zgbmv (l) - Linux Manuals

zgbmv: performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*Aaq*x + beta*y, or y := alpha*conjg( Aaq )*x + beta*y,

NAME

ZGBMV - performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*Aaq*x + beta*y, or y := alpha*conjg( Aaq )*x + beta*y,

SYNOPSIS

SUBROUTINE ZGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)

    
DOUBLE COMPLEX ALPHA,BETA

    
INTEGER INCX,INCY,KL,KU,LDA,M,N

    
CHARACTER TRANS

    
DOUBLE COMPLEX A(LDA,*),X(*),Y(*)

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.

ARGUMENTS

TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as follows:

TRANS = aqNaq or aqnaq y := alpha*A*x + beta*y.

TRANS = aqTaq or aqtaq y := alpha*Aaq*x + beta*y.

TRANS = aqCaq or aqcaq y := alpha*conjg( Aaq )*x + beta*y.

Unchanged on exit.

M - INTEGER.
On entry, M specifies the number of rows of the matrix A. M must be at least zero. Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit.
KL - INTEGER.
On entry, KL specifies the number of sub-diagonals of the matrix A. KL must satisfy 0 .le. KL. Unchanged on exit.
KU - INTEGER.
On entry, KU specifies the number of super-diagonals of the matrix A. KU must satisfy 0 .le. KU. Unchanged on exit.
ALPHA - COMPLEX*16 .
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
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.

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.
X - COMPLEX*16 array of DIMENSION at least
( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = aqNaq or aqnaq and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. Before entry, the incremented array X must contain the vector x. Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
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.
Y - COMPLEX*16 array of DIMENSION at least
( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = aqNaq or aqnaq 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.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.

FURTHER DETAILS

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.

Pages related to zgbmv

  • zgbmv (3)
  • zgbbrd (l) - reduces a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation
  • zgbcon (l) - estimates the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm,
  • zgbequ (l) - computes row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number
  • zgbequb (l) - computes row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number
  • zgbrfs (l) - improves the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
  • zgbrfsx (l) - ZGBRFSX improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution
  • zgbsv (l) - computes the solution to a complex system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices
  • zgbsvx (l) - uses the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B,