.TH ZGBMV 1 "November 2006" "BLAS routine" "BLAS routine" .SH NAME ZGBMV - one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A\(aq*x + beta*y, or y := alpha*conjg( A\(aq )*x + beta*y, .SH SYNOPSIS .TP 65 SUBROUTINE ZGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) .TP 65 .ti +4 DOUBLE COMPLEX ALPHA,BETA .TP 65 .ti +4 INTEGER INCX,INCY,KL,KU,LDA,M,N .TP 65 .ti +4 CHARACTER TRANS .TP 65 .ti +4 DOUBLE COMPLEX A(LDA,*),X(*),Y(*) .SH PURPOSE ZGBMV performs one of the matrix-vector operations 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. .SH ARGUMENTS .TP 7 TRANS - CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows: TRANS = \(aqN\(aq or \(aqn\(aq y := alpha*A*x + beta*y. TRANS = \(aqT\(aq or \(aqt\(aq y := alpha*A\(aq*x + beta*y. TRANS = \(aqC\(aq or \(aqc\(aq y := alpha*conjg( A\(aq )*x + beta*y. Unchanged on exit. .TP 7 M - INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero. Unchanged on exit. .TP 7 N - INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit. .TP 7 KL - INTEGER. On entry, KL specifies the number of sub-diagonals of the matrix A. KL must satisfy 0 .le. KL. Unchanged on exit. .TP 7 KU - INTEGER. On entry, KU specifies the number of super-diagonals of the matrix A. KU must satisfy 0 .le. KU. Unchanged on exit. .TP 7 ALPHA - COMPLEX*16 . On entry, ALPHA specifies the scalar alpha. Unchanged on exit. .TP 7 A - COMPLEX*16 array of 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 Unchanged on exit. .TP 7 LDA - 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 ). Unchanged on exit. .TP 7 X - COMPLEX*16 array of DIMENSION at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = \(aqN\(aq or \(aqn\(aq and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. Before entry, the incremented array X must contain the vector x. Unchanged on exit. .TP 7 INCX - INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. .TP 7 BETA - COMPLEX*16 . On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. Unchanged on exit. .TP 7 Y - COMPLEX*16 array of DIMENSION at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = \(aqN\(aq or \(aqn\(aq 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. .TP 7 INCY - INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit. Level 2 Blas routine. -- 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.