# 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.*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 <blair@orcaware.com>.

# COPYRIGHT

Copyright (C) 1998-2005 Blair Zajac. All rights reserved. This package is free software; you can redistribute it and/or modify it under the same terms as Perl itself.

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