More Example Code
Polynomial evaluation at multiple points in one or multiple dimensions:
The routine alibPolyEvald below evaluates an n-variate polynomial at m points. It handles double-precision real data, but analogous routines for other data types are obtained simply by changing the 'd' suffix on the RWalib routines, e.g. for double-precision complex data, change the d suffixes to z suffixes. Following the code for alibPolyEvald are examples in 1, 2, and 3 dimensions.
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "alib.h"
/* evaluate the n-variate polynomial defined by d and p at the m points x; */
/* p is the coefficient array ordered like an n-dimensional array of dimensions d, */
/* where p(j1,...,jn) is the coefficient for (x1^j1)*...*(xn^jn); */
/* array x contains the m evaluation points ordered like an (n,m) matrix; */
/* returned is pointer to m-element array of polynomial values at points x; */
double *alibPolyEvald( wvlong n, wvlong *d, double *p, wvlong m, double *x )
{ wvlong k, q, *i, *j[64];
double *f, *g, *r;
q = alibProdl(n,d);
i = (wvlong*)malloc(q*sizeof(wvlong));
for ( k=0; k<n; k++ ) j[k] = (wvlong*)malloc(q*sizeof(wvlong));
f = (double*)malloc(m*q*sizeof(double));
g = (double*)malloc(m*q*sizeof(double));
r = (double*)malloc(m*sizeof(double));
alibIndexl( q, 0, 1, i );
alibIndex1dToNd( n, d, q, i, j );
alibOuterd( alibPowId, m, q, x, NULL, j[0], f, NULL );
for ( k=1; k<n; k++ ) { alibOuterd( alibPowId, m, q, &x[m*k], NULL, j[k], g, NULL );
alibMultd( m*q, m*q, f, g, f );
}
alibMatMuld( m, q, 1, f, p, r );
free(i);
free(f);
free(g);
return r;
}
/* examples for alibPolyEval in 1, 2, and 3 dimensions */
void main() { /* array of dimensions to use for each of the examples */
wvlong d[3]={4,3,2}; /* array of polynomial coefficients to use for each example */
double p[24]={2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,2,3,4,5,6,7,8,9}; /* array of evaluation points to use for each example */
double x[16]={-2,-3,-4,-5,-6,-7,-8,-9,-10,-11,-12,-13,-14,-15,-16,-17}; /* output array to use for each example */
double *v;
v = (double*)malloc(4*sizeof(double));
printf( "\n\n show the coefficients for p = 2 + 3x + 4x^2 + 5x^3" );
alibinit( NULL, NULL, NULL, NULL );
alibPrintArrayd( 1, 1, 1, d[0], p, NULL );
printf( "\n\n show the three evaluation points x" );
alibPrintArrayd( 1, 1, 1, 3, x, NULL );
printf( "\n\n evaluate univariate polynomial p at the three points x" );
v = alibPolyEvald( 1, d, p, 3, x );
alibPrintArrayd( 1, 1, 1, 3, v, NULL );
printf( "\n\n show coefficients for p = 2 + 3y + 4y^2 \n" );
printf( " + x ( 5 + 6y + 7y^2 ) \n" );
printf( " + x^2 ( 8 + 9y + 10y^2 ) \n" );
printf( " + x^3 ( 11 + 12y + 13y^2 ) " );
alibPrintArrayd( 1, 1, d[0], d[1], p, NULL );
printf( "\n\n show the four evaluation points x" );
alibPrintArrayd( 1, 1, 2, 4, x, NULL );
printf( "\n\n evaluate bivariate polynomial p at the four points x" );
v = alibPolyEvald( 2, d, p, 4, x );
alibPrintArrayd( 1, 1, 1, 4, v, NULL );
printf( "\n\n show coefficients for trivariate polynomial p" );
alibPrintArrayd( 1, d[0], d[1], d[2], p, NULL );
printf( "\n\n show the two evaluation points x" );
alibPrintArrayd( 1, 1, 3, 2, x, NULL );
printf( "\n\n evaluate trivariate polynomial p at the two points x" );
v = alibPolyEvald( 3, d, p, 2, x );
alibPrintArrayd( 1, 1, 1, 2, v, NULL );
}
Output:
show the coefficients for p = 2 + 3x + 4x^2 + 5x^3
2.0000000e+00 3.0000000e+00 4.0000000e+00 5.0000000e+00
show the three evaluation points x
-2.0000000e+00 -3.0000000e+00 -4.0000000e+00
evaluate univariate polynomial p at the three points x
-2.8000000e+01 -1.0600000e+02 -2.6600000e+02
show coefficients for p = 2 + 3y + 4y^2
+ x ( 5 + 6y + 7y^2 )
+ x^2 ( 8 + 9y + 10y^2 )
+ x^3 ( 11 + 12y + 13y^2 )
2.0000000e+00 3.0000000e+00 4.0000000e+00
5.0000000e+00 6.0000000e+00 7.0000000e+00
8.0000000e+00 9.0000000e+00 1.0000000e+01
1.1000000e+01 1.2000000e+01 1.3000000e+01
show the four evaluation points x
-2.0000000e+00 -3.0000000e+00 -4.0000000e+00 -5.0000000e+00
-6.0000000e+00 -7.0000000e+00 -8.0000000e+00 -9.0000000e+00
evaluate bivariate polynomial p at the four points x
-2.3140000e+03 -1.2054000e+04 -3.9978000e+04 -1.0336600e+05
show coefficients for trivariate polynomial p
2.0000000e+00 3.0000000e+00
4.0000000e+00 5.0000000e+00
6.0000000e+00 7.0000000e+00
8.0000000e+00 9.0000000e+00
1.0000000e+01 1.1000000e+01
1.2000000e+01 1.3000000e+01
1.4000000e+01 1.5000000e+01
1.6000000e+01 1.7000000e+01
2.0000000e+00 3.0000000e+00
4.0000000e+00 5.0000000e+00
6.0000000e+00 7.0000000e+00
8.0000000e+00 9.0000000e+00
show the two evaluation points x
-2.0000000e+00 -3.0000000e+00
-4.0000000e+00 -5.0000000e+00
-6.0000000e+00 -7.0000000e+00
evaluate trivariate polynomial p at the two points x
6.2600000e+03 3.5844000e+04
Table of Equivalents for PV-WAVE, RWalib, and MATLAB
PV-WAVE RWalib MATLAB
Performance Utilities
set_omp alibinit, alibset, alibParallel
systime alibtime, alibtick now
Printing Utilities
pm alibPrintArray disp, format
print alibPrintArray disp, format
Array Initialization
*arr alibRep zeros
replicate alibRep repmat, zeros, ones
*indgen alibIndex :, linspace
make_array alibRep, alibIndex :, linspace, repmat
linspace alibIndex :, linspace
= alibCopy =
reverse alibFlip, alibFlipDim flip
Type Conversion
byte alibByte uint8
fix alibShort int16
int32 alibInt int32
long alibLong int64
float alibFloat single, real
double alibDouble double, real
complex cmplxflt, alibComplex complex
dcomplex cmplxdbl, alibComplex complex
imaginary alibImaginary imag
Array Indexing
get contiguous array alibGetRange get contiguous array
get general array alibGetSubset
get general set alibGetTrace
put contiguous array alibPutRange, alibPutRangeS put contiguous array
put general array alibPutSubset, alibPutSubsetS
put general set alibPutTrace, alibPutTraceS
index_conv alibIndex1dToNd ind2sub
index_conv alibIndexNdTo1d, alibGetOffsets sub2ind
Searches and Intersections
wherefirst alibCount, alibFind find
where alibCount, alibFind find
wherein alibIntersectS, alibIntersect intersect, setdiff
whereinvec alibIntersect intersect, setdiff
Concatenation and Tiling
[] alibConcat, alibInterleave cat, horzcat
[] alibConcatR cat, vertcat
rebin(,/sample) alibRepArray repmat
expand alibRepArray repmat
replv alibRepArray repmat
cprod alibCartProd ndgrid
Logical Operations
not alibNot bitcmp
and alibAnd bitand
or alibOr bitor
xor alibXor bitxor
Relational Operations
eq alibEq ==
ne alibNe, alibFirstDiff ~=
le alibLe <=
ge alibGe >=
lt alibLt <
gt alibGt >
< alibLesser, alibThreshold min
> alibGreater, alibThreshold max
Rounding Operations
great_int alibFloor floor
small_int alibCeil ceil
nint alibRound round
Min and Max
min alibMinMax, alibMinMaxDim min
max alibMinMax, alibMinMaxDim max
Sort and Unique
sort alibSort sort
sortdim alibSort sort
sortn alibSort sortrows
unique alibUnique unique
uniqn alibUnique unique
Arithmetic Operations
+ alibAdd +
- alibNeg, alibSubt -
* alibMult .*
/ alibDiv ./
mod alibMod mod
conj alibConj conj
abs alibAbs abs
total alibSum, alibSumDim sum
sum alibSum, alibSumDim sum
cumsum alibCumSum cumsum
product alibProd prod
Exponentiation and Logarithms
^ alibPowI, alibPow .^
expon alibPowI, alibPow .^
sqrt alibSqrt sqrt
exp alibExp exp
alog alibLog log
alog10 alibLog10 log10
Broadcast Vector Over Array
vecoverarr_* alibVecOverArr bsxfun
Hyperbolic Functions
cosh alibCosh cosh
sinh alibSinh sinh
tanh alibTanh tanh
Trigonometric Functions
cos alibCos cos
sin alibSin sin
tan alibTan tan
acos alibAcos acos
asin alibAsin asin
atan alibAtan, alibAtan2, alibArg atan, atan2
Linear Algebra
tensor_* alibOuter
# alibMatMul *
spmvm alibSpMVM
transpose alibTranspose .', permute
adjoint alibAdjoint '
arraytrace alibTrace
Version 2017.0
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