dlatmr.f

来自「famous linear algebra library (LAPACK) p」· F 代码 · 共 1,101 行 · 第 1/3 页

      SUBROUTINE DLATMR( 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 )
*
*  -- LAPACK test routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
      CHARACTER          DIST, GRADE, PACK, PIVTNG, RSIGN, SYM
      INTEGER            INFO, KL, KU, LDA, M, MODE, MODEL, MODER, N
      DOUBLE PRECISION   ANORM, COND, CONDL, CONDR, DMAX, SPARSE
*     ..
*     .. Array Arguments ..
      INTEGER            IPIVOT( * ), ISEED( 4 ), IWORK( * )
      DOUBLE PRECISION   A( LDA, * ), D( * ), DL( * ), DR( * )
*     ..
*
*  Purpose
*  =======
*
*     DLATMR generates random matrices of various types for testing
*     LAPACK programs.
*
*     DLATMR operates by applying the following sequence of
*     operations:
*
*       Generate a matrix A with random entries of distribution DIST
*          which is symmetric if SYM='S', 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)
*          zero out lower half (if symmetric)
*          store the upper half columnwise (if symmetric or
*              square upper triangular)
*          store the lower half columnwise (if symmetric or
*              square lower triangular)
*              same as upper half rowwise if symmetric
*          store the lower triangle in banded format (if symmetric)
*          store the upper triangle in banded format (if symmetric)
*          store the entire matrix in banded format
*
*     Note: If two calls to DLATMR differ only in the PACK parameter,
*           they will generate mathematically equivalent matrices.
*
*           If two calls to DLATMR 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.
*
*  Arguments
*  =========
*
*  M      - INTEGER
*           Number of rows of A. Not modified.
*
*  N      - INTEGER
*           Number of columns of A. Not modified.
*
*  DIST   - CHARACTER*1
*           On entry, DIST specifies the type of distribution to be used
*           to generate a random matrix .
*           'U' => UNIFORM( 0, 1 )  ( 'U' for uniform )
*           'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric )
*           'N' => NORMAL( 0, 1 )   ( 'N' for normal )
*           Not modified.
*
*  ISEED  - 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 DLATMR
*           to continue the same random number sequence.
*           Changed on exit.
*
*  SYM    - CHARACTER*1
*           If SYM='S' or 'H', generated matrix is symmetric.
*           If SYM='N', generated matrix is nonsymmetric.
*           Not modified.
*
*  D      - DOUBLE PRECISION 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. May be changed on exit if MODE is nonzero.
*
*  MODE   - 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   - DOUBLE PRECISION
*           On entry, used as described under MODE above.
*           If used, it must be >= 1. Not modified.
*
*  DMAX   - DOUBLE PRECISION
*           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 negative (or zero),
*           diagonal will be scaled by a negative number (or zero).
*
*  RSIGN  - CHARACTER*1
*           If MODE neither -6, 0 nor 6, specifies sign of diagonal
*           as follows:
*           'T' => diagonal entries are multiplied by 1 or -1
*                  with probability .5
*           'F' => diagonal unchanged
*           Not modified.
*
*  GRADE  - 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)
*           'S' or 'H'  => matrix premultiplied by diag( DL ) and
*                          postmultiplied by diag( DL )
*                          ('S' for symmetric, or 'H' for Hermitian)
*           'E'  => matrix premultiplied by diag( DL ) and
*                         postmultiplied by inv( diag( DL ) )
*                         ( 'E' for eigenvalue invariance)
*                   (only if matrix nonsymmetric)
*                   Note: if GRADE='E', then M must equal N.
*           Not modified.
*
*  DL     - DOUBLE PRECISION 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  - 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  - DOUBLE PRECISION
*           When MODEL is not zero, this specifies the condition number
*           of the computed DL.  Not modified.
*
*  DR     - DOUBLE PRECISION 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', 'S' or 'E'.
*           Changed on exit.
*
*  MODER  - 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  - DOUBLE PRECISION
*           When MODER is not zero, this specifies the condition number
*           of the computed DR.  Not modified.
*
*  PIVTNG - 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 DLATMR 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 - 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, DLATMR
*           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.
*
*  SPARSE - 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.
*
*  KL     - 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.
*           Not modified.
*
*  KU     - 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.
*           Not modified.
*
*  ANORM  - 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   - CHARACTER*1
*           On entry specifies packing of matrix as follows:
*           'N' => no packing
*           'U' => zero out all subdiagonal entries (if symmetric)
*           'L' => zero out all superdiagonal entries (if symmetric)
*           'C' => store the upper triangle columnwise
*                  (only if matrix symmetric or square upper triangular)
*           'R' => store the lower triangle columnwise
*                  (only if matrix symmetric or square lower triangular)
*                  (same as upper half rowwise if symmetric)
*           'B' => store the lower triangle in band storage scheme
*                  (only if matrix symmetric)
*           'Q' => store the upper triangle in band storage scheme
*                  (only if matrix symmetric)
*           '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, SB or TB     - use 'B' or 'Q'
*           PP, SP or TP     - use 'C' or 'R'
*
*           If two calls to DLATMR differ only in the PACK parameter,
*           they will generate mathematically equivalent matrices.
*           Not modified.
*
*  A      - DOUBLE PRECISION 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    - 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, N-1 )
*           Not modified.
*
*  IWORK  - INTEGER array, dimension ( N or M)
*           Workspace. Not referenced if PIVTNG = 'N'. Changed on exit.
*
*  INFO   - 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' or 'E' and
*                  SYM = 'S' or 'H'
*           -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 DLATM1 (computing D)
*             2 => Cannot scale diagonal to DMAX (max. entry is 0)
*             3 => Error return from DLATM1 (computing DL)
*             4 => Error return from DLATM1 (computing DR)
*             5 => ANORM is positive, but matrix constructed prior to
*                  attempting to scale it to have norm ANORM, is zero
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO
      PARAMETER          ( ZERO = 0.0D0 )
      DOUBLE PRECISION   ONE