# LININTERP is the jRidges module of jLab.

``` LININTERP  Fast linear interpolation for arbitrary-sized arrays.

LININTERP is a low-level function called by RIDGEINTERP.

XI=LININTERP(T1,T2,X1,X2,TI) interpolates a function X within an
independent variable T using a linear algorithm.

The function values X1 and X2 may be arrays of any size provided they
are the same size.  The "time" values T1 and T2 may be scalars, or
arrays of the same size as X1 and X2.

If T1 and T2 and X1 and X2 are non-scalar arrays, T should either be
a scalar or an array of the same size as the other arguments.

If T1 and T2 and X1 and X2 are all scalars, T may be of any size, and
XI will have the same size as T.

The function values X1 and X2 may be real or complex.

LININTERP uses the exact algebraic expressions to operate looplessly
on matrices, thus it is very fast.
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Locating x-intercept

LININTERP can also be used to find the x-intercept value of X(T).

TO=LININTERP(T1,T2,X1,X2) with only four input arguments returns TO,
the time at which X(T) vanishes.

TO is the same size as the input arrays.
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Algorithm details

Let X and T be related as

X = A*T + B

The coefficients A and B are uniquely determined by two (T,X) pairs.
LININTERP solves for these coefficients and uses the result to
interpolate X to any other value of T.
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