Product of a General Matrix and a Vector

Calling Sequence

CALL DGEMV	(TRANSA, M, N, DALPHA, DA, LDA, DX, INCX, DBETA, DY, INCY)
CALL SGEMV	(TRANSA, M, N, SALPHA, SA, LDA, SX, INCX, SBETA, SY, INCY)
CALL ZGEMV	(TRANSA, M, N, ZALPHA, ZA, LDA, ZX, INCX, ZBETA, ZY, INCY)
CALL CGEMV	(TRANSA, M, N, CALPHA, CA, LDA, CX, INCX, CBETA, CY, INCY)
void dgemv	(char trans, int m, int n, double dalpha, double *da, int lda, double *dx, int incx, double dbeta, double *dy, int incy)
void sgemv	(char trans, int m, int n, float salpha, float *sa, int lda, float *sx, int incx, float sbeta, float *sy, int incy)
void zgemv	(char trans, int m, int n, doublecomplex *zalpha, doublecomplex *za, int lda, doublecomplex *zx, int incx, doublecomplex *zbeta, doublecomplex *zy, int incy)
void cgemv	(char trans, int m, int n, complex *calpha, complex *ca, int lda, complex *cx, int incx, complex *cbeta, complex *cy, int incy)

Arguments

TRANSA	Indicates how to use the matrix stored in the array argument. The legal values for TRANSA are listed below. Any value not listed below is illegal.
	'N' or 'n'	Use the matrix as it is stored in the array.
	'T' or 't'	Use the transpose of the matrix.
	'C' or 'c'	Use the conjugate transpose of the matrix.
M	Number of rows in the matrix A. M 0.
N	Number of columns in the matrix A. N 0.
xALPHA	Scalar that scales the input value of the matrix A.
xA	Two-dimensional array that contains the input matrix.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA max(1,M).
xX	X and INCX describe a vector of length N if TRANSA = 'N' or 'n', otherwise of length M. X contains an input vector.
INCX	Scalar that contains the storage spacing between successive elements of the vector. INCX 0. If INCX = 1, then elements of the vector are contiguous in memory. INCX may take on values besides 1 to allow the programmer to extract from a matrix a vector that is not stored in contiguous memory locations.
	If X is a one-dimensional array and INCX = -1 then the array will be accessed in reverse order.
	If X is a two-dimensional array and INCX = LDA then the vector will be a row of the array.
	If X is a two-dimensional array and INCX = LDA+1 then the vector will be a diagonal of the array.
xBETA	Scalar that scales the input value of the vector Y.
xY	Y and INCY describe a vector of length M if TRANSA = 'N' or 'n', otherwise of length N.
	On entry, an input vector.
	On exit, a result vector.
INCY	Scalar that contains the storage spacing between successive elements of the vector Y. INCY 0. If INCY = 1, then elements of the vector are contiguous in memory. INCY may take on values besides 1 to allow the programmer to extract from a matrix a vector that is not stored in contiguous memory locations.
	If Y is a one-dimensional array and INCY = -1 then the array will be accessed in reverse order.
	If Y is a two-dimensional array and INCY = LDA then the vector will be a row of the array.
	If Y is a two-dimensional array and INCY = LDA+1 then the vector will be a diagonal of the array.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LDROT, M, N

PARAMETER (M = 2)

PARAMETER (LDROT = M)

PARAMETER (N = 2)

C

DOUBLE PRECISION ALPHA, PI, ROT(LDROT,N), SCALE, THETA

DOUBLE PRECISION VEC1(N), VEC2(N)

INTEGER INCX, INCY, M, N

C

EXTERNAL DGEMV

INTRINSIC ATAN, COS, SIN

C

PI = 4.0D0 * ATAN (1.0D0)

THETA = PI / 2.0D0

C

C Initialize the array ROT to contain the rotation matrix to

C be applied to the vector stored in VEC1.

C

ROT(1,1) = COS (THETA)

ROT(2,1) = SIN (THETA)

ROT(1,2) = -SIN (THETA)

ROT(2,2) = COS (THETA)

VEC1(1) = 3.0D0

VEC1(2) = 4.0D0

PRINT 1000

PRINT 1010, VEC1

SCALE = 5.0D-1

INCX = 1

ALPHA = 0.0D0

INCY = 1

CALL DGEMV ('NOT TRANSPOSED ROT', M, N, SCALE, ROT, LDROT,

$ VEC1, INCX, ALPHA, VEC2, INCY)

PRINT 1020

PRINT 1010, VEC2

C

1000 FORMAT (1X, 'Original vector:')

1010 FORMAT (3X, F4.1)

1020 FORMAT (/1X, 'Rotated vector:')

C

END

Sample Output

Original vector:
3.0
4.0
Rotated vector:
-2.0
1.5