SGBMV(3S)SGBMV(3S)NAME
SGBMV, DGBMV, CGBMV, ZGMBV - Multiplies a real or complex vector by a
real or complex general band matrix
SYNOPSIS
Single precision
Fortran:
CALL SGBMV (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta,
y, incy)
C/C++:
#include <scsl_blas.h>
void sgbmv(char *transa, int m, int n, int kl, int ku, float
alpha, float *a, int lda, float *x, int incx, float beta, float
*y, int incy);
Double precision
Fortran:
CALL DGBMV (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta,
y, incy)
C/C++:
#include <scsl_blas.h>
void dgbmv(char *transa, int m, int n, int kl, int ku, double
alpha, double *a, int lda, double *x, int incx, double beta,
double *y, int incy);
Single precision complex
Fortran:
CALL CGBMV (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta,
y, incy)
C/C++:
#include <scsl_blas.h>
void cgbmv(char *transa, int m, int n, int kl, int ku,
scsl_complex *alpha, scsl_complex *a, int lda, scsl_complex *x,
int incx, scsl_complex *beta, scsl_complex *y, int incy);
C++ STL:
#include <complex.h>
#include <scsl_blas.h>
void cgbmv(char *transa, int m, int n, int kl, int ku,
complex<float> *alpha, complex<float> *a, int lda,
complex<float> *x, int incx, complex<float> *beta,
complex<float> *y, int incy);
Double precision complex
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SGBMV(3S)SGBMV(3S)
Fortran:
CALL ZGBMV (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta,
y, incy)
C/C++:
#include <scsl_blas.h>
void zgbmv(char *transa, int m, int n, int kl, int ku,
scsl_zomplex *alpha, scsl_zomplex *a, int lda, scsl_zomplex *x,
int incx, scsl_zomplex *beta, scsl_zomplex *y, int incy);
C++ STL:
#include <complex.h>
#include <scsl_blas.h>
void zgbmv(char *transa, int m, int n, int kl, int ku,
complex<double> *alpha, complex<double> *a, int lda,
complex<double> *x, int incx, complex<double> *beta,
complex<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
SGBMV and DGBMV multiply a real vector by a real general band matrix.
CGBMV and ZGBMV multiply a complex vector by a complex general band
matrix.
These routines perform one of the following matrix-vector operations:
y <- alpha Ax + beta y
y <- alpha ATx + beta y
y <- alpha AHx + beta y
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SGBMV(3S)SGBMV(3S)
where
* alpha and beta are scalars,
* x and y are vectors
* A is an m-by-n band matrix with kl subdiagonals and ku superdiagonals
* AT is the transpose of A
* AH is the conjugate transpose of A
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:
trans Character. (input)
Specifies the operation to be performed:
trans = 'N' or 'n': y <- alpha Ax + beta y
trans = 'T' or 't': y <- alpha ATx + beta y
trans = 'C' or 'c': y <- alpha ATx + beta y (SGBMV, DGBMV)
or
y <- alpha AHx + beta y (CGBMV, ZGBMV)
For C/C++, a pointer to this character is passed.
m Integer. (input)
Specifies the number of rows in matrix A. m >= 0.
n Integer. (input)
Specifies the number of columns in the matrix A. n >= 0.
kl Integer. (input)
Specifies the number of subdiagonals of matrix A. kl >= 0.
ku Integer. (input)
Specifies the number of superdiagonals of matrix A. ku >= 0.
alpha Scalar alpha. (input)
SGBMV: Single precision.
DGBMV: Double precision.
CGBMV: Single precision complex.
ZGBMV: Double precision complex.
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SGBMV(3S)SGBMV(3S)
For C/C++, a pointer to this scalar is passed when alpha is
complex; otherwise, alpha is passed by value.
a Array of dimension (lda, n). (input)
SGBMV: Single precision array.
DGBMV: Double precision array.
CGBMV: Single precision complex array.
ZGBMV: Double precision complex array.
Before entry, the leading (kl+ku+1)-by-n part of array a must
contain the matrix of coefficients, supplied column-by-column,
with the leading diagonal of the matrix in row (ku+1) of the
array, the first superdiagonal starting at position 2 in row
ku, the first subdiagonal starting at position 1 in row (ku+2),
and so on. Elements in array a that do not correspond to
elements in the band matrix (such as the top left ku-by-ku
triangle) are not referenced.
See the NOTES section for an example of Fortran code that
transfers a band matrix from conventional full matrix storage
to band storage.
lda Integer. (input)
Specifies the first dimension of a as declared in the calling
program. lda >= (kl+ku+1).
x Array of dimension 1+(kx-1) * |incx|. (input)
SGBMV: Single precision array.
DGBMV: Double precision array.
CGBMV: Single precision complex array.
ZGBMV: Double precision complex array.
Contains the vector x. When trans = 'N' or 'n', kx is n;
otherwise, it is m.
incx Integer. (input)
Specifies the increment for the elements of x. incx must not
be 0.
beta Scalar beta. (input)
SGBMV: Single precision.
DGBMV: Double precision.
CGBMV: Single precision complex.
ZGBMV: Double precision complex.
When beta is supplied as 0, y need not be set on input.
For C/C++, a pointer to this scalar is passed when beta is
complex; otherwise, beta is passed by value.
y Array of dimension 1+(ky-1) * |incy|. (input and output)
SGBMV: Single precision array.
DGBMV: Double precision array.
CGBMV: Single precision complex array.
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ZGBMV: Double precision complex array.
Contains the vector y. When trans = 'N' or 'n', ky is m;
otherwise, it is n. 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 a band matrix from conventional
full matrix storage to band storage:
DO 20, J = 1, N
K = KU + 1 - J
DO 10, I = MAX(1, J - KU), MIN(M, J + KL)
A(K + I, J) = MATRIX(I, J)
10 CONTINUE
20 CONTINUE
SGBMV, DGBMV, ZGBMV and CGBMV are Level 2 Basic Linear Algebra
Subprograms (Level 2 BLAS).
When working backward (incx < 0 or incy < 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)
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
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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 ALSOINTRO_SCSL(3S), INTRO_BLAS2(3S)
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SGBMV(3S)SGBMV(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.
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