.TH "BLAS/SRC/zgbmv.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
BLAS/SRC/zgbmv.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzgbmv\fP (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy)"
.br
.RI "\fBZGBMV\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "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)"

.PP
\fBZGBMV\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.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
\fIKL\fP 
.PP
.nf
          KL is INTEGER
           On entry, KL specifies the number of sub-diagonals of the
           matrix A\&. KL must satisfy  0 \&.le\&. KL\&.
.fi
.PP
.br
\fIKU\fP 
.PP
.nf
          KU is INTEGER
           On entry, KU specifies the number of super-diagonals of the
           matrix A\&. KU must satisfy  0 \&.le\&. KU\&.
.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 ( 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
.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
           ( kl + ku + 1 )\&.
.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, 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

.PP
Definition at line \fB188\fP of file \fBzgbmv\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.