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 CHERK ( UPLO, TRANS, N, K, ALPHA, A, LDA,
$ BETA, C, LDC )
# .. Scalar Arguments ..
CHARACTER*1 UPLO, TRANS
INTEGER N, K, LDA, LDC
REAL ALPHA, BETA
# .. Array Arguments ..
COMPLEX A( LDA, * ), C( LDC, * )
# ..
#
# Purpose
# =======
#
# CHERK performs one of the hermitian rank k operations
#
# C := alpha*A*conjg( A' ) + beta*C,
#
# or
#
# C := alpha*conjg( A' )*A + beta*C,
#
# where alpha and beta are real scalars, C is an n by n hermitian
# matrix and A is an n by k matrix in the first case and a k by n
# matrix in the second case.
#
# Parameters
# ==========
#
# UPLO - CHARACTER*1.
# On entry, UPLO specifies whether the upper or lower
# triangular part of the array C is to be referenced as
# follows:
#
# UPLO = 'U' or 'u' Only the upper triangular part of C
# is to be referenced.
#
# UPLO = 'L' or 'l' Only the lower triangular part of C
# is to be referenced.
#
# Unchanged on exit.
#
# TRANS - CHARACTER*1.
# On entry, TRANS specifies the operation to be performed as
# follows:
#
# TRANS = 'N' or 'n' C := alpha*A*conjg( A' ) + beta*C.
#
# TRANS = 'C' or 'c' C := alpha*conjg( A' )*A + beta*C.
#
# Unchanged on exit.
#
# N - INTEGER.
# On entry, N specifies the order of the matrix C. N must be
# at least zero.
# Unchanged on exit.
#
# K - INTEGER.
# On entry with TRANS = 'N' or 'n', K specifies the number
# of columns of the matrix A, and on entry with
# TRANS = 'C' or 'c', K specifies the number of rows of the
# matrix A. K must be at least zero.
# Unchanged on exit.
#
# ALPHA - REAL .
# On entry, ALPHA specifies the scalar alpha.
# Unchanged on exit.
#
# A - COMPLEX array of DIMENSION ( LDA, ka ), where ka is
# k when TRANS = 'N' or 'n', and is n otherwise.
# Before entry with TRANS = 'N' or 'n', the leading n by k
# part of the array A must contain the matrix A, otherwise
# the leading k by n part of the array A must contain the
# matrix A.
# Unchanged on exit.
#
# LDA - INTEGER.
# On entry, LDA specifies the first dimension of A as declared
# in the calling (sub) program. When TRANS = 'N' or 'n'
# then LDA must be at least max( 1, n ), otherwise LDA must
# be at least max( 1, k ).
# Unchanged on exit.
#
# BETA - REAL .
# On entry, BETA specifies the scalar beta.
# Unchanged on exit.
#
# C - COMPLEX array of DIMENSION ( LDC, n ).
# Before entry with UPLO = 'U' or 'u', the leading n by n
# upper triangular part of the array C must contain the upper
# triangular part of the hermitian matrix and the strictly
# lower triangular part of C is not referenced. On exit, the
# upper triangular part of the array C is overwritten by the
# upper triangular part of the updated matrix.
# Before entry with UPLO = 'L' or 'l', the leading n by n
# lower triangular part of the array C must contain the lower
# triangular part of the hermitian matrix and the strictly
# upper triangular part of C is not referenced. On exit, the
# lower triangular part of the array C is overwritten by the
# lower triangular part of the updated matrix.
# Note that the imaginary parts of the diagonal elements need
# not be set, they are assumed to be zero, and on exit they
# are set to zero.
#
# 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, n ).
# 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.
#
# -- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1.
# Ed Anderson, Cray Research Inc.
#
#
# .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
# .. External Subroutines ..
EXTERNAL XERBLA
# .. Intrinsic Functions ..
INTRINSIC CMPLX, CONJG, MAX, REAL
# .. Local Scalars ..
LOGICAL UPPER
INTEGER I, INFO, J, L, NROWA
REAL RTEMP
COMPLEX TEMP
# .. Parameters ..
REAL ONE , ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
# ..
# .. Executable Statements ..
#
# Test the input parameters.
#
IF( LSAME( TRANS, 'N' ) )THEN
NROWA = N
ELSE
NROWA = K
END IF
UPPER = LSAME( UPLO, 'U' )
#
INFO = 0
IF( ( ! UPPER )&&
$ ( ! LSAME( UPLO , 'L' ) ) )THEN
INFO = 1
ELSE IF( ( ! LSAME( TRANS, 'N' ) )&&
$ ( ! LSAME( TRANS, 'C' ) ) )THEN
INFO = 2
ELSE IF( N <0 )THEN
INFO = 3
ELSE IF( K <0 )THEN
INFO = 4
ELSE IF( LDA<MAX( 1, NROWA ) )THEN
INFO = 7
ELSE IF( LDC<MAX( 1, N ) )THEN
INFO = 10
END IF
IF( INFO!=0 )THEN
CALL XERBLA( 'CHERK ', INFO )
RETURN
END IF
#
# Quick return if possible.
#
IF( ( N==0 )||
$ ( ( ( ALPHA==ZERO )||( K==0 ) )&&( BETA==ONE ) ) )
$ RETURN
#
# And when alpha.eq.zero.
#
IF( ALPHA==ZERO )THEN
IF( UPPER )THEN
IF( BETA==ZERO )THEN
DO 20, J = 1, N
DO 10, I = 1, J
C( I, J ) = ZERO
10 CONTINUE
20 CONTINUE
ELSE
DO 40, J = 1, N
DO 30, I = 1, J - 1
C( I, J ) = BETA*C( I, J )
30 CONTINUE
C( J, J ) = BETA*REAL( C( J, J ) )
40 CONTINUE
END IF
ELSE
IF( BETA==ZERO )THEN
DO 60, J = 1, N
DO 50, I = J, N
C( I, J ) = ZERO
50 CONTINUE
60 CONTINUE
ELSE
DO 80, J = 1, N
C( J, J ) = BETA*REAL( C( J, J ) )
DO 70, I = J + 1, N
C( I, J ) = BETA*C( I, J )
70 CONTINUE
80 CONTINUE
END IF
END IF
RETURN
END IF
#
# Start the operations.
#
IF( LSAME( TRANS, 'N' ) )THEN
#
# Form C := alpha*A*conjg( A' ) + beta*C.
#
IF( UPPER )THEN
DO 130, J = 1, N
IF( BETA==ZERO )THEN
DO 90, I = 1, J
C( I, J ) = ZERO
90 CONTINUE
ELSE IF( BETA!=ONE )THEN
DO 100, I = 1, J - 1
C( I, J ) = BETA*C( I, J )
100 CONTINUE
C( J, J ) = BETA*REAL( C( J, J ) )
ELSE
C( J, J ) = REAL( C( J, J ) )
END IF
DO 120, L = 1, K
IF( A( J, L )!=CMPLX( ZERO ) )THEN
TEMP = ALPHA*CONJG( A( J, L ) )
DO 110, I = 1, J - 1
C( I, J ) = C( I, J ) + TEMP*A( I, L )
110 CONTINUE
C( J, J ) = REAL( C( J, J ) ) +
$ REAL( TEMP*A( I, L ) )
END IF
120 CONTINUE
130 CONTINUE
ELSE
DO 180, J = 1, N
IF( BETA==ZERO )THEN
DO 140, I = J, N
C( I, J ) = ZERO
140 CONTINUE
ELSE IF( BETA!=ONE )THEN
C( J, J ) = BETA*REAL( C( J, J ) )
DO 150, I = J + 1, N
C( I, J ) = BETA*C( I, J )
150 CONTINUE
ELSE
C( J, J ) = REAL( C( J, J ) )
END IF
DO 170, L = 1, K
IF( A( J, L )!=CMPLX( ZERO ) )THEN
TEMP = ALPHA*CONJG( A( J, L ) )
C( J, J ) = REAL( C( J, J ) ) +
$ REAL( TEMP*A( J, L ) )
DO 160, I = J + 1, N
C( I, J ) = C( I, J ) + TEMP*A( I, L )
160 CONTINUE
END IF
170 CONTINUE
180 CONTINUE
END IF
ELSE
#
# Form C := alpha*conjg( A' )*A + beta*C.
#
IF( UPPER )THEN
DO 220, J = 1, N
DO 200, I = 1, J - 1
TEMP = ZERO
DO 190, L = 1, K
TEMP = TEMP + CONJG( A( L, I ) )*A( L, J )
190 CONTINUE
IF( BETA==ZERO )THEN
C( I, J ) = ALPHA*TEMP
ELSE
C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
END IF
200 CONTINUE
RTEMP = ZERO
DO 210, L = 1, K
RTEMP = RTEMP + CONJG( A( L, J ) )*A( L, J )
210 CONTINUE
IF( BETA==ZERO )THEN
C( J, J ) = ALPHA*RTEMP
ELSE
C( J, J ) = ALPHA*RTEMP + BETA*REAL( C( J, J ) )
END IF
220 CONTINUE
ELSE
DO 260, J = 1, N
RTEMP = ZERO
DO 230, L = 1, K
RTEMP = RTEMP + CONJG( A( L, J ) )*A( L, J )
230 CONTINUE
IF( BETA==ZERO )THEN
C( J, J ) = ALPHA*RTEMP
ELSE
C( J, J ) = ALPHA*RTEMP + BETA*REAL( C( J, J ) )
END IF
DO 250, I = J + 1, N
TEMP = ZERO
DO 240, L = 1, K
TEMP = TEMP + CONJG( A( L, I ) )*A( L, J )
240 CONTINUE
IF( BETA==ZERO )THEN
C( I, J ) = ALPHA*TEMP
ELSE
C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
END IF
250 CONTINUE
260 CONTINUE
END IF
END IF
#
RETURN
#
# End of CHERK .
#
END