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-/**
- */
-
-/*
-
-*
-* Template Numerical Toolkit (TNT): Linear Algebra Module
-*
-* Mathematical and Computational Sciences Division
-* National Institute of Technology,
-* Gaithersburg, MD USA
-*
-*
-* This software was developed at the National Institute of Standards and
-* Technology (NIST) by employees of the Federal Government in the course
-* of their official duties. Pursuant to title 17 Section 105 of the
-* United States Code, this software is not subject to copyright protection
-* and is in the public domain. The Template Numerical Toolkit (TNT) is
-* an experimental system. NIST assumes no responsibility whatsoever for
-* its use by other parties, and makes no guarantees, expressed or implied,
-* about its quality, reliability, or any other characteristic.
-*
-* BETA VERSION INCOMPLETE AND SUBJECT TO CHANGE
-* see http://math.nist.gov/tnt for latest updates.
-*
-*/
-
-
-
-// C compatible matrix: row-oriented, 0-based [i][j] and 1-based (i,j) indexing
-//
-
-#ifndef CMAT_H
-#define CMAT_H
-
-#include "subscript.h"
-#include "vec.h"
-#include <stdlib.h>
-#include <assert.h>
-#include <iostream>
-#ifdef TNT_USE_REGIONS
-#include "region2d.h"
-#endif
-
-namespace TNT
-{
-
-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;
-
- v_ = new T[mn_];
- row_ = new T*[M];
- rowm1_ = new T*[M];
-
- assert(v_ != NULL);
- assert(row_ != NULL);
- assert(rowm1_ != NULL);
-
- 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_; }
-
- // 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())
- {
- initialize(M,N);
- set(value);
- }
-
- Matrix(Subscript M, Subscript N, const T* v)
- {
- initialize(M,N);
- copy(v);
- }
-
-
- // 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;
- }
-
- void
- diagonal(Vector<T> &diag)
- {
- int sz = diag.dim();
- newsize(sz,sz);
- set(0);
-
- Subscript i;
- for (i = 0; i < sz; i++) {
- row_[i][i] = diag[i];
- }
- }
-
-
-
- // 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;
- }
-
-
- 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];
- }
-
- inline const T* operator[](Subscript i) const
- {
-#ifdef TNT_BOUNDS_CHECK
- assert(0<=i);
- assert(i < m_) ;
-#endif
- return row_[i];
- }
-
- inline reference operator()(Subscript i)
- {
-#ifdef TNT_BOUNDS_CHECK
- assert(1<=i);
- assert(i <= mn_) ;
-#endif
- return vm1_[i];
- }
-
- inline const_reference operator()(Subscript i) const
- {
-#ifdef TNT_BOUNDS_CHECK
- assert(1<=i);
- assert(i <= mn_) ;
-#endif
- return vm1_[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];
- }
-
-
-
- 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];
- }
-
-
-
-#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 ********************************/
-
-template <class T>
-std::ostream& operator<<(std::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 << A[i][j] << " ";
- }
- s << "\n";
- }
-
-
- return s;
-}
-
-template <class T>
-std::istream& operator>>(std::istream &s, Matrix<T> &A)
-{
-
- Subscript M, N;
-
- s >> M >> N;
-
- if ( !(M == A.num_rows() && N == A.num_cols() ))
- {
- A.newsize(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>
-void transpose(const Matrix<T> &A, Matrix<T> &S)
-{
- Subscript M = A.num_rows();
- Subscript N = A.num_cols();
-
- assert(M==S.num_cols());
- assert(N==S.num_rows());
-
- Subscript i, j;
-
- for (i=0; i<M; i++)
- for (j=0; j<N; j++)
- S[j][i] = A[i][j];
-
-}
-
-
-template <class T>
-inline void 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;
- }
-
-}
-
-template <class T>
-void matmult(Vector<T> &y, const Matrix<T> &A, const Vector<T> &x)
-{
-
-#ifdef TNT_BOUNDS_CHECK
- assert(A.num_cols() == x.dim());
- assert(A.num_rows() == y.dim());
-#endif
-
- Subscript M = A.num_rows();
- Subscript N = A.num_cols();
-
- 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];
-
- y[i] = sum;
- }
-}
-
-template <class T>
-inline void matmultdiag(
- Matrix<T>& C,
- const Matrix<T> &A,
- const Vector<T> &diag
-){
-#ifdef TNT_BOUNDS_CHECK
- assert(A.num_cols() ==A.num_rows()== diag.dim());
-#endif
-
- Subscript M = A.num_rows();
- Subscript K = diag.dim();
-
- C.newsize(M,K);
-
- const T* row_i;
- const T* col_k;
-
- for (Subscript i=0; i<M; i++) {
- for (Subscript k=0; k<K; k++)
- {
- C[i][k] = A[i][k] * diag[k];
- }
- }
-}
-
-
-template <class T>
-inline void matmultdiag(
- Matrix<T>& C,
- const Vector<T> &diag,
- const Matrix<T> &A
-){
-#ifdef TNT_BOUNDS_CHECK
- assert(A.num_cols() ==A.num_rows()== diag.dim());
-#endif
-
- Subscript M = A.num_rows();
- Subscript K = diag.dim();
-
- C.newsize(M,K);
-
- for (Subscript i=0; i<M; i++) {
-
- const T diag_element = diag[i];
-
- for (Subscript k=0; k<K; k++)
- {
- C[i][k] = A[i][k] * diag_element;
- }
- }
-}
-
-} // namespace TNT
-
-#endif // CMAT_H
-
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