333 lines
6.1 KiB
C++
333 lines
6.1 KiB
C++
//========= Copyright Valve Corporation, All rights reserved. ============//
|
|
//
|
|
// Purpose:
|
|
//
|
|
// $NoKeywords: $
|
|
//=============================================================================//
|
|
|
|
#ifndef NMATRIX_H
|
|
#define NMATRIX_H
|
|
#ifdef _WIN32
|
|
#pragma once
|
|
#endif
|
|
|
|
|
|
#include <assert.h>
|
|
#include "nvector.h"
|
|
|
|
|
|
#define NMatrixMN NMatrix<M,N>
|
|
|
|
|
|
template<int M, int N>
|
|
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<M> operator*( NVector<N> const &v ) const;
|
|
|
|
// Can't get the compiler to work with a real MxN * NxR matrix multiply...
|
|
NMatrix<M,M> operator*( NMatrix<N,M> const &b ) const;
|
|
|
|
NMatrixMN operator*( float val ) const;
|
|
|
|
bool InverseGeneral( NMatrixMN &mInverse ) const;
|
|
NMatrix<N,M> Transpose() const;
|
|
|
|
|
|
public:
|
|
|
|
float m[M][N];
|
|
};
|
|
|
|
|
|
|
|
// Return the matrix generated by multiplying a column vector 'a' by row vector 'b'.
|
|
template<int N>
|
|
inline NMatrix<N,N> OuterProduct( NVectorN const &a, NVectorN const &b )
|
|
{
|
|
NMatrix<N,N> 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<int M, int N>
|
|
inline NMatrixMN NMatrixMN::SetupNMatrixNull()
|
|
{
|
|
NMatrix ret;
|
|
memset( ret.m, 0, sizeof(float)*M*N );
|
|
return ret;
|
|
}
|
|
|
|
|
|
template<int M, int N>
|
|
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<int M, int N>
|
|
inline NMatrixMN const &NMatrixMN::operator=( NMatrixMN const &v )
|
|
{
|
|
memcpy( m, v.m, sizeof(float)*M*N );
|
|
return *this;
|
|
}
|
|
|
|
|
|
template<int M, int N>
|
|
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<int M, int N>
|
|
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<int M, int N>
|
|
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<int M, int N>
|
|
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<int M, int N>
|
|
inline NVector<M> 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<int M, int N>
|
|
inline NMatrix<M,M> NMatrixMN::operator*( NMatrix<N,M> const &b ) const
|
|
{
|
|
NMatrix<M,M> 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<int M, int N>
|
|
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<int M, int N>
|
|
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 = 0.001f;
|
|
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<int M, int N>
|
|
inline NMatrix<N,M> NMatrixMN::Transpose() const
|
|
{
|
|
NMatrix<N,M> 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
|
|
|