*DECK DTPSV
SUBROUTINE DTPSV (UPLO, TRANS, DIAG, N, AP, X, INCX)
C***BEGIN PROLOGUE DTPSV
C***PURPOSE Solve one of the systems of equations.
C***LIBRARY SLATEC (BLAS)
C***CATEGORY D1B4
C***TYPE DOUBLE PRECISION (STPSV-S, DTPSV-D, CTPSV-C)
C***KEYWORDS LEVEL 2 BLAS, LINEAR ALGEBRA
C***AUTHOR Dongarra, J. J., (ANL)
C Du Croz, J., (NAG)
C Hammarling, S., (NAG)
C Hanson, R. J., (SNLA)
C***DESCRIPTION
C
C DTPSV solves one of the systems of equations
C
C A*x = b, or A'*x = b,
C
C where b and x are n element vectors and A is an n by n unit, or
C non-unit, upper or lower triangular matrix, supplied in packed form.
C
C No test for singularity or near-singularity is included in this
C routine. Such tests must be performed before calling this routine.
C
C Parameters
C ==========
C
C UPLO - CHARACTER*1.
C On entry, UPLO specifies whether the matrix is an upper or
C lower triangular matrix as follows:
C
C UPLO = 'U' or 'u' A is an upper triangular matrix.
C
C UPLO = 'L' or 'l' A is a lower triangular matrix.
C
C Unchanged on exit.
C
C TRANS - CHARACTER*1.
C On entry, TRANS specifies the equations to be solved as
C follows:
C
C TRANS = 'N' or 'n' A*x = b.
C
C TRANS = 'T' or 't' A'*x = b.
C
C TRANS = 'C' or 'c' A'*x = b.
C
C Unchanged on exit.
C
C DIAG - CHARACTER*1.
C On entry, DIAG specifies whether or not A is unit
C triangular as follows:
C
C DIAG = 'U' or 'u' A is assumed to be unit triangular.
C
C DIAG = 'N' or 'n' A is not assumed to be unit
C triangular.
C
C Unchanged on exit.
C
C N - INTEGER.
C On entry, N specifies the order of the matrix A.
C N must be at least zero.
C Unchanged on exit.
C
C AP - DOUBLE PRECISION array of DIMENSION at least
C ( ( n*( n + 1))/2).
C Before entry with UPLO = 'U' or 'u', the array AP must
C contain the upper triangular matrix packed sequentially,
C column by column, so that AP( 1 ) contains a( 1, 1 ),
C AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
C respectively, and so on.
C Before entry with UPLO = 'L' or 'l', the array AP must
C contain the lower triangular matrix packed sequentially,
C column by column, so that AP( 1 ) contains a( 1, 1 ),
C AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
C respectively, and so on.
C Note that when DIAG = 'U' or 'u', the diagonal elements of
C A are not referenced, but are assumed to be unity.
C Unchanged on exit.
C
C X - DOUBLE PRECISION array of dimension at least
C ( 1 + ( n - 1 )*abs( INCX ) ).
C Before entry, the incremented array X must contain the n
C element right-hand side vector b. On exit, X is overwritten
C with the solution vector x.
C
C INCX - INTEGER.
C On entry, INCX specifies the increment for the elements of
C X. INCX must not be zero.
C Unchanged on exit.
C
C***REFERENCES Dongarra, J. J., Du Croz, J., Hammarling, S., and
C Hanson, R. J. An extended set of Fortran basic linear
C algebra subprograms. ACM TOMS, Vol. 14, No. 1,
C pp. 1-17, March 1988.
C***ROUTINES CALLED LSAME, XERBLA
C***REVISION HISTORY (YYMMDD)
C 861022 DATE WRITTEN
C 910605 Modified to meet SLATEC prologue standards. Only comment
C lines were modified. (BKS)
C***END PROLOGUE DTPSV
C .. Scalar Arguments ..
INTEGER INCX, N
CHARACTER*1 DIAG, TRANS, UPLO
C .. Array Arguments ..
DOUBLE PRECISION AP( * ), X( * )
C .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
C .. Local Scalars ..
DOUBLE PRECISION TEMP
INTEGER I, INFO, IX, J, JX, K, KK, KX
LOGICAL NOUNIT
C .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
C .. External Subroutines ..
EXTERNAL XERBLA
C***FIRST EXECUTABLE STATEMENT DTPSV
C
C Test the input parameters.
C
INFO = 0
IF ( .NOT.LSAME( UPLO , 'U' ).AND.
$ .NOT.LSAME( UPLO , 'L' ) )THEN
INFO = 1
ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND.
$ .NOT.LSAME( TRANS, 'T' ).AND.
$ .NOT.LSAME( TRANS, 'C' ) )THEN
INFO = 2
ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND.
$ .NOT.LSAME( DIAG , 'N' ) )THEN
INFO = 3
ELSE IF( N.LT.0 )THEN
INFO = 4
ELSE IF( INCX.EQ.0 )THEN
INFO = 7
END IF
IF( INFO.NE.0 )THEN
CALL XERBLA( 'DTPSV ', INFO )
RETURN
END IF
C
C Quick return if possible.
C
IF( N.EQ.0 )
$ RETURN
C
NOUNIT = LSAME( DIAG, 'N' )
C
C Set up the start point in X if the increment is not unity. This
C will be ( N - 1 )*INCX too small for descending loops.
C
IF( INCX.LE.0 )THEN
KX = 1 - ( N - 1 )*INCX
ELSE IF( INCX.NE.1 )THEN
KX = 1
END IF
C
C Start the operations. In this version the elements of AP are
C accessed sequentially with one pass through AP.
C
IF( LSAME( TRANS, 'N' ) )THEN
C
C Form x := inv( A )*x.
C
IF( LSAME( UPLO, 'U' ) )THEN
KK = ( N*( N + 1 ) )/2
IF( INCX.EQ.1 )THEN
DO 20, J = N, 1, -1
IF( X( J ).NE.ZERO )THEN
IF( NOUNIT )
$ X( J ) = X( J )/AP( KK )
TEMP = X( J )
K = KK - 1
DO 10, I = J - 1, 1, -1
X( I ) = X( I ) - TEMP*AP( K )
K = K - 1
10 CONTINUE
END IF
KK = KK - J
20 CONTINUE
ELSE
JX = KX + ( N - 1 )*INCX
DO 40, J = N, 1, -1
IF( X( JX ).NE.ZERO )THEN
IF( NOUNIT )
$ X( JX ) = X( JX )/AP( KK )
TEMP = X( JX )
IX = JX
DO 30, K = KK - 1, KK - J + 1, -1
IX = IX - INCX
X( IX ) = X( IX ) - TEMP*AP( K )
30 CONTINUE
END IF
JX = JX - INCX
KK = KK - J
40 CONTINUE
END IF
ELSE
KK = 1
IF( INCX.EQ.1 )THEN
DO 60, J = 1, N
IF( X( J ).NE.ZERO )THEN
IF( NOUNIT )
$ X( J ) = X( J )/AP( KK )
TEMP = X( J )
K = KK + 1
DO 50, I = J + 1, N
X( I ) = X( I ) - TEMP*AP( K )
K = K + 1
50 CONTINUE
END IF
KK = KK + ( N - J + 1 )
60 CONTINUE
ELSE
JX = KX
DO 80, J = 1, N
IF( X( JX ).NE.ZERO )THEN
IF( NOUNIT )
$ X( JX ) = X( JX )/AP( KK )
TEMP = X( JX )
IX = JX
DO 70, K = KK + 1, KK + N - J
IX = IX + INCX
X( IX ) = X( IX ) - TEMP*AP( K )
70 CONTINUE
END IF
JX = JX + INCX
KK = KK + ( N - J + 1 )
80 CONTINUE
END IF
END IF
ELSE
C
C Form x := inv( A' )*x.
C
IF( LSAME( UPLO, 'U' ) )THEN
KK = 1
IF( INCX.EQ.1 )THEN
DO 100, J = 1, N
TEMP = X( J )
K = KK
DO 90, I = 1, J - 1
TEMP = TEMP - AP( K )*X( I )
K = K + 1
90 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/AP( KK + J - 1 )
X( J ) = TEMP
KK = KK + J
100 CONTINUE
ELSE
JX = KX
DO 120, J = 1, N
TEMP = X( JX )
IX = KX
DO 110, K = KK, KK + J - 2
TEMP = TEMP - AP( K )*X( IX )
IX = IX + INCX
110 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/AP( KK + J - 1 )
X( JX ) = TEMP
JX = JX + INCX
KK = KK + J
120 CONTINUE
END IF
ELSE
KK = ( N*( N + 1 ) )/2
IF( INCX.EQ.1 )THEN
DO 140, J = N, 1, -1
TEMP = X( J )
K = KK
DO 130, I = N, J + 1, -1
TEMP = TEMP - AP( K )*X( I )
K = K - 1
130 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/AP( KK - N + J )
X( J ) = TEMP
KK = KK - ( N - J + 1 )
140 CONTINUE
ELSE
KX = KX + ( N - 1 )*INCX
JX = KX
DO 160, J = N, 1, -1
TEMP = X( JX )
IX = KX
DO 150, K = KK, KK - ( N - ( J + 1 ) ), -1
TEMP = TEMP - AP( K )*X( IX )
IX = IX - INCX
150 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/AP( KK - N + J )
X( JX ) = TEMP
JX = JX - INCX
KK = KK - (N - J + 1 )
160 CONTINUE
END IF
END IF
END IF
C
RETURN
C
C End of DTPSV .
C
END