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882 lines
30 KiB
882 lines
30 KiB
*> \brief \b SCHKSB2STG
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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 SCHKSB2STG( NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE,
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* ISEED, THRESH, NOUNIT, A, LDA, SD, SE, D1,
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* D2, D3, U, LDU, WORK, LWORK, RESULT, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES,
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* $ NWDTHS
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* REAL THRESH
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* ..
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* .. Array Arguments ..
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* LOGICAL DOTYPE( * )
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* INTEGER ISEED( 4 ), KK( * ), NN( * )
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* REAL A( LDA, * ), RESULT( * ), SD( * ), SE( * ),
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* $ D1( * ), D2( * ), D3( * ),
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* $ U( LDU, * ), WORK( * )
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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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*> SCHKSB2STG tests the reduction of a symmetric band matrix to tridiagonal
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*> form, used with the symmetric eigenvalue problem.
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*>
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*> SSBTRD factors a symmetric band matrix A as U S U' , where ' means
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*> transpose, S is symmetric tridiagonal, and U is orthogonal.
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*> SSBTRD can use either just the lower or just the upper triangle
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*> of A; SCHKSB2STG checks both cases.
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*>
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*> SSYTRD_SB2ST factors a symmetric band matrix A as U S U' ,
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*> where ' means transpose, S is symmetric tridiagonal, and U is
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*> orthogonal. SSYTRD_SB2ST can use either just the lower or just
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*> the upper triangle of A; SCHKSB2STG checks both cases.
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*>
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*> SSTEQR factors S as Z D1 Z'.
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*> D1 is the matrix of eigenvalues computed when Z is not computed
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*> and from the S resulting of SSBTRD "U" (used as reference for SSYTRD_SB2ST)
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*> D2 is the matrix of eigenvalues computed when Z is not computed
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*> and from the S resulting of SSYTRD_SB2ST "U".
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*> D3 is the matrix of eigenvalues computed when Z is not computed
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*> and from the S resulting of SSYTRD_SB2ST "L".
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*>
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*> When SCHKSB2STG is called, a number of matrix "sizes" ("n's"), a number
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*> of bandwidths ("k's"), and a number of matrix "types" are
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*> specified. For each size ("n"), each bandwidth ("k") less than or
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*> equal to "n", and each type of matrix, one matrix will be generated
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*> and used to test the symmetric banded reduction routine. For each
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*> matrix, a number of tests will be performed:
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*>
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*> (1) | A - V S V' | / ( |A| n ulp ) computed by SSBTRD with
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*> UPLO='U'
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*>
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*> (2) | I - UU' | / ( n ulp )
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*>
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*> (3) | A - V S V' | / ( |A| n ulp ) computed by SSBTRD with
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*> UPLO='L'
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*>
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*> (4) | I - UU' | / ( n ulp )
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*>
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*> (5) | D1 - D2 | / ( |D1| ulp ) where D1 is computed by
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*> SSBTRD with UPLO='U' and
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*> D2 is computed by
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*> SSYTRD_SB2ST with UPLO='U'
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*>
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*> (6) | D1 - D3 | / ( |D1| ulp ) where D1 is computed by
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*> SSBTRD with UPLO='U' and
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*> D3 is computed by
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*> SSYTRD_SB2ST with UPLO='L'
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*>
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*> The "sizes" are specified by an array NN(1:NSIZES); the value of
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*> each element NN(j) specifies one size.
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*> The "types" are specified by a logical array DOTYPE( 1:NTYPES );
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*> if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
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*> Currently, the list of possible types is:
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*>
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*> (1) The zero matrix.
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*> (2) The identity matrix.
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*>
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*> (3) A diagonal matrix with evenly spaced entries
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*> 1, ..., ULP and random signs.
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*> (ULP = (first number larger than 1) - 1 )
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*> (4) A diagonal matrix with geometrically spaced entries
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*> 1, ..., ULP and random signs.
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*> (5) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
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*> and random signs.
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*>
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*> (6) Same as (4), but multiplied by SQRT( overflow threshold )
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*> (7) Same as (4), but multiplied by SQRT( underflow threshold )
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*>
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*> (8) A matrix of the form U' D U, where U is orthogonal and
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*> D has evenly spaced entries 1, ..., ULP with random signs
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*> on the diagonal.
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*>
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*> (9) A matrix of the form U' D U, where U is orthogonal and
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*> D has geometrically spaced entries 1, ..., ULP with random
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*> signs on the diagonal.
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*>
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*> (10) A matrix of the form U' D U, where U is orthogonal and
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*> D has "clustered" entries 1, ULP,..., ULP with random
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*> signs on the diagonal.
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*>
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*> (11) Same as (8), but multiplied by SQRT( overflow threshold )
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*> (12) Same as (8), but multiplied by SQRT( underflow threshold )
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*>
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*> (13) Symmetric matrix with random entries chosen from (-1,1).
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*> (14) Same as (13), but multiplied by SQRT( overflow threshold )
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*> (15) Same as (13), but multiplied by SQRT( underflow threshold )
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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] NSIZES
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*> \verbatim
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*> NSIZES is INTEGER
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*> The number of sizes of matrices to use. If it is zero,
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*> SCHKSB2STG does nothing. It must be at least zero.
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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 array, dimension (NSIZES)
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*> An array containing the sizes to be used for the matrices.
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*> Zero values will be skipped. The values must be at least
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*> zero.
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*> \endverbatim
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*>
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*> \param[in] NWDTHS
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*> \verbatim
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*> NWDTHS is INTEGER
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*> The number of bandwidths to use. If it is zero,
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*> SCHKSB2STG does nothing. It must be at least zero.
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*> \endverbatim
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*>
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*> \param[in] KK
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*> \verbatim
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*> KK is INTEGER array, dimension (NWDTHS)
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*> An array containing the bandwidths to be used for the band
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*> matrices. The values must be at least zero.
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*> \endverbatim
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*>
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*> \param[in] NTYPES
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*> \verbatim
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*> NTYPES is INTEGER
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*> The number of elements in DOTYPE. If it is zero, SCHKSB2STG
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*> does nothing. It must be at least zero. If it is MAXTYP+1
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*> and NSIZES is 1, then an additional type, MAXTYP+1 is
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*> defined, which is to use whatever matrix is in A. This
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*> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
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*> DOTYPE(MAXTYP+1) is .TRUE. .
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*> \endverbatim
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*>
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*> \param[in] DOTYPE
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*> \verbatim
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*> DOTYPE is LOGICAL array, dimension (NTYPES)
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*> If DOTYPE(j) is .TRUE., then for each size in NN a
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*> matrix of that size and of type j will be generated.
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*> If NTYPES is smaller than the maximum number of types
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*> defined (PARAMETER MAXTYP), then types NTYPES+1 through
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*> MAXTYP will not be generated. If NTYPES is larger
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*> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
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*> will be ignored.
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*> \endverbatim
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*>
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*> \param[in,out] ISEED
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*> \verbatim
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*> ISEED is INTEGER array, dimension (4)
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*> On entry ISEED specifies the seed of the random number
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*> generator. The array elements should be between 0 and 4095;
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*> if not they will be reduced mod 4096. Also, ISEED(4) must
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*> be odd. The random number generator uses a linear
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*> congruential sequence limited to small integers, and so
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*> should produce machine independent random numbers. The
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*> values of ISEED are changed on exit, and can be used in the
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*> next call to SCHKSB2STG to continue the same random number
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*> sequence.
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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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*> A test will count as "failed" if the "error", computed as
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*> described above, exceeds THRESH. Note that the error
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*> is scaled to be O(1), so THRESH should be a reasonably
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*> small multiple of 1, e.g., 10 or 100. In particular,
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*> it should not depend on the precision (single vs. double)
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*> or the size of the matrix. It must be at least zero.
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*> \endverbatim
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*>
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*> \param[in] NOUNIT
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*> \verbatim
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*> NOUNIT is INTEGER
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*> The FORTRAN unit number for printing out error messages
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*> (e.g., if a routine returns IINFO not equal to 0.)
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is REAL array, dimension
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*> (LDA, max(NN))
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*> Used to hold the matrix whose eigenvalues are to be
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*> computed.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of A. It must be at least 2 (not 1!)
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*> and at least max( KK )+1.
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*> \endverbatim
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*>
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*> \param[out] SD
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*> \verbatim
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*> SD is REAL array, dimension (max(NN))
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*> Used to hold the diagonal of the tridiagonal matrix computed
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*> by SSBTRD.
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*> \endverbatim
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*>
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*> \param[out] SE
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*> \verbatim
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*> SE is REAL array, dimension (max(NN))
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*> Used to hold the off-diagonal of the tridiagonal matrix
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*> computed by SSBTRD.
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*> \endverbatim
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*>
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*> \param[out] D1
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*> \verbatim
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*> D1 is REAL array, dimension (max(NN))
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*> \endverbatim
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*>
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*> \param[out] D2
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*> \verbatim
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*> D2 is REAL array, dimension (max(NN))
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*> \endverbatim
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*>
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*> \param[out] D3
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*> \verbatim
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*> D3 is REAL array, dimension (max(NN))
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*> \endverbatim
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*>
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*> \param[out] U
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*> \verbatim
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*> U is REAL array, dimension (LDU, max(NN))
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*> Used to hold the orthogonal matrix computed by SSBTRD.
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*> \endverbatim
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*>
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*> \param[in] LDU
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*> \verbatim
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*> LDU is INTEGER
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*> The leading dimension of U. It must be at least 1
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*> and at least max( NN ).
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The number of entries in WORK. This must be at least
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*> max( LDA+1, max(NN)+1 )*max(NN).
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*> \endverbatim
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*>
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*> \param[out] RESULT
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*> \verbatim
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*> RESULT is REAL array, dimension (4)
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*> The values computed by the tests described above.
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*> The values are currently limited to 1/ulp, to avoid
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*> overflow.
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> If 0, then everything ran OK.
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*>
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*>-----------------------------------------------------------------------
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*>
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*> Some Local Variables and Parameters:
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*> ---- ----- --------- --- ----------
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*> ZERO, ONE Real 0 and 1.
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*> MAXTYP The number of types defined.
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*> NTEST The number of tests performed, or which can
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*> be performed so far, for the current matrix.
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*> NTESTT The total number of tests performed so far.
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*> NMAX Largest value in NN.
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*> NMATS The number of matrices generated so far.
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*> NERRS The number of tests which have exceeded THRESH
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*> so far.
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*> COND, IMODE Values to be passed to the matrix generators.
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*> ANORM Norm of A; passed to matrix generators.
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*>
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*> OVFL, UNFL Overflow and underflow thresholds.
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*> ULP, ULPINV Finest relative precision and its inverse.
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*> RTOVFL, RTUNFL Square roots of the previous 2 values.
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*> The following four arrays decode JTYPE:
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*> KTYPE(j) The general type (1-10) for type "j".
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*> KMODE(j) The MODE value to be passed to the matrix
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*> generator for type "j".
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*> KMAGN(j) The order of magnitude ( O(1),
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*> O(overflow^(1/2) ), O(underflow^(1/2) )
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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_eig
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*
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* =====================================================================
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SUBROUTINE SCHKSB2STG( NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE,
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$ ISEED, THRESH, NOUNIT, A, LDA, SD, SE, D1,
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$ D2, D3, U, LDU, WORK, LWORK, RESULT, INFO )
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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 INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES,
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$ NWDTHS
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REAL THRESH
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* ..
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* .. Array Arguments ..
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LOGICAL DOTYPE( * )
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INTEGER ISEED( 4 ), KK( * ), NN( * )
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REAL A( LDA, * ), RESULT( * ), SD( * ), SE( * ),
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$ D1( * ), D2( * ), D3( * ),
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$ U( LDU, * ), WORK( * )
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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, TWO, TEN
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PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0,
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$ TEN = 10.0E0 )
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REAL HALF
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PARAMETER ( HALF = ONE / TWO )
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INTEGER MAXTYP
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PARAMETER ( MAXTYP = 15 )
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* ..
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* .. Local Scalars ..
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LOGICAL BADNN, BADNNB
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INTEGER I, IINFO, IMODE, ITYPE, J, JC, JCOL, JR, JSIZE,
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$ JTYPE, JWIDTH, K, KMAX, LH, LW, MTYPES, N,
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$ NERRS, NMATS, NMAX, NTEST, NTESTT
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REAL ANINV, ANORM, COND, OVFL, RTOVFL, RTUNFL,
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$ TEMP1, TEMP2, TEMP3, TEMP4, ULP, ULPINV, UNFL
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* ..
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* .. Local Arrays ..
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INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KMAGN( MAXTYP ),
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$ KMODE( MAXTYP ), KTYPE( MAXTYP )
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* ..
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* .. External Functions ..
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REAL SLAMCH
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EXTERNAL SLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL SLACPY, SLASET, SLASUM, SLATMR, SLATMS, SSBT21,
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$ SSBTRD, XERBLA, SSYTRD_SB2ST, SSTEQR
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, REAL, MAX, MIN, SQRT
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* ..
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* .. Data statements ..
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DATA KTYPE / 1, 2, 5*4, 5*5, 3*8 /
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DATA KMAGN / 2*1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1,
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$ 2, 3 /
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DATA KMODE / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
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$ 0, 0 /
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* ..
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* .. Executable Statements ..
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*
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* Check for errors
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*
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NTESTT = 0
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INFO = 0
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*
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* Important constants
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*
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BADNN = .FALSE.
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NMAX = 1
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DO 10 J = 1, NSIZES
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NMAX = MAX( NMAX, NN( J ) )
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IF( NN( J ).LT.0 )
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$ BADNN = .TRUE.
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10 CONTINUE
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*
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BADNNB = .FALSE.
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KMAX = 0
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DO 20 J = 1, NSIZES
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KMAX = MAX( KMAX, KK( J ) )
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IF( KK( J ).LT.0 )
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$ BADNNB = .TRUE.
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20 CONTINUE
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KMAX = MIN( NMAX-1, KMAX )
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*
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* Check for errors
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*
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IF( NSIZES.LT.0 ) THEN
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INFO = -1
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ELSE IF( BADNN ) THEN
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INFO = -2
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ELSE IF( NWDTHS.LT.0 ) THEN
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INFO = -3
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ELSE IF( BADNNB ) THEN
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INFO = -4
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ELSE IF( NTYPES.LT.0 ) THEN
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INFO = -5
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ELSE IF( LDA.LT.KMAX+1 ) THEN
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INFO = -11
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ELSE IF( LDU.LT.NMAX ) THEN
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INFO = -15
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ELSE IF( ( MAX( LDA, NMAX )+1 )*NMAX.GT.LWORK ) THEN
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INFO = -17
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SCHKSB2STG', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 .OR. NWDTHS.EQ.0 )
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$ RETURN
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*
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* More Important constants
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*
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UNFL = SLAMCH( 'Safe minimum' )
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OVFL = ONE / UNFL
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ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' )
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ULPINV = ONE / ULP
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RTUNFL = SQRT( UNFL )
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RTOVFL = SQRT( OVFL )
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*
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* Loop over sizes, types
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*
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NERRS = 0
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NMATS = 0
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*
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DO 190 JSIZE = 1, NSIZES
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N = NN( JSIZE )
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ANINV = ONE / REAL( MAX( 1, N ) )
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*
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DO 180 JWIDTH = 1, NWDTHS
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K = KK( JWIDTH )
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IF( K.GT.N )
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$ GO TO 180
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K = MAX( 0, MIN( N-1, K ) )
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*
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IF( NSIZES.NE.1 ) THEN
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MTYPES = MIN( MAXTYP, NTYPES )
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ELSE
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MTYPES = MIN( MAXTYP+1, NTYPES )
|
|
END IF
|
|
*
|
|
DO 170 JTYPE = 1, MTYPES
|
|
IF( .NOT.DOTYPE( JTYPE ) )
|
|
$ GO TO 170
|
|
NMATS = NMATS + 1
|
|
NTEST = 0
|
|
*
|
|
DO 30 J = 1, 4
|
|
IOLDSD( J ) = ISEED( J )
|
|
30 CONTINUE
|
|
*
|
|
* Compute "A".
|
|
* Store as "Upper"; later, we will copy to other format.
|
|
*
|
|
* Control parameters:
|
|
*
|
|
* KMAGN KMODE KTYPE
|
|
* =1 O(1) clustered 1 zero
|
|
* =2 large clustered 2 identity
|
|
* =3 small exponential (none)
|
|
* =4 arithmetic diagonal, (w/ eigenvalues)
|
|
* =5 random log symmetric, w/ eigenvalues
|
|
* =6 random (none)
|
|
* =7 random diagonal
|
|
* =8 random symmetric
|
|
* =9 positive definite
|
|
* =10 diagonally dominant tridiagonal
|
|
*
|
|
IF( MTYPES.GT.MAXTYP )
|
|
$ GO TO 100
|
|
*
|
|
ITYPE = KTYPE( JTYPE )
|
|
IMODE = KMODE( JTYPE )
|
|
*
|
|
* Compute norm
|
|
*
|
|
GO TO ( 40, 50, 60 )KMAGN( JTYPE )
|
|
*
|
|
40 CONTINUE
|
|
ANORM = ONE
|
|
GO TO 70
|
|
*
|
|
50 CONTINUE
|
|
ANORM = ( RTOVFL*ULP )*ANINV
|
|
GO TO 70
|
|
*
|
|
60 CONTINUE
|
|
ANORM = RTUNFL*N*ULPINV
|
|
GO TO 70
|
|
*
|
|
70 CONTINUE
|
|
*
|
|
CALL SLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA )
|
|
IINFO = 0
|
|
IF( JTYPE.LE.15 ) THEN
|
|
COND = ULPINV
|
|
ELSE
|
|
COND = ULPINV*ANINV / TEN
|
|
END IF
|
|
*
|
|
* Special Matrices -- Identity & Jordan block
|
|
*
|
|
* Zero
|
|
*
|
|
IF( ITYPE.EQ.1 ) THEN
|
|
IINFO = 0
|
|
*
|
|
ELSE IF( ITYPE.EQ.2 ) THEN
|
|
*
|
|
* Identity
|
|
*
|
|
DO 80 JCOL = 1, N
|
|
A( K+1, JCOL ) = ANORM
|
|
80 CONTINUE
|
|
*
|
|
ELSE IF( ITYPE.EQ.4 ) THEN
|
|
*
|
|
* Diagonal Matrix, [Eigen]values Specified
|
|
*
|
|
CALL SLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
|
|
$ ANORM, 0, 0, 'Q', A( K+1, 1 ), LDA,
|
|
$ WORK( N+1 ), IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.5 ) THEN
|
|
*
|
|
* Symmetric, eigenvalues specified
|
|
*
|
|
CALL SLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
|
|
$ ANORM, K, K, 'Q', A, LDA, WORK( N+1 ),
|
|
$ IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.7 ) THEN
|
|
*
|
|
* Diagonal, random eigenvalues
|
|
*
|
|
CALL SLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
|
|
$ 'T', 'N', WORK( N+1 ), 1, ONE,
|
|
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0,
|
|
$ ZERO, ANORM, 'Q', A( K+1, 1 ), LDA,
|
|
$ IDUMMA, IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.8 ) THEN
|
|
*
|
|
* Symmetric, random eigenvalues
|
|
*
|
|
CALL SLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
|
|
$ 'T', 'N', WORK( N+1 ), 1, ONE,
|
|
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, K, K,
|
|
$ ZERO, ANORM, 'Q', A, LDA, IDUMMA, IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.9 ) THEN
|
|
*
|
|
* Positive definite, eigenvalues specified.
|
|
*
|
|
CALL SLATMS( N, N, 'S', ISEED, 'P', WORK, IMODE, COND,
|
|
$ ANORM, K, K, 'Q', A, LDA, WORK( N+1 ),
|
|
$ IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.10 ) THEN
|
|
*
|
|
* Positive definite tridiagonal, eigenvalues specified.
|
|
*
|
|
IF( N.GT.1 )
|
|
$ K = MAX( 1, K )
|
|
CALL SLATMS( N, N, 'S', ISEED, 'P', WORK, IMODE, COND,
|
|
$ ANORM, 1, 1, 'Q', A( K, 1 ), LDA,
|
|
$ WORK( N+1 ), IINFO )
|
|
DO 90 I = 2, N
|
|
TEMP1 = ABS( A( K, I ) ) /
|
|
$ SQRT( ABS( A( K+1, I-1 )*A( K+1, I ) ) )
|
|
IF( TEMP1.GT.HALF ) THEN
|
|
A( K, I ) = HALF*SQRT( ABS( A( K+1,
|
|
$ I-1 )*A( K+1, I ) ) )
|
|
END IF
|
|
90 CONTINUE
|
|
*
|
|
ELSE
|
|
*
|
|
IINFO = 1
|
|
END IF
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
100 CONTINUE
|
|
*
|
|
* Call SSBTRD to compute S and U from upper triangle.
|
|
*
|
|
CALL SLACPY( ' ', K+1, N, A, LDA, WORK, LDA )
|
|
*
|
|
NTEST = 1
|
|
CALL SSBTRD( 'V', 'U', N, K, WORK, LDA, SD, SE, U, LDU,
|
|
$ WORK( LDA*N+1 ), IINFO )
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'SSBTRD(U)', IINFO, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
IF( IINFO.LT.0 ) THEN
|
|
RETURN
|
|
ELSE
|
|
RESULT( 1 ) = ULPINV
|
|
GO TO 150
|
|
END IF
|
|
END IF
|
|
*
|
|
* Do tests 1 and 2
|
|
*
|
|
CALL SSBT21( 'Upper', N, K, 1, A, LDA, SD, SE, U, LDU,
|
|
$ WORK, RESULT( 1 ) )
|
|
*
|
|
* Before converting A into lower for SSBTRD, run SSYTRD_SB2ST
|
|
* otherwise matrix A will be converted to lower and then need
|
|
* to be converted back to upper in order to run the upper case
|
|
* ofSSYTRD_SB2ST
|
|
*
|
|
* Compute D1 the eigenvalues resulting from the tridiagonal
|
|
* form using the SSBTRD and used as reference to compare
|
|
* with the SSYTRD_SB2ST routine
|
|
*
|
|
* Compute D1 from the SSBTRD and used as reference for the
|
|
* SSYTRD_SB2ST
|
|
*
|
|
CALL SCOPY( N, SD, 1, D1, 1 )
|
|
IF( N.GT.0 )
|
|
$ CALL SCOPY( N-1, SE, 1, WORK, 1 )
|
|
*
|
|
CALL SSTEQR( 'N', N, D1, WORK, WORK( N+1 ), LDU,
|
|
$ WORK( N+1 ), IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'SSTEQR(N)', IINFO, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
IF( IINFO.LT.0 ) THEN
|
|
RETURN
|
|
ELSE
|
|
RESULT( 5 ) = ULPINV
|
|
GO TO 150
|
|
END IF
|
|
END IF
|
|
*
|
|
* SSYTRD_SB2ST Upper case is used to compute D2.
|
|
* Note to set SD and SE to zero to be sure not reusing
|
|
* the one from above. Compare it with D1 computed
|
|
* using the SSBTRD.
|
|
*
|
|
CALL SLASET( 'Full', N, 1, ZERO, ZERO, SD, N )
|
|
CALL SLASET( 'Full', N, 1, ZERO, ZERO, SE, N )
|
|
CALL SLACPY( ' ', K+1, N, A, LDA, U, LDU )
|
|
LH = MAX(1, 4*N)
|
|
LW = LWORK - LH
|
|
CALL SSYTRD_SB2ST( 'N', 'N', "U", N, K, U, LDU, SD, SE,
|
|
$ WORK, LH, WORK( LH+1 ), LW, IINFO )
|
|
*
|
|
* Compute D2 from the SSYTRD_SB2ST Upper case
|
|
*
|
|
CALL SCOPY( N, SD, 1, D2, 1 )
|
|
IF( N.GT.0 )
|
|
$ CALL SCOPY( N-1, SE, 1, WORK, 1 )
|
|
*
|
|
CALL SSTEQR( 'N', N, D2, WORK, WORK( N+1 ), LDU,
|
|
$ WORK( N+1 ), IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'SSTEQR(N)', IINFO, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
IF( IINFO.LT.0 ) THEN
|
|
RETURN
|
|
ELSE
|
|
RESULT( 5 ) = ULPINV
|
|
GO TO 150
|
|
END IF
|
|
END IF
|
|
*
|
|
* Convert A from Upper-Triangle-Only storage to
|
|
* Lower-Triangle-Only storage.
|
|
*
|
|
DO 120 JC = 1, N
|
|
DO 110 JR = 0, MIN( K, N-JC )
|
|
A( JR+1, JC ) = A( K+1-JR, JC+JR )
|
|
110 CONTINUE
|
|
120 CONTINUE
|
|
DO 140 JC = N + 1 - K, N
|
|
DO 130 JR = MIN( K, N-JC ) + 1, K
|
|
A( JR+1, JC ) = ZERO
|
|
130 CONTINUE
|
|
140 CONTINUE
|
|
*
|
|
* Call SSBTRD to compute S and U from lower triangle
|
|
*
|
|
CALL SLACPY( ' ', K+1, N, A, LDA, WORK, LDA )
|
|
*
|
|
NTEST = 3
|
|
CALL SSBTRD( 'V', 'L', N, K, WORK, LDA, SD, SE, U, LDU,
|
|
$ WORK( LDA*N+1 ), IINFO )
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'SSBTRD(L)', IINFO, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
IF( IINFO.LT.0 ) THEN
|
|
RETURN
|
|
ELSE
|
|
RESULT( 3 ) = ULPINV
|
|
GO TO 150
|
|
END IF
|
|
END IF
|
|
NTEST = 4
|
|
*
|
|
* Do tests 3 and 4
|
|
*
|
|
CALL SSBT21( 'Lower', N, K, 1, A, LDA, SD, SE, U, LDU,
|
|
$ WORK, RESULT( 3 ) )
|
|
*
|
|
* SSYTRD_SB2ST Lower case is used to compute D3.
|
|
* Note to set SD and SE to zero to be sure not reusing
|
|
* the one from above. Compare it with D1 computed
|
|
* using the SSBTRD.
|
|
*
|
|
CALL SLASET( 'Full', N, 1, ZERO, ZERO, SD, N )
|
|
CALL SLASET( 'Full', N, 1, ZERO, ZERO, SE, N )
|
|
CALL SLACPY( ' ', K+1, N, A, LDA, U, LDU )
|
|
LH = MAX(1, 4*N)
|
|
LW = LWORK - LH
|
|
CALL SSYTRD_SB2ST( 'N', 'N', "L", N, K, U, LDU, SD, SE,
|
|
$ WORK, LH, WORK( LH+1 ), LW, IINFO )
|
|
*
|
|
* Compute D3 from the 2-stage Upper case
|
|
*
|
|
CALL SCOPY( N, SD, 1, D3, 1 )
|
|
IF( N.GT.0 )
|
|
$ CALL SCOPY( N-1, SE, 1, WORK, 1 )
|
|
*
|
|
CALL SSTEQR( 'N', N, D3, WORK, WORK( N+1 ), LDU,
|
|
$ WORK( N+1 ), IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'SSTEQR(N)', IINFO, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
IF( IINFO.LT.0 ) THEN
|
|
RETURN
|
|
ELSE
|
|
RESULT( 6 ) = ULPINV
|
|
GO TO 150
|
|
END IF
|
|
END IF
|
|
*
|
|
*
|
|
* Do Tests 3 and 4 which are similar to 11 and 12 but with the
|
|
* D1 computed using the standard 1-stage reduction as reference
|
|
*
|
|
NTEST = 6
|
|
TEMP1 = ZERO
|
|
TEMP2 = ZERO
|
|
TEMP3 = ZERO
|
|
TEMP4 = ZERO
|
|
*
|
|
DO 151 J = 1, N
|
|
TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D2( J ) ) )
|
|
TEMP2 = MAX( TEMP2, ABS( D1( J )-D2( J ) ) )
|
|
TEMP3 = MAX( TEMP3, ABS( D1( J ) ), ABS( D3( J ) ) )
|
|
TEMP4 = MAX( TEMP4, ABS( D1( J )-D3( J ) ) )
|
|
151 CONTINUE
|
|
*
|
|
RESULT(5) = TEMP2 / MAX( UNFL, ULP*MAX( TEMP1, TEMP2 ) )
|
|
RESULT(6) = TEMP4 / MAX( UNFL, ULP*MAX( TEMP3, TEMP4 ) )
|
|
*
|
|
* End of Loop -- Check for RESULT(j) > THRESH
|
|
*
|
|
150 CONTINUE
|
|
NTESTT = NTESTT + NTEST
|
|
*
|
|
* Print out tests which fail.
|
|
*
|
|
DO 160 JR = 1, NTEST
|
|
IF( RESULT( JR ).GE.THRESH ) THEN
|
|
*
|
|
* If this is the first test to fail,
|
|
* print a header to the data file.
|
|
*
|
|
IF( NERRS.EQ.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'SSB'
|
|
WRITE( NOUNIT, FMT = 9997 )
|
|
WRITE( NOUNIT, FMT = 9996 )
|
|
WRITE( NOUNIT, FMT = 9995 )'Symmetric'
|
|
WRITE( NOUNIT, FMT = 9994 )'orthogonal', '''',
|
|
$ 'transpose', ( '''', J = 1, 6 )
|
|
END IF
|
|
NERRS = NERRS + 1
|
|
WRITE( NOUNIT, FMT = 9993 )N, K, IOLDSD, JTYPE,
|
|
$ JR, RESULT( JR )
|
|
END IF
|
|
160 CONTINUE
|
|
*
|
|
170 CONTINUE
|
|
180 CONTINUE
|
|
190 CONTINUE
|
|
*
|
|
* Summary
|
|
*
|
|
CALL SLASUM( 'SSB', NOUNIT, NERRS, NTESTT )
|
|
RETURN
|
|
*
|
|
9999 FORMAT( ' SCHKSB2STG: ', A, ' returned INFO=', I6, '.', / 9X,
|
|
$ 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5,
|
|
$ ')' )
|
|
*
|
|
9998 FORMAT( / 1X, A3,
|
|
$ ' -- Real Symmetric Banded Tridiagonal Reduction Routines' )
|
|
9997 FORMAT( ' Matrix types (see SCHKSB2STG for details): ' )
|
|
*
|
|
9996 FORMAT( / ' Special Matrices:',
|
|
$ / ' 1=Zero matrix. ',
|
|
$ ' 5=Diagonal: clustered entries.',
|
|
$ / ' 2=Identity matrix. ',
|
|
$ ' 6=Diagonal: large, evenly spaced.',
|
|
$ / ' 3=Diagonal: evenly spaced entries. ',
|
|
$ ' 7=Diagonal: small, evenly spaced.',
|
|
$ / ' 4=Diagonal: geometr. spaced entries.' )
|
|
9995 FORMAT( ' Dense ', A, ' Banded Matrices:',
|
|
$ / ' 8=Evenly spaced eigenvals. ',
|
|
$ ' 12=Small, evenly spaced eigenvals.',
|
|
$ / ' 9=Geometrically spaced eigenvals. ',
|
|
$ ' 13=Matrix with random O(1) entries.',
|
|
$ / ' 10=Clustered eigenvalues. ',
|
|
$ ' 14=Matrix with large random entries.',
|
|
$ / ' 11=Large, evenly spaced eigenvals. ',
|
|
$ ' 15=Matrix with small random entries.' )
|
|
*
|
|
9994 FORMAT( / ' Tests performed: (S is Tridiag, U is ', A, ',',
|
|
$ / 20X, A, ' means ', A, '.', / ' UPLO=''U'':',
|
|
$ / ' 1= | A - U S U', A1, ' | / ( |A| n ulp ) ',
|
|
$ ' 2= | I - U U', A1, ' | / ( n ulp )', / ' UPLO=''L'':',
|
|
$ / ' 3= | A - U S U', A1, ' | / ( |A| n ulp ) ',
|
|
$ ' 4= | I - U U', A1, ' | / ( n ulp )' / ' Eig check:',
|
|
$ /' 5= | D1 - D2', '', ' | / ( |D1| ulp ) ',
|
|
$ ' 6= | D1 - D3', '', ' | / ( |D1| ulp ) ' )
|
|
9993 FORMAT( ' N=', I5, ', K=', I4, ', seed=', 4( I4, ',' ), ' type ',
|
|
$ I2, ', test(', I2, ')=', G10.3 )
|
|
*
|
|
* End of SCHKSB2STG
|
|
*
|
|
END
|
|
|