Source module last modified on Thu, 2 Jul 1998, 23:17;
HTML image of Fortran source automatically generated by
for2html on Sun, 23 Jun 2002, 15:10.
SUBROUTINE ZHBMV ( UPLO, N, K, ALPHA, A, LDA, X, INCX,
$ BETA, Y, INCY )
# .. Scalar Arguments ..
COMPLEX*16 ALPHA, BETA
INTEGER INCX, INCY, K, LDA, N
CHARACTER*1 UPLO
# .. Array Arguments ..
COMPLEX*16 A( LDA, * ), X( * ), Y( * )
# ..
#
# Purpose
# =======
#
# ZHBMV performs the matrix-vector operation
#
# y := alpha*A*x + beta*y,
#
# where alpha and beta are scalars, x and y are n element vectors and
# A is an n by n hermitian band matrix, with k super-diagonals.
#
# Parameters
# ==========
#
# UPLO - CHARACTER*1.
# On entry, UPLO specifies whether the upper or lower
# triangular part of the band matrix A is being supplied as
# follows:
#
# UPLO = 'U' or 'u' The upper triangular part of A is
# being supplied.
#
# UPLO = 'L' or 'l' The lower triangular part of A is
# being supplied.
#
# Unchanged on exit.
#
# N - INTEGER.
# On entry, N specifies the order of the matrix A.
# N must be at least zero.
# Unchanged on exit.
#
# K - INTEGER.
# On entry, K specifies the number of super-diagonals of the
# matrix A. K must satisfy 0 .le. K.
# 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 with UPLO = 'U' or 'u', the leading ( k + 1 )
# by n part of the array A must contain the upper triangular
# band part of the hermitian matrix, supplied column by
# column, with the leading diagonal of the matrix in row
# ( k + 1 ) of the array, the first super-diagonal starting at
# position 2 in row k, and so on. The top left k by k triangle
# of the array A is not referenced.
# The following program segment will transfer the upper
# triangular part of a hermitian band matrix from conventional
# full matrix storage to band storage:
#
# DO 20, J = 1, N
# M = K + 1 - J
# DO 10, I = MAX( 1, J - K ), J
# A( M + I, J ) = matrix( I, J )
# 10 CONTINUE
# 20 CONTINUE
#
# Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
# by n part of the array A must contain the lower triangular
# band part of the hermitian matrix, supplied column by
# column, with the leading diagonal of the matrix in row 1 of
# the array, the first sub-diagonal starting at position 1 in
# row 2, and so on. The bottom right k by k triangle of the
# array A is not referenced.
# The following program segment will transfer the lower
# triangular part of a hermitian band matrix from conventional
# full matrix storage to band storage:
#
# DO 20, J = 1, N
# M = 1 - J
# DO 10, I = J, MIN( N, J + K )
# A( M + I, J ) = matrix( I, J )
# 10 CONTINUE
# 20 CONTINUE
#
# Note that the imaginary parts of the diagonal elements need
# not be set and are assumed to be zero.
# 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
# ( k + 1 ).
# Unchanged on exit.
#
# X - COMPLEX*16 array of DIMENSION at least
# ( 1 + ( n - 1 )*abs( INCX ) ).
# 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.
# Unchanged on exit.
#
# Y - COMPLEX*16 array of DIMENSION at least
# ( 1 + ( n - 1 )*abs( INCY ) ).
# 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.
#
#
# 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.
#
#
# .. Parameters ..
COMPLEX*16 ONE
PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
COMPLEX*16 ZERO
PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
# .. Local Scalars ..
COMPLEX*16 TEMP1, TEMP2
INTEGER I, INFO, IX, IY, J, JX, JY, KPLUS1, KX, KY, L
# .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
# .. External Subroutines ..
EXTERNAL XERBLA
# .. Intrinsic Functions ..
INTRINSIC DCONJG, MAX, MIN, DBLE
# ..
# .. Executable Statements ..
#
# Test the input parameters.
#
INFO = 0
IF ( ! LSAME( UPLO, 'U' )&&
$ ! LSAME( UPLO, 'L' ) )THEN
INFO = 1
ELSE IF( N<0 )THEN
INFO = 2
ELSE IF( K<0 )THEN
INFO = 3
ELSE IF( LDA<( K + 1 ) )THEN
INFO = 6
ELSE IF( INCX==0 )THEN
INFO = 8
ELSE IF( INCY==0 )THEN
INFO = 11
END IF
IF( INFO!=0 )THEN
CALL XERBLA( 'ZHBMV ', INFO )
RETURN
END IF
#
# Quick return if possible.
#
IF( ( N==0 )||( ( ALPHA==ZERO )&&( BETA==ONE ) ) )
$ RETURN
#
# Set up the start points in X and Y.
#
IF( INCX>0 )THEN
KX = 1
ELSE
KX = 1 - ( N - 1 )*INCX
END IF
IF( INCY>0 )THEN
KY = 1
ELSE
KY = 1 - ( N - 1 )*INCY
END IF
#
# Start the operations. In this version the elements of the array A
# are accessed sequentially with one pass through A.
#
# First form y := beta*y.
#
IF( BETA!=ONE )THEN
IF( INCY==1 )THEN
IF( BETA==ZERO )THEN
DO 10, I = 1, N
Y( I ) = ZERO
10 CONTINUE
ELSE
DO 20, I = 1, N
Y( I ) = BETA*Y( I )
20 CONTINUE
END IF
ELSE
IY = KY
IF( BETA==ZERO )THEN
DO 30, I = 1, N
Y( IY ) = ZERO
IY = IY + INCY
30 CONTINUE
ELSE
DO 40, I = 1, N
Y( IY ) = BETA*Y( IY )
IY = IY + INCY
40 CONTINUE
END IF
END IF
END IF
IF( ALPHA==ZERO )
$ RETURN
IF( LSAME( UPLO, 'U' ) )THEN
#
# Form y when upper triangle of A is stored.
#
KPLUS1 = K + 1
IF( ( INCX==1 )&&( INCY==1 ) )THEN
DO 60, J = 1, N
TEMP1 = ALPHA*X( J )
TEMP2 = ZERO
L = KPLUS1 - J
DO 50, I = MAX( 1, J - K ), J - 1
Y( I ) = Y( I ) + TEMP1*A( L + I, J )
TEMP2 = TEMP2 + DCONJG( A( L + I, J ) )*X( I )
50 CONTINUE
Y( J ) = Y( J ) + TEMP1*DBLE( A( KPLUS1, J ) )
$ + ALPHA*TEMP2
60 CONTINUE
ELSE
JX = KX
JY = KY
DO 80, J = 1, N
TEMP1 = ALPHA*X( JX )
TEMP2 = ZERO
IX = KX
IY = KY
L = KPLUS1 - J
DO 70, I = MAX( 1, J - K ), J - 1
Y( IY ) = Y( IY ) + TEMP1*A( L + I, J )
TEMP2 = TEMP2 + DCONJG( A( L + I, J ) )*X( IX )
IX = IX + INCX
IY = IY + INCY
70 CONTINUE
Y( JY ) = Y( JY ) + TEMP1*DBLE( A( KPLUS1, J ) )
$ + ALPHA*TEMP2
JX = JX + INCX
JY = JY + INCY
IF( J>K )THEN
KX = KX + INCX
KY = KY + INCY
END IF
80 CONTINUE
END IF
ELSE
#
# Form y when lower triangle of A is stored.
#
IF( ( INCX==1 )&&( INCY==1 ) )THEN
DO 100, J = 1, N
TEMP1 = ALPHA*X( J )
TEMP2 = ZERO
Y( J ) = Y( J ) + TEMP1*DBLE( A( 1, J ) )
L = 1 - J
DO 90, I = J + 1, MIN( N, J + K )
Y( I ) = Y( I ) + TEMP1*A( L + I, J )
TEMP2 = TEMP2 + DCONJG( A( L + I, J ) )*X( I )
90 CONTINUE
Y( J ) = Y( J ) + ALPHA*TEMP2
100 CONTINUE
ELSE
JX = KX
JY = KY
DO 120, J = 1, N
TEMP1 = ALPHA*X( JX )
TEMP2 = ZERO
Y( JY ) = Y( JY ) + TEMP1*DBLE( A( 1, J ) )
L = 1 - J
IX = JX
IY = JY
DO 110, I = J + 1, MIN( N, J + K )
IX = IX + INCX
IY = IY + INCY
Y( IY ) = Y( IY ) + TEMP1*A( L + I, J )
TEMP2 = TEMP2 + DCONJG( A( L + I, J ) )*X( IX )
110 CONTINUE
Y( JY ) = Y( JY ) + ALPHA*TEMP2
JX = JX + INCX
JY = JY + INCY
120 CONTINUE
END IF
END IF
#
RETURN
#
# End of ZHBMV .
#
END