chbevl.c
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1 /* chbevl.c
2  *
3  * Evaluate Chebyshev series
4  *
5  *
6  *
7  * SYNOPSIS:
8  *
9  * int N;
10  * double x, y, coef[N], chebevl();
11  *
12  * y = chbevl( x, coef, N );
13  *
14  *
15  *
16  * DESCRIPTION:
17  *
18  * Evaluates the series
19  *
20  * N-1
21  * - '
22  * y = > coef[i] T (x/2)
23  * - i
24  * i=0
25  *
26  * of Chebyshev polynomials Ti at argument x/2.
27  *
28  * Coefficients are stored in reverse order, i.e. the zero
29  * order term is last in the array. Note N is the number of
30  * coefficients, not the order.
31  *
32  * If coefficients are for the interval a to b, x must
33  * have been transformed to x -> 2(2x - b - a)/(b-a) before
34  * entering the routine. This maps x from (a, b) to (-1, 1),
35  * over which the Chebyshev polynomials are defined.
36  *
37  * If the coefficients are for the inverted interval, in
38  * which (a, b) is mapped to (1/b, 1/a), the transformation
39  * required is x -> 2(2ab/x - b - a)/(b-a). If b is infinity,
40  * this becomes x -> 4a/x - 1.
41  *
42  *
43  *
44  * SPEED:
45  *
46  * Taking advantage of the recurrence properties of the
47  * Chebyshev polynomials, the routine requires one more
48  * addition per loop than evaluating a nested polynomial of
49  * the same degree.
50  *
51  */
52  /* chbevl.c */
53 
54 /*
55  * Cephes Math Library Release 2.0: April, 1987
56  * Copyright 1985, 1987 by Stephen L. Moshier
57  * Direct inquiries to 30 Frost Street, Cambridge, MA 02140
58  */
59 
60 #include "mconf.h"
61 #include <stdio.h>
62 
63 double chbevl(double x, double array[], int n)
64 {
65  double b0, b1, b2, *p;
66  int i;
67 
68  p = array;
69  b0 = *p++;
70  b1 = 0.0;
71  i = n - 1;
72 
73  do {
74  b2 = b1;
75  b1 = b0;
76  b0 = x * b1 - b2 + *p++;
77  }
78  while (--i);
79 
80  return (0.5 * (b0 - b2));
81 }
simple_graph::b1
Vector2 b1(2, -1)
array
int array[24]
Definition: Map_general_stride.cpp:1
simple_graph::b2
Vector2 b2(4, -5)
x
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Definition: gnuplot_common_settings.hh:12
chbevl
double chbevl(double x, double array[], int n)
Definition: chbevl.c:63
n
int n
Definition: BiCGSTAB_simple.cpp:1
array
Definition: numpy.h:821
mconf.h
p
float * p
Definition: Tutorial_Map_using.cpp:9
i
int i
Definition: BiCGSTAB_step_by_step.cpp:9


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autogenerated on Fri Nov 1 2024 03:32:05