Source module last modified on Thu, 2 Jul 1998, 23:17;
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SUBROUTINE CHER ( UPLO, N, ALPHA, X, INCX, A, LDA )
# .. Scalar Arguments ..
REAL ALPHA
INTEGER INCX, LDA, N
CHARACTER*1 UPLO
# .. Array Arguments ..
COMPLEX A( LDA, * ), X( * )
# ..
#
# Purpose
# =======
#
# CHER performs the hermitian rank 1 operation
#
# A := alpha*x*conjg( x' ) + A,
#
# where alpha is a real scalar, x is an n element vector and A is an
# n by n hermitian matrix.
#
# Parameters
# ==========
#
# UPLO - CHARACTER*1.
# On entry, UPLO specifies whether the upper or lower
# triangular part of the array A is to be referenced as
# follows:
#
# UPLO = 'U' or 'u' Only the upper triangular part of A
# is to be referenced.
#
# UPLO = 'L' or 'l' Only the lower triangular part of A
# is to be referenced.
#
# Unchanged on exit.
#
# N - INTEGER.
# On entry, N specifies the order of the matrix A.
# N must be at least zero.
# Unchanged on exit.
#
# ALPHA - REAL .
# On entry, ALPHA specifies the scalar alpha.
# Unchanged on exit.
#
# X - COMPLEX array of dimension at least
# ( 1 + ( n - 1 )*abs( INCX ) ).
# Before entry, the incremented array X must contain the n
# element 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.
#
# A - COMPLEX array of DIMENSION ( LDA, n ).
# Before entry with UPLO = 'U' or 'u', the leading n by n
# upper triangular part of the array A must contain the upper
# triangular part of the hermitian matrix and the strictly
# lower triangular part of A is not referenced. On exit, the
# upper triangular part of the array A 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 A must contain the lower
# triangular part of the hermitian matrix and the strictly
# upper triangular part of A is not referenced. On exit, the
# lower triangular part of the array A 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.
#
# LDA - INTEGER.
# On entry, LDA specifies the first dimension of A as declared
# in the calling (sub) program. LDA must be at least
# max( 1, n ).
# 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 ZERO
PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) )
# .. Local Scalars ..
COMPLEX TEMP
INTEGER I, INFO, IX, J, JX, KX
# .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
# .. External Subroutines ..
EXTERNAL XERBLA
# .. Intrinsic Functions ..
INTRINSIC CONJG, MAX, REAL
# ..
# .. 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( INCX==0 )THEN
INFO = 5
ELSE IF( LDA<MAX( 1, N ) )THEN
INFO = 7
END IF
IF( INFO!=0 )THEN
CALL XERBLA( 'CHER ', INFO )
RETURN
END IF
#
# Quick return if possible.
#
IF( ( N==0 )||( ALPHA==REAL( ZERO ) ) )
$ RETURN
#
# Set the start point in X if the increment is not unity.
#
IF( INCX<=0 )THEN
KX = 1 - ( N - 1 )*INCX
ELSE IF( INCX!=1 )THEN
KX = 1
END IF
#
# Start the operations. In this version the elements of A are
# accessed sequentially with one pass through the triangular part
# of A.
#
IF( LSAME( UPLO, 'U' ) )THEN
#
# Form A when A is stored in upper triangle.
#
IF( INCX==1 )THEN
DO 20, J = 1, N
IF( X( J )!=ZERO )THEN
TEMP = ALPHA*CONJG( X( J ) )
DO 10, I = 1, J - 1
A( I, J ) = A( I, J ) + X( I )*TEMP
10 CONTINUE
A( J, J ) = REAL( A( J, J ) ) + REAL( X( J )*TEMP )
ELSE
A( J, J ) = REAL( A( J, J ) )
END IF
20 CONTINUE
ELSE
JX = KX
DO 40, J = 1, N
IF( X( JX )!=ZERO )THEN
TEMP = ALPHA*CONJG( X( JX ) )
IX = KX
DO 30, I = 1, J - 1
A( I, J ) = A( I, J ) + X( IX )*TEMP
IX = IX + INCX
30 CONTINUE
A( J, J ) = REAL( A( J, J ) ) + REAL( X( JX )*TEMP )
ELSE
A( J, J ) = REAL( A( J, J ) )
END IF
JX = JX + INCX
40 CONTINUE
END IF
ELSE
#
# Form A when A is stored in lower triangle.
#
IF( INCX==1 )THEN
DO 60, J = 1, N
IF( X( J )!=ZERO )THEN
TEMP = ALPHA*CONJG( X( J ) )
A( J, J ) = REAL( A( J, J ) ) + REAL( TEMP*X( J ) )
DO 50, I = J + 1, N
A( I, J ) = A( I, J ) + X( I )*TEMP
50 CONTINUE
ELSE
A( J, J ) = REAL( A( J, J ) )
END IF
60 CONTINUE
ELSE
JX = KX
DO 80, J = 1, N
IF( X( JX )!=ZERO )THEN
TEMP = ALPHA*CONJG( X( JX ) )
A( J, J ) = REAL( A( J, J ) ) + REAL( TEMP*X( JX ) )
IX = JX
DO 70, I = J + 1, N
IX = IX + INCX
A( I, J ) = A( I, J ) + X( IX )*TEMP
70 CONTINUE
ELSE
A( J, J ) = REAL( A( J, J ) )
END IF
JX = JX + INCX
80 CONTINUE
END IF
END IF
#
RETURN
#
# End of CHER .
#
END