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SUBROUTINE DDRVVX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
$ NIUNIT, NOUNIT, A, LDA, H, WR, WI, WR1, WI1, $ VL, LDVL, VR, LDVR, LRE, LDLRE, RCONDV, RCNDV1, $ RCDVIN, RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, $ RESULT, WORK, NWORK, IWORK, INFO ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NIUNIT, NOUNIT, $ NSIZES, NTYPES, NWORK DOUBLE PRECISION THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER ISEED( 4 ), IWORK( * ), NN( * ) DOUBLE PRECISION A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ), $ RCDEIN( * ), RCDVIN( * ), RCNDE1( * ), $ RCNDV1( * ), RCONDE( * ), RCONDV( * ), $ RESULT( 11 ), SCALE( * ), SCALE1( * ), $ VL( LDVL, * ), VR( LDVR, * ), WI( * ), $ WI1( * ), WORK( * ), WR( * ), WR1( * ) * .. * * Purpose * ======= * * DDRVVX checks the nonsymmetric eigenvalue problem expert driver * DGEEVX. * * DDRVVX uses both test matrices generated randomly depending on * data supplied in the calling sequence, as well as on data * read from an input file and including precomputed condition * numbers to which it compares the ones it computes. * * When DDRVVX is called, a number of matrix "sizes" ("n's") and a * number of matrix "types" are specified in the calling sequence. * For each size ("n") and each type of matrix, one matrix will be * generated and used to test the nonsymmetric eigenroutines. For * each matrix, 9 tests will be performed: * * (1) | A * VR - VR * W | / ( n |A| ulp ) * * Here VR is the matrix of unit right eigenvectors. * W is a block diagonal matrix, with a 1x1 block for each * real eigenvalue and a 2x2 block for each complex conjugate * pair. If eigenvalues j and j+1 are a complex conjugate pair, * so WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the * 2 x 2 block corresponding to the pair will be: * * ( wr wi ) * ( -wi wr ) * * Such a block multiplying an n x 2 matrix ( ur ui ) on the * right will be the same as multiplying ur + i*ui by wr + i*wi. * * (2) | A**H * VL - VL * W**H | / ( n |A| ulp ) * * Here VL is the matrix of unit left eigenvectors, A**H is the * conjugate transpose of A, and W is as above. * * (3) | |VR(i)| - 1 | / ulp and largest component real * * VR(i) denotes the i-th column of VR. * * (4) | |VL(i)| - 1 | / ulp and largest component real * * VL(i) denotes the i-th column of VL. * * (5) W(full) = W(partial) * * W(full) denotes the eigenvalues computed when VR, VL, RCONDV * and RCONDE are also computed, and W(partial) denotes the * eigenvalues computed when only some of VR, VL, RCONDV, and * RCONDE are computed. * * (6) VR(full) = VR(partial) * * VR(full) denotes the right eigenvectors computed when VL, RCONDV * and RCONDE are computed, and VR(partial) denotes the result * when only some of VL and RCONDV are computed. * * (7) VL(full) = VL(partial) * * VL(full) denotes the left eigenvectors computed when VR, RCONDV * and RCONDE are computed, and VL(partial) denotes the result * when only some of VR and RCONDV are computed. * * (8) 0 if SCALE, ILO, IHI, ABNRM (full) = * SCALE, ILO, IHI, ABNRM (partial) * 1/ulp otherwise * * SCALE, ILO, IHI and ABNRM describe how the matrix is balanced. * (full) is when VR, VL, RCONDE and RCONDV are also computed, and * (partial) is when some are not computed. * * (9) RCONDV(full) = RCONDV(partial) * * RCONDV(full) denotes the reciprocal condition numbers of the * right eigenvectors computed when VR, VL and RCONDE are also * computed. RCONDV(partial) denotes the reciprocal condition * numbers when only some of VR, VL and RCONDE are computed. * * 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 * * In addition, an input file will be read from logical unit number * NIUNIT. The file contains matrices along with precomputed * eigenvalues and reciprocal condition numbers for the eigenvalues * and right eigenvectors. For these matrices, in addition to tests * (1) to (9) we will compute the following two tests: * * (10) |RCONDV - RCDVIN| / cond(RCONDV) * * RCONDV is the reciprocal right eigenvector condition number * computed by DGEEVX and RCDVIN (the precomputed true value) * is supplied as input. cond(RCONDV) is the condition number of * RCONDV, and takes errors in computing RCONDV into account, so * that the resulting quantity should be O(ULP). cond(RCONDV) is * essentially given by norm(A)/RCONDE. * * (11) |RCONDE - RCDEIN| / cond(RCONDE) * * RCONDE is the reciprocal eigenvalue condition number * computed by DGEEVX and RCDEIN (the precomputed true value) * is supplied as input. cond(RCONDE) is the condition number * of RCONDE, and takes errors in computing RCONDE into account, * so that the resulting quantity should be O(ULP). cond(RCONDE) * is essentially given by norm(A)/RCONDV. * * Arguments * ========== * * NSIZES (input) INTEGER * The number of sizes of matrices to use. NSIZES must be at * least zero. If it is zero, no randomly generated matrices * are tested, but any test matrices read from NIUNIT will be * tested. * * 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. NTYPES must be at least * zero. If it is zero, no randomly generated test matrices * are tested, but and test matrices read from NIUNIT will be * tested. 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 DDRVVX 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. * * NIUNIT (input) INTEGER * The FORTRAN unit number for reading in the data file of * problems to solve. * * 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,12)) * 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 the arrays A and H. * LDA >= max(NN,12), since 12 is the dimension of the largest * matrix in the precomputed input file. * * H (workspace) DOUBLE PRECISION array, dimension * (LDA, max(NN,12)) * Another copy of the test matrix A, modified by DGEEVX. * * 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. * * WR1 (workspace) DOUBLE PRECISION array, dimension (max(NN,12)) * WI1 (workspace) DOUBLE PRECISION array, dimension (max(NN,12)) * Like WR, WI, these arrays contain the eigenvalues of A, * but those computed when DGEEVX only computes a partial * eigendecomposition, i.e. not the eigenvalues and left * and right eigenvectors. * * VL (workspace) DOUBLE PRECISION array, dimension * (LDVL, max(NN,12)) * VL holds the computed left eigenvectors. * * LDVL (input) INTEGER * Leading dimension of VL. Must be at least max(1,max(NN,12)). * * VR (workspace) DOUBLE PRECISION array, dimension * (LDVR, max(NN,12)) * VR holds the computed right eigenvectors. * * LDVR (input) INTEGER * Leading dimension of VR. Must be at least max(1,max(NN,12)). * * LRE (workspace) DOUBLE PRECISION array, dimension * (LDLRE, max(NN,12)) * LRE holds the computed right or left eigenvectors. * * LDLRE (input) INTEGER * Leading dimension of LRE. Must be at least max(1,max(NN,12)) * * RCONDV (workspace) DOUBLE PRECISION array, dimension (N) * RCONDV holds the computed reciprocal condition numbers * for eigenvectors. * * RCNDV1 (workspace) DOUBLE PRECISION array, dimension (N) * RCNDV1 holds more computed reciprocal condition numbers * for eigenvectors. * * RCDVIN (workspace) DOUBLE PRECISION array, dimension (N) * When COMP = .TRUE. RCDVIN holds the precomputed reciprocal * condition numbers for eigenvectors to be compared with * RCONDV. * * RCONDE (workspace) DOUBLE PRECISION array, dimension (N) * RCONDE holds the computed reciprocal condition numbers * for eigenvalues. * * RCNDE1 (workspace) DOUBLE PRECISION array, dimension (N) * RCNDE1 holds more computed reciprocal condition numbers * for eigenvalues. * * RCDEIN (workspace) DOUBLE PRECISION array, dimension (N) * When COMP = .TRUE. RCDEIN holds the precomputed reciprocal * condition numbers for eigenvalues to be compared with * RCONDE. * * RESULT (output) DOUBLE PRECISION array, dimension (11) * The values computed by the seven 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 * max(6*12+2*12**2,6*NN(j)+2*NN(j)**2) = * max( 360 ,6*NN(j)+2*NN(j)**2) for all j. * * IWORK (workspace) INTEGER array, dimension (2*max(NN,12)) * * INFO (output) INTEGER * If 0, then successful exit. * If <0, then input paramter -INFO is incorrect. * If >0, DLATMR, SLATMS, SLATME or DGET23 returned an error * code, and INFO is its absolute value. * *----------------------------------------------------------------------- * * Some Local Variables and Parameters: * ---- ----- --------- --- ---------- * * ZERO, ONE Real 0 and 1. * MAXTYP The number of types defined. * NMAX Largest value in NN or 12. * 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 BALANC CHARACTER*3 PATH INTEGER I, IBAL, IINFO, IMODE, ITYPE, IWK, J, JCOL, $ JSIZE, JTYPE, MTYPES, N, NERRS, NFAIL, NMAX, $ NNWORK, NTEST, NTESTF, NTESTT DOUBLE PRECISION ANORM, COND, CONDS, OVFL, RTULP, RTULPI, ULP, $ ULPINV, UNFL * .. * .. Local Arrays .. CHARACTER ADUMMA( 1 ), BAL( 4 ) INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ), $ KMAGN( MAXTYP ), KMODE( MAXTYP ), $ KTYPE( MAXTYP ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. External Subroutines .. EXTERNAL DGET23, DLABAD, DLASET, DLASUM, DLATME, DLATMR, $ DLATMS, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN, 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 / DATA BAL / 'N', 'P', 'S', 'B' / * .. * .. Executable Statements .. * PATH( 1: 1 ) = 'Double precision' PATH( 2: 3 ) = 'VX' * * Check for errors * NTESTT = 0 NTESTF = 0 INFO = 0 * * Important constants * BADNN = .FALSE. * * 12 is the largest dimension in the input file of precomputed * problems * NMAX = 12 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( LDA.LT.1 .OR. LDA.LT.NMAX ) THEN INFO = -10 ELSE IF( LDVL.LT.1 .OR. LDVL.LT.NMAX ) THEN INFO = -17 ELSE IF( LDVR.LT.1 .OR. LDVR.LT.NMAX ) THEN INFO = -19 ELSE IF( LDLRE.LT.1 .OR. LDLRE.LT.NMAX ) THEN INFO = -21 ELSE IF( 6*NMAX+2*NMAX**2.GT.NWORK ) THEN INFO = -32 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DDRVVX', -INFO ) RETURN END IF * * If nothing to do check on NIUNIT * IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 ) $ GO TO 160 * * 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 150 JSIZE = 1, NSIZES N = NN( JSIZE ) IF( NSIZES.NE.1 ) THEN MTYPES = MIN( MAXTYP, NTYPES ) ELSE MTYPES = MIN( MAXTYP+1, NTYPES ) END IF * DO 140 JTYPE = 1, MTYPES IF( .NOT.DOTYPE( JTYPE ) ) $ GO TO 140 * * 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 130 IWK = 1, 3 IF( IWK.EQ.1 ) THEN NNWORK = 3*N ELSE IF( IWK.EQ.2 ) THEN NNWORK = 6*N + N**2 ELSE NNWORK = 6*N + 2*N**2 END IF NNWORK = MAX( NNWORK, 1 ) * * Test for all balancing options * DO 120 IBAL = 1, 4 BALANC = BAL( IBAL ) * * Perform tests * CALL DGET23( .FALSE., BALANC, JTYPE, THRESH, IOLDSD, $ NOUNIT, N, A, LDA, H, WR, WI, WR1, WI1, $ VL, LDVL, VR, LDVR, LRE, LDLRE, RCONDV, $ RCNDV1, RCDVIN, RCONDE, RCNDE1, RCDEIN, $ SCALE, SCALE1, RESULT, WORK, NNWORK, $ IWORK, INFO ) * * Check for RESULT(j) > THRESH * NTEST = 0 NFAIL = 0 DO 100 J = 1, 9 IF( RESULT( J ).GE.ZERO ) $ NTEST = NTEST + 1 IF( RESULT( J ).GE.THRESH ) $ NFAIL = NFAIL + 1 100 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 NTESTF = 2 END IF * DO 110 J = 1, 9 IF( RESULT( J ).GE.THRESH ) THEN WRITE( NOUNIT, FMT = 9994 )BALANC, N, IWK, $ IOLDSD, JTYPE, J, RESULT( J ) END IF 110 CONTINUE * NERRS = NERRS + NFAIL NTESTT = NTESTT + NTEST * 120 CONTINUE 130 CONTINUE 140 CONTINUE 150 CONTINUE * 160 CONTINUE * * Read in data from file to check accuracy of condition estimation. * Assume input eigenvalues are sorted lexicographically (increasing * by real part, then decreasing by imaginary part) * JTYPE = 0 170 CONTINUE READ( NIUNIT, FMT = *, END = 220 )N * * Read input data until N=0 * IF( N.EQ.0 ) $ GO TO 220 JTYPE = JTYPE + 1 ISEED( 1 ) = JTYPE DO 180 I = 1, N READ( NIUNIT, FMT = * )( A( I, J ), J = 1, N ) 180 CONTINUE DO 190 I = 1, N READ( NIUNIT, FMT = * )WR1( I ), WI1( I ), RCDEIN( I ), $ RCDVIN( I ) 190 CONTINUE CALL DGET23( .TRUE., 'N', 22, THRESH, ISEED, NOUNIT, N, A, LDA, H, $ WR, WI, WR1, WI1, VL, LDVL, VR, LDVR, LRE, LDLRE, $ RCONDV, RCNDV1, RCDVIN, RCONDE, RCNDE1, RCDEIN, $ SCALE, SCALE1, RESULT, WORK, 6*N+2*N**2, IWORK, $ INFO ) * * Check for RESULT(j) > THRESH * NTEST = 0 NFAIL = 0 DO 200 J = 1, 11 IF( RESULT( J ).GE.ZERO ) $ NTEST = NTEST + 1 IF( RESULT( J ).GE.THRESH ) $ NFAIL = NFAIL + 1 200 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 NTESTF = 2 END IF * DO 210 J = 1, 11 IF( RESULT( J ).GE.THRESH ) THEN WRITE( NOUNIT, FMT = 9993 )N, JTYPE, J, RESULT( J ) END IF 210 CONTINUE * NERRS = NERRS + NFAIL NTESTT = NTESTT + NTEST GO TO 170 220 CONTINUE * * Summary * CALL DLASUM( PATH, NOUNIT, NERRS, NTESTT ) * 9999 FORMAT( / 1X, A3, ' -- Real Eigenvalue-Eigenvector Decomposition', $ ' Expert Driver', / $ ' Matrix types (see DDRVVX 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 ', ' ', $ ' 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. ', ' 22=Matrix read from input file', / ) 9995 FORMAT( ' Tests performed with test threshold =', F8.2, $ / / ' 1 = | A VR - VR W | / ( n |A| ulp ) ', $ / ' 2 = | transpose(A) VL - VL W | / ( n |A| ulp ) ', $ / ' 3 = | |VR(i)| - 1 | / ulp ', $ / ' 4 = | |VL(i)| - 1 | / ulp ', $ / ' 5 = 0 if W same no matter if VR or VL computed,', $ ' 1/ulp otherwise', / $ ' 6 = 0 if VR same no matter what else computed,', $ ' 1/ulp otherwise', / $ ' 7 = 0 if VL same no matter what else computed,', $ ' 1/ulp otherwise', / $ ' 8 = 0 if RCONDV same no matter what else computed,', $ ' 1/ulp otherwise', / $ ' 9 = 0 if SCALE, ILO, IHI, ABNRM same no matter what else', $ ' computed, 1/ulp otherwise', $ / ' 10 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV),', $ / ' 11 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE),' ) 9994 FORMAT( ' BALANC=''', A1, ''',N=', I4, ',IWK=', I1, ', seed=', $ 4( I4, ',' ), ' type ', I2, ', test(', I2, ')=', G10.3 ) 9993 FORMAT( ' N=', I5, ', input example =', I3, ', test(', I2, ')=', $ G10.3 ) 9992 FORMAT( ' DDRVVX: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', $ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' ) * RETURN * * End of DDRVVX * END |