UD01CD - SLICOT Library Routine Documentation

## UD01CD

### Reading a sparse matrix polynomial

[Specification] [Arguments] [Method] [References] [Comments] [Example]

Purpose

      To read the elements of a sparse matrix polynomial
                                                     dp-1           dp
         P(s) = P(0) + P(1) * s + . . . + P(dp-1) * s    + P(dp) * s  .

Specification

          SUBROUTINE UD01CD( MP, NP, DP, NIN, P, LDP1, LDP2, INFO )
    C     .. Scalar Arguments ..
          INTEGER           DP, INFO, LDP1, LDP2, MP, NP, NIN
    C     .. Array Arguments ..
          DOUBLE PRECISION  P(LDP1,LDP2,*)

Arguments

Input/Output Parameters

      MP      (input) INTEGER
              The number of rows of the matrix polynomial P(s).
              MP >= 1.

      NP      (input) INTEGER
              The number of columns of the matrix polynomial P(s).
              NP >= 1.

      DP      (input) INTEGER
              The degree of the matrix polynomial P(s).  DP >= 0.

      NIN     (input) INTEGER
              The input channel from which the elements of P(s) are
              read.  NIN >= 0.

      P       (output) DOUBLE PRECISION array, dimension
              (LDP1,LDP2,DP+1)
              The leading MP-by-NP-by-(DP+1) part of this array contains
              the coefficients of the matrix polynomial P(s).
              Specifically, P(i,j,k) contains the coefficient of
              s**(k-1) of the polynomial which is the (i,j)-th element
              of P(s), where i = 1,2,...,MP, j = 1,2,...,NP and
              k = 1,2,...,DP+1.
              The not assigned elements are set to zero.

      LDP1    INTEGER
              The leading dimension of array P.  LDP1 >= MP.

      LDP2    INTEGER
              The second dimension of array P.  LDP2 >= NP.

Error Indicator

      INFO    INTEGER
              = 0:  successful exit;
              < 0:  if INFO = -i, the i-th argument had an illegal
                    value;
              = 1 : if a row index i is read with i < 1 or i > MP or
                    a column index j is read with j < 1 or j > NP or
                    a coefficient degree d is read with d < 0 or
                    d > DP + 1. This is a warning.

Method

      First, the elements P(i,j,k) with 1 <= i <= MP, 1 <= j <= NP and
      1 <= k <= DP + 1 are set to zero. Next the nonzero (polynomial)
      elements are read from the input file NIN. Each nonzero element is
      given by the values i, j, d, P(i,j,k), k = 1, ..., d+1, where d is
      the degree and P(i,j,k) is the coefficient of s**(k-1) in the
      (i,j)-th element of P(s), i.e., let
                                                               d
          P   (s) = P   (0) + P   (1) * s + . . . + P   (d) * s
           i,j       i,j       i,j                   i,j

      be the nonzero (i,j)-th element of the matrix polynomial P(s).

      Then P(i,j,k) corresponds to coefficient P   (k-1), k = 1,...,d+1.
                                                i,j
      For each nonzero element, the values i, j, and d are read as one
      record of the file NIN, and the values P(i,j,k), k = 1,...,d+1,
      are read as the following record.
      The routine terminates after the last line has been read.

References

      None.

Numerical Aspects

      None.

Further Comments

      None

Example

Program Text

    *     UD01CD EXAMPLE PROGRAM TEXT
    *
    *     .. Parameters ..
          INTEGER          NIN, NOUT
          PARAMETER        ( NIN = 5, NOUT = 6 )
          INTEGER          MPMAX, NPMAX, DPMAX
          PARAMETER        ( MPMAX = 10, NPMAX = 10, DPMAX = 5 )
          INTEGER          LDP1, LDP2
          PARAMETER        ( LDP1 = MPMAX, LDP2 = NPMAX )
    *     .. Local Scalars ..
          INTEGER          DP, INFO, INFO1, L, MP, NP
    *     .. Local Arrays ..
          DOUBLE PRECISION P(LDP1,LDP2,DPMAX)
    *     .. External Subroutines ..
          EXTERNAL         UD01CD, UD01ND
    *     .. Executable Statements ..
    *
          WRITE ( NOUT, FMT = 99999 )
    *     Skip the heading in the data file and read the data.
          READ ( NIN, FMT = '()' )
          READ ( NIN, FMT = * ) MP, NP, DP
          IF ( MP.LE.0 .OR. MP.GT.MPMAX ) THEN
             WRITE ( NOUT, FMT = 99994 ) MP
          ELSE IF ( NP.LE.0 .OR. NP.GT.NPMAX ) THEN
             WRITE ( NOUT, FMT = 99995 ) NP
          ELSE IF ( DP.LT.0 .OR. DP.GT.DPMAX ) THEN
             WRITE ( NOUT, FMT = 99993 ) DP
          ELSE
    *        Read the coefficients of the matrix polynomial P(s).
             CALL UD01CD( MP, NP, DP, NIN, P, LDP1, LDP2, INFO )
             IF ( INFO.GE.0 ) THEN
                WRITE ( NOUT, 99996 ) MP, NP, DP
    *           Write the coefficients of the matrix polynomial P(s).
                L = 5
                CALL UD01ND( MP, NP, DP, L, NOUT, P, LDP1, LDP2, ' P',
         $                   INFO1 )
                IF ( INFO1.NE.0 )
         $         WRITE ( NOUT, FMT = 99997 ) INFO1
             END IF
             IF ( INFO.NE.0 )
         $      WRITE ( NOUT, FMT = 99998 ) INFO
          END IF
          STOP
    *
    99999 FORMAT (' UD01CD EXAMPLE PROGRAM RESULTS', /1X)
    99998 FORMAT (' INFO on exit from UD01CD = ',I2)
    99997 FORMAT (' INFO on exit from UD01ND = ',I2)
    99996 FORMAT (' MP =', I2, 2X, ' NP =', I2, 3X, 'DP =', I2)
    99995 FORMAT (/' NP is out of range.',/' NP = ',I5)
    99994 FORMAT (/' MP is out of range.',/' MP = ',I5)
    99993 FORMAT (/' DP is out of range.',/' DP = ',I5)
          END

Program Data

    UD01CD EXAMPLE PROGRAM DATA
       4   3   2
    1  1  1
    1.0  1.0
    2  2  2
    2.0  0.0  1.0
    3  3  2
    0.0  3.0  1.0
    4  1  0
    4.0

Program Results

     UD01CD EXAMPLE PROGRAM RESULTS

     MP = 4   NP = 3   DP = 2

      P( 0) ( 4X 3)
                1              2              3
      1    0.1000000D+01  0.0000000D+00  0.0000000D+00
      2    0.0000000D+00  0.2000000D+01  0.0000000D+00
      3    0.0000000D+00  0.0000000D+00  0.0000000D+00
      4    0.4000000D+01  0.0000000D+00  0.0000000D+00

      P( 1) ( 4X 3)
                1              2              3
      1    0.1000000D+01  0.0000000D+00  0.0000000D+00
      2    0.0000000D+00  0.0000000D+00  0.0000000D+00
      3    0.0000000D+00  0.0000000D+00  0.3000000D+01
      4    0.0000000D+00  0.0000000D+00  0.0000000D+00

      P( 2) ( 4X 3)
                1              2              3
      1    0.0000000D+00  0.0000000D+00  0.0000000D+00
      2    0.0000000D+00  0.1000000D+01  0.0000000D+00
      3    0.0000000D+00  0.0000000D+00  0.1000000D+01
      4    0.0000000D+00  0.0000000D+00  0.0000000D+00

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