NAME

Math::Interpolate - Interpolate the value Y from X using a list of (X, Y) pairs

SYNOPSIS

use Math::Interpolate qw(derivatives constant_interpolate
                         linear_interpolate robust_interpolate);
my @x = (1..5);
my @y = (5, 10, 13, -4.5, 3);
my @dy = derivatives(\@x, \@y);
my ($l_y, $l_dy) = linear_interpolate(3.4, \@x, \@y);
my ($r_y, $r_dy) = robust_interpolate(3.4, \@x, \@y);
($r_y, $r_dy) = robust_interpolate(3.4, \@x, \@y, [-2, 3, 4, -1, 4]);

DESCRIPTION

SUBROUTINES

derivatives x_sequence y_sequence

Given a reference to an array of x values in x_sequence and a reference to an array of y values in y_sequence, return an array of reasonable derivatives. The x_sequence values are presumed to be sorted in increasing numerical order.

If there is an error in the input, such as x_sequence and y_sequence containing a different number of elements, then the subroutine returns an empty list in list context, an undefined value in scalar context, or nothing in a void context.

constant_interpolate x x_sequence y_sequence

Given a reference to an array of x values in x_sequence and a reference to an array of y values in y_sequence, return the y value associated with the first x value less than or equal to x. In other words, if x_sequence->[i] <= x < x_sequence->[i+1]

then return y_sequence->[i]

If x is less than x_sequence->[0], then return y_sequence->[0]. If x is greater than x_sequence-[-1], then return y_sequence->[-1].

If there is an error in the input, such as x_sequence and y_sequence containing a different number of elements, then the subroutine returns an empty list in list context, an undefined value in scalar context, or nothing in a void context.

linear_interpolate x x_sequence y_sequence

Given a reference to an array of x values in x_sequence and a reference to an array of y values in y_sequence, calculate the interpolated value y that corresponds to the value x. The returned value y lies on the straight line between the two points surrounding x. If <x> lies outside of the range of values spanned by x_sequence then a linear extrapolation will be done.

In an array context, linear_interpolate will return an array containing the y value and and slope between the two nearest surrounding points.

If there is an error in the input, such as x_sequence and y_sequence containing a different number of elements, then the subroutine returns an empty list in list context, an undefined value in scalar context, or nothing in a void context.

robust_interpolate value x_sequence y_sequence [dy_sequence]

Given a reference to an array of x values in x_sequence and a reference to an array of y values in y_sequence, calculate the interpolated value y that corresponds to the value x. The interpolated curve generated by robust_interpolate is smooth and even the derivatives of the curve are smooth with only a few exceptions.

The returned value y lies on the curve between the two points surrounding x. If <x> lies outside of the range of values spanned by x_sequence then a linear extrapolation will be done.

In an array context, linear_interpolate will return an array containing the y value and and slope between the two nearest surrounding points.

If there is an error in the input, such as x_sequence and y_sequence containing a different number of elements, then the subroutine returns an empty list in list context, an undefined value in scalar context, or nothing in a void context.

AUTHOR

Blair Zajac <bzajac@geostaff.com>.

COPYRIGHT

Copyright (c) 1998 by Blair Zajac.