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SUBROUTINE DCHKHS( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
$ NOUNIT, A, LDA, H, T1, T2, U, LDU, Z, UZ, WR1, $ WI1, WR3, WI3, EVECTL, EVECTR, EVECTY, EVECTX, $ UU, TAU, WORK, NWORK, IWORK, SELECT, RESULT, $ INFO ) * * -- LAPACK test routine (version 3.1.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * February 2007 * * .. Scalar Arguments .. INTEGER INFO, LDA, LDU, NOUNIT, NSIZES, NTYPES, NWORK DOUBLE PRECISION THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ), SELECT( * ) INTEGER ISEED( 4 ), IWORK( * ), NN( * ) DOUBLE PRECISION A( LDA, * ), EVECTL( LDU, * ), $ EVECTR( LDU, * ), EVECTX( LDU, * ), $ EVECTY( LDU, * ), H( LDA, * ), RESULT( 14 ), $ T1( LDA, * ), T2( LDA, * ), TAU( * ), $ U( LDU, * ), UU( LDU, * ), UZ( LDU, * ), $ WI1( * ), WI3( * ), WORK( * ), WR1( * ), $ WR3( * ), Z( LDU, * ) * .. * * Purpose * ======= * * DCHKHS checks the nonsymmetric eigenvalue problem routines. * * DGEHRD factors A as U H U' , where ' means transpose, * H is hessenberg, and U is an orthogonal matrix. * * DORGHR generates the orthogonal matrix U. * * DORMHR multiplies a matrix by the orthogonal matrix U. * * DHSEQR factors H as Z T Z' , where Z is orthogonal and * T is "quasi-triangular", and the eigenvalue vector W. * * DTREVC computes the left and right eigenvector matrices * L and R for T. * * DHSEIN computes the left and right eigenvector matrices * Y and X for H, using inverse iteration. * * When DCHKHS 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, 14 * tests will be performed: * * (1) | A - U H U**T | / ( |A| n ulp ) * * (2) | I - UU**T | / ( n ulp ) * * (3) | H - Z T Z**T | / ( |H| n ulp ) * * (4) | I - ZZ**T | / ( n ulp ) * * (5) | A - UZ H (UZ)**T | / ( |A| n ulp ) * * (6) | I - UZ (UZ)**T | / ( n ulp ) * * (7) | T(Z computed) - T(Z not computed) | / ( |T| ulp ) * * (8) | W(Z computed) - W(Z not computed) | / ( |W| ulp ) * * (9) | TR - RW | / ( |T| |R| ulp ) * * (10) | L**H T - W**H L | / ( |T| |L| ulp ) * * (11) | HX - XW | / ( |H| |X| ulp ) * * (12) | Y**H H - W**H Y | / ( |H| |Y| ulp ) * * (13) | AX - XW | / ( |A| |X| ulp ) * * (14) | Y**H A - W**H Y | / ( |A| |Y| ulp ) * * 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 SQRT( overflow threshold ) * (8) Same as (4), but multiplied by SQRT( 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 SQRT( overflow threshold ) * (18) Same as (16), but multiplied by SQRT( underflow threshold ) * * (19) Nonsymmetric matrix with random entries chosen from (-1,1). * (20) Same as (19), but multiplied by SQRT( overflow threshold ) * (21) Same as (19), but multiplied by SQRT( underflow threshold ) * * Arguments * ========== * * NSIZES - INTEGER * The number of sizes of matrices to use. If it is zero, * DCHKHS does nothing. It must be at least zero. * Not modified. * * NN - 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. * Not modified. * * NTYPES - INTEGER * The number of elements in DOTYPE. If it is zero, DCHKHS * 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. . * Not modified. * * DOTYPE - 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. * Not modified. * * ISEED - 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 DCHKHS to continue the same random number * sequence. * Modified. * * THRESH - 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. * Not modified. * * NOUNIT - INTEGER * The FORTRAN unit number for printing out error messages * (e.g., if a routine returns IINFO not equal to 0.) * Not modified. * * A - 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. * Modified. * * LDA - INTEGER * The leading dimension of A, H, T1 and T2. It must be at * least 1 and at least max( NN ). * Not modified. * * H - DOUBLE PRECISION array, dimension (LDA,max(NN)) * The upper hessenberg matrix computed by DGEHRD. On exit, * H contains the Hessenberg form of the matrix in A. * Modified. * * T1 - DOUBLE PRECISION array, dimension (LDA,max(NN)) * The Schur (="quasi-triangular") matrix computed by DHSEQR * if Z is computed. On exit, T1 contains the Schur form of * the matrix in A. * Modified. * * T2 - DOUBLE PRECISION array, dimension (LDA,max(NN)) * The Schur matrix computed by DHSEQR when Z is not computed. * This should be identical to T1. * Modified. * * LDU - INTEGER * The leading dimension of U, Z, UZ and UU. It must be at * least 1 and at least max( NN ). * Not modified. * * U - DOUBLE PRECISION array, dimension (LDU,max(NN)) * The orthogonal matrix computed by DGEHRD. * Modified. * * Z - DOUBLE PRECISION array, dimension (LDU,max(NN)) * The orthogonal matrix computed by DHSEQR. * Modified. * * UZ - DOUBLE PRECISION array, dimension (LDU,max(NN)) * The product of U times Z. * Modified. * * WR1 - DOUBLE PRECISION array, dimension (max(NN)) * WI1 - DOUBLE PRECISION array, dimension (max(NN)) * The real and imaginary parts of the eigenvalues of A, * as computed when Z is computed. * On exit, WR1 + WI1*i are the eigenvalues of the matrix in A. * Modified. * * WR3 - DOUBLE PRECISION array, dimension (max(NN)) * WI3 - DOUBLE PRECISION array, dimension (max(NN)) * Like WR1, WI1, these arrays contain the eigenvalues of A, * but those computed when DHSEQR only computes the * eigenvalues, i.e., not the Schur vectors and no more of the * Schur form than is necessary for computing the * eigenvalues. * Modified. * * EVECTL - DOUBLE PRECISION array, dimension (LDU,max(NN)) * The (upper triangular) left eigenvector matrix for the * matrix in T1. For complex conjugate pairs, the real part * is stored in one row and the imaginary part in the next. * Modified. * * EVEZTR - DOUBLE PRECISION array, dimension (LDU,max(NN)) * The (upper triangular) right eigenvector matrix for the * matrix in T1. For complex conjugate pairs, the real part * is stored in one column and the imaginary part in the next. * Modified. * * EVECTY - DOUBLE PRECISION array, dimension (LDU,max(NN)) * The left eigenvector matrix for the * matrix in H. For complex conjugate pairs, the real part * is stored in one row and the imaginary part in the next. * Modified. * * EVECTX - DOUBLE PRECISION array, dimension (LDU,max(NN)) * The right eigenvector matrix for the * matrix in H. For complex conjugate pairs, the real part * is stored in one column and the imaginary part in the next. * Modified. * * UU - DOUBLE PRECISION array, dimension (LDU,max(NN)) * Details of the orthogonal matrix computed by DGEHRD. * Modified. * * TAU - DOUBLE PRECISION array, dimension(max(NN)) * Further details of the orthogonal matrix computed by DGEHRD. * Modified. * * WORK - DOUBLE PRECISION array, dimension (NWORK) * Workspace. * Modified. * * NWORK - INTEGER * The number of entries in WORK. NWORK >= 4*NN(j)*NN(j) + 2. * * IWORK - INTEGER array, dimension (max(NN)) * Workspace. * Modified. * * SELECT - LOGICAL array, dimension (max(NN)) * Workspace. * Modified. * * RESULT - DOUBLE PRECISION array, dimension (14) * The values computed by the fourteen tests described above. * The values are currently limited to 1/ulp, to avoid * overflow. * Modified. * * INFO - 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) ). * -14: LDU < 1 or LDU < NMAX. * -28: NWORK too small. * If DLATMR, SLATMS, or SLATME returns an error code, the * absolute value of it is returned. * If 1, then DHSEQR could not find all the shifts. * If 2, then the EISPACK code (for small blocks) failed. * If >2, then 30*N iterations were not enough to find an * eigenvalue or to decompose the problem. * Modified. * *----------------------------------------------------------------------- * * Some Local Variables and Parameters: * ---- ----- --------- --- ---------- * * ZERO, ONE Real 0 and 1. * MAXTYP The number of types defined. * MTEST The number of tests defined: care must be taken * that (1) the size of RESULT, (2) the number of * tests actually performed, and (3) MTEST agree. * NTEST The number of tests performed on this matrix * so far. This should be less than MTEST, and * equal to it by the last test. It will be less * if any of the routines being tested indicates * that it could not compute the matrices that * would be tested. * NMAX Largest value in NN. * NMATS The number of matrices generated so far. * NERRS The number of tests which have exceeded THRESH * so far (computed by DLAFTS). * 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. * RTOVFL, RTUNFL, * 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) Selects 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, MATCH INTEGER I, IHI, IINFO, ILO, IMODE, IN, ITYPE, J, JCOL, $ JJ, JSIZE, JTYPE, K, MTYPES, N, N1, NERRS, $ NMATS, NMAX, NSELC, NSELR, NTEST, NTESTT DOUBLE PRECISION ANINV, ANORM, COND, CONDS, OVFL, RTOVFL, RTULP, $ RTULPI, RTUNFL, TEMP1, TEMP2, ULP, ULPINV, UNFL * .. * .. Local Arrays .. CHARACTER ADUMMA( 1 ) INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ), $ KMAGN( MAXTYP ), KMODE( MAXTYP ), $ KTYPE( MAXTYP ) DOUBLE PRECISION DUMMA( 6 ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. External Subroutines .. EXTERNAL DCOPY, DGEHRD, DGEMM, DGET10, DGET22, DHSEIN, $ DHSEQR, DHST01, DLABAD, DLACPY, DLAFTS, DLASET, $ DLASUM, DLATME, DLATMR, DLATMS, DORGHR, DORMHR, $ DTREVC, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, 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 .. * * Check for errors * NTESTT = 0 INFO = 0 * 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( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN INFO = -9 ELSE IF( LDU.LE.1 .OR. LDU.LT.NMAX ) THEN INFO = -14 ELSE IF( 4*NMAX*NMAX+2.GT.NWORK ) THEN INFO = -28 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DCHKHS', -INFO ) RETURN END IF * * Quick return if possible * IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 ) $ RETURN * * More important constants * UNFL = DLAMCH( 'Safe minimum' ) OVFL = DLAMCH( 'Overflow' ) CALL DLABAD( UNFL, OVFL ) ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' ) ULPINV = ONE / ULP RTUNFL = SQRT( UNFL ) RTOVFL = SQRT( OVFL ) RTULP = SQRT( ULP ) RTULPI = ONE / RTULP * * Loop over sizes, types * NERRS = 0 NMATS = 0 * DO 270 JSIZE = 1, NSIZES N = NN( JSIZE ) IF( N.EQ.0 ) $ GO TO 270 N1 = MAX( 1, N ) ANINV = ONE / DBLE( N1 ) * IF( NSIZES.NE.1 ) THEN MTYPES = MIN( MAXTYP, NTYPES ) ELSE MTYPES = MIN( MAXTYP+1, NTYPES ) END IF * DO 260 JTYPE = 1, MTYPES IF( .NOT.DOTYPE( JTYPE ) ) $ GO TO 260 NMATS = NMATS + 1 NTEST = 0 * * Save ISEED in case of an error. * DO 20 J = 1, 4 IOLDSD( J ) = ISEED( J ) 20 CONTINUE * * Initialize RESULT * DO 30 J = 1, 14 RESULT( J ) = ZERO 30 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 100 * ITYPE = KTYPE( JTYPE ) IMODE = KMODE( JTYPE ) * * Compute norm * GO TO ( 40, 50, 60 )KMAGN( JTYPE ) * 40 CONTINUE ANORM = ONE GO TO 70 * 50 CONTINUE ANORM = ( RTOVFL*ULP )*ANINV GO TO 70 * 60 CONTINUE ANORM = RTUNFL*N*ULPINV GO TO 70 * 70 CONTINUE * CALL DLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA ) IINFO = 0 COND = ULPINV * * Special Matrices * IF( ITYPE.EQ.1 ) THEN * * Zero * IINFO = 0 * ELSE IF( ITYPE.EQ.2 ) THEN * * Identity * DO 80 JCOL = 1, N A( JCOL, JCOL ) = ANORM 80 CONTINUE * ELSE IF( ITYPE.EQ.3 ) THEN * * Jordan Block * DO 90 JCOL = 1, N A( JCOL, JCOL ) = ANORM IF( JCOL.GT.1 ) $ A( JCOL, JCOL-1 ) = ONE 90 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 ) * 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 = 9999 )'Generator', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) RETURN END IF * 100 CONTINUE * * Call DGEHRD to compute H and U, do tests. * CALL DLACPY( ' ', N, N, A, LDA, H, LDA ) * NTEST = 1 * ILO = 1 IHI = N * CALL DGEHRD( N, ILO, IHI, H, LDA, WORK, WORK( N+1 ), $ NWORK-N, IINFO ) * IF( IINFO.NE.0 ) THEN RESULT( 1 ) = ULPINV WRITE( NOUNIT, FMT = 9999 )'DGEHRD', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) GO TO 250 END IF * DO 120 J = 1, N - 1 UU( J+1, J ) = ZERO DO 110 I = J + 2, N U( I, J ) = H( I, J ) UU( I, J ) = H( I, J ) H( I, J ) = ZERO 110 CONTINUE 120 CONTINUE CALL DCOPY( N-1, WORK, 1, TAU, 1 ) CALL DORGHR( N, ILO, IHI, U, LDU, WORK, WORK( N+1 ), $ NWORK-N, IINFO ) NTEST = 2 * CALL DHST01( N, ILO, IHI, A, LDA, H, LDA, U, LDU, WORK, $ NWORK, RESULT( 1 ) ) * * Call DHSEQR to compute T1, T2 and Z, do tests. * * Eigenvalues only (WR3,WI3) * CALL DLACPY( ' ', N, N, H, LDA, T2, LDA ) NTEST = 3 RESULT( 3 ) = ULPINV * CALL DHSEQR( 'E', 'N', N, ILO, IHI, T2, LDA, WR3, WI3, UZ, $ LDU, WORK, NWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'DHSEQR(E)', IINFO, N, JTYPE, $ IOLDSD IF( IINFO.LE.N+2 ) THEN INFO = ABS( IINFO ) GO TO 250 END IF END IF * * Eigenvalues (WR1,WI1) and Full Schur Form (T2) * CALL DLACPY( ' ', N, N, H, LDA, T2, LDA ) * CALL DHSEQR( 'S', 'N', N, ILO, IHI, T2, LDA, WR1, WI1, UZ, $ LDU, WORK, NWORK, IINFO ) IF( IINFO.NE.0 .AND. IINFO.LE.N+2 ) THEN WRITE( NOUNIT, FMT = 9999 )'DHSEQR(S)', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) GO TO 250 END IF * * Eigenvalues (WR1,WI1), Schur Form (T1), and Schur vectors * (UZ) * CALL DLACPY( ' ', N, N, H, LDA, T1, LDA ) CALL DLACPY( ' ', N, N, U, LDU, UZ, LDA ) * CALL DHSEQR( 'S', 'V', N, ILO, IHI, T1, LDA, WR1, WI1, UZ, $ LDU, WORK, NWORK, IINFO ) IF( IINFO.NE.0 .AND. IINFO.LE.N+2 ) THEN WRITE( NOUNIT, FMT = 9999 )'DHSEQR(V)', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) GO TO 250 END IF * * Compute Z = U' UZ * CALL DGEMM( 'T', 'N', N, N, N, ONE, U, LDU, UZ, LDU, ZERO, $ Z, LDU ) NTEST = 8 * * Do Tests 3: | H - Z T Z' | / ( |H| n ulp ) * and 4: | I - Z Z' | / ( n ulp ) * CALL DHST01( N, ILO, IHI, H, LDA, T1, LDA, Z, LDU, WORK, $ NWORK, RESULT( 3 ) ) * * Do Tests 5: | A - UZ T (UZ)' | / ( |A| n ulp ) * and 6: | I - UZ (UZ)' | / ( n ulp ) * CALL DHST01( N, ILO, IHI, A, LDA, T1, LDA, UZ, LDU, WORK, $ NWORK, RESULT( 5 ) ) * * Do Test 7: | T2 - T1 | / ( |T| n ulp ) * CALL DGET10( N, N, T2, LDA, T1, LDA, WORK, RESULT( 7 ) ) * * Do Test 8: | W3 - W1 | / ( max(|W1|,|W3|) ulp ) * TEMP1 = ZERO TEMP2 = ZERO DO 130 J = 1, N TEMP1 = MAX( TEMP1, ABS( WR1( J ) )+ABS( WI1( J ) ), $ ABS( WR3( J ) )+ABS( WI3( J ) ) ) TEMP2 = MAX( TEMP2, ABS( WR1( J )-WR3( J ) )+ $ ABS( WR1( J )-WR3( J ) ) ) 130 CONTINUE * RESULT( 8 ) = TEMP2 / MAX( UNFL, ULP*MAX( TEMP1, TEMP2 ) ) * * Compute the Left and Right Eigenvectors of T * * Compute the Right eigenvector Matrix: * NTEST = 9 RESULT( 9 ) = ULPINV * * Select last max(N/4,1) real, max(N/4,1) complex eigenvectors * NSELC = 0 NSELR = 0 J = N 140 CONTINUE IF( WI1( J ).EQ.ZERO ) THEN IF( NSELR.LT.MAX( N / 4, 1 ) ) THEN NSELR = NSELR + 1 SELECT( J ) = .TRUE. ELSE SELECT( J ) = .FALSE. END IF J = J - 1 ELSE IF( NSELC.LT.MAX( N / 4, 1 ) ) THEN NSELC = NSELC + 1 SELECT( J ) = .TRUE. SELECT( J-1 ) = .FALSE. ELSE SELECT( J ) = .FALSE. SELECT( J-1 ) = .FALSE. END IF J = J - 2 END IF IF( J.GT.0 ) $ GO TO 140 * CALL DTREVC( 'Right', 'All', SELECT, N, T1, LDA, DUMMA, LDU, $ EVECTR, LDU, N, IN, WORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'DTREVC(R,A)', IINFO, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) GO TO 250 END IF * * Test 9: | TR - RW | / ( |T| |R| ulp ) * CALL DGET22( 'N', 'N', 'N', N, T1, LDA, EVECTR, LDU, WR1, $ WI1, WORK, DUMMA( 1 ) ) RESULT( 9 ) = DUMMA( 1 ) IF( DUMMA( 2 ).GT.THRESH ) THEN WRITE( NOUNIT, FMT = 9998 )'Right', 'DTREVC', $ DUMMA( 2 ), N, JTYPE, IOLDSD END IF * * Compute selected right eigenvectors and confirm that * they agree with previous right eigenvectors * CALL DTREVC( 'Right', 'Some', SELECT, N, T1, LDA, DUMMA, $ LDU, EVECTL, LDU, N, IN, WORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'DTREVC(R,S)', IINFO, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) GO TO 250 END IF * K = 1 MATCH = .TRUE. DO 170 J = 1, N IF( SELECT( J ) .AND. WI1( J ).EQ.ZERO ) THEN DO 150 JJ = 1, N IF( EVECTR( JJ, J ).NE.EVECTL( JJ, K ) ) THEN MATCH = .FALSE. GO TO 180 END IF 150 CONTINUE K = K + 1 ELSE IF( SELECT( J ) .AND. WI1( J ).NE.ZERO ) THEN DO 160 JJ = 1, N IF( EVECTR( JJ, J ).NE.EVECTL( JJ, K ) .OR. $ EVECTR( JJ, J+1 ).NE.EVECTL( JJ, K+1 ) ) THEN MATCH = .FALSE. GO TO 180 END IF 160 CONTINUE K = K + 2 END IF 170 CONTINUE 180 CONTINUE IF( .NOT.MATCH ) $ WRITE( NOUNIT, FMT = 9997 )'Right', 'DTREVC', N, JTYPE, $ IOLDSD * * Compute the Left eigenvector Matrix: * NTEST = 10 RESULT( 10 ) = ULPINV CALL DTREVC( 'Left', 'All', SELECT, N, T1, LDA, EVECTL, LDU, $ DUMMA, LDU, N, IN, WORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'DTREVC(L,A)', IINFO, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) GO TO 250 END IF * * Test 10: | LT - WL | / ( |T| |L| ulp ) * CALL DGET22( 'Trans', 'N', 'Conj', N, T1, LDA, EVECTL, LDU, $ WR1, WI1, WORK, DUMMA( 3 ) ) RESULT( 10 ) = DUMMA( 3 ) IF( DUMMA( 4 ).GT.THRESH ) THEN WRITE( NOUNIT, FMT = 9998 )'Left', 'DTREVC', DUMMA( 4 ), $ N, JTYPE, IOLDSD END IF * * Compute selected left eigenvectors and confirm that * they agree with previous left eigenvectors * CALL DTREVC( 'Left', 'Some', SELECT, N, T1, LDA, EVECTR, $ LDU, DUMMA, LDU, N, IN, WORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'DTREVC(L,S)', IINFO, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) GO TO 250 END IF * K = 1 MATCH = .TRUE. DO 210 J = 1, N IF( SELECT( J ) .AND. WI1( J ).EQ.ZERO ) THEN DO 190 JJ = 1, N IF( EVECTL( JJ, J ).NE.EVECTR( JJ, K ) ) THEN MATCH = .FALSE. GO TO 220 END IF 190 CONTINUE K = K + 1 ELSE IF( SELECT( J ) .AND. WI1( J ).NE.ZERO ) THEN DO 200 JJ = 1, N IF( EVECTL( JJ, J ).NE.EVECTR( JJ, K ) .OR. $ EVECTL( JJ, J+1 ).NE.EVECTR( JJ, K+1 ) ) THEN MATCH = .FALSE. GO TO 220 END IF 200 CONTINUE K = K + 2 END IF 210 CONTINUE 220 CONTINUE IF( .NOT.MATCH ) $ WRITE( NOUNIT, FMT = 9997 )'Left', 'DTREVC', N, JTYPE, $ IOLDSD * * Call DHSEIN for Right eigenvectors of H, do test 11 * NTEST = 11 RESULT( 11 ) = ULPINV DO 230 J = 1, N SELECT( J ) = .TRUE. 230 CONTINUE * CALL DHSEIN( 'Right', 'Qr', 'Ninitv', SELECT, N, H, LDA, $ WR3, WI3, DUMMA, LDU, EVECTX, LDU, N1, IN, $ WORK, IWORK, IWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'DHSEIN(R)', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) IF( IINFO.LT.0 ) $ GO TO 250 ELSE * * Test 11: | HX - XW | / ( |H| |X| ulp ) * * (from inverse iteration) * CALL DGET22( 'N', 'N', 'N', N, H, LDA, EVECTX, LDU, WR3, $ WI3, WORK, DUMMA( 1 ) ) IF( DUMMA( 1 ).LT.ULPINV ) $ RESULT( 11 ) = DUMMA( 1 )*ANINV IF( DUMMA( 2 ).GT.THRESH ) THEN WRITE( NOUNIT, FMT = 9998 )'Right', 'DHSEIN', $ DUMMA( 2 ), N, JTYPE, IOLDSD END IF END IF * * Call DHSEIN for Left eigenvectors of H, do test 12 * NTEST = 12 RESULT( 12 ) = ULPINV DO 240 J = 1, N SELECT( J ) = .TRUE. 240 CONTINUE * CALL DHSEIN( 'Left', 'Qr', 'Ninitv', SELECT, N, H, LDA, WR3, $ WI3, EVECTY, LDU, DUMMA, LDU, N1, IN, WORK, $ IWORK, IWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'DHSEIN(L)', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) IF( IINFO.LT.0 ) $ GO TO 250 ELSE * * Test 12: | YH - WY | / ( |H| |Y| ulp ) * * (from inverse iteration) * CALL DGET22( 'C', 'N', 'C', N, H, LDA, EVECTY, LDU, WR3, $ WI3, WORK, DUMMA( 3 ) ) IF( DUMMA( 3 ).LT.ULPINV ) $ RESULT( 12 ) = DUMMA( 3 )*ANINV IF( DUMMA( 4 ).GT.THRESH ) THEN WRITE( NOUNIT, FMT = 9998 )'Left', 'DHSEIN', $ DUMMA( 4 ), N, JTYPE, IOLDSD END IF END IF * * Call DORMHR for Right eigenvectors of A, do test 13 * NTEST = 13 RESULT( 13 ) = ULPINV * CALL DORMHR( 'Left', 'No transpose', N, N, ILO, IHI, UU, $ LDU, TAU, EVECTX, LDU, WORK, NWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'DORMHR(R)', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) IF( IINFO.LT.0 ) $ GO TO 250 ELSE * * Test 13: | AX - XW | / ( |A| |X| ulp ) * * (from inverse iteration) * CALL DGET22( 'N', 'N', 'N', N, A, LDA, EVECTX, LDU, WR3, $ WI3, WORK, DUMMA( 1 ) ) IF( DUMMA( 1 ).LT.ULPINV ) $ RESULT( 13 ) = DUMMA( 1 )*ANINV END IF * * Call DORMHR for Left eigenvectors of A, do test 14 * NTEST = 14 RESULT( 14 ) = ULPINV * CALL DORMHR( 'Left', 'No transpose', N, N, ILO, IHI, UU, $ LDU, TAU, EVECTY, LDU, WORK, NWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'DORMHR(L)', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) IF( IINFO.LT.0 ) $ GO TO 250 ELSE * * Test 14: | YA - WY | / ( |A| |Y| ulp ) * * (from inverse iteration) * CALL DGET22( 'C', 'N', 'C', N, A, LDA, EVECTY, LDU, WR3, $ WI3, WORK, DUMMA( 3 ) ) IF( DUMMA( 3 ).LT.ULPINV ) $ RESULT( 14 ) = DUMMA( 3 )*ANINV END IF * * End of Loop -- Check for RESULT(j) > THRESH * 250 CONTINUE * NTESTT = NTESTT + NTEST CALL DLAFTS( 'DHS', N, N, JTYPE, NTEST, RESULT, IOLDSD, $ THRESH, NOUNIT, NERRS ) * 260 CONTINUE 270 CONTINUE * * Summary * CALL DLASUM( 'DHS', NOUNIT, NERRS, NTESTT ) * RETURN * 9999 FORMAT( ' DCHKHS: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', $ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' ) 9998 FORMAT( ' DCHKHS: ', A, ' Eigenvectors from ', A, ' incorrectly ', $ 'normalized.', / ' Bits of error=', 0P, G10.3, ',', 9X, $ 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, $ ')' ) 9997 FORMAT( ' DCHKHS: Selected ', A, ' Eigenvectors from ', A, $ ' do not match other eigenvectors ', 9X, 'N=', I6, $ ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' ) * * End of DCHKHS * END |