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 CSYMM ( SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB,
$ BETA, C, LDC )
# .. Scalar Arguments ..
CHARACTER*1 SIDE, UPLO
INTEGER M, N, LDA, LDB, LDC
COMPLEX ALPHA, BETA
# .. Array Arguments ..
COMPLEX A( LDA, * ), B( LDB, * ), C( LDC, * )
# ..
#
# Purpose
# =======
#
# CSYMM performs one of the matrix-matrix operations
#
# C := alpha*A*B + beta*C,
#
# or
#
# C := alpha*B*A + beta*C,
#
# where alpha and beta are scalars, A is a symmetric matrix and B and
# C are m by n matrices.
#
# Parameters
# ==========
#
# SIDE - CHARACTER*1.
# On entry, SIDE specifies whether the symmetric matrix A
# appears on the left or right in the operation as follows:
#
# SIDE = 'L' or 'l' C := alpha*A*B + beta*C,
#
# SIDE = 'R' or 'r' C := alpha*B*A + beta*C,
#
# Unchanged on exit.
#
# UPLO - CHARACTER*1.
# On entry, UPLO specifies whether the upper or lower
# triangular part of the symmetric matrix A is to be
# referenced as follows:
#
# UPLO = 'U' or 'u' Only the upper triangular part of the
# symmetric matrix is to be referenced.
#
# UPLO = 'L' or 'l' Only the lower triangular part of the
# symmetric matrix is to be referenced.
#
# Unchanged on exit.
#
# M - INTEGER.
# On entry, M specifies the number of rows of the matrix C.
# M must be at least zero.
# Unchanged on exit.
#
# N - INTEGER.
# On entry, N specifies the number of columns of the matrix C.
# N must be at least zero.
# Unchanged on exit.
#
# ALPHA - COMPLEX .
# On entry, ALPHA specifies the scalar alpha.
# Unchanged on exit.
#
# A - COMPLEX array of DIMENSION ( LDA, ka ), where ka is
# m when SIDE = 'L' or 'l' and is n otherwise.
# Before entry with SIDE = 'L' or 'l', the m by m part of
# the array A must contain the symmetric matrix, such that
# when UPLO = 'U' or 'u', the leading m by m upper triangular
# part of the array A must contain the upper triangular part
# of the symmetric matrix and the strictly lower triangular
# part of A is not referenced, and when UPLO = 'L' or 'l',
# the leading m by m lower triangular part of the array A
# must contain the lower triangular part of the symmetric
# matrix and the strictly upper triangular part of A is not
# referenced.
# Before entry with SIDE = 'R' or 'r', the n by n part of
# the array A must contain the symmetric matrix, such that
# when UPLO = 'U' or 'u', the leading n by n upper triangular
# part of the array A must contain the upper triangular part
# of the symmetric matrix and the strictly lower triangular
# part of A is not referenced, and when UPLO = 'L' or 'l',
# the leading n by n lower triangular part of the array A
# must contain the lower triangular part of the symmetric
# matrix and the strictly upper triangular part of A is not
# referenced.
# Unchanged on exit.
#
# LDA - INTEGER.
# On entry, LDA specifies the first dimension of A as declared
# in the calling (sub) program. When SIDE = 'L' or 'l' then
# LDA must be at least max( 1, m ), otherwise LDA must be at
# least max( 1, n ).
# Unchanged on exit.
#
# B - COMPLEX array of DIMENSION ( LDB, n ).
# Before entry, the leading m by n part of the array B must
# contain the matrix B.
# Unchanged on exit.
#
# LDB - INTEGER.
# On entry, LDB specifies the first dimension of B as declared
# in the calling (sub) program. LDB must be at least
# max( 1, m ).
# Unchanged on exit.
#
# BETA - COMPLEX .
# On entry, BETA specifies the scalar beta. When BETA is
# supplied as zero then C need not be set on input.
# Unchanged on exit.
#
# C - COMPLEX array of DIMENSION ( LDC, n ).
# Before entry, the leading m by n part of the array C must
# contain the matrix C, except when beta is zero, in which
# case C need not be set on entry.
# On exit, the array C is overwritten by the m by n updated
# matrix.
#
# LDC - INTEGER.
# On entry, LDC specifies the first dimension of C as declared
# in the calling (sub) program. LDC must be at least
# max( 1, m ).
# Unchanged on exit.
#
#
# Level 3 Blas routine.
#
# -- Written on 8-February-1989.
# Jack Dongarra, Argonne National Laboratory.
# Iain Duff, AERE Harwell.
# Jeremy Du Croz, Numerical Algorithms Group Ltd.
# Sven Hammarling, Numerical Algorithms Group Ltd.
#
#
# .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
# .. External Subroutines ..
EXTERNAL XERBLA
# .. Intrinsic Functions ..
INTRINSIC MAX
# .. Local Scalars ..
LOGICAL UPPER
INTEGER I, INFO, J, K, NROWA
COMPLEX TEMP1, TEMP2
# .. Parameters ..
COMPLEX ONE
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) )
COMPLEX ZERO
PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) )
# ..
# .. Executable Statements ..
#
# Set NROWA as the number of rows of A.
#
IF( LSAME( SIDE, 'L' ) )THEN
NROWA = M
ELSE
NROWA = N
END IF
UPPER = LSAME( UPLO, 'U' )
#
# Test the input parameters.
#
INFO = 0
IF( ( ! LSAME( SIDE, 'L' ) )&&
$ ( ! LSAME( SIDE, 'R' ) ) )THEN
INFO = 1
ELSE IF( ( ! UPPER )&&
$ ( ! LSAME( UPLO, 'L' ) ) )THEN
INFO = 2
ELSE IF( M <0 )THEN
INFO = 3
ELSE IF( N <0 )THEN
INFO = 4
ELSE IF( LDA<MAX( 1, NROWA ) )THEN
INFO = 7
ELSE IF( LDB<MAX( 1, M ) )THEN
INFO = 9
ELSE IF( LDC<MAX( 1, M ) )THEN
INFO = 12
END IF
IF( INFO!=0 )THEN
CALL XERBLA( 'CSYMM ', INFO )
RETURN
END IF
#
# Quick return if possible.
#
IF( ( M==0 )||( N==0 )||
$ ( ( ALPHA==ZERO )&&( BETA==ONE ) ) )
$ RETURN
#
# And when alpha.eq.zero.
#
IF( ALPHA==ZERO )THEN
IF( BETA==ZERO )THEN
DO 20, J = 1, N
DO 10, I = 1, M
C( I, J ) = ZERO
10 CONTINUE
20 CONTINUE
ELSE
DO 40, J = 1, N
DO 30, I = 1, M
C( I, J ) = BETA*C( I, J )
30 CONTINUE
40 CONTINUE
END IF
RETURN
END IF
#
# Start the operations.
#
IF( LSAME( SIDE, 'L' ) )THEN
#
# Form C := alpha*A*B + beta*C.
#
IF( UPPER )THEN
DO 70, J = 1, N
DO 60, I = 1, M
TEMP1 = ALPHA*B( I, J )
TEMP2 = ZERO
DO 50, K = 1, I - 1
C( K, J ) = C( K, J ) + TEMP1 *A( K, I )
TEMP2 = TEMP2 + B( K, J )*A( K, I )
50 CONTINUE
IF( BETA==ZERO )THEN
C( I, J ) = TEMP1*A( I, I ) + ALPHA*TEMP2
ELSE
C( I, J ) = BETA *C( I, J ) +
$ TEMP1*A( I, I ) + ALPHA*TEMP2
END IF
60 CONTINUE
70 CONTINUE
ELSE
DO 100, J = 1, N
DO 90, I = M, 1, -1
TEMP1 = ALPHA*B( I, J )
TEMP2 = ZERO
DO 80, K = I + 1, M
C( K, J ) = C( K, J ) + TEMP1 *A( K, I )
TEMP2 = TEMP2 + B( K, J )*A( K, I )
80 CONTINUE
IF( BETA==ZERO )THEN
C( I, J ) = TEMP1*A( I, I ) + ALPHA*TEMP2
ELSE
C( I, J ) = BETA *C( I, J ) +
$ TEMP1*A( I, I ) + ALPHA*TEMP2
END IF
90 CONTINUE
100 CONTINUE
END IF
ELSE
#
# Form C := alpha*B*A + beta*C.
#
DO 170, J = 1, N
TEMP1 = ALPHA*A( J, J )
IF( BETA==ZERO )THEN
DO 110, I = 1, M
C( I, J ) = TEMP1*B( I, J )
110 CONTINUE
ELSE
DO 120, I = 1, M
C( I, J ) = BETA*C( I, J ) + TEMP1*B( I, J )
120 CONTINUE
END IF
DO 140, K = 1, J - 1
IF( UPPER )THEN
TEMP1 = ALPHA*A( K, J )
ELSE
TEMP1 = ALPHA*A( J, K )
END IF
DO 130, I = 1, M
C( I, J ) = C( I, J ) + TEMP1*B( I, K )
130 CONTINUE
140 CONTINUE
DO 160, K = J + 1, N
IF( UPPER )THEN
TEMP1 = ALPHA*A( J, K )
ELSE
TEMP1 = ALPHA*A( K, J )
END IF
DO 150, I = 1, M
C( I, J ) = C( I, J ) + TEMP1*B( I, K )
150 CONTINUE
160 CONTINUE
170 CONTINUE
END IF
#
RETURN
#
# End of CSYMM .
#
END