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SUBROUTINE DDRGSX( NSIZE, NCMAX, THRESH, NIN, NOUT, A, LDA, B, AI,
$ BI, Z, Q, ALPHAR, ALPHAI, BETA, C, LDC, S, $ WORK, LWORK, IWORK, LIWORK, BWORK, INFO ) * * -- LAPACK test routine (version 3.3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * -- April 2011 -- * * .. Scalar Arguments .. INTEGER INFO, LDA, LDC, LIWORK, LWORK, NCMAX, NIN, $ NOUT, NSIZE DOUBLE PRECISION THRESH * .. * .. Array Arguments .. LOGICAL BWORK( * ) INTEGER IWORK( * ) DOUBLE PRECISION A( LDA, * ), AI( LDA, * ), ALPHAI( * ), $ ALPHAR( * ), B( LDA, * ), BETA( * ), $ BI( LDA, * ), C( LDC, * ), Q( LDA, * ), S( * ), $ WORK( * ), Z( LDA, * ) * .. * * Purpose * ======= * * DDRGSX checks the nonsymmetric generalized eigenvalue (Schur form) * problem expert driver DGGESX. * * DGGESX 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)). Thus, w(j) = alpha(j)/beta(j) is a root of the * characteristic equation * * det( A - w(j) B ) = 0 * * Optionally it also reorders the eigenvalues so that a selected * cluster of eigenvalues appears in the leading diagonal block of the * Schur forms; computes a reciprocal condition number for the average * of the selected eigenvalues; and computes a reciprocal condition * number for the right and left deflating subspaces corresponding to * the selected eigenvalues. * * When DDRGSX is called with NSIZE > 0, five (5) types of built-in * matrix pairs are used to test the routine DGGESX. * * When DDRGSX is called with NSIZE = 0, it reads in test matrix data * to test DGGESX. * * For each matrix pair, the following tests will be performed and * compared with the threshhold THRESH except for the tests (7) and (9): * * (1) | A - Q S Z' | / ( |A| n ulp ) * * (2) | B - Q T Z' | / ( |B| n ulp ) * * (3) | I - QQ' | / ( n ulp ) * * (4) | I - ZZ' | / ( n ulp ) * * (5) if A is in Schur form (i.e. quasi-triangular form) * * (6) 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. * * (7) if sorting worked and SDIM is the number of eigenvalues * which were selected. * * (8) the estimated value DIF does not differ from the true values of * Difu and Difl more than a factor 10*THRESH. If the estimate DIF * equals zero the corresponding true values of Difu and Difl * should be less than EPS*norm(A, B). If the true value of Difu * and Difl equal zero, the estimate DIF should be less than * EPS*norm(A, B). * * (9) If INFO = N+3 is returned by DGGESX, the reordering "failed" * and we check that DIF = PL = PR = 0 and that the true value of * Difu and Difl is < EPS*norm(A, B). We count the events when * INFO=N+3. * * For read-in test matrices, the above tests are run except that the * exact value for DIF (and PL) is input data. Additionally, there is * one more test run for read-in test matrices: * * (10) the estimated value PL does not differ from the true value of * PLTRU more than a factor THRESH. If the estimate PL equals * zero the corresponding true value of PLTRU should be less than * EPS*norm(A, B). If the true value of PLTRU equal zero, the * estimate PL should be less than EPS*norm(A, B). * * Note that for the built-in tests, a total of 10*NSIZE*(NSIZE-1) * matrix pairs are generated and tested. NSIZE should be kept small. * * SVD (routine DGESVD) is used for computing the true value of DIF_u * and DIF_l when testing the built-in test problems. * * Built-in Test Matrices * ====================== * * All built-in test matrices are the 2 by 2 block of triangular * matrices * * A = [ A11 A12 ] and B = [ B11 B12 ] * [ A22 ] [ B22 ] * * where for different type of A11 and A22 are given as the following. * A12 and B12 are chosen so that the generalized Sylvester equation * * A11*R - L*A22 = -A12 * B11*R - L*B22 = -B12 * * have prescribed solution R and L. * * Type 1: A11 = J_m(1,-1) and A_22 = J_k(1-a,1). * B11 = I_m, B22 = I_k * where J_k(a,b) is the k-by-k Jordan block with ``a'' on * diagonal and ``b'' on superdiagonal. * * Type 2: A11 = (a_ij) = ( 2(.5-sin(i)) ) and * B11 = (b_ij) = ( 2(.5-sin(ij)) ) for i=1,...,m, j=i,...,m * A22 = (a_ij) = ( 2(.5-sin(i+j)) ) and * B22 = (b_ij) = ( 2(.5-sin(ij)) ) for i=m+1,...,k, j=i,...,k * * Type 3: A11, A22 and B11, B22 are chosen as for Type 2, but each * second diagonal block in A_11 and each third diagonal block * in A_22 are made as 2 by 2 blocks. * * Type 4: A11 = ( 20(.5 - sin(ij)) ) and B22 = ( 2(.5 - sin(i+j)) ) * for i=1,...,m, j=1,...,m and * A22 = ( 20(.5 - sin(i+j)) ) and B22 = ( 2(.5 - sin(ij)) ) * for i=m+1,...,k, j=m+1,...,k * * Type 5: (A,B) and have potentially close or common eigenvalues and * very large departure from block diagonality A_11 is chosen * as the m x m leading submatrix of A_1: * | 1 b | * | -b 1 | * | 1+d b | * | -b 1+d | * A_1 = | d 1 | * | -1 d | * | -d 1 | * | -1 -d | * | 1 | * and A_22 is chosen as the k x k leading submatrix of A_2: * | -1 b | * | -b -1 | * | 1-d b | * | -b 1-d | * A_2 = | d 1+b | * | -1-b d | * | -d 1+b | * | -1+b -d | * | 1-d | * and matrix B are chosen as identity matrices (see DLATM5). * * * Arguments * ========= * * NSIZE (input) INTEGER * The maximum size of the matrices to use. NSIZE >= 0. * If NSIZE = 0, no built-in tests matrices are used, but * read-in test matrices are used to test DGGESX. * * NCMAX (input) INTEGER * Maximum allowable NMAX for generating Kroneker matrix * in call to DLAKF2 * * 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. * * NIN (input) INTEGER * The FORTRAN unit number for reading in the data file of * problems to solve. * * NOUT (input) INTEGER * The FORTRAN unit number for printing out error messages * (e.g., if a routine returns IINFO not equal to 0.) * * A (workspace) DOUBLE PRECISION array, dimension (LDA, NSIZE) * Used to store the matrix whose eigenvalues are to be * computed. On exit, A contains the last matrix actually used. * * LDA (input) INTEGER * The leading dimension of A, B, AI, BI, Z and Q, * LDA >= max( 1, NSIZE ). For the read-in test, * LDA >= max( 1, N ), N is the size of the test matrices. * * B (workspace) DOUBLE PRECISION array, dimension (LDA, NSIZE) * Used to store the matrix whose eigenvalues are to be * computed. On exit, B contains the last matrix actually used. * * AI (workspace) DOUBLE PRECISION array, dimension (LDA, NSIZE) * Copy of A, modified by DGGESX. * * BI (workspace) DOUBLE PRECISION array, dimension (LDA, NSIZE) * Copy of B, modified by DGGESX. * * Z (workspace) DOUBLE PRECISION array, dimension (LDA, NSIZE) * Z holds the left Schur vectors computed by DGGESX. * * Q (workspace) DOUBLE PRECISION array, dimension (LDA, NSIZE) * Q holds the right Schur vectors computed by DGGESX. * * ALPHAR (workspace) DOUBLE PRECISION array, dimension (NSIZE) * ALPHAI (workspace) DOUBLE PRECISION array, dimension (NSIZE) * BETA (workspace) DOUBLE PRECISION array, dimension (NSIZE) * On exit, (ALPHAR + ALPHAI*i)/BETA are the eigenvalues. * * C (workspace) DOUBLE PRECISION array, dimension (LDC, LDC) * Store the matrix generated by subroutine DLAKF2, this is the * matrix formed by Kronecker products used for estimating * DIF. * * LDC (input) INTEGER * The leading dimension of C. LDC >= max(1, LDA*LDA/2 ). * * S (workspace) DOUBLE PRECISION array, dimension (LDC) * Singular values of C * * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) * * LWORK (input) INTEGER * The dimension of the array WORK. * LWORK >= MAX( 5*NSIZE*NSIZE/2 - 2, 10*(NSIZE+1) ) * * IWORK (workspace) INTEGER array, dimension (LIWORK) * * LIWORK (input) INTEGER * The dimension of the array IWORK. LIWORK >= NSIZE + 6. * * BWORK (workspace) LOGICAL array, dimension (LDA) * * 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. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TEN PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TEN = 1.0D+1 ) * .. * .. Local Scalars .. LOGICAL ILABAD CHARACTER SENSE INTEGER BDSPAC, I, I1, IFUNC, IINFO, J, LINFO, MAXWRK, $ MINWRK, MM, MN2, NERRS, NPTKNT, NTEST, NTESTT, $ PRTYPE, QBA, QBB DOUBLE PRECISION ABNRM, BIGNUM, DIFTRU, PLTRU, SMLNUM, TEMP1, $ TEMP2, THRSH2, ULP, ULPINV, WEIGHT * .. * .. Local Arrays .. DOUBLE PRECISION DIFEST( 2 ), PL( 2 ), RESULT( 10 ) * .. * .. External Functions .. LOGICAL DLCTSX INTEGER ILAENV DOUBLE PRECISION DLAMCH, DLANGE EXTERNAL DLCTSX, ILAENV, DLAMCH, DLANGE * .. * .. External Subroutines .. EXTERNAL ALASVM, DGESVD, DGET51, DGET53, DGGESX, DLABAD, $ DLACPY, DLAKF2, DLASET, DLATM5, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, SQRT * .. * .. Scalars in Common .. LOGICAL FS INTEGER K, M, MPLUSN, N * .. * .. Common blocks .. COMMON / MN / M, N, MPLUSN, K, FS * .. * .. Executable Statements .. * * Check for errors * IF( NSIZE.LT.0 ) THEN INFO = -1 ELSE IF( THRESH.LT.ZERO ) THEN INFO = -2 ELSE IF( NIN.LE.0 ) THEN INFO = -3 ELSE IF( NOUT.LE.0 ) THEN INFO = -4 ELSE IF( LDA.LT.1 .OR. LDA.LT.NSIZE ) THEN INFO = -6 ELSE IF( LDC.LT.1 .OR. LDC.LT.NSIZE*NSIZE / 2 ) THEN INFO = -17 ELSE IF( LIWORK.LT.NSIZE+6 ) THEN INFO = -21 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*( NSIZE+1 ), 5*NSIZE*NSIZE / 2 ) * * workspace for sggesx * MAXWRK = 9*( NSIZE+1 ) + NSIZE* $ ILAENV( 1, 'DGEQRF', ' ', NSIZE, 1, NSIZE, 0 ) MAXWRK = MAX( MAXWRK, 9*( NSIZE+1 )+NSIZE* $ ILAENV( 1, 'DORGQR', ' ', NSIZE, 1, NSIZE, -1 ) ) * * workspace for dgesvd * BDSPAC = 5*NSIZE*NSIZE / 2 MAXWRK = MAX( MAXWRK, 3*NSIZE*NSIZE / 2+NSIZE*NSIZE* $ ILAENV( 1, 'DGEBRD', ' ', NSIZE*NSIZE / 2, $ NSIZE*NSIZE / 2, -1, -1 ) ) MAXWRK = MAX( MAXWRK, BDSPAC ) * MAXWRK = MAX( MAXWRK, MINWRK ) * WORK( 1 ) = MAXWRK END IF * IF( LWORK.LT.MINWRK ) $ INFO = -19 * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DDRGSX', -INFO ) RETURN END IF * * Important constants * ULP = DLAMCH( 'P' ) ULPINV = ONE / ULP SMLNUM = DLAMCH( 'S' ) / ULP BIGNUM = ONE / SMLNUM CALL DLABAD( SMLNUM, BIGNUM ) THRSH2 = TEN*THRESH NTESTT = 0 NERRS = 0 * * Go to the tests for read-in matrix pairs * IFUNC = 0 IF( NSIZE.EQ.0 ) $ GO TO 70 * * Test the built-in matrix pairs. * Loop over different functions (IFUNC) of DGGESX, types (PRTYPE) * of test matrices, different size (M+N) * PRTYPE = 0 QBA = 3 QBB = 4 WEIGHT = SQRT( ULP ) * DO 60 IFUNC = 0, 3 DO 50 PRTYPE = 1, 5 DO 40 M = 1, NSIZE - 1 DO 30 N = 1, NSIZE - M * WEIGHT = ONE / WEIGHT MPLUSN = M + N * * Generate test matrices * FS = .TRUE. K = 0 * CALL DLASET( 'Full', MPLUSN, MPLUSN, ZERO, ZERO, AI, $ LDA ) CALL DLASET( 'Full', MPLUSN, MPLUSN, ZERO, ZERO, BI, $ LDA ) * CALL DLATM5( PRTYPE, M, N, AI, LDA, AI( M+1, M+1 ), $ LDA, AI( 1, M+1 ), LDA, BI, LDA, $ BI( M+1, M+1 ), LDA, BI( 1, M+1 ), LDA, $ Q, LDA, Z, LDA, WEIGHT, QBA, QBB ) * * Compute the Schur factorization and swapping the * m-by-m (1,1)-blocks with n-by-n (2,2)-blocks. * Swapping is accomplished via the function DLCTSX * which is supplied below. * IF( IFUNC.EQ.0 ) THEN SENSE = 'N' ELSE IF( IFUNC.EQ.1 ) THEN SENSE = 'E' ELSE IF( IFUNC.EQ.2 ) THEN SENSE = 'V' ELSE IF( IFUNC.EQ.3 ) THEN SENSE = 'B' END IF * CALL DLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, A, LDA ) CALL DLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA, B, LDA ) * CALL DGGESX( 'V', 'V', 'S', DLCTSX, SENSE, MPLUSN, AI, $ LDA, BI, LDA, MM, ALPHAR, ALPHAI, BETA, $ Q, LDA, Z, LDA, PL, DIFEST, WORK, LWORK, $ IWORK, LIWORK, BWORK, LINFO ) * IF( LINFO.NE.0 .AND. LINFO.NE.MPLUSN+2 ) THEN RESULT( 1 ) = ULPINV WRITE( NOUT, FMT = 9999 )'DGGESX', LINFO, MPLUSN, $ PRTYPE INFO = LINFO GO TO 30 END IF * * Compute the norm(A, B) * CALL DLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, WORK, $ MPLUSN ) CALL DLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA, $ WORK( MPLUSN*MPLUSN+1 ), MPLUSN ) ABNRM = DLANGE( 'Fro', MPLUSN, 2*MPLUSN, WORK, MPLUSN, $ WORK ) * * Do tests (1) to (4) * CALL DGET51( 1, MPLUSN, A, LDA, AI, LDA, Q, LDA, Z, $ LDA, WORK, RESULT( 1 ) ) CALL DGET51( 1, MPLUSN, B, LDA, BI, LDA, Q, LDA, Z, $ LDA, WORK, RESULT( 2 ) ) CALL DGET51( 3, MPLUSN, B, LDA, BI, LDA, Q, LDA, Q, $ LDA, WORK, RESULT( 3 ) ) CALL DGET51( 3, MPLUSN, B, LDA, BI, LDA, Z, LDA, Z, $ LDA, WORK, RESULT( 4 ) ) NTEST = 4 * * Do tests (5) and (6): check Schur form of A and * compare eigenvalues with diagonals. * TEMP1 = ZERO RESULT( 5 ) = ZERO RESULT( 6 ) = ZERO * DO 10 J = 1, MPLUSN ILABAD = .FALSE. IF( ALPHAI( J ).EQ.ZERO ) THEN TEMP2 = ( ABS( ALPHAR( J )-AI( J, J ) ) / $ MAX( SMLNUM, ABS( ALPHAR( J ) ), $ ABS( AI( J, J ) ) )+ $ ABS( BETA( J )-BI( J, J ) ) / $ MAX( SMLNUM, ABS( BETA( J ) ), $ ABS( BI( J, J ) ) ) ) / ULP IF( J.LT.MPLUSN ) THEN IF( AI( J+1, J ).NE.ZERO ) THEN ILABAD = .TRUE. RESULT( 5 ) = ULPINV END IF END IF IF( J.GT.1 ) THEN IF( AI( J, J-1 ).NE.ZERO ) THEN ILABAD = .TRUE. RESULT( 5 ) = 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.MPLUSN ) THEN ILABAD = .TRUE. ELSE IF( I1.LT.MPLUSN-1 ) THEN IF( AI( I1+2, I1+1 ).NE.ZERO ) THEN ILABAD = .TRUE. RESULT( 5 ) = ULPINV END IF ELSE IF( I1.GT.1 ) THEN IF( AI( I1, I1-1 ).NE.ZERO ) THEN ILABAD = .TRUE. RESULT( 5 ) = ULPINV END IF END IF IF( .NOT.ILABAD ) THEN CALL DGET53( AI( I1, I1 ), LDA, BI( I1, I1 ), $ LDA, BETA( J ), ALPHAR( J ), $ ALPHAI( J ), TEMP2, IINFO ) IF( IINFO.GE.3 ) THEN WRITE( NOUT, FMT = 9997 )IINFO, J, $ MPLUSN, PRTYPE INFO = ABS( IINFO ) END IF ELSE TEMP2 = ULPINV END IF END IF TEMP1 = MAX( TEMP1, TEMP2 ) IF( ILABAD ) THEN WRITE( NOUT, FMT = 9996 )J, MPLUSN, PRTYPE END IF 10 CONTINUE RESULT( 6 ) = TEMP1 NTEST = NTEST + 2 * * Test (7) (if sorting worked) * RESULT( 7 ) = ZERO IF( LINFO.EQ.MPLUSN+3 ) THEN RESULT( 7 ) = ULPINV ELSE IF( MM.NE.N ) THEN RESULT( 7 ) = ULPINV END IF NTEST = NTEST + 1 * * Test (8): compare the estimated value DIF and its * value. first, compute the exact DIF. * RESULT( 8 ) = ZERO MN2 = MM*( MPLUSN-MM )*2 IF( IFUNC.GE.2 .AND. MN2.LE.NCMAX*NCMAX ) THEN * * Note: for either following two causes, there are * almost same number of test cases fail the test. * CALL DLAKF2( MM, MPLUSN-MM, AI, LDA, $ AI( MM+1, MM+1 ), BI, $ BI( MM+1, MM+1 ), C, LDC ) * CALL DGESVD( 'N', 'N', MN2, MN2, C, LDC, S, WORK, $ 1, WORK( 2 ), 1, WORK( 3 ), LWORK-2, $ INFO ) DIFTRU = S( MN2 ) * IF( DIFEST( 2 ).EQ.ZERO ) THEN IF( DIFTRU.GT.ABNRM*ULP ) $ RESULT( 8 ) = ULPINV ELSE IF( DIFTRU.EQ.ZERO ) THEN IF( DIFEST( 2 ).GT.ABNRM*ULP ) $ RESULT( 8 ) = ULPINV ELSE IF( ( DIFTRU.GT.THRSH2*DIFEST( 2 ) ) .OR. $ ( DIFTRU*THRSH2.LT.DIFEST( 2 ) ) ) THEN RESULT( 8 ) = MAX( DIFTRU / DIFEST( 2 ), $ DIFEST( 2 ) / DIFTRU ) END IF NTEST = NTEST + 1 END IF * * Test (9) * RESULT( 9 ) = ZERO IF( LINFO.EQ.( MPLUSN+2 ) ) THEN IF( DIFTRU.GT.ABNRM*ULP ) $ RESULT( 9 ) = ULPINV IF( ( IFUNC.GT.1 ) .AND. ( DIFEST( 2 ).NE.ZERO ) ) $ RESULT( 9 ) = ULPINV IF( ( IFUNC.EQ.1 ) .AND. ( PL( 1 ).NE.ZERO ) ) $ RESULT( 9 ) = ULPINV NTEST = NTEST + 1 END IF * NTESTT = NTESTT + NTEST * * Print out tests which fail. * DO 20 J = 1, 9 IF( RESULT( J ).GE.THRESH ) THEN * * If this is the first test to fail, * print a header to the data file. * IF( NERRS.EQ.0 ) THEN WRITE( NOUT, FMT = 9995 )'DGX' * * Matrix types * WRITE( NOUT, FMT = 9993 ) * * Tests performed * WRITE( NOUT, FMT = 9992 )'orthogonal', '''', $ 'transpose', ( '''', I = 1, 4 ) * END IF NERRS = NERRS + 1 IF( RESULT( J ).LT.10000.0D0 ) THEN WRITE( NOUT, FMT = 9991 )MPLUSN, PRTYPE, $ WEIGHT, M, J, RESULT( J ) ELSE WRITE( NOUT, FMT = 9990 )MPLUSN, PRTYPE, $ WEIGHT, M, J, RESULT( J ) END IF END IF 20 CONTINUE * 30 CONTINUE 40 CONTINUE 50 CONTINUE 60 CONTINUE * GO TO 150 * 70 CONTINUE * * Read in data from file to check accuracy of condition estimation * Read input data until N=0 * NPTKNT = 0 * 80 CONTINUE READ( NIN, FMT = *, END = 140 )MPLUSN IF( MPLUSN.EQ.0 ) $ GO TO 140 READ( NIN, FMT = *, END = 140 )N DO 90 I = 1, MPLUSN READ( NIN, FMT = * )( AI( I, J ), J = 1, MPLUSN ) 90 CONTINUE DO 100 I = 1, MPLUSN READ( NIN, FMT = * )( BI( I, J ), J = 1, MPLUSN ) 100 CONTINUE READ( NIN, FMT = * )PLTRU, DIFTRU * NPTKNT = NPTKNT + 1 FS = .TRUE. K = 0 M = MPLUSN - N * CALL DLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, A, LDA ) CALL DLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA, B, LDA ) * * Compute the Schur factorization while swaping the * m-by-m (1,1)-blocks with n-by-n (2,2)-blocks. * CALL DGGESX( 'V', 'V', 'S', DLCTSX, 'B', MPLUSN, AI, LDA, BI, LDA, $ MM, ALPHAR, ALPHAI, BETA, Q, LDA, Z, LDA, PL, DIFEST, $ WORK, LWORK, IWORK, LIWORK, BWORK, LINFO ) * IF( LINFO.NE.0 .AND. LINFO.NE.MPLUSN+2 ) THEN RESULT( 1 ) = ULPINV WRITE( NOUT, FMT = 9998 )'DGGESX', LINFO, MPLUSN, NPTKNT GO TO 130 END IF * * Compute the norm(A, B) * (should this be norm of (A,B) or (AI,BI)?) * CALL DLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, WORK, MPLUSN ) CALL DLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA, $ WORK( MPLUSN*MPLUSN+1 ), MPLUSN ) ABNRM = DLANGE( 'Fro', MPLUSN, 2*MPLUSN, WORK, MPLUSN, WORK ) * * Do tests (1) to (4) * CALL DGET51( 1, MPLUSN, A, LDA, AI, LDA, Q, LDA, Z, LDA, WORK, $ RESULT( 1 ) ) CALL DGET51( 1, MPLUSN, B, LDA, BI, LDA, Q, LDA, Z, LDA, WORK, $ RESULT( 2 ) ) CALL DGET51( 3, MPLUSN, B, LDA, BI, LDA, Q, LDA, Q, LDA, WORK, $ RESULT( 3 ) ) CALL DGET51( 3, MPLUSN, B, LDA, BI, LDA, Z, LDA, Z, LDA, WORK, $ RESULT( 4 ) ) * * Do tests (5) and (6): check Schur form of A and compare * eigenvalues with diagonals. * NTEST = 6 TEMP1 = ZERO RESULT( 5 ) = ZERO RESULT( 6 ) = ZERO * DO 110 J = 1, MPLUSN ILABAD = .FALSE. IF( ALPHAI( J ).EQ.ZERO ) THEN TEMP2 = ( ABS( ALPHAR( J )-AI( J, J ) ) / $ MAX( SMLNUM, ABS( ALPHAR( J ) ), ABS( AI( J, $ J ) ) )+ABS( BETA( J )-BI( J, J ) ) / $ MAX( SMLNUM, ABS( BETA( J ) ), ABS( BI( J, J ) ) ) ) $ / ULP IF( J.LT.MPLUSN ) THEN IF( AI( J+1, J ).NE.ZERO ) THEN ILABAD = .TRUE. RESULT( 5 ) = ULPINV END IF END IF IF( J.GT.1 ) THEN IF( AI( J, J-1 ).NE.ZERO ) THEN ILABAD = .TRUE. RESULT( 5 ) = 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.MPLUSN ) THEN ILABAD = .TRUE. ELSE IF( I1.LT.MPLUSN-1 ) THEN IF( AI( I1+2, I1+1 ).NE.ZERO ) THEN ILABAD = .TRUE. RESULT( 5 ) = ULPINV END IF ELSE IF( I1.GT.1 ) THEN IF( AI( I1, I1-1 ).NE.ZERO ) THEN ILABAD = .TRUE. RESULT( 5 ) = ULPINV END IF END IF IF( .NOT.ILABAD ) THEN CALL DGET53( AI( I1, I1 ), LDA, BI( I1, I1 ), LDA, $ BETA( J ), ALPHAR( J ), ALPHAI( J ), TEMP2, $ IINFO ) IF( IINFO.GE.3 ) THEN WRITE( NOUT, FMT = 9997 )IINFO, J, MPLUSN, NPTKNT INFO = ABS( IINFO ) END IF ELSE TEMP2 = ULPINV END IF END IF TEMP1 = MAX( TEMP1, TEMP2 ) IF( ILABAD ) THEN WRITE( NOUT, FMT = 9996 )J, MPLUSN, NPTKNT END IF 110 CONTINUE RESULT( 6 ) = TEMP1 * * Test (7) (if sorting worked) <--------- need to be checked. * NTEST = 7 RESULT( 7 ) = ZERO IF( LINFO.EQ.MPLUSN+3 ) $ RESULT( 7 ) = ULPINV * * Test (8): compare the estimated value of DIF and its true value. * NTEST = 8 RESULT( 8 ) = ZERO IF( DIFEST( 2 ).EQ.ZERO ) THEN IF( DIFTRU.GT.ABNRM*ULP ) $ RESULT( 8 ) = ULPINV ELSE IF( DIFTRU.EQ.ZERO ) THEN IF( DIFEST( 2 ).GT.ABNRM*ULP ) $ RESULT( 8 ) = ULPINV ELSE IF( ( DIFTRU.GT.THRSH2*DIFEST( 2 ) ) .OR. $ ( DIFTRU*THRSH2.LT.DIFEST( 2 ) ) ) THEN RESULT( 8 ) = MAX( DIFTRU / DIFEST( 2 ), DIFEST( 2 ) / DIFTRU ) END IF * * Test (9) * NTEST = 9 RESULT( 9 ) = ZERO IF( LINFO.EQ.( MPLUSN+2 ) ) THEN IF( DIFTRU.GT.ABNRM*ULP ) $ RESULT( 9 ) = ULPINV IF( ( IFUNC.GT.1 ) .AND. ( DIFEST( 2 ).NE.ZERO ) ) $ RESULT( 9 ) = ULPINV IF( ( IFUNC.EQ.1 ) .AND. ( PL( 1 ).NE.ZERO ) ) $ RESULT( 9 ) = ULPINV END IF * * Test (10): compare the estimated value of PL and it true value. * NTEST = 10 RESULT( 10 ) = ZERO IF( PL( 1 ).EQ.ZERO ) THEN IF( PLTRU.GT.ABNRM*ULP ) $ RESULT( 10 ) = ULPINV ELSE IF( PLTRU.EQ.ZERO ) THEN IF( PL( 1 ).GT.ABNRM*ULP ) $ RESULT( 10 ) = ULPINV ELSE IF( ( PLTRU.GT.THRESH*PL( 1 ) ) .OR. $ ( PLTRU*THRESH.LT.PL( 1 ) ) ) THEN RESULT( 10 ) = ULPINV END IF * NTESTT = NTESTT + NTEST * * Print out tests which fail. * DO 120 J = 1, NTEST IF( RESULT( J ).GE.THRESH ) THEN * * If this is the first test to fail, * print a header to the data file. * IF( NERRS.EQ.0 ) THEN WRITE( NOUT, FMT = 9995 )'DGX' * * Matrix types * WRITE( NOUT, FMT = 9994 ) * * Tests performed * WRITE( NOUT, FMT = 9992 )'orthogonal', '''', $ 'transpose', ( '''', I = 1, 4 ) * END IF NERRS = NERRS + 1 IF( RESULT( J ).LT.10000.0D0 ) THEN WRITE( NOUT, FMT = 9989 )NPTKNT, MPLUSN, J, RESULT( J ) ELSE WRITE( NOUT, FMT = 9988 )NPTKNT, MPLUSN, J, RESULT( J ) END IF END IF * 120 CONTINUE * 130 CONTINUE GO TO 80 140 CONTINUE * 150 CONTINUE * * Summary * CALL ALASVM( 'DGX', NOUT, NERRS, NTESTT, 0 ) * WORK( 1 ) = MAXWRK * RETURN * 9999 FORMAT( ' DDRGSX: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', $ I6, ', JTYPE=', I6, ')' ) * 9998 FORMAT( ' DDRGSX: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', $ I6, ', Input Example #', I2, ')' ) * 9997 FORMAT( ' DDRGSX: DGET53 returned INFO=', I1, ' for eigenvalue ', $ I6, '.', / 9X, 'N=', I6, ', JTYPE=', I6, ')' ) * 9996 FORMAT( ' DDRGSX: S not in Schur form at eigenvalue ', I6, '.', $ / 9X, 'N=', I6, ', JTYPE=', I6, ')' ) * 9995 FORMAT( / 1X, A3, ' -- Real Expert Generalized Schur form', $ ' problem driver' ) * 9994 FORMAT( 'Input Example' ) * 9993 FORMAT( ' Matrix types: ', / $ ' 1: A is a block diagonal matrix of Jordan blocks ', $ 'and B is the identity ', / ' matrix, ', $ / ' 2: A and B are upper triangular matrices, ', $ / ' 3: A and B are as type 2, but each second diagonal ', $ 'block in A_11 and ', / $ ' each third diaongal block in A_22 are 2x2 blocks,', $ / ' 4: A and B are block diagonal matrices, ', $ / ' 5: (A,B) has potentially close or common ', $ 'eigenvalues.', / ) * 9992 FORMAT( / ' Tests performed: (S is Schur, T is triangular, ', $ 'Q and Z are ', A, ',', / 19X, $ ' a is alpha, b is beta, and ', 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 = 1/ULP if A is not in ', $ 'Schur form S', / ' 6 = difference between (alpha,beta)', $ ' and diagonals of (S,T)', / $ ' 7 = 1/ULP if SDIM is not the correct number of ', $ 'selected eigenvalues', / $ ' 8 = 1/ULP if DIFEST/DIFTRU > 10*THRESH or ', $ 'DIFTRU/DIFEST > 10*THRESH', $ / ' 9 = 1/ULP if DIFEST <> 0 or DIFTRU > ULP*norm(A,B) ', $ 'when reordering fails', / $ ' 10 = 1/ULP if PLEST/PLTRU > THRESH or ', $ 'PLTRU/PLEST > THRESH', / $ ' ( Test 10 is only for input examples )', / ) 9991 FORMAT( ' Matrix order=', I2, ', type=', I2, ', a=', D10.3, $ ', order(A_11)=', I2, ', result ', I2, ' is ', 0P, F8.2 ) 9990 FORMAT( ' Matrix order=', I2, ', type=', I2, ', a=', D10.3, $ ', order(A_11)=', I2, ', result ', I2, ' is ', 0P, D10.3 ) 9989 FORMAT( ' Input example #', I2, ', matrix order=', I4, ',', $ ' result ', I2, ' is', 0P, F8.2 ) 9988 FORMAT( ' Input example #', I2, ', matrix order=', I4, ',', $ ' result ', I2, ' is', 1P, D10.3 ) * * End of DDRGSX * END |