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/*
* Copyright (c) 2009 Samit Basu
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
#include "Array.hpp"
#include "Math.hpp"
#include "Complex.hpp"
//!
//@Module DOT Dot Product Function
//@@Section ELEMENTARY
//@@Usage
//Computes the scalar dot product of its two arguments. The general
//syntax for its use is
//@[
// y = dot(x,z)
//@]
//where @|x| and @|z| are numerical vectors of the same length. If
//@|x| and @|z| are multi-dimensional arrays of the same size, then
//the dot product is taken along the first non-singleton dimension.
//You can also specify the dimension to take the dot product along using
//the alternate form
//@[
// y = dot(x,z,dim)
//@]
//where @|dim| specifies the dimension to take the dot product along.
//@@Tests
//@$exact#y1=dot(x1,x2)
//@$exact#y1=dot(x1,x2,2)
//@@Signature
//function dot DotFunction
//inputs x1 x2 dim
//outputs y
//!
template <typename T>
static ArrayVector DotFunction(const BasicArray<T> &xreal,
const BasicArray<T> &ximag,
const BasicArray<T> &yreal,
const BasicArray<T> &yimag,
int DotDim) {
BasicArray<T> rvec_real(xreal.dimensions().forceOne(DotDim));
BasicArray<T> rvec_imag(ximag.dimensions().forceOne(DotDim));
ConstBasicIterator<T> xsource_real(&xreal,DotDim);
ConstBasicIterator<T> xsource_imag(&ximag,DotDim);
ConstBasicIterator<T> ysource_real(&yreal,DotDim);
ConstBasicIterator<T> ysource_imag(&yimag,DotDim);
BasicIterator<T> dest_real(&rvec_real,DotDim);
BasicIterator<T> dest_imag(&rvec_imag,DotDim);
index_t dimLen = xreal.dimensions()[DotDim];
while (xsource_real.isValid() &&
ysource_real.isValid() &&
xsource_imag.isValid() &&
ysource_imag.isValid() &&
dest_real.isValid() &&
dest_imag.isValid()) {
double accum_real = 0;
double accum_imag = 0;
for (index_t i=1;i<=dimLen;i++) {
T dot_real, dot_imag;
complex_multiply<T>(xsource_real.get(),-xsource_imag.get(),
ysource_real.get(),ysource_imag.get(),
dot_real, dot_imag);
accum_real += dot_real;
accum_imag += dot_imag;
xsource_real.next(); ysource_real.next();
xsource_imag.next(); ysource_imag.next();
}
dest_real.set(accum_real);
dest_imag.set(accum_imag);
dest_real.next(); dest_imag.next();
xsource_real.nextSlice(); ysource_real.nextSlice(); dest_real.nextSlice();
xsource_imag.nextSlice(); ysource_imag.nextSlice(); dest_imag.nextSlice();
}
return Array(rvec_real,rvec_imag);
}
template <typename T>
static ArrayVector DotFunction(const BasicArray<T> &xreal,
const BasicArray<T> &yreal,
int DotDim) {
if (xreal.isEmpty() && yreal.isEmpty() &&
xreal.is2D() && yreal.is2D()) {
if (DotDim == 0)
return ArrayVector(Array(T(0)));
else
return ArrayVector(Array(GetDataClass(T(0)),NTuple(0,1)));
}
BasicArray<T> rvec(xreal.dimensions().forceOne(DotDim));
ConstBasicIterator<T> xsource(&xreal,DotDim);
ConstBasicIterator<T> ysource(&yreal,DotDim);
BasicIterator<T> dest(&rvec,DotDim);
index_t dimLen = xreal.dimensions()[DotDim];
while (xsource.isValid() && ysource.isValid() && dest.isValid()) {
double accum = 0;
for (index_t i=1;i<=dimLen;i++) {
accum += xsource.get()*ysource.get();
xsource.next(); ysource.next();
}
dest.set(accum);
dest.next();
xsource.nextSlice(); ysource.nextSlice(); dest.nextSlice();
}
return Array(rvec);
}
ArrayVector SumFunction(int, const ArrayVector&);
template <typename T>
static ArrayVector DotFunction(const Array &x, const Array &y, int DotDim) {
if (x.isSparse()) {
Array z(DotMultiply(x,y));
ArrayVector v;
v.push_back(z);
v.push_back(Array(DotDim+1));
return SumFunction(1,v);
} else {
if (x.allReal())
return DotFunction(x.constReal<T>(),y.constReal<T>(),DotDim);
else
return DotFunction(x.constReal<T>(),x.constImag<T>(),
y.constReal<T>(),y.constImag<T>(),DotDim);
}
}
ArrayVector DotFunction(int nargout, const ArrayVector& arg) {
if (arg.size() < 2) throw Exception("dot requires at least two arguments");
Array x(arg[0]);
Array y(arg[1]);
if (x.isVector() && y.isVector() && arg.size() == 2) {
x.reshape(NTuple(x.length(),1));
y.reshape(NTuple(y.length(),1));
}
int DotDim;
if (arg.size() > 2) {
DotDim = arg[2].asInteger() - 1;
if (DotDim < 0) throw Exception("dimension argument to dot should be positive");
} else
DotDim = x.dimensions().firstNonsingular();
if (x.dimensions() != y.dimensions())
throw Exception("arguments to dot should be the same size");
if (x.isSparse() ^ y.isSparse()) {
x = x.asDenseArray();
y = y.asDenseArray();
}
if ((x.dataClass() == Float) || (y.dataClass() == Float)) {
x = x.toClass(Float);
y = y.toClass(Float);
} else {
x = x.toClass(Double);
y = y.toClass(Double);
}
if (!x.allReal() || !y.allReal()) {
x.forceComplex();
y.forceComplex();
}
if (x.dataClass() == Float)
return DotFunction<float>(x,y,DotDim);
else
return DotFunction<double>(x,y,DotDim);
}
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