You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
1327 lines
47 KiB
1327 lines
47 KiB
2 years ago
|
*> \brief \b CDRVSG
|
||
|
|
*
|
||
|
|
* =========== DOCUMENTATION ===========
|
||
|
|
*
|
||
|
|
* Online html documentation available at
|
||
|
|
* http://www.netlib.org/lapack/explore-html/
|
||
|
|
*
|
||
|
|
* Definition:
|
||
|
|
* ===========
|
||
|
|
*
|
||
|
|
* SUBROUTINE CDRVSG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
|
||
|
|
* NOUNIT, A, LDA, B, LDB, D, Z, LDZ, AB, BB, AP,
|
||
|
|
* BP, WORK, NWORK, RWORK, LRWORK, IWORK, LIWORK,
|
||
|
|
* RESULT, INFO )
|
||
|
|
*
|
||
|
|
* .. Scalar Arguments ..
|
||
|
|
* INTEGER INFO, LDA, LDB, LDZ, LIWORK, LRWORK, NOUNIT,
|
||
|
|
* $ NSIZES, NTYPES, NWORK
|
||
|
|
* REAL THRESH
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
* LOGICAL DOTYPE( * )
|
||
|
|
* INTEGER ISEED( 4 ), IWORK( * ), NN( * )
|
||
|
|
* REAL D( * ), RESULT( * ), RWORK( * )
|
||
|
|
* COMPLEX A( LDA, * ), AB( LDA, * ), AP( * ),
|
||
|
|
* $ B( LDB, * ), BB( LDB, * ), BP( * ), WORK( * ),
|
||
|
|
* $ Z( LDZ, * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
*
|
||
|
|
*> \par Purpose:
|
||
|
|
* =============
|
||
|
|
*>
|
||
|
|
*> \verbatim
|
||
|
|
*>
|
||
|
|
*> CDRVSG checks the complex Hermitian generalized eigenproblem
|
||
|
|
*> drivers.
|
||
|
|
*>
|
||
|
|
*> CHEGV computes all eigenvalues and, optionally,
|
||
|
|
*> eigenvectors of a complex Hermitian-definite generalized
|
||
|
|
*> eigenproblem.
|
||
|
|
*>
|
||
|
|
*> CHEGVD computes all eigenvalues and, optionally,
|
||
|
|
*> eigenvectors of a complex Hermitian-definite generalized
|
||
|
|
*> eigenproblem using a divide and conquer algorithm.
|
||
|
|
*>
|
||
|
|
*> CHEGVX computes selected eigenvalues and, optionally,
|
||
|
|
*> eigenvectors of a complex Hermitian-definite generalized
|
||
|
|
*> eigenproblem.
|
||
|
|
*>
|
||
|
|
*> CHPGV computes all eigenvalues and, optionally,
|
||
|
|
*> eigenvectors of a complex Hermitian-definite generalized
|
||
|
|
*> eigenproblem in packed storage.
|
||
|
|
*>
|
||
|
|
*> CHPGVD computes all eigenvalues and, optionally,
|
||
|
|
*> eigenvectors of a complex Hermitian-definite generalized
|
||
|
|
*> eigenproblem in packed storage using a divide and
|
||
|
|
*> conquer algorithm.
|
||
|
|
*>
|
||
|
|
*> CHPGVX computes selected eigenvalues and, optionally,
|
||
|
|
*> eigenvectors of a complex Hermitian-definite generalized
|
||
|
|
*> eigenproblem in packed storage.
|
||
|
|
*>
|
||
|
|
*> CHBGV computes all eigenvalues and, optionally,
|
||
|
|
*> eigenvectors of a complex Hermitian-definite banded
|
||
|
|
*> generalized eigenproblem.
|
||
|
|
*>
|
||
|
|
*> CHBGVD computes all eigenvalues and, optionally,
|
||
|
|
*> eigenvectors of a complex Hermitian-definite banded
|
||
|
|
*> generalized eigenproblem using a divide and conquer
|
||
|
|
*> algorithm.
|
||
|
|
*>
|
||
|
|
*> CHBGVX computes selected eigenvalues and, optionally,
|
||
|
|
*> eigenvectors of a complex Hermitian-definite banded
|
||
|
|
*> generalized eigenproblem.
|
||
|
|
*>
|
||
|
|
*> When CDRVSG is called, a number of matrix "sizes" ("n's") and a
|
||
|
|
*> number of matrix "types" are specified. For each size ("n")
|
||
|
|
*> and each type of matrix, one matrix A of the given type will be
|
||
|
|
*> generated; a random well-conditioned matrix B is also generated
|
||
|
|
*> and the pair (A,B) is used to test the drivers.
|
||
|
|
*>
|
||
|
|
*> For each pair (A,B), the following tests are performed:
|
||
|
|
*>
|
||
|
|
*> (1) CHEGV with ITYPE = 1 and UPLO ='U':
|
||
|
|
*>
|
||
|
|
*> | A Z - B Z D | / ( |A| |Z| n ulp )
|
||
|
|
*>
|
||
|
|
*> (2) as (1) but calling CHPGV
|
||
|
|
*> (3) as (1) but calling CHBGV
|
||
|
|
*> (4) as (1) but with UPLO = 'L'
|
||
|
|
*> (5) as (4) but calling CHPGV
|
||
|
|
*> (6) as (4) but calling CHBGV
|
||
|
|
*>
|
||
|
|
*> (7) CHEGV with ITYPE = 2 and UPLO ='U':
|
||
|
|
*>
|
||
|
|
*> | A B Z - Z D | / ( |A| |Z| n ulp )
|
||
|
|
*>
|
||
|
|
*> (8) as (7) but calling CHPGV
|
||
|
|
*> (9) as (7) but with UPLO = 'L'
|
||
|
|
*> (10) as (9) but calling CHPGV
|
||
|
|
*>
|
||
|
|
*> (11) CHEGV with ITYPE = 3 and UPLO ='U':
|
||
|
|
*>
|
||
|
|
*> | B A Z - Z D | / ( |A| |Z| n ulp )
|
||
|
|
*>
|
||
|
|
*> (12) as (11) but calling CHPGV
|
||
|
|
*> (13) as (11) but with UPLO = 'L'
|
||
|
|
*> (14) as (13) but calling CHPGV
|
||
|
|
*>
|
||
|
|
*> CHEGVD, CHPGVD and CHBGVD performed the same 14 tests.
|
||
|
|
*>
|
||
|
|
*> CHEGVX, CHPGVX and CHBGVX performed the above 14 tests with
|
||
|
|
*> the parameter RANGE = 'A', 'N' and 'I', respectively.
|
||
|
|
*>
|
||
|
|
*> The "sizes" are specified by an array NN(1:NSIZES); the value of
|
||
|
|
*> each element NN(j) specifies one size.
|
||
|
|
*> The "types" are specified by a logical array DOTYPE( 1:NTYPES );
|
||
|
|
*> if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
|
||
|
|
*> This type is used for the matrix A which has half-bandwidth KA.
|
||
|
|
*> B is generated as a well-conditioned positive definite matrix
|
||
|
|
*> with half-bandwidth KB (<= KA).
|
||
|
|
*> Currently, the list of possible types for A is:
|
||
|
|
*>
|
||
|
|
*> (1) The zero matrix.
|
||
|
|
*> (2) The identity matrix.
|
||
|
|
*>
|
||
|
|
*> (3) A diagonal matrix with evenly spaced entries
|
||
|
|
*> 1, ..., ULP and random signs.
|
||
|
|
*> (ULP = (first number larger than 1) - 1 )
|
||
|
|
*> (4) A diagonal matrix with geometrically spaced entries
|
||
|
|
*> 1, ..., ULP and random signs.
|
||
|
|
*> (5) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
|
||
|
|
*> and random signs.
|
||
|
|
*>
|
||
|
|
*> (6) Same as (4), but multiplied by SQRT( overflow threshold )
|
||
|
|
*> (7) Same as (4), but multiplied by SQRT( underflow threshold )
|
||
|
|
*>
|
||
|
|
*> (8) A matrix of the form U* D U, where U is unitary and
|
||
|
|
*> D has evenly spaced entries 1, ..., ULP with random signs
|
||
|
|
*> on the diagonal.
|
||
|
|
*>
|
||
|
|
*> (9) A matrix of the form U* D U, where U is unitary and
|
||
|
|
*> D has geometrically spaced entries 1, ..., ULP with random
|
||
|
|
*> signs on the diagonal.
|
||
|
|
*>
|
||
|
|
*> (10) A matrix of the form U* D U, where U is unitary and
|
||
|
|
*> D has "clustered" entries 1, ULP,..., ULP with random
|
||
|
|
*> signs on the diagonal.
|
||
|
|
*>
|
||
|
|
*> (11) Same as (8), but multiplied by SQRT( overflow threshold )
|
||
|
|
*> (12) Same as (8), but multiplied by SQRT( underflow threshold )
|
||
|
|
*>
|
||
|
|
*> (13) Hermitian matrix with random entries chosen from (-1,1).
|
||
|
|
*> (14) Same as (13), but multiplied by SQRT( overflow threshold )
|
||
|
|
*> (15) Same as (13), but multiplied by SQRT( underflow threshold )
|
||
|
|
*>
|
||
|
|
*> (16) Same as (8), but with KA = 1 and KB = 1
|
||
|
|
*> (17) Same as (8), but with KA = 2 and KB = 1
|
||
|
|
*> (18) Same as (8), but with KA = 2 and KB = 2
|
||
|
|
*> (19) Same as (8), but with KA = 3 and KB = 1
|
||
|
|
*> (20) Same as (8), but with KA = 3 and KB = 2
|
||
|
|
*> (21) Same as (8), but with KA = 3 and KB = 3
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Arguments:
|
||
|
|
* ==========
|
||
|
|
*
|
||
|
|
*> \verbatim
|
||
|
|
*> NSIZES INTEGER
|
||
|
|
*> The number of sizes of matrices to use. If it is zero,
|
||
|
|
*> CDRVSG does nothing. It must be at least zero.
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> NN INTEGER array, dimension (NSIZES)
|
||
|
|
*> An array containing the sizes to be used for the matrices.
|
||
|
|
*> Zero values will be skipped. The values must be at least
|
||
|
|
*> zero.
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> NTYPES INTEGER
|
||
|
|
*> The number of elements in DOTYPE. If it is zero, CDRVSG
|
||
|
|
*> does nothing. It must be at least zero. If it is MAXTYP+1
|
||
|
|
*> and NSIZES is 1, then an additional type, MAXTYP+1 is
|
||
|
|
*> defined, which is to use whatever matrix is in A. This
|
||
|
|
*> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
|
||
|
|
*> DOTYPE(MAXTYP+1) is .TRUE. .
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> DOTYPE LOGICAL array, dimension (NTYPES)
|
||
|
|
*> If DOTYPE(j) is .TRUE., then for each size in NN a
|
||
|
|
*> matrix of that size and of type j will be generated.
|
||
|
|
*> If NTYPES is smaller than the maximum number of types
|
||
|
|
*> defined (PARAMETER MAXTYP), then types NTYPES+1 through
|
||
|
|
*> MAXTYP will not be generated. If NTYPES is larger
|
||
|
|
*> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
|
||
|
|
*> will be ignored.
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> ISEED INTEGER array, dimension (4)
|
||
|
|
*> On entry ISEED specifies the seed of the random number
|
||
|
|
*> generator. The array elements should be between 0 and 4095;
|
||
|
|
*> if not they will be reduced mod 4096. Also, ISEED(4) must
|
||
|
|
*> be odd. The random number generator uses a linear
|
||
|
|
*> congruential sequence limited to small integers, and so
|
||
|
|
*> should produce machine independent random numbers. The
|
||
|
|
*> values of ISEED are changed on exit, and can be used in the
|
||
|
|
*> next call to CDRVSG to continue the same random number
|
||
|
|
*> sequence.
|
||
|
|
*> Modified.
|
||
|
|
*>
|
||
|
|
*> THRESH REAL
|
||
|
|
*> A test will count as "failed" if the "error", computed as
|
||
|
|
*> described above, exceeds THRESH. Note that the error
|
||
|
|
*> is scaled to be O(1), so THRESH should be a reasonably
|
||
|
|
*> small multiple of 1, e.g., 10 or 100. In particular,
|
||
|
|
*> it should not depend on the precision (single vs. double)
|
||
|
|
*> or the size of the matrix. It must be at least zero.
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> NOUNIT INTEGER
|
||
|
|
*> The FORTRAN unit number for printing out error messages
|
||
|
|
*> (e.g., if a routine returns IINFO not equal to 0.)
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> A COMPLEX array, dimension (LDA , max(NN))
|
||
|
|
*> Used to hold the matrix whose eigenvalues are to be
|
||
|
|
*> computed. On exit, A contains the last matrix actually
|
||
|
|
*> used.
|
||
|
|
*> Modified.
|
||
|
|
*>
|
||
|
|
*> LDA INTEGER
|
||
|
|
*> The leading dimension of A. It must be at
|
||
|
|
*> least 1 and at least max( NN ).
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> B COMPLEX array, dimension (LDB , max(NN))
|
||
|
|
*> Used to hold the Hermitian positive definite matrix for
|
||
|
|
*> the generalized problem.
|
||
|
|
*> On exit, B contains the last matrix actually
|
||
|
|
*> used.
|
||
|
|
*> Modified.
|
||
|
|
*>
|
||
|
|
*> LDB INTEGER
|
||
|
|
*> The leading dimension of B. It must be at
|
||
|
|
*> least 1 and at least max( NN ).
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> D REAL array, dimension (max(NN))
|
||
|
|
*> The eigenvalues of A. On exit, the eigenvalues in D
|
||
|
|
*> correspond with the matrix in A.
|
||
|
|
*> Modified.
|
||
|
|
*>
|
||
|
|
*> Z COMPLEX array, dimension (LDZ, max(NN))
|
||
|
|
*> The matrix of eigenvectors.
|
||
|
|
*> Modified.
|
||
|
|
*>
|
||
|
|
*> LDZ INTEGER
|
||
|
|
*> The leading dimension of ZZ. It must be at least 1 and
|
||
|
|
*> at least max( NN ).
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> AB COMPLEX array, dimension (LDA, max(NN))
|
||
|
|
*> Workspace.
|
||
|
|
*> Modified.
|
||
|
|
*>
|
||
|
|
*> BB COMPLEX array, dimension (LDB, max(NN))
|
||
|
|
*> Workspace.
|
||
|
|
*> Modified.
|
||
|
|
*>
|
||
|
|
*> AP COMPLEX array, dimension (max(NN)**2)
|
||
|
|
*> Workspace.
|
||
|
|
*> Modified.
|
||
|
|
*>
|
||
|
|
*> BP COMPLEX array, dimension (max(NN)**2)
|
||
|
|
*> Workspace.
|
||
|
|
*> Modified.
|
||
|
|
*>
|
||
|
|
*> WORK COMPLEX array, dimension (NWORK)
|
||
|
|
*> Workspace.
|
||
|
|
*> Modified.
|
||
|
|
*>
|
||
|
|
*> NWORK INTEGER
|
||
|
|
*> The number of entries in WORK. This must be at least
|
||
|
|
*> 2*N + N**2 where N = max( NN(j), 2 ).
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> RWORK REAL array, dimension (LRWORK)
|
||
|
|
*> Workspace.
|
||
|
|
*> Modified.
|
||
|
|
*>
|
||
|
|
*> LRWORK INTEGER
|
||
|
|
*> The number of entries in RWORK. This must be at least
|
||
|
|
*> max( 7*N, 1 + 4*N + 2*N*lg(N) + 3*N**2 ) where
|
||
|
|
*> N = max( NN(j) ) and lg( N ) = smallest integer k such
|
||
|
|
*> that 2**k >= N .
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> IWORK INTEGER array, dimension (LIWORK))
|
||
|
|
*> Workspace.
|
||
|
|
*> Modified.
|
||
|
|
*>
|
||
|
|
*> LIWORK INTEGER
|
||
|
|
*> The number of entries in IWORK. This must be at least
|
||
|
|
*> 2 + 5*max( NN(j) ).
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> RESULT REAL array, dimension (70)
|
||
|
|
*> The values computed by the 70 tests described above.
|
||
|
|
*> Modified.
|
||
|
|
*>
|
||
|
|
*> INFO INTEGER
|
||
|
|
*> If 0, then everything ran OK.
|
||
|
|
*> -1: NSIZES < 0
|
||
|
|
*> -2: Some NN(j) < 0
|
||
|
|
*> -3: NTYPES < 0
|
||
|
|
*> -5: THRESH < 0
|
||
|
|
*> -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
|
||
|
|
*> -16: LDZ < 1 or LDZ < NMAX.
|
||
|
|
*> -21: NWORK too small.
|
||
|
|
*> -23: LRWORK too small.
|
||
|
|
*> -25: LIWORK too small.
|
||
|
|
*> If CLATMR, CLATMS, CHEGV, CHPGV, CHBGV, CHEGVD, CHPGVD,
|
||
|
|
*> CHPGVD, CHEGVX, CHPGVX, CHBGVX returns an error code,
|
||
|
|
*> the absolute value of it is returned.
|
||
|
|
*> Modified.
|
||
|
|
*>
|
||
|
|
*>-----------------------------------------------------------------------
|
||
|
|
*>
|
||
|
|
*> Some Local Variables and Parameters:
|
||
|
|
*> ---- ----- --------- --- ----------
|
||
|
|
*> ZERO, ONE Real 0 and 1.
|
||
|
|
*> MAXTYP The number of types defined.
|
||
|
|
*> NTEST The number of tests that have been run
|
||
|
|
*> on this matrix.
|
||
|
|
*> NTESTT The total number of tests for this call.
|
||
|
|
*> NMAX Largest value in NN.
|
||
|
|
*> NMATS The number of matrices generated so far.
|
||
|
|
*> NERRS The number of tests which have exceeded THRESH
|
||
|
|
*> so far (computed by SLAFTS).
|
||
|
|
*> COND, IMODE Values to be passed to the matrix generators.
|
||
|
|
*> ANORM Norm of A; passed to matrix generators.
|
||
|
|
*>
|
||
|
|
*> OVFL, UNFL Overflow and underflow thresholds.
|
||
|
|
*> ULP, ULPINV Finest relative precision and its inverse.
|
||
|
|
*> RTOVFL, RTUNFL Square roots of the previous 2 values.
|
||
|
|
*> The following four arrays decode JTYPE:
|
||
|
|
*> KTYPE(j) The general type (1-10) for type "j".
|
||
|
|
*> KMODE(j) The MODE value to be passed to the matrix
|
||
|
|
*> generator for type "j".
|
||
|
|
*> KMAGN(j) The order of magnitude ( O(1),
|
||
|
|
*> O(overflow^(1/2) ), O(underflow^(1/2) )
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Authors:
|
||
|
|
* ========
|
||
|
|
*
|
||
|
|
*> \author Univ. of Tennessee
|
||
|
|
*> \author Univ. of California Berkeley
|
||
|
|
*> \author Univ. of Colorado Denver
|
||
|
|
*> \author NAG Ltd.
|
||
|
|
*
|
||
|
|
*> \ingroup complex_eig
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
SUBROUTINE CDRVSG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
|
||
|
|
$ NOUNIT, A, LDA, B, LDB, D, Z, LDZ, AB, BB, AP,
|
||
|
|
$ BP, WORK, NWORK, RWORK, LRWORK, IWORK, LIWORK,
|
||
|
|
$ RESULT, INFO )
|
||
|
|
*
|
||
|
|
* -- LAPACK test routine --
|
||
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
||
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||
|
|
*
|
||
|
|
* .. Scalar Arguments ..
|
||
|
|
INTEGER INFO, LDA, LDB, LDZ, LIWORK, LRWORK, NOUNIT,
|
||
|
|
$ NSIZES, NTYPES, NWORK
|
||
|
|
REAL THRESH
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
LOGICAL DOTYPE( * )
|
||
|
|
INTEGER ISEED( 4 ), IWORK( * ), NN( * )
|
||
|
|
REAL D( * ), RESULT( * ), RWORK( * )
|
||
|
|
COMPLEX A( LDA, * ), AB( LDA, * ), AP( * ),
|
||
|
|
$ B( LDB, * ), BB( LDB, * ), BP( * ), WORK( * ),
|
||
|
|
$ Z( LDZ, * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
*
|
||
|
|
* .. Parameters ..
|
||
|
|
REAL ZERO, ONE, TEN
|
||
|
|
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, TEN = 10.0E+0 )
|
||
|
|
COMPLEX CZERO, CONE
|
||
|
|
PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
|
||
|
|
$ CONE = ( 1.0E+0, 0.0E+0 ) )
|
||
|
|
INTEGER MAXTYP
|
||
|
|
PARAMETER ( MAXTYP = 21 )
|
||
|
|
* ..
|
||
|
|
* .. Local Scalars ..
|
||
|
|
LOGICAL BADNN
|
||
|
|
CHARACTER UPLO
|
||
|
|
INTEGER I, IBTYPE, IBUPLO, IINFO, IJ, IL, IMODE, ITEMP,
|
||
|
|
$ ITYPE, IU, J, JCOL, JSIZE, JTYPE, KA, KA9, KB,
|
||
|
|
$ KB9, M, MTYPES, N, NERRS, NMATS, NMAX, NTEST,
|
||
|
|
$ NTESTT
|
||
|
|
REAL ABSTOL, ANINV, ANORM, COND, OVFL, RTOVFL,
|
||
|
|
$ RTUNFL, ULP, ULPINV, UNFL, VL, VU
|
||
|
|
* ..
|
||
|
|
* .. Local Arrays ..
|
||
|
|
INTEGER IDUMMA( 1 ), IOLDSD( 4 ), ISEED2( 4 ),
|
||
|
|
$ KMAGN( MAXTYP ), KMODE( MAXTYP ),
|
||
|
|
$ KTYPE( MAXTYP )
|
||
|
|
* ..
|
||
|
|
* .. External Functions ..
|
||
|
|
LOGICAL LSAME
|
||
|
|
REAL SLAMCH, SLARND
|
||
|
|
EXTERNAL LSAME, SLAMCH, SLARND
|
||
|
|
* ..
|
||
|
|
* .. External Subroutines ..
|
||
|
|
EXTERNAL CHBGV, CHBGVD, CHBGVX, CHEGV, CHEGVD, CHEGVX,
|
||
|
|
$ CHPGV, CHPGVD, CHPGVX, CLACPY, CLASET, CLATMR,
|
||
|
|
$ CLATMS, CSGT01, SLAFTS, SLASUM, XERBLA
|
||
|
|
* ..
|
||
|
|
* .. Intrinsic Functions ..
|
||
|
|
INTRINSIC ABS, MAX, MIN, REAL, SQRT
|
||
|
|
* ..
|
||
|
|
* .. Data statements ..
|
||
|
|
DATA KTYPE / 1, 2, 5*4, 5*5, 3*8, 6*9 /
|
||
|
|
DATA KMAGN / 2*1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1,
|
||
|
|
$ 2, 3, 6*1 /
|
||
|
|
DATA KMODE / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
|
||
|
|
$ 0, 0, 6*4 /
|
||
|
|
* ..
|
||
|
|
* .. Executable Statements ..
|
||
|
|
*
|
||
|
|
* 1) Check for errors
|
||
|
|
*
|
||
|
|
NTESTT = 0
|
||
|
|
INFO = 0
|
||
|
|
*
|
||
|
|
BADNN = .FALSE.
|
||
|
|
NMAX = 0
|
||
|
|
DO 10 J = 1, NSIZES
|
||
|
|
NMAX = MAX( NMAX, NN( J ) )
|
||
|
|
IF( NN( J ).LT.0 )
|
||
|
|
$ BADNN = .TRUE.
|
||
|
|
10 CONTINUE
|
||
|
|
*
|
||
|
|
* Check for errors
|
||
|
|
*
|
||
|
|
IF( NSIZES.LT.0 ) THEN
|
||
|
|
INFO = -1
|
||
|
|
ELSE IF( BADNN ) THEN
|
||
|
|
INFO = -2
|
||
|
|
ELSE IF( NTYPES.LT.0 ) THEN
|
||
|
|
INFO = -3
|
||
|
|
ELSE IF( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN
|
||
|
|
INFO = -9
|
||
|
|
ELSE IF( LDZ.LE.1 .OR. LDZ.LT.NMAX ) THEN
|
||
|
|
INFO = -16
|
||
|
|
ELSE IF( 2*MAX( NMAX, 2 )**2.GT.NWORK ) THEN
|
||
|
|
INFO = -21
|
||
|
|
ELSE IF( 2*MAX( NMAX, 2 )**2.GT.LRWORK ) THEN
|
||
|
|
INFO = -23
|
||
|
|
ELSE IF( 2*MAX( NMAX, 2 )**2.GT.LIWORK ) THEN
|
||
|
|
INFO = -25
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
IF( INFO.NE.0 ) THEN
|
||
|
|
CALL XERBLA( 'CDRVSG', -INFO )
|
||
|
|
RETURN
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Quick return if possible
|
||
|
|
*
|
||
|
|
IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
|
||
|
|
$ RETURN
|
||
|
|
*
|
||
|
|
* More Important constants
|
||
|
|
*
|
||
|
|
UNFL = SLAMCH( 'Safe minimum' )
|
||
|
|
OVFL = SLAMCH( 'Overflow' )
|
||
|
|
ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' )
|
||
|
|
ULPINV = ONE / ULP
|
||
|
|
RTUNFL = SQRT( UNFL )
|
||
|
|
RTOVFL = SQRT( OVFL )
|
||
|
|
*
|
||
|
|
DO 20 I = 1, 4
|
||
|
|
ISEED2( I ) = ISEED( I )
|
||
|
|
20 CONTINUE
|
||
|
|
*
|
||
|
|
* Loop over sizes, types
|
||
|
|
*
|
||
|
|
NERRS = 0
|
||
|
|
NMATS = 0
|
||
|
|
*
|
||
|
|
DO 650 JSIZE = 1, NSIZES
|
||
|
|
N = NN( JSIZE )
|
||
|
|
ANINV = ONE / REAL( MAX( 1, N ) )
|
||
|
|
*
|
||
|
|
IF( NSIZES.NE.1 ) THEN
|
||
|
|
MTYPES = MIN( MAXTYP, NTYPES )
|
||
|
|
ELSE
|
||
|
|
MTYPES = MIN( MAXTYP+1, NTYPES )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
KA9 = 0
|
||
|
|
KB9 = 0
|
||
|
|
DO 640 JTYPE = 1, MTYPES
|
||
|
|
IF( .NOT.DOTYPE( JTYPE ) )
|
||
|
|
$ GO TO 640
|
||
|
|
NMATS = NMATS + 1
|
||
|
|
NTEST = 0
|
||
|
|
*
|
||
|
|
DO 30 J = 1, 4
|
||
|
|
IOLDSD( J ) = ISEED( J )
|
||
|
|
30 CONTINUE
|
||
|
|
*
|
||
|
|
* 2) Compute "A"
|
||
|
|
*
|
||
|
|
* 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 hermitian, w/ eigenvalues
|
||
|
|
* =6 random (none)
|
||
|
|
* =7 random diagonal
|
||
|
|
* =8 random hermitian
|
||
|
|
* =9 banded, w/ eigenvalues
|
||
|
|
*
|
||
|
|
IF( MTYPES.GT.MAXTYP )
|
||
|
|
$ GO TO 90
|
||
|
|
*
|
||
|
|
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
|
||
|
|
*
|
||
|
|
IINFO = 0
|
||
|
|
COND = ULPINV
|
||
|
|
*
|
||
|
|
* Special Matrices -- Identity & Jordan block
|
||
|
|
*
|
||
|
|
IF( ITYPE.EQ.1 ) THEN
|
||
|
|
*
|
||
|
|
* Zero
|
||
|
|
*
|
||
|
|
KA = 0
|
||
|
|
KB = 0
|
||
|
|
CALL CLASET( 'Full', LDA, N, CZERO, CZERO, A, LDA )
|
||
|
|
*
|
||
|
|
ELSE IF( ITYPE.EQ.2 ) THEN
|
||
|
|
*
|
||
|
|
* Identity
|
||
|
|
*
|
||
|
|
KA = 0
|
||
|
|
KB = 0
|
||
|
|
CALL CLASET( 'Full', LDA, N, CZERO, CZERO, A, LDA )
|
||
|
|
DO 80 JCOL = 1, N
|
||
|
|
A( JCOL, JCOL ) = ANORM
|
||
|
|
80 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( ITYPE.EQ.4 ) THEN
|
||
|
|
*
|
||
|
|
* Diagonal Matrix, [Eigen]values Specified
|
||
|
|
*
|
||
|
|
KA = 0
|
||
|
|
KB = 0
|
||
|
|
CALL CLATMS( N, N, 'S', ISEED, 'H', RWORK, IMODE, COND,
|
||
|
|
$ ANORM, 0, 0, 'N', A, LDA, WORK, IINFO )
|
||
|
|
*
|
||
|
|
ELSE IF( ITYPE.EQ.5 ) THEN
|
||
|
|
*
|
||
|
|
* Hermitian, eigenvalues specified
|
||
|
|
*
|
||
|
|
KA = MAX( 0, N-1 )
|
||
|
|
KB = KA
|
||
|
|
CALL CLATMS( N, N, 'S', ISEED, 'H', RWORK, IMODE, COND,
|
||
|
|
$ ANORM, N, N, 'N', A, LDA, WORK, IINFO )
|
||
|
|
*
|
||
|
|
ELSE IF( ITYPE.EQ.7 ) THEN
|
||
|
|
*
|
||
|
|
* Diagonal, random eigenvalues
|
||
|
|
*
|
||
|
|
KA = 0
|
||
|
|
KB = 0
|
||
|
|
CALL CLATMR( N, N, 'S', ISEED, 'H', WORK, 6, ONE, CONE,
|
||
|
|
$ 'T', 'N', WORK( N+1 ), 1, ONE,
|
||
|
|
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0,
|
||
|
|
$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
|
||
|
|
*
|
||
|
|
ELSE IF( ITYPE.EQ.8 ) THEN
|
||
|
|
*
|
||
|
|
* Hermitian, random eigenvalues
|
||
|
|
*
|
||
|
|
KA = MAX( 0, N-1 )
|
||
|
|
KB = KA
|
||
|
|
CALL CLATMR( N, N, 'S', ISEED, 'H', WORK, 6, ONE, CONE,
|
||
|
|
$ 'T', 'N', WORK( N+1 ), 1, ONE,
|
||
|
|
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
|
||
|
|
$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
|
||
|
|
*
|
||
|
|
ELSE IF( ITYPE.EQ.9 ) THEN
|
||
|
|
*
|
||
|
|
* Hermitian banded, eigenvalues specified
|
||
|
|
*
|
||
|
|
* The following values are used for the half-bandwidths:
|
||
|
|
*
|
||
|
|
* ka = 1 kb = 1
|
||
|
|
* ka = 2 kb = 1
|
||
|
|
* ka = 2 kb = 2
|
||
|
|
* ka = 3 kb = 1
|
||
|
|
* ka = 3 kb = 2
|
||
|
|
* ka = 3 kb = 3
|
||
|
|
*
|
||
|
|
KB9 = KB9 + 1
|
||
|
|
IF( KB9.GT.KA9 ) THEN
|
||
|
|
KA9 = KA9 + 1
|
||
|
|
KB9 = 1
|
||
|
|
END IF
|
||
|
|
KA = MAX( 0, MIN( N-1, KA9 ) )
|
||
|
|
KB = MAX( 0, MIN( N-1, KB9 ) )
|
||
|
|
CALL CLATMS( N, N, 'S', ISEED, 'H', RWORK, IMODE, COND,
|
||
|
|
$ ANORM, KA, KA, 'N', A, LDA, WORK, IINFO )
|
||
|
|
*
|
||
|
|
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
|
||
|
|
*
|
||
|
|
90 CONTINUE
|
||
|
|
*
|
||
|
|
ABSTOL = UNFL + UNFL
|
||
|
|
IF( N.LE.1 ) THEN
|
||
|
|
IL = 1
|
||
|
|
IU = N
|
||
|
|
ELSE
|
||
|
|
IL = 1 + INT( ( N-1 )*SLARND( 1, ISEED2 ) )
|
||
|
|
IU = 1 + INT( ( N-1 )*SLARND( 1, ISEED2 ) )
|
||
|
|
IF( IL.GT.IU ) THEN
|
||
|
|
ITEMP = IL
|
||
|
|
IL = IU
|
||
|
|
IU = ITEMP
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* 3) Call CHEGV, CHPGV, CHBGV, CHEGVD, CHPGVD, CHBGVD,
|
||
|
|
* CHEGVX, CHPGVX and CHBGVX, do tests.
|
||
|
|
*
|
||
|
|
* loop over the three generalized problems
|
||
|
|
* IBTYPE = 1: A*x = (lambda)*B*x
|
||
|
|
* IBTYPE = 2: A*B*x = (lambda)*x
|
||
|
|
* IBTYPE = 3: B*A*x = (lambda)*x
|
||
|
|
*
|
||
|
|
DO 630 IBTYPE = 1, 3
|
||
|
|
*
|
||
|
|
* loop over the setting UPLO
|
||
|
|
*
|
||
|
|
DO 620 IBUPLO = 1, 2
|
||
|
|
IF( IBUPLO.EQ.1 )
|
||
|
|
$ UPLO = 'U'
|
||
|
|
IF( IBUPLO.EQ.2 )
|
||
|
|
$ UPLO = 'L'
|
||
|
|
*
|
||
|
|
* Generate random well-conditioned positive definite
|
||
|
|
* matrix B, of bandwidth not greater than that of A.
|
||
|
|
*
|
||
|
|
CALL CLATMS( N, N, 'U', ISEED, 'P', RWORK, 5, TEN,
|
||
|
|
$ ONE, KB, KB, UPLO, B, LDB, WORK( N+1 ),
|
||
|
|
$ IINFO )
|
||
|
|
*
|
||
|
|
* Test CHEGV
|
||
|
|
*
|
||
|
|
NTEST = NTEST + 1
|
||
|
|
*
|
||
|
|
CALL CLACPY( ' ', N, N, A, LDA, Z, LDZ )
|
||
|
|
CALL CLACPY( UPLO, N, N, B, LDB, BB, LDB )
|
||
|
|
*
|
||
|
|
CALL CHEGV( IBTYPE, 'V', UPLO, N, Z, LDZ, BB, LDB, D,
|
||
|
|
$ WORK, NWORK, RWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'CHEGV(V,' // UPLO //
|
||
|
|
$ ')', IINFO, N, JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
IF( IINFO.LT.0 ) THEN
|
||
|
|
RETURN
|
||
|
|
ELSE
|
||
|
|
RESULT( NTEST ) = ULPINV
|
||
|
|
GO TO 100
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Do Test
|
||
|
|
*
|
||
|
|
CALL CSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z,
|
||
|
|
$ LDZ, D, WORK, RWORK, RESULT( NTEST ) )
|
||
|
|
*
|
||
|
|
* Test CHEGVD
|
||
|
|
*
|
||
|
|
NTEST = NTEST + 1
|
||
|
|
*
|
||
|
|
CALL CLACPY( ' ', N, N, A, LDA, Z, LDZ )
|
||
|
|
CALL CLACPY( UPLO, N, N, B, LDB, BB, LDB )
|
||
|
|
*
|
||
|
|
CALL CHEGVD( IBTYPE, 'V', UPLO, N, Z, LDZ, BB, LDB, D,
|
||
|
|
$ WORK, NWORK, RWORK, LRWORK, IWORK,
|
||
|
|
$ LIWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'CHEGVD(V,' // UPLO //
|
||
|
|
$ ')', IINFO, N, JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
IF( IINFO.LT.0 ) THEN
|
||
|
|
RETURN
|
||
|
|
ELSE
|
||
|
|
RESULT( NTEST ) = ULPINV
|
||
|
|
GO TO 100
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Do Test
|
||
|
|
*
|
||
|
|
CALL CSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z,
|
||
|
|
$ LDZ, D, WORK, RWORK, RESULT( NTEST ) )
|
||
|
|
*
|
||
|
|
* Test CHEGVX
|
||
|
|
*
|
||
|
|
NTEST = NTEST + 1
|
||
|
|
*
|
||
|
|
CALL CLACPY( ' ', N, N, A, LDA, AB, LDA )
|
||
|
|
CALL CLACPY( UPLO, N, N, B, LDB, BB, LDB )
|
||
|
|
*
|
||
|
|
CALL CHEGVX( IBTYPE, 'V', 'A', UPLO, N, AB, LDA, BB,
|
||
|
|
$ LDB, VL, VU, IL, IU, ABSTOL, M, D, Z,
|
||
|
|
$ LDZ, WORK, NWORK, RWORK, IWORK( N+1 ),
|
||
|
|
$ IWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'CHEGVX(V,A' // UPLO //
|
||
|
|
$ ')', IINFO, N, JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
IF( IINFO.LT.0 ) THEN
|
||
|
|
RETURN
|
||
|
|
ELSE
|
||
|
|
RESULT( NTEST ) = ULPINV
|
||
|
|
GO TO 100
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Do Test
|
||
|
|
*
|
||
|
|
CALL CSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z,
|
||
|
|
$ LDZ, D, WORK, RWORK, RESULT( NTEST ) )
|
||
|
|
*
|
||
|
|
NTEST = NTEST + 1
|
||
|
|
*
|
||
|
|
CALL CLACPY( ' ', N, N, A, LDA, AB, LDA )
|
||
|
|
CALL CLACPY( UPLO, N, N, B, LDB, BB, LDB )
|
||
|
|
*
|
||
|
|
* since we do not know the exact eigenvalues of this
|
||
|
|
* eigenpair, we just set VL and VU as constants.
|
||
|
|
* It is quite possible that there are no eigenvalues
|
||
|
|
* in this interval.
|
||
|
|
*
|
||
|
|
VL = ZERO
|
||
|
|
VU = ANORM
|
||
|
|
CALL CHEGVX( IBTYPE, 'V', 'V', UPLO, N, AB, LDA, BB,
|
||
|
|
$ LDB, VL, VU, IL, IU, ABSTOL, M, D, Z,
|
||
|
|
$ LDZ, WORK, NWORK, RWORK, IWORK( N+1 ),
|
||
|
|
$ IWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'CHEGVX(V,V,' //
|
||
|
|
$ UPLO // ')', IINFO, N, JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
IF( IINFO.LT.0 ) THEN
|
||
|
|
RETURN
|
||
|
|
ELSE
|
||
|
|
RESULT( NTEST ) = ULPINV
|
||
|
|
GO TO 100
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Do Test
|
||
|
|
*
|
||
|
|
CALL CSGT01( IBTYPE, UPLO, N, M, A, LDA, B, LDB, Z,
|
||
|
|
$ LDZ, D, WORK, RWORK, RESULT( NTEST ) )
|
||
|
|
*
|
||
|
|
NTEST = NTEST + 1
|
||
|
|
*
|
||
|
|
CALL CLACPY( ' ', N, N, A, LDA, AB, LDA )
|
||
|
|
CALL CLACPY( UPLO, N, N, B, LDB, BB, LDB )
|
||
|
|
*
|
||
|
|
CALL CHEGVX( IBTYPE, 'V', 'I', UPLO, N, AB, LDA, BB,
|
||
|
|
$ LDB, VL, VU, IL, IU, ABSTOL, M, D, Z,
|
||
|
|
$ LDZ, WORK, NWORK, RWORK, IWORK( N+1 ),
|
||
|
|
$ IWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'CHEGVX(V,I,' //
|
||
|
|
$ UPLO // ')', IINFO, N, JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
IF( IINFO.LT.0 ) THEN
|
||
|
|
RETURN
|
||
|
|
ELSE
|
||
|
|
RESULT( NTEST ) = ULPINV
|
||
|
|
GO TO 100
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Do Test
|
||
|
|
*
|
||
|
|
CALL CSGT01( IBTYPE, UPLO, N, M, A, LDA, B, LDB, Z,
|
||
|
|
$ LDZ, D, WORK, RWORK, RESULT( NTEST ) )
|
||
|
|
*
|
||
|
|
100 CONTINUE
|
||
|
|
*
|
||
|
|
* Test CHPGV
|
||
|
|
*
|
||
|
|
NTEST = NTEST + 1
|
||
|
|
*
|
||
|
|
* Copy the matrices into packed storage.
|
||
|
|
*
|
||
|
|
IF( LSAME( UPLO, 'U' ) ) THEN
|
||
|
|
IJ = 1
|
||
|
|
DO 120 J = 1, N
|
||
|
|
DO 110 I = 1, J
|
||
|
|
AP( IJ ) = A( I, J )
|
||
|
|
BP( IJ ) = B( I, J )
|
||
|
|
IJ = IJ + 1
|
||
|
|
110 CONTINUE
|
||
|
|
120 CONTINUE
|
||
|
|
ELSE
|
||
|
|
IJ = 1
|
||
|
|
DO 140 J = 1, N
|
||
|
|
DO 130 I = J, N
|
||
|
|
AP( IJ ) = A( I, J )
|
||
|
|
BP( IJ ) = B( I, J )
|
||
|
|
IJ = IJ + 1
|
||
|
|
130 CONTINUE
|
||
|
|
140 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
CALL CHPGV( IBTYPE, 'V', UPLO, N, AP, BP, D, Z, LDZ,
|
||
|
|
$ WORK, RWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'CHPGV(V,' // UPLO //
|
||
|
|
$ ')', IINFO, N, JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
IF( IINFO.LT.0 ) THEN
|
||
|
|
RETURN
|
||
|
|
ELSE
|
||
|
|
RESULT( NTEST ) = ULPINV
|
||
|
|
GO TO 310
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Do Test
|
||
|
|
*
|
||
|
|
CALL CSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z,
|
||
|
|
$ LDZ, D, WORK, RWORK, RESULT( NTEST ) )
|
||
|
|
*
|
||
|
|
* Test CHPGVD
|
||
|
|
*
|
||
|
|
NTEST = NTEST + 1
|
||
|
|
*
|
||
|
|
* Copy the matrices into packed storage.
|
||
|
|
*
|
||
|
|
IF( LSAME( UPLO, 'U' ) ) THEN
|
||
|
|
IJ = 1
|
||
|
|
DO 160 J = 1, N
|
||
|
|
DO 150 I = 1, J
|
||
|
|
AP( IJ ) = A( I, J )
|
||
|
|
BP( IJ ) = B( I, J )
|
||
|
|
IJ = IJ + 1
|
||
|
|
150 CONTINUE
|
||
|
|
160 CONTINUE
|
||
|
|
ELSE
|
||
|
|
IJ = 1
|
||
|
|
DO 180 J = 1, N
|
||
|
|
DO 170 I = J, N
|
||
|
|
AP( IJ ) = A( I, J )
|
||
|
|
BP( IJ ) = B( I, J )
|
||
|
|
IJ = IJ + 1
|
||
|
|
170 CONTINUE
|
||
|
|
180 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
CALL CHPGVD( IBTYPE, 'V', UPLO, N, AP, BP, D, Z, LDZ,
|
||
|
|
$ WORK, NWORK, RWORK, LRWORK, IWORK,
|
||
|
|
$ LIWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'CHPGVD(V,' // UPLO //
|
||
|
|
$ ')', IINFO, N, JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
IF( IINFO.LT.0 ) THEN
|
||
|
|
RETURN
|
||
|
|
ELSE
|
||
|
|
RESULT( NTEST ) = ULPINV
|
||
|
|
GO TO 310
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Do Test
|
||
|
|
*
|
||
|
|
CALL CSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z,
|
||
|
|
$ LDZ, D, WORK, RWORK, RESULT( NTEST ) )
|
||
|
|
*
|
||
|
|
* Test CHPGVX
|
||
|
|
*
|
||
|
|
NTEST = NTEST + 1
|
||
|
|
*
|
||
|
|
* Copy the matrices into packed storage.
|
||
|
|
*
|
||
|
|
IF( LSAME( UPLO, 'U' ) ) THEN
|
||
|
|
IJ = 1
|
||
|
|
DO 200 J = 1, N
|
||
|
|
DO 190 I = 1, J
|
||
|
|
AP( IJ ) = A( I, J )
|
||
|
|
BP( IJ ) = B( I, J )
|
||
|
|
IJ = IJ + 1
|
||
|
|
190 CONTINUE
|
||
|
|
200 CONTINUE
|
||
|
|
ELSE
|
||
|
|
IJ = 1
|
||
|
|
DO 220 J = 1, N
|
||
|
|
DO 210 I = J, N
|
||
|
|
AP( IJ ) = A( I, J )
|
||
|
|
BP( IJ ) = B( I, J )
|
||
|
|
IJ = IJ + 1
|
||
|
|
210 CONTINUE
|
||
|
|
220 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
CALL CHPGVX( IBTYPE, 'V', 'A', UPLO, N, AP, BP, VL,
|
||
|
|
$ VU, IL, IU, ABSTOL, M, D, Z, LDZ, WORK,
|
||
|
|
$ RWORK, IWORK( N+1 ), IWORK, INFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'CHPGVX(V,A' // UPLO //
|
||
|
|
$ ')', IINFO, N, JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
IF( IINFO.LT.0 ) THEN
|
||
|
|
RETURN
|
||
|
|
ELSE
|
||
|
|
RESULT( NTEST ) = ULPINV
|
||
|
|
GO TO 310
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Do Test
|
||
|
|
*
|
||
|
|
CALL CSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z,
|
||
|
|
$ LDZ, D, WORK, RWORK, RESULT( NTEST ) )
|
||
|
|
*
|
||
|
|
NTEST = NTEST + 1
|
||
|
|
*
|
||
|
|
* Copy the matrices into packed storage.
|
||
|
|
*
|
||
|
|
IF( LSAME( UPLO, 'U' ) ) THEN
|
||
|
|
IJ = 1
|
||
|
|
DO 240 J = 1, N
|
||
|
|
DO 230 I = 1, J
|
||
|
|
AP( IJ ) = A( I, J )
|
||
|
|
BP( IJ ) = B( I, J )
|
||
|
|
IJ = IJ + 1
|
||
|
|
230 CONTINUE
|
||
|
|
240 CONTINUE
|
||
|
|
ELSE
|
||
|
|
IJ = 1
|
||
|
|
DO 260 J = 1, N
|
||
|
|
DO 250 I = J, N
|
||
|
|
AP( IJ ) = A( I, J )
|
||
|
|
BP( IJ ) = B( I, J )
|
||
|
|
IJ = IJ + 1
|
||
|
|
250 CONTINUE
|
||
|
|
260 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
VL = ZERO
|
||
|
|
VU = ANORM
|
||
|
|
CALL CHPGVX( IBTYPE, 'V', 'V', UPLO, N, AP, BP, VL,
|
||
|
|
$ VU, IL, IU, ABSTOL, M, D, Z, LDZ, WORK,
|
||
|
|
$ RWORK, IWORK( N+1 ), IWORK, INFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'CHPGVX(V,V' // UPLO //
|
||
|
|
$ ')', IINFO, N, JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
IF( IINFO.LT.0 ) THEN
|
||
|
|
RETURN
|
||
|
|
ELSE
|
||
|
|
RESULT( NTEST ) = ULPINV
|
||
|
|
GO TO 310
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Do Test
|
||
|
|
*
|
||
|
|
CALL CSGT01( IBTYPE, UPLO, N, M, A, LDA, B, LDB, Z,
|
||
|
|
$ LDZ, D, WORK, RWORK, RESULT( NTEST ) )
|
||
|
|
*
|
||
|
|
NTEST = NTEST + 1
|
||
|
|
*
|
||
|
|
* Copy the matrices into packed storage.
|
||
|
|
*
|
||
|
|
IF( LSAME( UPLO, 'U' ) ) THEN
|
||
|
|
IJ = 1
|
||
|
|
DO 280 J = 1, N
|
||
|
|
DO 270 I = 1, J
|
||
|
|
AP( IJ ) = A( I, J )
|
||
|
|
BP( IJ ) = B( I, J )
|
||
|
|
IJ = IJ + 1
|
||
|
|
270 CONTINUE
|
||
|
|
280 CONTINUE
|
||
|
|
ELSE
|
||
|
|
IJ = 1
|
||
|
|
DO 300 J = 1, N
|
||
|
|
DO 290 I = J, N
|
||
|
|
AP( IJ ) = A( I, J )
|
||
|
|
BP( IJ ) = B( I, J )
|
||
|
|
IJ = IJ + 1
|
||
|
|
290 CONTINUE
|
||
|
|
300 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
CALL CHPGVX( IBTYPE, 'V', 'I', UPLO, N, AP, BP, VL,
|
||
|
|
$ VU, IL, IU, ABSTOL, M, D, Z, LDZ, WORK,
|
||
|
|
$ RWORK, IWORK( N+1 ), IWORK, INFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'CHPGVX(V,I' // UPLO //
|
||
|
|
$ ')', IINFO, N, JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
IF( IINFO.LT.0 ) THEN
|
||
|
|
RETURN
|
||
|
|
ELSE
|
||
|
|
RESULT( NTEST ) = ULPINV
|
||
|
|
GO TO 310
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Do Test
|
||
|
|
*
|
||
|
|
CALL CSGT01( IBTYPE, UPLO, N, M, A, LDA, B, LDB, Z,
|
||
|
|
$ LDZ, D, WORK, RWORK, RESULT( NTEST ) )
|
||
|
|
*
|
||
|
|
310 CONTINUE
|
||
|
|
*
|
||
|
|
IF( IBTYPE.EQ.1 ) THEN
|
||
|
|
*
|
||
|
|
* TEST CHBGV
|
||
|
|
*
|
||
|
|
NTEST = NTEST + 1
|
||
|
|
*
|
||
|
|
* Copy the matrices into band storage.
|
||
|
|
*
|
||
|
|
IF( LSAME( UPLO, 'U' ) ) THEN
|
||
|
|
DO 340 J = 1, N
|
||
|
|
DO 320 I = MAX( 1, J-KA ), J
|
||
|
|
AB( KA+1+I-J, J ) = A( I, J )
|
||
|
|
320 CONTINUE
|
||
|
|
DO 330 I = MAX( 1, J-KB ), J
|
||
|
|
BB( KB+1+I-J, J ) = B( I, J )
|
||
|
|
330 CONTINUE
|
||
|
|
340 CONTINUE
|
||
|
|
ELSE
|
||
|
|
DO 370 J = 1, N
|
||
|
|
DO 350 I = J, MIN( N, J+KA )
|
||
|
|
AB( 1+I-J, J ) = A( I, J )
|
||
|
|
350 CONTINUE
|
||
|
|
DO 360 I = J, MIN( N, J+KB )
|
||
|
|
BB( 1+I-J, J ) = B( I, J )
|
||
|
|
360 CONTINUE
|
||
|
|
370 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
CALL CHBGV( 'V', UPLO, N, KA, KB, AB, LDA, BB, LDB,
|
||
|
|
$ D, Z, LDZ, WORK, RWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'CHBGV(V,' //
|
||
|
|
$ UPLO // ')', IINFO, N, JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
IF( IINFO.LT.0 ) THEN
|
||
|
|
RETURN
|
||
|
|
ELSE
|
||
|
|
RESULT( NTEST ) = ULPINV
|
||
|
|
GO TO 620
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Do Test
|
||
|
|
*
|
||
|
|
CALL CSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z,
|
||
|
|
$ LDZ, D, WORK, RWORK, RESULT( NTEST ) )
|
||
|
|
*
|
||
|
|
* TEST CHBGVD
|
||
|
|
*
|
||
|
|
NTEST = NTEST + 1
|
||
|
|
*
|
||
|
|
* Copy the matrices into band storage.
|
||
|
|
*
|
||
|
|
IF( LSAME( UPLO, 'U' ) ) THEN
|
||
|
|
DO 400 J = 1, N
|
||
|
|
DO 380 I = MAX( 1, J-KA ), J
|
||
|
|
AB( KA+1+I-J, J ) = A( I, J )
|
||
|
|
380 CONTINUE
|
||
|
|
DO 390 I = MAX( 1, J-KB ), J
|
||
|
|
BB( KB+1+I-J, J ) = B( I, J )
|
||
|
|
390 CONTINUE
|
||
|
|
400 CONTINUE
|
||
|
|
ELSE
|
||
|
|
DO 430 J = 1, N
|
||
|
|
DO 410 I = J, MIN( N, J+KA )
|
||
|
|
AB( 1+I-J, J ) = A( I, J )
|
||
|
|
410 CONTINUE
|
||
|
|
DO 420 I = J, MIN( N, J+KB )
|
||
|
|
BB( 1+I-J, J ) = B( I, J )
|
||
|
|
420 CONTINUE
|
||
|
|
430 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
CALL CHBGVD( 'V', UPLO, N, KA, KB, AB, LDA, BB,
|
||
|
|
$ LDB, D, Z, LDZ, WORK, NWORK, RWORK,
|
||
|
|
$ LRWORK, IWORK, LIWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'CHBGVD(V,' //
|
||
|
|
$ UPLO // ')', IINFO, N, JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
IF( IINFO.LT.0 ) THEN
|
||
|
|
RETURN
|
||
|
|
ELSE
|
||
|
|
RESULT( NTEST ) = ULPINV
|
||
|
|
GO TO 620
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Do Test
|
||
|
|
*
|
||
|
|
CALL CSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z,
|
||
|
|
$ LDZ, D, WORK, RWORK, RESULT( NTEST ) )
|
||
|
|
*
|
||
|
|
* Test CHBGVX
|
||
|
|
*
|
||
|
|
NTEST = NTEST + 1
|
||
|
|
*
|
||
|
|
* Copy the matrices into band storage.
|
||
|
|
*
|
||
|
|
IF( LSAME( UPLO, 'U' ) ) THEN
|
||
|
|
DO 460 J = 1, N
|
||
|
|
DO 440 I = MAX( 1, J-KA ), J
|
||
|
|
AB( KA+1+I-J, J ) = A( I, J )
|
||
|
|
440 CONTINUE
|
||
|
|
DO 450 I = MAX( 1, J-KB ), J
|
||
|
|
BB( KB+1+I-J, J ) = B( I, J )
|
||
|
|
450 CONTINUE
|
||
|
|
460 CONTINUE
|
||
|
|
ELSE
|
||
|
|
DO 490 J = 1, N
|
||
|
|
DO 470 I = J, MIN( N, J+KA )
|
||
|
|
AB( 1+I-J, J ) = A( I, J )
|
||
|
|
470 CONTINUE
|
||
|
|
DO 480 I = J, MIN( N, J+KB )
|
||
|
|
BB( 1+I-J, J ) = B( I, J )
|
||
|
|
480 CONTINUE
|
||
|
|
490 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
CALL CHBGVX( 'V', 'A', UPLO, N, KA, KB, AB, LDA,
|
||
|
|
$ BB, LDB, BP, MAX( 1, N ), VL, VU, IL,
|
||
|
|
$ IU, ABSTOL, M, D, Z, LDZ, WORK, RWORK,
|
||
|
|
$ IWORK( N+1 ), IWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'CHBGVX(V,A' //
|
||
|
|
$ UPLO // ')', IINFO, N, JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
IF( IINFO.LT.0 ) THEN
|
||
|
|
RETURN
|
||
|
|
ELSE
|
||
|
|
RESULT( NTEST ) = ULPINV
|
||
|
|
GO TO 620
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Do Test
|
||
|
|
*
|
||
|
|
CALL CSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z,
|
||
|
|
$ LDZ, D, WORK, RWORK, RESULT( NTEST ) )
|
||
|
|
*
|
||
|
|
NTEST = NTEST + 1
|
||
|
|
*
|
||
|
|
* Copy the matrices into band storage.
|
||
|
|
*
|
||
|
|
IF( LSAME( UPLO, 'U' ) ) THEN
|
||
|
|
DO 520 J = 1, N
|
||
|
|
DO 500 I = MAX( 1, J-KA ), J
|
||
|
|
AB( KA+1+I-J, J ) = A( I, J )
|
||
|
|
500 CONTINUE
|
||
|
|
DO 510 I = MAX( 1, J-KB ), J
|
||
|
|
BB( KB+1+I-J, J ) = B( I, J )
|
||
|
|
510 CONTINUE
|
||
|
|
520 CONTINUE
|
||
|
|
ELSE
|
||
|
|
DO 550 J = 1, N
|
||
|
|
DO 530 I = J, MIN( N, J+KA )
|
||
|
|
AB( 1+I-J, J ) = A( I, J )
|
||
|
|
530 CONTINUE
|
||
|
|
DO 540 I = J, MIN( N, J+KB )
|
||
|
|
BB( 1+I-J, J ) = B( I, J )
|
||
|
|
540 CONTINUE
|
||
|
|
550 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
VL = ZERO
|
||
|
|
VU = ANORM
|
||
|
|
CALL CHBGVX( 'V', 'V', UPLO, N, KA, KB, AB, LDA,
|
||
|
|
$ BB, LDB, BP, MAX( 1, N ), VL, VU, IL,
|
||
|
|
$ IU, ABSTOL, M, D, Z, LDZ, WORK, RWORK,
|
||
|
|
$ IWORK( N+1 ), IWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'CHBGVX(V,V' //
|
||
|
|
$ UPLO // ')', IINFO, N, JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
IF( IINFO.LT.0 ) THEN
|
||
|
|
RETURN
|
||
|
|
ELSE
|
||
|
|
RESULT( NTEST ) = ULPINV
|
||
|
|
GO TO 620
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Do Test
|
||
|
|
*
|
||
|
|
CALL CSGT01( IBTYPE, UPLO, N, M, A, LDA, B, LDB, Z,
|
||
|
|
$ LDZ, D, WORK, RWORK, RESULT( NTEST ) )
|
||
|
|
*
|
||
|
|
NTEST = NTEST + 1
|
||
|
|
*
|
||
|
|
* Copy the matrices into band storage.
|
||
|
|
*
|
||
|
|
IF( LSAME( UPLO, 'U' ) ) THEN
|
||
|
|
DO 580 J = 1, N
|
||
|
|
DO 560 I = MAX( 1, J-KA ), J
|
||
|
|
AB( KA+1+I-J, J ) = A( I, J )
|
||
|
|
560 CONTINUE
|
||
|
|
DO 570 I = MAX( 1, J-KB ), J
|
||
|
|
BB( KB+1+I-J, J ) = B( I, J )
|
||
|
|
570 CONTINUE
|
||
|
|
580 CONTINUE
|
||
|
|
ELSE
|
||
|
|
DO 610 J = 1, N
|
||
|
|
DO 590 I = J, MIN( N, J+KA )
|
||
|
|
AB( 1+I-J, J ) = A( I, J )
|
||
|
|
590 CONTINUE
|
||
|
|
DO 600 I = J, MIN( N, J+KB )
|
||
|
|
BB( 1+I-J, J ) = B( I, J )
|
||
|
|
600 CONTINUE
|
||
|
|
610 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
CALL CHBGVX( 'V', 'I', UPLO, N, KA, KB, AB, LDA,
|
||
|
|
$ BB, LDB, BP, MAX( 1, N ), VL, VU, IL,
|
||
|
|
$ IU, ABSTOL, M, D, Z, LDZ, WORK, RWORK,
|
||
|
|
$ IWORK( N+1 ), IWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'CHBGVX(V,I' //
|
||
|
|
$ UPLO // ')', IINFO, N, JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
IF( IINFO.LT.0 ) THEN
|
||
|
|
RETURN
|
||
|
|
ELSE
|
||
|
|
RESULT( NTEST ) = ULPINV
|
||
|
|
GO TO 620
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Do Test
|
||
|
|
*
|
||
|
|
CALL CSGT01( IBTYPE, UPLO, N, M, A, LDA, B, LDB, Z,
|
||
|
|
$ LDZ, D, WORK, RWORK, RESULT( NTEST ) )
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
620 CONTINUE
|
||
|
|
630 CONTINUE
|
||
|
|
*
|
||
|
|
* End of Loop -- Check for RESULT(j) > THRESH
|
||
|
|
*
|
||
|
|
NTESTT = NTESTT + NTEST
|
||
|
|
CALL SLAFTS( 'CSG', N, N, JTYPE, NTEST, RESULT, IOLDSD,
|
||
|
|
$ THRESH, NOUNIT, NERRS )
|
||
|
|
640 CONTINUE
|
||
|
|
650 CONTINUE
|
||
|
|
*
|
||
|
|
* Summary
|
||
|
|
*
|
||
|
|
CALL SLASUM( 'CSG', NOUNIT, NERRS, NTESTT )
|
||
|
|
*
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
9999 FORMAT( ' CDRVSG: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
|
||
|
|
$ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
|
||
|
|
*
|
||
|
|
* End of CDRVSG
|
||
|
|
*
|
||
|
|
END
|