## MC01PD

### Coefficients of a real polynomial, given its zeros

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

Purpose

```  To compute the coefficients of a real polynomial P(x) from its
zeros.

```
Specification
```      SUBROUTINE MC01PD( K, REZ, IMZ, P, DWORK, INFO )
C     .. Scalar Arguments ..
INTEGER           INFO, K
C     .. Array Arguments ..
DOUBLE PRECISION  DWORK(*), IMZ(*), P(*), REZ(*)

```
Arguments

Input/Output Parameters

```  K       (input) INTEGER
The number of zeros (and hence the degree) of P(x).
K >= 0.

REZ     (input) DOUBLE PRECISION array, dimension (K)
IMZ     (input) DOUBLE PRECISION array, dimension (K)
The real and imaginary parts of the i-th zero of P(x)
must be stored in REZ(i) and IMZ(i), respectively, where
i = 1, 2, ..., K. The zeros may be supplied in any order,
except that complex conjugate zeros must appear
consecutively.

P       (output) DOUBLE PRECISION array, dimension (K+1)
This array contains the coefficients of P(x) in increasing
powers of x. If K = 0, then P(1) is set to one.

```
Workspace
```  DWORK   DOUBLE PRECISION array, dimension (K+1)
If K = 0, this array is not referenced.

```
Error Indicator
```  INFO    INTEGER
= 0:  successful exit;
< 0:  if INFO = -i, the i-th argument had an illegal
value;
> 0:  if INFO = i, (REZ(i),IMZ(i)) is a complex zero but
(REZ(i-1),IMZ(i-1)) is not its conjugate.

```
Method
```  The routine computes the coefficients of the real K-th degree
polynomial P(x) as

P(x) = (x - r(1)) * (x - r(2)) * ... * (x - r(K))

where r(i) = (REZ(i),IMZ(i)).

Note that REZ(i) = REZ(j) and IMZ(i) = -IMZ(j) if r(i) and r(j)
form a complex conjugate pair (where i <> j), and that IMZ(i) = 0
if r(i) is real.

```
Numerical Aspects
```  None.

```
```  None
```
Example

Program Text

```*     MC01PD EXAMPLE PROGRAM TEXT
*     Copyright (c) 2002-2017 NICONET e.V.
*
*     .. Parameters ..
INTEGER          NIN, NOUT
PARAMETER        ( NIN = 5, NOUT = 6 )
INTEGER          KMAX
PARAMETER        ( KMAX = 10 )
*     .. Local Scalars ..
INTEGER          I, INFO, K
*     .. Local Arrays ..
DOUBLE PRECISION DWORK(KMAX+1), IMZ(KMAX), P(KMAX+1), REZ(KMAX)
*     .. External Subroutines ..
EXTERNAL         MC01PD
*     .. Executable Statements ..
*
WRITE ( NOUT, FMT = 99999 )
*     Skip the heading in the data file and read the data.
READ ( NIN, FMT = '()' )
READ ( NIN, FMT = * ) K
IF ( K.LT.0 .OR. K.GT.KMAX ) THEN
WRITE ( NOUT, FMT = 99995 ) K
ELSE
READ ( NIN, FMT = * ) ( REZ(I), IMZ(I), I = 1,K )
*        Compute the coefficients of P(x) from the given zeros.
CALL MC01PD( K, REZ, IMZ, P, DWORK, INFO )
*
IF ( INFO.NE.0 ) THEN
WRITE ( NOUT, FMT = 99998 ) INFO
ELSE
WRITE ( NOUT, FMT = 99997 )
WRITE ( NOUT, FMT = 99996 ) ( I, P(I+1), I = 0,K )
END IF
END IF
STOP
*
99999 FORMAT (' MC01PD EXAMPLE PROGRAM RESULTS',/1X)
99998 FORMAT (' INFO on exit from MC01PD = ',I2)
99997 FORMAT (' The coefficients of the polynomial P(x) are ',//' powe',
\$       'r of x     coefficient ')
99996 FORMAT (2X,I5,9X,F9.4)
99995 FORMAT (' K is out of range.',/' K = ',I5)
END
```
Program Data
``` MC01PD EXAMPLE PROGRAM DATA
5
0.0   1.0
0.0  -1.0
2.0   0.0
1.0   3.0
1.0  -3.0
```
Program Results
``` MC01PD EXAMPLE PROGRAM RESULTS

The coefficients of the polynomial P(x) are

power of x     coefficient
0          -20.0000
1           14.0000
2          -24.0000
3           15.0000
4           -4.0000
5            1.0000
```