83 lines
1.6 KiB
C
83 lines
1.6 KiB
C
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/* chbevl.c
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*
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* Evaluate Chebyshev series
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*
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*
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*
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* SYNOPSIS:
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*
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* int N;
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* double x, y, coef[N], chebevl();
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*
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* y = chbevl( x, coef, N );
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*
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*
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*
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* DESCRIPTION:
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*
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* Evaluates the series
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*
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* N-1
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* - '
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* y = > coef[i] T (x/2)
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* - i
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* i=0
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*
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* of Chebyshev polynomials Ti at argument x/2.
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*
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* Coefficients are stored in reverse order, i.e. the zero
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* order term is last in the array. Note N is the number of
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* coefficients, not the order.
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*
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* If coefficients are for the interval a to b, x must
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* have been transformed to x -> 2(2x - b - a)/(b-a) before
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* entering the routine. This maps x from (a, b) to (-1, 1),
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* over which the Chebyshev polynomials are defined.
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*
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* If the coefficients are for the inverted interval, in
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* which (a, b) is mapped to (1/b, 1/a), the transformation
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* required is x -> 2(2ab/x - b - a)/(b-a). If b is infinity,
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* this becomes x -> 4a/x - 1.
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*
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*
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*
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* SPEED:
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*
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* Taking advantage of the recurrence properties of the
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* Chebyshev polynomials, the routine requires one more
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* addition per loop than evaluating a nested polynomial of
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* the same degree.
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*
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*/
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/* chbevl.c */
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/*
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Cephes Math Library Release 2.0: April, 1987
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Copyright 1985, 1987 by Stephen L. Moshier
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Direct inquiries to 30 Frost Street, Cambridge, MA 02140
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*/
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double chbevl( x, array, n )
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double x;
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double array[];
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int n;
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{
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double b0, b1, b2, *p;
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int i;
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p = array;
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b0 = *p++;
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b1 = 0.0;
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i = n - 1;
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do
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{
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b2 = b1;
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b1 = b0;
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b0 = x * b1 - b2 + *p++;
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}
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while( --i );
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return( 0.5*(b0-b2) );
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}
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