*> \brief \b ZDRVSG2STG * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZDRVSG2STG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, * NOUNIT, A, LDA, B, LDB, D, D2, Z, LDZ, AB, * BB, AP, BP, WORK, NWORK, RWORK, LRWORK, * IWORK, LIWORK, RESULT, INFO ) * * IMPLICIT NONE * * .. Scalar Arguments .. * INTEGER INFO, LDA, LDB, LDZ, LIWORK, LRWORK, NOUNIT, * $ NSIZES, NTYPES, NWORK * DOUBLE PRECISION THRESH * .. * .. Array Arguments .. * LOGICAL DOTYPE( * ) * INTEGER ISEED( 4 ), IWORK( * ), NN( * ) * DOUBLE PRECISION D( * ), RESULT( * ), RWORK( * ) * COMPLEX*16 A( LDA, * ), AB( LDA, * ), AP( * ), * $ B( LDB, * ), BB( LDB, * ), BP( * ), WORK( * ), * $ Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZDRVSG2STG checks the complex Hermitian generalized eigenproblem *> drivers. *> *> ZHEGV computes all eigenvalues and, optionally, *> eigenvectors of a complex Hermitian-definite generalized *> eigenproblem. *> *> ZHEGVD computes all eigenvalues and, optionally, *> eigenvectors of a complex Hermitian-definite generalized *> eigenproblem using a divide and conquer algorithm. *> *> ZHEGVX computes selected eigenvalues and, optionally, *> eigenvectors of a complex Hermitian-definite generalized *> eigenproblem. *> *> ZHPGV computes all eigenvalues and, optionally, *> eigenvectors of a complex Hermitian-definite generalized *> eigenproblem in packed storage. *> *> ZHPGVD computes all eigenvalues and, optionally, *> eigenvectors of a complex Hermitian-definite generalized *> eigenproblem in packed storage using a divide and *> conquer algorithm. *> *> ZHPGVX computes selected eigenvalues and, optionally, *> eigenvectors of a complex Hermitian-definite generalized *> eigenproblem in packed storage. *> *> ZHBGV computes all eigenvalues and, optionally, *> eigenvectors of a complex Hermitian-definite banded *> generalized eigenproblem. *> *> ZHBGVD computes all eigenvalues and, optionally, *> eigenvectors of a complex Hermitian-definite banded *> generalized eigenproblem using a divide and conquer *> algorithm. *> *> ZHBGVX computes selected eigenvalues and, optionally, *> eigenvectors of a complex Hermitian-definite banded *> generalized eigenproblem. *> *> When ZDRVSG2STG 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) ZHEGV with ITYPE = 1 and UPLO ='U': *> *> | A Z - B Z D | / ( |A| |Z| n ulp ) *> | D - D2 | / ( |D| ulp ) where D is computed by *> ZHEGV and D2 is computed by *> ZHEGV_2STAGE. This test is *> only performed for DSYGV *> *> (2) as (1) but calling ZHPGV *> (3) as (1) but calling ZHBGV *> (4) as (1) but with UPLO = 'L' *> (5) as (4) but calling ZHPGV *> (6) as (4) but calling ZHBGV *> *> (7) ZHEGV with ITYPE = 2 and UPLO ='U': *> *> | A B Z - Z D | / ( |A| |Z| n ulp ) *> *> (8) as (7) but calling ZHPGV *> (9) as (7) but with UPLO = 'L' *> (10) as (9) but calling ZHPGV *> *> (11) ZHEGV with ITYPE = 3 and UPLO ='U': *> *> | B A Z - Z D | / ( |A| |Z| n ulp ) *> *> (12) as (11) but calling ZHPGV *> (13) as (11) but with UPLO = 'L' *> (14) as (13) but calling ZHPGV *> *> ZHEGVD, ZHPGVD and ZHBGVD performed the same 14 tests. *> *> ZHEGVX, ZHPGVX and ZHBGVX 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, *> ZDRVSG2STG 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, ZDRVSG2STG *> 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 ZDRVSG2STG to continue the same random number *> sequence. *> Modified. *> *> THRESH DOUBLE PRECISION *> 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*16 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*16 array, dimension (LDB , max(NN)) *> Used to hold the Hermitian positive definite matrix for *> the generailzed 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 DOUBLE PRECISION array, dimension (max(NN)) *> The eigenvalues of A. On exit, the eigenvalues in D *> correspond with the matrix in A. *> Modified. *> *> Z COMPLEX*16 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*16 array, dimension (LDA, max(NN)) *> Workspace. *> Modified. *> *> BB COMPLEX*16 array, dimension (LDB, max(NN)) *> Workspace. *> Modified. *> *> AP COMPLEX*16 array, dimension (max(NN)**2) *> Workspace. *> Modified. *> *> BP COMPLEX*16 array, dimension (max(NN)**2) *> Workspace. *> Modified. *> *> WORK COMPLEX*16 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 ZLATMR, CLATMS, ZHEGV, ZHPGV, ZHBGV, CHEGVD, CHPGVD, *> ZHPGVD, ZHEGVX, CHPGVX, ZHBGVX 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 DLAFTS). *> 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 December 2016 * *> \ingroup complex16_eig * * ===================================================================== SUBROUTINE ZDRVSG2STG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, $ NOUNIT, A, LDA, B, LDB, D, D2, Z, LDZ, AB, $ BB, AP, BP, WORK, NWORK, RWORK, LRWORK, $ IWORK, LIWORK, RESULT, INFO ) * IMPLICIT NONE * * -- LAPACK test routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, LDA, LDB, LDZ, LIWORK, LRWORK, NOUNIT, $ NSIZES, NTYPES, NWORK DOUBLE PRECISION THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER ISEED( 4 ), IWORK( * ), NN( * ) DOUBLE PRECISION D( * ), D2( * ), RESULT( * ), RWORK( * ) COMPLEX*16 A( LDA, * ), AB( LDA, * ), AP( * ), $ B( LDB, * ), BB( LDB, * ), BP( * ), WORK( * ), $ Z( LDZ, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TEN PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TEN = 10.0D+0 ) COMPLEX*16 CZERO, CONE PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), $ CONE = ( 1.0D+0, 0.0D+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 DOUBLE PRECISION ABSTOL, ANINV, ANORM, COND, OVFL, RTOVFL, $ RTUNFL, ULP, ULPINV, UNFL, VL, VU, TEMP1, TEMP2 * .. * .. Local Arrays .. INTEGER IDUMMA( 1 ), IOLDSD( 4 ), ISEED2( 4 ), $ KMAGN( MAXTYP ), KMODE( MAXTYP ), $ KTYPE( MAXTYP ) * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, DLARND EXTERNAL LSAME, DLAMCH, DLARND * .. * .. External Subroutines .. EXTERNAL DLABAD, DLAFTS, DLASUM, XERBLA, ZHBGV, ZHBGVD, $ ZHBGVX, ZHEGV, ZHEGVD, ZHEGVX, ZHPGV, ZHPGVD, $ ZHPGVX, ZLACPY, ZLASET, ZLATMR, ZLATMS, ZSGT01, $ ZHEGV_2STAGE * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, MAX, MIN, 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( 'ZDRVSG2STG', -INFO ) RETURN END IF * * Quick return if possible * IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 ) $ RETURN * * More Important constants * UNFL = DLAMCH( 'Safe minimum' ) OVFL = DLAMCH( 'Overflow' ) CALL DLABAD( UNFL, OVFL ) ULP = DLAMCH( 'Epsilon' )*DLAMCH( '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 / DBLE( 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 ZLASET( 'Full', LDA, N, CZERO, CZERO, A, LDA ) * ELSE IF( ITYPE.EQ.2 ) THEN * * Identity * KA = 0 KB = 0 CALL ZLASET( '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 ZLATMS( 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 ZLATMS( 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 ZLATMR( 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 ZLATMR( 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 ZLATMS( 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 )*DLARND( 1, ISEED2 ) ) IU = 1 + INT( ( N-1 )*DLARND( 1, ISEED2 ) ) IF( IL.GT.IU ) THEN ITEMP = IL IL = IU IU = ITEMP END IF END IF * * 3) Call ZHEGV, ZHPGV, ZHBGV, CHEGVD, CHPGVD, CHBGVD, * ZHEGVX, ZHPGVX and ZHBGVX, 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 ZLATMS( N, N, 'U', ISEED, 'P', RWORK, 5, TEN, $ ONE, KB, KB, UPLO, B, LDB, WORK( N+1 ), $ IINFO ) * * Test ZHEGV * NTEST = NTEST + 1 * CALL ZLACPY( ' ', N, N, A, LDA, Z, LDZ ) CALL ZLACPY( UPLO, N, N, B, LDB, BB, LDB ) * CALL ZHEGV( IBTYPE, 'V', UPLO, N, Z, LDZ, BB, LDB, D, $ WORK, NWORK, RWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'ZHEGV(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 ZSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z, $ LDZ, D, WORK, RWORK, RESULT( NTEST ) ) * * Test ZHEGV_2STAGE * NTEST = NTEST + 1 * CALL ZLACPY( ' ', N, N, A, LDA, Z, LDZ ) CALL ZLACPY( UPLO, N, N, B, LDB, BB, LDB ) * CALL ZHEGV_2STAGE( IBTYPE, 'N', UPLO, N, Z, LDZ, $ BB, LDB, D2, WORK, NWORK, RWORK, $ IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 ) $ 'ZHEGV_2STAGE(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 * C CALL ZSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z, C $ LDZ, D, WORK, RWORK, RESULT( NTEST ) ) * * Do Tests | D1 - D2 | / ( |D1| ulp ) * D1 computed using the standard 1-stage reduction as reference * D2 computed using the 2-stage reduction * TEMP1 = ZERO TEMP2 = ZERO DO 151 J = 1, N TEMP1 = MAX( TEMP1, ABS( D( J ) ), $ ABS( D2( J ) ) ) TEMP2 = MAX( TEMP2, ABS( D( J )-D2( J ) ) ) 151 CONTINUE * RESULT( NTEST ) = TEMP2 / $ MAX( UNFL, ULP*MAX( TEMP1, TEMP2 ) ) * * Test ZHEGVD * NTEST = NTEST + 1 * CALL ZLACPY( ' ', N, N, A, LDA, Z, LDZ ) CALL ZLACPY( UPLO, N, N, B, LDB, BB, LDB ) * CALL ZHEGVD( 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 )'ZHEGVD(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 ZSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z, $ LDZ, D, WORK, RWORK, RESULT( NTEST ) ) * * Test ZHEGVX * NTEST = NTEST + 1 * CALL ZLACPY( ' ', N, N, A, LDA, AB, LDA ) CALL ZLACPY( UPLO, N, N, B, LDB, BB, LDB ) * CALL ZHEGVX( 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 )'ZHEGVX(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 ZSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z, $ LDZ, D, WORK, RWORK, RESULT( NTEST ) ) * NTEST = NTEST + 1 * CALL ZLACPY( ' ', N, N, A, LDA, AB, LDA ) CALL ZLACPY( 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 ZHEGVX( 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 )'ZHEGVX(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 ZSGT01( IBTYPE, UPLO, N, M, A, LDA, B, LDB, Z, $ LDZ, D, WORK, RWORK, RESULT( NTEST ) ) * NTEST = NTEST + 1 * CALL ZLACPY( ' ', N, N, A, LDA, AB, LDA ) CALL ZLACPY( UPLO, N, N, B, LDB, BB, LDB ) * CALL ZHEGVX( 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 )'ZHEGVX(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 ZSGT01( IBTYPE, UPLO, N, M, A, LDA, B, LDB, Z, $ LDZ, D, WORK, RWORK, RESULT( NTEST ) ) * 100 CONTINUE * * Test ZHPGV * 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 ZHPGV( IBTYPE, 'V', UPLO, N, AP, BP, D, Z, LDZ, $ WORK, RWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'ZHPGV(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 ZSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z, $ LDZ, D, WORK, RWORK, RESULT( NTEST ) ) * * Test ZHPGVD * 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 ZHPGVD( 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 )'ZHPGVD(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 ZSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z, $ LDZ, D, WORK, RWORK, RESULT( NTEST ) ) * * Test ZHPGVX * 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 ZHPGVX( 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 )'ZHPGVX(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 ZSGT01( 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 ZHPGVX( 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 )'ZHPGVX(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 ZSGT01( 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 ZHPGVX( 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 )'ZHPGVX(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 ZSGT01( IBTYPE, UPLO, N, M, A, LDA, B, LDB, Z, $ LDZ, D, WORK, RWORK, RESULT( NTEST ) ) * 310 CONTINUE * IF( IBTYPE.EQ.1 ) THEN * * TEST ZHBGV * 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 ZHBGV( 'V', UPLO, N, KA, KB, AB, LDA, BB, LDB, $ D, Z, LDZ, WORK, RWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'ZHBGV(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 ZSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z, $ LDZ, D, WORK, RWORK, RESULT( NTEST ) ) * * TEST ZHBGVD * 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 ZHBGVD( '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 )'ZHBGVD(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 ZSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z, $ LDZ, D, WORK, RWORK, RESULT( NTEST ) ) * * Test ZHBGVX * 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 ZHBGVX( '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 )'ZHBGVX(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 ZSGT01( 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 ZHBGVX( '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 )'ZHBGVX(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 ZSGT01( 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 ZHBGVX( '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 )'ZHBGVX(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 ZSGT01( 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 DLAFTS( 'ZSG', N, N, JTYPE, NTEST, RESULT, IOLDSD, $ THRESH, NOUNIT, NERRS ) 640 CONTINUE 650 CONTINUE * * Summary * CALL DLASUM( 'ZSG', NOUNIT, NERRS, NTESTT ) * RETURN * 9999 FORMAT( ' ZDRVSG2STG: ', A, ' returned INFO=', I6, '.', / 9X, $ 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' ) * * End of ZDRVSG2STG * END