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579 lines
19 KiB
579 lines
19 KiB
*> \brief \b SDRVRFP
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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 SDRVRFP( 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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* + S_WORK_SLATMS, S_WORK_SPOT01, S_TEMP_SPOT02,
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* + S_TEMP_SPOT03, S_WORK_SLANSY,
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* + S_WORK_SPOT02, S_WORK_SPOT03 )
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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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* REAL A( * )
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* REAL AINV( * )
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* REAL ASAV( * )
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* REAL B( * )
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* REAL BSAV( * )
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* REAL AFAC( * )
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* REAL ARF( * )
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* REAL ARFINV( * )
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* REAL XACT( * )
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* REAL X( * )
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* REAL S_WORK_SLATMS( * )
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* REAL S_WORK_SPOT01( * )
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* REAL S_TEMP_SPOT02( * )
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* REAL S_TEMP_SPOT03( * )
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* REAL S_WORK_SLANSY( * )
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* REAL S_WORK_SPOT02( * )
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* REAL S_WORK_SPOT03( * )
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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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*> SDRVRFP tests the LAPACK RFP routines:
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*> SPFTRF, SPFTRS, and SPFTRI.
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*>
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*> This testing routine follow the same tests as DDRVPO (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 STRTTF and
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*> STFTTR.
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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 SPFTRF, 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 SPFTRF 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL array, dimension ((NMAX*(NMAX+1))/2)
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*> \endverbatim
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*>
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*> \param[out] S_WORK_SLATMS
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*> \verbatim
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*> S_WORK_SLATMS is REAL array, dimension ( 3*NMAX )
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*> \endverbatim
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*>
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*> \param[out] S_WORK_SPOT01
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*> \verbatim
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*> S_WORK_SPOT01 is REAL array, dimension ( NMAX )
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*> \endverbatim
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*>
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*> \param[out] S_TEMP_SPOT02
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*> \verbatim
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*> S_TEMP_SPOT02 is REAL array, dimension ( NMAX*MAXRHS )
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*> \endverbatim
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*>
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*> \param[out] S_TEMP_SPOT03
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*> \verbatim
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*> S_TEMP_SPOT03 is REAL array, dimension ( NMAX*NMAX )
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*> \endverbatim
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*>
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*> \param[out] S_WORK_SLANSY
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*> \verbatim
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*> S_WORK_SLANSY is REAL array, dimension ( NMAX )
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*> \endverbatim
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*>
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*> \param[out] S_WORK_SPOT02
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*> \verbatim
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*> S_WORK_SPOT02 is REAL array, dimension ( NMAX )
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*> \endverbatim
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*>
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*> \param[out] S_WORK_SPOT03
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*> \verbatim
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*> S_WORK_SPOT03 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 single_lin
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*
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* =====================================================================
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SUBROUTINE SDRVRFP( 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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+ S_WORK_SLATMS, S_WORK_SPOT01, S_TEMP_SPOT02,
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+ S_TEMP_SPOT03, S_WORK_SLANSY,
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+ S_WORK_SPOT02, S_WORK_SPOT03 )
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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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REAL A( * )
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REAL AINV( * )
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REAL ASAV( * )
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REAL B( * )
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REAL BSAV( * )
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REAL AFAC( * )
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REAL ARF( * )
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REAL ARFINV( * )
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REAL XACT( * )
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REAL X( * )
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REAL S_WORK_SLATMS( * )
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REAL S_WORK_SPOT01( * )
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REAL S_TEMP_SPOT02( * )
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REAL S_TEMP_SPOT03( * )
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REAL S_WORK_SLANSY( * )
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REAL S_WORK_SPOT02( * )
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REAL S_WORK_SPOT03( * )
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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 ONE, ZERO
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PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+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 SLANSY
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EXTERNAL SLANSY
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* ..
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* .. External Subroutines ..
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EXTERNAL ALADHD, ALAERH, ALASVM, SGET04, STFTTR, SLACPY,
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+ SLARHS, SLATB4, SLATMS, SPFTRI, SPFTRF, SPFTRS,
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+ SPOT01, SPOT02, SPOT03, SPOTRI, SPOTRF, STRTTF
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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', 'T' /
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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 SLATB4 and generate a test
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* matrix with SLATMS.
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*
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CALL SLATB4( 'SPO', IMAT, N, N, CTYPE, KL, KU,
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+ ANORM, MODE, CNDNUM, DIST )
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*
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SRNAMT = 'SLATMS'
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CALL SLATMS( N, N, DIST, ISEED, CTYPE,
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+ S_WORK_SLATMS,
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+ MODE, CNDNUM, ANORM, KL, KU, UPLO, A,
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+ LDA, S_WORK_SLATMS, INFO )
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*
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* Check error code from SLATMS.
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*
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IF( INFO.NE.0 ) THEN
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CALL ALAERH( 'SPF', 'SLATMS', 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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* Save a copy of the matrix A in ASAV.
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*
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CALL SLACPY( 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 = SLANSY( '1', UPLO, N, A, LDA,
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+ S_WORK_SLANSY )
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*
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* Factor the matrix A.
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*
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CALL SPOTRF( 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 SPOTRI( 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 = SLANSY( '1', UPLO, N, A, LDA,
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+ S_WORK_SLANSY )
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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 SLACPY( 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 = 'SLARHS'
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CALL SLARHS( 'SPO', '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 SLACPY( '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 SLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
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CALL SLACPY( 'Full', N, NRHS, B, LDB, X, LDB )
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*
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SRNAMT = 'STRTTF'
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CALL STRTTF( CFORM, UPLO, N, AFAC, LDA, ARF, INFO )
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SRNAMT = 'SPFTRF'
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CALL SPFTRF( CFORM, UPLO, N, ARF, INFO )
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*
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* Check error code from SPFTRF.
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*
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IF( INFO.NE.IZERO ) THEN
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*
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* LANGOU: there is a small hick here: IZERO should
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* always be INFO however if INFO is ZERO, ALAERH does not
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* complain.
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*
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CALL ALAERH( 'SPF', 'SPFSV ', INFO, IZERO,
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+ UPLO, N, N, -1, -1, NRHS, IIT,
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+ NFAIL, NERRS, NOUT )
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GO TO 100
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END IF
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*
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* Skip the tests if INFO is not 0.
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*
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IF( INFO.NE.0 ) THEN
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GO TO 100
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END IF
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*
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SRNAMT = 'SPFTRS'
|
|
CALL SPFTRS( CFORM, UPLO, N, NRHS, ARF, X, LDB,
|
|
+ INFO )
|
|
*
|
|
SRNAMT = 'STFTTR'
|
|
CALL STFTTR( CFORM, UPLO, N, ARF, AFAC, LDA, INFO )
|
|
*
|
|
* Reconstruct matrix from factors and compute
|
|
* residual.
|
|
*
|
|
CALL SLACPY( UPLO, N, N, AFAC, LDA, ASAV, LDA )
|
|
CALL SPOT01( UPLO, N, A, LDA, AFAC, LDA,
|
|
+ S_WORK_SPOT01, RESULT( 1 ) )
|
|
CALL SLACPY( UPLO, N, N, ASAV, LDA, AFAC, LDA )
|
|
*
|
|
* Form the inverse and compute the residual.
|
|
*
|
|
IF(MOD(N,2).EQ.0)THEN
|
|
CALL SLACPY( 'A', N+1, N/2, ARF, N+1, ARFINV,
|
|
+ N+1 )
|
|
ELSE
|
|
CALL SLACPY( 'A', N, (N+1)/2, ARF, N, ARFINV,
|
|
+ N )
|
|
END IF
|
|
*
|
|
SRNAMT = 'SPFTRI'
|
|
CALL SPFTRI( CFORM, UPLO, N, ARFINV , INFO )
|
|
*
|
|
SRNAMT = 'STFTTR'
|
|
CALL STFTTR( CFORM, UPLO, N, ARFINV, AINV, LDA,
|
|
+ INFO )
|
|
*
|
|
* Check error code from SPFTRI.
|
|
*
|
|
IF( INFO.NE.0 )
|
|
+ CALL ALAERH( 'SPO', 'SPFTRI', INFO, 0, UPLO, N,
|
|
+ N, -1, -1, -1, IMAT, NFAIL, NERRS,
|
|
+ NOUT )
|
|
*
|
|
CALL SPOT03( UPLO, N, A, LDA, AINV, LDA,
|
|
+ S_TEMP_SPOT03, LDA, S_WORK_SPOT03,
|
|
+ RCONDC, RESULT( 2 ) )
|
|
*
|
|
* Compute residual of the computed solution.
|
|
*
|
|
CALL SLACPY( 'Full', N, NRHS, B, LDA,
|
|
+ S_TEMP_SPOT02, LDA )
|
|
CALL SPOT02( UPLO, N, NRHS, A, LDA, X, LDA,
|
|
+ S_TEMP_SPOT02, LDA, S_WORK_SPOT02,
|
|
+ RESULT( 3 ) )
|
|
*
|
|
* Check solution from generated exact solution.
|
|
|
|
CALL SGET04( 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, 'SPF' )
|
|
WRITE( NOUT, FMT = 9999 )'SPFSV ', 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( 'SPF', NOUT, NFAIL, NRUN, NERRS )
|
|
*
|
|
9999 FORMAT( 1X, A6, ', UPLO=''', A1, ''', N =', I5, ', type ', I1,
|
|
+ ', test(', I1, ')=', G12.5 )
|
|
*
|
|
RETURN
|
|
*
|
|
* End of SDRVRFP
|
|
*
|
|
END
|
|
|