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SUBROUTINE ZPST01( UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM,
$ PIV, RWORK, RESID, RANK ) * * -- LAPACK test routine (version 3.1) -- * Craig Lucas, University of Manchester / NAG Ltd. * October, 2008 * * .. Scalar Arguments .. DOUBLE PRECISION RESID INTEGER LDA, LDAFAC, LDPERM, N, RANK CHARACTER UPLO * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), $ PERM( LDPERM, * ) DOUBLE PRECISION RWORK( * ) INTEGER PIV( * ) * .. * * Purpose * ======= * * ZPST01 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. * * Arguments * ========== * * UPLO (input) CHARACTER*1 * Specifies whether the upper or lower triangular part of the * Hermitian matrix A is stored: * = 'U': Upper triangular * = 'L': Lower triangular * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input) COMPLEX*16 array, dimension (LDA,N) * The original Hermitian matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N) * * AFAC (input) COMPLEX*16 array, dimension (LDAFAC,N) * The factor L or U from the L*L' or U'*U * factorization of A. * * LDAFAC (input) INTEGER * The leading dimension of the array AFAC. LDAFAC >= max(1,N). * * PERM (output) COMPLEX*16 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) * * LDPERM (input) INTEGER * The leading dimension of the array PERM. * LDAPERM >= max(1,N). * * PIV (input) INTEGER array, dimension (N) * PIV is such that the nonzero entries are * P( PIV( K ), K ) = 1. * * RWORK (workspace) DOUBLE PRECISION array, dimension (N) * * RESID (output) DOUBLE PRECISION * If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS ) * If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS ) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) COMPLEX*16 CZERO PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. COMPLEX*16 TC DOUBLE PRECISION ANORM, EPS, TR INTEGER I, J, K * .. * .. External Functions .. COMPLEX*16 ZDOTC DOUBLE PRECISION DLAMCH, ZLANHE LOGICAL LSAME EXTERNAL ZDOTC, DLAMCH, ZLANHE, LSAME * .. * .. External Subroutines .. EXTERNAL ZHER, ZSCAL, ZTRMV * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DCONJG, DIMAG * .. * .. 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 = DLAMCH( 'Epsilon' ) ANORM = ZLANHE( '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( DIMAG( 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 = ZDOTC( K, AFAC( 1, K ), 1, AFAC( 1, K ), 1 ) AFAC( K, K ) = TR * * Compute the rest of column K. * CALL ZTRMV( '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 ZHER( '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 ZSCAL( 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 ) ) = DCONJG( 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 ) ) = DCONJG( 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 ) - DBLE( A( J, J ) ) 220 CONTINUE ELSE DO 240 J = 1, N PERM( J, J ) = PERM( J, J ) - DBLE( 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 = ZLANHE( '1', UPLO, N, PERM, LDAFAC, RWORK ) * RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS * RETURN * * End of ZPST01 * END |