numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/SRC/zpptri.f | 5131B | -rw-r--r-- |
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*> \brief \b ZPPTRI * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZPPTRI + dependencies *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpptri.f"> *> [TGZ]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpptri.f"> *> [ZIP]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpptri.f"> *> [TXT]</a> *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZPPTRI( UPLO, N, AP, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, N * .. * .. Array Arguments .. * COMPLEX*16 AP( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZPPTRI computes the inverse of a complex Hermitian positive definite *> matrix A using the Cholesky factorization A = U**H*U or A = L*L**H *> computed by ZPPTRF. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangular factor is stored in AP; *> = 'L': Lower triangular factor is stored in AP. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] AP *> \verbatim *> AP is COMPLEX*16 array, dimension (N*(N+1)/2) *> On entry, the triangular factor U or L from the Cholesky *> factorization A = U**H*U or A = L*L**H, packed columnwise as *> a linear array. The j-th column of U or L is stored in the *> array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. *> *> On exit, the upper or lower triangle of the (Hermitian) *> inverse of A, overwriting the input factor U or L. *> \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, the (i,i) element of the factor U or L is *> zero, and the inverse could not be computed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup pptri * * ===================================================================== SUBROUTINE ZPPTRI( UPLO, N, AP, INFO ) * * -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, N * .. * .. Array Arguments .. COMPLEX*16 AP( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER J, JC, JJ, JJN DOUBLE PRECISION AJJ * .. * .. External Functions .. LOGICAL LSAME COMPLEX*16 ZDOTC EXTERNAL LSAME, ZDOTC * .. * .. External Subroutines .. EXTERNAL XERBLA, ZDSCAL, ZHPR, ZTPMV, ZTPTRI * .. * .. Intrinsic Functions .. INTRINSIC DBLE * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZPPTRI', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Invert the triangular Cholesky factor U or L. * CALL ZTPTRI( UPLO, 'Non-unit', N, AP, INFO ) IF( INFO.GT.0 ) $ RETURN IF( UPPER ) THEN * * Compute the product inv(U) * inv(U)**H. * JJ = 0 DO 10 J = 1, N JC = JJ + 1 JJ = JJ + J IF( J.GT.1 ) $ CALL ZHPR( 'Upper', J-1, ONE, AP( JC ), 1, AP ) AJJ = DBLE( AP( JJ ) ) CALL ZDSCAL( J, AJJ, AP( JC ), 1 ) 10 CONTINUE * ELSE * * Compute the product inv(L)**H * inv(L). * JJ = 1 DO 20 J = 1, N JJN = JJ + N - J + 1 AP( JJ ) = DBLE( ZDOTC( N-J+1, AP( JJ ), 1, AP( JJ ), $ 1 ) ) IF( J.LT.N ) $ CALL ZTPMV( 'Lower', 'Conjugate transpose', $ 'Non-unit', $ N-J, AP( JJN ), AP( JJ+1 ), 1 ) JJ = JJN 20 CONTINUE END IF * RETURN * * End of ZPPTRI * END