NAKATA Maho
25d74b31a7
Replace hard-coded floating-point constants with existing named constants in the drvrf3 and drvrfp test drivers. This keeps the test initialization code consistent with surrounding LAPACK test style.
593 lines
19 KiB
FortranFixed
593 lines
19 KiB
FortranFixed
*> \brief \b CDRVRFP
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE CDRVRFP( NOUT, NN, NVAL, NNS, NSVAL, NNT, NTVAL,
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* + THRESH, A, ASAV, AFAC, AINV, B,
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* + BSAV, XACT, X, ARF, ARFINV,
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* + C_WORK_CLATMS, C_WORK_CPOT02,
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* + C_WORK_CPOT03, S_WORK_CLATMS, S_WORK_CLANHE,
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* + S_WORK_CPOT01, S_WORK_CPOT02, S_WORK_CPOT03 )
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*
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* .. Scalar Arguments ..
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* INTEGER NN, NNS, NNT, NOUT
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* REAL THRESH
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* ..
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* .. Array Arguments ..
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* INTEGER NVAL( NN ), NSVAL( NNS ), NTVAL( NNT )
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* COMPLEX A( * )
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* COMPLEX AINV( * )
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* COMPLEX ASAV( * )
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* COMPLEX B( * )
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* COMPLEX BSAV( * )
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* COMPLEX AFAC( * )
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* COMPLEX ARF( * )
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* COMPLEX ARFINV( * )
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* COMPLEX XACT( * )
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* COMPLEX X( * )
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* COMPLEX C_WORK_CLATMS( * )
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* COMPLEX C_WORK_CPOT02( * )
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* COMPLEX C_WORK_CPOT03( * )
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* REAL S_WORK_CLATMS( * )
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* REAL S_WORK_CLANHE( * )
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* REAL S_WORK_CPOT01( * )
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* REAL S_WORK_CPOT02( * )
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* REAL S_WORK_CPOT03( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> CDRVRFP tests the LAPACK RFP routines:
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*> CPFTRF, CPFTRS, and CPFTRI.
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*>
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*> This testing routine follow the same tests as CDRVPO (test for the full
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*> format Symmetric Positive Definite solver).
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*>
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*> The tests are performed in Full Format, conversion back and forth from
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*> full format to RFP format are performed using the routines CTRTTF and
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*> CTFTTR.
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*>
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*> First, a specific matrix A of size N is created. There is nine types of
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*> different matrixes possible.
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*> 1. Diagonal 6. Random, CNDNUM = sqrt(0.1/EPS)
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*> 2. Random, CNDNUM = 2 7. Random, CNDNUM = 0.1/EPS
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*> *3. First row and column zero 8. Scaled near underflow
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*> *4. Last row and column zero 9. Scaled near overflow
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*> *5. Middle row and column zero
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*> (* - tests error exits from CPFTRF, no test ratios are computed)
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*> A solution XACT of size N-by-NRHS is created and the associated right
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*> hand side B as well. Then CPFTRF is called to compute L (or U), the
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*> Cholesky factor of A. Then L (or U) is used to solve the linear system
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*> of equations AX = B. This gives X. Then L (or U) is used to compute the
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*> inverse of A, AINV. The following four tests are then performed:
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*> (1) norm( L*L' - A ) / ( N * norm(A) * EPS ) or
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*> norm( U'*U - A ) / ( N * norm(A) * EPS ),
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*> (2) norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
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*> (3) norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
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*> (4) ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
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*> where EPS is the machine precision, RCOND the condition number of A, and
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*> norm( . ) the 1-norm for (1,2,3) and the inf-norm for (4).
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*> Errors occur when INFO parameter is not as expected. Failures occur when
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*> a test ratios is greater than THRES.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] NOUT
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*> \verbatim
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*> NOUT is INTEGER
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*> The unit number for output.
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*> \endverbatim
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*>
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*> \param[in] NN
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*> \verbatim
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*> NN is INTEGER
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*> The number of values of N contained in the vector NVAL.
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*> \endverbatim
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*>
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*> \param[in] NVAL
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*> \verbatim
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*> NVAL is INTEGER array, dimension (NN)
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*> The values of the matrix dimension N.
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*> \endverbatim
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*>
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*> \param[in] NNS
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*> \verbatim
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*> NNS is INTEGER
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*> The number of values of NRHS contained in the vector NSVAL.
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*> \endverbatim
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*>
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*> \param[in] NSVAL
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*> \verbatim
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*> NSVAL is INTEGER array, dimension (NNS)
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*> The values of the number of right-hand sides NRHS.
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*> \endverbatim
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*>
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*> \param[in] NNT
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*> \verbatim
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*> NNT is INTEGER
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*> The number of values of MATRIX TYPE contained in the vector NTVAL.
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*> \endverbatim
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*>
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*> \param[in] NTVAL
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*> \verbatim
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*> NTVAL is INTEGER array, dimension (NNT)
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*> The values of matrix type (between 0 and 9 for PO/PP/PF matrices).
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*> \endverbatim
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*>
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*> \param[in] THRESH
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*> \verbatim
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*> THRESH is REAL
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*> The threshold value for the test ratios. A result is
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*> included in the output file if RESULT >= THRESH. To have
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*> every test ratio printed, use THRESH = 0.
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*> \endverbatim
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*>
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*> \param[out] A
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*> \verbatim
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*> A is COMPLEX array, dimension (NMAX*NMAX)
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*> \endverbatim
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*>
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*> \param[out] ASAV
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*> \verbatim
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*> ASAV is COMPLEX array, dimension (NMAX*NMAX)
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*> \endverbatim
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*>
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*> \param[out] AFAC
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*> \verbatim
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*> AFAC is COMPLEX array, dimension (NMAX*NMAX)
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*> \endverbatim
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*>
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*> \param[out] AINV
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*> \verbatim
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*> AINV is COMPLEX array, dimension (NMAX*NMAX)
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*> \endverbatim
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*>
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*> \param[out] B
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*> \verbatim
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*> B is COMPLEX array, dimension (NMAX*MAXRHS)
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*> \endverbatim
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*>
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*> \param[out] BSAV
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*> \verbatim
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*> BSAV is COMPLEX array, dimension (NMAX*MAXRHS)
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*> \endverbatim
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*>
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*> \param[out] XACT
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*> \verbatim
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*> XACT is COMPLEX array, dimension (NMAX*MAXRHS)
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*> \endverbatim
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*>
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*> \param[out] X
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*> \verbatim
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*> X is COMPLEX array, dimension (NMAX*MAXRHS)
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*> \endverbatim
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*>
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*> \param[out] ARF
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*> \verbatim
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*> ARF is COMPLEX array, dimension ((NMAX*(NMAX+1))/2)
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*> \endverbatim
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*>
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*> \param[out] ARFINV
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*> \verbatim
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*> ARFINV is COMPLEX array, dimension ((NMAX*(NMAX+1))/2)
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*> \endverbatim
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*>
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*> \param[out] C_WORK_CLATMS
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*> \verbatim
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*> C_WORK_CLATMS is COMPLEX array, dimension ( 3*NMAX )
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*> \endverbatim
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*>
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*> \param[out] C_WORK_CPOT02
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*> \verbatim
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*> C_WORK_CPOT02 is COMPLEX array, dimension ( NMAX*MAXRHS )
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*> \endverbatim
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*>
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*> \param[out] C_WORK_CPOT03
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*> \verbatim
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*> C_WORK_CPOT03 is COMPLEX array, dimension ( NMAX*NMAX )
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*> \endverbatim
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*>
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*> \param[out] S_WORK_CLATMS
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*> \verbatim
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*> S_WORK_CLATMS is REAL array, dimension ( NMAX )
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*> \endverbatim
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*>
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*> \param[out] S_WORK_CLANHE
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*> \verbatim
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*> S_WORK_CLANHE is REAL array, dimension ( NMAX )
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*> \endverbatim
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*>
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*> \param[out] S_WORK_CPOT01
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*> \verbatim
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*> S_WORK_CPOT01 is REAL array, dimension ( NMAX )
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*> \endverbatim
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*>
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*> \param[out] S_WORK_CPOT02
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*> \verbatim
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*> S_WORK_CPOT02 is REAL array, dimension ( NMAX )
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*> \endverbatim
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*>
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*> \param[out] S_WORK_CPOT03
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*> \verbatim
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*> S_WORK_CPOT03 is REAL array, dimension ( NMAX )
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup complex_lin
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*
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* =====================================================================
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SUBROUTINE CDRVRFP( NOUT, NN, NVAL, NNS, NSVAL, NNT, NTVAL,
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+ THRESH, A, ASAV, AFAC, AINV, B,
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+ BSAV, XACT, X, ARF, ARFINV,
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+ C_WORK_CLATMS, C_WORK_CPOT02,
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+ C_WORK_CPOT03, S_WORK_CLATMS, S_WORK_CLANHE,
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+ S_WORK_CPOT01, S_WORK_CPOT02, S_WORK_CPOT03 )
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IMPLICIT NONE
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*
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* -- LAPACK test routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER NN, NNS, NNT, NOUT
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REAL THRESH
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* ..
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* .. Array Arguments ..
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INTEGER NVAL( NN ), NSVAL( NNS ), NTVAL( NNT )
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COMPLEX A( * )
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COMPLEX AINV( * )
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COMPLEX ASAV( * )
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COMPLEX B( * )
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COMPLEX BSAV( * )
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COMPLEX AFAC( * )
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COMPLEX ARF( * )
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COMPLEX ARFINV( * )
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COMPLEX XACT( * )
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COMPLEX X( * )
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COMPLEX C_WORK_CLATMS( * )
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COMPLEX C_WORK_CPOT02( * )
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COMPLEX C_WORK_CPOT03( * )
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REAL S_WORK_CLATMS( * )
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REAL S_WORK_CLANHE( * )
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REAL S_WORK_CPOT01( * )
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REAL S_WORK_CPOT02( * )
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REAL S_WORK_CPOT03( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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INTEGER NTESTS
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PARAMETER ( NTESTS = 4 )
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* ..
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* .. Local Scalars ..
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LOGICAL ZEROT
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INTEGER I, INFO, IUPLO, LDA, LDB, IMAT, NERRS, NFAIL,
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+ NRHS, NRUN, IZERO, IOFF, K, NT, N, IFORM, IIN,
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+ IIT, IIS
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CHARACTER DIST, CTYPE, UPLO, CFORM
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INTEGER KL, KU, MODE
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REAL ANORM, AINVNM, CNDNUM, RCONDC
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* ..
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* .. Local Arrays ..
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CHARACTER UPLOS( 2 ), FORMS( 2 )
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INTEGER ISEED( 4 ), ISEEDY( 4 )
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REAL RESULT( NTESTS )
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* ..
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* .. External Functions ..
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REAL CLANHE
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EXTERNAL CLANHE
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* ..
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* .. External Subroutines ..
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EXTERNAL ALADHD, ALAERH, ALASVM, CGET04, CTFTTR, CLACPY,
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+ CLAIPD, CLARHS, CLATB4, CLATMS, CPFTRI, CPFTRF,
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+ CPFTRS, CPOT01, CPOT02, CPOT03, CPOTRI, CPOTRF,
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+ CTRTTF
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* ..
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* .. Scalars in Common ..
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CHARACTER*32 SRNAMT
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* ..
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* .. Common blocks ..
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COMMON / SRNAMC / SRNAMT
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* ..
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* .. Data statements ..
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DATA ISEEDY / 1988, 1989, 1990, 1991 /
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DATA UPLOS / 'U', 'L' /
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DATA FORMS / 'N', 'C' /
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* ..
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* .. Executable Statements ..
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*
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* Initialize constants and the random number seed.
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*
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NRUN = 0
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NFAIL = 0
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NERRS = 0
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DO 10 I = 1, 4
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ISEED( I ) = ISEEDY( I )
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10 CONTINUE
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*
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DO 130 IIN = 1, NN
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*
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N = NVAL( IIN )
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LDA = MAX( N, 1 )
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LDB = MAX( N, 1 )
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*
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DO 980 IIS = 1, NNS
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*
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NRHS = NSVAL( IIS )
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*
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DO 120 IIT = 1, NNT
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*
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IMAT = NTVAL( IIT )
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*
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* If N.EQ.0, only consider the first type
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*
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IF( N.EQ.0 .AND. IIT.GE.1 ) GO TO 120
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*
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* Skip types 3, 4, or 5 if the matrix size is too small.
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*
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IF( IMAT.EQ.4 .AND. N.LE.1 ) GO TO 120
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IF( IMAT.EQ.5 .AND. N.LE.2 ) GO TO 120
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*
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* Do first for UPLO = 'U', then for UPLO = 'L'
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*
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DO 110 IUPLO = 1, 2
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UPLO = UPLOS( IUPLO )
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*
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* Do first for CFORM = 'N', then for CFORM = 'C'
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*
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DO 100 IFORM = 1, 2
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CFORM = FORMS( IFORM )
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*
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* Set up parameters with CLATB4 and generate a test
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* matrix with CLATMS.
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*
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CALL CLATB4( 'CPO', IMAT, N, N, CTYPE, KL, KU,
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+ ANORM, MODE, CNDNUM, DIST )
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*
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SRNAMT = 'CLATMS'
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CALL CLATMS( N, N, DIST, ISEED, CTYPE,
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+ S_WORK_CLATMS,
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+ MODE, CNDNUM, ANORM, KL, KU, UPLO, A,
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+ LDA, C_WORK_CLATMS, INFO )
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*
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* Check error code from CLATMS.
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*
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IF( INFO.NE.0 ) THEN
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CALL ALAERH( 'CPF', 'CLATMS', INFO, 0, UPLO, N,
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+ N, -1, -1, -1, IIT, NFAIL, NERRS,
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+ NOUT )
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GO TO 100
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END IF
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*
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* For types 3-5, zero one row and column of the matrix to
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* test that INFO is returned correctly.
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*
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ZEROT = IMAT.GE.3 .AND. IMAT.LE.5
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IF( ZEROT ) THEN
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IF( IIT.EQ.3 ) THEN
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IZERO = 1
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ELSE IF( IIT.EQ.4 ) THEN
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IZERO = N
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ELSE
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IZERO = N / 2 + 1
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END IF
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IOFF = ( IZERO-1 )*LDA
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*
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* Set row and column IZERO of A to 0.
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*
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IF( IUPLO.EQ.1 ) THEN
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DO 20 I = 1, IZERO - 1
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A( IOFF+I ) = ZERO
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20 CONTINUE
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IOFF = IOFF + IZERO
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DO 30 I = IZERO, N
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A( IOFF ) = ZERO
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IOFF = IOFF + LDA
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30 CONTINUE
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ELSE
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IOFF = IZERO
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DO 40 I = 1, IZERO - 1
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A( IOFF ) = ZERO
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IOFF = IOFF + LDA
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40 CONTINUE
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IOFF = IOFF - IZERO
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DO 50 I = IZERO, N
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A( IOFF+I ) = ZERO
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50 CONTINUE
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END IF
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ELSE
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IZERO = 0
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END IF
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*
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* Set the imaginary part of the diagonals.
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*
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CALL CLAIPD( N, A, LDA+1, 0 )
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*
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* Save a copy of the matrix A in ASAV.
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*
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CALL CLACPY( UPLO, N, N, A, LDA, ASAV, LDA )
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*
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* Compute the condition number of A (RCONDC).
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*
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IF( ZEROT ) THEN
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RCONDC = ZERO
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ELSE
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*
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* Compute the 1-norm of A.
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*
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ANORM = CLANHE( '1', UPLO, N, A, LDA,
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+ S_WORK_CLANHE )
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*
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* Factor the matrix A.
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*
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CALL CPOTRF( UPLO, N, A, LDA, INFO )
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*
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* Form the inverse of A.
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*
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CALL CPOTRI( UPLO, N, A, LDA, INFO )
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IF ( N .NE. 0 ) THEN
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*
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* Compute the 1-norm condition number of A.
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*
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AINVNM = CLANHE( '1', UPLO, N, A, LDA,
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+ S_WORK_CLANHE )
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RCONDC = ( ONE / ANORM ) / AINVNM
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*
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* Restore the matrix A.
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*
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CALL CLACPY( UPLO, N, N, ASAV, LDA, A, LDA )
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END IF
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*
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END IF
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*
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* Form an exact solution and set the right hand side.
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*
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SRNAMT = 'CLARHS'
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CALL CLARHS( 'CPO', 'N', UPLO, ' ', N, N, KL, KU,
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+ NRHS, A, LDA, XACT, LDA, B, LDA,
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+ ISEED, INFO )
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CALL CLACPY( 'Full', N, NRHS, B, LDA, BSAV, LDA )
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*
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* Compute the L*L' or U'*U factorization of the
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* matrix and solve the system.
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*
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CALL CLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
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CALL CLACPY( 'Full', N, NRHS, B, LDB, X, LDB )
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*
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SRNAMT = 'CTRTTF'
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CALL CTRTTF( CFORM, UPLO, N, AFAC, LDA, ARF, INFO )
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SRNAMT = 'CPFTRF'
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CALL CPFTRF( CFORM, UPLO, N, ARF, INFO )
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*
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* Check error code from CPFTRF.
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*
|
|
IF( INFO.NE.IZERO ) THEN
|
|
*
|
|
* LANGOU: there is a small hick here: IZERO should
|
|
* always be INFO however if INFO is ZERO, ALAERH does not
|
|
* complain.
|
|
*
|
|
CALL ALAERH( 'CPF', 'CPFSV ', INFO, IZERO,
|
|
+ UPLO, N, N, -1, -1, NRHS, IIT,
|
|
+ NFAIL, NERRS, NOUT )
|
|
GO TO 100
|
|
END IF
|
|
*
|
|
* Skip the tests if INFO is not 0.
|
|
*
|
|
IF( INFO.NE.0 ) THEN
|
|
GO TO 100
|
|
END IF
|
|
*
|
|
SRNAMT = 'CPFTRS'
|
|
CALL CPFTRS( CFORM, UPLO, N, NRHS, ARF, X, LDB,
|
|
+ INFO )
|
|
*
|
|
SRNAMT = 'CTFTTR'
|
|
CALL CTFTTR( CFORM, UPLO, N, ARF, AFAC, LDA, INFO )
|
|
*
|
|
* Reconstruct matrix from factors and compute
|
|
* residual.
|
|
*
|
|
CALL CLACPY( UPLO, N, N, AFAC, LDA, ASAV, LDA )
|
|
CALL CPOT01( UPLO, N, A, LDA, AFAC, LDA,
|
|
+ S_WORK_CPOT01, RESULT( 1 ) )
|
|
CALL CLACPY( UPLO, N, N, ASAV, LDA, AFAC, LDA )
|
|
*
|
|
* Form the inverse and compute the residual.
|
|
*
|
|
IF(MOD(N,2).EQ.0)THEN
|
|
CALL CLACPY( 'A', N+1, N/2, ARF, N+1, ARFINV,
|
|
+ N+1 )
|
|
ELSE
|
|
CALL CLACPY( 'A', N, (N+1)/2, ARF, N, ARFINV,
|
|
+ N )
|
|
END IF
|
|
*
|
|
SRNAMT = 'CPFTRI'
|
|
CALL CPFTRI( CFORM, UPLO, N, ARFINV , INFO )
|
|
*
|
|
SRNAMT = 'CTFTTR'
|
|
CALL CTFTTR( CFORM, UPLO, N, ARFINV, AINV, LDA,
|
|
+ INFO )
|
|
*
|
|
* Check error code from CPFTRI.
|
|
*
|
|
IF( INFO.NE.0 )
|
|
+ CALL ALAERH( 'CPO', 'CPFTRI', INFO, 0, UPLO, N,
|
|
+ N, -1, -1, -1, IMAT, NFAIL, NERRS,
|
|
+ NOUT )
|
|
*
|
|
CALL CPOT03( UPLO, N, A, LDA, AINV, LDA,
|
|
+ C_WORK_CPOT03, LDA, S_WORK_CPOT03,
|
|
+ RCONDC, RESULT( 2 ) )
|
|
*
|
|
* Compute residual of the computed solution.
|
|
*
|
|
CALL CLACPY( 'Full', N, NRHS, B, LDA,
|
|
+ C_WORK_CPOT02, LDA )
|
|
CALL CPOT02( UPLO, N, NRHS, A, LDA, X, LDA,
|
|
+ C_WORK_CPOT02, LDA, S_WORK_CPOT02,
|
|
+ RESULT( 3 ) )
|
|
*
|
|
* Check solution from generated exact solution.
|
|
*
|
|
CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
|
|
+ RESULT( 4 ) )
|
|
NT = 4
|
|
*
|
|
* Print information about the tests that did not
|
|
* pass the threshold.
|
|
*
|
|
DO 60 K = 1, NT
|
|
IF( RESULT( K ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
+ CALL ALADHD( NOUT, 'CPF' )
|
|
WRITE( NOUT, FMT = 9999 )'CPFSV ', UPLO,
|
|
+ N, IIT, K, RESULT( K )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
60 CONTINUE
|
|
NRUN = NRUN + NT
|
|
100 CONTINUE
|
|
110 CONTINUE
|
|
120 CONTINUE
|
|
980 CONTINUE
|
|
130 CONTINUE
|
|
*
|
|
* Print a summary of the results.
|
|
*
|
|
CALL ALASVM( 'CPF', NOUT, NFAIL, NRUN, NERRS )
|
|
*
|
|
9999 FORMAT( 1X, A6, ', UPLO=''', A1, ''', N =', I5, ', type ', I1,
|
|
+ ', test(', I1, ')=', G12.5 )
|
|
*
|
|
RETURN
|
|
*
|
|
* End of CDRVRFP
|
|
*
|
|
END
|