strsv(3S)
STRSV, DTRSV, CTRSV, ZTRSV - Solves a real or complex triangular system of equations
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NAME STRSV, DTRSV, CTRSV, ZTRSV - Solves a real or complex triangular system of equations SYNOPSIS Single precision Fortran: CALL STRSV (uplo, trans, diag, n, a, lda, x, incx) C/C++: #include <scsl_blas.h> void strsv (char *uplo, char *trans, char *diag, int n, float *a, int lda, float *x, int incx); Double precision Fortran: CALL DTRSV (uplo, trans, diag, n, a, lda, x, incx) C/C++: #include <scsl_blas.h> void dtrsv (char *uplo, char *trans, char *diag, int n, double *a, int lda, double *x, int incx); Single precision complex Fortran: CALL CTRSV (uplo, trans, diag, n, a, lda, x, incx) C/C++: #include <scsl_blas.h> void ctrsv (char *uplo, char *trans, char *diag, int n, scsl_complex *a, int lda, scsl_complex *x, int incx); C++ STL: #include <complex.h> #include <scsl_blas.h> void ctrsv (char *uplo, char *trans, char *diag, int n, complex<float> *a, int lda, complex<float> *x, int incx); Double precision complex Fortran: CALL ZTRSV (uplo, trans, diag, n, a, lda, x, incx) C/C++: #include <scsl_blas.h> void ztrsv (char *uplo, char *trans, char *diag, int n, scsl_zomplex *a, int lda, scsl_zomplex *x, int incx); C++ STL: #include <complex.h> #include <scsl_blas.h> void ztrsv (char *uplo, char *trans, char *diag, int n, 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 STRSV and DTRSV solve a real triangular system of equations. CTRSV and ZTRSV solve a complex triangular 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 (CTRSV, ZTRSV only) where * b and x are n-element vectors * A is either a unit or nonunit n-by-n upper or lower triangular matrix * 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 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 (STRSV, DTRSV), or x <- A-Hx (CTRSV, ZTRSV) 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. a Array of dimension (lda,n). (input) STRSV: Single preicsion array. DTRSV: Double precision array. CTRSV: Single precision complex array. ZTRSV: Double precision complex array. Before entry with uplo = 'U' or 'u', the leading n-by-n upper triangular part of array a must contain the upper triangular matrix. The strictly lower triangular part of a is not referenced. Before entry with uplo = 'L' or 'l', the leading n-by-n lower triangular part of array a must contain the lower triangular matrix. The strictly upper triangular part of a is not referenced. When diag = 'U' or 'u', these routines assume that all elements of array a that represent diagonal elements of 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 >= MAX(1,n). x Array of dimension 1+(n-1) * |incx|. (input and output) STRSV: Single precision array. DTRSV: Double precision array. CTRSV: Single precision complex array. ZTRSV: Double precision complex array. On input, x contains the right-hand side vector b. On output, x is overwritten with the solution vector x. incx Integer. (input) Specifies the increment for the elements of x. incx must not be 0. NOTES Tests for singularity or near-singularity are not included in these routines. You must perform such tests before calling either routine. 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.