TESTING/MATGEN/zlatmr.f(3)

NAME
TESTING/MATGEN/zlatmr.f

SYNOPSIS

  Functions/Subroutines
subroutine zlatmr (m, n, dist, iseed, sym, d, mode, cond, dmax, rsign, grade, dl, model, condl, dr, moder, condr, pivtng, ipivot, kl, ku, sparse, anorm, pack, a, lda, iwork, info)
ZLATMR

Function/Subroutine Documentation

  subroutine zlatmr (integer m, integer n, character dist, integer, dimension( 4 ) iseed, character sym, complex*16, dimension( * ) d, integer mode, double precision cond, complex*16 dmax, character rsign, character grade, complex*16, dimension( * ) dl, integer model, double precision condl, complex*16, dimension( * ) dr, integer moder, double precision condr, character pivtng, integer, dimension( * ) ipivot, integer kl, integer ku, double precision sparse, double precision anorm, character pack, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) iwork, integer info)

ZLATMR

Purpose:

        ZLATMR generates random matrices of various types for testing
        LAPACK programs.
        ZLATMR operates by applying the following sequence of
        operations:
          Generate a matrix A with random entries of distribution DIST
             which is symmetric if SYM='S', Hermitian if SYM='H', and
             nonsymmetric if SYM='N'.
          Set the diagonal to D, where D may be input or
             computed according to MODE, COND, DMAX and RSIGN
             as described below.
          Grade the matrix, if desired, from the left and/or right
             as specified by GRADE. The inputs DL, MODEL, CONDL, DR,
             MODER and CONDR also determine the grading as described
             below.
          Permute, if desired, the rows and/or columns as specified by
             PIVTNG and IPIVOT.
          Set random entries to zero, if desired, to get a random sparse
             matrix as specified by SPARSE.
          Make A a band matrix, if desired, by zeroing out the matrix
             outside a band of lower bandwidth KL and upper bandwidth KU.
          Scale A, if desired, to have maximum entry ANORM.
          Pack the matrix if desired. Options specified by PACK are:
             no packing
             zero out upper half (if symmetric or Hermitian)
             zero out lower half (if symmetric or Hermitian)
             store the upper half columnwise (if symmetric or Hermitian
                 or square upper triangular)
             store the lower half columnwise (if symmetric or Hermitian
                 or square lower triangular)
                 same as upper half rowwise if symmetric
                 same as conjugate upper half rowwise if Hermitian
             store the lower triangle in banded format
                 (if symmetric or Hermitian)
             store the upper triangle in banded format
                 (if symmetric or Hermitian)
             store the entire matrix in banded format
        Note: If two calls to ZLATMR differ only in the PACK parameter,
              they will generate mathematically equivalent matrices.
              If two calls to ZLATMR both have full bandwidth (KL = M-1
              and KU = N-1), and differ only in the PIVTNG and PACK
              parameters, then the matrices generated will differ only
              in the order of the rows and/or columns, and otherwise
              contain the same data. This consistency cannot be and
              is not maintained with less than full bandwidth.

Parameters
    M

              M is INTEGER
               Number of rows of A. Not modified.

    N

              N is INTEGER
               Number of columns of A. Not modified.

    DIST

              DIST is CHARACTER*1
               On entry, DIST specifies the type of distribution to be used
               to generate a random matrix .
               'U' => real and imaginary parts are independent
                      UNIFORM( 0, 1 )  ( 'U' for uniform )
               'S' => real and imaginary parts are independent
                      UNIFORM( -1, 1 ) ( 'S' for symmetric )
               'N' => real and imaginary parts are independent
                      NORMAL( 0, 1 )   ( 'N' for normal )
               'D' => uniform on interior of unit disk ( 'D' for disk )
               Not modified.

    ISEED

              ISEED is INTEGER array, dimension (4)
               On entry ISEED specifies the seed of the random number
               generator. They should lie between 0 and 4095 inclusive,
               and ISEED(4) should 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 ZLATMR
               to continue the same random number sequence.
               Changed on exit.

    SYM

              SYM is CHARACTER*1
               If SYM='S', generated matrix is symmetric.
               If SYM='H', generated matrix is Hermitian.
               If SYM='N', generated matrix is nonsymmetric.
               Not modified.

    D

              D is COMPLEX*16 array, dimension (min(M,N))
               On entry this array specifies the diagonal entries
               of the diagonal of A.  D may either be specified
               on entry, or set according to MODE and COND as described
               below. If the matrix is Hermitian, the real part of D
               will be taken. May be changed on exit if MODE is nonzero.

    MODE

              MODE is INTEGER
               On entry describes how D is to be used:
               MODE = 0 means use D as input
               MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND
               MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND
               MODE = 3 sets D(I)=COND**(-(I-1)/(N-1))
               MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND)
               MODE = 5 sets D to random numbers in the range
                        ( 1/COND , 1 ) such that their logarithms
                        are uniformly distributed.
               MODE = 6 set D to random numbers from same distribution
                        as the rest of the matrix.
               MODE < 0 has the same meaning as ABS(MODE), except that
                  the order of the elements of D is reversed.
               Thus if MODE is positive, D has entries ranging from
                  1 to 1/COND, if negative, from 1/COND to 1,
               Not modified.

    COND

              COND is DOUBLE PRECISION
               On entry, used as described under MODE above.
               If used, it must be >= 1. Not modified.

    DMAX

              DMAX is COMPLEX*16
               If MODE neither -6, 0 nor 6, the diagonal is scaled by
               DMAX / max(abs(D(i))), so that maximum absolute entry
               of diagonal is abs(DMAX). If DMAX is complex (or zero),
               diagonal will be scaled by a complex number (or zero).

    RSIGN

              RSIGN is CHARACTER*1
               If MODE neither -6, 0 nor 6, specifies sign of diagonal
               as follows:
               'T' => diagonal entries are multiplied by a random complex
                      number uniformly distributed with absolute value 1
               'F' => diagonal unchanged
               Not modified.

    GRADE

              GRADE is CHARACTER*1
               Specifies grading of matrix as follows:
               'N'  => no grading
               'L'  => matrix premultiplied by diag( DL )
                       (only if matrix nonsymmetric)
               'R'  => matrix postmultiplied by diag( DR )
                       (only if matrix nonsymmetric)
               'B'  => matrix premultiplied by diag( DL ) and
                             postmultiplied by diag( DR )
                       (only if matrix nonsymmetric)
               'H'  => matrix premultiplied by diag( DL ) and
                             postmultiplied by diag( CONJG(DL) )
                       (only if matrix Hermitian or nonsymmetric)
               'S'  => matrix premultiplied by diag( DL ) and
                             postmultiplied by diag( DL )
                       (only if matrix symmetric or nonsymmetric)
               'E'  => matrix premultiplied by diag( DL ) and
                             postmultiplied by inv( diag( DL ) )
                             ( 'S' for similarity )
                       (only if matrix nonsymmetric)
                       Note: if GRADE='S', then M must equal N.
               Not modified.

    DL

              DL is COMPLEX*16 array, dimension (M)
               If MODEL=0, then on entry this array specifies the diagonal
               entries of a diagonal matrix used as described under GRADE
               above. If MODEL is not zero, then DL will be set according
               to MODEL and CONDL, analogous to the way D is set according
               to MODE and COND (except there is no DMAX parameter for DL).
               If GRADE='E', then DL cannot have zero entries.
               Not referenced if GRADE = 'N' or 'R'. Changed on exit.

    MODEL

              MODEL is INTEGER
               This specifies how the diagonal array DL is to be computed,
               just as MODE specifies how D is to be computed.
               Not modified.

    CONDL

              CONDL is DOUBLE PRECISION
               When MODEL is not zero, this specifies the condition number
               of the computed DL.  Not modified.

    DR

              DR is COMPLEX*16 array, dimension (N)
               If MODER=0, then on entry this array specifies the diagonal
               entries of a diagonal matrix used as described under GRADE
               above. If MODER is not zero, then DR will be set according
               to MODER and CONDR, analogous to the way D is set according
               to MODE and COND (except there is no DMAX parameter for DR).
               Not referenced if GRADE = 'N', 'L', 'H' or 'S'.
               Changed on exit.

    MODER

              MODER is INTEGER
               This specifies how the diagonal array DR is to be computed,
               just as MODE specifies how D is to be computed.
               Not modified.

    CONDR

              CONDR is DOUBLE PRECISION
               When MODER is not zero, this specifies the condition number
               of the computed DR.  Not modified.

    PIVTNG

              PIVTNG is CHARACTER*1
               On entry specifies pivoting permutations as follows:
               'N' or ' ' => none.
               'L' => left or row pivoting (matrix must be nonsymmetric).
               'R' => right or column pivoting (matrix must be
                      nonsymmetric).
               'B' or 'F' => both or full pivoting, i.e., on both sides.
                             In this case, M must equal N
               If two calls to ZLATMR both have full bandwidth (KL = M-1
               and KU = N-1), and differ only in the PIVTNG and PACK
               parameters, then the matrices generated will differ only
               in the order of the rows and/or columns, and otherwise
               contain the same data. This consistency cannot be
               maintained with less than full bandwidth.

    IPIVOT

              IPIVOT is INTEGER array, dimension (N or M)
               This array specifies the permutation used.  After the
               basic matrix is generated, the rows, columns, or both
               are permuted.   If, say, row pivoting is selected, ZLATMR
               starts with the *last* row and interchanges the M-th and
               IPIVOT(M)-th rows, then moves to the next-to-last row,
               interchanging the (M-1)-th and the IPIVOT(M-1)-th rows,
               and so on.  In terms of '2-cycles', the permutation is
               (1 IPIVOT(1)) (2 IPIVOT(2)) ... (M IPIVOT(M))
               where the rightmost cycle is applied first.  This is the
               *inverse* of the effect of pivoting in LINPACK.  The idea
               is that factoring (with pivoting) an identity matrix
               which has been inverse-pivoted in this way should
               result in a pivot vector identical to IPIVOT.
               Not referenced if PIVTNG = 'N'. Not modified.

    KL

              KL is INTEGER
               On entry specifies the lower bandwidth of the  matrix. For
               example, KL=0 implies upper triangular, KL=1 implies upper
               Hessenberg, and KL at least M-1 implies the matrix is not
               banded. Must equal KU if matrix is symmetric or Hermitian.
               Not modified.

    KU

              KU is INTEGER
               On entry specifies the upper bandwidth of the  matrix. For
               example, KU=0 implies lower triangular, KU=1 implies lower
               Hessenberg, and KU at least N-1 implies the matrix is not
               banded. Must equal KL if matrix is symmetric or Hermitian.
               Not modified.

    SPARSE

              SPARSE is DOUBLE PRECISION
               On entry specifies the sparsity of the matrix if a sparse
               matrix is to be generated. SPARSE should lie between
               0 and 1. To generate a sparse matrix, for each matrix entry
               a uniform ( 0, 1 ) random number x is generated and
               compared to SPARSE; if x is larger the matrix entry
               is unchanged and if x is smaller the entry is set
               to zero. Thus on the average a fraction SPARSE of the
               entries will be set to zero.
               Not modified.

    ANORM

              ANORM is DOUBLE PRECISION
               On entry specifies maximum entry of output matrix
               (output matrix will by multiplied by a constant so that
               its largest absolute entry equal ANORM)
               if ANORM is nonnegative. If ANORM is negative no scaling
               is done. Not modified.

    PACK

              PACK is CHARACTER*1
               On entry specifies packing of matrix as follows:
               'N' => no packing
               'U' => zero out all subdiagonal entries
                      (if symmetric or Hermitian)
               'L' => zero out all superdiagonal entries
                      (if symmetric or Hermitian)
               'C' => store the upper triangle columnwise
                      (only if matrix symmetric or Hermitian or
                       square upper triangular)
               'R' => store the lower triangle columnwise
                      (only if matrix symmetric or Hermitian or
                       square lower triangular)
                      (same as upper half rowwise if symmetric)
                      (same as conjugate upper half rowwise if Hermitian)
               'B' => store the lower triangle in band storage scheme
                      (only if matrix symmetric or Hermitian)
               'Q' => store the upper triangle in band storage scheme
                      (only if matrix symmetric or Hermitian)
               'Z' => store the entire matrix in band storage scheme
                          (pivoting can be provided for by using this
                          option to store A in the trailing rows of
                          the allocated storage)
               Using these options, the various LAPACK packed and banded
               storage schemes can be obtained:
               GB               - use 'Z'
               PB, HB or TB     - use 'B' or 'Q'
               PP, HP or TP     - use 'C' or 'R'
               If two calls to ZLATMR differ only in the PACK parameter,
               they will generate mathematically equivalent matrices.
               Not modified.

    A

              A is COMPLEX*16 array, dimension (LDA,N)
               On exit A is the desired test matrix. Only those
               entries of A which are significant on output
               will be referenced (even if A is in packed or band
               storage format). The 'unoccupied corners' of A in
               band format will be zeroed out.

    LDA

              LDA is INTEGER
               on entry LDA specifies the first dimension of A as
               declared in the calling program.
               If PACK='N', 'U' or 'L', LDA must be at least max ( 1, M ).
               If PACK='C' or 'R', LDA must be at least 1.
               If PACK='B', or 'Q', LDA must be MIN ( KU+1, N )
               If PACK='Z', LDA must be at least KUU+KLL+1, where
               KUU = MIN ( KU, N-1 ) and KLL = MIN ( KL, M-1 )
               Not modified.

    IWORK

              IWORK is INTEGER array, dimension (N or M)
               Workspace. Not referenced if PIVTNG = 'N'. Changed on exit.

    INFO

              INFO is INTEGER
               Error parameter on exit:
                 0 => normal return
                -1 => M negative or unequal to N and SYM='S' or 'H'
                -2 => N negative
                -3 => DIST illegal string
                -5 => SYM illegal string
                -7 => MODE not in range -6 to 6
                -8 => COND less than 1.0, and MODE neither -6, 0 nor 6
               -10 => MODE neither -6, 0 nor 6 and RSIGN illegal string
               -11 => GRADE illegal string, or GRADE='E' and
                      M not equal to N, or GRADE='L', 'R', 'B', 'S' or 'E'
                      and SYM = 'H', or GRADE='L', 'R', 'B', 'H' or 'E'
                      and SYM = 'S'
               -12 => GRADE = 'E' and DL contains zero
               -13 => MODEL not in range -6 to 6 and GRADE= 'L', 'B', 'H',
                      'S' or 'E'
               -14 => CONDL less than 1.0, GRADE='L', 'B', 'H', 'S' or 'E',
                      and MODEL neither -6, 0 nor 6
               -16 => MODER not in range -6 to 6 and GRADE= 'R' or 'B'
               -17 => CONDR less than 1.0, GRADE='R' or 'B', and
                      MODER neither -6, 0 nor 6
               -18 => PIVTNG illegal string, or PIVTNG='B' or 'F' and
                      M not equal to N, or PIVTNG='L' or 'R' and SYM='S'
                      or 'H'
               -19 => IPIVOT contains out of range number and
                      PIVTNG not equal to 'N'
               -20 => KL negative
               -21 => KU negative, or SYM='S' or 'H' and KU not equal to KL
               -22 => SPARSE not in range 0. to 1.
               -24 => PACK illegal string, or PACK='U', 'L', 'B' or 'Q'
                      and SYM='N', or PACK='C' and SYM='N' and either KL
                      not equal to 0 or N not equal to M, or PACK='R' and
                      SYM='N', and either KU not equal to 0 or N not equal
                      to M
               -26 => LDA too small
                 1 => Error return from ZLATM1 (computing D)
                 2 => Cannot scale diagonal to DMAX (max. entry is 0)
                 3 => Error return from ZLATM1 (computing DL)
                 4 => Error return from ZLATM1 (computing DR)
                 5 => ANORM is positive, but matrix constructed prior to
                      attempting to scale it to have norm ANORM, is zero

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 486 of file zlatmr.f.

Author

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