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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 "Operators.hpp"
#include "Math.hpp"
#include "Complex.hpp"
struct OpVecVar {
template <typename T>
static inline void func(const ConstSparseIterator<T> & src,
SparseSlice<T>& dest) {
throw Exception("Variance not implemented for sparse matrices");
}
template <typename T>
static inline void func(const ConstComplexSparseIterator<T> & src,
SparseSlice<T>& dest_real,
SparseSlice<T>& dest_imag) {
throw Exception("Variance not implemented for sparse matrices");
}
template <typename T>
static inline void func(const BasicArray<T> & src,
BasicArray<T>& dest) {
if ((src.length() == 1) && (!IsFinite(src[1]))) {
dest[1] = NaN();
return;
}
T accum = 0;
for (index_t i=1;i<=src.length();i++)
accum += src[i];
T mean = accum/src.length();
accum = 0;
if (src.length() > 1) {
T normalizer = 1.0/(src.length()-1.0);
for (index_t i=1;i<=src.length();i++) {
T tmp = src[i] - mean;
accum += tmp*tmp*normalizer;
}
}
dest[1] = accum;
}
template <typename T>
static inline void func(const BasicArray<T> & src_real,
const BasicArray<T> & src_imag,
BasicArray<T>& dest_real,
BasicArray<T>& dest_imag) {
if ((src_real.length() == 1) &&
(!IsFinite(src_real[1]) || !IsFinite(src_imag[1]))) {
dest_real[1] = NaN();
dest_imag[1] = 0;
return;
}
T accum_real = 0;
T accum_imag = 0;
for (index_t i=1;i<=src_real.length();i++) {
accum_real += src_real[i];
accum_imag += src_imag[i];
}
T mean_real = accum_real/src_real.length();
T mean_imag = accum_imag/src_imag.length();
T accum = 0;
if (src_real.length() > 1) {
T normalizer = 1.0/(src_real.length()-1.0);
for (index_t i=1;i<=src_real.length();i++) {
T tmp_real = src_real[i] - mean_real;
T tmp_imag = src_imag[i] - mean_imag;
T tmp_val = complex_abs(tmp_real,tmp_imag);
accum += tmp_val*tmp_val*normalizer;
}
}
dest_real[1] = accum;
dest_imag[1] = 0;
}
};
//!
//@Module VAR Variance Function
//@@Section ELEMENTARY
//@@Usage
//Computes the variance of an array along a given dimension. The general
//syntax for its use is
//@[
// y = var(x,d)
//@]
//where @|x| is an @|n|-dimensions array of numerical type.
//The output is of the same numerical type as the input. The argument
//@|d| is optional, and denotes the dimension along which to take
//the variance. The output @|y| is the same size as @|x|, except
//that it is singular along the mean direction. So, for example,
//if @|x| is a @|3 x 3 x 4| array, and we compute the mean along
//dimension @|d=2|, then the output is of size @|3 x 1 x 4|.
//@@Function Internals
//The output is computed via
//\[
//y(m_1,\ldots,m_{d-1},1,m_{d+1},\ldots,m_{p}) = \frac{1}{N-1}
//\sum_{k=1}^{N} \left(x(m_1,\ldots,m_{d-1},k,m_{d+1},\ldots,m_{p})
// - \bar{x}\right)^2,
//\]
//where
//\[
//\bar{x} = \frac{1}{N}
//\sum_{k=1}^{N} x(m_1,\ldots,m_{d-1},k,m_{d+1},\ldots,m_{p})
//\]
//If @|d| is omitted, then the mean is taken along the
//first non-singleton dimension of @|x|.
//@@Example
//The following piece of code demonstrates various uses of the var
//function
//@<
//A = [5,1,3;3,2,1;0,3,1]
//@>
//We start by calling @|var| without a dimension argument, in which
//case it defaults to the first nonsingular dimension (in this case,
//along the columns or @|d = 1|).
//@<
//var(A)
//@>
//Next, we take the variance along the rows.
//@<
//var(A,2)
//@>
//@@Tests
//@$near#y1=var(x1)
//@$near#y1=var(x1,2)
//@@Signature
//function var VarFunction
//inputs x dim
//outputs y
//!
ArrayVector VarFunction(int nargout, const ArrayVector& arg) {
// Get the data argument
if (arg.size() < 1)
throw Exception("mean requires at least one argument");
Array input(arg[0]);
if (input.dimensions() == NTuple(0,0))
return ArrayVector(Array(NaN()));
int dim;
if (arg.size() > 1)
dim = arg[1].asInteger()-1;
else
dim = input.dimensions().firstNonsingular();
return ArrayVector(VectorOp<OpVecVar>(input,1,dim));
}
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