|
- *> \brief \b SDRVSG
- *
- * =========== DOCUMENTATION ===========
- *
- * Online html documentation available at
- * http://www.netlib.org/lapack/explore-html/
- *
- * Definition:
- * ===========
- *
- * SUBROUTINE SDRVSG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
- * NOUNIT, A, LDA, B, LDB, D, Z, LDZ, AB, BB, AP,
- * BP, WORK, NWORK, IWORK, LIWORK, RESULT, INFO )
- *
- * .. Scalar Arguments ..
- * INTEGER INFO, LDA, LDB, LDZ, LIWORK, NOUNIT, NSIZES,
- * $ NTYPES, NWORK
- * REAL THRESH
- * ..
- * .. Array Arguments ..
- * LOGICAL DOTYPE( * )
- * INTEGER ISEED( 4 ), IWORK( * ), NN( * )
- * REAL A( LDA, * ), AB( LDA, * ), AP( * ),
- * $ B( LDB, * ), BB( LDB, * ), BP( * ), D( * ),
- * $ RESULT( * ), WORK( * ), Z( LDZ, * )
- * ..
- *
- *
- *> \par Purpose:
- * =============
- *>
- *> \verbatim
- *>
- *> SDRVSG checks the real symmetric generalized eigenproblem
- *> drivers.
- *>
- *> SSYGV computes all eigenvalues and, optionally,
- *> eigenvectors of a real symmetric-definite generalized
- *> eigenproblem.
- *>
- *> SSYGVD computes all eigenvalues and, optionally,
- *> eigenvectors of a real symmetric-definite generalized
- *> eigenproblem using a divide and conquer algorithm.
- *>
- *> SSYGVX computes selected eigenvalues and, optionally,
- *> eigenvectors of a real symmetric-definite generalized
- *> eigenproblem.
- *>
- *> SSPGV computes all eigenvalues and, optionally,
- *> eigenvectors of a real symmetric-definite generalized
- *> eigenproblem in packed storage.
- *>
- *> SSPGVD computes all eigenvalues and, optionally,
- *> eigenvectors of a real symmetric-definite generalized
- *> eigenproblem in packed storage using a divide and
- *> conquer algorithm.
- *>
- *> SSPGVX computes selected eigenvalues and, optionally,
- *> eigenvectors of a real symmetric-definite generalized
- *> eigenproblem in packed storage.
- *>
- *> SSBGV computes all eigenvalues and, optionally,
- *> eigenvectors of a real symmetric-definite banded
- *> generalized eigenproblem.
- *>
- *> SSBGVD computes all eigenvalues and, optionally,
- *> eigenvectors of a real symmetric-definite banded
- *> generalized eigenproblem using a divide and conquer
- *> algorithm.
- *>
- *> SSBGVX computes selected eigenvalues and, optionally,
- *> eigenvectors of a real symmetric-definite banded
- *> generalized eigenproblem.
- *>
- *> When SDRVSG 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) SSYGV with ITYPE = 1 and UPLO ='U':
- *>
- *> | A Z - B Z D | / ( |A| |Z| n ulp )
- *>
- *> (2) as (1) but calling SSPGV
- *> (3) as (1) but calling SSBGV
- *> (4) as (1) but with UPLO = 'L'
- *> (5) as (4) but calling SSPGV
- *> (6) as (4) but calling SSBGV
- *>
- *> (7) SSYGV with ITYPE = 2 and UPLO ='U':
- *>
- *> | A B Z - Z D | / ( |A| |Z| n ulp )
- *>
- *> (8) as (7) but calling SSPGV
- *> (9) as (7) but with UPLO = 'L'
- *> (10) as (9) but calling SSPGV
- *>
- *> (11) SSYGV with ITYPE = 3 and UPLO ='U':
- *>
- *> | B A Z - Z D | / ( |A| |Z| n ulp )
- *>
- *> (12) as (11) but calling SSPGV
- *> (13) as (11) but with UPLO = 'L'
- *> (14) as (13) but calling SSPGV
- *>
- *> SSYGVD, SSPGVD and SSBGVD performed the same 14 tests.
- *>
- *> SSYGVX, SSPGVX and SSBGVX 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 orthogonal 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 orthogonal 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 orthogonal 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) symmetric 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,
- *> SDRVSG 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, SDRVSG
- *> 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 SDRVSG 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 REAL 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 and AB. It must be at
- *> least 1 and at least max( NN ).
- *> Not modified.
- *>
- *> B REAL array, dimension (LDB , max(NN))
- *> Used to hold the symmetric positive definite matrix for
- *> the generailzed problem.
- *> On exit, B contains the last matrix actually
- *> used.
- *> Modified.
- *>
- *> LDB INTEGER
- *> The leading dimension of B and BB. 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 REAL array, dimension (LDZ, max(NN))
- *> The matrix of eigenvectors.
- *> Modified.
- *>
- *> LDZ INTEGER
- *> The leading dimension of Z. It must be at least 1 and
- *> at least max( NN ).
- *> Not modified.
- *>
- *> AB REAL array, dimension (LDA, max(NN))
- *> Workspace.
- *> Modified.
- *>
- *> BB REAL array, dimension (LDB, max(NN))
- *> Workspace.
- *> Modified.
- *>
- *> AP REAL array, dimension (max(NN)**2)
- *> Workspace.
- *> Modified.
- *>
- *> BP REAL array, dimension (max(NN)**2)
- *> Workspace.
- *> Modified.
- *>
- *> WORK REAL array, dimension (NWORK)
- *> Workspace.
- *> Modified.
- *>
- *> NWORK INTEGER
- *> The number of entries in WORK. This must be at least
- *> 1+5*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 WORK. This must be at least 6*N.
- *> 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: LIWORK too small.
- *> If SLATMR, SLATMS, SSYGV, SSPGV, SSBGV, SSYGVD, SSPGVD,
- *> SSBGVD, SSYGVX, SSPGVX or SSBGVX 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.
- *
- *> \date November 2011
- *
- *> \ingroup single_eig
- *
- * =====================================================================
- SUBROUTINE SDRVSG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
- $ NOUNIT, A, LDA, B, LDB, D, Z, LDZ, AB, BB, AP,
- $ BP, WORK, NWORK, IWORK, LIWORK, RESULT, INFO )
- *
- * -- LAPACK test routine (version 3.4.0) --
- * -- LAPACK is a software package provided by Univ. of Tennessee, --
- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
- * November 2011
- *
- * .. Scalar Arguments ..
- INTEGER INFO, LDA, LDB, LDZ, LIWORK, NOUNIT, NSIZES,
- $ NTYPES, NWORK
- REAL THRESH
- * ..
- * .. Array Arguments ..
- LOGICAL DOTYPE( * )
- INTEGER ISEED( 4 ), IWORK( * ), NN( * )
- REAL A( LDA, * ), AB( LDA, * ), AP( * ),
- $ B( LDB, * ), BB( LDB, * ), BP( * ), D( * ),
- $ RESULT( * ), WORK( * ), Z( LDZ, * )
- * ..
- *
- * =====================================================================
- *
- * .. Parameters ..
- REAL ZERO, ONE, TEN
- PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0, TEN = 10.0E0 )
- 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 SLABAD, SLACPY, SLAFTS, SLASET, SLASUM, SLATMR,
- $ SLATMS, SSBGV, SSBGVD, SSBGVX, SSGT01, SSPGV,
- $ SSPGVD, SSPGVX, SSYGV, SSYGVD, SSYGVX, 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, 3 )**2.GT.NWORK ) THEN
- INFO = -21
- ELSE IF( 2*MAX( NMAX, 3 )**2.GT.LIWORK ) THEN
- INFO = -23
- END IF
- *
- IF( INFO.NE.0 ) THEN
- CALL XERBLA( 'SDRVSG', -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' )
- CALL SLABAD( UNFL, OVFL )
- 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 SLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA )
- *
- ELSE IF( ITYPE.EQ.2 ) THEN
- *
- * Identity
- *
- KA = 0
- KB = 0
- CALL SLASET( 'Full', LDA, N, ZERO, ZERO, 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 SLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
- $ ANORM, 0, 0, 'N', A, LDA, WORK( N+1 ),
- $ IINFO )
- *
- ELSE IF( ITYPE.EQ.5 ) THEN
- *
- * symmetric, eigenvalues specified
- *
- KA = MAX( 0, N-1 )
- KB = KA
- CALL SLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
- $ ANORM, N, N, 'N', A, LDA, WORK( N+1 ),
- $ IINFO )
- *
- ELSE IF( ITYPE.EQ.7 ) THEN
- *
- * Diagonal, random eigenvalues
- *
- KA = 0
- KB = 0
- 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, 'NO', A, LDA, IWORK, IINFO )
- *
- ELSE IF( ITYPE.EQ.8 ) THEN
- *
- * symmetric, random eigenvalues
- *
- KA = MAX( 0, N-1 )
- KB = KA
- CALL SLATMR( N, N, 'S', ISEED, 'H', WORK, 6, ONE, ONE,
- $ '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
- *
- * symmetric 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 SLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
- $ ANORM, KA, KA, 'N', A, LDA, WORK( N+1 ),
- $ 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 + ( N-1 )*SLARND( 1, ISEED2 )
- IU = 1 + ( N-1 )*SLARND( 1, ISEED2 )
- IF( IL.GT.IU ) THEN
- ITEMP = IL
- IL = IU
- IU = ITEMP
- END IF
- END IF
- *
- * 3) Call SSYGV, SSPGV, SSBGV, SSYGVD, SSPGVD, SSBGVD,
- * SSYGVX, SSPGVX, and SSBGVX, 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 SLATMS( N, N, 'U', ISEED, 'P', WORK, 5, TEN, ONE,
- $ KB, KB, UPLO, B, LDB, WORK( N+1 ),
- $ IINFO )
- *
- * Test SSYGV
- *
- NTEST = NTEST + 1
- *
- CALL SLACPY( ' ', N, N, A, LDA, Z, LDZ )
- CALL SLACPY( UPLO, N, N, B, LDB, BB, LDB )
- *
- CALL SSYGV( IBTYPE, 'V', UPLO, N, Z, LDZ, BB, LDB, D,
- $ WORK, NWORK, IINFO )
- IF( IINFO.NE.0 ) THEN
- WRITE( NOUNIT, FMT = 9999 )'SSYGV(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 SSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z,
- $ LDZ, D, WORK, RESULT( NTEST ) )
- *
- * Test SSYGVD
- *
- NTEST = NTEST + 1
- *
- CALL SLACPY( ' ', N, N, A, LDA, Z, LDZ )
- CALL SLACPY( UPLO, N, N, B, LDB, BB, LDB )
- *
- CALL SSYGVD( IBTYPE, 'V', UPLO, N, Z, LDZ, BB, LDB, D,
- $ WORK, NWORK, IWORK, LIWORK, IINFO )
- IF( IINFO.NE.0 ) THEN
- WRITE( NOUNIT, FMT = 9999 )'SSYGVD(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 SSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z,
- $ LDZ, D, WORK, RESULT( NTEST ) )
- *
- * Test SSYGVX
- *
- NTEST = NTEST + 1
- *
- CALL SLACPY( ' ', N, N, A, LDA, AB, LDA )
- CALL SLACPY( UPLO, N, N, B, LDB, BB, LDB )
- *
- CALL SSYGVX( IBTYPE, 'V', 'A', UPLO, N, AB, LDA, BB,
- $ LDB, VL, VU, IL, IU, ABSTOL, M, D, Z,
- $ LDZ, WORK, NWORK, IWORK( N+1 ), IWORK,
- $ IINFO )
- IF( IINFO.NE.0 ) THEN
- WRITE( NOUNIT, FMT = 9999 )'SSYGVX(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 SSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z,
- $ LDZ, D, WORK, RESULT( NTEST ) )
- *
- NTEST = NTEST + 1
- *
- CALL SLACPY( ' ', N, N, A, LDA, AB, LDA )
- CALL SLACPY( 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 SSYGVX( IBTYPE, 'V', 'V', UPLO, N, AB, LDA, BB,
- $ LDB, VL, VU, IL, IU, ABSTOL, M, D, Z,
- $ LDZ, WORK, NWORK, IWORK( N+1 ), IWORK,
- $ IINFO )
- IF( IINFO.NE.0 ) THEN
- WRITE( NOUNIT, FMT = 9999 )'SSYGVX(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 SSGT01( IBTYPE, UPLO, N, M, A, LDA, B, LDB, Z,
- $ LDZ, D, WORK, RESULT( NTEST ) )
- *
- NTEST = NTEST + 1
- *
- CALL SLACPY( ' ', N, N, A, LDA, AB, LDA )
- CALL SLACPY( UPLO, N, N, B, LDB, BB, LDB )
- *
- CALL SSYGVX( IBTYPE, 'V', 'I', UPLO, N, AB, LDA, BB,
- $ LDB, VL, VU, IL, IU, ABSTOL, M, D, Z,
- $ LDZ, WORK, NWORK, IWORK( N+1 ), IWORK,
- $ IINFO )
- IF( IINFO.NE.0 ) THEN
- WRITE( NOUNIT, FMT = 9999 )'SSYGVX(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 SSGT01( IBTYPE, UPLO, N, M, A, LDA, B, LDB, Z,
- $ LDZ, D, WORK, RESULT( NTEST ) )
- *
- 100 CONTINUE
- *
- * Test SSPGV
- *
- 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 SSPGV( IBTYPE, 'V', UPLO, N, AP, BP, D, Z, LDZ,
- $ WORK, IINFO )
- IF( IINFO.NE.0 ) THEN
- WRITE( NOUNIT, FMT = 9999 )'SSPGV(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 SSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z,
- $ LDZ, D, WORK, RESULT( NTEST ) )
- *
- * Test SSPGVD
- *
- 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 SSPGVD( IBTYPE, 'V', UPLO, N, AP, BP, D, Z, LDZ,
- $ WORK, NWORK, IWORK, LIWORK, IINFO )
- IF( IINFO.NE.0 ) THEN
- WRITE( NOUNIT, FMT = 9999 )'SSPGVD(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 SSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z,
- $ LDZ, D, WORK, RESULT( NTEST ) )
- *
- * Test SSPGVX
- *
- 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 SSPGVX( IBTYPE, 'V', 'A', UPLO, N, AP, BP, VL,
- $ VU, IL, IU, ABSTOL, M, D, Z, LDZ, WORK,
- $ IWORK( N+1 ), IWORK, INFO )
- IF( IINFO.NE.0 ) THEN
- WRITE( NOUNIT, FMT = 9999 )'SSPGVX(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 SSGT01( IBTYPE, UPLO, N, M, A, LDA, B, LDB, Z,
- $ LDZ, D, WORK, 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 SSPGVX( IBTYPE, 'V', 'V', UPLO, N, AP, BP, VL,
- $ VU, IL, IU, ABSTOL, M, D, Z, LDZ, WORK,
- $ IWORK( N+1 ), IWORK, INFO )
- IF( IINFO.NE.0 ) THEN
- WRITE( NOUNIT, FMT = 9999 )'SSPGVX(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 SSGT01( IBTYPE, UPLO, N, M, A, LDA, B, LDB, Z,
- $ LDZ, D, WORK, 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 SSPGVX( IBTYPE, 'V', 'I', UPLO, N, AP, BP, VL,
- $ VU, IL, IU, ABSTOL, M, D, Z, LDZ, WORK,
- $ IWORK( N+1 ), IWORK, INFO )
- IF( IINFO.NE.0 ) THEN
- WRITE( NOUNIT, FMT = 9999 )'SSPGVX(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 SSGT01( IBTYPE, UPLO, N, M, A, LDA, B, LDB, Z,
- $ LDZ, D, WORK, RESULT( NTEST ) )
- *
- 310 CONTINUE
- *
- IF( IBTYPE.EQ.1 ) THEN
- *
- * TEST SSBGV
- *
- 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 SSBGV( 'V', UPLO, N, KA, KB, AB, LDA, BB, LDB,
- $ D, Z, LDZ, WORK, IINFO )
- IF( IINFO.NE.0 ) THEN
- WRITE( NOUNIT, FMT = 9999 )'SSBGV(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 SSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z,
- $ LDZ, D, WORK, RESULT( NTEST ) )
- *
- * TEST SSBGVD
- *
- 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 SSBGVD( 'V', UPLO, N, KA, KB, AB, LDA, BB,
- $ LDB, D, Z, LDZ, WORK, NWORK, IWORK,
- $ LIWORK, IINFO )
- IF( IINFO.NE.0 ) THEN
- WRITE( NOUNIT, FMT = 9999 )'SSBGVD(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 SSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z,
- $ LDZ, D, WORK, RESULT( NTEST ) )
- *
- * Test SSBGVX
- *
- 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 SSBGVX( 'V', 'A', UPLO, N, KA, KB, AB, LDA,
- $ BB, LDB, BP, MAX( 1, N ), VL, VU, IL,
- $ IU, ABSTOL, M, D, Z, LDZ, WORK,
- $ IWORK( N+1 ), IWORK, IINFO )
- IF( IINFO.NE.0 ) THEN
- WRITE( NOUNIT, FMT = 9999 )'SSBGVX(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 SSGT01( IBTYPE, UPLO, N, M, A, LDA, B, LDB, Z,
- $ LDZ, D, WORK, 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 SSBGVX( 'V', 'V', UPLO, N, KA, KB, AB, LDA,
- $ BB, LDB, BP, MAX( 1, N ), VL, VU, IL,
- $ IU, ABSTOL, M, D, Z, LDZ, WORK,
- $ IWORK( N+1 ), IWORK, IINFO )
- IF( IINFO.NE.0 ) THEN
- WRITE( NOUNIT, FMT = 9999 )'SSBGVX(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 SSGT01( IBTYPE, UPLO, N, M, A, LDA, B, LDB, Z,
- $ LDZ, D, WORK, 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 SSBGVX( 'V', 'I', UPLO, N, KA, KB, AB, LDA,
- $ BB, LDB, BP, MAX( 1, N ), VL, VU, IL,
- $ IU, ABSTOL, M, D, Z, LDZ, WORK,
- $ IWORK( N+1 ), IWORK, IINFO )
- IF( IINFO.NE.0 ) THEN
- WRITE( NOUNIT, FMT = 9999 )'SSBGVX(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 SSGT01( IBTYPE, UPLO, N, M, A, LDA, B, LDB, Z,
- $ LDZ, D, WORK, RESULT( NTEST ) )
- *
- END IF
- *
- 620 CONTINUE
- 630 CONTINUE
- *
- * End of Loop -- Check for RESULT(j) > THRESH
- *
- NTESTT = NTESTT + NTEST
- CALL SLAFTS( 'SSG', N, N, JTYPE, NTEST, RESULT, IOLDSD,
- $ THRESH, NOUNIT, NERRS )
- 640 CONTINUE
- 650 CONTINUE
- *
- * Summary
- *
- CALL SLASUM( 'SSG', NOUNIT, NERRS, NTESTT )
- *
- RETURN
- *
- * End of SDRVSG
- *
- 9999 FORMAT( ' SDRVSG: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
- $ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
- END
|