ssbmv(3S)
SSBMV, DSBMV - Multiplies a real vector by a real symmetric band matrix
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NAME SSBMV, DSBMV - Multiplies a real vector by a real symmetric band matrix SYNOPSIS Single precision Fortran: CALL SSBMV (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy) C/C++: #include <scsl_blas.h> void ssbmv (char uplo, int n, int k, float alpha, float *a, int lda, float *x, int incx, float beta, float *y, int incy); Double precision Fortran: CALL DSBMV (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy) C/C++: #include <scsl_blas.h> void dsbmv (char uplo, int n, int k, double alpha, double *a, int lda, double *x, int incx, double beta, double *y, int incy); 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 the following matrix-vector operation: y <- alpha Ax + beta y where alpha and beta are scalars, x and y are n-element vectors, and A is an n-by-n symmetric band matrix. See the NOTES section of this man page for information about the interpretation of the data types described in the following arguments. This routine has the following arguments: uplo Character. (input) Specifies whether the upper or lower triangular part of band matrix A is supplied, as follows: uplo= 'U' or 'u': the upper triangular part of A is being supplied. uplo= 'L' or 'l': the lower triangular part of A is being supplied. n Integer. (input) Specifies the order of matrix A. n >= 0. k Integer. (input) Specifies the number of superdiagonals of matrix A. k >= 0. alpha Scalar alpha. (input) SSBMV: Single precision. DSBMV: Double precision. a Array of dimension (lda,n). (input) SSBMV: Single precision array. DSBMV: Double precision array. Before entry with uplo = 'U' or 'u', the leading (k+1)-by-n part of array a must contain the upper triangular band part of the symmetric matrix, 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 symmetric matrix, 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. See the NOTES section for examples of Fortran code that transfer upper and lower parts of symmetric band matrices from conventional full matrix storage to band storage. lda Integer. (input) Specifies the first dimension of a as declared in the calling program. lda >= (k+1). x Real array of dimension 1+(n-1) * |incx|. (input) SSBMV: Single precision array. DSBMV: Double precision array. Contains vector x. incx Integer. (input) Specifies the increment for the elements of x. incx must not be 0. beta Scalar beta. (input) SSBMV: Single precision. DSBMV: Double precision. y Array of dimension 1+(n-1) * |incy|. (input and output) SSBMV: Single precision array. DSBMV: Double precision array. Contains vector y. On exit, the updated vector overwrites array y. incy Integer. (input) Specifies the increment for the elements of y. incy must not be 0. NOTES The following program segment transfers the upper triangular part of a symmetric 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 the lower triangular part of a symmetric 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 SSBMV/DSBMV is a Level 2 Basic Linear Algebra Subprogram (Level 2 BLAS). When working backward (incx < 0 or incy < 0), this 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) y(1-incy * (n-1)), y(1-incy * (n-2)) , ..., y(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 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 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.