## 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

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.

```
```  None
```
Example

Program Text

```*     UD01CD EXAMPLE PROGRAM TEXT
*     Copyright (c) 2002-2017 NICONET e.V.
*
*     .. 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

```