# QUADINTERP is the jRidges module of jLab.

``` QUADINTERP  Fast quadratic interpolation for arbitrary-sized arrays.

QUADINTERP is a low-level function called by RIDGEINTERP.

within an independent variable T using a quadratic algorithm.

The function values X1--X3 may be arrays of any size provided
they are all the same size.  The "time" values T1--T3 may be
scalars, or arrays of the same size as X1--X3.

If T1--T3 and X1--X3 are non-scalar arrays, T should either be
a scalar or an array of the same size as the other arguments.

If T1--T3 and X1--X3 are all scalars, T may be of any size, and
XI will have the same size as T.

The function values X1--X3 may be real or complex.

QUADINTERP uses the exact algebraic expressions to operate
looplessly on matrices, thus it is very fast.
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Locating maxima or minima

QUADINTERP can also be used to find the extreme value of X(T),
that is its maxima or minima.

[XE,TE]=QUADINTERP(T1,T2,T3,X1,X2,X3) with only six input arguments
solves for TE, the time at which X(T) obtains an extreme value XE.

XE and TE are the same size as the input arrays.
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Algorithm details

Let X and T be related as

X = A*T.^2 + B*T + C

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