stpmv(3S)
STPMV, DTPMV, CTPMV, ZTPMV - Multiplies a real or complex vector by a real or complex triangular packed matrix
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NAME STPMV, DTPMV, CTPMV, ZTPMV - Multiplies a real or complex vector by a real or complex triangular packed matrix SYNOPSIS Single precision Fortran: CALL STPMV (uplo, trans, diag, n, ap, x, incx) C/C++: #include <scsl_blas.h> void stpmv (char *uplo, char *trans, char *diag, int n, float *ap, float *x, int incx); Double precision Fortran: CALL DTPMV (uplo, trans, diag, n, ap, x, incx) C/C++: #include <scsl_blas.h> void dtpmv (char *uplo, char *trans, char *diag, int n, double *ap, double *x, int incx); Single precision complex Fortran: CALL CTPMV (uplo, trans, diag, n, ap, x, incx) C/C++: #include <scsl_blas.h> void ctpmv (char *uplo, char *trans, char *diag, int n, scsl_complex *ap, scsl_complex *x, int incx); C++ STL: #include <complex.h> #include <scsl_blas.h> void ctpmv (char *uplo, char *trans, char *diag, int n, complex<float> *ap, complex<float> *x, int incx); Double precision complex Fortran: CALL ZTPMV (uplo, trans, diag, n, ap, x, incx) C/C++: #include <scsl_blas.h> void ztpmv (char *uplo, char *trans, char *diag, int n, scsl_zomplex *ap, scsl_zomplex *x, int incx); C++ STL: #include <complex.h> #include <scsl_blas.h> void ztpmv (char *uplo, char *trans, char *diag, int n, complex<double> *ap, 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 These routines perform one of the following matrix-vector operations: x <- Ax x <- ATx x <- AHx (CTPMV, ZTPMV only) where AT is the transpose of A, AH is the conjugate transpose of A, x is an n-element vector, and A may be either a unit or nonunit n-by-n upper or lower triangular matrix. 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 <- Ax trans = 'T' or 't': x <- ATx trans = 'C' or 'c': x <- ATx (STPMV, DTPMV), or x <- AHx (CTPMV, ZTPMV) 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. ap Array of dimension (n(n+1))/2. (input) STPMV: Single precision array. DTPMV: Double precision array. CTPMV: Single precision complex array. ZTPMV: Double precision complex array. Before entry with uplo = 'U' or 'u', array ap must contain the upper triangular matrix packed sequentially, column-by-column, so that ap(1) contains A(1,1), ap(2) contains A(1,2), ap(3) contains A(2,2), and so on. Before entry with uplo = 'L' or 'l', array ap must contain the lower triangular matrix packed sequentially, column-by-column, so that ap(1) contains A(1,1), ap(2) contains A(2,1), ap(3) contains A(3,1), and so on. When diag = 'U' or 'u', these routines assume that all elements of the 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. x Array of dimension 1+(n-1) * |incx|. (input and output) STPMV: Single precision array. DTPMV: Double precision array. CTPMV: Single precision complex array. ZTPMV: Double precision complex array. Contains the vector x. On exit, the transformed vector overwrites array x. incx Integer. (input) Specifies the increment for the elements of x. incx must not be 0. NOTES 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) 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] 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] 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> 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.