stbsv(3S)
STBSV, DTBSV, CTBSV, ZTBSV - Solves a real or complex triangular banded system of equations
As shipped in IRIX 6.5.15. Added in IRIX 6.5.15.
NAME STBSV, DTBSV, CTBSV, ZTBSV - Solves a real or complex triangular banded system of equations SYNOPSIS Single precision Fortran: CALL STBSV (uplo, trans, diag, n, k, a, lda, x, incx) C/C++: #include <scsl_blas.h> void stbsv (char *uplo, char *trans, char *diag, int n, int k, float *a, int lda, float *x, int incx); Double precision Fortran: CALL DTBSV (uplo, trans, diag, n, k, a, lda, x, incx) C/C++: #include <scsl_blas.h> void dtbsv (char *uplo, char *trans, char *diag, int n, int k, double *a, int lda, double *x, int incx); Single precision complex Fortran: CALL CTBSV (uplo, trans, diag, n, k, a, lda, x, incx) C/C++: #include <scsl_blas.h> void ctbsv (char *uplo, char *trans, char *diag, int n, int k, scsl_complex *a, int lda, scsl_complex *x, int incx); C++ STL: #include <complex.h> #include <scsl_blas.h> void ctbsv (char *uplo, char *trans, char *diag, int n, int k, complex<float> *a, int lda, complex<float> *x, int incx); Double precision complex Fortran: CALL ZTBSV (uplo, trans, diag, n, k, a, lda, x, incx) C/C++: #include <scsl_blas.h> void ztbsv (char *uplo, char *trans, char diag, int n, int k, scsl_zomplex *a, int lda, scsl_zomplex *x, int incx); C++ STL: #include <complex.h> #include <scsl_blas.h> void ztbsv (char *uplo, char *trans, char *diag, int n, int k, complex<double> *a, int lda, complex<double> *x, int incx); IMPLEMENTATION These routines are part of the SCSL Scientific Library and can be loaded using either the -lscs or the -lscs_mp option. The -lscs_mp option directs the linker to use the multi-processor version of the library. When linking to SCSL with -lscs or -lscs_mp, the default integer size is 4 bytes (32 bits). Another version of SCSL is available in which integers are 8 bytes (64 bits). This version allows the user access to larger memory sizes and helps when porting legacy Cray codes. It can be loaded by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use only one of the two versions; 4-byte integer and 8-byte integer library calls cannot be mixed. The C and C++ prototypes shown above are appropriate for the 4-byte integer version of SCSL. When using the 8-byte integer version, the variables of type int become long long and the <scsl_blas_i8.h> header file should be included. DESCRIPTION STBSV and DTBSV solve a real triangular banded system of equations. CTBSV and ZTBSV solve a complex triangular banded system of equations. These routines solve one of the following systems of equations, using the operation associated with each: Equations Operation Ax=b x <- A-1x ATx=b x <- A-Tx AHx=b x <- A-Hx (CTBSV and ZTBSV only) where * b and x are n-element vectors * A is either a unit or nonunit n-by-n upper or lower triangular band matrix with (k+1) diagonals * A-1 is the inverse of A * AT is the transpose of A * A-T is the inverse of AT * AH is the conjugate transpose of A * A-H is the inverse of AH On input, the right-hand side vector b is stored in the array argument x. On output, the solution vector x overwrites b in the same array argument x. See the NOTES section of this man page for information about the interpretation of the data types described in the following arguments. These routines have the following arguments: uplo Character. (input) Specifies whether the matrix is an upper or lower triangular matrix, as follows: uplo = 'U' or 'u': A is an upper triangular matrix. uplo = 'L' or 'l': A is a lower triangular matrix. For C/C++, a pointer to this character is passed. trans Character. (input) Specifies the operation to be performed, as follows: trans = 'N' or 'n': x <- A-1x trans = 'T' or 't': x <- A-Tx trans = 'C' or 'c': x <- A-Tx (STBSV, DTBSV), or x <- A-Hx (CTBSV, ZTBSV) For C/C++, a pointer to this character is passed. diag Character. (input) Specifies whether A is unit triangular, as follows: diag = 'U' or 'u': A is assumed to be unit triangular. diag = 'N' or 'n': A is not assumed to be unit triangular. For C/C++, a pointer to this character is passed. n Integer. (input) Specifies the order of matrix A. n >= 0. k Integer. (input) uplo = 'U' or 'u': k specifies the number of superdiagonals of matrix A. uplo = 'L' or 'l' k specifies the number of subdiagonals of matrix A. k >= 0. a Array of dimension (lda,n). (input) STBSV: Single precision array. DTBSV: Double precision array. CTBSV: Single precison complex array. ZTBSV: Double precision complex array. Before entry with uplo = 'U' or 'u', the leading (k+1)-by-n upper triangular part of array a must contain the upper triangular band part of the matrix of coefficients, supplied column-by-column, with the leading diagonal of the matrix in row (k+1) of the array, the first superdiagonal starting at position 2 in row k, and so on. The top left k-by-k triangle of array a is not referenced. Before entry with uplo = 'L' or 'l', the leading (k+1)-by-n part of array a must contain the lower triangular band part of the matrix of coefficients, supplied column-by-column, with the leading diagonal of the matrix in row 1 of the array, the first subdiagonal starting at position 1 in row 2, and so on. The bottom right k-by-k triangle of array a is not referenced. When diag = 'U' or 'u', these routines assume that all elements of array a that represent diagonal elements of the matrix A are 1. In this case, neither of these routines will reference any of the diagonal elements. lda Integer. (input) Specifies the first dimension of a as declared in the calling program. lda >= (k+1). x Array of dimension 1+(n-1) * |incx|. (input and output) STBSV: Single precision array. DTBSV: Double precision array. CTBSV: Single precision complex array. ZTBSV: Double precision complex array. Contains the vector x. On input, x contains the right-hand side vector b. On output, the solution vector overwrites array x. incx Integer. (input) Specifies the increment for the elements of x. incx must not be 0. NOTES The following program segment transfers an upper triangular band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = K + 1 - J DO 10, I = MAX( 1, J - K ), J A( M + I, J ) = MATRIX( I, J ) 10 CONTINUE 20 CONTINUE The following program segment transfers a lower triangular band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = 1 - J DO 10, I = J, MIN( N, J + K ) A( M + I, J ) = MATRIX( I, J ) 10 CONTINUE 20 CONTINUE Tests for singularity or near-singularity are not included in these routines. You must perform such tests before calling these routines. These routines are Level 2 Basic Linear Algebra Subprograms (Level 2 BLAS). When working backward (incx < 0), each routine starts at the end of the vector and moves backward, as follows: x(1-incx * (n-1)), x(1-incx * (n-2)), ..., x(1) Data Types The following data types are described in this documentation: Term Used Data type Fortran: Array dimensioned n x(n) Array of dimensions (m,n) x(m,n) Character CHARACTER Integer INTEGER (INTEGER*8 for -lscs_i8[_mp]) Single precision REAL Double precision DOUBLE PRECISION Single precision complex COMPLEX Double precision complex DOUBLE COMPLEX C/C++: Array dimensioned n x[n] Array of dimensions (m,n) x[m*n] Character char Integer int (long long for -lscs_i8[_mp]) Single precision float Double precision double Single precision complex scsl_complex Double precision complex scsl_zomplex C++ STL: Array dimensioned n x[n] Array of dimensions (m,n) x[m*n] Character char Integer int (long long for -lscs_i8[_mp]) Single precision float Double precision double Single precision complex complex<float> Double precision complex complex<double> Note that you can explicitly declare multidimensional C/C++ arrays provided that the array dimensions are swapped with respect to the Fortran declaration (e.g., x[n][m] in C/C++ versus x(m,n) in Fortran). To avoid a compiler type mismatch error in C++ (or a compiler warning message in C), however, the array should be cast to a pointer of the appropriate type when passed as an argument to a SCSL routine. SEE ALSO INTRO_SCSL(3S), INTRO_BLAS2(3S) INTRO_CBLAS(3S) for information about using the C interface to Fortran 77 Basic Linear Algebra Subprograms (legacy BLAS) set forth by the Basic Linear Algebra Subprograms Technical Forum.