.TH "gemv" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME gemv \- gemv: general matrix-vector multiply .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBcgemv\fP (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)" .br .RI "\fBCGEMV\fP " .ti -1c .RI "subroutine \fBdgemv\fP (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)" .br .RI "\fBDGEMV\fP " .ti -1c .RI "subroutine \fBsgemv\fP (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)" .br .RI "\fBSGEMV\fP " .ti -1c .RI "subroutine \fBzgemv\fP (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)" .br .RI "\fBZGEMV\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine cgemv (character trans, integer m, integer n, complex alpha, complex, dimension(lda,*) a, integer lda, complex, dimension(*) x, integer incx, complex beta, complex, dimension(*) y, integer incy)" .PP \fBCGEMV\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CGEMV performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or y := alpha*A**H*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n matrix\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fITRANS\fP .PP .nf TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' y := alpha*A*x + beta*y\&. TRANS = 'T' or 't' y := alpha*A**T*x + beta*y\&. TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER On entry, M specifies the number of rows of the matrix A\&. M must be at least zero\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the number of columns of the matrix A\&. N must be at least zero\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is COMPLEX On entry, ALPHA specifies the scalar alpha\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX array, dimension ( LDA, N ) Before entry, the leading m by n part of the array A must contain the matrix of coefficients\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program\&. LDA must be at least max( 1, m )\&. .fi .PP .br \fIX\fP .PP .nf X is COMPLEX array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise\&. Before entry, the incremented array X must contain the vector x\&. .fi .PP .br \fIINCX\fP .PP .nf INCX is INTEGER On entry, INCX specifies the increment for the elements of X\&. INCX must not be zero\&. .fi .PP .br \fIBETA\fP .PP .nf BETA is COMPLEX On entry, BETA specifies the scalar beta\&. When BETA is supplied as zero then Y need not be set on input\&. .fi .PP .br \fIY\fP .PP .nf Y is COMPLEX array, dimension at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise\&. Before entry with BETA non-zero, the incremented array Y must contain the vector y\&. On exit, Y is overwritten by the updated vector y\&. If either m or n is zero, then Y not referenced and the function performs a quick return\&. .fi .PP .br \fIINCY\fP .PP .nf INCY is INTEGER On entry, INCY specifies the increment for the elements of Y\&. INCY must not be zero\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf Level 2 Blas routine\&. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- Written on 22-October-1986\&. Jack Dongarra, Argonne National Lab\&. Jeremy Du Croz, Nag Central Office\&. Sven Hammarling, Nag Central Office\&. Richard Hanson, Sandia National Labs\&. .fi .PP .RE .PP .SS "subroutine dgemv (character trans, integer m, integer n, double precision alpha, double precision, dimension(lda,*) a, integer lda, double precision, dimension(*) x, integer incx, double precision beta, double precision, dimension(*) y, integer incy)" .PP \fBDGEMV\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DGEMV performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n matrix\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fITRANS\fP .PP .nf TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' y := alpha*A*x + beta*y\&. TRANS = 'T' or 't' y := alpha*A**T*x + beta*y\&. TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER On entry, M specifies the number of rows of the matrix A\&. M must be at least zero\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the number of columns of the matrix A\&. N must be at least zero\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is DOUBLE PRECISION\&. On entry, ALPHA specifies the scalar alpha\&. .fi .PP .br \fIA\fP .PP .nf A is DOUBLE PRECISION array, dimension ( LDA, N ) Before entry, the leading m by n part of the array A must contain the matrix of coefficients\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program\&. LDA must be at least max( 1, m )\&. .fi .PP .br \fIX\fP .PP .nf X is DOUBLE PRECISION array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise\&. Before entry, the incremented array X must contain the vector x\&. .fi .PP .br \fIINCX\fP .PP .nf INCX is INTEGER On entry, INCX specifies the increment for the elements of X\&. INCX must not be zero\&. .fi .PP .br \fIBETA\fP .PP .nf BETA is DOUBLE PRECISION\&. On entry, BETA specifies the scalar beta\&. When BETA is supplied as zero then Y need not be set on input\&. .fi .PP .br \fIY\fP .PP .nf Y is DOUBLE PRECISION array, dimension at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise\&. Before entry with BETA non-zero, the incremented array Y must contain the vector y\&. On exit, Y is overwritten by the updated vector y\&. If either m or n is zero, then Y not referenced and the function performs a quick return\&. .fi .PP .br \fIINCY\fP .PP .nf INCY is INTEGER On entry, INCY specifies the increment for the elements of Y\&. INCY must not be zero\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf Level 2 Blas routine\&. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- Written on 22-October-1986\&. Jack Dongarra, Argonne National Lab\&. Jeremy Du Croz, Nag Central Office\&. Sven Hammarling, Nag Central Office\&. Richard Hanson, Sandia National Labs\&. .fi .PP .RE .PP .SS "subroutine sgemv (character trans, integer m, integer n, real alpha, real, dimension(lda,*) a, integer lda, real, dimension(*) x, integer incx, real beta, real, dimension(*) y, integer incy)" .PP \fBSGEMV\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SGEMV performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n matrix\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fITRANS\fP .PP .nf TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' y := alpha*A*x + beta*y\&. TRANS = 'T' or 't' y := alpha*A**T*x + beta*y\&. TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER On entry, M specifies the number of rows of the matrix A\&. M must be at least zero\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the number of columns of the matrix A\&. N must be at least zero\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is REAL On entry, ALPHA specifies the scalar alpha\&. .fi .PP .br \fIA\fP .PP .nf A is REAL array, dimension ( LDA, N ) Before entry, the leading m by n part of the array A must contain the matrix of coefficients\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program\&. LDA must be at least max( 1, m )\&. .fi .PP .br \fIX\fP .PP .nf X is REAL array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise\&. Before entry, the incremented array X must contain the vector x\&. .fi .PP .br \fIINCX\fP .PP .nf INCX is INTEGER On entry, INCX specifies the increment for the elements of X\&. INCX must not be zero\&. .fi .PP .br \fIBETA\fP .PP .nf BETA is REAL On entry, BETA specifies the scalar beta\&. When BETA is supplied as zero then Y need not be set on input\&. .fi .PP .br \fIY\fP .PP .nf Y is REAL array, dimension at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise\&. Before entry with BETA non-zero, the incremented array Y must contain the vector y\&. On exit, Y is overwritten by the updated vector y\&. If either m or n is zero, then Y not referenced and the function performs a quick return\&. .fi .PP .br \fIINCY\fP .PP .nf INCY is INTEGER On entry, INCY specifies the increment for the elements of Y\&. INCY must not be zero\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf Level 2 Blas routine\&. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- Written on 22-October-1986\&. Jack Dongarra, Argonne National Lab\&. Jeremy Du Croz, Nag Central Office\&. Sven Hammarling, Nag Central Office\&. Richard Hanson, Sandia National Labs\&. .fi .PP .RE .PP .SS "subroutine zgemv (character trans, integer m, integer n, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx, complex*16 beta, complex*16, dimension(*) y, integer incy)" .PP \fBZGEMV\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZGEMV performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or y := alpha*A**H*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n matrix\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fITRANS\fP .PP .nf TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' y := alpha*A*x + beta*y\&. TRANS = 'T' or 't' y := alpha*A**T*x + beta*y\&. TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER On entry, M specifies the number of rows of the matrix A\&. M must be at least zero\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the number of columns of the matrix A\&. N must be at least zero\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is COMPLEX*16 On entry, ALPHA specifies the scalar alpha\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX*16 array, dimension ( LDA, N ) Before entry, the leading m by n part of the array A must contain the matrix of coefficients\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program\&. LDA must be at least max( 1, m )\&. .fi .PP .br \fIX\fP .PP .nf X is COMPLEX*16 array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise\&. Before entry, the incremented array X must contain the vector x\&. .fi .PP .br \fIINCX\fP .PP .nf INCX is INTEGER On entry, INCX specifies the increment for the elements of X\&. INCX must not be zero\&. .fi .PP .br \fIBETA\fP .PP .nf BETA is COMPLEX*16 On entry, BETA specifies the scalar beta\&. When BETA is supplied as zero then Y need not be set on input\&. .fi .PP .br \fIY\fP .PP .nf Y is COMPLEX*16 array, dimension at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise\&. Before entry with BETA non-zero, the incremented array Y must contain the vector y\&. On exit, Y is overwritten by the updated vector y\&. If either m or n is zero, then Y not referenced and the function performs a quick return\&. .fi .PP .br \fIINCY\fP .PP .nf INCY is INTEGER On entry, INCY specifies the increment for the elements of Y\&. INCY must not be zero\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf Level 2 Blas routine\&. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- Written on 22-October-1986\&. Jack Dongarra, Argonne National Lab\&. Jeremy Du Croz, Nag Central Office\&. Sven Hammarling, Nag Central Office\&. Richard Hanson, Sandia National Labs\&. .fi .PP .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.