forked from lijiext/lammps
243 lines
6.5 KiB
Fortran
243 lines
6.5 KiB
Fortran
*> \brief \b ZTPTRI
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download ZTPTRI + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztptri.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztptri.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztptri.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE ZTPTRI( UPLO, DIAG, N, AP, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER DIAG, UPLO
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* INTEGER INFO, N
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* ..
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* .. Array Arguments ..
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* COMPLEX*16 AP( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> ZTPTRI computes the inverse of a complex upper or lower triangular
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*> matrix A stored in packed format.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> = 'U': A is upper triangular;
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*> = 'L': A is lower triangular.
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*> \endverbatim
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*>
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*> \param[in] DIAG
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*> \verbatim
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*> DIAG is CHARACTER*1
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*> = 'N': A is non-unit triangular;
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*> = 'U': A is unit triangular.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] AP
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*> \verbatim
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*> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
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*> On entry, the upper or lower triangular matrix A, stored
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*> columnwise in a linear array. The j-th column of A is stored
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*> in the array AP as follows:
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*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
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*> if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n.
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*> See below for further details.
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*> On exit, the (triangular) inverse of the original matrix, in
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*> the same packed storage format.
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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*> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
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*> matrix is singular and its inverse can not be computed.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date December 2016
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*
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*> \ingroup complex16OTHERcomputational
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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*>
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*> A triangular matrix A can be transferred to packed storage using one
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*> of the following program segments:
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*>
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*> UPLO = 'U': UPLO = 'L':
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*>
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*> JC = 1 JC = 1
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*> DO 2 J = 1, N DO 2 J = 1, N
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*> DO 1 I = 1, J DO 1 I = J, N
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*> AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J)
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*> 1 CONTINUE 1 CONTINUE
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*> JC = JC + J JC = JC + N - J + 1
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*> 2 CONTINUE 2 CONTINUE
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE ZTPTRI( UPLO, DIAG, N, AP, INFO )
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*
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* -- LAPACK computational routine (version 3.7.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* December 2016
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*
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* .. Scalar Arguments ..
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CHARACTER DIAG, UPLO
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INTEGER INFO, N
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* ..
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* .. Array Arguments ..
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COMPLEX*16 AP( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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COMPLEX*16 ONE, ZERO
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PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
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$ ZERO = ( 0.0D+0, 0.0D+0 ) )
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* ..
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* .. Local Scalars ..
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LOGICAL NOUNIT, UPPER
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INTEGER J, JC, JCLAST, JJ
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COMPLEX*16 AJJ
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZSCAL, ZTPMV
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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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UPPER = LSAME( UPLO, 'U' )
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NOUNIT = LSAME( DIAG, 'N' )
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IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = -1
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ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
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INFO = -2
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ELSE IF( N.LT.0 ) THEN
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INFO = -3
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZTPTRI', -INFO )
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RETURN
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END IF
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*
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* Check for singularity if non-unit.
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*
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IF( NOUNIT ) THEN
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IF( UPPER ) THEN
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JJ = 0
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DO 10 INFO = 1, N
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JJ = JJ + INFO
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IF( AP( JJ ).EQ.ZERO )
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$ RETURN
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10 CONTINUE
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ELSE
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JJ = 1
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DO 20 INFO = 1, N
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IF( AP( JJ ).EQ.ZERO )
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$ RETURN
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JJ = JJ + N - INFO + 1
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20 CONTINUE
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END IF
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INFO = 0
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END IF
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*
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IF( UPPER ) THEN
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*
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* Compute inverse of upper triangular matrix.
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*
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JC = 1
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DO 30 J = 1, N
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IF( NOUNIT ) THEN
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AP( JC+J-1 ) = ONE / AP( JC+J-1 )
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AJJ = -AP( JC+J-1 )
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ELSE
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AJJ = -ONE
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END IF
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*
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* Compute elements 1:j-1 of j-th column.
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*
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CALL ZTPMV( 'Upper', 'No transpose', DIAG, J-1, AP,
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$ AP( JC ), 1 )
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CALL ZSCAL( J-1, AJJ, AP( JC ), 1 )
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JC = JC + J
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30 CONTINUE
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*
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ELSE
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*
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* Compute inverse of lower triangular matrix.
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*
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JC = N*( N+1 ) / 2
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DO 40 J = N, 1, -1
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IF( NOUNIT ) THEN
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AP( JC ) = ONE / AP( JC )
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AJJ = -AP( JC )
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ELSE
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AJJ = -ONE
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END IF
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IF( J.LT.N ) THEN
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*
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* Compute elements j+1:n of j-th column.
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*
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CALL ZTPMV( 'Lower', 'No transpose', DIAG, N-J,
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$ AP( JCLAST ), AP( JC+1 ), 1 )
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CALL ZSCAL( N-J, AJJ, AP( JC+1 ), 1 )
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END IF
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JCLAST = JC
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JC = JC - N + J - 2
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40 CONTINUE
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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 ZTPTRI
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*
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END
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