Geology Reference
In-Depth Information
Gaussian integration (Abramowitz and Stegun, 1964, p. 887) replaces the integ-
ral by a weighted sum, as in
b
i
=
1
w
i
f
(
t
i
),
n
b
−
a
f
(
t
)
dt
=
(2.418)
2
a
with
b
−
a
2
x
i
b
+
a
2
t
i
=
+
.
(2.419)
For five-point Gaussian integration the weights are
w
1
=
0.236926885056189, w
2
=
0.478628670499366,
w
3
=
0.568888888888889, w
4
=
w
2
,
w
5
=
w
1
,
(2.420)
and the abscissas are
x
1
=−
0.906179845938664,
x
2
=−
0.538469310105683,
x
3
=
0,
x
4
=−
x
2
,
x
5
=−
x
1
.
(2.421)
The five-point Gaussian integration is ninth-order accurate (Abramowitz and
Stegun, 1964, p. 916).
The subroutine CUMDF calculates the cumulative distribution function for the
product spectrum of four individual spectra. It calls the subroutine GAMI, which
in turn calls either the subroutine SEGAMI, for the series computation of the
incomplete gamma function, or the subroutine CFGAMI, for the continued fraction
computation, as required. It also uses the function subprogramme ALOGAM(X)
for the calculation of the natural logarithm of the gamma function of
x
.
SUBROUTINE CUMDF(CDF,Z,ANU,N)
C A subroutine for the direct numerical calculation of the cumulative
C distribution function for N, chi-squared distributed random variables
C multiplied together.
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
DIMENSION ANU(N),A(N),X(5),W(5),TN(11),XIJ(10,5),BMA(10)
C Take natural logarithm of Z.
ZLOG=DLOG(Z)
C Construct array of half-degrees of freedom.
DO 10 I=1,N
A(I)=ANU(I)/2.D0
10 CONTINUE
C Enter abscissas for 5-point Gaussian integration.
X(1)=-0.906179845938664D0
X(2)=-0.538469310105683D0
X(3)=0.D0
X(4)=-X(2)
X(5)=-X(1)
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