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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 "LAPACK.hpp"
#include "Array.hpp"
#include "MemPtr.hpp"
#include "Algorithms.hpp"
template <class T>
static bool isFiniteNonzero(T a) {
return ((a != 0) && IsFinite(a));
}
static float complexRecipCond(int m, int n, float *a) {
if ((m == 1) && (n == 1) && (isFiniteNonzero(a[0]) ||
isFiniteNonzero(a[1]))) return 1;
// Getting the estimated reciprocal condition number involves
// three steps:
// 1. Compute the 1-norm of a
float Anorm = 0;
float rcond = 0;
{
char NORM = '1';
Anorm = clange_(&NORM,&m,&n,a,&m,NULL);
}
// 2. Compute the LU-decomposition of a
{
MemBlock<int> ipiv(std::min(m,n));
int info;
cgetrf_(&m,&n,a,&m,&ipiv,&info);
}
// 3. Call sgecon to compute rcond
{
char NORM = '1';
int info;
MemBlock<float> work(4*n);
MemBlock<float> rwork(2*n);
cgecon_(&NORM,&n,a,&m,&Anorm,&rcond,&work,&rwork,&info);
}
return rcond;
}
static float floatRecipCond(int m, int n, float *a) {
if ((m == 1) && (n == 1) && isFiniteNonzero(a[0])) return 1;
// Getting the estimated reciprocal condition number involves
// three steps:
// 1. Compute the 1-norm of a
float Anorm = 0;
float rcond = 0;
{
char NORM = '1';
Anorm = slange_(&NORM,&m,&n,a,&m,NULL);
}
// 2. Compute the LU-decomposition of a
{
MemBlock<int> ipiv(std::min(m,n));
int info;
sgetrf_(&m,&n,a,&m,&ipiv,&info);
}
// 3. Call sgecon to compute rcond
{
char NORM = '1';
int info;
MemBlock<float> work(4*n);
MemBlock<int> iwork(n);
sgecon_(&NORM,&n,a,&m,&Anorm,&rcond,&work,&iwork,&info);
}
return rcond;
}
static double dcomplexRecipCond(int m, int n, double *a) {
if ((m == 1) && (n == 1) && (isFiniteNonzero(a[0]) || isFiniteNonzero(a[1])))
return 1;
// Getting the estimated reciprocal condition number involves
// three steps:
// 1. Compute the 1-norm of a
double Anorm = 0;
double rcond = 0;
{
char NORM = '1';
Anorm = zlange_(&NORM,&m,&n,a,&m,NULL);
}
// 2. Compute the LU-decomposition of a
{
MemBlock<int> ipiv(std::min(m,n));
int info;
zgetrf_(&m,&n,a,&m,&ipiv,&info);
}
// 3. Call sgecon to compute rcond
{
char NORM = '1';
int info;
MemBlock<double> work(4*n);
MemBlock<double> rwork(2*n);
zgecon_(&NORM,&n,a,&m,&Anorm,&rcond,&work,&rwork,&info);
}
return rcond;
}
static double doubleRecipCond(int m, int n, double *a) {
if ((m == 1) && (n == 1) && isFiniteNonzero(a[0])) return 1;
// Getting the estimated reciprocal condition number involves
// three steps:
// 1. Compute the 1-norm of a
double Anorm = 0;
double rcond = 0;
{
char NORM = '1';
Anorm = dlange_(&NORM,&m,&n,a,&m,NULL);
}
// 2. Compute the LU-decomposition of a
{
MemBlock<int> ipiv(std::min(m,n));
int info;
dgetrf_(&m,&n,a,&m,&ipiv,&info);
}
// 3. Call sgecon to compute rcond
{
char NORM = '1';
int info;
MemBlock<double> work(4*n);
MemBlock<int> iwork(n);
dgecon_(&NORM,&n,a,&m,&Anorm,&rcond,&work,&iwork,&info);
}
return rcond;
}
//!
//@Module RCOND Reciprocal Condition Number Estimate
//@@Section ARRAY
//@@Usage
//The @|rcond| function is a FreeMat wrapper around LAPACKs
//function @|XGECON|, which estimates the 1-norm condition
//number (reciprocal). For the details of the algorithm see
//the LAPACK documentation. The syntax for its use is
//@[
// x = rcond(A)
//@]
//where @|A| is a matrix.
//@@Example
//Here is the reciprocal condition number for a random square
//matrix
//@<
//A = rand(30);
//rcond(A)
//@>
//And here we calculate the same value using the definition of
//(reciprocal) condition number
//@<
//1/(norm(A,1)*norm(inv(A),1))
//@>
//Note that the values are very similar. LAPACKs @|rcond|
//function is far more efficient than the explicit calculation
//(which is also used by the @|cond| function.
//@@Tests
//@$near#y1=rcond(x1)
//@@Signature
//function rcond RcondFunction
//inputs A
//outputs x
//!
ArrayVector RcondFunction(int nargout, const ArrayVector& arg) {
if (arg.size() < 1)
throw Exception("rcond function requires at least one argument - the matrix to compute the condition number for.");
Array A(arg[0].asDenseArray());
if (!A.is2D()) throw Exception("Cannot apply matrix operations to N-dimensional arrays.");
if (!A.isSquare()) throw Exception("rcond only applies to square matrices");
if (A.isEmpty())
return ArrayVector(Array(Inf()));
if (AnyNaN(A))
return ArrayVector(Array(NaN()));
switch (A.dataClass()) {
default: throw Exception("Unsupported type for rcond operation");
case Float:
if (A.allReal())
return ArrayVector(Array(floatRecipCond(int(A.rows()),
int(A.cols()),
A.real<float>().data())));
else
return ArrayVector(Array(complexRecipCond(int(A.rows()),
int(A.cols()),
A.fortran<float>().data())));
case Double:
if (A.allReal())
return ArrayVector(Array(doubleRecipCond(int(A.rows()),
int(A.cols()),
A.real<double>().data())));
else
return ArrayVector(Array(dcomplexRecipCond(int(A.rows()),
int(A.cols()),
A.fortran<double>().data())));
}
}
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