X-Git-Url: http://git.tdb.fi/?a=blobdiff_plain;f=source%2Flinal%2Fmatrix.h;h=2ad03447a9b10454f73ab982cf49f26dd25f983f;hb=60caa19c84877c89d750140a90e5d891bce30ee7;hp=4fc2bc620136a37200629f9d72a3764cbaec2118;hpb=79b2de777a3841bced5fd782a46166fc4d9d7489;p=libs%2Fmath.git

diff --git a/source/linal/matrix.h b/source/linal/matrix.h
index 4fc2bc6..2ad0344 100644
--- a/source/linal/matrix.h
+++ b/source/linal/matrix.h
@@ -1,17 +1,23 @@
 #ifndef MSP_LINAL_MATRIX_H_
 #define MSP_LINAL_MATRIX_H_
 
+#include <algorithm>
+#include <ostream>
+#include "matrixops.h"
 #include "vector.h"
 
 namespace Msp {
 namespace LinAl {
 
 /**
-A general mathematical matrix.
+A general mathematical matrix with M rows and N columns.
 */
 template<typename T, unsigned M, unsigned N>
 class Matrix
 {
+public:
+	typedef T ElementType;
+
 private:
 	T data[M*N];
 
@@ -20,30 +26,112 @@ public:
 	Matrix(const T *);
 	template<typename U>
 	Matrix(const Matrix<U, M, N> &);
+
+	static Matrix identity();
 	static Matrix from_columns(const Vector<T, M> *);
 	static Matrix from_rows(const Vector<T, N> *);
 
-	T &operator()(unsigned, unsigned);
-	const T &operator()(unsigned, unsigned) const;
+	unsigned rows() const { return M; }
+	unsigned columns() const { return N; }
+
+	T &element(unsigned i, unsigned j) { return data[i+M*j]; }
+	const T &element(unsigned i, unsigned j) const { return data[i+M*j]; }
+	T &operator()(unsigned i, unsigned j) { return element(i, j); }
+	const T &operator()(unsigned i, unsigned j) const { return element(i, j); }
+
+	Vector<T, M> column(unsigned i) const { return Vector<T, M>(data+M*i); }
+	Vector<T, N> row(unsigned i) const { return Vector<T, N>(data+i, M); }
+
+	template<unsigned P, unsigned Q>
+	Matrix<T, P, Q> select(const Vector<unsigned, P> &, const Vector<unsigned, Q> &) const;
+
+	template<unsigned P, unsigned Q>
+	Matrix<T, P, Q> block(unsigned, unsigned) const;
 
 	Matrix &operator*=(T);
+	Matrix &operator*=(const Matrix &);
 	Matrix &operator/=(T);
 	Matrix &operator+=(const Matrix &);
 	Matrix &operator-=(const Matrix &);
 
-	Matrix<T, N, M> transpose() const;
+	Matrix &invert();
+
+	Matrix &exchange_columns(unsigned, unsigned);
+	Matrix &multiply_column(unsigned, T);
+	Matrix &add_column(unsigned, unsigned, T);
 };
 
 template<typename T, unsigned M, unsigned N>
-inline T &Matrix<T, M, N>::operator()(unsigned i, unsigned j)
+inline Matrix<T, M, N>::Matrix()
+{
+	std::fill(data, data+M*N, T());
+}
+
+template<typename T, unsigned M, unsigned N>
+inline Matrix<T, M, N>::Matrix(const T *d)
+{
+	std::copy(d, d+M*N, data);
+}
+
+template<typename T, unsigned M, unsigned N>
+template<typename U>
+inline Matrix<T, M, N>::Matrix(const Matrix<U, M, N> &other)
+{
+	for(unsigned i=0; i<M; ++i)
+		for(unsigned j=0; j<N; ++j)
+			element(i, j) = other(i, j);
+}
+
+template<typename T, unsigned M, unsigned N>
+inline Matrix<T, M, N> Matrix<T, M, N>::identity()
 {
-	return data[i+M*j];
+	static_assert(M==N, "An identity matrix must be square");
+	Matrix<T, M, N> m;
+	for(unsigned i=0; i<M; ++i)
+		m(i, i) = T(1);
+	return m;
 }
 
 template<typename T, unsigned M, unsigned N>
-inline const T &Matrix<T, M, N>::operator()(unsigned i, unsigned j) const
+inline Matrix<T, M, N> Matrix<T, M, N>::from_columns(const Vector<T, M> *v)
 {
-	return data[i+M*j];
+	Matrix<T, M, N> m;
+	for(unsigned i=0; i<M; ++i)
+		for(unsigned j=0; j<N; ++j)
+			m(i, j) = v[j][i];
+	return m;
+}
+
+template<typename T, unsigned M, unsigned N>
+inline Matrix<T, M, N> Matrix<T, M, N>::from_rows(const Vector<T, N> *v)
+{
+	Matrix<T, M, N> m;
+	for(unsigned i=0; i<M; ++i)
+		for(unsigned j=0; j<N; ++j)
+			m(i, j) = v[i][j];
+	return m;
+}
+
+template<typename T, unsigned M, unsigned N>
+template<unsigned P, unsigned Q>
+inline Matrix<T, P, Q> Matrix<T, M, N>::select(const Vector<unsigned, P> &row_indices, const Vector<unsigned, Q> &col_indices) const
+{
+	Matrix<T, P, Q> r;
+	for(unsigned j=0; j<P; ++j)
+		for(unsigned i=0; i<Q; ++i)
+			r(j, i) = element(row_indices[j], col_indices[i]);
+	return r;
+}
+
+template<typename T, unsigned M, unsigned N>
+template<unsigned P, unsigned Q>
+inline Matrix<T, P, Q> Matrix<T, M, N>::block(unsigned y, unsigned x) const
+{
+	Matrix<T, P, Q> r;
+	for(unsigned j=0; j<P; ++j)
+		for(unsigned i=0; i<Q; ++i)
+			r(j, i) = element(y+j, x+i);
+	return r;
 }
 
 template<typename T, unsigned M, unsigned N>
@@ -54,6 +142,13 @@ inline Matrix<T, M, N> &Matrix<T, M, N>::operator*=(T s)
 	return *this;
 }
 
+template<typename T, unsigned M, unsigned N>
+inline Matrix<T, M, N> &Matrix<T, M, N>::operator*=(const Matrix<T, M, N> &m)
+{
+	static_assert(M==N, "Multiplication-assignment is only possible on square matrices");
+	return *this = *this*m;
+}
+
 template<typename T, unsigned M, unsigned N>
 inline Matrix<T, M, N> operator*(const Matrix<T, M, N> &m, T s)
 {
@@ -67,6 +162,37 @@ inline Matrix<T, M, N> operator*(T s, const Matrix<T, M, N> &m)
 	return m*s;
 }
 
+template<typename T, unsigned M, unsigned P, unsigned N>
+inline Matrix<T, M, N> operator*(const Matrix<T, M, P> &m1, const Matrix<T, P, N> &m2)
+{
+	Matrix<T, M, N> r;
+	for(unsigned i=0; i<M; ++i)
+		for(unsigned j=0; j<N; ++j)
+			for(unsigned k=0; k<P; ++k)
+				r(i, j) += m1(i, k)*m2(k, j);
+	return r;
+}
+
+template<typename T, unsigned M, unsigned N>
+inline Vector<T, M> operator*(const Matrix<T, M, N> &m, const Vector<T, N> &v)
+{
+	Vector<T, M> r;
+	for(unsigned i=0; i<M; ++i)
+		for(unsigned j=0; j<N; ++j)
+			r[i] += m(i, j)*v[j];
+	return r;
+}
+
+template<typename T, unsigned M, unsigned N>
+inline Vector<T, N> operator*(const Vector<T, M> &v, const Matrix<T, M, N> &m)
+{
+	Vector<T, N> r;
+	for(unsigned j=0; j<N; ++j)
+		for(unsigned i=0; i<M; ++i)
+			r[j] += v[i]*m(i, j);
+	return r;
+}
+
 template<typename T, unsigned M, unsigned N>
 inline Matrix<T, M, N> &Matrix<T, M, N>::operator/=(T s)
 {
@@ -112,37 +238,89 @@ inline Matrix<T, M, N> operator-(const Matrix<T, M, N> &m1, const Matrix<T, M, N
 	return r -= m2;
 }
 
-template<typename T, unsigned M, unsigned P, unsigned N>
-Matrix<T, M, N> operator*(const Matrix<T, M, P> &m1, const Matrix<T, P, N> &m2)
+template<typename T, unsigned M, unsigned N>
+inline Matrix<T, M, N>& Matrix<T, M, N>::invert()
 {
-	Matrix<T, M, N> r;
-	for(unsigned i=0; i<M; ++i)
-		for(unsigned j=0; j<N; ++j)
-			for(unsigned k=0; k<P; ++k)
-				r.at(i, j) += m1(i, k)*m2(k, j);
-	return r;
+	static_assert(M==N, "Inversion is only possible on square matrices");
+	Matrix<T, M, N> r = identity();
+	gauss_jordan(*this, r);
+	return *this = r;
+}
+
+template<typename T, unsigned S>
+inline Matrix<T, S, S> invert(const Matrix<T, S, S> &m)
+{
+	Matrix<T, S, S> temp = m;
+	Matrix<T, S, S> r = Matrix<T, S, S>::identity();
+	return gauss_jordan(temp, r);
 }
 
 template<typename T, unsigned M, unsigned N>
-Vector<T, M> operator*(const Matrix<T, M, N> &m, const Vector<T, N> &v)
+inline bool operator==(const Matrix<T, M, N> &a, const Matrix<T, M, N> &b)
 {
-	Vector<T, M> r;
-	for(unsigned i=0; i<M; ++i)
-		for(unsigned j=0; j<N; ++j)
-			r[i] += m(i, j)*v[j];
-	return r;
+	for(unsigned j=0; j<N; ++j)
+		for(unsigned i=0; i<M; ++i)
+			if(a(i, j)!=b(i, j))
+				return false;
+	return true;
 }
 
 template<typename T, unsigned M, unsigned N>
-Vector<T, N> operator*(const Vector<T, M> &v, const Matrix<T, M, N> &m)
+inline Matrix<T, M, N> &Matrix<T, M, N>::exchange_columns(unsigned i, unsigned j)
 {
-	Vector<T, N> r;
+	using std::swap;
+	for(unsigned k=0; k<M; ++k)
+		swap(element(k, i), element(k, j));
+	return *this;
+}
+
+template<typename T, unsigned M, unsigned N>
+inline Matrix<T, M, N> &Matrix<T, M, N>::multiply_column(unsigned i, T s)
+{
+	for(unsigned k=0; k<M; ++k)
+		element(k, i) *= s;
+	return *this;
+}
+
+template<typename T, unsigned M, unsigned N>
+inline Matrix<T, M, N> &Matrix<T, M, N>::add_column(unsigned i, unsigned j, T s)
+{
+	for(unsigned k=0; k<M; ++k)
+		element(k, j) += element(k, i)*s;
+	return *this;
+}
+
+template<typename T, unsigned M, unsigned N>
+inline Matrix<T, N, M> transpose(const Matrix<T, M, N> &m)
+{
+	Matrix<T, N, M> r;
 	for(unsigned j=0; j<N; ++j)
 		for(unsigned i=0; i<M; ++i)
-			r[j] += v[i]*m(i, j);
+			r(j, i) = m(i, j);
 	return r;
 }
 
+template<typename T, unsigned M, unsigned N>
+inline std::ostream &operator<<(std::ostream &s, const Matrix<T, M, N> &m)
+{
+	s << "Matrix" << M << 'x' << N << '(';
+	for(unsigned i=0; i<N; ++i)
+	{
+		if(i)
+			s << ", ";
+		s << '[';
+		for(unsigned j=0; j<M; ++j)
+		{
+			if(j)
+				s << ", ";
+			s << m(j, i);
+		}
+		s << ']';
+	}
+	s << ')';
+	return s;
+}
+
 } // namespace LinAl
 } // namespace Msp