Source module last modified on Thu, 2 Jul 1998, 23:17;
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SUBROUTINE DTPMV ( UPLO, TRANS, DIAG, N, AP, X, INCX )
# .. Scalar Arguments ..
INTEGER INCX, N
CHARACTER*1 DIAG, TRANS, UPLO
# .. Array Arguments ..
DOUBLE PRECISION AP( * ), X( * )
# ..
#
# Purpose
# =======
#
# DTPMV performs one of the matrix-vector operations
#
# x := A*x, or x := A'*x,
#
# where x is an n element vector and A is an n by n unit, or non-unit,
# upper or lower triangular matrix, supplied in packed form.
#
# 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 operation to be performed as
# follows:
#
# TRANS = 'N' or 'n' x := A*x.
#
# TRANS = 'T' or 't' x := A'*x.
#
# TRANS = 'C' or 'c' x := A'*x.
#
# 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.
#
# AP - DOUBLE PRECISION array of DIMENSION at least
# ( ( n*( n + 1 ) )/2 ).
# Before entry with UPLO = 'U' or 'u', the array AP must
# contain the upper triangular matrix packed sequentially,
# column by column, so that AP( 1 ) contains a( 1, 1 ),
# AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
# respectively, and so on.
# Before entry with UPLO = 'L' or 'l', the array AP must
# contain the lower triangular matrix packed sequentially,
# column by column, so that AP( 1 ) contains a( 1, 1 ),
# AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
# respectively, and so on.
# Note that when DIAG = 'U' or 'u', the diagonal elements of
# A are not referenced, but are assumed to be unity.
# Unchanged on exit.
#
# X - DOUBLE PRECISION array of dimension at least
# ( 1 + ( n - 1 )*abs( INCX ) ).
# Before entry, the incremented array X must contain the n
# element vector x. On exit, X is overwritten with the
# tranformed 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 ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
# .. Local Scalars ..
DOUBLE PRECISION TEMP
INTEGER I, INFO, IX, J, JX, K, KK, KX
LOGICAL NOUNIT
# .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
# .. External Subroutines ..
EXTERNAL XERBLA
# ..
# .. 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( INCX==0 )THEN
INFO = 7
END IF
IF( INFO!=0 )THEN
CALL XERBLA( 'DTPMV ', INFO )
RETURN
END IF
#
# Quick return if possible.
#
IF( N==0 )
$ RETURN
#
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 AP are
# accessed sequentially with one pass through AP.
#
IF( LSAME( TRANS, 'N' ) )THEN
#
# Form x:= A*x.
#
IF( LSAME( UPLO, 'U' ) )THEN
KK =1
IF( INCX==1 )THEN
DO 20, J = 1, N
IF( X( J )!=ZERO )THEN
TEMP = X( J )
K = KK
DO 10, I = 1, J - 1
X( I ) = X( I ) + TEMP*AP( K )
K = K + 1
10 CONTINUE
IF( NOUNIT )
$ X( J ) = X( J )*AP( KK + J - 1 )
END IF
KK = KK + J
20 CONTINUE
ELSE
JX = KX
DO 40, J = 1, N
IF( X( JX )!=ZERO )THEN
TEMP = X( JX )
IX = KX
DO 30, K = KK, KK + J - 2
X( IX ) = X( IX ) + TEMP*AP( K )
IX = IX + INCX
30 CONTINUE
IF( NOUNIT )
$ X( JX ) = X( JX )*AP( KK + J - 1 )
END IF
JX = JX + INCX
KK = KK + J
40 CONTINUE
END IF
ELSE
KK = ( N*( N + 1 ) )/2
IF( INCX==1 )THEN
DO 60, J = N, 1, -1
IF( X( J )!=ZERO )THEN
TEMP = X( J )
K = KK
DO 50, I = N, J + 1, -1
X( I ) = X( I ) + TEMP*AP( K )
K = K - 1
50 CONTINUE
IF( NOUNIT )
$ X( J ) = X( J )*AP( KK - N + J )
END IF
KK = KK - ( N - J + 1 )
60 CONTINUE
ELSE
KX = KX + ( N - 1 )*INCX
JX = KX
DO 80, J = N, 1, -1
IF( X( JX )!=ZERO )THEN
TEMP = X( JX )
IX = KX
DO 70, K = KK, KK - ( N - ( J + 1 ) ), -1
X( IX ) = X( IX ) + TEMP*AP( K )
IX = IX - INCX
70 CONTINUE
IF( NOUNIT )
$ X( JX ) = X( JX )*AP( KK - N + J )
END IF
JX = JX - INCX
KK = KK - ( N - J + 1 )
80 CONTINUE
END IF
END IF
ELSE
#
# Form x := A'*x.
#
IF( LSAME( UPLO, 'U' ) )THEN
KK = ( N*( N + 1 ) )/2
IF( INCX==1 )THEN
DO 100, J = N, 1, -1
TEMP = X( J )
IF( NOUNIT )
$ TEMP = TEMP*AP( KK )
K = KK - 1
DO 90, I = J - 1, 1, -1
TEMP = TEMP + AP( K )*X( I )
K = K - 1
90 CONTINUE
X( J ) = TEMP
KK = KK - J
100 CONTINUE
ELSE
JX = KX + ( N - 1 )*INCX
DO 120, J = N, 1, -1
TEMP = X( JX )
IX = JX
IF( NOUNIT )
$ TEMP = TEMP*AP( KK )
DO 110, K = KK - 1, KK - J + 1, -1
IX = IX - INCX
TEMP = TEMP + AP( K )*X( IX )
110 CONTINUE
X( JX ) = TEMP
JX = JX - INCX
KK = KK - J
120 CONTINUE
END IF
ELSE
KK = 1
IF( INCX==1 )THEN
DO 140, J = 1, N
TEMP = X( J )
IF( NOUNIT )
$ TEMP = TEMP*AP( KK )
K = KK + 1
DO 130, I = J + 1, N
TEMP = TEMP + AP( K )*X( I )
K = K + 1
130 CONTINUE
X( J ) = TEMP
KK = KK + ( N - J + 1 )
140 CONTINUE
ELSE
JX = KX
DO 160, J = 1, N
TEMP = X( JX )
IX = JX
IF( NOUNIT )
$ TEMP = TEMP*AP( KK )
DO 150, K = KK + 1, KK + N - J
IX = IX + INCX
TEMP = TEMP + AP( K )*X( IX )
150 CONTINUE
X( JX ) = TEMP
JX = JX + INCX
KK = KK + ( N - J + 1 )
160 CONTINUE
END IF
END IF
END IF
#
RETURN
#
# End of DTPMV .
#
END