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