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SUBROUTINE DDRVSG( 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 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * ******************************************************************* * * modified August 1997, a new parameter LIWORK is added * in the calling sequence. * * test routine DDGT01 is also modified * ******************************************************************* * * .. Scalar Arguments .. INTEGER INFO, LDA, LDB, LDZ, LIWORK, NOUNIT, NSIZES, $ NTYPES, NWORK DOUBLE PRECISION THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER ISEED( 4 ), IWORK( * ), NN( * ) DOUBLE PRECISION A( LDA, * ), AB( LDA, * ), AP( * ), $ B( LDB, * ), BB( LDB, * ), BP( * ), D( * ), $ RESULT( * ), WORK( * ), Z( LDZ, * ) * .. * * Purpose * ======= * * DDRVSG checks the real symmetric generalized eigenproblem * drivers. * * DSYGV computes all eigenvalues and, optionally, * eigenvectors of a real symmetric-definite generalized * eigenproblem. * * DSYGVD computes all eigenvalues and, optionally, * eigenvectors of a real symmetric-definite generalized * eigenproblem using a divide and conquer algorithm. * * DSYGVX computes selected eigenvalues and, optionally, * eigenvectors of a real symmetric-definite generalized * eigenproblem. * * DSPGV computes all eigenvalues and, optionally, * eigenvectors of a real symmetric-definite generalized * eigenproblem in packed storage. * * DSPGVD computes all eigenvalues and, optionally, * eigenvectors of a real symmetric-definite generalized * eigenproblem in packed storage using a divide and * conquer algorithm. * * DSPGVX computes selected eigenvalues and, optionally, * eigenvectors of a real symmetric-definite generalized * eigenproblem in packed storage. * * DSBGV computes all eigenvalues and, optionally, * eigenvectors of a real symmetric-definite banded * generalized eigenproblem. * * DSBGVD computes all eigenvalues and, optionally, * eigenvectors of a real symmetric-definite banded * generalized eigenproblem using a divide and conquer * algorithm. * * DSBGVX computes selected eigenvalues and, optionally, * eigenvectors of a real symmetric-definite banded * generalized eigenproblem. * * When DDRVSG 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) DSYGV with ITYPE = 1 and UPLO ='U': * * | A Z - B Z D | / ( |A| |Z| n ulp ) * * (2) as (1) but calling DSPGV * (3) as (1) but calling DSBGV * (4) as (1) but with UPLO = 'L' * (5) as (4) but calling DSPGV * (6) as (4) but calling DSBGV * * (7) DSYGV with ITYPE = 2 and UPLO ='U': * * | A B Z - Z D | / ( |A| |Z| n ulp ) * * (8) as (7) but calling DSPGV * (9) as (7) but with UPLO = 'L' * (10) as (9) but calling DSPGV * * (11) DSYGV with ITYPE = 3 and UPLO ='U': * * | B A Z - Z D | / ( |A| |Z| n ulp ) * * (12) as (11) but calling DSPGV * (13) as (11) but with UPLO = 'L' * (14) as (13) but calling DSPGV * * DSYGVD, DSPGVD and DSBGVD performed the same 14 tests. * * DSYGVX, DSPGVX and DSBGVX 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 * * Arguments * ========= * * NSIZES INTEGER * The number of sizes of matrices to use. If it is zero, * DDRVSG 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, DDRVSG * 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 DDRVSG 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (max(NN)) * The eigenvalues of A. On exit, the eigenvalues in D * correspond with the matrix in A. * Modified. * * Z DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDA, max(NN)) * Workspace. * Modified. * * BB DOUBLE PRECISION array, dimension (LDB, max(NN)) * Workspace. * Modified. * * AP DOUBLE PRECISION array, dimension (max(NN)**2) * Workspace. * Modified. * * BP DOUBLE PRECISION array, dimension (max(NN)**2) * Workspace. * Modified. * * WORK DOUBLE PRECISION 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 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: LIWORK too small. * If DLATMR, SLATMS, DSYGV, DSPGV, DSBGV, SSYGVD, SSPGVD, * DSBGVD, DSYGVX, DSPGVX 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 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) ) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TEN PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TEN = 10.0D0 ) 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 * .. * .. 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, DLACPY, DLAFTS, DLASET, DLASUM, DLATMR, $ DLATMS, DSBGV, DSBGVD, DSBGVX, DSGT01, DSPGV, $ DSPGVD, DSPGVX, DSYGV, DSYGVD, DSYGVX, XERBLA * .. * .. 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, 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( 'DDRVSG', -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 DLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA ) * ELSE IF( ITYPE.EQ.2 ) THEN * * Identity * KA = 0 KB = 0 CALL DLASET( '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 DLATMS( 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 DLATMS( 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 DLATMR( 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 DLATMR( 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 DLATMS( 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 )*DLARND( 1, ISEED2 ) IU = 1 + ( N-1 )*DLARND( 1, ISEED2 ) IF( IL.GT.IU ) THEN ITEMP = IL IL = IU IU = ITEMP END IF END IF * * 3) Call DSYGV, DSPGV, DSBGV, SSYGVD, SSPGVD, SSBGVD, * DSYGVX, DSPGVX, and DSBGVX, 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 DLATMS( N, N, 'U', ISEED, 'P', WORK, 5, TEN, ONE, $ KB, KB, UPLO, B, LDB, WORK( N+1 ), $ IINFO ) * * Test DSYGV * NTEST = NTEST + 1 * CALL DLACPY( ' ', N, N, A, LDA, Z, LDZ ) CALL DLACPY( UPLO, N, N, B, LDB, BB, LDB ) * CALL DSYGV( IBTYPE, 'V', UPLO, N, Z, LDZ, BB, LDB, D, $ WORK, NWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'DSYGV(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 DSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z, $ LDZ, D, WORK, RESULT( NTEST ) ) * * Test DSYGVD * NTEST = NTEST + 1 * CALL DLACPY( ' ', N, N, A, LDA, Z, LDZ ) CALL DLACPY( UPLO, N, N, B, LDB, BB, LDB ) * CALL DSYGVD( IBTYPE, 'V', UPLO, N, Z, LDZ, BB, LDB, D, $ WORK, NWORK, IWORK, LIWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'DSYGVD(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 DSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z, $ LDZ, D, WORK, RESULT( NTEST ) ) * * Test DSYGVX * NTEST = NTEST + 1 * CALL DLACPY( ' ', N, N, A, LDA, AB, LDA ) CALL DLACPY( UPLO, N, N, B, LDB, BB, LDB ) * CALL DSYGVX( 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 )'DSYGVX(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 DSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z, $ LDZ, D, WORK, RESULT( NTEST ) ) * NTEST = NTEST + 1 * CALL DLACPY( ' ', N, N, A, LDA, AB, LDA ) CALL DLACPY( 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 DSYGVX( 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 )'DSYGVX(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 DSGT01( IBTYPE, UPLO, N, M, A, LDA, B, LDB, Z, $ LDZ, D, WORK, RESULT( NTEST ) ) * NTEST = NTEST + 1 * CALL DLACPY( ' ', N, N, A, LDA, AB, LDA ) CALL DLACPY( UPLO, N, N, B, LDB, BB, LDB ) * CALL DSYGVX( 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 )'DSYGVX(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 DSGT01( IBTYPE, UPLO, N, M, A, LDA, B, LDB, Z, $ LDZ, D, WORK, RESULT( NTEST ) ) * 100 CONTINUE * * Test DSPGV * 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 DSPGV( IBTYPE, 'V', UPLO, N, AP, BP, D, Z, LDZ, $ WORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'DSPGV(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 DSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z, $ LDZ, D, WORK, RESULT( NTEST ) ) * * Test DSPGVD * 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 DSPGVD( IBTYPE, 'V', UPLO, N, AP, BP, D, Z, LDZ, $ WORK, NWORK, IWORK, LIWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'DSPGVD(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 DSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z, $ LDZ, D, WORK, RESULT( NTEST ) ) * * Test DSPGVX * 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 DSPGVX( 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 )'DSPGVX(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 DSGT01( 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 DSPGVX( 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 )'DSPGVX(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 DSGT01( 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 DSPGVX( 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 )'DSPGVX(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 DSGT01( IBTYPE, UPLO, N, M, A, LDA, B, LDB, Z, $ LDZ, D, WORK, RESULT( NTEST ) ) * 310 CONTINUE * IF( IBTYPE.EQ.1 ) THEN * * TEST DSBGV * 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 DSBGV( 'V', UPLO, N, KA, KB, AB, LDA, BB, LDB, $ D, Z, LDZ, WORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'DSBGV(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 DSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z, $ LDZ, D, WORK, RESULT( NTEST ) ) * * TEST DSBGVD * 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 DSBGVD( '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 )'DSBGVD(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 DSGT01( IBTYPE, UPLO, N, N, A, LDA, B, LDB, Z, $ LDZ, D, WORK, RESULT( NTEST ) ) * * Test DSBGVX * 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 DSBGVX( '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 )'DSBGVX(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 DSGT01( 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 DSBGVX( '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 )'DSBGVX(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 DSGT01( 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 DSBGVX( '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 )'DSBGVX(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 DSGT01( 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 DLAFTS( 'DSG', N, N, JTYPE, NTEST, RESULT, IOLDSD, $ THRESH, NOUNIT, NERRS ) 640 CONTINUE 650 CONTINUE * * Summary * CALL DLASUM( 'DSG', NOUNIT, NERRS, NTESTT ) * RETURN * * End of DDRVSG * 9999 FORMAT( ' DDRVSG: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', $ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' ) END |