Source module last modified on Thu, 2 Jul 1998, 23:17;
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SUBROUTINE ZTRSV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )
# .. Scalar Arguments ..
INTEGER INCX, LDA, N
CHARACTER*1 DIAG, TRANS, UPLO
# .. Array Arguments ..
COMPLEX*16 A( LDA, * ), X( * )
# ..
#
# Purpose
# =======
#
# ZTRSV solves one of the systems of equations
#
# A*x = b, or A'*x = b, or conjg( A' )*x = b,
#
# where b and x are n element vectors and A is an n by n unit, or
# non-unit, upper or lower triangular matrix.
#
# No test for singularity or near-singularity is included in this
# routine. Such tests must be performed before calling this routine.
#
# Parameters
# ==========
#
# UPLO - CHARACTER*1.
# On entry, UPLO specifies whether the matrix is an upper or
# lower triangular matrix as follows:
#
# UPLO = 'U' or 'u' A is an upper triangular matrix.
#
# UPLO = 'L' or 'l' A is a lower triangular matrix.
#
# Unchanged on exit.
#
# TRANS - CHARACTER*1.
# On entry, TRANS specifies the equations to be solved as
# follows:
#
# TRANS = 'N' or 'n' A*x = b.
#
# TRANS = 'T' or 't' A'*x = b.
#
# TRANS = 'C' or 'c' conjg( A' )*x = b.
#
# Unchanged on exit.
#
# DIAG - CHARACTER*1.
# On entry, DIAG specifies whether or not A is unit
# triangular as follows:
#
# DIAG = 'U' or 'u' A is assumed to be unit triangular.
#
# DIAG = 'N' or 'n' A is not assumed to be unit
# triangular.
#
# Unchanged on exit.
#
# N - INTEGER.
# On entry, N specifies the order of the matrix A.
# N must be at least zero.
# Unchanged on exit.
#
# A - COMPLEX*16 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 matrix and the strictly lower triangular part of
# A is not referenced.
# Before entry with UPLO = 'L' or 'l', the leading n by n
# lower triangular part of the array A must contain the lower
# triangular matrix and the strictly upper triangular part of
# A is not referenced.
# Note that when DIAG = 'U' or 'u', the diagonal elements of
# A are not referenced either, but are assumed to be unity.
# 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
# max( 1, n ).
# 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 n
# element right-hand side vector b. On exit, X is overwritten
# with the solution vector x.
#
# INCX - INTEGER.
# On entry, INCX specifies the increment for the elements of
# X. INCX 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 ZERO
PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
# .. Local Scalars ..
COMPLEX*16 TEMP
INTEGER I, INFO, IX, J, JX, KX
LOGICAL NOCONJ, NOUNIT
# .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
# .. External Subroutines ..
EXTERNAL XERBLA
# .. Intrinsic Functions ..
INTRINSIC DCONJG, MAX
# ..
# .. Executable Statements ..
#
# Test the input parameters.
#
INFO = 0
IF ( ! LSAME( UPLO , 'U' )&&
$ ! LSAME( UPLO , 'L' ) )THEN
INFO = 1
ELSE IF( ! LSAME( TRANS, 'N' )&&
$ ! LSAME( TRANS, 'T' )&&
$ ! LSAME( TRANS, 'C' ) )THEN
INFO = 2
ELSE IF( ! LSAME( DIAG , 'U' )&&
$ ! LSAME( DIAG , 'N' ) )THEN
INFO = 3
ELSE IF( N<0 )THEN
INFO = 4
ELSE IF( LDA<MAX( 1, N ) )THEN
INFO = 6
ELSE IF( INCX==0 )THEN
INFO = 8
END IF
IF( INFO!=0 )THEN
CALL XERBLA( 'ZTRSV ', INFO )
RETURN
END IF
#
# Quick return if possible.
#
IF( N==0 )
$ RETURN
#
NOCONJ = LSAME( TRANS, 'T' )
NOUNIT = LSAME( DIAG , 'N' )
#
# Set up the start point in X if the increment is not unity. This
# will be ( N - 1 )*INCX too small for descending loops.
#
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 A.
#
IF( LSAME( TRANS, 'N' ) )THEN
#
# Form x := inv( A )*x.
#
IF( LSAME( UPLO, 'U' ) )THEN
IF( INCX==1 )THEN
DO 20, J = N, 1, -1
IF( X( J )!=ZERO )THEN
IF( NOUNIT )
$ X( J ) = X( J )/A( J, J )
TEMP = X( J )
DO 10, I = J - 1, 1, -1
X( I ) = X( I ) - TEMP*A( I, J )
10 CONTINUE
END IF
20 CONTINUE
ELSE
JX = KX + ( N - 1 )*INCX
DO 40, J = N, 1, -1
IF( X( JX )!=ZERO )THEN
IF( NOUNIT )
$ X( JX ) = X( JX )/A( J, J )
TEMP = X( JX )
IX = JX
DO 30, I = J - 1, 1, -1
IX = IX - INCX
X( IX ) = X( IX ) - TEMP*A( I, J )
30 CONTINUE
END IF
JX = JX - INCX
40 CONTINUE
END IF
ELSE
IF( INCX==1 )THEN
DO 60, J = 1, N
IF( X( J )!=ZERO )THEN
IF( NOUNIT )
$ X( J ) = X( J )/A( J, J )
TEMP = X( J )
DO 50, I = J + 1, N
X( I ) = X( I ) - TEMP*A( I, J )
50 CONTINUE
END IF
60 CONTINUE
ELSE
JX = KX
DO 80, J = 1, N
IF( X( JX )!=ZERO )THEN
IF( NOUNIT )
$ X( JX ) = X( JX )/A( J, J )
TEMP = X( JX )
IX = JX
DO 70, I = J + 1, N
IX = IX + INCX
X( IX ) = X( IX ) - TEMP*A( I, J )
70 CONTINUE
END IF
JX = JX + INCX
80 CONTINUE
END IF
END IF
ELSE
#
# Form x := inv( A' )*x or x := inv( conjg( A' ) )*x.
#
IF( LSAME( UPLO, 'U' ) )THEN
IF( INCX==1 )THEN
DO 110, J = 1, N
TEMP = X( J )
IF( NOCONJ )THEN
DO 90, I = 1, J - 1
TEMP = TEMP - A( I, J )*X( I )
90 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/A( J, J )
ELSE
DO 100, I = 1, J - 1
TEMP = TEMP - DCONJG( A( I, J ) )*X( I )
100 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/DCONJG( A( J, J ) )
END IF
X( J ) = TEMP
110 CONTINUE
ELSE
JX = KX
DO 140, J = 1, N
IX = KX
TEMP = X( JX )
IF( NOCONJ )THEN
DO 120, I = 1, J - 1
TEMP = TEMP - A( I, J )*X( IX )
IX = IX + INCX
120 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/A( J, J )
ELSE
DO 130, I = 1, J - 1
TEMP = TEMP - DCONJG( A( I, J ) )*X( IX )
IX = IX + INCX
130 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/DCONJG( A( J, J ) )
END IF
X( JX ) = TEMP
JX = JX + INCX
140 CONTINUE
END IF
ELSE
IF( INCX==1 )THEN
DO 170, J = N, 1, -1
TEMP = X( J )
IF( NOCONJ )THEN
DO 150, I = N, J + 1, -1
TEMP = TEMP - A( I, J )*X( I )
150 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/A( J, J )
ELSE
DO 160, I = N, J + 1, -1
TEMP = TEMP - DCONJG( A( I, J ) )*X( I )
160 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/DCONJG( A( J, J ) )
END IF
X( J ) = TEMP
170 CONTINUE
ELSE
KX = KX + ( N - 1 )*INCX
JX = KX
DO 200, J = N, 1, -1
IX = KX
TEMP = X( JX )
IF( NOCONJ )THEN
DO 180, I = N, J + 1, -1
TEMP = TEMP - A( I, J )*X( IX )
IX = IX - INCX
180 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/A( J, J )
ELSE
DO 190, I = N, J + 1, -1
TEMP = TEMP - DCONJG( A( I, J ) )*X( IX )
IX = IX - INCX
190 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/DCONJG( A( J, J ) )
END IF
X( JX ) = TEMP
JX = JX - INCX
200 CONTINUE
END IF
END IF
END IF
#
RETURN
#
# End of ZTRSV .
#
END