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SUBROUTINE DDRGES( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
$ NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, ALPHAR, $ ALPHAI, BETA, WORK, LWORK, RESULT, BWORK, $ 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 * .. * .. Array Arguments .. LOGICAL BWORK( * ), DOTYPE( * ) INTEGER ISEED( 4 ), NN( * ) DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ), $ B( LDA, * ), BETA( * ), Q( LDQ, * ), $ RESULT( 13 ), S( LDA, * ), T( LDA, * ), $ WORK( * ), Z( LDQ, * ) * .. * * Purpose * ======= * * DDRGES checks the nonsymmetric generalized eigenvalue (Schur form) * problem driver DGGES. * * DGGES 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(j),beta(j)), j=1,...,n, * Thus, w(j) = alpha(j)/beta(j) is a root of the characteristic * equation * det( A - w(j) B ) = 0 * Optionally it also reorder the eigenvalues so that a selected * cluster of eigenvalues appears in the leading diagonal block of the * Schur forms. * * When DDRGES 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, a pair of matrices (A, B) will be generated * and used for testing. For each matrix pair, the following 13 tests * will be performed and compared with the threshhold THRESH except * the tests (5), (11) and (13). * * * (1) | A - Q S Z' | / ( |A| n ulp ) (no sorting of eigenvalues) * * * (2) | B - Q T Z' | / ( |B| n ulp ) (no sorting of eigenvalues) * * * (3) | I - QQ' | / ( n ulp ) (no sorting of eigenvalues) * * * (4) | I - ZZ' | / ( n ulp ) (no sorting of eigenvalues) * * (5) if A is in Schur form (i.e. quasi-triangular form) * (no sorting of eigenvalues) * * (6) if eigenvalues = diagonal blocks of the Schur form (S, T), * i.e., test the 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 and j+1-th eigenvalues. * (no sorting of eigenvalues) * * (7) | (A,B) - Q (S,T) Z' | / ( | (A,B) | n ulp ) * (with sorting of eigenvalues). * * (8) | I - QQ' | / ( n ulp ) (with sorting of eigenvalues). * * (9) | I - ZZ' | / ( n ulp ) (with sorting of eigenvalues). * * (10) if A is in Schur form (i.e. quasi-triangular form) * (with sorting of eigenvalues). * * (11) if eigenvalues = diagonal blocks of the Schur form (S, T), * i.e. test the 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 and j+1-th eigenvalues. * (with sorting of eigenvalues). * * (12) if sorting worked and SDIM is the number of eigenvalues * which were SELECTed. * * 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, * DDRGES does nothing. NSIZES >= 0. * * NN (input) INTEGER array, dimension (NSIZES) * An array containing the sizes to be used for the matrices. * Zero values will be skipped. NN >= 0. * * NTYPES (input) INTEGER * The number of elements in DOTYPE. If it is zero, DDRGES * 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 on input. * 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 DDRGES 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. THRESH >= 0. * * 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, and T. * 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 DGGES. 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 DGGES. * * Q (workspace) DOUBLE PRECISION array, dimension (LDQ, max(NN)) * The (left) orthogonal matrix computed by DGGES. * * LDQ (input) INTEGER * The leading dimension of Q and Z. It must * be at least 1 and at least max( NN ). * * Z (workspace) DOUBLE PRECISION array, dimension( LDQ, max(NN) ) * The (right) orthogonal matrix computed by DGGES. * * ALPHAR (workspace) DOUBLE PRECISION array, dimension (max(NN)) * ALPHAI (workspace) DOUBLE PRECISION array, dimension (max(NN)) * BETA (workspace) DOUBLE PRECISION array, dimension (max(NN)) * The generalized eigenvalues of (A,B) computed by DGGES. * ( ALPHAR(k)+ALPHAI(k)*i ) / BETA(k) is the k-th * generalized eigenvalue of A and B. * * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) * * LWORK (input) INTEGER * The dimension of the array WORK. * LWORK >= MAX( 10*(N+1), 3*N*N ), where N is the largest * matrix dimension. * * 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. * * BWORK (workspace) LOGICAL array, dimension (N) * * 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 = 0.0D+0, ONE = 1.0D+0 ) INTEGER MAXTYP PARAMETER ( MAXTYP = 26 ) * .. * .. Local Scalars .. LOGICAL BADNN, ILABAD CHARACTER SORT INTEGER I, I1, IADD, IERR, IINFO, IN, ISORT, J, JC, JR, $ JSIZE, JTYPE, KNTEIG, MAXWRK, MINWRK, MTYPES, $ N, N1, NB, NERRS, NMATS, NMAX, NTEST, NTESTT, $ RSUB, SDIM 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 RMAGN( 0: 3 ) * .. * .. External Functions .. LOGICAL DLCTES INTEGER ILAENV DOUBLE PRECISION DLAMCH, DLARND EXTERNAL DLCTES, ILAENV, DLAMCH, DLARND * .. * .. External Subroutines .. EXTERNAL ALASVM, DGET51, DGET53, DGET54, DGGES, 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 * 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 = -9 ELSE IF( LDQ.LE.1 .OR. LDQ.LT.NMAX ) THEN INFO = -14 END IF * * Compute workspace * (Note: Comments in the code beginning "Workspace:" describe the * minimal amount of workspace needed at that point in the code, * as well as the preferred amount for good performance. * NB refers to the optimal block size for the immediately * following subroutine, as returned by ILAENV. * MINWRK = 1 IF( INFO.EQ.0 .AND. LWORK.GE.1 ) THEN MINWRK = MAX( 10*( NMAX+1 ), 3*NMAX*NMAX ) 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 ) ) MAXWRK = MAX( 10*( NMAX+1 ), 2*NMAX+NMAX*NB, 3*NMAX*NMAX ) WORK( 1 ) = MAXWRK END IF * IF( LWORK.LT.MINWRK ) $ INFO = -20 * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DDRGES', -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 matrix sizes * NTESTT = 0 NERRS = 0 NMATS = 0 * DO 190 JSIZE = 1, NSIZES N = NN( JSIZE ) N1 = MAX( 1, N ) RMAGN( 2 ) = SAFMAX*ULP / DBLE( N1 ) RMAGN( 3 ) = SAFMIN*ULPINV*DBLE( N1 ) * IF( NSIZES.NE.1 ) THEN MTYPES = MIN( MAXTYP, NTYPES ) ELSE MTYPES = MIN( MAXTYP+1, NTYPES ) END IF * * Loop over matrix types * DO 180 JTYPE = 1, MTYPES IF( .NOT.DOTYPE( JTYPE ) ) $ GO TO 180 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, 13 RESULT( J ) = ZERO 30 CONTINUE * * Generate test matrices 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 * DO 120 I = 1, 13 RESULT( I ) = -ONE 120 CONTINUE * * Test with and without sorting of eigenvalues * DO 150 ISORT = 0, 1 IF( ISORT.EQ.0 ) THEN SORT = 'N' RSUB = 0 ELSE SORT = 'S' RSUB = 5 END IF * * Call DGGES to compute H, T, Q, Z, alpha, and beta. * CALL DLACPY( 'Full', N, N, A, LDA, S, LDA ) CALL DLACPY( 'Full', N, N, B, LDA, T, LDA ) NTEST = 1 + RSUB + ISORT RESULT( 1+RSUB+ISORT ) = ULPINV CALL DGGES( 'V', 'V', SORT, DLCTES, N, S, LDA, T, LDA, $ SDIM, ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDQ, $ WORK, LWORK, BWORK, IINFO ) IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN RESULT( 1+RSUB+ISORT ) = ULPINV WRITE( NOUNIT, FMT = 9999 )'DGGES', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) GO TO 160 END IF * NTEST = 4 + RSUB * * Do tests 1--4 (or tests 7--9 when reordering ) * IF( ISORT.EQ.0 ) THEN 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 ) ) ELSE CALL DGET54( N, A, LDA, B, LDA, S, LDA, T, LDA, Q, $ LDQ, Z, LDQ, WORK, RESULT( 7 ) ) END IF CALL DGET51( 3, N, A, LDA, T, LDA, Q, LDQ, Q, LDQ, WORK, $ RESULT( 3+RSUB ) ) CALL DGET51( 3, N, B, LDA, T, LDA, Z, LDQ, Z, LDQ, WORK, $ RESULT( 4+RSUB ) ) * * Do test 5 and 6 (or Tests 10 and 11 when reordering): * check Schur form of A and compare eigenvalues with * diagonals. * NTEST = 6 + RSUB TEMP1 = ZERO * DO 130 J = 1, N ILABAD = .FALSE. IF( ALPHAI( J ).EQ.ZERO ) THEN TEMP2 = ( ABS( ALPHAR( J )-S( J, J ) ) / $ MAX( SAFMIN, ABS( ALPHAR( J ) ), ABS( S( J, $ J ) ) )+ABS( BETA( J )-T( J, J ) ) / $ MAX( SAFMIN, ABS( BETA( J ) ), ABS( T( J, $ J ) ) ) ) / ULP * IF( J.LT.N ) THEN IF( S( J+1, J ).NE.ZERO ) THEN ILABAD = .TRUE. RESULT( 5+RSUB ) = ULPINV END IF END IF IF( J.GT.1 ) THEN IF( S( J, J-1 ).NE.ZERO ) THEN ILABAD = .TRUE. RESULT( 5+RSUB ) = ULPINV END IF END IF * ELSE IF( ALPHAI( 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 ) THEN ILABAD = .TRUE. RESULT( 5+RSUB ) = ULPINV END IF ELSE IF( I1.GT.1 ) THEN IF( S( I1, I1-1 ).NE.ZERO ) THEN ILABAD = .TRUE. RESULT( 5+RSUB ) = ULPINV END IF END IF IF( .NOT.ILABAD ) THEN CALL DGET53( S( I1, I1 ), LDA, T( I1, I1 ), LDA, $ BETA( J ), ALPHAR( J ), $ ALPHAI( J ), TEMP2, IERR ) IF( IERR.GE.3 ) THEN WRITE( NOUNIT, FMT = 9998 )IERR, J, N, $ JTYPE, IOLDSD INFO = ABS( IERR ) END IF ELSE TEMP2 = ULPINV END IF * END IF TEMP1 = MAX( TEMP1, TEMP2 ) IF( ILABAD ) THEN WRITE( NOUNIT, FMT = 9997 )J, N, JTYPE, IOLDSD END IF 130 CONTINUE RESULT( 6+RSUB ) = TEMP1 * IF( ISORT.GE.1 ) THEN * * Do test 12 * NTEST = 12 RESULT( 12 ) = ZERO KNTEIG = 0 DO 140 I = 1, N IF( DLCTES( ALPHAR( I ), ALPHAI( I ), $ BETA( I ) ) .OR. DLCTES( ALPHAR( I ), $ -ALPHAI( I ), BETA( I ) ) ) THEN KNTEIG = KNTEIG + 1 END IF IF( I.LT.N ) THEN IF( ( DLCTES( ALPHAR( I+1 ), ALPHAI( I+1 ), $ BETA( I+1 ) ) .OR. DLCTES( ALPHAR( I+1 ), $ -ALPHAI( I+1 ), BETA( I+1 ) ) ) .AND. $ ( .NOT.( DLCTES( ALPHAR( I ), ALPHAI( I ), $ BETA( I ) ) .OR. DLCTES( ALPHAR( I ), $ -ALPHAI( I ), BETA( I ) ) ) ) .AND. $ IINFO.NE.N+2 ) THEN RESULT( 12 ) = ULPINV END IF END IF 140 CONTINUE IF( SDIM.NE.KNTEIG ) THEN RESULT( 12 ) = ULPINV END IF END IF * 150 CONTINUE * * End of Loop -- Check for RESULT(j) > THRESH * 160 CONTINUE * NTESTT = NTESTT + NTEST * * Print out tests which fail. * DO 170 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 = 9996 )'DGS' * * Matrix types * WRITE( NOUNIT, FMT = 9995 ) WRITE( NOUNIT, FMT = 9994 ) WRITE( NOUNIT, FMT = 9993 )'Orthogonal' * * Tests performed * WRITE( NOUNIT, FMT = 9992 )'orthogonal', '''', $ 'transpose', ( '''', J = 1, 8 ) * END IF NERRS = NERRS + 1 IF( RESULT( JR ).LT.10000.0D0 ) THEN WRITE( NOUNIT, FMT = 9991 )N, JTYPE, IOLDSD, JR, $ RESULT( JR ) ELSE WRITE( NOUNIT, FMT = 9990 )N, JTYPE, IOLDSD, JR, $ RESULT( JR ) END IF END IF 170 CONTINUE * 180 CONTINUE 190 CONTINUE * * Summary * CALL ALASVM( 'DGS', NOUNIT, NERRS, NTESTT, 0 ) * WORK( 1 ) = MAXWRK * RETURN * 9999 FORMAT( ' DDRGES: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', $ I6, ', JTYPE=', I6, ', ISEED=(', 4( I4, ',' ), I5, ')' ) * 9998 FORMAT( ' DDRGES: DGET53 returned INFO=', I1, ' for eigenvalue ', $ I6, '.', / 9X, 'N=', I6, ', JTYPE=', I6, ', ISEED=(', $ 4( I4, ',' ), I5, ')' ) * 9997 FORMAT( ' DDRGES: S not in Schur form at eigenvalue ', I6, '.', $ / 9X, 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), $ I5, ')' ) * 9996 FORMAT( / 1X, A3, ' -- Real Generalized Schur form driver' ) * 9995 FORMAT( ' Matrix types (see DDRGES for details): ' ) * 9994 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)' ) 9993 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.' ) * 9992 FORMAT( / ' Tests performed: (S is Schur, T is triangular, ', $ 'Q and Z are ', A, ',', / 19X, $ 'l and r are the appropriate left and right', / 19X, $ 'eigenvectors, resp., a is alpha, b is beta, and', / 19X, A, $ ' means ', A, '.)', / ' Without ordering: ', $ / ' 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 = A is in Schur form S', $ / ' 6 = difference between (alpha,beta)', $ ' and diagonals of (S,T)', / ' With ordering: ', $ / ' 7 = | (A,B) - Q (S,T) Z', A, $ ' | / ( |(A,B)| n ulp ) ', / ' 8 = | I - QQ', A, $ ' | / ( n ulp ) 9 = | I - ZZ', A, $ ' | / ( n ulp )', / ' 10 = A is in Schur form S', $ / ' 11 = difference between (alpha,beta) and diagonals', $ ' of (S,T)', / ' 12 = SDIM is the correct number of ', $ 'selected eigenvalues', / ) 9991 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=', $ 4( I4, ',' ), ' result ', I2, ' is', 0P, F8.2 ) 9990 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=', $ 4( I4, ',' ), ' result ', I2, ' is', 1P, D10.3 ) * * End of DDRGES * END |