Purpose
To compute the coefficients of the polynomial
P(x) = P1(x) * P2(x) + alpha * P3(x),
where P1(x), P2(x) and P3(x) are given real polynomials and alpha
is a real scalar.
Each of the polynomials P1(x), P2(x) and P3(x) may be the zero
polynomial.
Specification
SUBROUTINE MC01RD( DP1, DP2, DP3, ALPHA, P1, P2, P3, INFO )
C .. Scalar Arguments ..
INTEGER DP1, DP2, DP3, INFO
DOUBLE PRECISION ALPHA
C .. Array Arguments ..
DOUBLE PRECISION P1(*), P2(*), P3(*)
Arguments
Input/Output Parameters
DP1 (input) INTEGER
The degree of the polynomial P1(x). DP1 >= -1.
DP2 (input) INTEGER
The degree of the polynomial P2(x). DP2 >= -1.
DP3 (input/output) INTEGER
On entry, the degree of the polynomial P3(x). DP3 >= -1.
On exit, the degree of the polynomial P(x).
ALPHA (input) DOUBLE PRECISION
The scalar value alpha of the problem.
P1 (input) DOUBLE PRECISION array, dimension (lenp1)
where lenp1 = DP1 + 1 if DP1 >= 0 and 1 otherwise.
If DP1 >= 0, then this array must contain the
coefficients of P1(x) in increasing powers of x.
If DP1 = -1, then P1(x) is taken to be the zero
polynomial, P1 is not referenced and can be supplied
as a dummy array.
P2 (input) DOUBLE PRECISION array, dimension (lenp2)
where lenp2 = DP2 + 1 if DP2 >= 0 and 1 otherwise.
If DP2 >= 0, then this array must contain the
coefficients of P2(x) in increasing powers of x.
If DP2 = -1, then P2(x) is taken to be the zero
polynomial, P2 is not referenced and can be supplied
as a dummy array.
P3 (input/output) DOUBLE PRECISION array, dimension (lenp3)
where lenp3 = MAX(DP1+DP2,DP3,0) + 1.
On entry, if DP3 >= 0, then this array must contain the
coefficients of P3(x) in increasing powers of x.
On entry, if DP3 = -1, then P3(x) is taken to be the zero
polynomial.
On exit, the leading (DP3+1) elements of this array
contain the coefficients of P(x) in increasing powers of x
unless DP3 = -1 on exit, in which case the coefficients of
P(x) (the zero polynomial) are not stored in the array.
This is the case, for instance, when ALPHA = 0.0 and
P1(x) or P2(x) is the zero polynomial.
Error Indicator
INFO INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal
value.
Method
Given real polynomials
DP1 i DP2 i
P1(x) = SUM a(i+1) * x , P2(x) = SUM b(i+1) * x and
i=0 i=0
DP3 i
P3(x) = SUM c(i+1) * x ,
i=0
the routine computes the coefficents of P(x) = P1(x) * P2(x) +
DP3 i
alpha * P3(x) = SUM d(i+1) * x as follows.
i=0
Let e(i) = c(i) for 1 <= i <= DP3+1 and e(i) = 0 for i > DP3+1.
Then if DP1 >= DP2,
i
d(i) = SUM a(k) * b(i-k+1) + f(i), for i = 1, ..., DP2+1,
k=1
i
d(i) = SUM a(k) * b(i-k+1) + f(i), for i = DP2+2, ..., DP1+1
k=i-DP2
and
DP1+1
d(i) = SUM a(k) * b(i-k+1) + f(i) for i = DP1+2,...,DP1+DP2+1,
k=i-DP2
where f(i) = alpha * e(i).
Similar formulas hold for the case DP1 < DP2.
Numerical Aspects
None.Further Comments
NoneExample
Program Text
* MC01RD EXAMPLE PROGRAM TEXT
* Copyright (c) 2002-2017 NICONET e.V.
*
* .. Parameters ..
INTEGER NIN, NOUT
PARAMETER ( NIN = 5, NOUT = 6 )
INTEGER DP1MAX, DP2MAX, DP3MAX
PARAMETER ( DP1MAX = 10, DP2MAX = 10, DP3MAX = 10 )
INTEGER LENP3
PARAMETER ( LENP3 = MAX(DP1MAX+DP2MAX,DP3MAX)+1 )
* .. Local Scalars ..
DOUBLE PRECISION ALPHA
INTEGER DP1, DP2, DP3, I, INFO
* .. Local Arrays ..
DOUBLE PRECISION P1(DP1MAX+1), P2(DP2MAX+1), P3(LENP3)
* $ P3(DP1MAX+DP2MAX+DP3MAX+1)
* .. External Subroutines ..
EXTERNAL MC01RD
* .. Intrinsic Functions ..
INTRINSIC MAX
* .. Executable Statements ..
*
WRITE ( NOUT, FMT = 99999 )
* Skip the heading in the data file and read the data.
READ ( NIN, FMT = '()' )
READ ( NIN, FMT = * ) DP1
IF ( DP1.LE.-2 .OR. DP1.GT.DP1MAX ) THEN
WRITE ( NOUT, FMT = 99994 ) DP1
ELSE
READ ( NIN, FMT = * ) ( P1(I), I = 1,DP1+1 )
READ ( NIN, FMT = * ) DP2
IF ( DP2.LE.-2 .OR. DP2.GT.DP2MAX ) THEN
WRITE ( NOUT, FMT = 99993 ) DP2
ELSE
READ ( NIN, FMT = * ) ( P2(I), I = 1,DP2+1 )
READ ( NIN, FMT = * ) DP3
IF ( DP3.LE.-2 .OR. DP3.GT.DP3MAX ) THEN
WRITE ( NOUT, FMT = 99992 ) DP3
ELSE
READ ( NIN, FMT = * ) ( P3(I), I = 1,DP3+1 )
END IF
READ ( NIN, FMT = * ) ALPHA
* Compute the coefficients of the polynomial P(x).
CALL MC01RD( DP1, DP2, DP3, ALPHA, P1, P2, P3, INFO )
*
IF ( INFO.NE.0 ) THEN
WRITE ( NOUT, FMT = 99998 ) INFO
ELSE
WRITE ( NOUT, FMT = 99997 ) DP3
IF ( DP3.GE.0 ) THEN
WRITE ( NOUT, FMT = 99996 )
DO 20 I = 0, DP3
WRITE ( NOUT, FMT = 99995 ) I, P3(I+1)
20 CONTINUE
END IF
END IF
END IF
END IF
*
STOP
*
99999 FORMAT (' MC01RD EXAMPLE PROGRAM RESULTS',/1X)
99998 FORMAT (' INFO on exit from MC01RD = ',I2)
99997 FORMAT (' Degree of the resulting polynomial P(x) = ',I2)
99996 FORMAT (/' The coefficients of P(x) are ',//' power of x coe',
$ 'fficient ')
99995 FORMAT (2X,I5,9X,F9.4)
99994 FORMAT (/' DP1 is out of range.',/' DP1 = ',I5)
99993 FORMAT (/' DP2 is out of range.',/' DP2 = ',I5)
99992 FORMAT (/' DP3 is out of range.',/' DP3 = ',I5)
END
Program Data
MC01RD EXAMPLE PROGRAM DATA 1 1.00 2.50 2 1.00 0.10 -0.40 1 1.15 1.50 -2.20Program Results
MC01RD EXAMPLE PROGRAM RESULTS
Degree of the resulting polynomial P(x) = 3
The coefficients of P(x) are
power of x coefficient
0 -1.5300
1 -0.7000
2 -0.1500
3 -1.0000