dchkhs.f - Man Page

TESTING/EIG/dchkhs.f

Synopsis

Functions/Subroutines

subroutine dchkhs (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a, lda, h, t1, t2, u, ldu, z, uz, wr1, wi1, wr2, wi2, wr3, wi3, evectl, evectr, evecty, evectx, uu, tau, work, nwork, iwork, select, result, info)
DCHKHS

Function/Subroutine Documentation

subroutine dchkhs (integer nsizes, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, double precision thresh, integer nounit, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( lda, * ) h, double precision, dimension( lda, * ) t1, double precision, dimension( lda, * ) t2, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( ldu, * ) z, double precision, dimension( ldu, * ) uz, double precision, dimension( * ) wr1, double precision, dimension( * ) wi1, double precision, dimension( * ) wr2, double precision, dimension( * ) wi2, double precision, dimension( * ) wr3, double precision, dimension( * ) wi3, double precision, dimension( ldu, * ) evectl, double precision, dimension( ldu, * ) evectr, double precision, dimension( ldu, * ) evecty, double precision, dimension( ldu, * ) evectx, double precision, dimension( ldu, * ) uu, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer nwork, integer, dimension( * ) iwork, logical, dimension( * ) select, double precision, dimension( 16 ) result, integer info)

DCHKHS

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. L is lower quasi-triangular, and R is
            upper quasi-triangular.

            DHSEIN computes the left and right eigenvector matrices
            Y and X for H, using inverse iteration.

            DTREVC3 computes left and right eigenvector matrices
            from a Schur matrix T and backtransforms them with Z
            to eigenvector matrices L and R for A. L and R are
            GE matrices.

    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, 16
    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 )

    (15)    | AR - RW | / ( |A| |R| ulp )

    (16)    | LA - WL | / ( |A| |L| 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 )
  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.

  WR2    - DOUBLE PRECISION array, dimension (max(NN))
  WI2    - DOUBLE PRECISION array, dimension (max(NN))
           The real and imaginary parts of the eigenvalues of A,
           as computed when T is computed but not Z.
           On exit, WR2 + WI2*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 (16)
           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.)
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 417 of file dchkhs.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page dchkhs(3) is an alias of dchkhs.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK