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SUBROUTINE DDRVES( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
$ NOUNIT, A, LDA, H, HT, WR, WI, WRT, WIT, VS, $ LDVS, RESULT, WORK, NWORK, IWORK, 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, LDVS, NOUNIT, NSIZES, NTYPES, NWORK DOUBLE PRECISION THRESH * .. * .. Array Arguments .. LOGICAL BWORK( * ), DOTYPE( * ) INTEGER ISEED( 4 ), IWORK( * ), NN( * ) DOUBLE PRECISION A( LDA, * ), H( LDA, * ), HT( LDA, * ), $ RESULT( 13 ), VS( LDVS, * ), WI( * ), WIT( * ), $ WORK( * ), WR( * ), WRT( * ) * .. * * Purpose * ======= * * DDRVES checks the nonsymmetric eigenvalue (Schur form) problem * driver DGEES. * * When DDRVES 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, 13 * tests will be performed: * * (1) 0 if T is in Schur form, 1/ulp otherwise * (no sorting of eigenvalues) * * (2) | A - VS T VS' | / ( n |A| ulp ) * * Here VS is the matrix of Schur eigenvectors, and T is in Schur * form (no sorting of eigenvalues). * * (3) | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues). * * (4) 0 if WR+sqrt(-1)*WI are eigenvalues of T * 1/ulp otherwise * (no sorting of eigenvalues) * * (5) 0 if T(with VS) = T(without VS), * 1/ulp otherwise * (no sorting of eigenvalues) * * (6) 0 if eigenvalues(with VS) = eigenvalues(without VS), * 1/ulp otherwise * (no sorting of eigenvalues) * * (7) 0 if T is in Schur form, 1/ulp otherwise * (with sorting of eigenvalues) * * (8) | A - VS T VS' | / ( n |A| ulp ) * * Here VS is the matrix of Schur eigenvectors, and T is in Schur * form (with sorting of eigenvalues). * * (9) | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues). * * (10) 0 if WR+sqrt(-1)*WI are eigenvalues of T * 1/ulp otherwise * (with sorting of eigenvalues) * * (11) 0 if T(with VS) = T(without VS), * 1/ulp otherwise * (with sorting of eigenvalues) * * (12) 0 if eigenvalues(with VS) = eigenvalues(without VS), * 1/ulp otherwise * (with sorting of eigenvalues) * * (13) if sorting worked and SDIM is the number of * eigenvalues which were SELECTed * * 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. * Currently, the list of possible types is: * * (1) The zero matrix. * (2) The identity matrix. * (3) A (transposed) Jordan block, with 1's on the diagonal. * * (4) A diagonal matrix with evenly spaced entries * 1, ..., ULP and random signs. * (ULP = (first number larger than 1) - 1 ) * (5) A diagonal matrix with geometrically spaced entries * 1, ..., ULP and random signs. * (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP * and random signs. * * (7) Same as (4), but multiplied by a constant near * the overflow threshold * (8) Same as (4), but multiplied by a constant near * the underflow threshold * * (9) A matrix of the form U' T U, where U is orthogonal and * T has evenly spaced entries 1, ..., ULP with random signs * on the diagonal and random O(1) entries in the upper * triangle. * * (10) A matrix of the form U' T U, where U is orthogonal and * T has geometrically spaced entries 1, ..., ULP with random * signs on the diagonal and random O(1) entries in the upper * triangle. * * (11) A matrix of the form U' T U, where U is orthogonal and * T has "clustered" entries 1, ULP,..., ULP with random * signs on the diagonal and random O(1) entries in the upper * triangle. * * (12) A matrix of the form U' T U, where U is orthogonal and * T has real or complex conjugate paired eigenvalues randomly * chosen from ( ULP, 1 ) and random O(1) entries in the upper * triangle. * * (13) A matrix of the form X' T X, where X has condition * SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP * with random signs on the diagonal and random O(1) entries * in the upper triangle. * * (14) A matrix of the form X' T X, where X has condition * SQRT( ULP ) and T has geometrically spaced entries * 1, ..., ULP with random signs on the diagonal and random * O(1) entries in the upper triangle. * * (15) A matrix of the form X' T X, where X has condition * SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP * with random signs on the diagonal and random O(1) entries * in the upper triangle. * * (16) A matrix of the form X' T X, where X has condition * SQRT( ULP ) and T has real or complex conjugate paired * eigenvalues randomly chosen from ( ULP, 1 ) and random * O(1) entries in the upper triangle. * * (17) Same as (16), but multiplied by a constant * near the overflow threshold * (18) Same as (16), but multiplied by a constant * near the underflow threshold * * (19) Nonsymmetric matrix with random entries chosen from (-1,1). * If N is at least 4, all entries in first two rows and last * row, and first column and last two columns are zero. * (20) Same as (19), but multiplied by a constant * near the overflow threshold * (21) Same as (19), but multiplied by a constant * near the underflow threshold * * Arguments * ========= * * NSIZES (input) INTEGER * The number of sizes of matrices to use. If it is zero, * DDRVES 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, DDRVES * 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 DDRVES 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. * * NOUNIT (input) INTEGER * The FORTRAN unit number for printing out error messages * (e.g., if a routine returns INFO not equal to 0.) * * A (workspace) 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. * * LDA (input) INTEGER * The leading dimension of A, and H. LDA must be at * least 1 and at least max(NN). * * H (workspace) DOUBLE PRECISION array, dimension (LDA, max(NN)) * Another copy of the test matrix A, modified by DGEES. * * HT (workspace) DOUBLE PRECISION array, dimension (LDA, max(NN)) * Yet another copy of the test matrix A, modified by DGEES. * * WR (workspace) DOUBLE PRECISION array, dimension (max(NN)) * WI (workspace) DOUBLE PRECISION array, dimension (max(NN)) * The real and imaginary parts of the eigenvalues of A. * On exit, WR + WI*i are the eigenvalues of the matrix in A. * * WRT (workspace) DOUBLE PRECISION array, dimension (max(NN)) * WIT (workspace) DOUBLE PRECISION array, dimension (max(NN)) * Like WR, WI, these arrays contain the eigenvalues of A, * but those computed when DGEES only computes a partial * eigendecomposition, i.e. not Schur vectors * * VS (workspace) DOUBLE PRECISION array, dimension (LDVS, max(NN)) * VS holds the computed Schur vectors. * * LDVS (input) INTEGER * Leading dimension of VS. Must be at least max(1,max(NN)). * * RESULT (output) DOUBLE PRECISION array, dimension (13) * The values computed by the 13 tests described above. * The values are currently limited to 1/ulp, to avoid overflow. * * WORK (workspace) DOUBLE PRECISION array, dimension (NWORK) * * NWORK (input) INTEGER * The number of entries in WORK. This must be at least * 5*NN(j)+2*NN(j)**2 for all j. * * IWORK (workspace) INTEGER array, dimension (max(NN)) * * INFO (output) INTEGER * If 0, then everything ran OK. * -1: NSIZES < 0 * -2: Some NN(j) < 0 * -3: NTYPES < 0 * -6: THRESH < 0 * -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ). * -17: LDVS < 1 or LDVS < NMAX, where NMAX is max( NN(j) ). * -20: NWORK too small. * If DLATMR, SLATMS, SLATME or DGEES returns an error code, * the absolute value of it is returned. * *----------------------------------------------------------------------- * * Some Local Variables and Parameters: * ---- ----- --------- --- ---------- * * ZERO, ONE Real 0 and 1. * MAXTYP The number of types defined. * NMAX Largest value in NN. * NERRS The number of tests which have exceeded THRESH * COND, CONDS, * 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. * RTULP, RTULPI Square roots of the previous 4 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) ) * KCONDS(j) Selectw whether CONDS is to be 1 or * 1/sqrt(ulp). (0 means irrelevant.) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) INTEGER MAXTYP PARAMETER ( MAXTYP = 21 ) * .. * .. Local Scalars .. LOGICAL BADNN CHARACTER SORT CHARACTER*3 PATH INTEGER I, IINFO, IMODE, ISORT, ITYPE, IWK, J, JCOL, $ JSIZE, JTYPE, KNTEIG, LWORK, MTYPES, N, NERRS, $ NFAIL, NMAX, NNWORK, NTEST, NTESTF, NTESTT, $ RSUB, SDIM DOUBLE PRECISION ANORM, COND, CONDS, OVFL, RTULP, RTULPI, TMP, $ ULP, ULPINV, UNFL * .. * .. Local Arrays .. CHARACTER ADUMMA( 1 ) INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ), $ KMAGN( MAXTYP ), KMODE( MAXTYP ), $ KTYPE( MAXTYP ) DOUBLE PRECISION RES( 2 ) * .. * .. Arrays in Common .. LOGICAL SELVAL( 20 ) DOUBLE PRECISION SELWI( 20 ), SELWR( 20 ) * .. * .. Scalars in Common .. INTEGER SELDIM, SELOPT * .. * .. Common blocks .. COMMON / SSLCT / SELOPT, SELDIM, SELVAL, SELWR, SELWI * .. * .. External Functions .. LOGICAL DSLECT DOUBLE PRECISION DLAMCH EXTERNAL DSLECT, DLAMCH * .. * .. External Subroutines .. EXTERNAL DGEES, DHST01, DLABAD, DLACPY, DLASET, DLASUM, $ DLATME, DLATMR, DLATMS, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, SIGN, SQRT * .. * .. Data statements .. DATA KTYPE / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 / DATA KMAGN / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2, $ 3, 1, 2, 3 / DATA KMODE / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3, $ 1, 5, 5, 5, 4, 3, 1 / DATA KCONDS / 3*0, 5*0, 4*1, 6*2, 3*0 / * .. * .. Executable Statements .. * PATH( 1: 1 ) = 'Double precision' PATH( 2: 3 ) = 'ES' * * Check for errors * NTESTT = 0 NTESTF = 0 INFO = 0 SELOPT = 0 * * Important constants * 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( THRESH.LT.ZERO ) THEN INFO = -6 ELSE IF( NOUNIT.LE.0 ) THEN INFO = -7 ELSE IF( LDA.LT.1 .OR. LDA.LT.NMAX ) THEN INFO = -9 ELSE IF( LDVS.LT.1 .OR. LDVS.LT.NMAX ) THEN INFO = -17 ELSE IF( 5*NMAX+2*NMAX**2.GT.NWORK ) THEN INFO = -20 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DDRVES', -INFO ) RETURN END IF * * Quick return if nothing to do * IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 ) $ RETURN * * More Important constants * UNFL = DLAMCH( 'Safe minimum' ) OVFL = ONE / UNFL CALL DLABAD( UNFL, OVFL ) ULP = DLAMCH( 'Precision' ) ULPINV = ONE / ULP RTULP = SQRT( ULP ) RTULPI = ONE / RTULP * * Loop over sizes, types * NERRS = 0 * DO 270 JSIZE = 1, NSIZES N = NN( JSIZE ) MTYPES = MAXTYP IF( NSIZES.EQ.1 .AND. NTYPES.EQ.MAXTYP+1 ) $ MTYPES = MTYPES + 1 * DO 260 JTYPE = 1, MTYPES IF( .NOT.DOTYPE( JTYPE ) ) $ GO TO 260 * * Save ISEED in case of an error. * DO 20 J = 1, 4 IOLDSD( J ) = ISEED( J ) 20 CONTINUE * * Compute "A" * * Control parameters: * * KMAGN KCONDS KMODE KTYPE * =1 O(1) 1 clustered 1 zero * =2 large large clustered 2 identity * =3 small exponential Jordan * =4 arithmetic diagonal, (w/ eigenvalues) * =5 random log symmetric, w/ eigenvalues * =6 random general, w/ eigenvalues * =7 random diagonal * =8 random symmetric * =9 random general * =10 random triangular * IF( MTYPES.GT.MAXTYP ) $ GO TO 90 * ITYPE = KTYPE( JTYPE ) IMODE = KMODE( JTYPE ) * * Compute norm * GO TO ( 30, 40, 50 )KMAGN( JTYPE ) * 30 CONTINUE ANORM = ONE GO TO 60 * 40 CONTINUE ANORM = OVFL*ULP GO TO 60 * 50 CONTINUE ANORM = UNFL*ULPINV GO TO 60 * 60 CONTINUE * CALL DLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA ) IINFO = 0 COND = ULPINV * * Special Matrices -- Identity & Jordan block * * Zero * IF( ITYPE.EQ.1 ) THEN IINFO = 0 * ELSE IF( ITYPE.EQ.2 ) THEN * * Identity * DO 70 JCOL = 1, N A( JCOL, JCOL ) = ANORM 70 CONTINUE * ELSE IF( ITYPE.EQ.3 ) THEN * * Jordan Block * DO 80 JCOL = 1, N A( JCOL, JCOL ) = ANORM IF( JCOL.GT.1 ) $ A( JCOL, JCOL-1 ) = ONE 80 CONTINUE * ELSE IF( ITYPE.EQ.4 ) THEN * * Diagonal Matrix, [Eigen]values Specified * 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 * CALL DLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND, $ ANORM, N, N, 'N', A, LDA, WORK( N+1 ), $ IINFO ) * ELSE IF( ITYPE.EQ.6 ) THEN * * General, eigenvalues specified * IF( KCONDS( JTYPE ).EQ.1 ) THEN CONDS = ONE ELSE IF( KCONDS( JTYPE ).EQ.2 ) THEN CONDS = RTULPI ELSE CONDS = ZERO END IF * ADUMMA( 1 ) = ' ' CALL DLATME( N, 'S', ISEED, WORK, IMODE, COND, ONE, $ ADUMMA, 'T', 'T', 'T', WORK( N+1 ), 4, $ CONDS, N, N, ANORM, A, LDA, WORK( 2*N+1 ), $ IINFO ) * ELSE IF( ITYPE.EQ.7 ) THEN * * Diagonal, random eigenvalues * 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 * 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, N, N, $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO ) * ELSE IF( ITYPE.EQ.9 ) THEN * * General, random eigenvalues * CALL DLATMR( N, N, 'S', ISEED, 'N', 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 ) IF( N.GE.4 ) THEN CALL DLASET( 'Full', 2, N, ZERO, ZERO, A, LDA ) CALL DLASET( 'Full', N-3, 1, ZERO, ZERO, A( 3, 1 ), $ LDA ) CALL DLASET( 'Full', N-3, 2, ZERO, ZERO, A( 3, N-1 ), $ LDA ) CALL DLASET( 'Full', 1, N, ZERO, ZERO, A( N, 1 ), $ LDA ) END IF * ELSE IF( ITYPE.EQ.10 ) THEN * * Triangular, random eigenvalues * CALL DLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE, $ 'T', 'N', WORK( N+1 ), 1, ONE, $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, 0, $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO ) * ELSE * IINFO = 1 END IF * IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9992 )'Generator', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) RETURN END IF * 90 CONTINUE * * Test for minimal and generous workspace * DO 250 IWK = 1, 2 IF( IWK.EQ.1 ) THEN NNWORK = 3*N ELSE NNWORK = 5*N + 2*N**2 END IF NNWORK = MAX( NNWORK, 1 ) * * Initialize RESULT * DO 100 J = 1, 13 RESULT( J ) = -ONE 100 CONTINUE * * Test with and without sorting of eigenvalues * DO 210 ISORT = 0, 1 IF( ISORT.EQ.0 ) THEN SORT = 'N' RSUB = 0 ELSE SORT = 'S' RSUB = 6 END IF * * Compute Schur form and Schur vectors, and test them * CALL DLACPY( 'F', N, N, A, LDA, H, LDA ) CALL DGEES( 'V', SORT, DSLECT, N, H, LDA, SDIM, WR, $ WI, VS, LDVS, WORK, NNWORK, BWORK, IINFO ) IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN RESULT( 1+RSUB ) = ULPINV WRITE( NOUNIT, FMT = 9992 )'DGEES1', IINFO, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) GO TO 220 END IF * * Do Test (1) or Test (7) * RESULT( 1+RSUB ) = ZERO DO 120 J = 1, N - 2 DO 110 I = J + 2, N IF( H( I, J ).NE.ZERO ) $ RESULT( 1+RSUB ) = ULPINV 110 CONTINUE 120 CONTINUE DO 130 I = 1, N - 2 IF( H( I+1, I ).NE.ZERO .AND. H( I+2, I+1 ).NE. $ ZERO )RESULT( 1+RSUB ) = ULPINV 130 CONTINUE DO 140 I = 1, N - 1 IF( H( I+1, I ).NE.ZERO ) THEN IF( H( I, I ).NE.H( I+1, I+1 ) .OR. $ H( I, I+1 ).EQ.ZERO .OR. $ SIGN( ONE, H( I+1, I ) ).EQ. $ SIGN( ONE, H( I, I+1 ) ) )RESULT( 1+RSUB ) $ = ULPINV END IF 140 CONTINUE * * Do Tests (2) and (3) or Tests (8) and (9) * LWORK = MAX( 1, 2*N*N ) CALL DHST01( N, 1, N, A, LDA, H, LDA, VS, LDVS, WORK, $ LWORK, RES ) RESULT( 2+RSUB ) = RES( 1 ) RESULT( 3+RSUB ) = RES( 2 ) * * Do Test (4) or Test (10) * RESULT( 4+RSUB ) = ZERO DO 150 I = 1, N IF( H( I, I ).NE.WR( I ) ) $ RESULT( 4+RSUB ) = ULPINV 150 CONTINUE IF( N.GT.1 ) THEN IF( H( 2, 1 ).EQ.ZERO .AND. WI( 1 ).NE.ZERO ) $ RESULT( 4+RSUB ) = ULPINV IF( H( N, N-1 ).EQ.ZERO .AND. WI( N ).NE.ZERO ) $ RESULT( 4+RSUB ) = ULPINV END IF DO 160 I = 1, N - 1 IF( H( I+1, I ).NE.ZERO ) THEN TMP = SQRT( ABS( H( I+1, I ) ) )* $ SQRT( ABS( H( I, I+1 ) ) ) RESULT( 4+RSUB ) = MAX( RESULT( 4+RSUB ), $ ABS( WI( I )-TMP ) / $ MAX( ULP*TMP, UNFL ) ) RESULT( 4+RSUB ) = MAX( RESULT( 4+RSUB ), $ ABS( WI( I+1 )+TMP ) / $ MAX( ULP*TMP, UNFL ) ) ELSE IF( I.GT.1 ) THEN IF( H( I+1, I ).EQ.ZERO .AND. H( I, I-1 ).EQ. $ ZERO .AND. WI( I ).NE.ZERO )RESULT( 4+RSUB ) $ = ULPINV END IF 160 CONTINUE * * Do Test (5) or Test (11) * CALL DLACPY( 'F', N, N, A, LDA, HT, LDA ) CALL DGEES( 'N', SORT, DSLECT, N, HT, LDA, SDIM, WRT, $ WIT, VS, LDVS, WORK, NNWORK, BWORK, $ IINFO ) IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN RESULT( 5+RSUB ) = ULPINV WRITE( NOUNIT, FMT = 9992 )'DGEES2', IINFO, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) GO TO 220 END IF * RESULT( 5+RSUB ) = ZERO DO 180 J = 1, N DO 170 I = 1, N IF( H( I, J ).NE.HT( I, J ) ) $ RESULT( 5+RSUB ) = ULPINV 170 CONTINUE 180 CONTINUE * * Do Test (6) or Test (12) * RESULT( 6+RSUB ) = ZERO DO 190 I = 1, N IF( WR( I ).NE.WRT( I ) .OR. WI( I ).NE.WIT( I ) ) $ RESULT( 6+RSUB ) = ULPINV 190 CONTINUE * * Do Test (13) * IF( ISORT.EQ.1 ) THEN RESULT( 13 ) = ZERO KNTEIG = 0 DO 200 I = 1, N IF( DSLECT( WR( I ), WI( I ) ) .OR. $ DSLECT( WR( I ), -WI( I ) ) ) $ KNTEIG = KNTEIG + 1 IF( I.LT.N ) THEN IF( ( DSLECT( WR( I+1 ), $ WI( I+1 ) ) .OR. DSLECT( WR( I+1 ), $ -WI( I+1 ) ) ) .AND. $ ( .NOT.( DSLECT( WR( I ), $ WI( I ) ) .OR. DSLECT( WR( I ), $ -WI( I ) ) ) ) .AND. IINFO.NE.N+2 ) $ RESULT( 13 ) = ULPINV END IF 200 CONTINUE IF( SDIM.NE.KNTEIG ) THEN RESULT( 13 ) = ULPINV END IF END IF * 210 CONTINUE * * End of Loop -- Check for RESULT(j) > THRESH * 220 CONTINUE * NTEST = 0 NFAIL = 0 DO 230 J = 1, 13 IF( RESULT( J ).GE.ZERO ) $ NTEST = NTEST + 1 IF( RESULT( J ).GE.THRESH ) $ NFAIL = NFAIL + 1 230 CONTINUE * IF( NFAIL.GT.0 ) $ NTESTF = NTESTF + 1 IF( NTESTF.EQ.1 ) THEN WRITE( NOUNIT, FMT = 9999 )PATH WRITE( NOUNIT, FMT = 9998 ) WRITE( NOUNIT, FMT = 9997 ) WRITE( NOUNIT, FMT = 9996 ) WRITE( NOUNIT, FMT = 9995 )THRESH WRITE( NOUNIT, FMT = 9994 ) NTESTF = 2 END IF * DO 240 J = 1, 13 IF( RESULT( J ).GE.THRESH ) THEN WRITE( NOUNIT, FMT = 9993 )N, IWK, IOLDSD, JTYPE, $ J, RESULT( J ) END IF 240 CONTINUE * NERRS = NERRS + NFAIL NTESTT = NTESTT + NTEST * 250 CONTINUE 260 CONTINUE 270 CONTINUE * * Summary * CALL DLASUM( PATH, NOUNIT, NERRS, NTESTT ) * 9999 FORMAT( / 1X, A3, ' -- Real Schur Form Decomposition Driver', $ / ' Matrix types (see DDRVES for details): ' ) * 9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ', $ ' ', ' 5=Diagonal: geometr. spaced entries.', $ / ' 2=Identity matrix. ', ' 6=Diagona', $ 'l: clustered entries.', / ' 3=Transposed Jordan block. ', $ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ', $ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s', $ 'mall, evenly spaced.' ) 9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev', $ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e', $ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ', $ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond', $ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp', $ 'lex ', / ' 12=Well-cond., random complex ', 6X, ' ', $ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi', $ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.', $ ' complx ' ) 9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ', $ 'with small random entries.', / ' 20=Matrix with large ran', $ 'dom entries. ', / ) 9995 FORMAT( ' Tests performed with test threshold =', F8.2, $ / ' ( A denotes A on input and T denotes A on output)', $ / / ' 1 = 0 if T in Schur form (no sort), ', $ ' 1/ulp otherwise', / $ ' 2 = | A - VS T transpose(VS) | / ( n |A| ulp ) (no sort)', $ / ' 3 = | I - VS transpose(VS) | / ( n ulp ) (no sort) ', / $ ' 4 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (no sort),', $ ' 1/ulp otherwise', / $ ' 5 = 0 if T same no matter if VS computed (no sort),', $ ' 1/ulp otherwise', / $ ' 6 = 0 if WR, WI same no matter if VS computed (no sort)', $ ', 1/ulp otherwise' ) 9994 FORMAT( ' 7 = 0 if T in Schur form (sort), ', ' 1/ulp otherwise', $ / ' 8 = | A - VS T transpose(VS) | / ( n |A| ulp ) (sort)', $ / ' 9 = | I - VS transpose(VS) | / ( n ulp ) (sort) ', $ / ' 10 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (sort),', $ ' 1/ulp otherwise', / $ ' 11 = 0 if T same no matter if VS computed (sort),', $ ' 1/ulp otherwise', / $ ' 12 = 0 if WR, WI same no matter if VS computed (sort),', $ ' 1/ulp otherwise', / $ ' 13 = 0 if sorting succesful, 1/ulp otherwise', / ) 9993 FORMAT( ' N=', I5, ', IWK=', I2, ', seed=', 4( I4, ',' ), $ ' type ', I2, ', test(', I2, ')=', G10.3 ) 9992 FORMAT( ' DDRVES: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', $ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' ) * RETURN * * End of DDRVES * END |