Source module last modified on Thu, 2 Jul 1998, 23:17;
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for2html on Sun, 23 Jun 2002, 15:10.
SUBROUTINE ZHER2K( UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA,
$ C, LDC )
# .. Scalar Arguments ..
CHARACTER TRANS, UPLO
INTEGER K, LDA, LDB, LDC, N
DOUBLE PRECISION BETA
COMPLEX*16 ALPHA
# ..
# .. Array Arguments ..
COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * )
# ..
#
# Purpose
# =======
#
# ZHER2K performs one of the hermitian rank 2k operations
#
# C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C,
#
# or
#
# C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C,
#
# where alpha and beta are scalars with beta real, C is an n by n
# hermitian matrix and A and B are n by k matrices in the first case
# and k by n matrices 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( B' ) +
# conjg( alpha )*B*conjg( A' ) +
# beta*C.
#
# TRANS = 'C' or 'c' C := alpha*conjg( A' )*B +
# conjg( alpha )*conjg( B' )*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 matrices A and B, and on entry with
# TRANS = 'C' or 'c', K specifies the number of rows of the
# matrices A and B. K must be at least zero.
# Unchanged on exit.
#
# ALPHA - COMPLEX*16 .
# On entry, ALPHA specifies the scalar alpha.
# Unchanged on exit.
#
# A - COMPLEX*16 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.
#
# B - COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb 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 B must contain the matrix B, otherwise
# the leading k 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. When TRANS = 'N' or 'n'
# then LDB must be at least max( 1, n ), otherwise LDB must
# be at least max( 1, k ).
# Unchanged on exit.
#
# BETA - DOUBLE PRECISION .
# On entry, BETA specifies the scalar beta.
# Unchanged on exit.
#
# C - COMPLEX*16 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 DBLE( C(J,J) ) when BETA = 1.
# Ed Anderson, Cray Research Inc.
#
#
# .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
# ..
# .. External Subroutines ..
EXTERNAL XERBLA
# ..
# .. Intrinsic Functions ..
INTRINSIC DBLE, DCONJG, MAX
# ..
# .. Local Scalars ..
LOGICAL UPPER
INTEGER I, INFO, J, L, NROWA
COMPLEX*16 TEMP1, TEMP2
# ..
# .. Parameters ..
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D+0 )
COMPLEX*16 ZERO
PARAMETER ( ZERO = ( 0.0D+0, 0.0D+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( LDB<MAX( 1, NROWA ) ) THEN
INFO = 9
ELSE IF( LDC<MAX( 1, N ) ) THEN
INFO = 12
END IF
IF( INFO!=0 ) THEN
CALL XERBLA( 'ZHER2K', 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==DBLE( 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*DBLE( C( J, J ) )
40 CONTINUE
END IF
ELSE
IF( BETA==DBLE( 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*DBLE( 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( B' ) + conjg( alpha )*B*conjg( A' ) +
# C.
#
IF( UPPER ) THEN
DO 130 J = 1, N
IF( BETA==DBLE( 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*DBLE( C( J, J ) )
ELSE
C( J, J ) = DBLE( C( J, J ) )
END IF
DO 120 L = 1, K
IF( ( A( J, L )!=ZERO ) || ( B( J, L )!=ZERO ) )
$ THEN
TEMP1 = ALPHA*DCONJG( B( J, L ) )
TEMP2 = DCONJG( ALPHA*A( J, L ) )
DO 110 I = 1, J - 1
C( I, J ) = C( I, J ) + A( I, L )*TEMP1 +
$ B( I, L )*TEMP2
110 CONTINUE
C( J, J ) = DBLE( C( J, J ) ) +
$ DBLE( A( J, L )*TEMP1+B( J, L )*TEMP2 )
END IF
120 CONTINUE
130 CONTINUE
ELSE
DO 180 J = 1, N
IF( BETA==DBLE( ZERO ) ) THEN
DO 140 I = J, N
C( I, J ) = ZERO
140 CONTINUE
ELSE IF( BETA!=ONE ) THEN
DO 150 I = J + 1, N
C( I, J ) = BETA*C( I, J )
150 CONTINUE
C( J, J ) = BETA*DBLE( C( J, J ) )
ELSE
C( J, J ) = DBLE( C( J, J ) )
END IF
DO 170 L = 1, K
IF( ( A( J, L )!=ZERO ) || ( B( J, L )!=ZERO ) )
$ THEN
TEMP1 = ALPHA*DCONJG( B( J, L ) )
TEMP2 = DCONJG( ALPHA*A( J, L ) )
DO 160 I = J + 1, N
C( I, J ) = C( I, J ) + A( I, L )*TEMP1 +
$ B( I, L )*TEMP2
160 CONTINUE
C( J, J ) = DBLE( C( J, J ) ) +
$ DBLE( A( J, L )*TEMP1+B( J, L )*TEMP2 )
END IF
170 CONTINUE
180 CONTINUE
END IF
ELSE
#
# Form C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A +
# C.
#
IF( UPPER ) THEN
DO 210 J = 1, N
DO 200 I = 1, J
TEMP1 = ZERO
TEMP2 = ZERO
DO 190 L = 1, K
TEMP1 = TEMP1 + DCONJG( A( L, I ) )*B( L, J )
TEMP2 = TEMP2 + DCONJG( B( L, I ) )*A( L, J )
190 CONTINUE
IF( I==J ) THEN
IF( BETA==DBLE( ZERO ) ) THEN
C( J, J ) = DBLE( ALPHA*TEMP1+DCONJG( ALPHA )*
$ TEMP2 )
ELSE
C( J, J ) = BETA*DBLE( C( J, J ) ) +
$ DBLE( ALPHA*TEMP1+DCONJG( ALPHA )*
$ TEMP2 )
END IF
ELSE
IF( BETA==DBLE( ZERO ) ) THEN
C( I, J ) = ALPHA*TEMP1 + DCONJG( ALPHA )*TEMP2
ELSE
C( I, J ) = BETA*C( I, J ) + ALPHA*TEMP1 +
$ DCONJG( ALPHA )*TEMP2
END IF
END IF
200 CONTINUE
210 CONTINUE
ELSE
DO 240 J = 1, N
DO 230 I = J, N
TEMP1 = ZERO
TEMP2 = ZERO
DO 220 L = 1, K
TEMP1 = TEMP1 + DCONJG( A( L, I ) )*B( L, J )
TEMP2 = TEMP2 + DCONJG( B( L, I ) )*A( L, J )
220 CONTINUE
IF( I==J ) THEN
IF( BETA==DBLE( ZERO ) ) THEN
C( J, J ) = DBLE( ALPHA*TEMP1+DCONJG( ALPHA )*
$ TEMP2 )
ELSE
C( J, J ) = BETA*DBLE( C( J, J ) ) +
$ DBLE( ALPHA*TEMP1+DCONJG( ALPHA )*
$ TEMP2 )
END IF
ELSE
IF( BETA==DBLE( ZERO ) ) THEN
C( I, J ) = ALPHA*TEMP1 + DCONJG( ALPHA )*TEMP2
ELSE
C( I, J ) = BETA*C( I, J ) + ALPHA*TEMP1 +
$ DCONJG( ALPHA )*TEMP2
END IF
END IF
230 CONTINUE
240 CONTINUE
END IF
END IF
#
RETURN
#
# End of ZHER2K.
#
END