*> \brief \b CPST01 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE CPST01( UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM, * PIV, RWORK, RESID, RANK ) * * .. Scalar Arguments .. * REAL RESID * INTEGER LDA, LDAFAC, LDPERM, N, RANK * CHARACTER UPLO * .. * .. Array Arguments .. * COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), * \$ PERM( LDPERM, * ) * REAL RWORK( * ) * INTEGER PIV( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CPST01 reconstructs an Hermitian positive semidefinite matrix A *> from its L or U factors and the permutation matrix P and computes *> the residual *> norm( P*L*L'*P' - A ) / ( N * norm(A) * EPS ) or *> norm( P*U'*U*P' - A ) / ( N * norm(A) * EPS ), *> where EPS is the machine epsilon, L' is the conjugate transpose of L, *> and U' is the conjugate transpose of U. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the upper or lower triangular part of the *> Hermitian matrix A is stored: *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of rows and columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX array, dimension (LDA,N) *> The original Hermitian matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N) *> \endverbatim *> *> \param[in] AFAC *> \verbatim *> AFAC is COMPLEX array, dimension (LDAFAC,N) *> The factor L or U from the L*L' or U'*U *> factorization of A. *> \endverbatim *> *> \param[in] LDAFAC *> \verbatim *> LDAFAC is INTEGER *> The leading dimension of the array AFAC. LDAFAC >= max(1,N). *> \endverbatim *> *> \param[out] PERM *> \verbatim *> PERM is COMPLEX array, dimension (LDPERM,N) *> Overwritten with the reconstructed matrix, and then with the *> difference P*L*L'*P' - A (or P*U'*U*P' - A) *> \endverbatim *> *> \param[in] LDPERM *> \verbatim *> LDPERM is INTEGER *> The leading dimension of the array PERM. *> LDAPERM >= max(1,N). *> \endverbatim *> *> \param[in] PIV *> \verbatim *> PIV is INTEGER array, dimension (N) *> PIV is such that the nonzero entries are *> P( PIV( K ), K ) = 1. *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is REAL array, dimension (N) *> \endverbatim *> *> \param[out] RESID *> \verbatim *> RESID is REAL *> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS ) *> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS ) *> \endverbatim *> *> \param[in] RANK *> \verbatim *> RANK is INTEGER *> number of nonzero singular values of A. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complex_lin * * ===================================================================== SUBROUTINE CPST01( UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM, \$ PIV, RWORK, RESID, RANK ) * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. REAL RESID INTEGER LDA, LDAFAC, LDPERM, N, RANK CHARACTER UPLO * .. * .. Array Arguments .. COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), \$ PERM( LDPERM, * ) REAL RWORK( * ) INTEGER PIV( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) COMPLEX CZERO PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. COMPLEX TC REAL ANORM, EPS, TR INTEGER I, J, K * .. * .. External Functions .. COMPLEX CDOTC REAL CLANHE, SLAMCH LOGICAL LSAME EXTERNAL CDOTC, CLANHE, SLAMCH, LSAME * .. * .. External Subroutines .. EXTERNAL CHER, CSCAL, CTRMV * .. * .. Intrinsic Functions .. INTRINSIC AIMAG, CONJG, REAL * .. * .. Executable Statements .. * * Quick exit if N = 0. * IF( N.LE.0 ) THEN RESID = ZERO RETURN END IF * * Exit with RESID = 1/EPS if ANORM = 0. * EPS = SLAMCH( 'Epsilon' ) ANORM = CLANHE( '1', UPLO, N, A, LDA, RWORK ) IF( ANORM.LE.ZERO ) THEN RESID = ONE / EPS RETURN END IF * * Check the imaginary parts of the diagonal elements and return with * an error code if any are nonzero. * DO 100 J = 1, N IF( AIMAG( AFAC( J, J ) ).NE.ZERO ) THEN RESID = ONE / EPS RETURN END IF 100 CONTINUE * * Compute the product U'*U, overwriting U. * IF( LSAME( UPLO, 'U' ) ) THEN * IF( RANK.LT.N ) THEN DO 120 J = RANK + 1, N DO 110 I = RANK + 1, J AFAC( I, J ) = CZERO 110 CONTINUE 120 CONTINUE END IF * DO 130 K = N, 1, -1 * * Compute the (K,K) element of the result. * TR = CDOTC( K, AFAC( 1, K ), 1, AFAC( 1, K ), 1 ) AFAC( K, K ) = TR * * Compute the rest of column K. * CALL CTRMV( 'Upper', 'Conjugate', 'Non-unit', K-1, AFAC, \$ LDAFAC, AFAC( 1, K ), 1 ) * 130 CONTINUE * * Compute the product L*L', overwriting L. * ELSE * IF( RANK.LT.N ) THEN DO 150 J = RANK + 1, N DO 140 I = J, N AFAC( I, J ) = CZERO 140 CONTINUE 150 CONTINUE END IF * DO 160 K = N, 1, -1 * Add a multiple of column K of the factor L to each of * columns K+1 through N. * IF( K+1.LE.N ) \$ CALL CHER( 'Lower', N-K, ONE, AFAC( K+1, K ), 1, \$ AFAC( K+1, K+1 ), LDAFAC ) * * Scale column K by the diagonal element. * TC = AFAC( K, K ) CALL CSCAL( N-K+1, TC, AFAC( K, K ), 1 ) 160 CONTINUE * END IF * * Form P*L*L'*P' or P*U'*U*P' * IF( LSAME( UPLO, 'U' ) ) THEN * DO 180 J = 1, N DO 170 I = 1, N IF( PIV( I ).LE.PIV( J ) ) THEN IF( I.LE.J ) THEN PERM( PIV( I ), PIV( J ) ) = AFAC( I, J ) ELSE PERM( PIV( I ), PIV( J ) ) = CONJG( AFAC( J, I ) ) END IF END IF 170 CONTINUE 180 CONTINUE * * ELSE * DO 200 J = 1, N DO 190 I = 1, N IF( PIV( I ).GE.PIV( J ) ) THEN IF( I.GE.J ) THEN PERM( PIV( I ), PIV( J ) ) = AFAC( I, J ) ELSE PERM( PIV( I ), PIV( J ) ) = CONJG( AFAC( J, I ) ) END IF END IF 190 CONTINUE 200 CONTINUE * END IF * * Compute the difference P*L*L'*P' - A (or P*U'*U*P' - A). * IF( LSAME( UPLO, 'U' ) ) THEN DO 220 J = 1, N DO 210 I = 1, J - 1 PERM( I, J ) = PERM( I, J ) - A( I, J ) 210 CONTINUE PERM( J, J ) = PERM( J, J ) - REAL( A( J, J ) ) 220 CONTINUE ELSE DO 240 J = 1, N PERM( J, J ) = PERM( J, J ) - REAL( A( J, J ) ) DO 230 I = J + 1, N PERM( I, J ) = PERM( I, J ) - A( I, J ) 230 CONTINUE 240 CONTINUE END IF * * Compute norm( P*L*L'P - A ) / ( N * norm(A) * EPS ), or * ( P*U'*U*P' - A )/ ( N * norm(A) * EPS ). * RESID = CLANHE( '1', UPLO, N, PERM, LDAFAC, RWORK ) * RESID = ( ( RESID / REAL( N ) ) / ANORM ) / EPS * RETURN * * End of CPST01 * END