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cmat.h
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cmat.h
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// Template Numerical Toolkit (TNT) for Linear Algebra
//
// BETA VERSION INCOMPLETE AND SUBJECT TO CHANGE
// Please see http://math.nist.gov/tnt for updates
//
// R. Pozo
// Mathematical and Computational Sciences Division
// National Institute of Standards and Technology
// Modified 6/2003 to make it work with new compilers.
// P.L. (Anne) Shepherd
// ***********************************************************
// ****IMPORTANT NOTE:
// I have modified this code so the overloaded reference
// operator () has C-type 0-based indexing. This is
// a CHANGE from the original, which uses Fortran-type
// 1-based indexing. Any program that calls the operator
// in this version of cmat.h expecting 1-based indexing,
// or uses an old version of cmat.h and expects 0-based
// indexing, will get BAD RESULTS. Please BE SURE
// you know which version of cmat.h you are using and
// which one you need to be using.
// ----Anne Shepherd, 6/17/03 ********************
// ***********************************************************
// C compatible matrix: row-oriented, 0-based [i][j] and 1-based (i,j) indexing
//
// Chris Siefert's modified namespace free version - 5/26/99
// function (row) has been added.
// It returns the vector that contains that row.
// function (col) has been added.
// It returns the vector that contains that column.
// Also, support for multiplication by a scalar has been added.
// Support for Vector * Matrix acting as if the vector was a row
// vector is added.
//Since Mr. Pozo never did it, here is the complete catalog of outside
//accessable Matrix operations:
//
// Matrix<T>& newsize(Subscript M, Subscript N) - resize matrix
// operator T**(){ return row_;} - ???
// Subscript size() const { return mn_; }
// operator = Matrix
// operator = scalar - assigns all elements to the scalar.
// Subscript dim(Subscript d)
// num_rows()
// num_cols()
// operator[](Subscript i)
// operator()(Subscript i)
// operator()(Subscript i, Subscript j)
// ostream << Matrix
// istream >> Matrix
// Region operator()(const Index1D &I, const Index1D &J) - ???
// Matrix + Matrix
// Matrix - Matrix
// mult_element(A,B) - element by element multiplication
// transpose(A) - matrix transposition
// Matrix * Matrix (also matmult)
// matmult(C, B, A) - result stored in C
// Matrix * Vector (also matmult)
// Chris Siefert Additions:
// row(i) - returns a Vector containing the ith row.
// col(i) - returns a Vector containing the ith column.
// Matrix * Scalar, Scalar * Matrix (also scalmult, 1st form only).
// Vector * Matrix (also matmult). Pretends vector is a row vector.
//
// Modified 7/00 by Anne Shepherd to allow for different implementations
// of the operators new and new[]. If your compiler does not support the
// ANSI Standard try-catch syntax, compile with -DDOLD_ALLOC flag or just
// #define DOLD_ALLOC in your file before including our files.
#ifndef CMAT_H
#define CMAT_H
#ifndef DOLD_ALLOC
#include <new>
#endif
#include "vec.h"
#include <cstdlib>
#include <cassert>
#include <iostream>
#ifdef TNT_USE_REGIONS
#include "region2d.h"
#endif
#include <iomanip>
#define D_PRECISION 16
typedef int Subscript;
template <class T>
class Matrix
{
public:
typedef Subscript size_type;
typedef T value_type;
typedef T element_type;
typedef T* pointer;
typedef T* iterator;
typedef T& reference;
typedef const T* const_iterator;
typedef const T& const_reference;
Subscript lbound() const { return 1; }
protected:
Subscript m_;
Subscript n_;
Subscript mn_; // total size
T* v_;
T** row_;
T* vm1_; // these point to the same data, but are 1-based
T** rowm1_;
// internal helper function to create the array
// of row pointers
void initialize(Subscript M, Subscript N)
{
mn_ = M * N;
m_ = M;
n_ = N;
#ifdef DOLD_ALLOC
v_ = new T[mn_];
row_ = new T*[M];
rowm1_ = new T*[M];
assert(v_ != NULL);
assert(row_ != NULL);
assert(rowm1_ != NULL);
#else
try {
v_ = new T[mn_];
} //try
catch (bad_alloc exception) {
cerr << "Memory allocation failed in file cmat.h, method initialize()."
<< "Exiting with value 1.\n";
exit(1);
} //catch
try {
row_ = new T*[M];
} //try
catch (bad_alloc exception) {
cerr << "Memory allocation failed in file cmat.h, method initialize()."
<< "Exiting with value 1.\n";
exit(1);
} //catch
try {
rowm1_ = new T*[M];
} //try
catch (bad_alloc exception) {
cerr << "Memory allocation failed in file cmat.h, method initialize()."
<< "Exiting with value 1.\n";
exit(1);
} //catch
#endif
T* p = v_;
vm1_ = v_ - 1;
for (Subscript i = 0; i < M; i++)
{
row_[i] = p;
rowm1_[i] = p - 1;
p += N;
}
rowm1_--; // compensate for 1-based offset
}
void copy(const T* v)
{
Subscript N = m_ * n_;
Subscript i;
#ifdef TNT_UNROLL_LOOPS
Subscript Nmod4 = N & 3;
Subscript N4 = N - Nmod4;
for (i = 0; i < N4; i += 4)
{
v_[i] = v[i];
v_[i + 1] = v[i + 1];
v_[i + 2] = v[i + 2];
v_[i + 3] = v[i + 3];
}
for (i = N4; i < N; i++)
v_[i] = v[i];
#else
for (i = 0; i < N; i++)
v_[i] = v[i];
#endif
}
void set(const T& val)
{
Subscript N = m_ * n_;
Subscript i;
#ifdef TNT_UNROLL_LOOPS
Subscript Nmod4 = N & 3;
Subscript N4 = N - Nmod4;
for (i = 0; i < N4; i += 4)
{
v_[i] = val;
v_[i + 1] = val;
v_[i + 2] = val;
v_[i + 3] = val;
}
for (i = N4; i < N; i++)
v_[i] = val;
#else
for (i = 0; i < N; i++)
v_[i] = val;
#endif
}
void destroy()
{
/* do nothing, if no memory has been previously allocated */
if (v_ == NULL) return;
/* if we are here, then matrix was previously allocated */
if (v_ != NULL) delete[](v_);
if (row_ != NULL) delete[](row_);
/* return rowm1_ back to original value */
rowm1_++;
if (rowm1_ != NULL) delete[](rowm1_);
}
public:
operator T**() { return row_; }
operator T**() const { return row_; }
Subscript size() const { return mn_; }
void setRow(int r, int c, double value)
{
Subscript i, j;
i = r;
j = c;
row_[i][j] = value;
}
void Zeros()
{
int M = num_rows();
int N = num_cols();
Subscript i, j;
for (i = 0; i<M; i++)
for (j = 0; j<N; j++)
row_[i][j] = 0.0;
}
void Ones()
{
int M = num_rows();
int N = num_cols();
Subscript i, j;
for (i = 0; i<M; i++)
for (j = 0; j<N; j++)
row_[i][j] = 1.0;
}
// constructors
Matrix() : m_(0), n_(0), mn_(0), v_(0), row_(0), vm1_(0), rowm1_(0) {};
Matrix(const Matrix<T> &A)
{
initialize(A.m_, A.n_);
copy(A.v_);
}
Matrix(Subscript M, Subscript N, const T& value = T(0))
{
initialize(M,N);
set(value);
}
Matrix(Subscript M, Subscript N, const T* v)
{
initialize(M,N);
copy(v);
}
Matrix(Subscript M, Subscript N, char *s)
{
initialize(M,N);
istringstream ins(s);
Subscript i, j;
for (i=0; i<M; i++)
for (j=0; j<N; j++)
ins >> row_[i][j];
}
// destructor
//
~Matrix()
{
destroy();
}
// reallocating
//
Matrix<T>& newsize(Subscript M, Subscript N)
{
if (num_rows() == M && num_cols() == N)
return *this;
destroy();
initialize(M,N);
return *this;
}
// assignments
//
Matrix<T>& operator=(const Matrix<T> &A)
{
if (v_ == A.v_)
return *this;
if (m_ == A.m_ && n_ == A.n_) // no need to re-alloc
copy(A.v_);
else
{
destroy();
initialize(A.m_, A.n_);
copy(A.v_);
}
return *this;
}
Matrix<T>& operator=(const T& scalar)
{
set(scalar);
return *this;
}
std::vector<T> slice(int i)
{
Vector<T>temp(n_, row_[i]);
std::vector<T> vec(temp.begin(), temp.end());
return vec;
}
Subscript dim(Subscript d) const
{
#ifdef TNT_BOUNDS_CHECK
assert( d >= 1);
assert( d <= 2);
#endif
return (d==1) ? m_ : ((d==2) ? n_ : 0);
}
Subscript num_rows() const { return m_; }
Subscript num_cols() const { return n_; }
inline T* operator[](Subscript i)
{
#ifdef TNT_BOUNDS_CHECK
assert(0<=i);
assert(i < m_) ;
#endif
return row_[i];
}
/*START - cmsief************************/
/*This is a Chris Siefert original that attempts to return a vector*/
inline Vector<T> row (Subscript i) const
{
#ifdef TNT_BOUNDS_CHECK
assert(0<=i);
assert(i < m_) ;
#endif
Vector<T>temp(n_,row_[i]);
return (temp);
}
inline Vector<T> col (Subscript i) const
{
#ifdef TNT_BOUNDS_CHECK
assert(0<=i);
assert(i < n_) ;
#endif
Vector<T>temp(m_);
for(long f=0;f<m_;f++) temp[f]=row_[f][i];
return (temp);
}
/*END - cmsief************************/
inline const T* operator[](Subscript i) const
{
#ifdef TNT_BOUNDS_CHECK
assert(0<=i);
assert(i < m_) ;
#endif
return row_[i];
}
/* Changed all this from being 1-based to good ol' C-type
* 0-based indexing.
* pls, 5/15/03
*/
// this is for a sanity check later---using an old version of this
// file will result in off-by-1 errors and give incorrect results.
#define _changed_f_indexing_to_c_pls
inline reference operator()(Subscript i)
{
#ifdef TNT_BOUNDS_CHECK
assert(1<=i);
assert(i <= mn_) ;
#endif
//return vm1_[i];
return v_[i];
}
inline const_reference operator()(Subscript i) const
{
#ifdef TNT_BOUNDS_CHECK
assert(1<=i);
assert(i <= mn_) ;
#endif
//return vm1_[i];
return v_[i];
}
inline reference operator()(Subscript i, Subscript j)
{
#ifdef TNT_BOUNDS_CHECK
assert(1<=i);
assert(i <= m_) ;
assert(1<=j);
assert(j <= n_);
#endif
//return rowm1_[i][j];
return row_[i][j];
}
inline const_reference operator() (Subscript i, Subscript j) const
{
#ifdef TNT_BOUNDS_CHECK
assert(1<=i);
assert(i <= m_) ;
assert(1<=j);
assert(j <= n_);
#endif
//return rowm1_[i][j];
return row_[i][j];
}
/* end P.L. Shepherd hacks to C-ize the () operators */
#ifdef OLD_LIBC
friend istream & operator>>(istream &s, Matrix<T> &A);
#else
// template<class T>
friend istream & operator>><>(istream &s, Matrix<T> &A);
#endif
// friend std::istream & operator>>(std::istream &s, Matrix<T> &A);
#ifdef TNT_USE_REGIONS
typedef Region2D<Matrix<T> > Region;
Region operator()(const Index1D &I, const Index1D &J)
{
return Region(*this, I,J);
}
typedef const_Region2D< Matrix<T> > const_Region;
const_Region operator()(const Index1D &I, const Index1D &J) const
{
return const_Region(*this, I,J);
}
#endif
};
/* *************************** I/O ********************************/
//std::ostream& operator<<(std::ostream &s, const Matrix<T> &A)
template <class T>
ostream& operator<<(ostream &s, const Matrix<T> &A)
{
Subscript M=A.num_rows();
Subscript N=A.num_cols();
s << M << " " << N << "\n";
for (Subscript i=0; i<M; i++)
{
for (Subscript j=0; j<N; j++)
{
s <<setprecision(D_PRECISION)<< A[i][j] << " ";
}
s << "\n";
}
return s;
}
//std::istream& operator>>(std::istream &s, Matrix<T> &A)
template <class T>
istream& operator>>(istream &s, Matrix<T> &A)
{
Subscript M, N;
s >> M >> N;
if ( !(M == A.m_ && N == A.n_) )
{
A.destroy();
A.initialize(M,N);
}
for (Subscript i=0; i<M; i++)
for (Subscript j=0; j<N; j++)
{
s >> A[i][j];
}
return s;
}
// *******************[ basic matrix algorithms ]***************************
template <class T>
Matrix<T> operator+(const Matrix<T> &A,
const Matrix<T> &B)
{
Subscript M = A.num_rows();
Subscript N = A.num_cols();
assert(M==B.num_rows());
assert(N==B.num_cols());
Matrix<T> tmp(M,N);
Subscript i,j;
for (i=0; i<M; i++)
for (j=0; j<N; j++)
tmp[i][j] = A[i][j] + B[i][j];
return tmp;
}
template <class T>
Matrix<T> operator-(const Matrix<T> &A,
const Matrix<T> &B)
{
Subscript M = A.num_rows();
Subscript N = A.num_cols();
assert(M==B.num_rows());
assert(N==B.num_cols());
Matrix<T> tmp(M,N);
Subscript i,j;
for (i=0; i<M; i++)
for (j=0; j<N; j++)
tmp[i][j] = A[i][j] - B[i][j];
return tmp;
}
template <class T>
Matrix<T> mult_element(const Matrix<T> &A,
const Matrix<T> &B)
{
Subscript M = A.num_rows();
Subscript N = A.num_cols();
assert(M==B.num_rows());
assert(N==B.num_cols());
Matrix<T> tmp(M,N);
Subscript i,j;
for (i=0; i<M; i++)
for (j=0; j<N; j++)
tmp[i][j] = A[i][j] * B[i][j];
return tmp;
}
template <class T>
Matrix<T> transpose(const Matrix<T> &A)
{
Subscript M = A.num_rows();
Subscript N = A.num_cols();
Matrix<T> S(N,M);
Subscript i, j;
for (i=0; i<M; i++)
for (j=0; j<N; j++)
S[j][i] = A[i][j];
return S;
}
template <class T>
inline Matrix<T> matmult(const Matrix<T> &A,
const Matrix<T> &B)
{
#ifdef TNT_BOUNDS_CHECK
assert(A.num_cols() == B.num_rows());
#endif
Subscript M = A.num_rows();
Subscript N = A.num_cols();
Subscript K = B.num_cols();
Matrix<T> tmp(M,K);
T sum;
for (Subscript i=0; i<M; i++)
for (Subscript k=0; k<K; k++)
{
sum = 0;
for (Subscript j=0; j<N; j++)
sum = sum + A[i][j] * B[j][k];
tmp[i][k] = sum;
}
return tmp;
}
template <class T>
inline Matrix<T> operator*(const Matrix<T> &A,
const Matrix<T> &B)
{
return matmult(A,B);
}
/*More Chris Siefert additions*/
template <class T>
inline Matrix<T> scalmult(const Matrix<T> &A,
const T &x)
{
Matrix<T> tmp=A;
Subscript M = A.num_rows();
Subscript N = A.num_cols();
for(Subscript i=0;i<M;i++)
for(Subscript j=0;j<N;j++)
tmp[i][j]*=x;
return tmp;
}
template <class T>
inline Matrix<T> operator*(const Matrix<T> &A,
const T &x)
{
return scalmult(A,x);
}
template <class T>
inline Matrix<T> operator*(const T &x,
const Matrix<T> &A)
{
return scalmult(A,x);
}
template <class T>
Vector<T> matmult(const Vector<T> &x, const Matrix<T> &A) {
/*pretends that x is a row-vector*/
#ifdef TNT_BOUNDS_CHECK
assert(A.num_rows() == x.dim());
#endif
Subscript M = A.num_rows();
Subscript N = A.num_cols();
Vector<T> tmp(N);
T sum;
for (Subscript i=0; i<N; i++)
{
sum = 0;
// Vector<T> coli=A.col(i);
for (Subscript j=0; j<M; j++)
sum = sum + A[j][i] * x[j];
tmp[i] = sum;
}
return tmp;
}/*end matmult*/
template <class T>
inline Vector<T> operator*(const Vector<T> &x,
const Matrix<T> &A)
{
return matmult(x,A);
}
/*end Chris Siefert additions*/
template <class T>
inline int matmult(Matrix<T>& C, const Matrix<T> &A,
const Matrix<T> &B)
{
assert(A.num_cols() == B.num_rows());
Subscript M = A.num_rows();
Subscript N = A.num_cols();
Subscript K = B.num_cols();
C.newsize(M,K);
T sum;
const T* row_i;
const T* col_k;
for (Subscript i=0; i<M; i++)
for (Subscript k=0; k<K; k++)
{
row_i = &(A[i][0]);
col_k = &(B[0][k]);
sum = 0;
for (Subscript j=0; j<N; j++)
{
sum += *row_i * *col_k;
row_i++;
col_k += K;
}
C[i][k] = sum;
}
return 0;
}
template <class T>
Vector<T> matmult(const Matrix<T> &A, const Vector<T> &x)
{
#ifdef TNT_BOUNDS_CHECK
assert(A.num_cols() == x.dim());
#endif
Subscript M = A.num_rows();
Subscript N = A.num_cols();
Vector<T> tmp(M);
T sum;
for (Subscript i=0; i<M; i++)
{
sum = 0;
const T* rowi = A[i];
for (Subscript j=0; j<N; j++)
sum = sum + rowi[j] * x[j];
tmp[i] = sum;
}
return tmp;
}
template <class T>
inline Vector<T> operator*(const Matrix<T> &A, const Vector<T> &x)
{
return matmult(A,x);
}
//} // namespace TNT
#endif
// CMAT_H