numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/TESTING/LIN/zspt03.f | 7937B | -rw-r--r-- |
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*> \brief \b ZSPT03 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZSPT03( UPLO, N, A, AINV, WORK, LDW, RWORK, RCOND, * RESID ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER LDW, N * DOUBLE PRECISION RCOND, RESID * .. * .. Array Arguments .. * DOUBLE PRECISION RWORK( * ) * COMPLEX*16 A( * ), AINV( * ), WORK( LDW, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZSPT03 computes the residual for a complex symmetric packed matrix *> times its inverse: *> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ), *> where EPS is the machine epsilon. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the upper or lower triangular part of the *> complex symmetric 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*16 array, dimension (N*(N+1)/2) *> The original complex symmetric matrix A, stored as a packed *> triangular matrix. *> \endverbatim *> *> \param[in] AINV *> \verbatim *> AINV is COMPLEX*16 array, dimension (N*(N+1)/2) *> The (symmetric) inverse of the matrix A, stored as a packed *> triangular matrix. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (LDW,N) *> \endverbatim *> *> \param[in] LDW *> \verbatim *> LDW is INTEGER *> The leading dimension of the array WORK. LDW >= max(1,N). *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (N) *> \endverbatim *> *> \param[out] RCOND *> \verbatim *> RCOND is DOUBLE PRECISION *> The reciprocal of the condition number of A, computed as *> ( 1/norm(A) ) / norm(AINV). *> \endverbatim *> *> \param[out] RESID *> \verbatim *> RESID is DOUBLE PRECISION *> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS ) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complex16_lin * * ===================================================================== SUBROUTINE ZSPT03( UPLO, N, A, AINV, WORK, LDW, RWORK, RCOND, $ RESID ) * * -- 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 .. CHARACTER UPLO INTEGER LDW, N DOUBLE PRECISION RCOND, RESID * .. * .. Array Arguments .. DOUBLE PRECISION RWORK( * ) COMPLEX*16 A( * ), AINV( * ), WORK( LDW, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. INTEGER I, ICOL, J, JCOL, K, KCOL, NALL DOUBLE PRECISION AINVNM, ANORM, EPS COMPLEX*16 T * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSP COMPLEX*16 ZDOTU EXTERNAL LSAME, DLAMCH, ZLANGE, ZLANSP, ZDOTU * .. * .. Intrinsic Functions .. INTRINSIC DBLE * .. * .. Executable Statements .. * * Quick exit if N = 0. * IF( N.LE.0 ) THEN RCOND = ONE RESID = ZERO RETURN END IF * * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0. * EPS = DLAMCH( 'Epsilon' ) ANORM = ZLANSP( '1', UPLO, N, A, RWORK ) AINVNM = ZLANSP( '1', UPLO, N, AINV, RWORK ) IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCOND = ZERO RESID = ONE / EPS RETURN END IF RCOND = ( ONE / ANORM ) / AINVNM * * Case where both A and AINV are upper triangular: * Each element of - A * AINV is computed by taking the dot product * of a row of A with a column of AINV. * IF( LSAME( UPLO, 'U' ) ) THEN DO 70 I = 1, N ICOL = ( ( I-1 )*I ) / 2 + 1 * * Code when J <= I * DO 30 J = 1, I JCOL = ( ( J-1 )*J ) / 2 + 1 T = ZDOTU( J, A( ICOL ), 1, AINV( JCOL ), 1 ) JCOL = JCOL + 2*J - 1 KCOL = ICOL - 1 DO 10 K = J + 1, I T = T + A( KCOL+K )*AINV( JCOL ) JCOL = JCOL + K 10 CONTINUE KCOL = KCOL + 2*I DO 20 K = I + 1, N T = T + A( KCOL )*AINV( JCOL ) KCOL = KCOL + K JCOL = JCOL + K 20 CONTINUE WORK( I, J ) = -T 30 CONTINUE * * Code when J > I * DO 60 J = I + 1, N JCOL = ( ( J-1 )*J ) / 2 + 1 T = ZDOTU( I, A( ICOL ), 1, AINV( JCOL ), 1 ) JCOL = JCOL - 1 KCOL = ICOL + 2*I - 1 DO 40 K = I + 1, J T = T + A( KCOL )*AINV( JCOL+K ) KCOL = KCOL + K 40 CONTINUE JCOL = JCOL + 2*J DO 50 K = J + 1, N T = T + A( KCOL )*AINV( JCOL ) KCOL = KCOL + K JCOL = JCOL + K 50 CONTINUE WORK( I, J ) = -T 60 CONTINUE 70 CONTINUE ELSE * * Case where both A and AINV are lower triangular * NALL = ( N*( N+1 ) ) / 2 DO 140 I = 1, N * * Code when J <= I * ICOL = NALL - ( ( N-I+1 )*( N-I+2 ) ) / 2 + 1 DO 100 J = 1, I JCOL = NALL - ( ( N-J )*( N-J+1 ) ) / 2 - ( N-I ) T = ZDOTU( N-I+1, A( ICOL ), 1, AINV( JCOL ), 1 ) KCOL = I JCOL = J DO 80 K = 1, J - 1 T = T + A( KCOL )*AINV( JCOL ) JCOL = JCOL + N - K KCOL = KCOL + N - K 80 CONTINUE JCOL = JCOL - J DO 90 K = J, I - 1 T = T + A( KCOL )*AINV( JCOL+K ) KCOL = KCOL + N - K 90 CONTINUE WORK( I, J ) = -T 100 CONTINUE * * Code when J > I * ICOL = NALL - ( ( N-I )*( N-I+1 ) ) / 2 DO 130 J = I + 1, N JCOL = NALL - ( ( N-J+1 )*( N-J+2 ) ) / 2 + 1 T = ZDOTU( N-J+1, A( ICOL-N+J ), 1, AINV( JCOL ), 1 ) KCOL = I JCOL = J DO 110 K = 1, I - 1 T = T + A( KCOL )*AINV( JCOL ) JCOL = JCOL + N - K KCOL = KCOL + N - K 110 CONTINUE KCOL = KCOL - I DO 120 K = I, J - 1 T = T + A( KCOL+K )*AINV( JCOL ) JCOL = JCOL + N - K 120 CONTINUE WORK( I, J ) = -T 130 CONTINUE 140 CONTINUE END IF * * Add the identity matrix to WORK . * DO 150 I = 1, N WORK( I, I ) = WORK( I, I ) + ONE 150 CONTINUE * * Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS) * RESID = ZLANGE( '1', N, N, WORK, LDW, RWORK ) * RESID = ( ( RESID*RCOND ) / EPS ) / DBLE( N ) * RETURN * * End of ZSPT03 * END