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SUBROUTINE SDRVSX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
$ NIUNIT, NOUNIT, A, LDA, H, HT, WR, WI, WRT, $ WIT, WRTMP, WITMP, VS, LDVS, VS1, RESULT, WORK, $ LWORK, 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, LWORK, NIUNIT, NOUNIT, NSIZES, $ NTYPES REAL THRESH * .. * .. Array Arguments .. LOGICAL BWORK( * ), DOTYPE( * ) INTEGER ISEED( 4 ), IWORK( * ), NN( * ) REAL A( LDA, * ), H( LDA, * ), HT( LDA, * ), $ RESULT( 17 ), VS( LDVS, * ), VS1( LDVS, * ), $ WI( * ), WIT( * ), WITMP( * ), WORK( * ), $ WR( * ), WRT( * ), WRTMP( * ) * .. * * Purpose * ======= * * SDRVSX checks the nonsymmetric eigenvalue (Schur form) problem * expert driver SGEESX. * * SDRVSX 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 SDRVSX 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, 15 * 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 * If workspace sufficient, also compare WR, WI with and * without reciprocal condition numbers * (with sorting of eigenvalues) * * (11) 0 if T(with VS) = T(without VS), * 1/ulp otherwise * If workspace sufficient, also compare T with and without * reciprocal condition numbers * (with sorting of eigenvalues) * * (12) 0 if eigenvalues(with VS) = eigenvalues(without VS), * 1/ulp otherwise * If workspace sufficient, also compare VS with and without * reciprocal condition numbers * (with sorting of eigenvalues) * * (13) if sorting worked and SDIM is the number of * eigenvalues which were SELECTed * If workspace sufficient, also compare SDIM with and * without reciprocal condition numbers * * (14) if RCONDE the same no matter if VS and/or RCONDV computed * * (15) if RCONDV the same no matter if VS and/or RCONDE 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 eigenvalue * average and right invariant subspace. For these matrices, in * addition to tests (1) to (15) we will compute the following two * tests: * * (16) |RCONDE - RCDEIN| / cond(RCONDE) * * RCONDE is the reciprocal average eigenvalue condition number * computed by SGEESX 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. * * (17) |RCONDV - RCDVIN| / cond(RCONDV) * * RCONDV is the reciprocal right invariant subspace condition * number computed by SGEESX 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. * * 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 SDRVSX to continue the same random number * sequence. * * THRESH (input) REAL * 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) REAL 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) REAL array, dimension (LDA, max(NN)) * Another copy of the test matrix A, modified by SGEESX. * * HT (workspace) REAL array, dimension (LDA, max(NN)) * Yet another copy of the test matrix A, modified by SGEESX. * * WR (workspace) REAL array, dimension (max(NN)) * WI (workspace) REAL 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) REAL array, dimension (max(NN)) * WIT (workspace) REAL array, dimension (max(NN)) * Like WR, WI, these arrays contain the eigenvalues of A, * but those computed when SGEESX only computes a partial * eigendecomposition, i.e. not Schur vectors * * WRTMP (workspace) REAL array, dimension (max(NN)) * WITMP (workspace) REAL array, dimension (max(NN)) * More temporary storage for eigenvalues. * * VS (workspace) REAL 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)). * * VS1 (workspace) REAL array, dimension (LDVS, max(NN)) * VS1 holds another copy of the computed Schur vectors. * * RESULT (output) REAL array, dimension (17) * The values computed by the 17 tests described above. * The values are currently limited to 1/ulp, to avoid overflow. * * WORK (workspace) REAL array, dimension (LWORK) * * LWORK (input) INTEGER * The number of entries in WORK. This must be at least * max(3*NN(j),2*NN(j)**2) for all j. * * IWORK (workspace) INTEGER array, dimension (max(NN)*max(NN)) * * INFO (output) INTEGER * If 0, successful exit. * <0, input parameter -INFO is incorrect * >0, SLATMR, SLATMS, SLATME or SGET24 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. * 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 .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) INTEGER MAXTYP PARAMETER ( MAXTYP = 21 ) * .. * .. Local Scalars .. LOGICAL BADNN CHARACTER*3 PATH INTEGER I, IINFO, IMODE, ITYPE, IWK, J, JCOL, JSIZE, $ JTYPE, MTYPES, N, NERRS, NFAIL, NMAX, $ NNWORK, NSLCT, NTEST, NTESTF, NTESTT REAL ANORM, COND, CONDS, OVFL, RCDEIN, RCDVIN, $ RTULP, RTULPI, ULP, ULPINV, UNFL * .. * .. Local Arrays .. CHARACTER ADUMMA( 1 ) INTEGER IDUMMA( 1 ), IOLDSD( 4 ), ISLCT( 20 ), $ KCONDS( MAXTYP ), KMAGN( MAXTYP ), $ KMODE( MAXTYP ), KTYPE( MAXTYP ) * .. * .. Arrays in Common .. LOGICAL SELVAL( 20 ) REAL SELWI( 20 ), SELWR( 20 ) * .. * .. Scalars in Common .. INTEGER SELDIM, SELOPT * .. * .. Common blocks .. COMMON / SSLCT / SELOPT, SELDIM, SELVAL, SELWR, SELWI * .. * .. External Functions .. REAL SLAMCH EXTERNAL SLAMCH * .. * .. External Subroutines .. EXTERNAL SGET24, SLABAD, SLASUM, SLATME, SLATMR, SLATMS, $ SLASET, 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 / * .. * .. Executable Statements .. * PATH( 1: 1 ) = 'Single precision' PATH( 2: 3 ) = 'SX' * * 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( NIUNIT.LE.0 ) THEN INFO = -7 ELSE IF( NOUNIT.LE.0 ) THEN INFO = -8 ELSE IF( LDA.LT.1 .OR. LDA.LT.NMAX ) THEN INFO = -10 ELSE IF( LDVS.LT.1 .OR. LDVS.LT.NMAX ) THEN INFO = -20 ELSE IF( MAX( 3*NMAX, 2*NMAX**2 ).GT.LWORK ) THEN INFO = -24 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'SDRVSX', -INFO ) RETURN END IF * * If nothing to do check on NIUNIT * IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 ) $ GO TO 150 * * More Important constants * UNFL = SLAMCH( 'Safe minimum' ) OVFL = ONE / UNFL CALL SLABAD( UNFL, OVFL ) ULP = SLAMCH( 'Precision' ) ULPINV = ONE / ULP RTULP = SQRT( ULP ) RTULPI = ONE / RTULP * * Loop over sizes, types * NERRS = 0 * DO 140 JSIZE = 1, NSIZES N = NN( JSIZE ) IF( NSIZES.NE.1 ) THEN MTYPES = MIN( MAXTYP, NTYPES ) ELSE MTYPES = MIN( MAXTYP+1, NTYPES ) END IF * DO 130 JTYPE = 1, MTYPES IF( .NOT.DOTYPE( JTYPE ) ) $ GO TO 130 * * 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 SLASET( '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 SLATMS( 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 SLATMS( 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 SLATME( 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 SLATMR( 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 SLATMR( 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 SLATMR( 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 SLASET( 'Full', 2, N, ZERO, ZERO, A, LDA ) CALL SLASET( 'Full', N-3, 1, ZERO, ZERO, A( 3, 1 ), $ LDA ) CALL SLASET( 'Full', N-3, 2, ZERO, ZERO, A( 3, N-1 ), $ LDA ) CALL SLASET( 'Full', 1, N, ZERO, ZERO, A( N, 1 ), $ LDA ) END IF * ELSE IF( ITYPE.EQ.10 ) THEN * * Triangular, random eigenvalues * CALL SLATMR( 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 = 9991 )'Generator', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) RETURN END IF * 90 CONTINUE * * Test for minimal and generous workspace * DO 120 IWK = 1, 2 IF( IWK.EQ.1 ) THEN NNWORK = 3*N ELSE NNWORK = MAX( 3*N, 2*N*N ) END IF NNWORK = MAX( NNWORK, 1 ) * CALL SGET24( .FALSE., JTYPE, THRESH, IOLDSD, NOUNIT, N, $ A, LDA, H, HT, WR, WI, WRT, WIT, WRTMP, $ WITMP, VS, LDVS, VS1, RCDEIN, RCDVIN, NSLCT, $ ISLCT, RESULT, WORK, NNWORK, IWORK, BWORK, $ INFO ) * * Check for RESULT(j) > THRESH * NTEST = 0 NFAIL = 0 DO 100 J = 1, 15 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 WRITE( NOUNIT, FMT = 9994 ) NTESTF = 2 END IF * DO 110 J = 1, 15 IF( RESULT( J ).GE.THRESH ) THEN WRITE( NOUNIT, FMT = 9993 )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 * * Read in data from file to check accuracy of condition estimation * Read input data until N=0 * JTYPE = 0 160 CONTINUE READ( NIUNIT, FMT = *, END = 200 )N, NSLCT IF( N.EQ.0 ) $ GO TO 200 JTYPE = JTYPE + 1 ISEED( 1 ) = JTYPE IF( NSLCT.GT.0 ) $ READ( NIUNIT, FMT = * )( ISLCT( I ), I = 1, NSLCT ) DO 170 I = 1, N READ( NIUNIT, FMT = * )( A( I, J ), J = 1, N ) 170 CONTINUE READ( NIUNIT, FMT = * )RCDEIN, RCDVIN * CALL SGET24( .TRUE., 22, THRESH, ISEED, NOUNIT, N, A, LDA, H, HT, $ WR, WI, WRT, WIT, WRTMP, WITMP, VS, LDVS, VS1, $ RCDEIN, RCDVIN, NSLCT, ISLCT, RESULT, WORK, LWORK, $ IWORK, BWORK, INFO ) * * Check for RESULT(j) > THRESH * NTEST = 0 NFAIL = 0 DO 180 J = 1, 17 IF( RESULT( J ).GE.ZERO ) $ NTEST = NTEST + 1 IF( RESULT( J ).GE.THRESH ) $ NFAIL = NFAIL + 1 180 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 190 J = 1, 17 IF( RESULT( J ).GE.THRESH ) THEN WRITE( NOUNIT, FMT = 9992 )N, JTYPE, J, RESULT( J ) END IF 190 CONTINUE * NERRS = NERRS + NFAIL NTESTT = NTESTT + NTEST GO TO 160 200 CONTINUE * * Summary * CALL SLASUM( PATH, NOUNIT, NERRS, NTESTT ) * 9999 FORMAT( / 1X, A3, ' -- Real Schur Form Decomposition Expert ', $ 'Driver', / ' Matrix types (see SDRVSX 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. ', / ) 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 what else computed (sort),', $ ' 1/ulp otherwise', / $ ' 12 = 0 if WR, WI same no matter what else computed ', $ '(sort), 1/ulp otherwise', / $ ' 13 = 0 if sorting succesful, 1/ulp otherwise', $ / ' 14 = 0 if RCONDE same no matter what else computed,', $ ' 1/ulp otherwise', / $ ' 15 = 0 if RCONDv same no matter what else computed,', $ ' 1/ulp otherwise', / $ ' 16 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE),', $ / ' 17 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV),' ) 9993 FORMAT( ' N=', I5, ', IWK=', I2, ', seed=', 4( I4, ',' ), $ ' type ', I2, ', test(', I2, ')=', G10.3 ) 9992 FORMAT( ' N=', I5, ', input example =', I3, ', test(', I2, ')=', $ G10.3 ) 9991 FORMAT( ' SDRVSX: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', $ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' ) * RETURN * * End of SDRVSX * END |