
dlaed4(3F) DLAED4 - subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0
dlaed5(3F) DLAED5 - subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j
dlaed6(3F) DLAED6 - compute the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true
dlaed7(3F) DLAED7 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
dlaed8(3F) DLAED8 - merge the two sets of eigenvalues together into a single sorted set
dlaed9(3F) DLAED9 - find the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP
dlaeda(3F) DLAEDA - compute the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem
dlaein(3F) DLAEIN - use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H
dlaev2(3F) DLAEV2 - compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ]
dlaexc(3F) DLAEXC - swap adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation
dlag2(3F) DLAG2 - compute the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflow
dlags2(3F) DLAGS2 - compute 2-by-2 orthogonal matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q = V'*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) The rows of the transformed A and B are parallel, where U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ ) ( -SNU CSU ) ( -SNV CSV ) ( -SNQ CSQ ) Z' denotes the transpose of Z
dlagtf(3F) DLAGTF - factorize the matrix (T - lambda*I), where T is an n by n tridiagonal matrix and lambda is a scalar, as T - lambda*I = PLU,
dlagtm(3F) DLAGTM - perform a matrix-vector product of the form B := alpha * A * X + beta * B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1
dlagts(3F) DLAGTS - may be used to solve one of the systems of equations (T - lambda*I)*x = y or (T - lambda*I)'*x = y,
dlahqr(3F) DLAHQR - i an auxiliary routine called by DHSEQR to update the eigenvalues and Schur decomposition already computed by DHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI
dlahrd(3F) DLAHRD - reduce the first NB columns of a real general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero
dlaic1(3F) DLAIC1 - applie one step of incremental condition estimation in its simplest version
dlaln2(3F) DLALN2 - solve a system of the form (ca A - w D ) X = s B or (ca A' - w D) X = s B with possible scaling ("s") and perturbation of A
dlamch(3F) DLAMCH - determine double precision machine parameters
dlamrg(3F) DLAMRG - will create a permutation list which will merge the elements of A (which is composed of two independently sorted sets) into a single set which is sorted in ascending order
dlangb(3F) DLANGB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals
dlange(3F) DLANGE - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A
dlangt(3F) DLANGT - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A
dlanhs(3F) DLANHS - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
dlansb(3F) DLANSB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals
dlansp(3F) DLANSP - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form
dlanst(3F) DLANST - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A
dlansy(3F) DLANSY - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A
dlantb(3F) DLANTB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals
dlantp(3F) DLANTP - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
dlantr(3F) DLANTR - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A
dlanv2(3F) DLANV2 - compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form
dlapll(3F) DLAPLL - two column vectors X and Y, let A = ( X Y )
dlapmt(3F) DLAPMT - rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N
dlapy2(3F) DLAPY2 - return sqrt(x**2+y**2), taking care not to cause unnecessary overflow
dlapy3(3F) DLAPY3 - return sqrt(x**2+y**2+z**2), taking care not to cause unnecessary overflow
dlaqgb(3F) DLAQGB - equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C
dlaqge(3F) DLAQGE - equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
dlaqsb(3F) DLAQSB - equilibrate a symmetric band matrix A using the scaling factors in the vector S
dlaqsp(3F) DLAQSP - equilibrate a symmetric matrix A using the scaling factors in the vector S
dlaqsy(3F) DLAQSY - equilibrate a symmetric matrix A using the scaling factors in the vector S
dlaqtr(3F) DLAQTR - solve the real quasi-triangular system op(T)*p = scale*c, if LREAL = .TRUE
dlar2v(3F) DLAR2V - applie a vector of real plane rotations from both sides to a sequence of 2-by-2 real symmetric matrices, defined by the elements of the vectors x, y and z
dlarf(3F) DLARF - applie a real elementary reflector H to a real m by n matrix C, from either the left or the right
dlarfb(3F) DLARFB - applie a real block reflector H or its transpose H' to a real m by n matrix C, from either the left or the right
dlarfg(3F) DLARFG - generate a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H' * H = I
dlarft(3F) DLARFT - form the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors
dlarfx(3F) DLARFX - applie a real elementary reflector H to a real m by n matrix C, from either the left or the right
dlargv(3F) DLARGV - generate a vector of real plane rotations, determined by elements of the real vectors x and y
dlarnv(3F) DLARNV - return a vector of n random real numbers from a uniform or normal distribution
dlartg(3F) DLARTG - generate a plane rotation so that [ CS SN ]
dlartv(3F) DLARTV - applie a vector of real plane rotations to elements of the real vectors x and y
dlaruv(3F) DLARUV - return a vector of n random real numbers from a uniform (0,1)
dlas2(3F) DLAS2 - compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ]
dlascl(3F) DLASCL - multiplie the M by N real matrix A by the real scalar CTO/CFROM
dlaset(3F) DLASET - initialize an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals
dlasq1(3F) DLASQ1 - DLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E
dlasq2(3F) DLASQ2 - DLASQ2 computes the singular values of a real N-by-N unreduced bidiagonal matrix with squared diagonal elements in Q and squared off- diagonal elements in E
dlasq3(3F) DLASQ3 - DLASQ3 is the workhorse of the whole bidiagonal SVD algorithm
dlasq4(3F) DLASQ4 - DLASQ4 estimates TAU, the smallest eigenvalue of a matrix
dlasr(3F) DLASR - perform the transformation A := P*A, when SIDE = 'L' or 'l' ( Left-hand side ) A := A*P', when SIDE = 'R' or 'r' ( Right-hand side ) where A is an m by n real matrix and P is an orthogonal matrix,
dlasrt(3F) DLASRT - the numbers in D in increasing order (if ID = 'I') or in decreasing order (if ID = 'D' )
dlassq(3F) DLASSQ - return the values scl and smsq such that ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
dlasv2(3F) DLASV2 - compute the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ]
dlaswp(3F) DLASWP - perform a series of row interchanges on the matrix A
dlasy2(3F) DLASY2 - solve for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in op(TL)*X + ISGN*X*op(TR) = SCALE*B,
dlasyf(3F) DLASYF - compute a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
dlatbs(3F) DLATBS - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow, where A is an upper or lower triangular band matrix
dlatps(3F) DLATPS - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form
dlatrd(3F) DLATRD - reduce NB rows and columns of a real symmetric matrix A to symmetric tridiagonal form by an orthogonal similarity transformation Q' * A * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A
dlatrs(3F) DLATRS - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow
dlatzm(3F) DLATZM - applie a Householder matrix generated by DTZRQF to a matrix
dlauu2(3F) DLAUU2 - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
dlauum(3F) DLAUUM - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
dopgtr(3F) DOPGTR - generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by DSPTRD using packed storage
dopmtr(3F) DOPMTR - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dorg2l(3F) DORG2L - generate an m by n real matrix Q with orthonormal columns,
dorg2r(3F) DORG2R - generate an m by n real matrix Q with orthonormal columns,
dorgbr(3F) DORGBR - generate one of the real orthogonal matrices Q or P**T determined by DGEBRD when reducing a real matrix A to bidiagonal form
dorghr(3F) DORGHR - generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD
dorgl2(3F) DORGL2 - generate an m by n real matrix Q with orthonormal rows,
dorglq(3F) DORGLQ - generate an M-by-N real matrix Q with orthonormal rows,
dorgql(3F) DORGQL - generate an M-by-N real matrix Q with orthonormal columns,
dorgqr(3F) DORGQR - generate an M-by-N real matrix Q with orthonormal columns,
dorgr2(3F) DORGR2 - generate an m by n real matrix Q with orthonormal rows,
dorgrq(3F) DORGRQ - generate an M-by-N real matrix Q with orthonormal rows,
dorgtr(3F) DORGTR - generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by DSYTRD
dorm2l(3F) DORM2L - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
dorm2r(3F) DORM2R - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
dormbr(3F) DORMBR - VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dormhr(3F) DORMHR - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dorml2(3F) DORML2 - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
dormlq(3F) DORMLQ - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dormql(3F) DORMQL - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dormqr(3F) DORMQR - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dormr2(3F) DORMR2 - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
dormrq(3F) DORMRQ - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dormtr(3F) DORMTR - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
dot(3F) ddot, sdot, zdotc, cdotc, zdotu, cdotu - BLAS level ONE, dot product functions
DPBCO(3F) DPBCO - DPBCO factors a double precision symmetric positive definite matrix stored in band form and estimates the condition of the matrix.
dpbcon(3F) DPBCON - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF
DPBDI(3F) DPBDI - DPBDI computes the determinant of a double precision symmetric positive definite band matrix using the factors computed by DPBCO or DPBFA. If the inverse is needed, use DPBSL N times.
dpbequ(3F) DPBEQU - compute row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition number (with respect to the two-norm)
DPBFA(3F) DPBFA - DPBFA factors a double precision symmetric positive definite matrix stored in band form.
dpbrfs(3F) DPBRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution
DPBSL(3F) DPBSL - DPBSL solves the double precision symmetric positive definite band system A*X = B using the factors computed by DPBCO or DPBFA.
dpbstf(3F) DPBSTF - compute a split Cholesky factorization of a real symmetric positive definite band matrix A
dpbsv(3F) DPBSV - compute the solution to a real system of linear equations A * X = B,
dpbsvx(3F) DPBSVX - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,
dpbtf2(3F) DPBTF2 - compute the Cholesky factorization of a real symmetric positive definite band matrix A
dpbtrf(3F) DPBTRF - compute the Cholesky factorization of a real symmetric positive definite band matrix A
dpbtrs(3F) DPBTRS - solve a system of linear equations A*X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF
DPOCO(3F) DPOCO - DPOCO factors a double precision symmetric positive definite matrix and estimates the condition of the matrix.
dpocon(3F) DPOCON - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF
DPODI(3F) DPODI - DPODI computes the determinant and inverse of a certain double precision symmetric positive definite matrix (see below) using the factors computed by DPOCO, DPOFA or DQRDC.
dpoequ(3F) DPOEQU - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm)
DPOFA(3F) DPOFA - DPOFA factors a double precision symmetric positive definite matrix.
dporfs(3F) DPORFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite,
DPOSL(3F) DPOSL - DPOSL solves the double precision symmetric positive definite system A * X = B using the factors computed by DPOCO or DPOFA.
dposv(3F) DPOSV - compute the solution to a real system of linear equations A * X = B,
dposvx(3F) DPOSVX - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,
dpotf2(3F) DPOTF2 - compute the Cholesky factorization of a real symmetric positive definite matrix A
dpotrf(3F) DPOTRF - compute the Cholesky factorization of a real symmetric positive definite matrix A
dpotri(3F) DPOTRI - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF
dpotrs(3F) DPOTRS - solve a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF
DPPCO(3F) DPPCO - DPPCO factors a double precision symmetric positive definite matrix stored in packed form and estimates the condition of the matrix.
dppcon(3F) DPPCON - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF
DPPDI(3F) DPPDI - DPPDI computes the determinant and inverse of a double precision symmetric positive definite matrix using the factors computed by DPPCO or DPPFA .
dppequ(3F) DPPEQU - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
DPPFA(3F) DPPFA - DPPFA factors a double precision symmetric positive definite matrix stored in packed form.
dpprfs(3F) DPPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward error estimates for the solution
DPPSL(3F) DPPSL - DPPSL solves the double precision symmetric positive definite system A * X = B using the factors computed by DPPCO or DPPFA.
dppsv(3F) DPPSV - compute the solution to a real system of linear equations A * X = B,
dppsvx(3F) DPPSVX - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,
dpptrf(3F) DPPTRF - compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format
dpptri(3F) DPPTRI - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF
dpptrs(3F) DPPTRS - solve a system of linear equations A*X = B with a symmetric positive definite matrix A in packed storage using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF
dprod(3F) dprod, qprod - FORTRAN double precision and quad precision product intrinsic functions
dptcon(3F) DPTCON - compute the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by DPTTRF
dpteqr(3F) DPTEQR - compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using DPTTRF, and then calling DBDSQR to compute the singular values of the bidiagonal factor
dptrfs(3F) DPTRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
DPTSL(3F) DPTSL - DPTSL, given a positive definite symmetric tridiagonal matrix and a right hand side, will find the solution.
dptsv(3F) DPTSV - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices
dptsvx(3F) DPTSVX - use the factorization A = L*D*L**T to compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix and X and B are N-by-NRHS matrices
dpttrf(3F) DPTTRF - compute the factorization of a real symmetric positive definite tridiagonal matrix A
dpttrs(3F) DPTTRS - solve a system of linear equations A * X = B with a symmetric positive definite tridiagonal matrix A using the factorization A = L*D*L**T or A = U**T*D*U computed by DPTTRF
DQRDC(3F) DQRDC - DQRDC uses Householder transformations to compute the QR factorization of an N by P matrix X. Column pivoting based on the 2- norms of the reduced columns may be performed at the user's option.
DQRSL(3F) DQRSL - DQRSL applies the output of DQRDC to compute coordinate transformations, projections, and least squares solutions. For K .LE. MIN(N,P), let XK be the matrix
drscl(3F) DRSCL - multiplie an n-element real vector x by the real scalar 1/a
dsbev(3F) DSBEV - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
dsbevd(3F) DSBEVD - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
dsbevx(3F) DSBEVX - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
dsbgst(3F) DSBGST - reduce a real symmetric-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,
dsbgv(3F) DSBGV - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x
dsbtrd(3F) DSBTRD - reduce a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation
dsecnd(3F)
DSICO(3F) DSICO - DSICO factors a double precision symmetric matrix by elimination with symmetric pivoting and estimates the condition of the matrix.
DSIDI(3F) DSIDI - DSIDI computes the determinant, inertia and inverse of a double precision symmetric matrix using the factors from DSIFA.
DSIFA(3F) DSIFA - DSIFA factors a double precision symmetric matrix by elimination with symmetric pivoting.
DSISL(3F) DSISL - DSISL solves the double precision symmetric system A * X = B using the factors computed by DSIFA.
DSPCO(3F) DSPCO - DSPCO factors a double precision symmetric matrix stored in packed form by elimination with symmetric pivoting and estimates the condition of the matrix.
dspcon(3F) DSPCON - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF
DSPDI(3F) DSPDI - DSPDI computes the determinant, inertia and inverse of a double precision symmetric matrix using the factors from DSPFA, where the matrix is stored in packed form.
dspev(3F) DSPEV - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage
dspevd(3F) DSPEVD - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage
dspevx(3F) DSPEVX - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage
DSPFA(3F) DSPFA - DSPFA factors a double precision symmetric matrix stored in packed form by elimination with symmetric pivoting.
dspgst(3F) DSPGST - reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage
dspgv(3F) DSPGV - compute all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
dsprfs(3F) DSPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution
DSPSL(3F) DSPSL - DSISL solves the double precision symmetric system A * X = B using the factors computed by DSPFA.
dspsv(3F) DSPSV - compute the solution to a real system of linear equations A * X = B,
dspsvx(3F) DSPSVX - use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices
dsptrd(3F) DSPTRD - reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation
dsptrf(3F) DSPTRF - compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method
dsptri(3F) DSPTRI - compute the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF
dsptrs(3F) DSPTRS - solve a system of linear equations A*X = B with a real symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF
dstebz(3F) DSTEBZ - compute the eigenvalues of a symmetric tridiagonal matrix T
dstedc(3F) DSTEDC - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
dstein(3F) DSTEIN - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration
dsteqr(3F) DSTEQR - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method
dsterf(3F) DSTERF - compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm
dstev(3F) DSTEV - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A
dstevd(3F) DSTEVD - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
dstevx(3F) DSTEVX - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A
DSVDC(3F) DSVDC - DSVDC is a subroutine to reduce a double precision NxP matrix X by orthogonal transformations U and V to diagonal form. The diagonal elements S(I) are the singular values of X. The columns of U are the corresponding left singular vectors, and the columns of V the right singular vectors.
dsycon(3F) DSYCON - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF
dsyev(3F) DSYEV - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
dsyevd(3F) DSYEVD - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
dsyevx(3F) DSYEVX - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
dsygs2(3F) DSYGS2 - reduce a real symmetric-definite generalized eigenproblem to standard form
dsygst(3F) DSYGST - reduce a real symmetric-definite generalized eigenproblem to standard form
dsygv(3F) DSYGV - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
dsyrfs(3F) DSYRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution
dsysv(3F) DSYSV - compute the solution to a real system of linear equations A * X = B,
dsysvx(3F) DSYSVX - use the diagonal pivoting factorization to compute the solution to a real system of linear equations A * X = B,
dsytd2(3F) DSYTD2 - reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation
dsytf2(3F) DSYTF2 - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
dsytrd(3F) DSYTRD - reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation
dsytrf(3F) DSYTRF - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
dsytri(3F) DSYTRI - compute the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF
dsytrs(3F) DSYTRS - solve a system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF
dtbcon(3F) DTBCON - estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm
dtbrfs(3F) DTBRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
dtbtrs(3F) DTBTRS - solve a triangular system of the form A * X = B or A**T * X = B,
dtgevc(3F) DTGEVC - compute some or all of the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B)
dtgsja(3F) DTGSJA - compute the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B
dtpcon(3F) DTPCON - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm
dtprfs(3F) DTPRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix
dtptri(3F) DTPTRI - compute the inverse of a real upper or lower triangular matrix A stored in packed format
dtptrs(3F) DTPTRS - solve a triangular system of the form A * X = B or A**T * X = B,
DTRCO(3F) DTRCO - DTRCO estimates the condition of a double precision triangular matrix.
dtrcon(3F) DTRCON - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
DTRDI(3F) DTRDI - DTRDI computes the determinant and inverse of a double precision triangular matrix.
dtrevc(3F) DTREVC - compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T
dtrexc(3F) DTREXC - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that the diagonal block of T with row index IFST is moved to row ILST
dtrrfs(3F) DTRRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
dtrsen(3F) DTRSEN - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T,
DTRSL(3F) DTRSL - DTRSL solves systems of the form
dtrsna(3F) DTRSNA - estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q orthogonal)
dtrsyl(3F) DTRSYL - solve the real Sylvester matrix equation
dtrti2(3F) DTRTI2 - compute the inverse of a real upper or lower triangular matrix
dtrtri(3F) DTRTRI - compute the inverse of a real upper or lower triangular matrix A
dtrtrs(3F) DTRTRS - solve a triangular system of the form A * X = B or A**T * X = B,
dtzrqf(3F) DTZRQF - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations
dzsum1(3F) DZSUM1 - take the sum of the absolute values of a complex vector and returns a double precision result
ELMBAK(3F) ELMBAK, SELMBAK - EISPACK routine. This subroutine forms the eigenvectors of a REAL GENERAL matrix by back transforming those of the corresponding upper Hessenberg matrix determined by ELMHES.
ELMHES(3F) elmhes, selmhes - EISPACK routine. Given a REAL GENERAL matrix, this subroutine reduces a submatrix situated in rows and columns LOW through IGH to upper Hessenberg form by stabilized elementary similarity transformations.
ELTRAN(3F) ELTRAN, SELTRAN - EISPACK routine. This subroutine accumulates the stabilized elementary similarity transformations used in the reduction of a REAL GENERAL matrix to upper Hessenberg form by ELMHES.
ep(3F) ep: epbase, epprec, epemin, epemax, eptiny, ephuge, epmrsp - FORTRAN numeric characteristic constants
EPSLON(3F) EPSLON, SEPSLON - EISPACK auxiliary routine.
erf(3F) erf, erfc, derf, derfc, qerf, qerfc - error function and complementary error function
etime(3F) etime, dtime - return user+system execution time
exit(3F) EXIT - Exits from a Fortran program
exp(3F) exp, dexp, qexp, cexp, zexp - FORTRAN exponential intrinsic function
fdate(3F) fdate - return date and time in an ASCII string
fft(3F) FFT, libfft - libcomplib.sgimath - Fast Fourier Transforms
fft1d(3F) cfft1d, zfft1d - 1D, Real Complex-to-Complex, Fast Fourier Transforms.
fft1di(3F) cfft1di, zfft1di - initialize the coefficient array for Complex-to- Complex 1D FFT modules.
fft1du(3F) scfft1du, dzfft1du - 1D, Real to Complex, Direct Fast Fourier Transforms.
fft1dui(3F) scfft1dui, dzfft1dui - initialize the coefficient array for real-to- complex 1D FFT modules.
fft2d(3F) cfft2d, zfft2d - 2D Complex-to-Complex Fast Fourier Transform.
fft2di(3F) cfft2di, zfft2di - initialize the coefficient array for complex-to- complex 2D FFT modules.
fft2du(3F) scfft2du, dzfft2du - 2D, Real to Complex, Direct Fast Fourier Transforms.
fft2dui(3F) scfft2dui, dzfft2dui - initialize the coefficient array for real-to- complex 2D FFT modules.
fft3d(3F) cfft3d, zfft3d - 3D Complex-to-Complex Fast Fourier Transform.
fft3di(3F) cfft3di, zfft3di - initialize the coefficient array for complex-to- complex 3D FFT modules.
fft3du(3F) scfft3du, dzfft3du - 3D, Real to Complex, Direct Fast Fourier Transforms.
fft3dui(3F) scfft3dui, dzfft3dui - initialize the coefficient array for real-to- complex 3D FFT modules.
FIGI(3F) FIGI, SFIGI - EISPACK routine. Given a NONSYMMETRIC TRIDIAGONAL matrix such that the products of corresponding pairs of off-diagonal elements are all non-negative, this subroutine reduces it to a symmetric tridiagonal matrix with the same eigenvalues. If, further, a zero product only occurs when both factors are zero, the reduced matrix is similar to the original matrix.
FIGI2(3F) FIGI2, SFIGI2 - EISPACK routine. Given a NONSYMMETRIC TRIDIAGONAL matrix such that the products of corresponding pairs of off-diagonal elements are all non-negative, and zero only when both factors are zero, this subroutine reduces it to a SYMMETRIC TRIDIAGONAL matrix using and accumulating diagonal similarity transformations.
fir1d(3F) SFIR1D, DFIR1D, CFIR1D, ZFIR1D - 1D Convolution in the time domain.
fir2d(3F) SFIR2D, DFIR2D, CFIR2D, ZFIR2D - 2D Convolution in the time domain.
firm1d(3F) SFIRM1D, DFIRM1D, CFIRM1D, ZFIRM1D - N 1D convolutions in the time domain.
floating(3F) - return scalar values associated with the argument derived from the model of floating point data.
flush(3F) [p_man/cat3/f90] FLUSH - Writes data buffered by Fortran output statements to a file
flush(3F) [p_man/cat3/ftn] flush - flush output to a logical unit
fseek(3F) fseek, fseek64, ftell, ftell64 - reposition a file on a logical unit
fsigfpe(3F) handle_sigfpes - floating-point exception handler package
ftype(3F) ftype: int, ifix, iifix, jifix, idint, iqint, real, float, floati, floatj, sngl, dble, dfloti, dflotj, dfloat, qfloat, qfloti, qflotj, qflotk, cmplx, dcmplx, qcmplx, ichar, char - explicit FORTRAN type conversion
gbmv(3F) dgbmv, sgbmv, zgbmv, cgbmv - BLAS Level Two Matrix-Vector Product
gemm(3F) dgemm, sgemm, zgemm, cgemm - BLAS level three Matrix Product
gemv(3F) dgemv, sgemv, zgemv, cgemv - BLAS Level Two Matrix-Vector Product
ger(3F) dger, sger, zgeru, cgeru, zgerc, cgerc - BLAS Level Two Rank 1 Operation
getarg(3F) getarg, iargc - return Fortran command-line argument
getc(3F) getc, fgetc - get a character from a logical unit
getenv(3F) getenv - get value of environment variable
getlog(3F) getlog - get user's login name
glio_group(3F) glio_group_mpi, glio_group_shmem - Defines a group of processes to be associated with a global file.
hemm(3F) zhemm, chemm - BLAS level three Hermitian Matrix Product
her2k(3F) zher2k, cher2k - BLAS level three Hermitian Rank 2K Update
herk(3F) zherk, cherk - BLAS level three Hermitian Rank K Update
HQR(3F) HQR, SHQR - EISPACK routine. This subroutine finds the eigenvalues of a REAL UPPER Hessenberg matrix by the QR method.
HQR2(3F) HQR2, SHQR2 - EISPACK routine. This subroutine finds the eigenvalues and eigenvectors of a REAL UPPER Hessenberg matrix by the QR method. The eigenvectors of a REAL GENERAL matrix can also be found if ELMHES and ELTRAN or ORTHES and ORTRAN have been used to reduce this general matrix to Hessenberg form and to accumulate the similarity transformations.
HTRIB3(3F) HTRIB3, SHTRIB3 - EISPACK routine. This subroutine forms the eigenvectors of a COMPLEX HERMITIAN matrix by back transforming those of the corresponding real symmetric tridiagonal matrix determined by HTRID3.
HTRIBK(3F) HTRIBK, SHTRIBK - EISPACK routine. This subroutine forms the eigenvectors of a COMPLEX HERMITIAN matrix by back transforming those of the corresponding real symmetric tridiagonal matrix determined by HTRIDI.
HTRID3(3F) HTRID3, SHTRID3 - EISPACK routine. This subroutine reduces a COMPLEX HERMITIAN matrix, stored as a single square array, to a real symmetric tridiagonal matrix using unitary similarity transformations.
HTRIDI(3F) HTRIDI, SHTRIDI - EISPACK routine. This subroutine reduces a COMPLEX HERMITIAN matrix to a real symmetric tridiagonal matrix using unitary similarity transformations.
icmax1(3F) ICMAX1 - find the index of the element whose real part has maximum absolute value
idate(3F) idate, itime - return date or time in numerical form
iir1d(3F) SIIR1D, DIIR1D, CIIR1D, ZIIR1D - 1D recursive convolution in the time domain.
iir2d(3F) SIIR2D, DIIR2D, CIIR2D, ZIIR2D - 2D Convolution in the time domain.
iirm1d(3F) SIIRM1D, DIIRM1D, CIIRM1D, ZIIRM1D - N 1D convolutions in the time domain.
ilaenv(3F) ILAENV - i called from the LAPACK routines to choose problem-dependent parameters for the local environment
imag(3F) imag, aimag, dimag, qimag - FORTRAN imaginary part of complex argument
IMTQL1(3F) IMTQL1, SIMTQL1 - EISPACK routine. This subroutine finds the eigenvalues of a SYMMETRIC TRIDIAGONAL matrix by the implicit QL method.
IMTQL2(3F) IMTQL2, SIMTQL2 - EISPACK routine. This subroutine finds the eigenvalues and eigenvectors of a SYMMETRIC TRIDIAGONAL matrix by the implicit QL method. The eigenvectors of a FULL SYMMETRIC matrix can also be found if TRED2 has been used to reduce this full matrix to tridiagonal form.
IMTQLV(3F) IMTQLV, SIMTQLV - EISPACK routine. This subroutine is a variant of IMTQL1.
index(3F) index - return location of FORTRAN substring
intro_conversion(3F) INTRO_CONVERSION - Introduction to conversion routines
intro_ffio(3F) INTRO_FFIO - Describes performance options available with the FFIO layers
intro_pxf(3F) INTRO_PXF - Introduction to PXF POSIX library
INVIT(3F) INVIT, SINVIT - EISPACK routine. This subroutine finds those eigenvectors of a REAL UPPER Hessenberg matrix corresponding to specified eigenvalues, using inverse iteration.
ipxfargc(3F) IPXFARGC - Returns the number of command-line arguments excluding the command name
ipxfwstopsig(3F) IPXFWSTOPSIG - Returns part of the lower bits of signal number that terminates child process
ipxfwtermsig(3F) IPXFWTERMSIG - Returns lower bit of signal that terminates a child process
ishell(3F) ISHELL - Executes a UNICOS shell command
izmax1(3F) IZMAX1 - find the index of the element whose real part has maximum absolute value
lapack(3F)
len(3F) len - return length of Fortran string
libexc(3F) trace_back_stack, trace_back_stack_and_print - call stack trace library for Fortran applications
loc(3F) loc - return the address of an object
log(3F) log, alog, dlog, qlog, clog, zlog - FORTRAN natural logarithm intrinsic function
log10(3F) log10, alog10, dlog10, qlog10 - FORTRAN common logarithm intrinsic function
lsame(3F) LSAME - return .TRUE
lsamen(3F) LSAMEN - test if the first N letters of CA are the same as the first N letters of CB, regardless of case
malloc(3F) malloc, free - main memory allocator
maplun(3F) maplun - returns the integer file descriptor for a Fortran logical unit number
max(3F) max, max0, imax0, jmax0, amax0, max1, amax1, dmax1, qmax1, imax1, jmax1, aimax0, ajmax0 - FORTRAN maximum-value functions
mclock(3F) mclock - return Fortran time accounting
min(3F) min, min0, imin0, jmin0, amin0, min1, amin1, dmin1, qmin1, imin1, jmin1, aimin0, ajmin0 - FORTRAN minimum-value functions
MINFIT(3F) MINFIT, SMINFIT - EISPACK routine. This subroutine determines, towards the solution of the linear T system AX=B, the singular value decomposition A=USV of a real T M by N rectangular matrix, forming U B rather than U. Householder bidiagonalization and a variant of the QR algorithm are used.
mod(3F) mod, imod, jmod, amod, dmod, qmod - FORTRAN remaindering intrinsic functions
mp(3F) mp: mp_block, mp_blocktime, mp_create, mp_destroy, mp_my_threadnum, mp_numthreads, mp_set_numthreads, mp_setup, mp_unblock, mp_setlock, mp_suggested_numthreads,mp_unsetlock, mp_barrier, mp_in_doacross_loop, mp_set_slave_stacksize - FORTRAN multiprocessing utility routines
nrm2(3F) dnrm2, snrm2, zdnrm2, csnrm2 - BLAS level ONE Euclidean norm functions.
numblks(3F) NUMBLKS - Returns the current size of a file in 4096-byte blocks
numeric(3F) - return scalar values related to parameters of an associated model
o32FFT(3F) o32FFT - o32 vs. n32/64 FFT library differences
ORTBAK(3F) ORTBAK, SORTBAK - EISPACK routine. This subroutine forms the eigenvectors of a REAL GENERAL matrix by back transforming those of the corresponding upper Hessenberg matrix determined by ORTHES.
ORTHES(3F) ORTHES, SORTHES - EISPACK routine. Given a REAL GENERAL matrix, this subroutine reduces a submatrix situated in rows and columns LOW through IGH to upper Hessenberg form by orthogonal similarity transformations.
ORTRAN(3F) ORTRAN, SORTRAN - EISPACK routine. This subroutine accumulates the orthogonal similarity transformations used in the reduction of a REAL GENERAL matrix to upper Hessenberg form by ORTHES.
perror(3F) perror, gerror, ierrno, strerror - get system error messages
psldlt(3F) PSLDLT_Preprocess, PSLDLT_Factor, PSLDLT_Solve, PSLDLT_Destroy, PSLDLT_Ordering - parallel sparse symmetric linear system solver
psldu(3F) PSLDU_Preprocess, PSLDU_Factor, PSLDU_Solve, PSLDU_Destroy, PSLDU_Ordering - parallel sparse unsymmetric linear system solver
putc(3F) putc, fputc - write a character to a fortran logical unit
putenv(3F) putenv - change or add Fortran environment variable
pxfaccess(3F) PXFACCESS - Checks the accessibility of a named file
pxfalarm(3F) PXFALARM - Schedule alarm signal
pxfchdir(3F) PXFCHDIR - Changes the current directory to a specified directory
pxfchmod(3F) PXFCHMOD - Sets file modes for a named file
pxfchown(3F) PXFCHOWN - Changes the owner and group of a file
pxfchroot(3F) PXFCHROOT - Changes the root directory to a specified directory
pxfclearenv(3F) PXFCLEARENV - Clears all environment variables
pxfconst(3F) PXFCONST, PXFISCONST, IPXFCONST - Returns the value associated with symbolic constants
pxfcreat(3F) PXFCREAT - Creates a new file or rewrites an existing file
pxfctermid(3F) PXFCTERMID - Generates terminal pathname
pxfdirectory(3F) PXFOPENDIR, PXFREADDIR, PXFREWINDDIR, PXFCLOSEDIR, - Performs directory operations
pxfestrget(3F) PXFESTRGET - Accesses a single string element of a structure component that is an array
pxfexecv(3F) PXFEXECV, PXFEXECVE, PXFEXECVP - Executes a new process image file
pxffastexit(3F) PXFFASTEXIT - Terminates a Fortran program
pxffcntl(3F) PXFFCNTL - Provides a subset of fcntl(2) functionality, except the third argument is always an integer
pxffileno(3F) PXFFILENO - Returns the file descriptor for a specified unit
pxffork(3F) PXFFORK - Creates a process
pxfgetarg(3F) PXFGETARG - Returns a command-line argument
pxfgetcwd(3F) PXFGETCWD - Gets the pathname of the working directory
pxfgetegid(3F) PXFGETEGID - Gets the effective group ID
pxfgetenv(3F) PXFGETENV - Returns a value for the environment name
pxfgeteuid(3F) PXFGETEUID - Gets effective user ID
pxfgetgid(3F) PXFGETGID - Gets the real group ID
pxfgetgrgid(3F) PXFGETGRGID - Gets group information using the group ID
pxfgetgrnam(3F) PXFGETGRNAM - Gets group information using the group name
pxfgetgroups(3F) PXFGETGROUPS - Gets supplementary group IDs
pxfgetlogin(3F) PXFGETLOGIN - Gets user name
pxfgetpgrp(3F) PXFGETPGRP -Gets the process group ID
pxfgetpid(3F) PXFGETPID - Gets the process ID
pxfgetppid(3F) PXFGETPPID - Gets the parent process ID
pxfgetpwnam(3F) PXFGETPWNAM - Gets password information about login name
pxfgetpwuid(3F) PXFGETPWUID - Gets password information by using user ID
pxfgetuid(3F) PXFGETUID - Gets the real user ID
pxfintget(3F) PXFINTGET - Allows values stored in individual components of a structure to be extracted and used
pxfintset(3F) PXFINTSET - Allows components of a structure to be set or modified
pxfisatty(3F) PXFISATTY - Determines if file descriptor corresponds to a valid file descriptor
pxfisblk(3F) PXFISBLK - Tests for block special file
pxfischr(3F) PXFISCHR - Tests for character special file
pxfisdir(3F) PXFISDIR - Tests for directory file
pxfisfifo(3F) PXFISFIFO - Tests for pipe or a FIFO special file
pxfisreg(3F) PXFISREG - Tests for regular file
pxfkill(3F) PXFKILL - Sends a signal to a process or group of processes
pxflink(3F) PXFLINK - Creates a link to a file
pxflocaltime(3F) PXFLOCALTIME - Converts to local time
pxfopen(3F) PXFOPEN - Provides a Fortran interface to the open(2) system call
pxfpause(3F) PXFPAUSE - Suspends process execution until signal
pxfrename(3F) PXFRENAME - Renames a file
pxfrmdir(3F) PXFRMDIR - Removes a directory entry
pxfsetenv(3F) PXFSETENV - Sets environment variable pair
pxfsetgid(3F) PXFSETGID - Sets group ID
pxfsetpgid(3F) PXFSETPGID - Set process group ID
pxfsetsid(3F) PXFSETSID - Creates a new session for a calling process
pxfsetuid(3F) PXFSETUID - Sets user ID
pxfsigaddset(3F) PXFSIGADDSET - Adds an individual signal to the specified signal set
pxfsigdelset(3F) PXFSIGDELSET - Deletes an individual signal in the specified signal set
pxfsigemptyset(3F) PXFSIGEMPTYSET - Initializes signal set such that all signals defined in POSIX standard are excluded
pxfsigfillset(3F) PXFSIGFILLSET - Initializes signal set such that all signals defined in POSIX standard are included
pxfsigismember(3F) PXFSIGISMEMBER - Determines if the specified signal is a member of the specified signal set
pxfsigpending(3F) PXFSIGPENDING - Examines pending signals
pxfsigprocmask(3F) PXFSIGPROCMASK - Examines and changes blocked signals
pxfsigsuspend(3F) PXFSIGSUSPEND - Waits for a signal
pxfsleep(3F) PXFSLEEP - Delays process execution
pxfstat(3F) PXFSTAT - Retrieves the file status
pxfstrget(3F) PXFSTRGET - Allows values stored in individual components of a structure to be extracted and used
pxfstrset(3F) PXFSTRSET - Allows values stored in individual components of a structure to be set
pxfstructcopy(3F) PXFSTRUCTCOPY - Copies structure
pxfstructcreate(3F) PXFSTRUCTCREATE - Creates an instance of the desired structure and returns a nonzero handle in the argument jhandle
pxfstructfree(3F) PXFSTRUCTFREE - Deletes the instance of the structure referenced by jhandle
pxfsysconf(3F) PXFSYSCONF - Retrieves the value of configurable system variables
pxftime(3F) PXFTIME - Gets system time
pxftimes(3F) PXFTIMES - Gets process times
pxfucompare(3F) PXFUCOMPARE - Compares unsigned integers
pxfumask(3F) PXFUMASK - Sets the file creation mask
pxfuname(3F) PXFUNAME - Retrieves the operating system name
pxfunlink(3F) PXFUNLINK - Removes a directory entry
pxfutime(3F) PXFUTIME - Sets access and modification times of a file
pxfwait(3F) PXFWAIT, PXFWAITPID - Obtains information about a calling process' child process
pxfwifexited(3F) PXFWIFEXITED - Determines if child process exited with exit
pxfwifsignaled(3F) PXFWIFSIGNALED - Determines if the child process terminated because of a signal
pxfwifstopped(3F) PXFWIFSTOPPED - Determines if a child process has stopped
PYTHAG(3F) PYTHAG, SPYTHAG - EISPACK auxiliary routine.
qsort(3F) qsort - quick sort
QZHES(3F) QZHES, SQZHES - EISPACK routine. This subroutine is the first step of the QZ algorithm for solving generalized matrix eigenvalue problems.
QZIT(3F) QZIT, SQZIT - EISPACK routine. This subroutine is the second step of the QZ algorithm for solving generalized matrix eigenvalue problems,
QZVAL(3F) QZVAL, SQZVAL - EISPACK routine. This subroutine is the third step of the QZ algorithm for solving generalized matrix eigenvalue problems,
QZVEC(3F) QZVEC, ZQZVEC - EISPACK routine. This subroutine is the optional fourth step of the QZ algorithm for solving generalized matrix eigenvalue problems,
ran(3F) ran - pseudo random number generator
rand(3F) rand, irand, srand - random number generator
random(3F) - generate pseudorandom numbers from a seed
RATQR(3F) RATQR, SRATQR - EISPACK routine. This subroutine finds the algebraically smallest or largest eigenvalues of a SYMMETRIC TRIDIAGONAL matrix by the rational QR method with Newton corrections.
RCFFT2(3F) RCFFT2 - Calculate a real-to-complex Fourier synthesis/analysis.
REBAK(3F) REBAK, SREBAK - EISPACK routine. This subroutine forms the eigenvectors of a generalized SYMMETRIC eigensystem by back transforming those of the derived symmetric matrix determined by REDUC.
REBAKB(3F) REBAKB, SREBAKB - EISPACK routine. This subroutine forms the eigenvectors of a generalized SYMMETRIC eigensystem by back transforming those of the derived symmetric matrix determined by REDUC2.
REDUC(3F) REDUC, SREDUC - EISPACK routine. This subroutine reduces the generalized SYMMETRIC eigenproblem Ax=(LAMBDA)Bx, where B is POSITIVE DEFINITE, to the standard symmetric eigenproblem using the Cholesky factorization of B.
REDUC2(3F) REDUC2, SREDUC2 - EISPACK routine. This subroutine reduces the generalized SYMMETRIC eigenproblems ABx=(LAMBDA)x OR BAy=(LAMBDA)y, where B is POSITIVE DEFINITE, to the standard symmetric eigenproblem using the Cholesky factorization of B.
rename(3F) rename - rename a file
RG(3F) RG, SRG - EISPACK routine. This subroutine calls the recommended sequence of subroutines from the eigensystem subroutine package (EISPACK) To find the eigenvalues and eigenvectors (if desired) of a REAL GENERAL matrix.
RGG(3F) RGG, SRGG - EISPACK routine. This subroutine calls the recommended sequence of subroutines from the eigensystem subroutine package (EISPACK) to find the eigenvalues and eigenvectors (if desired) for the REAL GENERAL GENERALIZED eigenproblem Ax = (LAMBDA)Bx.
rnl(3F) RNLFLAG, RNLDELM, RNLSEP, RNLREP, RNLCOMM - Manipulates characters recognized by NAMELIST
rnlecho(3F) RNLECHO - Specifies output unit for NAMELIST error messages and echo lines
rnlskip(3F) RNLSKIP - Takes appropriate action when an undesired NAMELIST group is encountered
rnltype(3F) RNLTYPE - Determines action if type mismatch occurs across equal sign on NAMELIST input record
rot(3F) drotg, srotg, drot, srot - BLAS level ONE rotation subroutines
rotm(3F) drotm, srotm - BLAS Level-1. Applies a modified Givens rotation.
rotmg(3F) drotmg, srotmg - BLAS Level-1. Compute the elements of a modified Givens plane rotation.
round(3F) round: anint, dnint, qnint, nint, inint, jnint, idnint, iqnint, iidnnt, jidnnt, iiqnnt, jiqnnt, kiqnnt - FORTRAN nearest integer functions
RS(3F) RS, SRS - EISPACK routine. This subroutine calls the recommended sequence of subroutines from the eigensystem subroutine package (EISPACK) to find the eigenvalues and eigenvectors (if desired) of a REAL SYMMETRIC matrix.
RSB(3F) RSB, SRSB - EISPACK routine. This subroutine calls the recommended sequence of subroutines from the eigensystem subroutine package (EISPACK) to find the eigenvalues and eigenvectors (if desired) of a REAL SYMMETRIC BAND matrix.
RSG(3F) RSG, SRSG - EISPACK routine. This subroutine calls the recommended sequence of subroutines from the eigensystem subroutine package (EISPACK) to find the eigenvalues and eigenvectors (if desired) for the REAL SYMMETRIC generalized eigenproblem Ax = (LAMBDA)Bx.
RSGAB(3F) RSGAB, SRSGAB - EISPACK routine. This subroutine calls the recommended sequence of subroutines from the eigensystem subroutine package (EISPACK) to find the eigenvalues and eigenvectors (if desired) for the REAL SYMMETRIC generalized eigenproblem ABx = (LAMBDA)x.
RSGBA(3F) RSGBA, SRSGBA - EISPACK routine. This subroutine calls the recommended sequence of subroutines from the eigensystem subroutine package (EISPACK) to find the eigenvalues and eigenvectors (if desired) for the REAL SYMMETRIC generalized eigenproblem BAx = (LAMBDA)x.
RSM(3F) RSM, SRSM - EISPACK routine. This subroutine calls the recommended sequence of subroutines from the eigensystem subroutine package (EISPACK) to find all of the eigenvalues and some of the eigenvectors of a real symmetric matrix.
RSP(3F) RSP, SRSP - EISPACK routine. This subroutine calls the recommended sequence of subroutines from the eigensystem subroutine package (EISPACK) to find the eigenvalues and eigenvectors (if desired) of a REAL SYMMETRIC PACKED matrix.
RST(3F) RST, SRST - EISPACK routine. This subroutine calls the recommended sequence of subroutines from the eigensystem subroutine package (EISPACK) to find the eigenvalues and eigenvectors (if desired) of a REAL SYMMETRIC TRIDIAGONAL matrix.
RT(3F) RT, SRT - EISPACK routine. This subroutine calls the recommended sequence of subroutines from the eigensystem subroutine package (EISPACK) to find the eigenvalues and eigenvectors (if desired) of a special REAL TRIDIAGONAL matrix.
sbdsqr(3F) SBDSQR - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
sbmv(3F) dsbmv, ssbmv, zhbmv, chbmv - BLAS Level Two (Symmetric/Hermitian) Banded Matrix - Vector Product
scal(3F) dscal, sscal, zscal, cscal, zdscal, csscal - BLAS level ONE scaling subroutines
scfftm1du(3F) scfftm1du, dzfftm1du - Multiple 1D, Real to Complex, Direct Fast Fourier Transforms.
scfftm1dui(3F) scfftm1dui, dzfftm1dui - initialize the coefficient array for real-to- complex Multiple 1D FFT modules.
SCHDC(3F) SCHDC - SCHDC computes the Cholesky decomposition of a positive definite matrix. A pivoting option allows the user to estimate the condition of a positive definite matrix or determine the rank of a positive semidefinite matrix.
SCHDD(3F) SCHDD - SCHDD downdates an augmented Cholesky decomposition or the triangular factor of an augmented QR decomposition. Specifically, given an upper triangular matrix R of order P, a row vector X, a column vector Z, and a scalar Y, SCHDD determines an orthogonal matrix U and a scalar ZETA such that
SCHEX(3F) SCHEX - SCHEX updates the Cholesky factorization
SCHUD(3F) SCHUD - SCHUD updates an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. Specifically, given an upper triangular matrix R of order P, a row vector X, a column vector Z, and a scalar Y, SCHUD determines a unitary matrix U and a scalar ZETA such that
scsum1(3F) SCSUM1 - take the sum of the absolute values of a complex vector and returns a single precision result
sdfft1du(3F) dfft1du, sfft1du - 1D Real to Complex Fast Fourier Transform.
sdfft1dui(3F) sfft1dui, dfft1dui - 1D FFT Real to Complex workspace initialization routines.
sdfft2du(3F) dfft2du, sfft2du - 2D Real to Complex Fast Fourier Transform.
sdfft2dui(3F) sfft2dui, dfft2dui - 2D FFT Real to Complex workspace initialization routines.
sdfft3du(3F) dfft3du, sfft3du - 3D Real to Complex Fast Fourier Transform.
sdfft3dui(3F) sfft3dui, dfft3dui - 3D FFT Real to Complex workspace initialization routines.
sdfftm1du(3F) dfftm1du, sfftm1du - Multiple 1D, Real to Complex Fast Fourier Transform.
sdfftm1dui(3F) sfftm1dui, dfftm1dui - Multiple 1D, FFT Real to Complex workspace initialization routines.
sdisna(3F) SDISNA - compute the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general m-by-n matrix
second(3F) [p_man/cat3/complib]
second(3F) [p_man/cat3/f90] SECOND - Returns elapsed CPU time
secondr(3F) SECONDR - Returns elapsed wall-clock time in seconds
selected(3F) - return a kind type parameter given a decimal exponent range or precision.
setbuf(3F) setbuf, setvbuf, setbuffer, setlinebuf - assign buffering to a stream logical unit
sgbbrd(3F) SGBBRD - reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation
SGBCO(3F) SGBCO - SBGCO factors a real band matrix by Gaussian elimination and estimates the condition of the matrix.
sgbcon(3F) SGBCON - estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm,
SGBDI(3F) SGBDI - SGBDI computes the determinant of a band matrix using the factors computed by SBGCO or SGBFA. If the inverse is needed, use SGBSL N times.
sgbequ(3F) SGBEQU - compute row and column scalings intended to equilibrate an M- by-N band matrix A and reduce its condition number
SGBFA(3F) SGBFA - SGBFA factors a real band matrix by elimination.
sgbrfs(3F) SGBRFS - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
SGBSL(3F) SGBSL - SGBSL solves the real band system A * X = B or TRANS(A) * X = B using the factors computed by SBGCO or SGBFA.
sgbsv(3F) SGBSV - compute the solution to a real system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices
sgbsvx(3F) SGBSVX - use the LU factorization to compute the solution to a real system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
sgbtf2(3F) SGBTF2 - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges
sgbtrf(3F) SGBTRF - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges
sgbtrs(3F) SGBTRS - solve a system of linear equations A * X = B or A' * X = B with a general band matrix A using the LU factorization computed by SGBTRF
sgebak(3F) SGEBAK - form the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by SGEBAL
sgebal(3F) SGEBAL - balance a general real matrix A
sgebd2(3F) SGEBD2 - reduce a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation
sgebrd(3F) SGEBRD - reduce a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation
SGECO(3F) SGECO - SGECO factors a real matrix by Gaussian elimination and estimates the condition of the matrix.
sgecon(3F) SGECON - estimate the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGETRF
SGEDI(3F) SGEDI - SGEDI computes the determinant and inverse of a matrix using the factors computed by SGECO or SGEFA.
sgeequ(3F) SGEEQU - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number
sgees(3F) SGEES - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z
sgeesx(3F) SGEESX - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z
sgeev(3F) SGEEV - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
sgeevx(3F) SGEEVX - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
SGEFA(3F) SGEFA - SGEFA factors a real matrix by Gaussian elimination.
sgegs(3F) SGEGS - compute for a pair of N-by-N real nonsymmetric matrices A, B
sgegv(3F) SGEGV - compute for a pair of n-by-n real nonsymmetric matrices A and B, the generalized eigenvalues (alphar +/- alphai*i, beta), and optionally, the left and/or right generalized eigenvectors (VL and VR)
sgehd2(3F) SGEHD2 - reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation
sgehrd(3F) SGEHRD - reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation
sgelq2(3F) SGELQ2 - compute an LQ factorization of a real m by n matrix A
sgelqf(3F) SGELQF - compute an LQ factorization of a real M-by-N matrix A
sgels(3F) SGELS - solve overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A
sgelss(3F) SGELSS - compute the minimum norm solution to a real linear least squares problem
sgelsx(3F) SGELSX - compute the minimum-norm solution to a real linear least squares problem
sgeql2(3F) SGEQL2 - compute a QL factorization of a real m by n matrix A
sgeqlf(3F) SGEQLF - compute a QL factorization of a real M-by-N matrix A
sgeqpf(3F) SGEQPF - compute a QR factorization with column pivoting of a real M-by-N matrix A
sgeqr2(3F) SGEQR2 - compute a QR factorization of a real m by n matrix A
sgeqrf(3F) SGEQRF - compute a QR factorization of a real M-by-N matrix A
sgerfs(3F) SGERFS - improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution
sgerq2(3F) SGERQ2 - compute an RQ factorization of a real m by n matrix A
sgerqf(3F) SGERQF - compute an RQ factorization of a real M-by-N matrix A
SGESL(3F) SGESL - SGESL solves the real system A * X = B or TRANS(A) * X = B using the factors computed by SGECO or SGEFA.
sgesv(3F) SGESV - compute the solution to a real system of linear equations A * X = B,
sgesvd(3F) SGESVD - compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors
sgesvx(3F) SGESVX - use the LU factorization to compute the solution to a real system of linear equations A * X = B,
sgetf2(3F) SGETF2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges
sgetrf(3F) SGETRF - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges
sgetri(3F) SGETRI - compute the inverse of a matrix using the LU factorization computed by SGETRF
sgetrs(3F) SGETRS - solve a system of linear equations A * X = B or A' * X = B with a general N-by-N matrix A using the LU factorization computed by SGETRF
sggbak(3F) SGGBAK - form the right or left eigenvectors of a real generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by SGGBAL
sggbal(3F) SGGBAL - balance a pair of general real matrices (A,B)
sggglm(3F) SGGGLM - solve a general Gauss-Markov linear model (GLM) problem
sgghrd(3F) SGGHRD - reduce a pair of real matrices (A,B) to generalized upper Hessenberg form using orthogonal transformations, where A is a general matrix and B is upper triangular
sgglse(3F) SGGLSE - solve the linear equality-constrained least squares (LSE) problem
sggqrf(3F) SGGQRF - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B
sggrqf(3F) SGGRQF - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B
sggsvd(3F) SGGSVD - compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B
sggsvp(3F) SGGSVP - compute orthogonal matrices U, V and Q such that N-K-L K L U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0
sgimath(3F) complib, complib.sgimath, sgimath - Scientific and Mathematical Library
sgtcon(3F) SGTCON - estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF
sgtrfs(3F) SGTRFS - improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution
SGTSL(3F) SGTSL - SGTSL given a general tridiagonal matrix and a right hand side will find the solution.
sgtsv(3F) SGTSV - solve the equation A*X = B,
sgtsvx(3F) SGTSVX - use the LU factorization to compute the solution to a real system of linear equations A * X = B or A**T * X = B,
sgttrf(3F) SGTTRF - compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges
sgttrs(3F) SGTTRS - solve one of the systems of equations A*X = B or A'*X = B,
shgeqz(3F) SHGEQZ - implement a single-/double-shift version of the QZ method for finding the generalized eigenvalues w(j)=(ALPHAR(j) + i*ALPHAI(j))/BETAR(j) of the equation det( A - w(i) B ) = 0 In addition, the pair A,B may be reduced to generalized Schur form
shsein(3F) SHSEIN - use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H
shseqr(3F) SHSEQR - compute the eigenvalues of a real upper Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**T, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors
sign(3F) sign, isign, iisign, jisign, dsign, qsign - FORTRAN transfer-of-sign intrinsic function
sin(3F) sin, dsin, qsin, csin, zsin, cqsin, sind, dsind, qsind - FORTRAN sine intrinsic function
sinh(3F) sinh, dsinh, qsinh - FORTRAN hyperbolic sine intrinsic function
slabad(3F) SLABAD - take as input the values computed by SLAMCH for underflow and overflow, and returns the square root of each of these values if the log of LARGE is sufficiently large
slabrd(3F) SLABRD - reduce the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A
slacon(3F) SLACON - estimate the 1-norm of a square, real matrix A
slacpy(3F) SLACPY - copie all or part of a two-dimensional matrix A to another matrix B
sladiv(3F) SLADIV - perform complex division in real arithmetic a + i*b p + i*q = --------- c + i*d The algorithm is due to Robert L
slae2(3F) SLAE2 - compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]
slaebz(3F) SLAEBZ - contain the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix T less than or equal to its argument w
slaed0(3F) SLAED0 - compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
slaed1(3F) SLAED1 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
slaed2(3F) SLAED2 - merge the two sets of eigenvalues together into a single sorted set
slaed3(3F) SLAED3 - find the roots of the secular equation, as defined by the values in D, W, and RHO, between KSTART and KSTOP
slaed4(3F) SLAED4 - subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0
slaed5(3F) SLAED5 - subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j
slaed6(3F) SLAED6 - compute the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true
slaed7(3F) SLAED7 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
slaed8(3F) SLAED8 - merge the two sets of eigenvalues together into a single sorted set
slaed9(3F) SLAED9 - find the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP
slaeda(3F) SLAEDA - compute the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem
slaein(3F) SLAEIN - use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H
slaev2(3F) SLAEV2 - compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ]
slaexc(3F) SLAEXC - swap adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation
slag2(3F) SLAG2 - compute the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflow
slags2(3F) SLAGS2 - compute 2-by-2 orthogonal matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q = V'*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) The rows of the transformed A and B are parallel, where U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ ) ( -SNU CSU ) ( -SNV CSV ) ( -SNQ CSQ ) Z' denotes the transpose of Z
slagtf(3F) SLAGTF - factorize the matrix (T - lambda*I), where T is an n by n tridiagonal matrix and lambda is a scalar, as T - lambda*I = PLU,
slagtm(3F) SLAGTM - perform a matrix-vector product of the form B := alpha * A * X + beta * B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1
slagts(3F) SLAGTS - may be used to solve one of the systems of equations (T - lambda*I)*x = y or (T - lambda*I)'*x = y,
slahqr(3F) SLAHQR - i an auxiliary routine called by SHSEQR to update the eigenvalues and Schur decomposition already computed by SHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI
slahrd(3F) SLAHRD - reduce the first NB columns of a real general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero
slaic1(3F) SLAIC1 - applie one step of incremental condition estimation in its simplest version
slaln2(3F) SLALN2 - solve a system of the form (ca A - w D ) X = s B or (ca A' - w D) X = s B with possible scaling ("s") and perturbation of A
slamch(3F) SLAMCH - determine single precision machine parameters
slamrg(3F) SLAMRG - will create a permutation list which will merge the elements of A (which is composed of two independently sorted sets) into a single set which is sorted in ascending order
slangb(3F) SLANGB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals
slange(3F) SLANGE - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A
slangt(3F) SLANGT - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A
slanhs(3F) SLANHS - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
slansb(3F) SLANSB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals
slansp(3F) SLANSP - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form
slanst(3F) SLANST - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A
slansy(3F) SLANSY - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A
slantb(3F) SLANTB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals
slantp(3F) SLANTP - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
slantr(3F) SLANTR - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A
slanv2(3F) SLANV2 - compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form
slapll(3F) SLAPLL - two column vectors X and Y, let A = ( X Y )
slapmt(3F) SLAPMT - rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N
slapy2(3F) SLAPY2 - return sqrt(x**2+y**2), taking care not to cause unnecessary overflow
slapy3(3F) SLAPY3 - return sqrt(x**2+y**2+z**2), taking care not to cause unnecessary overflow
slaqgb(3F) SLAQGB - equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C
slaqge(3F) SLAQGE - equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
slaqsb(3F) SLAQSB - equilibrate a symmetric band matrix A using the scaling factors in the vector S
slaqsp(3F) SLAQSP - equilibrate a symmetric matrix A using the scaling factors in the vector S
slaqsy(3F) SLAQSY - equilibrate a symmetric matrix A using the scaling factors in the vector S
slaqtr(3F) SLAQTR - solve the real quasi-triangular system op(T)*p = scale*c, if LREAL = .TRUE
slar2v(3F) SLAR2V - applie a vector of real plane rotations from both sides to a sequence of 2-by-2 real symmetric matrices, defined by the elements of the vectors x, y and z
slarf(3F) SLARF - applie a real elementary reflector H to a real m by n matrix C, from either the left or the right
slarfb(3F) SLARFB - applie a real block reflector H or its transpose H' to a real m by n matrix C, from either the left or the right
slarfg(3F) SLARFG - generate a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H' * H = I
slarft(3F) SLARFT - form the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors
slarfx(3F) SLARFX - applie a real elementary reflector H to a real m by n matrix C, from either the left or the right
slargv(3F) SLARGV - generate a vector of real plane rotations, determined by elements of the real vectors x and y
slarnv(3F) SLARNV - return a vector of n random real numbers from a uniform or normal distribution
slartg(3F) SLARTG - generate a plane rotation so that [ CS SN ]
slartv(3F) SLARTV - applie a vector of real plane rotations to elements of the real vectors x and y
slaruv(3F) SLARUV - return a vector of n random real numbers from a uniform (0,1)
slas2(3F) SLAS2 - compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ]
slascl(3F) SLASCL - multiplie the M by N real matrix A by the real scalar CTO/CFROM
slaset(3F) SLASET - initialize an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals
slasq1(3F) SLASQ1 - SLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E
slasq2(3F) SLASQ2 - SLASQ2 computes the singular values of a real N-by-N unreduced bidiagonal matrix with squared diagonal elements in Q and squared off- diagonal elements in E
slasq3(3F) SLASQ3 - SLASQ3 is the workhorse of the whole bidiagonal SVD algorithm
slasq4(3F) SLASQ4 - SLASQ4 estimates TAU, the smallest eigenvalue of a matrix
slasr(3F) SLASR - perform the transformation A := P*A, when SIDE = 'L' or 'l' ( Left-hand side ) A := A*P', when SIDE = 'R' or 'r' ( Right-hand side ) where A is an m by n real matrix and P is an orthogonal matrix,
slasrt(3F) SLASRT - the numbers in D in increasing order (if ID = 'I') or in decreasing order (if ID = 'D' )
slassq(3F) SLASSQ - return the values scl and smsq such that ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
slasv2(3F) SLASV2 - compute the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ]
slaswp(3F) SLASWP - perform a series of row interchanges on the matrix A
slasy2(3F) SLASY2 - solve for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in op(TL)*X + ISGN*X*op(TR) = SCALE*B,
slasyf(3F) SLASYF - compute a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
slatbs(3F) SLATBS - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow, where A is an upper or lower triangular band matrix
slatps(3F) SLATPS - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form
slatrd(3F) SLATRD - reduce NB rows and columns of a real symmetric matrix A to symmetric tridiagonal form by an orthogonal similarity transformation Q' * A * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A
slatrs(3F) SLATRS - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow
slatzm(3F) SLATZM - applie a Householder matrix generated by STZRQF to a matrix
slauu2(3F) SLAUU2 - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
slauum(3F) SLAUUM - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
sleep(3F) sleep - suspend execution for an interval
solvers(3F) SOLVERS - SGI developed linear equations solvers.
sopgtr(3F) SOPGTR - generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by SSPTRD using packed storage
sopmtr(3F) SOPMTR - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
sorg2l(3F) SORG2L - generate an m by n real matrix Q with orthonormal columns,
sorg2r(3F) SORG2R - generate an m by n real matrix Q with orthonormal columns,
sorgbr(3F) SORGBR - generate one of the real orthogonal matrices Q or P**T determined by SGEBRD when reducing a real matrix A to bidiagonal form
sorghr(3F) SORGHR - generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by SGEHRD
sorgl2(3F) SORGL2 - generate an m by n real matrix Q with orthonormal rows,
sorglq(3F) SORGLQ - generate an M-by-N real matrix Q with orthonormal rows,
sorgql(3F) SORGQL - generate an M-by-N real matrix Q with orthonormal columns,
sorgqr(3F) SORGQR - generate an M-by-N real matrix Q with orthonormal columns,
sorgr2(3F) SORGR2 - generate an m by n real matrix Q with orthonormal rows,
sorgrq(3F) SORGRQ - generate an M-by-N real matrix Q with orthonormal rows,
sorgtr(3F) SORGTR - generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by SSYTRD
sorm2l(3F) SORM2L - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
sorm2r(3F) SORM2R - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
sormbr(3F) SORMBR - VECT = 'Q', SORMBR overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
sormhr(3F) SORMHR - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
sorml2(3F) SORML2 - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
sormlq(3F) SORMLQ - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
sormql(3F) SORMQL - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
sormqr(3F) SORMQR - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
sormr2(3F) SORMR2 - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
sormrq(3F) SORMRQ - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
sormtr(3F) SORMTR - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
SPBCO(3F) SPBCO - SPBCO factors a real symmetric positive definite matrix stored in band form and estimates the condition of the matrix.
spbcon(3F) SPBCON - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF
SPBDI(3F) SPBDI - SPBDI computes the determinant of a real symmetric positive definite band matrix using the factors computed by SPBCO or SPBFA. If the inverse is needed, use SPBSL N times.
spbequ(3F) SPBEQU - compute row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition number (with respect to the two-norm)
SPBFA(3F) SPBFA - SPBFA factors a real symmetric positive definite matrix stored in band form.
spbrfs(3F) SPBRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution
SPBSL(3F) SPBSL - SPBSL solves the real symmetric positive definite band system A*X = B using the factors computed by SPBCO or SPBFA.
spbstf(3F) SPBSTF - compute a split Cholesky factorization of a real symmetric positive definite band matrix A
spbsv(3F) SPBSV - compute the solution to a real system of linear equations A * X = B,
spbsvx(3F) SPBSVX - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,
spbtf2(3F) SPBTF2 - compute the Cholesky factorization of a real symmetric positive definite band matrix A
spbtrf(3F) SPBTRF - compute the Cholesky factorization of a real symmetric positive definite band matrix A
spbtrs(3F) SPBTRS - solve a system of linear equations A*X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF
spmv(3F) dspmv, sspmv, zhpmv, chpmv - BLAS Level Two (Symmetric/Hermitian) Packed Matrix - Vector Product
SPOCO(3F) SPOCO - SPOCO factors a real symmetric positive definite matrix and estimates the condition of the matrix.
spocon(3F) SPOCON - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF
SPODI(3F) SPODI - SPODI computes the determinant and inverse of a certain real symmetric positive definite matrix (see below) using the factors computed by SPOCO, SPOFA or SQRDC.
spoequ(3F) SPOEQU - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm)
SPOFA(3F) SPOFA - SPOFA factors a real symmetric positive definite matrix.
sporfs(3F) SPORFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite,
SPOSL(3F) SPOSL - SPOSL solves the real symmetric positive definite system A * X = B using the factors computed by SPOCO or SPOFA.
sposv(3F) SPOSV - compute the solution to a real system of linear equations A * X = B,
sposvx(3F) SPOSVX - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,
spotf2(3F) SPOTF2 - compute the Cholesky factorization of a real symmetric positive definite matrix A
spotrf(3F) SPOTRF - compute the Cholesky factorization of a real symmetric positive definite matrix A
spotri(3F) SPOTRI - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF
spotrs(3F) SPOTRS - solve a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF
SPPCO(3F) SPPCO - SPPCO factors a real symmetric positive definite matrix stored in packed form and estimates the condition of the matrix.
sppcon(3F) SPPCON - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF
SPPDI(3F) SPPDI - SPPDI computes the determinant and inverse of a real symmetric positive definite matrix using the factors computed by SPPCO or SPPFA .
sppequ(3F) SPPEQU - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
SPPFA(3F) SPPFA - SPPFA factors a real symmetric positive definite matrix stored in packed form.
spprfs(3F) SPPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward error estimates for the solution
SPPSL(3F) SPPSL - SPPSL solves the real symmetric positive definite system A * X = B using the factors computed by SPPCO or SPPFA.
sppsv(3F) SPPSV - compute the solution to a real system of linear equations A * X = B,
sppsvx(3F) SPPSVX - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,
spptrf(3F) SPPTRF - compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format
spptri(3F) SPPTRI - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF
spptrs(3F) SPPTRS - solve a system of linear equations A*X = B with a symmetric positive definite matrix A in packed storage using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF
spr(3F) dspr, sspr, zhpr, chpr - BLAS Level Two Symmetric Packed Matrix Rank 1 Update
spr2(3F) dspr2, sspr2, zhpr2, chpr2 - BLAS Level Two Symmetric Packed Matrix Rank 2 Update
sprod1du(3F) sprod1du, dprod1du - Compute the product of a 1D Fourier transform with a 1D filter.
sprod2du(3F) sprod2du, dprod2du - Compute the product of a 2D Fourier transforms with a 2D filter.
sprod3du(3F) sprod3du, dprod3du - Compute the product of a 3D Fourier transforms with a 3D filter.
sprodm1du(3F) sprodm1du, dprodm1du - Compute the product of Multiple 1D Fourier transforms with Multiple 1D filters.
sptcon(3F) SPTCON - compute the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by SPTTRF
spteqr(3F) SPTEQR - compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF, and then calling SBDSQR to compute the singular values of the bidiagonal factor
sptrfs(3F) SPTRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
SPTSL(3F) SPTSL - SPTSL given a positive definite tridiagonal matrix and a right hand side will find the solution.
sptsv(3F) SPTSV - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices
sptsvx(3F) SPTSVX - use the factorization A = L*D*L**T to compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix and X and B are N-by-NRHS matrices
spttrf(3F) SPTTRF - compute the factorization of a real symmetric positive definite tridiagonal matrix A
spttrs(3F) SPTTRS - solve a system of linear equations A * X = B with a symmetric positive definite tridiagonal matrix A using the factorization A = L*D*L**T or A = U**T*D*U computed by SPTTRF
SQRDC(3F) SQRDC - SQRDC uses Householder transformations to compute the QR factorization of an N by P matrix X. Column pivoting based on the 2- norms of the reduced columns may be performed at the user's option.
SQRSL(3F) SQRSL - SQRSL applies the output of SQRDC to compute coordinate transformations, projections, and least squares solutions. For K .LE. MIN(N,P), let XK be the matrix
sqrt(3F) sqrt, dsqrt, qsqrt, csqrt, zsqrt, cqsqrt - FORTRAN square root intrinsic function
srscl(3F) SRSCL - multiplie an n-element real vector x by the real scalar 1/a
ssapi(3F) ssrt_caliper_point, ssrt_buffer_clear - SpeedShop runtime library for Fortran applications
ssbev(3F) SSBEV - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
ssbevd(3F) SSBEVD - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
ssbevx(3F) SSBEVX - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
ssbgst(3F) SSBGST - reduce a real symmetric-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,
ssbgv(3F) SSBGV - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x
ssbtrd(3F) SSBTRD - reduce a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation
sscal1d(3F) sscal1d, dscal1d - scales a 1D real sequence.
sscal2d(3F) sscal2d, dscal2d - scales 2D real sequence.
sscal3d(3F) sscal3d, dscal3d - scales 3D real sequence.
sscalm1d(3F) sscalm1d, dscalm1d - scales Multiple 1D real sequences.
SSICO(3F) SSICO - SSICO factors a real symmetric matrix by elimination with symmetric pivoting and estimates the condition of the matrix.
SSIDI(3F) SSIDI - SSIDI computes the determinant, inertia and inverse of a real symmetric matrix using the factors from SSIFA.
SSIFA(3F) SSIFA - SSIFA factors a real symmetric matrix by elimination with symmetric pivoting.
SSISL(3F) SSISL - SSISL solves the real symmetric system A * X = B using the factors computed by SSIFA.
SSPCO(3F) SSPCO - SSPCO factors a real symmetric matrix stored in packed form by elimination with symmetric pivoting and estimates the condition of the matrix.
sspcon(3F) SSPCON - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF
SSPDI(3F) SSPDI - SSPDI computes the determinant, inertia and inverse of a real symmetric matrix using the factors from SSPFA, where the matrix is stored in packed form.
sspev(3F) SSPEV - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage
sspevd(3F) SSPEVD - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage
sspevx(3F) SSPEVX - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage
SSPFA(3F) SSPFA - SSPFA factors a real symmetric matrix stored in packed form by elimination with symmetric pivoting.
sspgst(3F) SSPGST - reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage
sspgv(3F) SSPGV - compute all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
ssprfs(3F) SSPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution
SSPSL(3F) SSPSL - SSISL solves the real symmetric system A * X = B using the factors computed by SSPFA.
sspsv(3F) SSPSV - compute the solution to a real system of linear equations A * X = B,
sspsvx(3F) SSPSVX - use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices
ssptrd(3F) SSPTRD - reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation
ssptrf(3F) SSPTRF - compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method
ssptri(3F) SSPTRI - compute the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF
ssptrs(3F) SSPTRS - solve a system of linear equations A*X = B with a real symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF
sstebz(3F) SSTEBZ - compute the eigenvalues of a symmetric tridiagonal matrix T
sstedc(3F) SSTEDC - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
sstein(3F) SSTEIN - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration
ssteqr(3F) SSTEQR - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method
ssterf(3F) SSTERF - compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm
sstev(3F) SSTEV - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A
sstevd(3F) SSTEVD - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
sstevx(3F) SSTEVX - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A
SSVDC(3F) SSVDC - SSVDC is a subroutine to reduce a real NxP matrix X by orthogonal transformations U and V to diagonal form. The diagonal elements S(I) are the singular values of X. The columns of U are the corresponding left singular vectors, and the columns of V the right singular vectors.
ssycon(3F) SSYCON - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF
ssyev(3F) SSYEV - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
ssyevd(3F) SSYEVD - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
ssyevx(3F) SSYEVX - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
ssygs2(3F) SSYGS2 - reduce a real symmetric-definite generalized eigenproblem to standard form
ssygst(3F) SSYGST - reduce a real symmetric-definite generalized eigenproblem to standard form
ssygv(3F) SSYGV - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
ssyrfs(3F) SSYRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution
ssysv(3F) SSYSV - compute the solution to a real system of linear equations A * X = B,
ssysvx(3F) SSYSVX - use the diagonal pivoting factorization to compute the solution to a real system of linear equations A * X = B,
ssytd2(3F) SSYTD2 - reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation
ssytf2(3F) SSYTF2 - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
ssytrd(3F) SSYTRD - reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation
ssytrf(3F) SSYTRF - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
ssytri(3F) SSYTRI - compute the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF
ssytrs(3F) SSYTRS - solve a system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF
stbcon(3F) STBCON - estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm
stbrfs(3F) STBRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
stbtrs(3F) STBTRS - solve a triangular system of the form A * X = B or A**T * X = B,
stgevc(3F) STGEVC - compute some or all of the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B)
stgsja(3F) STGSJA - compute the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B
stpcon(3F) STPCON - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm
stprfs(3F) STPRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix
stptri(3F) STPTRI - compute the inverse of a real upper or lower triangular matrix A stored in packed format
stptrs(3F) STPTRS - solve a triangular system of the form A * X = B or A**T * X = B,
strcmp(3F) strcmp: lge, lgt, lle, llt - FORTRAN string comparison intrinsic functions
STRCO(3F) STRCO - STRCO estimates the condition of a real triangular matrix.
strcon(3F) STRCON - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
STRDI(3F) STRDI - STRDI computes the determinant and inverse of a real triangular matrix.
strevc(3F) STREVC - compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T
strexc(3F) STREXC - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that the diagonal block of T with row index IFST is moved to row ILST
strrfs(3F) STRRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
strsen(3F) STRSEN - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T,
STRSL(3F) STRSL - STRSL solves systems of the form
strsna(3F) STRSNA - estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q orthogonal)
strsyl(3F) STRSYL - solve the real Sylvester matrix equation
strti2(3F) STRTI2 - compute the inverse of a real upper or lower triangular matrix
strtri(3F) STRTRI - compute the inverse of a real upper or lower triangular matrix A
strtrs(3F) STRTRS - solve a triangular system of the form A * X = B or A**T * X = B,
stzrqf(3F) STZRQF - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations
SVD(3F) SVD, SSVD - EISPACK routine. This subroutine determines the singular value decomposition T A=USV of a REAL M by N rectangular matrix. Householder bidiagonalization and a variant of the QR algorithm are used.
swap(3F) dswap, sswap, zswap, cswap - BLAS level ONE swap subroutines
symm(3F) dsymm, ssymm, zsymm, csymm - BLAS level three Symmetric Matrix Product
symv(3F) dsymv, ssymv, zhemv, chemv - BLAS Level Two (Symmetric/Hermitian)Matrix - Vector Product
sync(3F) sync: synchronize, fetch_and_add, fetch_and_sub, fetch_and_or, fetch_and_and, fetch_and_xor, fetch_and_nand, add_and_fetch, sub_and_fetch, or_and_fetch, and_and_fetch, xor_and_fetch, nand_and_fetch, lock_test_and_set, lock_release - FORTRAN synchronization primitives for multiprocessing
syr(3F) dsyr, ssyr, zher, cher - BLAS Level Two (Symmetric/Hermitian)Matrix Rank 1 Update
syr2(3F) dsyr2, ssyr2, zher2, cher2 - BLAS Level Two (Symmetric/Hermitian)Matrix Rank 2 Update
syr2k(3F) dsyr2k, ssyr2k, zsyr2k, csyr2k - BLAS level three Symmetric Rank 2K Update.
syrk(3F) dsyrk, ssyrk, zsyrk, csyrk - BLAS level three Symmetric Rank K Update.
sysclock(3F) SYSCLOCK - Returns real-time clock value and number of wraps
system(3F) system - issue a shell command from Fortran
tan(3F) tan, dtan, qtan, tand, dtand, qtand - FORTRAN tangent intrinsic function
tanh(3F) tanh, dtanh, qtanh - FORTRAN hyperbolic tangent intrinsic function
tapeio(3F) tapeio: topen, tclose, tread, twrite, trewin, tskipf, tstate - FORTRAN tape device specific I/O routines
tbmv(3F) dtbmv, stbmv, ztbmv, ctbmv, dtbsv, stbsv, ztbsv, ctbsv - BLAS Level Two Matrix-Vector Product and Solution of System of Equations.
time(3F) time, ctime, ltime, gmtime - return system time
timef(3F) TIMEF - Returns elapsed wall-clock time in milliseconds since the previous call to TIMEF
TINVIT(3F) TINVIT, STINVIT - EISPACK routine. This subroutine finds those eigenvectors of a TRIDIAGONAL SYMMETRIC matrix corresponding to specified eigenvalues, using inverse iteration.
tpmv(3F) dtpmv, stpmv, ztpmv, ctpmv, dtpsv, stpsv, ztpsv, ctpsv - BLAS Level Two Matrix-Vector Product and Solution of System of Equations
TQL1(3F) TQL1, STQL1 - EISPACK routine. This subroutine finds the eigenvalues of a SYMMETRIC TRIDIAGONAL matrix by the QL method.
TQL2(3F) TQL2, STQL2 - EISPACK routine. This subroutine finds the eigenvalues and eigenvectors of a SYMMETRIC TRIDIAGONAL matrix by the QL method. The eigenvectors of a FULL SYMMETRIC matrix can also be found if TRED2 has been used to reduce this full matrix to tridiagonal form.
TQLRAT(3F) TQLRAT, STQLRAT - EISPACK routine. This subroutine finds the eigenvalues of a SYMMETRIC TRIDIAGONAL matrix by the rational QL method.
TRBAK1(3F) TRBAK1, STRBAK1 - EISPACK routine. This subroutine forms the eigenvectors of a REAL SYMMETRIC matrix by back transforming those of the corresponding symmetric tridiagonal matrix determined by TRED1.
TRBAK3(3F) TRBAK3, STRBAK3 - EISPACK routine. This subroutine forms the eigenvectors of a REAL SYMMETRIC matrix by back transforming those of the corresponding symmetric tridiagonal matrix determined by TRED3.
TRED1(3F) TRED1, STRED1 - EISPACK routine. This subroutine reduces a REAL SYMMETRIC matrix to a symmetric tridiagonal matrix using orthogonal similarity transformations.
TRED2(3F) TRED2, STRED2 - EISPACK routine. This subroutine reduces a REAL SYMMETRIC matrix to a symmetric tridiagonal matrix using and accumulating orthogonal similarity transformations.
TRED3(3F) TRED3, STRED3 - EISPACK routine. This subroutine reduces a REAL SYMMETRIC matrix, stored as a one-dimensional array, to a symmetric tridiagonal matrix using orthogonal similarity transformations.
TRIDIB(3F) TRIDIB, STRIDIB - EISPACK routine. This subroutine finds those eigenvalues of a TRIDIAGONAL SYMMETRIC matrix between specified boundary indices, using bisection.
trimlen(3F) TRIMLEN - Returns the length of a character argument without counting trailing blanks
trmm(3F) dtrmm, strmm, ztrmm, ctrmm - BLAS level three Matrix Product
trmv(3F) dtrmv, strmv, ztrmv, ctrmv, dtrsv, strsv, ztrsv, ctrsv - BLAS Level Two Matrix-Vector Product and Solution of system of equations.
trsm(3F) dtrsm, strsm, ztrsm, ctrsm - BLAS level three Solution of Systems of Equations
TSTURM(3F) TSTURM, STSTURM - EISPACK routine. This subroutine finds those eigenvalues of a TRIDIAGONAL SYMMETRIC matrix which lie in a specified interval and their associated eigenvectors, using bisection and inverse iteration.
ttynam(3F) ttynam, isatty - find name of a terminal port
uscctc(3F) USCCTC, USCCTI - Converts EBCDIC character data to ASCII character data, and vice versa
varargs(3F) varargs, argmnt, getadr, nullok, xetarg, retour - allow variable number of arguments in argument list
wnl(3F) WNLFLAG, WNLDELM, WNLSEP, WNLREP - Provides user control of NAMELIST output format
wnlline(3F) WNLLINE - Allows each NAMELIST variable to begin on a new line
wnllong(3F) WNLLONG - Selects NAMELIST output line length
xerbla(3F) XERBLA - i an error handler for the LAPACK routines
zbdsqr(3F) ZBDSQR - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
zdrscl(3F) ZDRSCL - multiplie an n-element complex vector x by the real scalar 1/a
zgbbrd(3F) ZGBBRD - reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation
zgbcon(3F) ZGBCON - estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm,
zgbequ(3F) ZGBEQU - compute row and column scalings intended to equilibrate an M- by-N band matrix A and reduce its condition number
zgbrfs(3F) ZGBRFS - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
zgbsv(3F) ZGBSV - compute the solution to a complex system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices
zgbsvx(3F) ZGBSVX - use the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
zgbtf2(3F) ZGBTF2 - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges
zgbtrf(3F) ZGBTRF - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges
zgbtrs(3F) ZGBTRS - solve a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general band matrix A using the LU factorization computed by ZGBTRF
zgebak(3F) ZGEBAK - form the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by ZGEBAL
zgebal(3F) ZGEBAL - balance a general complex matrix A
zgebd2(3F) ZGEBD2 - reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation
zgebrd(3F) ZGEBRD - reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation
zgecon(3F) ZGECON - estimate the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGETRF
zgeequ(3F) ZGEEQU - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number
zgees(3F) ZGEES - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z
zgeesx(3F) ZGEESX - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z
zgeev(3F) ZGEEV - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
zgeevx(3F) ZGEEVX - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
zgegs(3F) ZGEGS - compute for a pair of N-by-N complex nonsymmetric matrices A,
zgegv(3F) ZGEGV - compute for a pair of N-by-N complex nonsymmetric matrices A and B, the generalized eigenvalues (alpha, beta), and optionally,
zgehd2(3F) ZGEHD2 - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation
zgehrd(3F) ZGEHRD - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation
zgelq2(3F) ZGELQ2 - compute an LQ factorization of a complex m by n matrix A
zgelqf(3F) ZGELQF - compute an LQ factorization of a complex M-by-N matrix A
zgels(3F) ZGELS - solve overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A
zgelss(3F) ZGELSS - compute the minimum norm solution to a complex linear least squares problem
zgelsx(3F) ZGELSX - compute the minimum-norm solution to a complex linear least squares problem
zgeql2(3F) ZGEQL2 - compute a QL factorization of a complex m by n matrix A
zgeqlf(3F) ZGEQLF - compute a QL factorization of a complex M-by-N matrix A
zgeqpf(3F) ZGEQPF - compute a QR factorization with column pivoting of a complex M- by-N matrix A
zgeqr2(3F) ZGEQR2 - compute a QR factorization of a complex m by n matrix A
zgeqrf(3F) ZGEQRF - compute a QR factorization of a complex M-by-N matrix A
zgerfs(3F) ZGERFS - improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution
zgerq2(3F) ZGERQ2 - compute an RQ factorization of a complex m by n matrix A
zgerqf(3F) ZGERQF - compute an RQ factorization of a complex M-by-N matrix A
zgesv(3F) ZGESV - compute the solution to a complex system of linear equations A * X = B,
zgesvd(3F) ZGESVD - compute the singular value decomposition (SVD) of a complex M- by-N matrix A, optionally computing the left and/or right singular vectors
zgesvx(3F) ZGESVX - use the LU factorization to compute the solution to a complex system of linear equations A * X = B,
zgetf2(3F) ZGETF2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges
zgetrf(3F) ZGETRF - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges
zgetri(3F) ZGETRI - compute the inverse of a matrix using the LU factorization computed by ZGETRF
zgetrs(3F) ZGETRS - solve a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general N-by-N matrix A using the LU factorization computed by ZGETRF
zggbak(3F) ZGGBAK - form the right or left eigenvectors of a complex generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by ZGGBAL
zggbal(3F) ZGGBAL - balance a pair of general complex matrices (A,B)
zggglm(3F) ZGGGLM - solve a general Gauss-Markov linear model (GLM) problem
zgghrd(3F) ZGGHRD - reduce a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, where A is a general matrix and B is upper triangular
zgglse(3F) ZGGLSE - solve the linear equality-constrained least squares (LSE) problem
zggqrf(3F) ZGGQRF - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B
zggrqf(3F) ZGGRQF - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B
zggsvd(3F) ZGGSVD - compute the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B
zggsvp(3F) ZGGSVP - compute unitary matrices U, V and Q such that N-K-L K L U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0
zgtcon(3F) ZGTCON - estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF
zgtrfs(3F) ZGTRFS - improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution
zgtsv(3F) ZGTSV - solve the equation A*X = B,
zgtsvx(3F) ZGTSVX - use the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
zgttrf(3F) ZGTTRF - compute an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges
zgttrs(3F) ZGTTRS - solve one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B,
zhbev(3F) ZHBEV - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
zhbevd(3F) ZHBEVD - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
zhbevx(3F) ZHBEVX - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
zhbgst(3F) ZHBGST - reduce a complex Hermitian-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,
zhbgv(3F) ZHBGV - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x
zhbtrd(3F) ZHBTRD - reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
zhecon(3F) ZHECON - estimate the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF
zheev(3F) ZHEEV - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
zheevd(3F) ZHEEVD - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
zheevx(3F) ZHEEVX - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
zhegs2(3F) ZHEGS2 - reduce a complex Hermitian-definite generalized eigenproblem to standard form
zhegst(3F) ZHEGST - reduce a complex Hermitian-definite generalized eigenproblem to standard form
zhegv(3F) ZHEGV - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
zherfs(3F) ZHERFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution
zhesv(3F) ZHESV - compute the solution to a complex system of linear equations A * X = B,
zhesvx(3F) ZHESVX - use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A * X = B,
zhetd2(3F) ZHETD2 - reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
zhetf2(3F) ZHETF2 - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
zhetrd(3F) ZHETRD - reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
zhetrf(3F) ZHETRF - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
zhetri(3F) ZHETRI - compute the inverse of a complex Hermitian indefinite matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF
zhetrs(3F) ZHETRS - solve a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF
zhgeqz(3F) ZHGEQZ - implement a single-shift version of the QZ method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the equation det( A - w(i) B ) = 0 If JOB='S', then the pair (A,B) is simultaneously reduced to Schur form (i.e., A and B are both upper triangular) by applying one unitary tranformation (usually called Q) on the left and another (usually called Z) on the right
zhpcon(3F) ZHPCON - estimate the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF
zhpev(3F) ZHPEV - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage
zhpevd(3F) ZHPEVD - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
zhpevx(3F) ZHPEVX - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
zhpgst(3F) ZHPGST - reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage
zhpgv(3F) ZHPGV - compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
zhprfs(3F) ZHPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and backward error estimates for the solution
zhpsv(3F) ZHPSV - compute the solution to a complex system of linear equations A * X = B,
zhpsvx(3F) ZHPSVX - use the diagonal pivoting factorization A = U*D*U**H or A = L*D*L**H to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices
zhptrd(3F) ZHPTRD - reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation
zhptrf(3F) ZHPTRF - compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method
zhptri(3F) ZHPTRI - compute the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF
zhptrs(3F) ZHPTRS - solve a system of linear equations A*X = B with a complex Hermitian matrix A stored in packed format using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF
zhsein(3F) ZHSEIN - use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H
zhseqr(3F) ZHSEQR - compute the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors
zlabrd(3F) ZLABRD - reduce the first NB rows and columns of a complex general m by n matrix A to upper or lower real bidiagonal form by a unitary transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A
zlacgv(3F) ZLACGV - conjugate a complex vector of length N
zlacon(3F) ZLACON - estimate the 1-norm of a square, complex matrix A
zlacpy(3F) ZLACPY - copie all or part of a two-dimensional matrix A to another matrix B
zlacrm(3F) ZLACRM - perform a very simple matrix-matrix multiplication
zlacrt(3F) ZLACRT - applie a plane rotation, where the cos and sin (C and S) are complex and the vectors CX and CY are complex
zladiv(3F) ZLADIV - := X / Y, where X and Y are complex
zlaed0(3F) ZLAED0 - the divide and conquer method, ZLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix
zlaed7(3F) ZLAED7 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
zlaed8(3F) ZLAED8 - merge the two sets of eigenvalues together into a single sorted set
zlaein(3F) ZLAEIN - use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H
zlaesy(3F) ZLAESY - compute the eigendecomposition of a 2-by-2 symmetric matrix ( ( A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger than some threshold value
zlaev2(3F) ZLAEV2 - compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ]
zlags2(3F) ZLAGS2 - compute 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q = V'*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = ( CSV SNV ),
zlagtm(3F) ZLAGTM - perform a matrix-vector product of the form B := alpha * A * X + beta * B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1
zlahef(3F) ZLAHEF - compute a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
zlahqr(3F) ZLAHQR - i an auxiliary routine called by ZHSEQR to update the eigenvalues and Schur decomposition already computed by ZHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI
zlahrd(3F) ZLAHRD - reduce the first NB columns of a complex general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero
zlaic1(3F) ZLAIC1 - applie one step of incremental condition estimation in its simplest version
zlangb(3F) ZLANGB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals
zlange(3F) ZLANGE - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex matrix A
zlangt(3F) ZLANGT - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex tridiagonal matrix A
zlanhb(3F) ZLANHB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n hermitian band matrix A, with k super-diagonals
zlanhe(3F) ZLANHE - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A
zlanhp(3F) ZLANHP - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A, supplied in packed form
zlanhs(3F) ZLANHS - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
zlanht(3F) ZLANHT - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix A
zlansb(3F) ZLANSB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals
zlansp(3F) ZLANSP - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A, supplied in packed form
zlansy(3F) ZLANSY - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A
zlantb(3F) ZLANTB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals
zlantp(3F) ZLANTP - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
zlantr(3F) ZLANTR - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A
zlapll(3F) ZLAPLL - two column vectors X and Y, let A = ( X Y )
zlapmt(3F) ZLAPMT - rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N
zlaqgb(3F) ZLAQGB - equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C
zlaqge(3F) ZLAQGE - equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
zlaqhb(3F) ZLAQHB - equilibrate a symmetric band matrix A using the scaling factors in the vector S
zlaqhe(3F) ZLAQHE - equilibrate a Hermitian matrix A using the scaling factors in the vector S
zlaqhp(3F) ZLAQHP - equilibrate a Hermitian matrix A using the scaling factors in the vector S
zlaqsb(3F) ZLAQSB - equilibrate a symmetric band matrix A using the scaling factors in the vector S
zlaqsp(3F) ZLAQSP - equilibrate a symmetric matrix A using the scaling factors in the vector S
zlaqsy(3F) ZLAQSY - equilibrate a symmetric matrix A using the scaling factors in the vector S
zlar2v(3F) ZLAR2V - applie a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices,
zlarf(3F) ZLARF - applie a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right
zlarfb(3F) ZLARFB - applie a complex block reflector H or its transpose H' to a complex M-by-N matrix C, from either the left or the right
zlarfg(3F) ZLARFG - generate a complex elementary reflector H of order n, such that H' * ( alpha ) = ( beta ), H' * H = I
zlarft(3F) ZLARFT - form the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors
zlarfx(3F) ZLARFX - applie a complex elementary reflector H to a complex m by n matrix C, from either the left or the right
zlargv(3F) ZLARGV - generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y
zlarnv(3F) ZLARNV - return a vector of n random complex numbers from a uniform or normal distribution
zlartg(3F) ZLARTG - generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ]
zlartv(3F) ZLARTV - applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y
zlascl(3F) ZLASCL - multiplie the M by N complex matrix A by the real scalar CTO/CFROM
zlaset(3F) ZLASET - initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals
zlasr(3F) ZLASR - perform the transformation A := P*A, when SIDE = 'L' or 'l' ( Left-hand side ) A := A*P', when SIDE = 'R' or 'r' ( Right-hand side ) where A is an m by n complex matrix and P is an orthogonal matrix,
zlassq(3F) ZLASSQ - return the values scl and ssq such that ( scl**2 )*ssq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
zlaswp(3F) ZLASWP - perform a series of row interchanges on the matrix A
zlasyf(3F) ZLASYF - compute a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
zlatbs(3F) ZLATBS - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
zlatps(3F) ZLATPS - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
zlatrd(3F) ZLATRD - reduce NB rows and columns of a complex Hermitian matrix A to Hermitian tridiagonal form by a unitary similarity transformation Q' * A * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A
zlatrs(3F) ZLATRS - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
zlatzm(3F) ZLATZM - applie a Householder matrix generated by ZTZRQF to a matrix
zlauu2(3F) ZLAUU2 - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
zlauum(3F) ZLAUUM - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
zpbcon(3F) ZPBCON - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPBTRF
zpbequ(3F) ZPBEQU - compute row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the two-norm)
zpbrfs(3F) ZPBRFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward error estimates for the solution
zpbstf(3F) ZPBSTF - compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A
zpbsv(3F) ZPBSV - compute the solution to a complex system of linear equations A * X = B,
zpbsvx(3F) ZPBSVX - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B,
zpbtf2(3F) ZPBTF2 - compute the Cholesky factorization of a complex Hermitian positive definite band matrix A
zpbtrf(3F) ZPBTRF - compute the Cholesky factorization of a complex Hermitian positive definite band matrix A
zpbtrs(3F) ZPBTRS - solve a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPBTRF
zpocon(3F) ZPOCON - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF
zpoequ(3F) ZPOEQU - compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm)
zporfs(3F) ZPORFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite,
zposv(3F) ZPOSV - compute the solution to a complex system of linear equations A * X = B,
zposvx(3F) ZPOSVX - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B,
zpotf2(3F) ZPOTF2 - compute the Cholesky factorization of a complex Hermitian positive definite matrix A
zpotrf(3F) ZPOTRF - compute the Cholesky factorization of a complex Hermitian positive definite matrix A
zpotri(3F) ZPOTRI - compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF
zpotrs(3F) ZPOTRS - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF
zppcon(3F) ZPPCON - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPPTRF
zppequ(3F) ZPPEQU - compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
zpprfs(3F) ZPPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution
zppsv(3F) ZPPSV - compute the solution to a complex system of linear equations A * X = B,
zppsvx(3F) ZPPSVX - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B,
zpptrf(3F) ZPPTRF - compute the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format
zpptri(3F) ZPPTRI - compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPPTRF
zpptrs(3F) ZPPTRS - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPPTRF
zptcon(3F) ZPTCON - compute the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by ZPTTRF
zpteqr(3F) ZPTEQR - compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using DPTTRF and then calling ZBDSQR to compute the singular values of the bidiagonal factor
zptrfs(3F) ZPTRFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
zptsv(3F) ZPTSV - compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices
zptsvx(3F) ZPTSVX - use the factorization A = L*D*L**H to compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix and X and B are N-by-NRHS matrices
zpttrf(3F) ZPTTRF - compute the factorization of a complex Hermitian positive definite tridiagonal matrix A
zpttrs(3F) ZPTTRS - solve a system of linear equations A * X = B with a Hermitian positive definite tridiagonal matrix A using the factorization A = U**H*D*U or A = L*D*L**H computed by ZPTTRF
zspcon(3F) ZSPCON - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF
zspr(3F) ZSPR - perform the symmetric rank 1 operation A := alpha*x*conjg( x' ) + A,
zsprfs(3F) ZSPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution
zspsv(3F) ZSPSV - compute the solution to a complex system of linear equations A * X = B,
zspsvx(3F) ZSPSVX - use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices
zsptrf(3F) ZSPTRF - compute the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method
zsptri(3F) ZSPTRI - compute the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF
zsptrs(3F) ZSPTRS - solve a system of linear equations A*X = B with a complex symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF
zsrscl(3F) ZSRSCL - multiplie an n-element complex vector x by the real scalar 1/a
zstedc(3F) ZSTEDC - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
zstein(3F) ZSTEIN - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration
zsteqr(3F) ZSTEQR - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method
zsycon(3F) ZSYCON - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF
zsyr(3F) ZSYR - perform the symmetric rank 1 operation A := alpha*x*( x' ) + A,
zsyrfs(3F) ZSYRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution
zsysv(3F) ZSYSV - compute the solution to a complex system of linear equations A * X = B,
zsysvx(3F) ZSYSVX - use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A * X = B,
zsytf2(3F) ZSYTF2 - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
zsytrf(3F) ZSYTRF - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
zsytri(3F) ZSYTRI - compute the inverse of a complex symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF
zsytrs(3F) ZSYTRS - solve a system of linear equations A*X = B with a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF
ztbcon(3F) ZTBCON - estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm
ztbrfs(3F) ZTBRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
ztbtrs(3F) ZTBTRS - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,
ztgevc(3F) ZTGEVC - compute some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B)
ztgsja(3F) ZTGSJA - compute the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) matrices A and B
ztpcon(3F) ZTPCON - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm
ztprfs(3F) ZTPRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix
ztptri(3F) ZTPTRI - compute the inverse of a complex upper or lower triangular matrix A stored in packed format
ztptrs(3F) ZTPTRS - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,
ztrcon(3F) ZTRCON - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
ztrevc(3F) ZTREVC - compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T
ztrexc(3F) ZTREXC - reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that the diagonal element of T with row index IFST is moved to row ILST
ztrrfs(3F) ZTRRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
ztrsen(3F) ZTRSEN - reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace
ztrsna(3F) ZTRSNA - estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q*T*Q**H with Q unitary)
ztrsyl(3F) ZTRSYL - solve the complex Sylvester matrix equation
ztrti2(3F) ZTRTI2 - compute the inverse of a complex upper or lower triangular matrix
ztrtri(3F) ZTRTRI - compute the inverse of a complex upper or lower triangular matrix A
ztrtrs(3F) ZTRTRS - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,
ztzrqf(3F) ZTZRQF - reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations
zung2l(3F) ZUNG2L - generate an m by n complex matrix Q with orthonormal columns,
zung2r(3F) ZUNG2R - generate an m by n complex matrix Q with orthonormal columns,
zungbr(3F) ZUNGBR - generate one of the complex unitary matrices Q or P**H determined by ZGEBRD when reducing a complex matrix A to bidiagonal form
zunghr(3F) ZUNGHR - generate a complex unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by ZGEHRD
zungl2(3F) ZUNGL2 - generate an m-by-n complex matrix Q with orthonormal rows,
zunglq(3F) ZUNGLQ - generate an M-by-N complex matrix Q with orthonormal rows,
zungql(3F) ZUNGQL - generate an M-by-N complex matrix Q with orthonormal columns,
zungqr(3F) ZUNGQR - generate an M-by-N complex matrix Q with orthonormal columns,
zungr2(3F) ZUNGR2 - generate an m by n complex matrix Q with orthonormal rows,
zungrq(3F) ZUNGRQ - generate an M-by-N complex matrix Q with orthonormal rows,
zungtr(3F) ZUNGTR - generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by ZHETRD
zunm2l(3F) ZUNM2L - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',
zunm2r(3F) ZUNM2R - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',
zunmbr(3F) ZUNMBR - VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
zunmhr(3F) ZUNMHR - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
zunml2(3F) ZUNML2 - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',
zunmlq(3F) ZUNMLQ - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
zunmql(3F) ZUNMQL - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
zunmqr(3F) ZUNMQR - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
zunmr2(3F) ZUNMR2 - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',
zunmrq(3F) ZUNMRQ - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
zunmtr(3F) ZUNMTR - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
zupgtr(3F) ZUPGTR - generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by ZHPTRD using packed storage
zupmtr(3F) ZUPMTR - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'