Prototype_pattern_exercise/MatrixMechanisms.cpp at master · cablegui/Prototype_pattern_exercise · GitHub

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// MatrixMechanisms.cpp

// Mechanism functions for matrices.

// Modification dates

// DD 2004-4-3 Kick off

// DD 2004-4-9 Power method, code review and round-off

// DD 2005-12-1 Extracting a row fom a Matrix (can be optmised)

// DD 2006-8-6 set_diagomnal() commented out

// (C) Datasim Education BV 2004-2006

#ifndef MatrixMechanisms_cpp

#define MatrixMechanisms_cpp

#include "MatrixMechanisms.hpp"

#include "UtilitiesDJD/PropertySet/SimplePropertySet.cpp"

// Properties

// Sum of absolute values of row and column

template <class V, class I> V sumAbsRow(const NumericMatrix<V,I>& m, const I& i)

{ // Add up for a given row i

V result = fabs(m(i, m.MinColumnIndex()));

for (I j = m.MinColumnIndex() + 1; j <= m.MaxColumnIndex(); j++)

{

result += fabs(m(i,j));

}

return result;

}

template <class V, class I> V sumAbsColumn(const NumericMatrix<V,I>& m, const I& j)

{ // Add up for a given column j

V result = fabs(m(m.MinRowIndex(), j));

for (I i = m.MinRowIndex() + 1; i <= m.MaxRowIndex(); i++)

{

result += fabs(m(i,j));

}

return result;

}

// Now Abs sume of rows and columns for all indices

template <class V, class I> Vector<V,I> sumAbsRow(const NumericMatrix<V,I>& m)

{

Vector<V,I> result (m.Rows(), m.MinRowIndex());

// Do for all rows

for (I i = m.MinRowIndex(); i <= m.MaxRowIndex(); i++)

{

result[i] = sumAbsRow(m, i);

}

return result;

}

template <class V, class I> Vector<V,I> sumAbsColumn(const NumericMatrix<V,I>& m)

{

Vector<V,I> result (m.Columns(), m.MinColumnIndex());

// Do for all columns

for (I j = m.MinColumnIndex(); j <= m.MaxColumnIndex(); j++)

{

result[j] = sumAbsColumn(m, j);

}

return result;

}

template <class V, class I> V l1Norm(const NumericMatrix<V,I>& matrix)

{ // Largest coulmn

V ans = V(0.0);

V tmp(ans);

for (I j = matrix.MinColumnIndex(); j <= matrix.MaxColumnIndex(); j++)

{

for (I i = matrix.MinRowIndex(); i <= matrix.MaxRowIndex(); i++)

{

tmp = sumAbsColumn(matrix, i);

}

if (tmp > ans)

ans = tmp;

}

return ans;

}

template <class V, class I> V FrobeniusNorm(const NumericMatrix<V,I>& matrix)

{

V ans(0.0);

V tmp(0.0);

for (I i = matrix.MinRowIndex(); i <= matrix.MaxRowIndex(); i++)

{

for (I j = matrix.MinColumnIndex(); j<= matrix.MaxColumnIndex(); j++)

{

tmp = matrix(i, j);

ans += (tmp * tmp);

}

return sqrt(ans);

}

template <class V, class I> V lInfinityNorm(const NumericMatrix<V,I>& matrix)

{ // Largest row

V ans = V(0.0);

V tmp(ans);

for (I i = matrix.MinRowIndex(); i <= matrix.MaxRowIndex(); i++)

{

for (I j = matrix.MinRowIndex(); j <= matrix.MaxRowIndex(); j++)

{

tmp = sumAbsRow(matrix, j);

}

if (tmp > ans)

ans = tmp;

}

return ans;

}

template <class V, class I> SimplePropertySet<string, double> allNorms(const NumericMatrix<V,I>& m)

{

SimplePropertySet<string, double> result; // Empty list

result.add(Property<string, double> ("l1", l1Norm(m)));

result.add(Property<string, double> ("l2", FrobeniusNorm(m)));

result.add(Property<string, double> ("linf", lInfinityNorm(m)));

return result;

}

template <class V, class I> setDiagonal(Matrix<V,I>& m, const V& v)

{ // All diagonal elements get the value v

// Matrix must be square, otherwise ...

for (I j = m.MinRowIndex(); j <= m.MaxRowIndex(); j++)

{

m(j,j) = v;

}

template <class V, class I> void initMatrix(Matrix<V,I>& m, const V& v)

{ // All elements get the value v

for (I i = m.MinRowIndex(); i <= m.MaxRowIndex(); i++)

{

for (I j = m.MinColumnIndex(); j <= m.MaxColumnIndex(); j++)

{

m(i,j) = v;

}

template <class V, class I> NumericMatrix<V,I> createMatrix(

const Vector<V,I>& lower, const Vector<V,I>& diagonal, const Vector<V,I>& upper)

{ // Create a matrix based on the diagonal elements of a tridiagonal matrix; bit wasteful of

// space but who cares! I've got a Pentium with a giga of memory

// We use the indexing as with LU decomposition routines, i.e.

// lower [2, J]

// diagonal [1, J]

// upper [1, J-1]

NumericMatrix<V, I> result(diagonal.Size(), diagonal.Size(), 1, 1);

// All values set to 0

initMatrix(result, V(0.0));

// Initialise the 'extremities' of the matrix

result(result.MaxRowIndex(), result.MaxColumnIndex()) = diagonal[diagonal.MaxIndex()];

result(result.MaxRowIndex(), result.MaxColumnIndex() -1) = lower[lower.MaxIndex()];

result(1, 1) = diagonal[diagonal.MinIndex()];

result(1, 2) = upper[upper.MinIndex()];

// Now the 'uniform' part of the matrix

for (I i = result.MinRowIndex() + 1; i <= result.MaxRowIndex() - 1; i++)

{

// Create the diagonal element

result(i, i-1) = lower[i];

result(i, i) = diagonal[i];

result(i, i+1) = upper[i];

}

return result;

}

// Other results for vectors and matrces

template <class V, class I> V quadraticForm(const NumericMatrix<V,I>& matrix, const Vector<V,I>& x)

{

V ans = V(0.0);

for (I i = matrix.MinRowIndex(); i <= matrix.MaxRowIndex(); i++)

{

for (I j = matrix.MinColumnIndex(); j<= matrix.MaxColumnIndex(); j++)

{

ans += matrix(i,j) * x[i] * x[j];

}

return ans;

}

template <class V, class I> V RayleighQuotient(const NumericMatrix<V,I>& A, const Vector<V,I>& x)

{

// PREC: Compatibiity, number of columns of A == number of rows of x

// PREC: inner product does not evaluate to 0.0

return quadraticForm(A, x) / innerProduct (x,x);

}

template <class V, class I> bool operator < (const NumericMatrix<V,I>& m1, const NumericMatrix<V,I>& m2)

{

for (I i = m1.MinRowIndex(); i <= m1.MaxRowIndex(); i++)

{

for (I j = m1.MinColumnIndex(); j<= m1.MaxColumnIndex(); j++)

{

if (m1(i,j) >= m2(i,j))

return false;

}

return true;

}

template <class V, class I> bool operator <= (const NumericMatrix<V,I>& m1, const NumericMatrix<V,I>& m2)

{

for (I i = m1.MinRowIndex(); i <= m1.MaxRowIndex(); i++)

{

for (I j = m1.MinColumnIndex(); j<= m1.MaxColumnIndex(); j++)

{

if (m1(i,j) > m2(i,j))

return false;

}

return true;

}

template <class V, class I> bool operator > (const NumericMatrix<V,I>& m1, const NumericMatrix<V,I>& m2)

{

if (m2 < m1)

return true;

return false;

}

template <class V, class I> bool operator >= (const NumericMatrix<V,I>& m1, const NumericMatrix<V,I>& m2)

{

if (m2 <= m1)

return true;

return false;

}

template <class V, class I> bool operator == (const NumericMatrix<V,I>& m1, const NumericMatrix<V,I>& m2)

{

for (I i = m1.MinRowIndex(); i <= m1.MaxRowIndex(); i++)

{

for (I j = m1.MinColumnIndex(); j<= m1.MaxColumnIndex(); j++)

{

if (m1(i,j) != m2(i,j))

return false;

}

return true;

}

template <class V, class I> bool operator != (const NumericMatrix<V,I>& m1, const NumericMatrix<V,I>& m2)

{

if (m1 == m2)

return false;

return true;

}

// Are all elements of a matrix positive?

template <class V, class I> bool positive(const NumericMatrix<V,I>& matrix)

{

V zero = V(0.0);

for (I i = matrix.MinRowIndex(); i <= matrix.MaxRowIndex(); i++)

{

for (I j = matrix.MinColumnIndex(); j<= matrix.MaxColumnIndex(); j++)

{

if (matrix(i,j) <= zero)

return false;

}

return true;

}

template <class V, class I> bool negative(const NumericMatrix<V,I>& matrix)

{

V zero = V(0.0);

for (I i = matrix.MinRowIndex(); i <= matrix.MaxRowIndex(); i++)

{

for (I j = matrix.MinColumnIndex(); j<= matrix.MaxColumnIndex(); j++)

{

if (matrix(i,j) >= zero)

return false;

}

return true;

}

// Special functions for Numerical Linear Algebra

template <class V, class I> bool diagonallyDominant(const NumericMatrix<V,I>& m)

{

for (I i = m.MinRowIndex(); i <= m.MaxRowIndex(); i++)

{

V tmp = fabs(m(i,i));

if (tmp < sumAbsRow(m, i) - tmp)

return false;

}

return true;

}

// Gerschgorin's circle theorem: n eigenvalues of a matrix in a nX2 matrix of

// lower and upper bounds

template <class V, class I> NumericMatrix<V,I> eigenvalueBounds(const NumericMatrix<V,I>& m)

{

NumericMatrix<V, I> mat(m.Rows(), 2, 1, 1); // 2 columns

for (I i = m.MinRowIndex(); i <= m.MaxRowIndex(); i++)

{

V tmp = fabs(m(i,i));

V rsum = sumAbsRow(m, i);

mat(i, 2) = tmp - rsum; // Lower limit

mat(i, 1) = rsum;

}

return mat;

}

// Calculate largest eigenvalue by Power method

template <class V, class I> V dominantEigenvalue(const NumericMatrix<V,I>& A, const Vector<V,I>& svec,

const V& tolerance)

{

Vector<V,I> startV = svec;

Vector<V,I> currVector = (A * svec);

V tmp(0.0);

V nextValue (tmp);

L1:

tmp = RayleighQuotient(A, currVector);

if (fabs(tmp-nextValue) > tolerance)

{

nextValue = tmp;

startV = currVector;

currVector = A * startV;

goto L1;

}

return nextValue;

}

////////////// Useful and Basic Print Functions ////////////////////////////////////////////////////

template <class V, class I> void print(const Matrix<V,I>& mat)

{

for (int i = mat.MinRowIndex(); i <= mat.MaxRowIndex(); i++)

{

cout << "\n[";

for (I j = mat.MinColumnIndex(); j <= mat.MaxColumnIndex()-1; j++)

{

cout << mat(i,j) << ", ";

}

cout << mat(i, mat.MaxColumnIndex());

cout << "]" << endl;

}

cout << endl;

}

#endif

Prototype_pattern_exercise/MatrixMechanisms.cpp at master · cablegui/Prototype_pattern_exercise · GitHub

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