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// -*- C++ -*-
// -------------------------------------------------------------------
// MAdLib - Copyright (C) 2008-2009 Universite catholique de Louvain
//
// See the Copyright.txt and License.txt files for license information.
// You should have received a copy of these files along with MAdLib.
// If not, see <http://www.madlib.be/license/>
//
// Please report all bugs and problems to <contrib@madlib.be>
//
// Authors: Gaetan Compere, Jean-Francois Remacle
// -------------------------------------------------------------------
#ifndef _H_MATRIX_MAD
#define _H_MATRIX_MAD
#include "MAdMessage.h"
#include <assert.h>
#include <math.h>
#include <iostream>
#include <stdio.h>
#if defined(_HAVE_GSL_)
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_blas.h>
#endif
// -------------------------------------------------------------------
#if defined(HAVE_BLAS)
extern "C" {
void dgemm_(const char *transa, const char *transb, int *m, int *n, int *k,
double *alpha, double *a, int *lda, double *b, int *ldb,
double *beta, double *c, int *ldc);
void dgemv_(const char *trans, int *m, int *n, double *alpha, double *a,
int *lda, double *x, int *incx, double *beta, double *y, int *incy);
}
#endif
// -------------------------------------------------------------------
#if defined(HAVE_LAPACK)
extern "C" {
void dgesv_(int *N, int *nrhs, double *A, int *lda, int *ipiv,
double *b, int *ldb, int *info);
void dgetrf_(int *M, int *N, double *A, int *lda, int *ipiv, int *info);
void dgesvd_(const char* jobu, const char *jobvt, int *M, int *N,
double *A, int *lda, double *S, double* U, int *ldu,
double *VT, int *ldvt, double *work, int *lwork, int *info);
void dgeev_(const char *jobvl, const char *jobvr,
int *n, double *a, int *lda,
double *wr, double *wi,
double *vl, int *ldvl,
double *vr, int *ldvr,
double *work, int *lwork,
int *info);
}
#endif
// -------------------------------------------------------------------
namespace MAd {
// -------------------------------------------------------------------
// Basic vector / matrix
// -------------------------------------------------------------------
template <class SCALAR>
class MAd_Vector
{
private:
int r;
public:
inline int size() const { return r; }
SCALAR *data;
~MAd_Vector() { if(data) delete [] data; }
MAd_Vector() : r(0)
{
data = 0;
}
MAd_Vector(int R) : r(R)
{
data = new SCALAR[r];
scale(0);
}
MAd_Vector(const MAd_Vector<SCALAR> &other) : r(other.r)
{
data = new SCALAR[r];
for (int i = 0; i < r; ++i) data[i] = other.data[i];
}
inline MAd_Vector<SCALAR> operator= (const MAd_Vector<SCALAR> &other)
{
if ( this != &other ) {
r = other.r;
if (data) delete [] data;
data = new SCALAR[r];
for (int i = 0; i < r; ++i) data[i] = other.data[i];
}
return *this;
}
inline SCALAR operator () (int i) const
{
return data[i];
}
inline SCALAR & operator () (int i)
{
return data[i];
}
inline double norm()
{
double n = 0.;
for(int i = 0; i < r; ++i) n += data[i] * data[i];
return sqrt(n);
}
inline void scale(const SCALAR s)
{
for (int i = 0; i < r; ++i) data[i] *= s;
}
inline void set_all(const double &m)
{
for (int i = 0; i < r; ++i) data[i] = m;
}
inline void add(const MAd_Vector &v)
{
for (int i = 0; i < r; ++i) data[i] += v(i);
}
void print(std::string name) const
{
printf("Vector %s:\n ",name.c_str());
for (int i = 0; i < r; ++i) printf("%12.5E ",data[i]);
printf("\n");
}
};
// -------------------------------------------------------------------
template <class SCALAR>
class MAd_Matrix
{
private:
int _r, _c; // r = nb rows, c = nb columns
SCALAR *_data;
public:
MAd_Matrix(int R,int C) : _r(R), _c(C)
{
_data = new SCALAR[_r * _c];
scale(0.);
}
MAd_Matrix(const MAd_Matrix<SCALAR> &other) : _r(other._r), _c(other._c)
{
_data = new double[_r * _c];
memcpy(other);
}
MAd_Matrix() : _r(0), _c(0), _data(0) {}
~MAd_Matrix() { delete [] _data; }
public:
void print()const {
printf("matrix(%d,%d)",_r,_c);
for(int i=0;i<_r;i++){
for(int j=0;j<_c;j++){
printf("%0.3e\t",_data[i + _r * j]);
}
printf("\n");
}
printf("--------\n");
}
inline int size1() const { return _r; }
inline int size2() const { return _c; }
inline SCALAR operator () (int i, int j) const
{
return _data[i + _r * j];
}
inline SCALAR & operator () (int i, int j)
{
return _data[i + _r * j];
}
MAd_Matrix<SCALAR> & operator = (const MAd_Matrix<SCALAR> &other)
{
if(this != &other){
_r = other._r;
_c = other._c;
_data = new SCALAR[_r * _c];
memcpy(other);
}
return *this;
}
void memcpy(const MAd_Matrix &other)
{
for (int i = 0; i < _r * _c; ++i) _data[i] = other._data[i];
}
void copy(const MAd_Matrix<SCALAR> &a, int i0, int ni, int j0, int nj,
int desti0, int destj0)
{
for(int i = i0, desti = desti0; i < i0 + ni; i++, desti++)
for(int j = j0, destj = destj0; j < j0 + nj; j++, destj++)
(*this)(desti, destj) = a(i, j);
}
// c = c + data * b
inline void mult(const MAd_Matrix<SCALAR> &b, MAd_Matrix<SCALAR> &c)
{
c.scale(0.);
for(int i = 0; i < _r; i++)
for(int j = 0; j < b.size2(); j++)
for(int k = 0; k < _c; k++)
c._data[i + _r * j] += (*this)(i, k) * b(k, j);
}
// y = y + data * x
inline void mult(const MAd_Vector<SCALAR> &x, MAd_Vector<SCALAR> &y)
{
y.scale(0.);
for(int i = 0; i < _r; i++)
for(int j = 0; j < _c; j++)
y._data[i] += (*this)(i, j) * x(j);
}
// data = alpha * ( a * b ) + beta * data
inline void blas_dgemm(MAd_Matrix<SCALAR> &a, MAd_Matrix<SCALAR> &b,
SCALAR alpha=1., SCALAR beta=1.)
{
MAd_Matrix<SCALAR> temp(a.size1(), b.size2()); // temp = 0;
a.mult(b, temp); // temp = a * b
temp.scale(alpha); // temp = alpha * ( a * b )
scale(beta);
add(temp);
}
inline void set_all(const double &m)
{
for (int i = 0; i < _r * _c; ++i) _data[i] = m;
}
inline void setValues(const SCALAR *M[])
{
for (int i = 0; i < _r ; ++i)
for (int j = 0; j < _c ; ++j) _data[i + _r * j] = M[i][j];
}
inline void scale(const double s)
{
if(s == 0.)
for(int i = 0; i < _r * _c; ++i) _data[i] = 0.;
else
for(int i = 0; i < _r * _c; ++i) _data[i] *= s;
}
inline void add(const double &a)
{
for(int i = 0; i < _r * _c; ++i) _data[i] += a;
}
inline void add(const MAd_Matrix<SCALAR> &m)
{
for(int i = 0; i < size1(); i++)
for(int j = 0; j < size2(); j++)
(*this)(i, j) += m(i, j);
}
inline MAd_Matrix<SCALAR> transpose()
{
MAd_Matrix<SCALAR> T(size2(), size1());
for(int i = 0; i < size1(); i++)
for(int j = 0; j < size2(); j++)
T(j, i) = (*this)(i, j);
return T;
}
inline bool lu_solve(const MAd_Vector<SCALAR> &rhs, MAd_Vector<SCALAR> &result)
{
MAdMsgSgl::instance().error(__LINE__,__FILE__,"LU factorization requires LAPACK");
return false;
}
MAd_Matrix<SCALAR> cofactor(int i, int j) const
{
int ni = size1();
int nj = size2();
MAd_Matrix<SCALAR> cof(ni - 1, nj - 1);
for(int I = 0; I < ni; I++){
for(int J = 0; J < nj; J++){
if(J != j && I != i)
cof(I < i ? I : I - 1, J < j ? J : J - 1) = (*this)(I, J);
}
}
return cof;
}
SCALAR determinant() const
{
MAdMsgSgl::instance().error(__LINE__,__FILE__,"Determinant computation requires LAPACK");
return 0.;
}
bool svd(MAd_Matrix<SCALAR> &V, MAd_Vector<SCALAR> &S)
{
MAdMsgSgl::instance().error(__LINE__,__FILE__,"Singular value decomposition requires LAPACK");
return false;
}
bool eig(MAd_Matrix<double> &VL, // left eigenvectors
MAd_Vector<double> &DR, // Real part of eigenvalues
MAd_Vector<double> &DI, // Im part of eigenvalues
MAd_Matrix<double> &VR,
bool sortRealPart=false )
{
MAdMsgSgl::instance().error(__LINE__,__FILE__,"Eigen vectors computation requires LAPACK");
return false;
}
void print(std::string name) const
{
printf("Matrix %s (%d, %d):\n ",name.c_str(),_r,_c);
for(int i = 0; i < _r ; ++i) {
for(int j = 0; j < _c ; ++j) printf("%12.5E ",(*this)(i, j));
printf("\n");
}
}
};
// -------------------------------------------------------------------
// With BLAS / LAPACK
// -------------------------------------------------------------------
// -------------------------------------------------------------------
template <class SCALAR>
class MAd_BLASLAPACK_Vector
{
private:
int r;
public:
inline int size() const { return r; }
SCALAR *data;
~MAd_BLASLAPACK_Vector() { delete [] data; }
MAd_BLASLAPACK_Vector() : r(0)
{
data = 0;
}
MAd_BLASLAPACK_Vector(int R) : r(R)
{
data = new SCALAR[r];
scale(0);
}
MAd_BLASLAPACK_Vector(const MAd_BLASLAPACK_Vector<SCALAR> &other) : r(other.r)
{
data = new double[r];
for (int i = 0; i < r; ++i) data[i] = other.data[i];
}
inline SCALAR operator () (int i) const
{
return data[i];
}
inline SCALAR & operator () (int i)
{
return data[i];
}
inline double norm()
{
double n = 0.;
for(int i = 0; i < r; ++i) n += data[i] * data[i];
return sqrt(n);
}
inline void scale(const SCALAR s)
{
for (int i = 0; i < r; ++i) data[i] *= s;
}
inline void set_all(const double &m)
{
for (int i = 0; i < r; ++i) data[i] = m;
}
inline void add(const MAd_BLASLAPACK_Vector &v)
{
for (int i = 0; i < r; ++i) data[i] += v(i);
}
void print(std::string name) const
{
printf("Vector %s:\n ",name.c_str());
for (int i = 0; i < r; ++i) printf("%12.5E ",data[i]);
printf("\n");
}
};
// -------------------------------------------------------------------
template <class SCALAR>
class MAd_BLASLAPACK_Matrix
{
private:
int _r, _c; // r = nb rows, c = nb columns
SCALAR *_data;
public:
MAd_BLASLAPACK_Matrix(int R,int C) : _r(R), _c(C)
{
_data = new SCALAR[_r * _c];
scale(0.);
}
MAd_BLASLAPACK_Matrix(const MAd_BLASLAPACK_Matrix<SCALAR> &other) : _r(other._r), _c(other._c)
{
_data = new double[_r * _c];
memcpy(other);
}
MAd_BLASLAPACK_Matrix() : _r(0), _c(0), _data(0) {}
~MAd_BLASLAPACK_Matrix() { delete [] _data; }
public:
inline int size1() const { return _r; }
inline int size2() const { return _c; }
inline SCALAR operator () (int i, int j) const
{
return _data[i + _r * j];
}
inline SCALAR & operator () (int i, int j)
{
return _data[i + _r * j];
}
MAd_BLASLAPACK_Matrix<SCALAR> & operator = (const MAd_BLASLAPACK_Matrix<SCALAR> &other)
{
if(this != &other){
_r = other._r;
_c = other._c;
_data = new SCALAR[_r * _c];
memcpy(other);
}
return *this;
}
void memcpy(const MAd_BLASLAPACK_Matrix &other)
{
for (int i = 0; i < _r * _c; ++i) _data[i] = other._data[i];
}
void copy(const MAd_BLASLAPACK_Matrix<SCALAR> &a, int i0, int ni, int j0, int nj,
int desti0, int destj0)
{
for(int i = i0, desti = desti0; i < i0 + ni; i++, desti++)
for(int j = j0, destj = destj0; j < j0 + nj; j++, destj++)
(*this)(desti, destj) = a(i, j);
}
// c = c + data * b
inline void mult(const MAd_BLASLAPACK_Matrix<SCALAR> &b, MAd_BLASLAPACK_Matrix<SCALAR> &c)
{
#if defined(HAVE_BLAS)
int M = c.size1(), N = c.size2(), K = _c;
int LDA = _r, LDB = b.size1(), LDC = c.size1();
double alpha = 1., beta = 0.;
dgemm_("N", "N", &M, &N, &K, &alpha, _data, &LDA, b._data, &LDB,
&beta, c._data, &LDC);
#else
c.scale(0.);
for(int i = 0; i < _r; i++)
for(int j = 0; j < b.size2(); j++)
for(int k = 0; k < _c; k++)
c._data[i + _r * j] += (*this)(i, k) * b(k, j);
#endif
}
// y = y + data * x
inline void mult(const MAd_BLASLAPACK_Vector<SCALAR> &x, MAd_BLASLAPACK_Vector<SCALAR> &y)
{
#if defined(HAVE_BLAS)
int M = _r, N = _c, LDA = _r, INCX = 1, INCY = 1;
double alpha = 1., beta = 0.;
dgemv_("N", &M, &N, &alpha, _data, &LDA, x._data, &INCX,
&beta, y._data, &INCY);
#else
y.scale(0.);
for(int i = 0; i < _r; i++)
for(int j = 0; j < _c; j++)
y._data[i] += (*this)(i, j) * x(j);
#endif
}
// data = alpha * ( a * b ) + beta * data
inline void blas_dgemm(MAd_BLASLAPACK_Matrix<SCALAR> &a, MAd_BLASLAPACK_Matrix<SCALAR> &b,
SCALAR alpha=1., SCALAR beta=1.)
{
#if defined(HAVE_BLAS)
int M = size1(), N = size2(), K = a.size2();
int LDA = a.size1(), LDB = b.size1(), LDC = size1();
dgemm_("N", "N", &M, &N, &K, &alpha, a._data, &LDA, b._data, &LDB,
&beta, _data, &LDC);
#else
MAd_BLASLAPACK_Matrix<SCALAR> temp(a.size1(), b.size2()); // temp = 0;
a.mult(b, temp); // temp = a * b
temp.scale(alpha); // temp = alpha * ( a * b )
scale(beta);
add(temp);
#endif
}
inline void set_all(const double &m)
{
for (int i = 0; i < _r * _c; ++i) _data[i] = m;
}
inline void setValues(const SCALAR *M[])
{
for (int i = 0; i < _r ; ++i)
for (int j = 0; j < _c ; ++j) _data[i + _r * j] = M[i][j];
}
inline void scale(const double s)
{
if(s == 0.)
for(int i = 0; i < _r * _c; ++i) _data[i] = 0.;
else
for(int i = 0; i < _r * _c; ++i) _data[i] *= s;
}
inline void add(const double &a)
{
for(int i = 0; i < _r * _c; ++i) _data[i] += a;
}
inline void add(const MAd_BLASLAPACK_Matrix<SCALAR> &m)
{
for(int i = 0; i < size1(); i++)
for(int j = 0; j < size2(); j++)
(*this)(i, j) += m(i, j);
}
inline MAd_BLASLAPACK_Matrix<SCALAR> transpose()
{
MAd_BLASLAPACK_Matrix<SCALAR> T(size2(), size1());
for(int i = 0; i < size1(); i++)
for(int j = 0; j < size2(); j++)
T(j, i) = (*this)(i, j);
return T;
}
inline bool lu_solve(const MAd_BLASLAPACK_Vector<SCALAR> &rhs, MAd_BLASLAPACK_Vector<SCALAR> &result)
{
#if defined(HAVE_LAPACK)
int N = size1(), nrhs = 1, lda = N, ldb = N, info;
int *ipiv = new int[N];
for(int i = 0; i < N; i++) result(i) = rhs(i);
dgesv_(&N, &nrhs, _data, &lda, ipiv, result.data, &ldb, &info);
delete [] ipiv;
if(info == 0) return true;
MAdMsgSgl::instance().error(__LINE__,__FILE__,"Problem in LAPACK LU (info=%d)", info);
#else
MAdMsgSgl::instance().error(__LINE__,__FILE__,"LU factorization requires LAPACK");
#endif
return false;
}
MAd_BLASLAPACK_Matrix<SCALAR> cofactor(int i, int j) const
{
int ni = size1();
int nj = size2();
MAd_BLASLAPACK_Matrix<SCALAR> cof(ni - 1, nj - 1);
for(int I = 0; I < ni; I++){
for(int J = 0; J < nj; J++){
if(J != j && I != i)
cof(I < i ? I : I - 1, J < j ? J : J - 1) = (*this)(I, J);
}
}
return cof;
}
SCALAR determinant() const
{
#if defined(HAVE_LAPACK)
MAd_BLASLAPACK_Matrix<SCALAR> tmp(*this);
int M = size1(), N = size2(), lda = size1(), info;
int *ipiv = new int[std::min(M, N)];
dgetrf_(&M, &N, tmp._data, &lda, ipiv, &info);
SCALAR det = 1.;
for(int i = 0; i < size1(); i++){
det *= tmp(i, i);
if(ipiv[i] != i + 1) det = -det;
}
return det;
#else
MAdMsgSgl::instance().error(__LINE__,__FILE__,"Determinant computation requires LAPACK");
return 0.;
#endif
}
bool svd(MAd_BLASLAPACK_Matrix<SCALAR> &V, MAd_BLASLAPACK_Vector<SCALAR> &S)
{
#if defined(HAVE_LAPACK)
MAd_BLASLAPACK_Matrix<SCALAR> VT(V.size2(), V.size1());
int M = size1(), N = size2(), LDA = size1(), LDVT = VT.size1(), info;
int LWORK = std::max(3 * std::min(M, N) + std::max(M, N), 5 * std::min(M, N));
MAd_BLASLAPACK_Vector<SCALAR> WORK(LWORK);
dgesvd_("O", "A", &M, &N, _data, &LDA, S._data, _data, &LDA,
VT._data, &LDVT, WORK._data, &LWORK, &info);
V = VT.transpose();
if(info == 0) return true;
MAdMsgSgl::instance().error(__LINE__,__FILE__,"Problem in LAPACK SVD (info=%d)", info);
#else
MAdMsgSgl::instance().error(__LINE__,__FILE__,"Singular value decomposition requires LAPACK");
#endif
return false;
}
bool eig(MAd_BLASLAPACK_Matrix<double> &VL, // left eigenvectors
MAd_BLASLAPACK_Vector<double> &DR, // Real part of eigenvalues
MAd_BLASLAPACK_Vector<double> &DI, // Im part of eigenvalues
MAd_BLASLAPACK_Matrix<double> &VR,
bool sortRealPart=false ) // if true: sorted from max '|DR|' to min '|DR|'
#if defined(HAVE_LAPACK)
;
#else
{
MAdMsgSgl::instance().error(__LINE__,__FILE__,"Eigen vectors computation requires LAPACK");
return false;
}
#endif
void print(std::string name) const
{
printf("Matrix %s (%d, %d):\n ",name.c_str(),_r,_c);
for(int i = 0; i < _r ; ++i) {
for(int j = 0; j < _c ; ++j) printf("%12.5E ",(*this)(i, j));
printf("\n");
}
}
};
// -------------------------------------------------------------------
// With GSL
// -------------------------------------------------------------------
#ifdef _HAVE_GSL_
class MAd_GSL_Vector
{
private:
int _r;
gsl_vector *_data;
friend class MAd_GSL_Matrix;
public:
MAd_GSL_Vector(int r) : _r(r)
{
_data = gsl_vector_calloc(_r);
}
MAd_GSL_Vector(const MAd_GSL_Vector &other) : _r(other._r)
{
_data = gsl_vector_calloc(_r);
gsl_vector_memcpy(_data, other._data);
}
~MAd_GSL_Vector() { gsl_vector_free(_data); }
inline int size() const { return _r; }
inline double operator () (int i) const
{
return gsl_vector_get(_data, i);
}
inline double & operator () (int i)
{
return *gsl_vector_ptr(_data, i);
}
inline double norm()
{
return gsl_blas_dnrm2(_data);
}
inline void scale(const double s)
{
if(s == 0.) gsl_vector_set_zero(_data);
else gsl_vector_scale(_data, s);
}
inline void set_all(const double &m)
{
gsl_vector_set_all(_data, m);
}
inline void add(const MAd_GSL_Vector &v)
{
gsl_vector_add (_data, v._data);
}
void print(std::string name) const
{
printf("Vector %s:\n ",name.c_str());
for (int i = 0; i < _r; ++i) printf("%12.5E ",gsl_vector_get(_data, i));
printf("\n");
}
};
// -------------------------------------------------------------------
class MAd_GSL_Matrix
{
private:
gsl_matrix *_data;
public:
MAd_GSL_Matrix(int r, int c) { _data = gsl_matrix_calloc(r, c); }
MAd_GSL_Matrix(const MAd_GSL_Matrix &other) : _data(0)
{
if(_data) gsl_matrix_free(_data);
_data = gsl_matrix_calloc(other._data->size1, other._data->size2);
gsl_matrix_memcpy(_data, other._data);
}
MAd_GSL_Matrix() : _data(0) {}
~MAd_GSL_Matrix() { if(_data && _data->owner == 1) gsl_matrix_free(_data); }
public:
inline int size1() const { return _data->size1; }
inline int size2() const { return _data->size2; }
MAd_GSL_Matrix & operator = (const MAd_GSL_Matrix &other)
{
if(&other != this){
if(_data) gsl_matrix_free(_data);
_data = gsl_matrix_calloc(other._data->size1, other._data->size2);
gsl_matrix_memcpy(_data, other._data);
}
return *this;
}
void memcpy(const MAd_GSL_Matrix &other)
{
gsl_matrix_memcpy(_data, other._data);
}
inline double operator () (int i, int j) const
{
return gsl_matrix_get(_data, i, j);
}
inline double & operator () (int i, int j)
{
return *gsl_matrix_ptr(_data, i, j);
}
void copy(const MAd_GSL_Matrix &a, int i0, int ni, int j0, int nj,
int desti0, int destj0)
{
for(int i = i0, desti = desti0; i < i0 + ni; i++, desti++)
for(int j = j0, destj = destj0; j < j0 + nj; j++, destj++)
(*this)(desti, destj) = a(i, j);
}
inline void mult(const MAd_GSL_Matrix &b, MAd_GSL_Matrix &c)
{
gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1., _data, b._data, 0., c._data);
}
inline void mult(const MAd_GSL_Vector &x, MAd_GSL_Vector &y)
{
gsl_blas_dgemv(CblasNoTrans, 1., _data, x._data, 0., y._data);
}
inline void blas_dgemm(MAd_GSL_Matrix &a, MAd_GSL_Matrix &b,
double alpha=1., double beta=1.)
{
gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, alpha, a._data, b._data, beta, _data);
}
inline void set_all(const double &m)
{
gsl_matrix_set_all(_data, m);
}
inline void setValues(const double *M[])
{
for (int i = 0; i < size1() ; ++i)
for (int j = 0; j < size2() ; ++j) *gsl_matrix_ptr(_data, i, j) = M[i][j];
}
inline void scale(const double s)
{
if(s == 0.) gsl_matrix_set_zero(_data);
else gsl_matrix_scale(_data, s);
}
inline void add(const double &a)
{
gsl_matrix_add_constant(_data, a);
}
inline void add(const MAd_GSL_Matrix &m)
{
gsl_matrix_add(_data, m._data);
}
inline MAd_GSL_Matrix transpose()
{
MAd_GSL_Matrix T(size2(), size1());
for(int i = 0; i < size1(); i++)
for(int j = 0; j < size2(); j++)
T(j, i) = (*this)(i, j);
return T;
}
inline bool lu_solve(const MAd_GSL_Vector &rhs, MAd_GSL_Vector &result)
{
int s;
gsl_permutation *p = gsl_permutation_alloc(size1());
gsl_linalg_LU_decomp(_data, p, &s);
gsl_linalg_LU_solve(_data, p, rhs._data, result._data);
gsl_permutation_free(p);
return true;
}
MAd_GSL_Matrix cofactor(int i, int j) const
{
int ni = size1();
int nj = size2();
MAd_GSL_Matrix cof(ni - 1, nj - 1);
for(int I = 0; I < ni; I++){
for(int J = 0; J < nj; J++){
if(J != j && I != i)
cof(I < i ? I : I - 1, J < j ? J : J - 1) = (*this)(I, J);
}
}
return cof;
}
double determinant() const
{
MAd_GSL_Matrix tmp = *this;
gsl_permutation *p = gsl_permutation_alloc(size1());
int s;
gsl_linalg_LU_decomp(tmp._data, p, &s);
gsl_permutation_free(p);
return gsl_linalg_LU_det(tmp._data, s);
}
bool svd(MAd_GSL_Matrix &V, MAd_GSL_Vector &S)
{
MAd_GSL_Vector tmp(S.size());
gsl_linalg_SV_decomp(_data, V._data, S._data, tmp._data);
return true;
}
inline void invert ()
{
int s;
gsl_permutation *p = gsl_permutation_alloc (size1());
gsl_linalg_LU_decomp(_data, p, &s);
gsl_matrix *data_inv = gsl_matrix_calloc(size1(), size2());
gsl_linalg_LU_invert(_data, p, data_inv) ;
gsl_matrix_memcpy(_data, data_inv);
gsl_matrix_free(data_inv);
gsl_permutation_free(p);
}
inline bool invertSecure(double &det)
{
int s;
gsl_permutation *p = gsl_permutation_alloc (size1());
gsl_linalg_LU_decomp(_data, p, &s);
det = gsl_linalg_LU_det(_data, s);
gsl_matrix *data_inv = gsl_matrix_calloc(size1(), size2());
gsl_linalg_LU_invert(_data, p, data_inv);
gsl_matrix_memcpy(_data, data_inv);
gsl_matrix_free(data_inv);
gsl_permutation_free(p);
return (det != 0.);
}
bool eig(MAd_GSL_Matrix &VL, // left eigenvectors
MAd_GSL_Vector &DR, // Real part of eigenvalues
MAd_GSL_Vector &DI, // Im part of eigenvalues
MAd_GSL_Matrix &VR,
bool sortRealPart=false )
{
MAdMsgSgl::instance().error(__LINE__,__FILE__,"Eigen vectors computation requires LAPACK");
return false;
}
void print(std::string name) const
{
printf("Matrix %s (%d, %d):\n ",name.c_str(),_data->size1,_data->size2);
for(int i = 0; i < _data->size1 ; ++i) {
for(int j = 0; j < _data->size2 ; ++j) printf("%12.5E ",(*this)(i, j));
printf("\n");
}
}
};
#endif
// -------------------------------------------------------------------
// -------------------------------------------------------------------
#if defined(HAVE_LAPACK)
typedef MAd_BLASLAPACK_Matrix<double> doubleMatrix;
typedef MAd_BLASLAPACK_Vector<double> doubleVector;
#else
#if defined(_HAVE_GSL_)
typedef MAd_GSL_Matrix doubleMatrix;
typedef MAd_GSL_Vector doubleVector;
#else
typedef MAd_Matrix<double> doubleMatrix;
typedef MAd_Vector<double> doubleVector;
#endif
#endif
// -------------------------------------------------------------------
// Should be used for operations on small matrices
typedef MAd_Matrix<double> smallMatrix;
typedef MAd_Vector<double> smallVector;
// -------------------------------------------------------------------
}
#endif
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