//========= Copyright © 1996-2005, Valve Corporation, All rights reserved. ============// // // Purpose: // // $NoKeywords: $ //=============================================================================// #ifndef NMATRIX_H #define NMATRIX_H #ifdef _WIN32 #pragma once #endif #include #include "nvector.h" #define NMatrixMN NMatrix template class NMatrix { public: NMatrixMN() {} static NMatrixMN SetupNMatrixNull(); // Return a matrix of all zeros. static NMatrixMN SetupNMatrixIdentity(); // Return an identity matrix. NMatrixMN const& operator=( NMatrixMN const &other ); NMatrixMN operator+( NMatrixMN const &v ) const; NMatrixMN const& operator+=( NMatrixMN const &v ); NMatrixMN operator-() const; NMatrixMN operator-( NMatrixMN const &v ) const; // Multiplies the column vector on the right-hand side. NVector operator*( NVector const &v ) const; // Can't get the compiler to work with a real MxN * NxR matrix multiply... NMatrix operator*( NMatrix const &b ) const; NMatrixMN operator*( float val ) const; bool InverseGeneral( NMatrixMN &mInverse ) const; NMatrix Transpose() const; public: float m[M][N]; }; // Return the matrix generated by multiplying a column vector 'a' by row vector 'b'. template inline NMatrix OuterProduct( NVectorN const &a, NVectorN const &b ) { NMatrix ret; for( int i=0; i < N; i++ ) for( int j=0; j < N; j++ ) ret.m[i][j] = a.v[i] * b.v[j]; return ret; } // -------------------------------------------------------------------------------- // // NMatrix inlines. // -------------------------------------------------------------------------------- // template inline NMatrixMN NMatrixMN::SetupNMatrixNull() { NMatrix ret; memset( ret.m, 0, sizeof(float)*M*N ); return ret; } template inline NMatrixMN NMatrixMN::SetupNMatrixIdentity() { assert( M == N ); // Identity matrices must be square. NMatrix ret; memset( ret.m, 0, sizeof(float)*M*N ); for( int i=0; i < N; i++ ) ret.m[i][i] = 1; return ret; } template inline NMatrixMN const &NMatrixMN::operator=( NMatrixMN const &v ) { memcpy( m, v.m, sizeof(float)*M*N ); return *this; } template inline NMatrixMN NMatrixMN::operator+( NMatrixMN const &v ) const { NMatrixMN ret; for( int i=0; i < M; i++ ) for( int j=0; j < N; j++ ) ret.m[i][j] = m[i][j] + v.m[i][j]; return ret; } template inline NMatrixMN const &NMatrixMN::operator+=( NMatrixMN const &v ) { for( int i=0; i < M; i++ ) for( int j=0; j < N; j++ ) m[i][j] += v.m[i][j]; return *this; } template inline NMatrixMN NMatrixMN::operator-() const { NMatrixMN ret; for( int i=0; i < M*N; i++ ) ((float*)ret.m)[i] = -((float*)m)[i]; return ret; } template inline NMatrixMN NMatrixMN::operator-( NMatrixMN const &v ) const { NMatrixMN ret; for( int i=0; i < M; i++ ) for( int j=0; j < N; j++ ) ret.m[i][j] = m[i][j] - v.m[i][j]; return ret; } template inline NVector NMatrixMN::operator*( NVectorN const &v ) const { NVectorN ret; for( int i=0; i < M; i++ ) { ret.v[i] = 0; for( int j=0; j < N; j++ ) ret.v[i] += m[i][j] * v.v[j]; } return ret; } template inline NMatrix NMatrixMN::operator*( NMatrix const &b ) const { NMatrix ret; for( int myRow=0; myRow < M; myRow++ ) { for( int otherCol=0; otherCol < M; otherCol++ ) { ret[myRow][otherCol] = 0; for( int i=0; i < N; i++ ) ret[myRow][otherCol] += a.m[myRow][i] * b.m[i][otherCol]; } } return ret; } template inline NMatrixMN NMatrixMN::operator*( float val ) const { NMatrixMN ret; for( int i=0; i < N*M; i++ ) ((float*)ret.m)[i] = ((float*)m)[i] * val; return ret; } template bool NMatrixMN::InverseGeneral( NMatrixMN &mInverse ) const { int iRow, i, j, iTemp, iTest; float mul, fTest, fLargest; float mat[N][2*N]; int rowMap[N], iLargest; float *pOut, *pRow, *pScaleRow; // Can only invert square matrices. if( M != N ) { assert( !"Tried to invert a non-square matrix" ); return false; } // How it's done. // AX = I // A = this // X = the matrix we're looking for // I = identity // Setup AI for(i=0; i < N; i++) { const float *pIn = m[i]; pOut = mat[i]; for(j=0; j < N; j++) { pOut[j] = pIn[j]; } for(j=N; j < 2*N; j++) pOut[j] = 0; pOut[i+N] = 1.0f; rowMap[i] = i; } // Use row operations to get to reduced row-echelon form using these rules: // 1. Multiply or divide a row by a nonzero number. // 2. Add a multiple of one row to another. // 3. Interchange two rows. for(iRow=0; iRow < N; iRow++) { // Find the row with the largest element in this column. fLargest = 1e-6f; iLargest = -1; for(iTest=iRow; iTest < N; iTest++) { fTest = (float)fabs(mat[rowMap[iTest]][iRow]); if(fTest > fLargest) { iLargest = iTest; fLargest = fTest; } } // They're all too small.. sorry. if(iLargest == -1) { return false; } // Swap the rows. iTemp = rowMap[iLargest]; rowMap[iLargest] = rowMap[iRow]; rowMap[iRow] = iTemp; pRow = mat[rowMap[iRow]]; // Divide this row by the element. mul = 1.0f / pRow[iRow]; for(j=0; j < 2*N; j++) pRow[j] *= mul; pRow[iRow] = 1.0f; // Preserve accuracy... // Eliminate this element from the other rows using operation 2. for(i=0; i < N; i++) { if(i == iRow) continue; pScaleRow = mat[rowMap[i]]; // Multiply this row by -(iRow*the element). mul = -pScaleRow[iRow]; for(j=0; j < 2*N; j++) { pScaleRow[j] += pRow[j] * mul; } pScaleRow[iRow] = 0.0f; // Preserve accuracy... } } // The inverse is on the right side of AX now (the identity is on the left). for(i=0; i < N; i++) { const float *pIn = mat[rowMap[i]] + N; pOut = mInverse.m[i]; for(j=0; j < N; j++) { pOut[j] = pIn[j]; } } return true; } template inline NMatrix NMatrixMN::Transpose() const { NMatrix ret; for( int i=0; i < M; i++ ) for( int j=0; j < N; j++ ) ret.m[j][i] = m[i][j]; return ret; } #endif // NMATRIX_H