*> \brief \b STRT01 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE STRT01( UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND, * WORK, RESID ) * * .. Scalar Arguments .. * CHARACTER DIAG, UPLO * INTEGER LDA, LDAINV, N * REAL RCOND, RESID * .. * .. Array Arguments .. * REAL A( LDA, * ), AINV( LDAINV, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> STRT01 computes the residual for a triangular matrix A times its *> inverse: *> RESID = norm( A*AINV - I ) / ( 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 matrix A is upper or lower triangular. *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> Specifies whether or not the matrix A is unit triangular. *> = 'N': Non-unit triangular *> = 'U': Unit triangular *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is REAL array, dimension (LDA,N) *> The triangular matrix A. If UPLO = 'U', the leading n by n *> upper triangular part of the array A contains the upper *> triangular matrix, and the strictly lower triangular part of *> A is not referenced. If UPLO = 'L', the leading n by n lower *> triangular part of the array A contains the lower triangular *> matrix, and the strictly upper triangular part of A is not *> referenced. If DIAG = 'U', the diagonal elements of A are *> also not referenced and are assumed to be 1. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in,out] AINV *> \verbatim *> AINV is REAL array, dimension (LDAINV,N) *> On entry, the (triangular) inverse of the matrix A, in the *> same storage format as A. *> On exit, the contents of AINV are destroyed. *> \endverbatim *> *> \param[in] LDAINV *> \verbatim *> LDAINV is INTEGER *> The leading dimension of the array AINV. LDAINV >= max(1,N). *> \endverbatim *> *> \param[out] RCOND *> \verbatim *> RCOND is REAL *> The reciprocal condition number of A, computed as *> 1/(norm(A) * norm(AINV)). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension (N) *> \endverbatim *> *> \param[out] RESID *> \verbatim *> RESID is REAL *> norm(A*AINV - I) / ( 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 single_lin * * ===================================================================== SUBROUTINE STRT01( UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND, $ WORK, 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 DIAG, UPLO INTEGER LDA, LDAINV, N REAL RCOND, RESID * .. * .. Array Arguments .. REAL A( LDA, * ), AINV( LDAINV, * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER J REAL AINVNM, ANORM, EPS * .. * .. External Functions .. LOGICAL LSAME REAL SLAMCH, SLANTR EXTERNAL LSAME, SLAMCH, SLANTR * .. * .. External Subroutines .. EXTERNAL STRMV * .. * .. Intrinsic Functions .. INTRINSIC REAL * .. * .. 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 = SLAMCH( 'Epsilon' ) ANORM = SLANTR( '1', UPLO, DIAG, N, N, A, LDA, WORK ) AINVNM = SLANTR( '1', UPLO, DIAG, N, N, AINV, LDAINV, WORK ) IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCOND = ZERO RESID = ONE / EPS RETURN END IF RCOND = ( ONE / ANORM ) / AINVNM * * Set the diagonal of AINV to 1 if AINV has unit diagonal. * IF( LSAME( DIAG, 'U' ) ) THEN DO 10 J = 1, N AINV( J, J ) = ONE 10 CONTINUE END IF * * Compute A * AINV, overwriting AINV. * IF( LSAME( UPLO, 'U' ) ) THEN DO 20 J = 1, N CALL STRMV( 'Upper', 'No transpose', DIAG, J, A, LDA, $ AINV( 1, J ), 1 ) 20 CONTINUE ELSE DO 30 J = 1, N CALL STRMV( 'Lower', 'No transpose', DIAG, N-J+1, A( J, J ), $ LDA, AINV( J, J ), 1 ) 30 CONTINUE END IF * * Subtract 1 from each diagonal element to form A*AINV - I. * DO 40 J = 1, N AINV( J, J ) = AINV( J, J ) - ONE 40 CONTINUE * * Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS) * RESID = SLANTR( '1', UPLO, 'Non-unit', N, N, AINV, LDAINV, WORK ) * RESID = ( ( RESID*RCOND ) / REAL( N ) ) / EPS * RETURN * * End of STRT01 * END