dchkhs.f

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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.
*