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333 lines
6.1 KiB
C++
333 lines
6.1 KiB
C++
//========= Copyright Valve Corporation, All rights reserved. ============//
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//
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// Purpose:
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//
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// $NoKeywords: $
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//=============================================================================//
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#ifndef NMATRIX_H
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#define NMATRIX_H
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#ifdef _WIN32
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#pragma once
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#endif
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#include <assert.h>
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#include "nvector.h"
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#define NMatrixMN NMatrix<M,N>
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template<int M, int N>
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class NMatrix
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{
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public:
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NMatrixMN() {}
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static NMatrixMN SetupNMatrixNull(); // Return a matrix of all zeros.
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static NMatrixMN SetupNMatrixIdentity(); // Return an identity matrix.
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NMatrixMN const& operator=( NMatrixMN const &other );
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NMatrixMN operator+( NMatrixMN const &v ) const;
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NMatrixMN const& operator+=( NMatrixMN const &v );
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NMatrixMN operator-() const;
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NMatrixMN operator-( NMatrixMN const &v ) const;
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// Multiplies the column vector on the right-hand side.
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NVector<M> operator*( NVector<N> const &v ) const;
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// Can't get the compiler to work with a real MxN * NxR matrix multiply...
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NMatrix<M,M> operator*( NMatrix<N,M> const &b ) const;
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NMatrixMN operator*( float val ) const;
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bool InverseGeneral( NMatrixMN &mInverse ) const;
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NMatrix<N,M> Transpose() const;
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public:
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float m[M][N];
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};
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// Return the matrix generated by multiplying a column vector 'a' by row vector 'b'.
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template<int N>
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inline NMatrix<N,N> OuterProduct( NVectorN const &a, NVectorN const &b )
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{
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NMatrix<N,N> ret;
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for( int i=0; i < N; i++ )
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for( int j=0; j < N; j++ )
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ret.m[i][j] = a.v[i] * b.v[j];
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return ret;
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}
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// -------------------------------------------------------------------------------- //
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// NMatrix inlines.
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// -------------------------------------------------------------------------------- //
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template<int M, int N>
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inline NMatrixMN NMatrixMN::SetupNMatrixNull()
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{
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NMatrix ret;
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memset( ret.m, 0, sizeof(float)*M*N );
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return ret;
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}
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template<int M, int N>
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inline NMatrixMN NMatrixMN::SetupNMatrixIdentity()
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{
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assert( M == N ); // Identity matrices must be square.
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NMatrix ret;
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memset( ret.m, 0, sizeof(float)*M*N );
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for( int i=0; i < N; i++ )
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ret.m[i][i] = 1;
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return ret;
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}
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template<int M, int N>
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inline NMatrixMN const &NMatrixMN::operator=( NMatrixMN const &v )
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{
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memcpy( m, v.m, sizeof(float)*M*N );
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return *this;
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}
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template<int M, int N>
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inline NMatrixMN NMatrixMN::operator+( NMatrixMN const &v ) const
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{
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NMatrixMN ret;
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for( int i=0; i < M; i++ )
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for( int j=0; j < N; j++ )
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ret.m[i][j] = m[i][j] + v.m[i][j];
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return ret;
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}
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template<int M, int N>
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inline NMatrixMN const &NMatrixMN::operator+=( NMatrixMN const &v )
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{
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for( int i=0; i < M; i++ )
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for( int j=0; j < N; j++ )
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m[i][j] += v.m[i][j];
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return *this;
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}
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template<int M, int N>
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inline NMatrixMN NMatrixMN::operator-() const
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{
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NMatrixMN ret;
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for( int i=0; i < M*N; i++ )
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((float*)ret.m)[i] = -((float*)m)[i];
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return ret;
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}
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template<int M, int N>
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inline NMatrixMN NMatrixMN::operator-( NMatrixMN const &v ) const
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{
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NMatrixMN ret;
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for( int i=0; i < M; i++ )
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for( int j=0; j < N; j++ )
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ret.m[i][j] = m[i][j] - v.m[i][j];
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return ret;
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}
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template<int M, int N>
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inline NVector<M> NMatrixMN::operator*( NVectorN const &v ) const
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{
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NVectorN ret;
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for( int i=0; i < M; i++ )
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{
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ret.v[i] = 0;
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for( int j=0; j < N; j++ )
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ret.v[i] += m[i][j] * v.v[j];
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}
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return ret;
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}
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template<int M, int N>
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inline NMatrix<M,M> NMatrixMN::operator*( NMatrix<N,M> const &b ) const
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{
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NMatrix<M,M> ret;
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for( int myRow=0; myRow < M; myRow++ )
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{
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for( int otherCol=0; otherCol < M; otherCol++ )
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{
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ret[myRow][otherCol] = 0;
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for( int i=0; i < N; i++ )
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ret[myRow][otherCol] += a.m[myRow][i] * b.m[i][otherCol];
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}
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}
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return ret;
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}
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template<int M, int N>
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inline NMatrixMN NMatrixMN::operator*( float val ) const
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{
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NMatrixMN ret;
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for( int i=0; i < N*M; i++ )
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((float*)ret.m)[i] = ((float*)m)[i] * val;
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return ret;
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}
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template<int M, int N>
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bool NMatrixMN::InverseGeneral( NMatrixMN &mInverse ) const
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{
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int iRow, i, j, iTemp, iTest;
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float mul, fTest, fLargest;
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float mat[N][2*N];
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int rowMap[N], iLargest;
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float *pOut, *pRow, *pScaleRow;
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// Can only invert square matrices.
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if( M != N )
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{
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assert( !"Tried to invert a non-square matrix" );
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return false;
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}
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// How it's done.
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// AX = I
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// A = this
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// X = the matrix we're looking for
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// I = identity
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// Setup AI
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for(i=0; i < N; i++)
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{
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const float *pIn = m[i];
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pOut = mat[i];
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for(j=0; j < N; j++)
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{
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pOut[j] = pIn[j];
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}
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for(j=N; j < 2*N; j++)
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pOut[j] = 0;
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pOut[i+N] = 1.0f;
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rowMap[i] = i;
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}
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// Use row operations to get to reduced row-echelon form using these rules:
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// 1. Multiply or divide a row by a nonzero number.
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// 2. Add a multiple of one row to another.
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// 3. Interchange two rows.
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for(iRow=0; iRow < N; iRow++)
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{
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// Find the row with the largest element in this column.
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fLargest = 0.001f;
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iLargest = -1;
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for(iTest=iRow; iTest < N; iTest++)
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{
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fTest = (float)fabs(mat[rowMap[iTest]][iRow]);
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if(fTest > fLargest)
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{
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iLargest = iTest;
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fLargest = fTest;
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}
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}
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// They're all too small.. sorry.
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if(iLargest == -1)
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{
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return false;
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}
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// Swap the rows.
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iTemp = rowMap[iLargest];
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rowMap[iLargest] = rowMap[iRow];
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rowMap[iRow] = iTemp;
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pRow = mat[rowMap[iRow]];
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// Divide this row by the element.
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mul = 1.0f / pRow[iRow];
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for(j=0; j < 2*N; j++)
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pRow[j] *= mul;
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pRow[iRow] = 1.0f; // Preserve accuracy...
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// Eliminate this element from the other rows using operation 2.
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for(i=0; i < N; i++)
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{
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if(i == iRow)
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continue;
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pScaleRow = mat[rowMap[i]];
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// Multiply this row by -(iRow*the element).
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mul = -pScaleRow[iRow];
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for(j=0; j < 2*N; j++)
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{
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pScaleRow[j] += pRow[j] * mul;
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}
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pScaleRow[iRow] = 0.0f; // Preserve accuracy...
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}
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}
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// The inverse is on the right side of AX now (the identity is on the left).
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for(i=0; i < N; i++)
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{
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const float *pIn = mat[rowMap[i]] + N;
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pOut = mInverse.m[i];
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for(j=0; j < N; j++)
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{
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pOut[j] = pIn[j];
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}
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}
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return true;
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}
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template<int M, int N>
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inline NMatrix<N,M> NMatrixMN::Transpose() const
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{
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NMatrix<N,M> ret;
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for( int i=0; i < M; i++ )
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for( int j=0; j < N; j++ )
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ret.m[j][i] = m[i][j];
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return ret;
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}
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#endif // NMATRIX_H
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