## UD01ND

### Printing a matrix polynomial

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

Purpose

```  To print the MP-by-NP coefficient matrices of a matrix polynomial
dp-1           dp
P(s) = P(0) + P(1) * s + . . . + P(dp-1) * s    + P(dp) * s  .

The elements of the matrices are output to 7 significant figures.

```
Specification
```      SUBROUTINE UD01ND( MP, NP, DP, L, NOUT, P, LDP1, LDP2, TEXT,
\$                   INFO )
C     .. Scalar Arguments ..
INTEGER           DP, INFO, L, LDP1, LDP2, MP, NP, NOUT
CHARACTER*(*)     TEXT
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.

L       (input) INTEGER
The number of elements of the coefficient matrices to be
printed per line.  1 <= L <= 5.

NOUT    (input) INTEGER
The output channel to which the results are sent.
NOUT >= 0.

P       (input) DOUBLE PRECISION array, dimension (LDP1,LDP2,DP+1)
The leading MP-by-NP-by-(DP+1) part of this array must
contain the coefficients of the matrix polynomial P(s).
Specifically, P(i,j,k) must contain 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.

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

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

TEXT    (input) CHARACTER*72
Title caption of the coefficient matrices to be printed.
TEXT is followed by the degree of the coefficient matrix,
within brackets. If TEXT = ' ', then the coefficient
matrices are separated by an empty line.

```
Error Indicator
```  INFO    INTEGER
= 0:  successful exit;
< 0:  if INFO = -i, the i-th argument had an illegal
value.

```
Method
```  For i = 1, 2, ..., DP + 1 the routine first prints the contents of
TEXT followed by (i-1) as a title, followed by the elements of the
MP-by-NP coefficient matrix P(i) such that
(i)  if NP < L, then the leading MP-by-NP part is printed;
(ii) if NP = k*L + p (where k, p > 0), then k MP-by-L blocks of
consecutive columns of P(i) are printed one after another
followed by one MP-by-p block containing the last p columns
of P(i).
Row numbers are printed on the left of each row and a column
number on top of each column.

```
References
```  None.

```
Numerical Aspects
```  None.

```
```  None
```
Example

Program Text

```*     UD01ND 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, L, MP, NP
CHARACTER*72     TEXT
*     .. Local Arrays ..
DOUBLE PRECISION P(LDP1,LDP2,DPMAX)
*     .. External Subroutines ..
EXTERNAL         UD01BD, 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, L, TEXT
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 UD01BD( MP, NP, DP, NIN, P, LDP1, LDP2, INFO )
IF ( INFO.EQ.0 ) THEN
WRITE ( NOUT, 99996 ) MP, NP, DP
*           Write the coefficients of the matrix polynomial P(s).
CALL UD01ND( MP, NP, DP, L, NOUT, P, LDP1, LDP2, TEXT,
\$                   INFO )
IF ( INFO.NE.0 )
\$         WRITE ( NOUT, FMT = 99998 ) INFO
ELSE
WRITE ( NOUT, FMT = 99997 ) INFO
END IF
END IF
STOP
*
99999 FORMAT (' UD01ND EXAMPLE PROGRAM RESULTS', /1X)
99998 FORMAT (' INFO on exit from UD01ND = ',I2)
99997 FORMAT (' INFO on exit from UD01BD = ',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
```UD01ND EXAMPLE PROGRAM DATA
4     3     2     5   P
P0
1.0D-00  0.0D-00  0.0D-00
0.0D-00  2.0D-00  4.0D-00
0.0D-00  4.0D-00  8.0D-00
0.0D-00  6.0D-00  1.2D+01
P1
0.0D-00  1.0D-00  2.0D-00
1.0D-00  0.0D-00  0.0D-00
2.0D-00  0.0D-00  0.0D-00
3.0D-00  0.0D-00  0.0D-00
P2
1.0D-00  0.0D-00  0.0D-00
0.0D-00  0.0D-00  0.0D-00
0.0D-00  0.0D-00  0.0D-00
0.0D-00  0.0D-00  0.0D-00
```
Program Results
``` UD01ND 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  0.4000000D+01
3    0.0000000D+00  0.4000000D+01  0.8000000D+01
4    0.0000000D+00  0.6000000D+01  0.1200000D+02

P( 1) ( 4X 3)
1              2              3
1    0.0000000D+00  0.1000000D+01  0.2000000D+01
2    0.1000000D+01  0.0000000D+00  0.0000000D+00
3    0.2000000D+01  0.0000000D+00  0.0000000D+00
4    0.3000000D+01  0.0000000D+00  0.0000000D+00

P( 2) ( 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  0.0000000D+00
4    0.0000000D+00  0.0000000D+00  0.0000000D+00

```