gbmv(3) Library Functions Manual gbmv(3) NAME gbmv - gbmv: general matrix-vector multiply SYNOPSIS Functions subroutine cgbmv (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy) CGBMV subroutine dgbmv (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy) DGBMV subroutine sgbmv (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy) SGBMV subroutine zgbmv (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy) ZGBMV Detailed Description Function Documentation subroutine cgbmv (character trans, integer m, integer n, integer kl, integer ku, complex alpha, complex, dimension(lda,*) a, integer lda, complex, dimension(*) x, integer incx, complex beta, complex, dimension(*) y, integer incy) CGBMV Purpose: CGBMV 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 band matrix, with kl sub-diagonals and ku super-diagonals. Parameters TRANS 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. M M is INTEGER On entry, M specifies the number of rows of the matrix A. M must be at least zero. N N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero. KL KL is INTEGER On entry, KL specifies the number of sub-diagonals of the matrix A. KL must satisfy 0 .le. KL. KU KU is INTEGER On entry, KU specifies the number of super-diagonals of the matrix A. KU must satisfy 0 .le. KU. ALPHA ALPHA is COMPLEX On entry, ALPHA specifies the scalar alpha. A A is COMPLEX array, dimension ( LDA, N ) Before entry, the leading ( kl + ku + 1 ) by n part of the 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 super-diagonal starting at position 2 in row ku, the first sub-diagonal starting at position 1 in row ( ku + 2 ), and so on. Elements in the array A that do not correspond to elements in the band matrix (such as the top left ku by ku triangle) are not referenced. The following program segment will transfer 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 LDA LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( kl + ku + 1 ). X 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. INCX INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. BETA BETA is COMPLEX On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. Y 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, 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. INCY INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Further Details: 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. Definition at line 188 of file cgbmv.f. subroutine dgbmv (character trans, integer m, integer n, integer kl, integer ku, 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) DGBMV Purpose: DGBMV 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 band matrix, with kl sub-diagonals and ku super-diagonals. Parameters TRANS 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. M M is INTEGER On entry, M specifies the number of rows of the matrix A. M must be at least zero. N N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero. KL KL is INTEGER On entry, KL specifies the number of sub-diagonals of the matrix A. KL must satisfy 0 .le. KL. KU KU is INTEGER On entry, KU specifies the number of super-diagonals of the matrix A. KU must satisfy 0 .le. KU. ALPHA ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. A A is DOUBLE PRECISION array, dimension ( LDA, N ) Before entry, the leading ( kl + ku + 1 ) by n part of the 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 super-diagonal starting at position 2 in row ku, the first sub-diagonal starting at position 1 in row ( ku + 2 ), and so on. Elements in the array A that do not correspond to elements in the band matrix (such as the top left ku by ku triangle) are not referenced. The following program segment will transfer 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 LDA LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( kl + ku + 1 ). X 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. INCX INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. BETA 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. Y 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, 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. INCY INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Further Details: 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. Definition at line 186 of file dgbmv.f. subroutine sgbmv (character trans, integer m, integer n, integer kl, integer ku, real alpha, real, dimension(lda,*) a, integer lda, real, dimension(*) x, integer incx, real beta, real, dimension(*) y, integer incy) SGBMV Purpose: SGBMV 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 band matrix, with kl sub-diagonals and ku super-diagonals. Parameters TRANS 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. M M is INTEGER On entry, M specifies the number of rows of the matrix A. M must be at least zero. N N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero. KL KL is INTEGER On entry, KL specifies the number of sub-diagonals of the matrix A. KL must satisfy 0 .le. KL. KU KU is INTEGER On entry, KU specifies the number of super-diagonals of the matrix A. KU must satisfy 0 .le. KU. ALPHA ALPHA is REAL On entry, ALPHA specifies the scalar alpha. A A is REAL array, dimension ( LDA, N ) Before entry, the leading ( kl + ku + 1 ) by n part of the 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 super-diagonal starting at position 2 in row ku, the first sub-diagonal starting at position 1 in row ( ku + 2 ), and so on. Elements in the array A that do not correspond to elements in the band matrix (such as the top left ku by ku triangle) are not referenced. The following program segment will transfer 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 LDA LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( kl + ku + 1 ). X 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. INCX INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. BETA BETA is REAL On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. Y 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, 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. INCY INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Further Details: 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. Definition at line 186 of file sgbmv.f. subroutine zgbmv (character trans, integer m, integer n, integer kl, integer ku, 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) ZGBMV Purpose: ZGBMV 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 band matrix, with kl sub-diagonals and ku super-diagonals. Parameters TRANS 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. M M is INTEGER On entry, M specifies the number of rows of the matrix A. M must be at least zero. N N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero. KL KL is INTEGER On entry, KL specifies the number of sub-diagonals of the matrix A. KL must satisfy 0 .le. KL. KU KU is INTEGER On entry, KU specifies the number of super-diagonals of the matrix A. KU must satisfy 0 .le. KU. ALPHA ALPHA is COMPLEX*16 On entry, ALPHA specifies the scalar alpha. A A is COMPLEX*16 array, dimension ( LDA, N ) Before entry, the leading ( kl + ku + 1 ) by n part of the 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 super-diagonal starting at position 2 in row ku, the first sub-diagonal starting at position 1 in row ( ku + 2 ), and so on. Elements in the array A that do not correspond to elements in the band matrix (such as the top left ku by ku triangle) are not referenced. The following program segment will transfer 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 LDA LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( kl + ku + 1 ). X 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. INCX INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. BETA 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. Y 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, 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. INCY INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Further Details: 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. Definition at line 188 of file zgbmv.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 gbmv(3)