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有的 INTERP1 1-D interpolation (table lookup)
YI = INTERP1(X,Y,XI) interpolates to find YI, the values of the
underlying function Y at the points in the array XI. X must be a
vector of length N.
If Y is a vector, then it must also have length N, and YI is the
same size as XI. If Y is an array of size [N,D1,D2,...,Dk], then
the interpolation is performed for each D1-by-D2-by-...-Dk value
in Y(i,:,:,...,:).
If XI is a vector of length M, then YI has size [M,D1,D2,...,Dk].
If XI is an array of size [M1,M2,...,Mj], then YI is of size
[M1,M2,...,Mj,D1,D2,...,Dk].
YI = INTERP1(Y,XI) assumes X = 1:N, where N is LENGTH(Y)
for vector Y or SIZE(Y,1) for array Y.
Interpolation is the same operation as "table lookup". Described in
"table lookup" terms, the "table" is [X,Y] and INTERP1 "looks-up"
the elements of XI in X, and, based upon their location, returns
values YI interpolated within the elements of Y.
YI = INTERP1(X,Y,XI,METHOD) specifies alternate methods.
The default is linear interpolation. Use an empty matrix [] to specify
the default. Available methods are:
'nearest' - nearest neighbor interpolation
'linear' - linear interpolation
'spline' - piecewise cubic spline interpolation (SPLINE)
'pchip' - shape-preserving piecewise cubic interpolation
'cubic' - same as 'pchip'
'v5cubic' - the cubic interpolation from MATLAB 5, which does not
extrapolate and uses 'spline' if X is not equally
spaced.
YI = INTERP1(X,Y,XI,METHOD,'extrap') uses the specified method for
extrapolation for any elements of XI outside the interval spanned by X.
Alternatively, YI = INTERP1(X,Y,XI,METHOD,EXTRAPVAL) replaces
the values outside of the interval spanned by X with EXTRAPVAL.
NaN and 0 are often used for EXTRAPVAL. The default extrapolation
behavior with four input arguments is 'extrap' for 'spline' and 'pchip'
and EXTRAPVAL = NaN for the other methods.
PP = INTERP1(X,Y,METHOD,'pp') will use the specified method to
generate the ppform (piecewise polynomial form) of Y. The method may be
any of the above except for 'v5cubic'. PP may then be evaluated via
PPVAL. PPVAL(PP,XI) is the same as INTERP1(X,Y,XI,METHOD,'extrap').
For example, generate a coarse sine curve and interpolate over a
finer abscissa:
x = 0:10; y = sin(x); xi = 0:.25:10;
yi = interp1(x,y,xi); plot(x,y,'o',xi,yi)
For a multi-dimensional example, we construct a table of functional
values:
x = [1:10]'; y = [ x.^2, x.^3, x.^4 ];
xi = [ 1.5, 1.75; 7.5, 7.75]; yi = interp1(x,y,xi);
creates 2-by-2 matrices of interpolated function values, one matrix for
each of the 3 functions. yi will be of size 2-by-2-by-3. |
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发表于 2007-5-30 21:33
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发表于 2007-5-30 21:51
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