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SUBROUTINE DDRVGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
$ THRSHN, NOUNIT, A, LDA, B, S, T, S2, T2, Q, $ LDQ, Z, ALPHR1, ALPHI1, BETA1, ALPHR2, ALPHI2, $ BETA2, VL, VR, WORK, LWORK, RESULT, INFO ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER INFO, LDA, LDQ, LWORK, NOUNIT, NSIZES, NTYPES DOUBLE PRECISION THRESH, THRSHN * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER ISEED( 4 ), NN( * ) DOUBLE PRECISION A( LDA, * ), ALPHI1( * ), ALPHI2( * ), $ ALPHR1( * ), ALPHR2( * ), B( LDA, * ), $ BETA1( * ), BETA2( * ), Q( LDQ, * ), $ RESULT( * ), S( LDA, * ), S2( LDA, * ), $ T( LDA, * ), T2( LDA, * ), VL( LDQ, * ), $ VR( LDQ, * ), WORK( * ), Z( LDQ, * ) * .. * * Purpose * ======= * * DDRVGG checks the nonsymmetric generalized eigenvalue driver * routines. * T T T * DGEGS factors A and B as Q S Z and Q T Z , where means * transpose, T is upper triangular, S is in generalized Schur form * (block upper triangular, with 1x1 and 2x2 blocks on the diagonal, * the 2x2 blocks corresponding to complex conjugate pairs of * generalized eigenvalues), and Q and Z are orthogonal. It also * computes the generalized eigenvalues (alpha(1),beta(1)), ..., * (alpha(n),beta(n)), where alpha(j)=S(j,j) and beta(j)=P(j,j) -- * thus, w(j) = alpha(j)/beta(j) is a root of the generalized * eigenvalue problem * * det( A - w(j) B ) = 0 * * and m(j) = beta(j)/alpha(j) is a root of the essentially equivalent * problem * * det( m(j) A - B ) = 0 * * DGEGV computes the generalized eigenvalues (alpha(1),beta(1)), ..., * (alpha(n),beta(n)), the matrix L whose columns contain the * generalized left eigenvectors l, and the matrix R whose columns * contain the generalized right eigenvectors r for the pair (A,B). * * When DDRVGG 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 will be generated and used * to test the nonsymmetric eigenroutines. For each matrix, 7 * tests will be performed and compared with the threshhold THRESH: * * Results from DGEGS: * * T * (1) | A - Q S Z | / ( |A| n ulp ) * * T * (2) | B - Q T Z | / ( |B| n ulp ) * * T * (3) | I - QQ | / ( n ulp ) * * T * (4) | I - ZZ | / ( n ulp ) * * (5) maximum over j of D(j) where: * * if alpha(j) is real: * |alpha(j) - S(j,j)| |beta(j) - T(j,j)| * D(j) = ------------------------ + ----------------------- * max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|) * * if alpha(j) is complex: * | det( s S - w T ) | * D(j) = --------------------------------------------------- * ulp max( s norm(S), |w| norm(T) )*norm( s S - w T ) * * and S and T are here the 2 x 2 diagonal blocks of S and T * corresponding to the j-th eigenvalue. * * Results from DGEGV: * * (6) max over all left eigenvalue/-vector pairs (beta/alpha,l) of * * | l**H * (beta A - alpha B) | / ( ulp max( |beta A|, |alpha B| ) ) * * where l**H is the conjugate tranpose of l. * * (7) max over all right eigenvalue/-vector pairs (beta/alpha,r) of * * | (beta A - alpha B) r | / ( ulp max( |beta A|, |alpha B| ) ) * * Test Matrices * ---- -------- * * The sizes of the test matrices 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. * Currently, the list of possible types is: * * (1) ( 0, 0 ) (a pair of zero matrices) * * (2) ( I, 0 ) (an identity and a zero matrix) * * (3) ( 0, I ) (an identity and a zero matrix) * * (4) ( I, I ) (a pair of identity matrices) * * t t * (5) ( J , J ) (a pair of transposed Jordan blocks) * * t ( I 0 ) * (6) ( X, Y ) where X = ( J 0 ) and Y = ( t ) * ( 0 I ) ( 0 J ) * and I is a k x k identity and J a (k+1)x(k+1) * Jordan block; k=(N-1)/2 * * (7) ( D, I ) where D is diag( 0, 1,..., N-1 ) (a diagonal * matrix with those diagonal entries.) * (8) ( I, D ) * * (9) ( big*D, small*I ) where "big" is near overflow and small=1/big * * (10) ( small*D, big*I ) * * (11) ( big*I, small*D ) * * (12) ( small*I, big*D ) * * (13) ( big*D, big*I ) * * (14) ( small*D, small*I ) * * (15) ( D1, D2 ) where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and * D2 is diag( 0, N-3, N-4,..., 1, 0, 0 ) * t t * (16) Q ( J , J ) Z where Q and Z are random orthogonal matrices. * * (17) Q ( T1, T2 ) Z where T1 and T2 are upper triangular matrices * with random O(1) entries above the diagonal * and diagonal entries diag(T1) = * ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) = * ( 0, N-3, N-4,..., 1, 0, 0 ) * * (18) Q ( T1, T2 ) Z diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 ) * diag(T2) = ( 0, 1, 0, 1,..., 1, 0 ) * s = machine precision. * * (19) Q ( T1, T2 ) Z diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 ) * diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 ) * * N-5 * (20) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, 1, a, ..., a =s, 0 ) * diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) * * (21) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 ) * diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) * where r1,..., r(N-4) are random. * * (22) Q ( big*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) * diag(T2) = ( 0, 1, ..., 1, 0, 0 ) * * (23) Q ( small*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) * diag(T2) = ( 0, 1, ..., 1, 0, 0 ) * * (24) Q ( small*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) * diag(T2) = ( 0, 1, ..., 1, 0, 0 ) * * (25) Q ( big*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) * diag(T2) = ( 0, 1, ..., 1, 0, 0 ) * * (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular * matrices. * * Arguments * ========= * * NSIZES (input) INTEGER * The number of sizes of matrices to use. If it is zero, * DDRVGG does nothing. It must be at least zero. * * NN (input) 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. * * NTYPES (input) INTEGER * The number of elements in DOTYPE. If it is zero, DDRVGG * 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. . * * DOTYPE (input) 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. * * ISEED (input/output) 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 DDRVGG to continue the same random number * sequence. * * THRESH (input) 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. * * THRSHN (input) DOUBLE PRECISION * Threshhold for reporting eigenvector normalization error. * If the normalization of any eigenvector differs from 1 by * more than THRSHN*ulp, then a special error message will be * printed. (This is handled separately from the other tests, * since only a compiler or programming error should cause an * error message, at least if THRSHN is at least 5--10.) * * NOUNIT (input) INTEGER * The FORTRAN unit number for printing out error messages * (e.g., if a routine returns IINFO not equal to 0.) * * A (input/workspace) DOUBLE PRECISION array, dimension * (LDA, max(NN)) * Used to hold the original A matrix. Used as input only * if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and * DOTYPE(MAXTYP+1)=.TRUE. * * LDA (input) INTEGER * The leading dimension of A, B, S, T, S2, and T2. * It must be at least 1 and at least max( NN ). * * B (input/workspace) DOUBLE PRECISION array, dimension * (LDA, max(NN)) * Used to hold the original B matrix. Used as input only * if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and * DOTYPE(MAXTYP+1)=.TRUE. * * S (workspace) DOUBLE PRECISION array, dimension (LDA, max(NN)) * The Schur form matrix computed from A by DGEGS. On exit, S * contains the Schur form matrix corresponding to the matrix * in A. * * T (workspace) DOUBLE PRECISION array, dimension (LDA, max(NN)) * The upper triangular matrix computed from B by DGEGS. * * S2 (workspace) DOUBLE PRECISION array, dimension (LDA, max(NN)) * The matrix computed from A by DGEGV. This will be the * Schur form of some matrix related to A, but will not, in * general, be the same as S. * * T2 (workspace) DOUBLE PRECISION array, dimension (LDA, max(NN)) * The matrix computed from B by DGEGV. This will be the * Schur form of some matrix related to B, but will not, in * general, be the same as T. * * Q (workspace) DOUBLE PRECISION array, dimension (LDQ, max(NN)) * The (left) orthogonal matrix computed by DGEGS. * * LDQ (input) INTEGER * The leading dimension of Q, Z, VL, and VR. It must * be at least 1 and at least max( NN ). * * Z (workspace) DOUBLE PRECISION array of * dimension( LDQ, max(NN) ) * The (right) orthogonal matrix computed by DGEGS. * * ALPHR1 (workspace) DOUBLE PRECISION array, dimension (max(NN)) * ALPHI1 (workspace) DOUBLE PRECISION array, dimension (max(NN)) * BETA1 (workspace) DOUBLE PRECISION array, dimension (max(NN)) * * The generalized eigenvalues of (A,B) computed by DGEGS. * ( ALPHR1(k)+ALPHI1(k)*i ) / BETA1(k) is the k-th * generalized eigenvalue of the matrices in A and B. * * ALPHR2 (workspace) DOUBLE PRECISION array, dimension (max(NN)) * ALPHI2 (workspace) DOUBLE PRECISION array, dimension (max(NN)) * BETA2 (workspace) DOUBLE PRECISION array, dimension (max(NN)) * * The generalized eigenvalues of (A,B) computed by DGEGV. * ( ALPHR2(k)+ALPHI2(k)*i ) / BETA2(k) is the k-th * generalized eigenvalue of the matrices in A and B. * * VL (workspace) DOUBLE PRECISION array, dimension (LDQ, max(NN)) * The (block lower triangular) left eigenvector matrix for * the matrices in A and B. (See DTGEVC for the format.) * * VR (workspace) DOUBLE PRECISION array, dimension (LDQ, max(NN)) * The (block upper triangular) right eigenvector matrix for * the matrices in A and B. (See DTGEVC for the format.) * * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) * * LWORK (input) INTEGER * The number of entries in WORK. This must be at least * 2*N + MAX( 6*N, N*(NB+1), (k+1)*(2*k+N+1) ), where * "k" is the sum of the blocksize and number-of-shifts for * DHGEQZ, and NB is the greatest of the blocksizes for * DGEQRF, DORMQR, and DORGQR. (The blocksizes and the * number-of-shifts are retrieved through calls to ILAENV.) * * RESULT (output) DOUBLE PRECISION array, dimension (15) * The values computed by the tests described above. * The values are currently limited to 1/ulp, to avoid * overflow. * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value. * > 0: A routine returned an error code. INFO is the * absolute value of the INFO value returned. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) INTEGER MAXTYP PARAMETER ( MAXTYP = 26 ) * .. * .. Local Scalars .. LOGICAL BADNN, ILABAD INTEGER I1, IADD, IINFO, IN, J, JC, JR, JSIZE, JTYPE, $ LWKOPT, MTYPES, N, N1, NB, NBZ, NERRS, NMATS, $ NMAX, NS, NTEST, NTESTT DOUBLE PRECISION SAFMAX, SAFMIN, TEMP1, TEMP2, ULP, ULPINV * .. * .. Local Arrays .. INTEGER IASIGN( MAXTYP ), IBSIGN( MAXTYP ), $ IOLDSD( 4 ), KADD( 6 ), KAMAGN( MAXTYP ), $ KATYPE( MAXTYP ), KAZERO( MAXTYP ), $ KBMAGN( MAXTYP ), KBTYPE( MAXTYP ), $ KBZERO( MAXTYP ), KCLASS( MAXTYP ), $ KTRIAN( MAXTYP ), KZ1( 6 ), KZ2( 6 ) DOUBLE PRECISION DUMMA( 4 ), RMAGN( 0: 3 ) * .. * .. External Functions .. INTEGER ILAENV DOUBLE PRECISION DLAMCH, DLARND EXTERNAL ILAENV, DLAMCH, DLARND * .. * .. External Subroutines .. EXTERNAL ALASVM, DGEGS, DGEGV, DGET51, DGET52, DGET53, $ DLABAD, DLACPY, DLARFG, DLASET, DLATM4, DORM2R, $ XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, MAX, MIN, SIGN * .. * .. Data statements .. DATA KCLASS / 15*1, 10*2, 1*3 / DATA KZ1 / 0, 1, 2, 1, 3, 3 / DATA KZ2 / 0, 0, 1, 2, 1, 1 / DATA KADD / 0, 0, 0, 0, 3, 2 / DATA KATYPE / 0, 1, 0, 1, 2, 3, 4, 1, 4, 4, 1, 1, 4, $ 4, 4, 2, 4, 5, 8, 7, 9, 4*4, 0 / DATA KBTYPE / 0, 0, 1, 1, 2, -3, 1, 4, 1, 1, 4, 4, $ 1, 1, -4, 2, -4, 8*8, 0 / DATA KAZERO / 6*1, 2, 1, 2*2, 2*1, 2*2, 3, 1, 3, $ 4*5, 4*3, 1 / DATA KBZERO / 6*1, 1, 2, 2*1, 2*2, 2*1, 4, 1, 4, $ 4*6, 4*4, 1 / DATA KAMAGN / 8*1, 2, 3, 2, 3, 2, 3, 7*1, 2, 3, 3, $ 2, 1 / DATA KBMAGN / 8*1, 3, 2, 3, 2, 2, 3, 7*1, 3, 2, 3, $ 2, 1 / DATA KTRIAN / 16*0, 10*1 / DATA IASIGN / 6*0, 2, 0, 2*2, 2*0, 3*2, 0, 2, 3*0, $ 5*2, 0 / DATA IBSIGN / 7*0, 2, 2*0, 2*2, 2*0, 2, 0, 2, 9*0 / * .. * .. Executable Statements .. * * Check for errors * INFO = 0 * BADNN = .FALSE. NMAX = 1 DO 10 J = 1, NSIZES NMAX = MAX( NMAX, NN( J ) ) IF( NN( J ).LT.0 ) $ BADNN = .TRUE. 10 CONTINUE * * Maximum blocksize and shift -- we assume that blocksize and number * of shifts are monotone increasing functions of N. * NB = MAX( 1, ILAENV( 1, 'DGEQRF', ' ', NMAX, NMAX, -1, -1 ), $ ILAENV( 1, 'DORMQR', 'LT', NMAX, NMAX, NMAX, -1 ), $ ILAENV( 1, 'DORGQR', ' ', NMAX, NMAX, NMAX, -1 ) ) NBZ = ILAENV( 1, 'DHGEQZ', 'SII', NMAX, 1, NMAX, 0 ) NS = ILAENV( 4, 'DHGEQZ', 'SII', NMAX, 1, NMAX, 0 ) I1 = NBZ + NS LWKOPT = 2*NMAX + MAX( 6*NMAX, NMAX*( NB+1 ), $ ( 2*I1+NMAX+1 )*( I1+1 ) ) * * 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( THRESH.LT.ZERO ) THEN INFO = -6 ELSE IF( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN INFO = -10 ELSE IF( LDQ.LE.1 .OR. LDQ.LT.NMAX ) THEN INFO = -19 ELSE IF( LWKOPT.GT.LWORK ) THEN INFO = -30 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DDRVGG', -INFO ) RETURN END IF * * Quick return if possible * IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 ) $ RETURN * SAFMIN = DLAMCH( 'Safe minimum' ) ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' ) SAFMIN = SAFMIN / ULP SAFMAX = ONE / SAFMIN CALL DLABAD( SAFMIN, SAFMAX ) ULPINV = ONE / ULP * * The values RMAGN(2:3) depend on N, see below. * RMAGN( 0 ) = ZERO RMAGN( 1 ) = ONE * * Loop over sizes, types * NTESTT = 0 NERRS = 0 NMATS = 0 * DO 170 JSIZE = 1, NSIZES N = NN( JSIZE ) N1 = MAX( 1, N ) RMAGN( 2 ) = SAFMAX*ULP / DBLE( N1 ) RMAGN( 3 ) = SAFMIN*ULPINV*N1 * IF( NSIZES.NE.1 ) THEN MTYPES = MIN( MAXTYP, NTYPES ) ELSE MTYPES = MIN( MAXTYP+1, NTYPES ) END IF * DO 160 JTYPE = 1, MTYPES IF( .NOT.DOTYPE( JTYPE ) ) $ GO TO 160 NMATS = NMATS + 1 NTEST = 0 * * Save ISEED in case of an error. * DO 20 J = 1, 4 IOLDSD( J ) = ISEED( J ) 20 CONTINUE * * Initialize RESULT * DO 30 J = 1, 15 RESULT( J ) = ZERO 30 CONTINUE * * Compute A and B * * Description of control parameters: * * KZLASS: =1 means w/o rotation, =2 means w/ rotation, * =3 means random. * KATYPE: the "type" to be passed to DLATM4 for computing A. * KAZERO: the pattern of zeros on the diagonal for A: * =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ), * =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ), * =6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of * non-zero entries.) * KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1), * =2: large, =3: small. * IASIGN: 1 if the diagonal elements of A are to be * multiplied by a random magnitude 1 number, =2 if * randomly chosen diagonal blocks are to be rotated * to form 2x2 blocks. * KBTYPE, KBZERO, KBMAGN, IBSIGN: the same, but for B. * KTRIAN: =0: don't fill in the upper triangle, =1: do. * KZ1, KZ2, KADD: used to implement KAZERO and KBZERO. * RMAGN: used to implement KAMAGN and KBMAGN. * IF( MTYPES.GT.MAXTYP ) $ GO TO 110 IINFO = 0 IF( KCLASS( JTYPE ).LT.3 ) THEN * * Generate A (w/o rotation) * IF( ABS( KATYPE( JTYPE ) ).EQ.3 ) THEN IN = 2*( ( N-1 ) / 2 ) + 1 IF( IN.NE.N ) $ CALL DLASET( 'Full', N, N, ZERO, ZERO, A, LDA ) ELSE IN = N END IF CALL DLATM4( KATYPE( JTYPE ), IN, KZ1( KAZERO( JTYPE ) ), $ KZ2( KAZERO( JTYPE ) ), IASIGN( JTYPE ), $ RMAGN( KAMAGN( JTYPE ) ), ULP, $ RMAGN( KTRIAN( JTYPE )*KAMAGN( JTYPE ) ), 2, $ ISEED, A, LDA ) IADD = KADD( KAZERO( JTYPE ) ) IF( IADD.GT.0 .AND. IADD.LE.N ) $ A( IADD, IADD ) = ONE * * Generate B (w/o rotation) * IF( ABS( KBTYPE( JTYPE ) ).EQ.3 ) THEN IN = 2*( ( N-1 ) / 2 ) + 1 IF( IN.NE.N ) $ CALL DLASET( 'Full', N, N, ZERO, ZERO, B, LDA ) ELSE IN = N END IF CALL DLATM4( KBTYPE( JTYPE ), IN, KZ1( KBZERO( JTYPE ) ), $ KZ2( KBZERO( JTYPE ) ), IBSIGN( JTYPE ), $ RMAGN( KBMAGN( JTYPE ) ), ONE, $ RMAGN( KTRIAN( JTYPE )*KBMAGN( JTYPE ) ), 2, $ ISEED, B, LDA ) IADD = KADD( KBZERO( JTYPE ) ) IF( IADD.NE.0 .AND. IADD.LE.N ) $ B( IADD, IADD ) = ONE * IF( KCLASS( JTYPE ).EQ.2 .AND. N.GT.0 ) THEN * * Include rotations * * Generate Q, Z as Householder transformations times * a diagonal matrix. * DO 50 JC = 1, N - 1 DO 40 JR = JC, N Q( JR, JC ) = DLARND( 3, ISEED ) Z( JR, JC ) = DLARND( 3, ISEED ) 40 CONTINUE CALL DLARFG( N+1-JC, Q( JC, JC ), Q( JC+1, JC ), 1, $ WORK( JC ) ) WORK( 2*N+JC ) = SIGN( ONE, Q( JC, JC ) ) Q( JC, JC ) = ONE CALL DLARFG( N+1-JC, Z( JC, JC ), Z( JC+1, JC ), 1, $ WORK( N+JC ) ) WORK( 3*N+JC ) = SIGN( ONE, Z( JC, JC ) ) Z( JC, JC ) = ONE 50 CONTINUE Q( N, N ) = ONE WORK( N ) = ZERO WORK( 3*N ) = SIGN( ONE, DLARND( 2, ISEED ) ) Z( N, N ) = ONE WORK( 2*N ) = ZERO WORK( 4*N ) = SIGN( ONE, DLARND( 2, ISEED ) ) * * Apply the diagonal matrices * DO 70 JC = 1, N DO 60 JR = 1, N A( JR, JC ) = WORK( 2*N+JR )*WORK( 3*N+JC )* $ A( JR, JC ) B( JR, JC ) = WORK( 2*N+JR )*WORK( 3*N+JC )* $ B( JR, JC ) 60 CONTINUE 70 CONTINUE CALL DORM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, A, $ LDA, WORK( 2*N+1 ), IINFO ) IF( IINFO.NE.0 ) $ GO TO 100 CALL DORM2R( 'R', 'T', N, N, N-1, Z, LDQ, WORK( N+1 ), $ A, LDA, WORK( 2*N+1 ), IINFO ) IF( IINFO.NE.0 ) $ GO TO 100 CALL DORM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, B, $ LDA, WORK( 2*N+1 ), IINFO ) IF( IINFO.NE.0 ) $ GO TO 100 CALL DORM2R( 'R', 'T', N, N, N-1, Z, LDQ, WORK( N+1 ), $ B, LDA, WORK( 2*N+1 ), IINFO ) IF( IINFO.NE.0 ) $ GO TO 100 END IF ELSE * * Random matrices * DO 90 JC = 1, N DO 80 JR = 1, N A( JR, JC ) = RMAGN( KAMAGN( JTYPE ) )* $ DLARND( 2, ISEED ) B( JR, JC ) = RMAGN( KBMAGN( JTYPE ) )* $ DLARND( 2, ISEED ) 80 CONTINUE 90 CONTINUE END IF * 100 CONTINUE * IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) RETURN END IF * 110 CONTINUE * * Call DGEGS to compute H, T, Q, Z, alpha, and beta. * CALL DLACPY( ' ', N, N, A, LDA, S, LDA ) CALL DLACPY( ' ', N, N, B, LDA, T, LDA ) NTEST = 1 RESULT( 1 ) = ULPINV * CALL DGEGS( 'V', 'V', N, S, LDA, T, LDA, ALPHR1, ALPHI1, $ BETA1, Q, LDQ, Z, LDQ, WORK, LWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'DGEGS', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) GO TO 140 END IF * NTEST = 4 * * Do tests 1--4 * CALL DGET51( 1, N, A, LDA, S, LDA, Q, LDQ, Z, LDQ, WORK, $ RESULT( 1 ) ) CALL DGET51( 1, N, B, LDA, T, LDA, Q, LDQ, Z, LDQ, WORK, $ RESULT( 2 ) ) CALL DGET51( 3, N, B, LDA, T, LDA, Q, LDQ, Q, LDQ, WORK, $ RESULT( 3 ) ) CALL DGET51( 3, N, B, LDA, T, LDA, Z, LDQ, Z, LDQ, WORK, $ RESULT( 4 ) ) * * Do test 5: compare eigenvalues with diagonals. * Also check Schur form of A. * TEMP1 = ZERO * DO 120 J = 1, N ILABAD = .FALSE. IF( ALPHI1( J ).EQ.ZERO ) THEN TEMP2 = ( ABS( ALPHR1( J )-S( J, J ) ) / $ MAX( SAFMIN, ABS( ALPHR1( J ) ), ABS( S( J, $ J ) ) )+ABS( BETA1( J )-T( J, J ) ) / $ MAX( SAFMIN, ABS( BETA1( J ) ), ABS( T( J, $ J ) ) ) ) / ULP IF( J.LT.N ) THEN IF( S( J+1, J ).NE.ZERO ) $ ILABAD = .TRUE. END IF IF( J.GT.1 ) THEN IF( S( J, J-1 ).NE.ZERO ) $ ILABAD = .TRUE. END IF ELSE IF( ALPHI1( J ).GT.ZERO ) THEN I1 = J ELSE I1 = J - 1 END IF IF( I1.LE.0 .OR. I1.GE.N ) THEN ILABAD = .TRUE. ELSE IF( I1.LT.N-1 ) THEN IF( S( I1+2, I1+1 ).NE.ZERO ) $ ILABAD = .TRUE. ELSE IF( I1.GT.1 ) THEN IF( S( I1, I1-1 ).NE.ZERO ) $ ILABAD = .TRUE. END IF IF( .NOT.ILABAD ) THEN CALL DGET53( S( I1, I1 ), LDA, T( I1, I1 ), LDA, $ BETA1( J ), ALPHR1( J ), ALPHI1( J ), $ TEMP2, IINFO ) IF( IINFO.GE.3 ) THEN WRITE( NOUNIT, FMT = 9997 )IINFO, J, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) END IF ELSE TEMP2 = ULPINV END IF END IF TEMP1 = MAX( TEMP1, TEMP2 ) IF( ILABAD ) THEN WRITE( NOUNIT, FMT = 9996 )J, N, JTYPE, IOLDSD END IF 120 CONTINUE RESULT( 5 ) = TEMP1 * * Call DGEGV to compute S2, T2, VL, and VR, do tests. * * Eigenvalues and Eigenvectors * CALL DLACPY( ' ', N, N, A, LDA, S2, LDA ) CALL DLACPY( ' ', N, N, B, LDA, T2, LDA ) NTEST = 6 RESULT( 6 ) = ULPINV * CALL DGEGV( 'V', 'V', N, S2, LDA, T2, LDA, ALPHR2, ALPHI2, $ BETA2, VL, LDQ, VR, LDQ, WORK, LWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'DGEGV', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) GO TO 140 END IF * NTEST = 7 * * Do Tests 6 and 7 * CALL DGET52( .TRUE., N, A, LDA, B, LDA, VL, LDQ, ALPHR2, $ ALPHI2, BETA2, WORK, DUMMA( 1 ) ) RESULT( 6 ) = DUMMA( 1 ) IF( DUMMA( 2 ).GT.THRSHN ) THEN WRITE( NOUNIT, FMT = 9998 )'Left', 'DGEGV', DUMMA( 2 ), $ N, JTYPE, IOLDSD END IF * CALL DGET52( .FALSE., N, A, LDA, B, LDA, VR, LDQ, ALPHR2, $ ALPHI2, BETA2, WORK, DUMMA( 1 ) ) RESULT( 7 ) = DUMMA( 1 ) IF( DUMMA( 2 ).GT.THRESH ) THEN WRITE( NOUNIT, FMT = 9998 )'Right', 'DGEGV', DUMMA( 2 ), $ N, JTYPE, IOLDSD END IF * * Check form of Complex eigenvalues. * DO 130 J = 1, N ILABAD = .FALSE. IF( ALPHI2( J ).GT.ZERO ) THEN IF( J.EQ.N ) THEN ILABAD = .TRUE. ELSE IF( ALPHI2( J+1 ).GE.ZERO ) THEN ILABAD = .TRUE. END IF ELSE IF( ALPHI2( J ).LT.ZERO ) THEN IF( J.EQ.1 ) THEN ILABAD = .TRUE. ELSE IF( ALPHI2( J-1 ).LE.ZERO ) THEN ILABAD = .TRUE. END IF END IF IF( ILABAD ) THEN WRITE( NOUNIT, FMT = 9996 )J, N, JTYPE, IOLDSD END IF 130 CONTINUE * * End of Loop -- Check for RESULT(j) > THRESH * 140 CONTINUE * NTESTT = NTESTT + NTEST * * Print out tests which fail. * DO 150 JR = 1, NTEST IF( RESULT( JR ).GE.THRESH ) THEN * * If this is the first test to fail, * print a header to the data file. * IF( NERRS.EQ.0 ) THEN WRITE( NOUNIT, FMT = 9995 )'DGG' * * Matrix types * WRITE( NOUNIT, FMT = 9994 ) WRITE( NOUNIT, FMT = 9993 ) WRITE( NOUNIT, FMT = 9992 )'Orthogonal' * * Tests performed * WRITE( NOUNIT, FMT = 9991 )'orthogonal', '''', $ 'transpose', ( '''', J = 1, 5 ) * END IF NERRS = NERRS + 1 IF( RESULT( JR ).LT.10000.0D0 ) THEN WRITE( NOUNIT, FMT = 9990 )N, JTYPE, IOLDSD, JR, $ RESULT( JR ) ELSE WRITE( NOUNIT, FMT = 9989 )N, JTYPE, IOLDSD, JR, $ RESULT( JR ) END IF END IF 150 CONTINUE * 160 CONTINUE 170 CONTINUE * * Summary * CALL ALASVM( 'DGG', NOUNIT, NERRS, NTESTT, 0 ) RETURN * 9999 FORMAT( ' DDRVGG: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', $ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' ) * 9998 FORMAT( ' DDRVGG: ', A, ' Eigenvectors from ', A, ' incorrectly ', $ 'normalized.', / ' Bits of error=', 0P, G10.3, ',', 9X, $ 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, $ ')' ) * 9997 FORMAT( ' DDRVGG: DGET53 returned INFO=', I1, ' for eigenvalue ', $ I6, '.', / 9X, 'N=', I6, ', JTYPE=', I6, ', ISEED=(', $ 3( I5, ',' ), I5, ')' ) * 9996 FORMAT( ' DDRVGG: S not in Schur form at eigenvalue ', I6, '.', $ / 9X, 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), $ I5, ')' ) * 9995 FORMAT( / 1X, A3, ' -- Real Generalized eigenvalue problem driver' $ ) * 9994 FORMAT( ' Matrix types (see DDRVGG for details): ' ) * 9993 FORMAT( ' Special Matrices:', 23X, $ '(J''=transposed Jordan block)', $ / ' 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I) 5=(J'',J'') ', $ '6=(diag(J'',I), diag(I,J''))', / ' Diagonal Matrices: ( ', $ 'D=diag(0,1,2,...) )', / ' 7=(D,I) 9=(large*D, small*I', $ ') 11=(large*I, small*D) 13=(large*D, large*I)', / $ ' 8=(I,D) 10=(small*D, large*I) 12=(small*I, large*D) ', $ ' 14=(small*D, small*I)', / ' 15=(D, reversed D)' ) 9992 FORMAT( ' Matrices Rotated by Random ', A, ' Matrices U, V:', $ / ' 16=Transposed Jordan Blocks 19=geometric ', $ 'alpha, beta=0,1', / ' 17=arithm. alpha&beta ', $ ' 20=arithmetic alpha, beta=0,1', / ' 18=clustered ', $ 'alpha, beta=0,1 21=random alpha, beta=0,1', $ / ' Large & Small Matrices:', / ' 22=(large, small) ', $ '23=(small,large) 24=(small,small) 25=(large,large)', $ / ' 26=random O(1) matrices.' ) * 9991 FORMAT( / ' Tests performed: (S is Schur, T is triangular, ', $ 'Q and Z are ', A, ',', / 20X, $ 'l and r are the appropriate left and right', / 19X, $ 'eigenvectors, resp., a is alpha, b is beta, and', / 19X, A, $ ' means ', A, '.)', / ' 1 = | A - Q S Z', A, $ ' | / ( |A| n ulp ) 2 = | B - Q T Z', A, $ ' | / ( |B| n ulp )', / ' 3 = | I - QQ', A, $ ' | / ( n ulp ) 4 = | I - ZZ', A, $ ' | / ( n ulp )', / $ ' 5 = difference between (alpha,beta) and diagonals of', $ ' (S,T)', / ' 6 = max | ( b A - a B )', A, $ ' l | / const. 7 = max | ( b A - a B ) r | / const.', $ / 1X ) 9990 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=', $ 4( I4, ',' ), ' result ', I3, ' is', 0P, F8.2 ) 9989 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=', $ 4( I4, ',' ), ' result ', I3, ' is', 1P, D10.3 ) * * End of DDRVGG * END |