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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.
-*
-*/
-
-
-
-// Fortran-compatible matrix: column oriented, 1-based (i,j) indexing
-
-#ifndef FMAT_H
-#define FMAT_H
-
-#include "subscript.h"
-#include "vec.h"
-#include <cstdlib>
-#include <cassert>
-#include <iostream>
-#ifdef TNT_USE_REGIONS
-#include "region2d.h"
-#endif
-
-// simple 1-based, column oriented Matrix class
-
-namespace TNT
-{
-
-template <class T>
-class Fortran_Matrix
-{
-
-
- public:
-
- 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:
- T* v_; // these are adjusted to simulate 1-offset
- Subscript m_;
- Subscript n_;
- T** col_; // these are adjusted to simulate 1-offset
-
- // internal helper function to create the array
- // of row pointers
-
- void initialize(Subscript M, Subscript N)
- {
- // adjust col_[] pointers so that they are 1-offset:
- // col_[j][i] is really col_[j-1][i-1];
- //
- // v_[] is the internal contiguous array, it is still 0-offset
- //
- v_ = new T[M*N];
- col_ = new T*[N];
-
- assert(v_ != NULL);
- assert(col_ != NULL);
-
-
- m_ = M;
- n_ = N;
- T* p = v_ - 1;
- for (Subscript i=0; i<N; i++)
- {
- col_[i] = p;
- p += M ;
-
- }
- col_ --;
- }
-
- 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 */
- delete [] (v_);
- col_ ++; // changed back to 0-offset
- delete [] (col_);
- }
-
-
- public:
-
- T* begin() { return v_; }
- const T* begin() const { return v_;}
-
- T* end() { return v_ + m_*n_; }
- const T* end() const { return v_ + m_*n_; }
-
-
- // constructors
-
- Fortran_Matrix() : v_(0), m_(0), n_(0), col_(0) {};
- Fortran_Matrix(const Fortran_Matrix<T> &A)
- {
- initialize(A.m_, A.n_);
- copy(A.v_);
- }
-
- Fortran_Matrix(Subscript M, Subscript N, const T& value = T())
- {
- initialize(M,N);
- set(value);
- }
-
- Fortran_Matrix(Subscript M, Subscript N, const T* v)
- {
- initialize(M,N);
- copy(v);
- }
-
-
- // destructor
- ~Fortran_Matrix()
- {
- destroy();
- }
-
-
- // assignments
- //
- Fortran_Matrix<T>& operator=(const Fortran_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;
- }
-
- Fortran_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_; }
-
- Fortran_Matrix<T>& newsize(Subscript M, Subscript N)
- {
- if (num_rows() == M && num_cols() == N)
- return *this;
-
- destroy();
- initialize(M,N);
-
- return *this;
- }
-
-
-
- // 1-based element access
- //
- 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 col_[j][i];
- }
-
- 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 col_[j][i];
- }
-
-
-#ifdef TNT_USE_REGIONS
-
- typedef Region2D<Fortran_Matrix<T> > Region;
- typedef const_Region2D< Fortran_Matrix<T> > const_Region;
-
- Region operator()(const Index1D &I, const Index1D &J)
- {
- return Region(*this, I,J);
- }
-
- 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 Fortran_Matrix<T> &A)
-{
- Subscript M=A.num_rows();
- Subscript N=A.num_cols();
-
- s << M << " " << N << "\n";
-
- for (Subscript i=1; i<=M; i++)
- {
- for (Subscript j=1; j<=N; j++)
- {
- s << A(i,j) << " ";
- }
- s << "\n";
- }
-
-
- return s;
-}
-
-template <class T>
-std::istream& operator>>(std::istream &s, Fortran_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=1; i<=M; i++)
- for (Subscript j=1; j<=N; j++)
- {
- s >> A(i,j);
- }
-
-
- return s;
-}
-
-// *******************[ basic matrix algorithms ]***************************
-
-
-template <class T>
-Fortran_Matrix<T> operator+(const Fortran_Matrix<T> &A,
- const Fortran_Matrix<T> &B)
-{
- Subscript M = A.num_rows();
- Subscript N = A.num_cols();
-
- assert(M==B.num_rows());
- assert(N==B.num_cols());
-
- Fortran_Matrix<T> tmp(M,N);
- Subscript i,j;
-
- for (i=1; i<=M; i++)
- for (j=1; j<=N; j++)
- tmp(i,j) = A(i,j) + B(i,j);
-
- return tmp;
-}
-
-template <class T>
-Fortran_Matrix<T> operator-(const Fortran_Matrix<T> &A,
- const Fortran_Matrix<T> &B)
-{
- Subscript M = A.num_rows();
- Subscript N = A.num_cols();
-
- assert(M==B.num_rows());
- assert(N==B.num_cols());
-
- Fortran_Matrix<T> tmp(M,N);
- Subscript i,j;
-
- for (i=1; i<=M; i++)
- for (j=1; j<=N; j++)
- tmp(i,j) = A(i,j) - B(i,j);
-
- return tmp;
-}
-
-// element-wise multiplication (use matmult() below for matrix
-// multiplication in the linear algebra sense.)
-//
-//
-template <class T>
-Fortran_Matrix<T> mult_element(const Fortran_Matrix<T> &A,
- const Fortran_Matrix<T> &B)
-{
- Subscript M = A.num_rows();
- Subscript N = A.num_cols();
-
- assert(M==B.num_rows());
- assert(N==B.num_cols());
-
- Fortran_Matrix<T> tmp(M,N);
- Subscript i,j;
-
- for (i=1; i<=M; i++)
- for (j=1; j<=N; j++)
- tmp(i,j) = A(i,j) * B(i,j);
-
- return tmp;
-}
-
-
-template <class T>
-Fortran_Matrix<T> transpose(const Fortran_Matrix<T> &A)
-{
- Subscript M = A.num_rows();
- Subscript N = A.num_cols();
-
- Fortran_Matrix<T> S(N,M);
- Subscript i, j;
-
- for (i=1; i<=M; i++)
- for (j=1; j<=N; j++)
- S(j,i) = A(i,j);
-
- return S;
-}
-
-
-
-template <class T>
-inline Fortran_Matrix<T> matmult(const Fortran_Matrix<T> &A,
- const Fortran_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();
-
- Fortran_Matrix<T> tmp(M,K);
- T sum;
-
- for (Subscript i=1; i<=M; i++)
- for (Subscript k=1; k<=K; k++)
- {
- sum = 0;
- for (Subscript j=1; j<=N; j++)
- sum = sum + A(i,j) * B(j,k);
-
- tmp(i,k) = sum;
- }
-
- return tmp;
-}
-
-template <class T>
-inline Fortran_Matrix<T> operator*(const Fortran_Matrix<T> &A,
- const Fortran_Matrix<T> &B)
-{
- return matmult(A,B);
-}
-
-template <class T>
-inline int matmult(Fortran_Matrix<T>& C, const Fortran_Matrix<T> &A,
- const Fortran_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); // adjust shape of C, if necessary
-
-
- T sum;
-
- const T* row_i;
- const T* col_k;
-
- for (Subscript i=1; i<=M; i++)
- {
- for (Subscript k=1; k<=K; k++)
- {
- row_i = &A(i,1);
- col_k = &B(1,k);
- sum = 0;
- for (Subscript j=1; j<=N; j++)
- {
- sum += *row_i * *col_k;
- row_i += M;
- col_k ++;
- }
-
- C(i,k) = sum;
- }
-
- }
-
- return 0;
-}
-
-
-template <class T>
-Vector<T> matmult(const Fortran_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=1; i<=M; i++)
- {
- sum = 0;
- for (Subscript j=1; j<=N; j++)
- sum = sum + A(i,j) * x(j);
-
- tmp(i) = sum;
- }
-
- return tmp;
-}
-
-template <class T>
-inline Vector<T> operator*(const Fortran_Matrix<T> &A, const Vector<T> &x)
-{
- return matmult(A,x);
-}
-
-template <class T>
-inline Fortran_Matrix<T> operator*(const Fortran_Matrix<T> &A, const T &x)
-{
- Subscript M = A.num_rows();
- Subscript N = A.num_cols();
-
- Subscript MN = M*N;
-
- Fortran_Matrix<T> res(M,N);
- const T* a = A.begin();
- T* t = res.begin();
- T* tend = res.end();
-
- for (t=res.begin(); t < tend; t++, a++)
- *t = *a * x;
-
- return res;
-}
-
-} // namespace TNT
-
-#endif // FMAT_H
-
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