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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 "Math.hpp"
#include "EigenDecompose.hpp"
#include "Algorithms.hpp"
static ArrayVector GenEigFunction(int nargout, const ArrayVector &arg) {
Array A(arg[0]);
Array B(arg[1]);
if (A.isSparse() || B.isSparse())
throw Exception("eig only defined for full matrices.");
if (AnyNotFinite(A) || AnyNotFinite(B))
throw Exception("eig only defined for matrices with finite entries.");
if (A.isReferenceType() || B.isReferenceType())
throw Exception("Cannot apply eigendecomposition to reference types.");
if (!A.is2D() || !B.is2D())
throw Exception("Cannot apply eigendecomposition to N-Dimensional arrays.");
if (!A.isSquare())
throw Exception("Cannot eigendecompose a non-square matrix.");
if (!B.isSquare())
throw Exception("Cannot eigendecompose a non-square matrix.");
if (A.rows() != B.rows())
throw Exception("B and A must be the same size when computing a generalized eigendecomposition");
// Handle the type of A - if it is an integer type, then promote to double
if (A.dataClass() != B.dataClass())
throw Exception("B and A must be the same data class when computing a generalized eigendecomposition");
ArrayVector retval;
Array V, D;
if (nargout > 1) {
if (IsSymmetric(A) && IsSymmetric(B)) {
if (!GeneralizedEigenDecomposeFullSymmetric(A,B,V,D))
GeneralizedEigenDecomposeFullGeneral(A,B,V,D);
} else
GeneralizedEigenDecomposeFullGeneral(A,B,V,D);
retval.push_back(V);
retval.push_back(D);
} else {
if (IsSymmetric(A) && IsSymmetric(B)) {
if (!GeneralizedEigenDecomposeCompactSymmetric(A,B,D))
GeneralizedEigenDecomposeCompactGeneral(A,B,D);
} else
GeneralizedEigenDecomposeCompactGeneral(A,B,D);
retval.push_back(D);
}
return retval;
}
//@@Signature
//function eig EigFunction
//inputs A flag
//outputs V D
//DOCBLOCK transforms_eig
ArrayVector EigFunction(int nargout, const ArrayVector& arg) {
bool balance;
if (arg.size() == 0)
throw Exception("eig function requires at least one argument");
if (arg.size() == 1)
balance = true;
else {
Array b(arg[1]);
if (b.isString()) {
QString b2 = b.asString().toUpper();
if (b2=="NOBALANCE")
balance = false;
}
else
return GenEigFunction(nargout, arg);
}
Array A(arg[0]);
A.ensureNotScalarEncoded();
if (!A.is2D())
throw Exception("Cannot apply matrix operations to N-Dimensional arrays.");
if (AnyNotFinite(A))
throw Exception("eig only defined for matrices with finite entries.");
ArrayVector retval;
if (A.isEmpty()) {
if (nargout > 1) {
retval.push_back(A);
retval.push_back(A);
} else {
retval.push_back(Array(Double,NTuple(0,1)));
}
return retval;
}
Array V, D;
if (nargout > 1) {
if (IsSymmetric(A))
EigenDecomposeFullSymmetric(A,V,D);
else
EigenDecomposeFullGeneral(A,V,D,balance);
retval.push_back(V);
retval.push_back(D);
} else {
if (IsSymmetric(A))
EigenDecomposeCompactSymmetric(A,D);
else
EigenDecomposeCompactGeneral(A,D,balance);
retval.push_back(D);
}
return retval;
}
//@@Signature
//function eigs EigsFunction
//inputs A k sigma
//outputs V D
//DOCBLOCK sparse_eigs
ArrayVector EigsFunction(int nargout, const ArrayVector& arg) {
if (arg.size() == 0)
throw Exception("eigs function requires at least one argument");
Array A(arg[0]);
if (!A.isSparse())
throw Exception("eigs only applies to sparse matrix arguments");
int k;
if (!A.isSquare())
throw Exception("eigs can only be applied to square matrices.");
if (arg.size() < 2) {
k = 6;
if (k >= (int)A.rows())
k = int(A.rows() - 1);
} else {
Array kval(arg[1]);
k = kval.asInteger();
}
if (A.dataClass() != Double)
throw Exception("eigs only works on double data class");
bool shiftFlag;
QString whichflag;
double sigma[2];
if (arg.size() < 3) {
shiftFlag = false;
whichflag = "LM";
} else {
Array S(arg[2]);
if (S.isString()) {
shiftFlag = false;
QString stxt = S.asString().toUpper();
if ((stxt == "LM") || (stxt == "SM") || (stxt == "LA") || (stxt == "SA") ||
(stxt == "BE") || (stxt == "LR") || (stxt == "SR") || (stxt == "LI") ||
(stxt == "SI"))
whichflag = stxt;
else
throw Exception("Unrecognized option for sigma - it must be either 'lm', 'sm', 'la', 'sa', 'be', 'lr', 'sr', 'li', or 'si'");
} else {
if (!S.isScalar())
throw Exception("shift parameter sigma must be a scalar");
if (S.dataClass() != Double) throw Exception("shift parameter must be a double dataclass");
if (!S.allReal()) {
sigma[0] = S.constRealScalar<double>();
sigma[1] = S.constImagScalar<double>();
} else {
sigma[0] = S.constRealScalar<double>();
sigma[1] = 0;
}
shiftFlag = true;
}
}
if (!shiftFlag)
return SparseEigDecompose(nargout,A,k,whichflag);
else
return SparseEigDecomposeShifted(nargout,A,k,sigma);
}
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