numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/TESTING/LIN/stpt01.f | 5661B | -rw-r--r-- |
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*> \brief \b STPT01 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE STPT01( UPLO, DIAG, N, AP, AINVP, RCOND, WORK, RESID ) * * .. Scalar Arguments .. * CHARACTER DIAG, UPLO * INTEGER N * REAL RCOND, RESID * .. * .. Array Arguments .. * REAL AINVP( * ), AP( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> STPT01 computes the residual for a triangular matrix A times its *> inverse when A is stored in packed format: *> 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] AP *> \verbatim *> AP is REAL array, dimension (N*(N+1)/2) *> The original upper or lower triangular matrix A, packed *> columnwise in a linear array. The j-th column of A is stored *> in the array AP as follows: *> if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', *> AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n. *> \endverbatim *> *> \param[in,out] AINVP *> \verbatim *> AINVP is REAL array, dimension (N*(N+1)/2) *> On entry, the (triangular) inverse of the matrix A, packed *> columnwise in a linear array as in AP. *> On exit, the contents of AINVP are destroyed. *> \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 STPT01( UPLO, DIAG, N, AP, AINVP, 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 N REAL RCOND, RESID * .. * .. Array Arguments .. REAL AINVP( * ), AP( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) * .. * .. Local Scalars .. LOGICAL UNITD INTEGER J, JC REAL AINVNM, ANORM, EPS * .. * .. External Functions .. LOGICAL LSAME REAL SLAMCH, SLANTP EXTERNAL LSAME, SLAMCH, SLANTP * .. * .. External Subroutines .. EXTERNAL STPMV * .. * .. 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 = SLANTP( '1', UPLO, DIAG, N, AP, WORK ) AINVNM = SLANTP( '1', UPLO, DIAG, N, AINVP, WORK ) IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCOND = ZERO RESID = ONE / EPS RETURN END IF RCOND = ( ONE / ANORM ) / AINVNM * * Compute A * AINV, overwriting AINV. * UNITD = LSAME( DIAG, 'U' ) IF( LSAME( UPLO, 'U' ) ) THEN JC = 1 DO 10 J = 1, N IF( UNITD ) $ AINVP( JC+J-1 ) = ONE * * Form the j-th column of A*AINV * CALL STPMV( 'Upper', 'No transpose', DIAG, J, AP, $ AINVP( JC ), 1 ) * * Subtract 1 from the diagonal * AINVP( JC+J-1 ) = AINVP( JC+J-1 ) - ONE JC = JC + J 10 CONTINUE ELSE JC = 1 DO 20 J = 1, N IF( UNITD ) $ AINVP( JC ) = ONE * * Form the j-th column of A*AINV * CALL STPMV( 'Lower', 'No transpose', DIAG, N-J+1, AP( JC ), $ AINVP( JC ), 1 ) * * Subtract 1 from the diagonal * AINVP( JC ) = AINVP( JC ) - ONE JC = JC + N - J + 1 20 CONTINUE END IF * * Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS) * RESID = SLANTP( '1', UPLO, 'Non-unit', N, AINVP, WORK ) * RESID = ( ( RESID*RCOND ) / REAL( N ) ) / EPS * RETURN * * End of STPT01 * END