380 lines
12 KiB
Fortran
380 lines
12 KiB
Fortran
SUBROUTINE CTPSVF( UPLO, TRANS, DIAG, N, AP, X, INCX )
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* .. Scalar Arguments ..
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INTEGER INCX, N
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CHARACTER*1 DIAG, TRANS, UPLO
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* .. Array Arguments ..
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COMPLEX AP( * ), X( * )
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* ..
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*
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* Purpose
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* =======
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*
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* CTPSV solves one of the systems of equations
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*
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* A*x = b, or A'*x = b, or conjg( A' )*x = b,
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*
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* where b and x are n element vectors and A is an n by n unit, or
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* non-unit, upper or lower triangular matrix, supplied in packed form.
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*
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* No test for singularity or near-singularity is included in this
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* routine. Such tests must be performed before calling this routine.
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*
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* Parameters
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* ==========
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*
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* UPLO - CHARACTER*1.
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* On entry, UPLO specifies whether the matrix is an upper or
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* lower triangular matrix as follows:
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*
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* UPLO = 'U' or 'u' A is an upper triangular matrix.
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*
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* UPLO = 'L' or 'l' A is a lower triangular matrix.
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*
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* Unchanged on exit.
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*
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* TRANS - CHARACTER*1.
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* On entry, TRANS specifies the equations to be solved as
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* follows:
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*
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* TRANS = 'N' or 'n' A*x = b.
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*
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* TRANS = 'T' or 't' A'*x = b.
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*
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* TRANS = 'C' or 'c' conjg( A' )*x = b.
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*
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* Unchanged on exit.
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*
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* DIAG - CHARACTER*1.
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* On entry, DIAG specifies whether or not A is unit
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* triangular as follows:
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*
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* DIAG = 'U' or 'u' A is assumed to be unit triangular.
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*
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* DIAG = 'N' or 'n' A is not assumed to be unit
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* triangular.
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*
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* Unchanged on exit.
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*
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* N - INTEGER.
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* On entry, N specifies the order of the matrix A.
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* N must be at least zero.
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* Unchanged on exit.
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*
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* AP - COMPLEX array of DIMENSION at least
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* ( ( n*( n + 1 ) )/2 ).
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* Before entry with UPLO = 'U' or 'u', the array AP must
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* contain the upper triangular matrix packed sequentially,
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* column by column, so that AP( 1 ) contains a( 1, 1 ),
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* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
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* respectively, and so on.
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* Before entry with UPLO = 'L' or 'l', the array AP must
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* contain the lower triangular matrix packed sequentially,
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* column by column, so that AP( 1 ) contains a( 1, 1 ),
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* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
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* respectively, and so on.
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* Note that when DIAG = 'U' or 'u', the diagonal elements of
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* A are not referenced, but are assumed to be unity.
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* Unchanged on exit.
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*
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* X - COMPLEX array of dimension at least
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* ( 1 + ( n - 1 )*abs( INCX ) ).
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* Before entry, the incremented array X must contain the n
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* element right-hand side vector b. On exit, X is overwritten
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* with the solution vector x.
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*
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* INCX - INTEGER.
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* On entry, INCX specifies the increment for the elements of
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* X. INCX must not be zero.
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* Unchanged on exit.
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*
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*
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* Level 2 Blas routine.
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*
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* -- Written on 22-October-1986.
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* Jack Dongarra, Argonne National Lab.
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* Jeremy Du Croz, Nag Central Office.
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* Sven Hammarling, Nag Central Office.
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* Richard Hanson, Sandia National Labs.
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*
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*
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* .. Parameters ..
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COMPLEX ZERO
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PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) )
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* .. Local Scalars ..
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COMPLEX TEMP
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INTEGER I, INFO, IX, J, JX, K, KK, KX
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LOGICAL NOCONJ, NOUNIT
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* .. External Subroutines ..
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EXTERNAL XERBLA
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* .. Intrinsic Functions ..
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INTRINSIC CONJG
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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IF ( .NOT.LSAME( UPLO , 'U' ).AND.
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$ .NOT.LSAME( UPLO , 'L' ) )THEN
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INFO = 1
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ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND.
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$ .NOT.LSAME( TRANS, 'T' ).AND.
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$ .NOT.LSAME( TRANS, 'R' ).AND.
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$ .NOT.LSAME( TRANS, 'C' ) )THEN
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INFO = 2
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ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND.
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$ .NOT.LSAME( DIAG , 'N' ) )THEN
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INFO = 3
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ELSE IF( N.LT.0 )THEN
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INFO = 4
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ELSE IF( INCX.EQ.0 )THEN
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INFO = 7
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END IF
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IF( INFO.NE.0 )THEN
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CALL XERBLA( 'CTPSV ', INFO )
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RETURN
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END IF
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*
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* Quick return if possible.
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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NOCONJ = LSAME( TRANS, 'N' ) .OR. LSAME( TRANS, 'T' )
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NOUNIT = LSAME( DIAG , 'N' )
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*
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* Set up the start point in X if the increment is not unity. This
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* will be ( N - 1 )*INCX too small for descending loops.
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*
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IF( INCX.LE.0 )THEN
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KX = 1 - ( N - 1 )*INCX
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ELSE IF( INCX.NE.1 )THEN
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KX = 1
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END IF
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*
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* Start the operations. In this version the elements of AP are
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* accessed sequentially with one pass through AP.
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*
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IF( LSAME( TRANS, 'N' ) .OR.LSAME( TRANS, 'R' ))THEN
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*
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* Form x := inv( A )*x.
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*
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IF( LSAME( UPLO, 'U' ) )THEN
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KK = ( N*( N + 1 ) )/2
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IF( INCX.EQ.1 )THEN
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DO 20, J = N, 1, -1
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IF( X( J ).NE.ZERO )THEN
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IF( NOCONJ )THEN
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IF( NOUNIT )
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$ X( J ) = X( J )/AP( KK )
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ELSE
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IF( NOUNIT )
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$ X( J ) = X( J )/CONJG(AP( KK ))
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END IF
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TEMP = X( J )
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K = KK - 1
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DO 10, I = J - 1, 1, -1
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IF( NOCONJ )THEN
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X( I ) = X( I ) - TEMP*AP( K )
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ELSE
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X( I ) = X( I ) - TEMP*CONJG(AP( K ))
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END IF
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K = K - 1
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10 CONTINUE
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END IF
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KK = KK - J
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20 CONTINUE
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ELSE
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JX = KX + ( N - 1 )*INCX
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DO 40, J = N, 1, -1
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IF( X( JX ).NE.ZERO )THEN
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IF( NOCONJ )THEN
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IF( NOUNIT )
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$ X( JX ) = X( JX )/AP( KK )
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ELSE
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IF( NOUNIT )
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$ X( JX ) = X( JX )/CONJG(AP( KK ))
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END IF
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TEMP = X( JX )
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IX = JX
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DO 30, K = KK - 1, KK - J + 1, -1
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IX = IX - INCX
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IF( NOCONJ )THEN
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X( IX ) = X( IX ) - TEMP*AP( K )
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ELSE
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X( IX ) = X( IX ) - TEMP*CONJG(AP( K ))
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END IF
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30 CONTINUE
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END IF
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JX = JX - INCX
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KK = KK - J
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40 CONTINUE
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END IF
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ELSE
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KK = 1
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IF( INCX.EQ.1 )THEN
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DO 60, J = 1, N
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IF( X( J ).NE.ZERO )THEN
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IF( NOCONJ )THEN
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IF( NOUNIT )
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$ X( J ) = X( J )/AP( KK )
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ELSE
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IF( NOUNIT )
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$ X( J ) = X( J )/CONJG(AP( KK ))
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END IF
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TEMP = X( J )
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K = KK + 1
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DO 50, I = J + 1, N
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IF( NOCONJ )THEN
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X( I ) = X( I ) - TEMP*AP( K )
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ELSE
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X( I ) = X( I ) - TEMP*CONJG(AP( K ))
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END IF
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K = K + 1
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50 CONTINUE
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END IF
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KK = KK + ( N - J + 1 )
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60 CONTINUE
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ELSE
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JX = KX
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DO 80, J = 1, N
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IF( X( JX ).NE.ZERO )THEN
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IF( NOCONJ )THEN
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IF( NOUNIT )
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$ X( JX ) = X( JX )/AP( KK )
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ELSE
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IF( NOUNIT )
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$ X( JX ) = X( JX )/CONJG(AP( KK ))
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END IF
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TEMP = X( JX )
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IX = JX
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DO 70, K = KK + 1, KK + N - J
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IX = IX + INCX
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IF( NOCONJ )THEN
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X( IX ) = X( IX ) - TEMP*AP( K )
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ELSE
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X( IX ) = X( IX ) - TEMP*CONJG(AP( K ))
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END IF
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70 CONTINUE
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END IF
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JX = JX + INCX
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KK = KK + ( N - J + 1 )
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80 CONTINUE
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END IF
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END IF
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ELSE
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*
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* Form x := inv( A' )*x or x := inv( conjg( A' ) )*x.
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*
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IF( LSAME( UPLO, 'U' ) )THEN
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KK = 1
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IF( INCX.EQ.1 )THEN
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DO 110, J = 1, N
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TEMP = X( J )
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K = KK
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IF( NOCONJ )THEN
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DO 90, I = 1, J - 1
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TEMP = TEMP - AP( K )*X( I )
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K = K + 1
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90 CONTINUE
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IF( NOUNIT )
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$ TEMP = TEMP/AP( KK + J - 1 )
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ELSE
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DO 100, I = 1, J - 1
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TEMP = TEMP - CONJG( AP( K ) )*X( I )
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K = K + 1
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100 CONTINUE
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IF( NOUNIT )
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$ TEMP = TEMP/CONJG( AP( KK + J - 1 ) )
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END IF
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X( J ) = TEMP
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KK = KK + J
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110 CONTINUE
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ELSE
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JX = KX
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DO 140, J = 1, N
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TEMP = X( JX )
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IX = KX
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IF( NOCONJ )THEN
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DO 120, K = KK, KK + J - 2
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TEMP = TEMP - AP( K )*X( IX )
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IX = IX + INCX
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120 CONTINUE
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IF( NOUNIT )
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$ TEMP = TEMP/AP( KK + J - 1 )
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ELSE
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DO 130, K = KK, KK + J - 2
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TEMP = TEMP - CONJG( AP( K ) )*X( IX )
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IX = IX + INCX
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130 CONTINUE
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IF( NOUNIT )
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$ TEMP = TEMP/CONJG( AP( KK + J - 1 ) )
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END IF
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X( JX ) = TEMP
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JX = JX + INCX
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KK = KK + J
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140 CONTINUE
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END IF
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ELSE
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KK = ( N*( N + 1 ) )/2
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IF( INCX.EQ.1 )THEN
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DO 170, J = N, 1, -1
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TEMP = X( J )
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K = KK
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IF( NOCONJ )THEN
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DO 150, I = N, J + 1, -1
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TEMP = TEMP - AP( K )*X( I )
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K = K - 1
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150 CONTINUE
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IF( NOUNIT )
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$ TEMP = TEMP/AP( KK - N + J )
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ELSE
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DO 160, I = N, J + 1, -1
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TEMP = TEMP - CONJG( AP( K ) )*X( I )
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K = K - 1
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160 CONTINUE
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IF( NOUNIT )
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$ TEMP = TEMP/CONJG( AP( KK - N + J ) )
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END IF
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X( J ) = TEMP
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KK = KK - ( N - J + 1 )
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170 CONTINUE
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ELSE
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KX = KX + ( N - 1 )*INCX
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JX = KX
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DO 200, J = N, 1, -1
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TEMP = X( JX )
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IX = KX
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IF( NOCONJ )THEN
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DO 180, K = KK, KK - ( N - ( J + 1 ) ), -1
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TEMP = TEMP - AP( K )*X( IX )
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IX = IX - INCX
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180 CONTINUE
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IF( NOUNIT )
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$ TEMP = TEMP/AP( KK - N + J )
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ELSE
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DO 190, K = KK, KK - ( N - ( J + 1 ) ), -1
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TEMP = TEMP - CONJG( AP( K ) )*X( IX )
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IX = IX - INCX
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190 CONTINUE
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IF( NOUNIT )
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$ TEMP = TEMP/CONJG( AP( KK - N + J ) )
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END IF
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X( JX ) = TEMP
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JX = JX - INCX
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KK = KK - ( N - J + 1 )
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200 CONTINUE
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END IF
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END IF
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END IF
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*
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RETURN
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*
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* End of CTPSV .
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*
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END
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