890 lines
19 KiB
C++
890 lines
19 KiB
C++
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// This code is in the public domain -- Ignacio Casta<74>o <castanyo@yahoo.es>
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#include "Sparse.h"
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#include "KahanSum.h"
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#include "nvcore/Array.inl"
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#define USE_KAHAN_SUM 0
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using namespace nv;
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FullVector::FullVector(uint dim)
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{
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m_array.resize(dim);
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}
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FullVector::FullVector(const FullVector & v) : m_array(v.m_array)
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{
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}
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const FullVector & FullVector::operator=(const FullVector & v)
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{
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nvCheck(dimension() == v.dimension());
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m_array = v.m_array;
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return *this;
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}
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void FullVector::fill(float f)
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{
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const uint dim = dimension();
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for (uint i = 0; i < dim; i++)
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{
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m_array[i] = f;
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}
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}
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void FullVector::operator+= (const FullVector & v)
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{
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nvDebugCheck(dimension() == v.dimension());
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const uint dim = dimension();
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for (uint i = 0; i < dim; i++)
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{
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m_array[i] += v.m_array[i];
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}
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}
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void FullVector::operator-= (const FullVector & v)
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{
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nvDebugCheck(dimension() == v.dimension());
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const uint dim = dimension();
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for (uint i = 0; i < dim; i++)
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{
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m_array[i] -= v.m_array[i];
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}
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}
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void FullVector::operator*= (const FullVector & v)
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{
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nvDebugCheck(dimension() == v.dimension());
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const uint dim = dimension();
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for (uint i = 0; i < dim; i++)
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{
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m_array[i] *= v.m_array[i];
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}
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}
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void FullVector::operator+= (float f)
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{
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const uint dim = dimension();
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for (uint i = 0; i < dim; i++)
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{
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m_array[i] += f;
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}
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}
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void FullVector::operator-= (float f)
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{
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const uint dim = dimension();
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for (uint i = 0; i < dim; i++)
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{
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m_array[i] -= f;
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}
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}
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void FullVector::operator*= (float f)
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{
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const uint dim = dimension();
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for (uint i = 0; i < dim; i++)
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{
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m_array[i] *= f;
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}
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}
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void nv::saxpy(float a, const FullVector & x, FullVector & y)
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{
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nvDebugCheck(x.dimension() == y.dimension());
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const uint dim = x.dimension();
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for (uint i = 0; i < dim; i++)
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{
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y[i] += a * x[i];
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}
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}
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void nv::copy(const FullVector & x, FullVector & y)
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{
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nvDebugCheck(x.dimension() == y.dimension());
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const uint dim = x.dimension();
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for (uint i = 0; i < dim; i++)
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{
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y[i] = x[i];
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}
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}
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void nv::scal(float a, FullVector & x)
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{
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const uint dim = x.dimension();
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for (uint i = 0; i < dim; i++)
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{
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x[i] *= a;
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}
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}
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float nv::dot(const FullVector & x, const FullVector & y)
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{
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nvDebugCheck(x.dimension() == y.dimension());
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const uint dim = x.dimension();
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#if USE_KAHAN_SUM
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KahanSum kahan;
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for (uint i = 0; i < dim; i++)
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{
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kahan.add(x[i] * y[i]);
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}
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return kahan.sum();
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#else
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float sum = 0;
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for (uint i = 0; i < dim; i++)
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{
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sum += x[i] * y[i];
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}
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return sum;
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#endif
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}
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FullMatrix::FullMatrix(uint d) : m_width(d), m_height(d)
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{
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m_array.resize(d*d, 0.0f);
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}
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FullMatrix::FullMatrix(uint w, uint h) : m_width(w), m_height(h)
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{
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m_array.resize(w*h, 0.0f);
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}
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FullMatrix::FullMatrix(const FullMatrix & m) : m_width(m.m_width), m_height(m.m_height)
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{
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m_array = m.m_array;
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}
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const FullMatrix & FullMatrix::operator=(const FullMatrix & m)
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{
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nvCheck(width() == m.width());
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nvCheck(height() == m.height());
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m_array = m.m_array;
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return *this;
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}
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float FullMatrix::getCoefficient(uint x, uint y) const
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{
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nvDebugCheck( x < width() );
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nvDebugCheck( y < height() );
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return m_array[y * width() + x];
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}
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void FullMatrix::setCoefficient(uint x, uint y, float f)
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{
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nvDebugCheck( x < width() );
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nvDebugCheck( y < height() );
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m_array[y * width() + x] = f;
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}
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void FullMatrix::addCoefficient(uint x, uint y, float f)
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{
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nvDebugCheck( x < width() );
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nvDebugCheck( y < height() );
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m_array[y * width() + x] += f;
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}
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void FullMatrix::mulCoefficient(uint x, uint y, float f)
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{
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nvDebugCheck( x < width() );
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nvDebugCheck( y < height() );
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m_array[y * width() + x] *= f;
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}
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float FullMatrix::dotRow(uint y, const FullVector & v) const
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{
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nvDebugCheck( v.dimension() == width() );
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nvDebugCheck( y < height() );
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float sum = 0;
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const uint count = v.dimension();
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for (uint i = 0; i < count; i++)
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{
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sum += m_array[y * count + i] * v[i];
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}
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return sum;
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}
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void FullMatrix::madRow(uint y, float alpha, FullVector & v) const
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{
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nvDebugCheck( v.dimension() == width() );
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nvDebugCheck( y < height() );
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const uint count = v.dimension();
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for (uint i = 0; i < count; i++)
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{
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v[i] += m_array[y * count + i];
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}
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}
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// y = M * x
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void nv::mult(const FullMatrix & M, const FullVector & x, FullVector & y)
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{
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mult(NoTransposed, M, x, y);
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}
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void nv::mult(Transpose TM, const FullMatrix & M, const FullVector & x, FullVector & y)
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{
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const uint w = M.width();
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const uint h = M.height();
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if (TM == Transposed)
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{
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nvDebugCheck( h == x.dimension() );
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nvDebugCheck( w == y.dimension() );
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y.fill(0.0f);
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for (uint i = 0; i < h; i++)
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{
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M.madRow(i, x[i], y);
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}
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}
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else
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{
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nvDebugCheck( w == x.dimension() );
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nvDebugCheck( h == y.dimension() );
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for (uint i = 0; i < h; i++)
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{
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y[i] = M.dotRow(i, x);
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}
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}
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}
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// y = alpha*A*x + beta*y
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void nv::sgemv(float alpha, const FullMatrix & A, const FullVector & x, float beta, FullVector & y)
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{
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sgemv(alpha, NoTransposed, A, x, beta, y);
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}
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void nv::sgemv(float alpha, Transpose TA, const FullMatrix & A, const FullVector & x, float beta, FullVector & y)
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{
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const uint w = A.width();
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const uint h = A.height();
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if (TA == Transposed)
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{
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nvDebugCheck( h == x.dimension() );
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nvDebugCheck( w == y.dimension() );
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for (uint i = 0; i < h; i++)
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{
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A.madRow(i, alpha * x[i], y);
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}
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}
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else
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{
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nvDebugCheck( w == x.dimension() );
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nvDebugCheck( h == y.dimension() );
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for (uint i = 0; i < h; i++)
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{
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y[i] = alpha * A.dotRow(i, x) + beta * y[i];
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}
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}
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}
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// Multiply a row of A by a column of B.
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static float dot(uint j, Transpose TA, const FullMatrix & A, uint i, Transpose TB, const FullMatrix & B)
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{
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const uint w = (TA == NoTransposed) ? A.width() : A.height();
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nvDebugCheck(w == ((TB == NoTransposed) ? B.height() : A.width()));
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float sum = 0.0f;
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for (uint k = 0; k < w; k++)
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{
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const float a = (TA == NoTransposed) ? A.getCoefficient(k, j) : A.getCoefficient(j, k); // @@ Move branches out of the loop?
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const float b = (TB == NoTransposed) ? B.getCoefficient(i, k) : A.getCoefficient(k, i);
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sum += a * b;
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}
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return sum;
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}
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// C = A * B
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void nv::mult(const FullMatrix & A, const FullMatrix & B, FullMatrix & C)
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{
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mult(NoTransposed, A, NoTransposed, B, C);
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}
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void nv::mult(Transpose TA, const FullMatrix & A, Transpose TB, const FullMatrix & B, FullMatrix & C)
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{
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sgemm(1.0f, TA, A, TB, B, 0.0f, C);
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}
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// C = alpha*A*B + beta*C
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void nv::sgemm(float alpha, const FullMatrix & A, const FullMatrix & B, float beta, FullMatrix & C)
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{
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sgemm(alpha, NoTransposed, A, NoTransposed, B, beta, C);
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}
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void nv::sgemm(float alpha, Transpose TA, const FullMatrix & A, Transpose TB, const FullMatrix & B, float beta, FullMatrix & C)
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{
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const uint w = C.width();
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const uint h = C.height();
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uint aw = (TA == NoTransposed) ? A.width() : A.height();
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uint ah = (TA == NoTransposed) ? A.height() : A.width();
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uint bw = (TB == NoTransposed) ? B.width() : B.height();
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uint bh = (TB == NoTransposed) ? B.height() : B.width();
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nvDebugCheck(aw == bh);
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nvDebugCheck(bw == ah);
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nvDebugCheck(w == bw);
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nvDebugCheck(h == ah);
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for (uint y = 0; y < h; y++)
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{
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for (uint x = 0; x < w; x++)
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{
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float c = alpha * ::dot(x, TA, A, y, TB, B) + beta * C.getCoefficient(x, y);
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C.setCoefficient(x, y, c);
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}
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}
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}
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|||
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/// Ctor. Init the size of the sparse matrix.
|
|||
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SparseMatrix::SparseMatrix(uint d) : m_width(d)
|
|||
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{
|
|||
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m_array.resize(d);
|
|||
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}
|
|||
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|
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/// Ctor. Init the size of the sparse matrix.
|
|||
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SparseMatrix::SparseMatrix(uint w, uint h) : m_width(w)
|
|||
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{
|
|||
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m_array.resize(h);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
SparseMatrix::SparseMatrix(const SparseMatrix & m) : m_width(m.m_width)
|
|||
|
|
{
|
|||
|
|
m_array = m.m_array;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
const SparseMatrix & SparseMatrix::operator=(const SparseMatrix & m)
|
|||
|
|
{
|
|||
|
|
nvCheck(width() == m.width());
|
|||
|
|
nvCheck(height() == m.height());
|
|||
|
|
|
|||
|
|
m_array = m.m_array;
|
|||
|
|
|
|||
|
|
return *this;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
|
|||
|
|
// x is column, y is row
|
|||
|
|
float SparseMatrix::getCoefficient(uint x, uint y) const
|
|||
|
|
{
|
|||
|
|
nvDebugCheck( x < width() );
|
|||
|
|
nvDebugCheck( y < height() );
|
|||
|
|
|
|||
|
|
const uint count = m_array[y].count();
|
|||
|
|
for (uint i = 0; i < count; i++)
|
|||
|
|
{
|
|||
|
|
if (m_array[y][i].x == x) return m_array[y][i].v;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
return 0.0f;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
void SparseMatrix::setCoefficient(uint x, uint y, float f)
|
|||
|
|
{
|
|||
|
|
nvDebugCheck( x < width() );
|
|||
|
|
nvDebugCheck( y < height() );
|
|||
|
|
|
|||
|
|
const uint count = m_array[y].count();
|
|||
|
|
for (uint i = 0; i < count; i++)
|
|||
|
|
{
|
|||
|
|
if (m_array[y][i].x == x)
|
|||
|
|
{
|
|||
|
|
m_array[y][i].v = f;
|
|||
|
|
return;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if (f != 0.0f)
|
|||
|
|
{
|
|||
|
|
Coefficient c = { x, f };
|
|||
|
|
m_array[y].append( c );
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
void SparseMatrix::addCoefficient(uint x, uint y, float f)
|
|||
|
|
{
|
|||
|
|
nvDebugCheck( x < width() );
|
|||
|
|
nvDebugCheck( y < height() );
|
|||
|
|
|
|||
|
|
if (f != 0.0f)
|
|||
|
|
{
|
|||
|
|
const uint count = m_array[y].count();
|
|||
|
|
for (uint i = 0; i < count; i++)
|
|||
|
|
{
|
|||
|
|
if (m_array[y][i].x == x)
|
|||
|
|
{
|
|||
|
|
m_array[y][i].v += f;
|
|||
|
|
return;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
Coefficient c = { x, f };
|
|||
|
|
m_array[y].append( c );
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
void SparseMatrix::mulCoefficient(uint x, uint y, float f)
|
|||
|
|
{
|
|||
|
|
nvDebugCheck( x < width() );
|
|||
|
|
nvDebugCheck( y < height() );
|
|||
|
|
|
|||
|
|
const uint count = m_array[y].count();
|
|||
|
|
for (uint i = 0; i < count; i++)
|
|||
|
|
{
|
|||
|
|
if (m_array[y][i].x == x)
|
|||
|
|
{
|
|||
|
|
m_array[y][i].v *= f;
|
|||
|
|
return;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if (f != 0.0f)
|
|||
|
|
{
|
|||
|
|
Coefficient c = { x, f };
|
|||
|
|
m_array[y].append( c );
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
|
|||
|
|
float SparseMatrix::sumRow(uint y) const
|
|||
|
|
{
|
|||
|
|
nvDebugCheck( y < height() );
|
|||
|
|
|
|||
|
|
const uint count = m_array[y].count();
|
|||
|
|
|
|||
|
|
#if USE_KAHAN_SUM
|
|||
|
|
KahanSum kahan;
|
|||
|
|
for (uint i = 0; i < count; i++)
|
|||
|
|
{
|
|||
|
|
kahan.add(m_array[y][i].v);
|
|||
|
|
}
|
|||
|
|
return kahan.sum();
|
|||
|
|
#else
|
|||
|
|
float sum = 0;
|
|||
|
|
for (uint i = 0; i < count; i++)
|
|||
|
|
{
|
|||
|
|
sum += m_array[y][i].v;
|
|||
|
|
}
|
|||
|
|
return sum;
|
|||
|
|
#endif
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
float SparseMatrix::dotRow(uint y, const FullVector & v) const
|
|||
|
|
{
|
|||
|
|
nvDebugCheck( y < height() );
|
|||
|
|
|
|||
|
|
const uint count = m_array[y].count();
|
|||
|
|
|
|||
|
|
#if USE_KAHAN_SUM
|
|||
|
|
KahanSum kahan;
|
|||
|
|
for (uint i = 0; i < count; i++)
|
|||
|
|
{
|
|||
|
|
kahan.add(m_array[y][i].v * v[m_array[y][i].x]);
|
|||
|
|
}
|
|||
|
|
return kahan.sum();
|
|||
|
|
#else
|
|||
|
|
float sum = 0;
|
|||
|
|
for (uint i = 0; i < count; i++)
|
|||
|
|
{
|
|||
|
|
sum += m_array[y][i].v * v[m_array[y][i].x];
|
|||
|
|
}
|
|||
|
|
return sum;
|
|||
|
|
#endif
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
void SparseMatrix::madRow(uint y, float alpha, FullVector & v) const
|
|||
|
|
{
|
|||
|
|
nvDebugCheck(y < height());
|
|||
|
|
|
|||
|
|
const uint count = m_array[y].count();
|
|||
|
|
for (uint i = 0; i < count; i++)
|
|||
|
|
{
|
|||
|
|
v[m_array[y][i].x] += alpha * m_array[y][i].v;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
|
|||
|
|
void SparseMatrix::clearRow(uint y)
|
|||
|
|
{
|
|||
|
|
nvDebugCheck( y < height() );
|
|||
|
|
|
|||
|
|
m_array[y].clear();
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
void SparseMatrix::scaleRow(uint y, float f)
|
|||
|
|
{
|
|||
|
|
nvDebugCheck( y < height() );
|
|||
|
|
|
|||
|
|
const uint count = m_array[y].count();
|
|||
|
|
for (uint i = 0; i < count; i++)
|
|||
|
|
{
|
|||
|
|
m_array[y][i].v *= f;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
void SparseMatrix::normalizeRow(uint y)
|
|||
|
|
{
|
|||
|
|
nvDebugCheck( y < height() );
|
|||
|
|
|
|||
|
|
float norm = 0.0f;
|
|||
|
|
|
|||
|
|
const uint count = m_array[y].count();
|
|||
|
|
for (uint i = 0; i < count; i++)
|
|||
|
|
{
|
|||
|
|
float f = m_array[y][i].v;
|
|||
|
|
norm += f * f;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
scaleRow(y, 1.0f / sqrtf(norm));
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
|
|||
|
|
void SparseMatrix::clearColumn(uint x)
|
|||
|
|
{
|
|||
|
|
nvDebugCheck(x < width());
|
|||
|
|
|
|||
|
|
for (uint y = 0; y < height(); y++)
|
|||
|
|
{
|
|||
|
|
const uint count = m_array[y].count();
|
|||
|
|
for (uint e = 0; e < count; e++)
|
|||
|
|
{
|
|||
|
|
if (m_array[y][e].x == x)
|
|||
|
|
{
|
|||
|
|
m_array[y][e].v = 0.0f;
|
|||
|
|
break;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
void SparseMatrix::scaleColumn(uint x, float f)
|
|||
|
|
{
|
|||
|
|
nvDebugCheck(x < width());
|
|||
|
|
|
|||
|
|
for (uint y = 0; y < height(); y++)
|
|||
|
|
{
|
|||
|
|
const uint count = m_array[y].count();
|
|||
|
|
for (uint e = 0; e < count; e++)
|
|||
|
|
{
|
|||
|
|
if (m_array[y][e].x == x)
|
|||
|
|
{
|
|||
|
|
m_array[y][e].v *= f;
|
|||
|
|
break;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
const Array<SparseMatrix::Coefficient> & SparseMatrix::getRow(uint y) const
|
|||
|
|
{
|
|||
|
|
return m_array[y];
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
|
|||
|
|
bool SparseMatrix::isSymmetric() const
|
|||
|
|
{
|
|||
|
|
for (uint y = 0; y < height(); y++)
|
|||
|
|
{
|
|||
|
|
const uint count = m_array[y].count();
|
|||
|
|
for (uint e = 0; e < count; e++)
|
|||
|
|
{
|
|||
|
|
const uint x = m_array[y][e].x;
|
|||
|
|
if (x > y) {
|
|||
|
|
float v = m_array[y][e].v;
|
|||
|
|
|
|||
|
|
if (!equal(getCoefficient(y, x), v)) { // @@ epsilon
|
|||
|
|
return false;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
return true;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
|
|||
|
|
// y = M * x
|
|||
|
|
void nv::mult(const SparseMatrix & M, const FullVector & x, FullVector & y)
|
|||
|
|
{
|
|||
|
|
mult(NoTransposed, M, x, y);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
void nv::mult(Transpose TM, const SparseMatrix & M, const FullVector & x, FullVector & y)
|
|||
|
|
{
|
|||
|
|
const uint w = M.width();
|
|||
|
|
const uint h = M.height();
|
|||
|
|
|
|||
|
|
if (TM == Transposed)
|
|||
|
|
{
|
|||
|
|
nvDebugCheck( h == x.dimension() );
|
|||
|
|
nvDebugCheck( w == y.dimension() );
|
|||
|
|
|
|||
|
|
y.fill(0.0f);
|
|||
|
|
|
|||
|
|
for (uint i = 0; i < h; i++)
|
|||
|
|
{
|
|||
|
|
M.madRow(i, x[i], y);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
else
|
|||
|
|
{
|
|||
|
|
nvDebugCheck( w == x.dimension() );
|
|||
|
|
nvDebugCheck( h == y.dimension() );
|
|||
|
|
|
|||
|
|
for (uint i = 0; i < h; i++)
|
|||
|
|
{
|
|||
|
|
y[i] = M.dotRow(i, x);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// y = alpha*A*x + beta*y
|
|||
|
|
void nv::sgemv(float alpha, const SparseMatrix & A, const FullVector & x, float beta, FullVector & y)
|
|||
|
|
{
|
|||
|
|
sgemv(alpha, NoTransposed, A, x, beta, y);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
void nv::sgemv(float alpha, Transpose TA, const SparseMatrix & A, const FullVector & x, float beta, FullVector & y)
|
|||
|
|
{
|
|||
|
|
const uint w = A.width();
|
|||
|
|
const uint h = A.height();
|
|||
|
|
|
|||
|
|
if (TA == Transposed)
|
|||
|
|
{
|
|||
|
|
nvDebugCheck( h == x.dimension() );
|
|||
|
|
nvDebugCheck( w == y.dimension() );
|
|||
|
|
|
|||
|
|
for (uint i = 0; i < h; i++)
|
|||
|
|
{
|
|||
|
|
A.madRow(i, alpha * x[i], y);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
else
|
|||
|
|
{
|
|||
|
|
nvDebugCheck( w == x.dimension() );
|
|||
|
|
nvDebugCheck( h == y.dimension() );
|
|||
|
|
|
|||
|
|
for (uint i = 0; i < h; i++)
|
|||
|
|
{
|
|||
|
|
y[i] = alpha * A.dotRow(i, x) + beta * y[i];
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
|
|||
|
|
// dot y-row of A by x-column of B
|
|||
|
|
static float dotRowColumn(int y, const SparseMatrix & A, int x, const SparseMatrix & B)
|
|||
|
|
{
|
|||
|
|
const Array<SparseMatrix::Coefficient> & row = A.getRow(y);
|
|||
|
|
|
|||
|
|
const uint count = row.count();
|
|||
|
|
|
|||
|
|
#if USE_KAHAN_SUM
|
|||
|
|
KahanSum kahan;
|
|||
|
|
for (uint i = 0; i < count; i++)
|
|||
|
|
{
|
|||
|
|
const SparseMatrix::Coefficient & c = row[i];
|
|||
|
|
kahan.add(c.v * B.getCoefficient(x, c.x));
|
|||
|
|
}
|
|||
|
|
return kahan.sum();
|
|||
|
|
#else
|
|||
|
|
float sum = 0.0f;
|
|||
|
|
for (uint i = 0; i < count; i++)
|
|||
|
|
{
|
|||
|
|
const SparseMatrix::Coefficient & c = row[i];
|
|||
|
|
sum += c.v * B.getCoefficient(x, c.x);
|
|||
|
|
}
|
|||
|
|
return sum;
|
|||
|
|
#endif
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// dot y-row of A by x-row of B
|
|||
|
|
static float dotRowRow(int y, const SparseMatrix & A, int x, const SparseMatrix & B)
|
|||
|
|
{
|
|||
|
|
const Array<SparseMatrix::Coefficient> & row = A.getRow(y);
|
|||
|
|
|
|||
|
|
const uint count = row.count();
|
|||
|
|
|
|||
|
|
#if USE_KAHAN_SUM
|
|||
|
|
KahanSum kahan;
|
|||
|
|
for (uint i = 0; i < count; i++)
|
|||
|
|
{
|
|||
|
|
const SparseMatrix::Coefficient & c = row[i];
|
|||
|
|
kahan.add(c.v * B.getCoefficient(c.x, x));
|
|||
|
|
}
|
|||
|
|
return kahan.sum();
|
|||
|
|
#else
|
|||
|
|
float sum = 0.0f;
|
|||
|
|
for (uint i = 0; i < count; i++)
|
|||
|
|
{
|
|||
|
|
const SparseMatrix::Coefficient & c = row[i];
|
|||
|
|
sum += c.v * B.getCoefficient(c.x, x);
|
|||
|
|
}
|
|||
|
|
return sum;
|
|||
|
|
#endif
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// dot y-column of A by x-column of B
|
|||
|
|
static float dotColumnColumn(int y, const SparseMatrix & A, int x, const SparseMatrix & B)
|
|||
|
|
{
|
|||
|
|
nvDebugCheck(A.height() == B.height());
|
|||
|
|
|
|||
|
|
const uint h = A.height();
|
|||
|
|
|
|||
|
|
#if USE_KAHAN_SUM
|
|||
|
|
KahanSum kahan;
|
|||
|
|
for (uint i = 0; i < h; i++)
|
|||
|
|
{
|
|||
|
|
kahan.add(A.getCoefficient(y, i) * B.getCoefficient(x, i));
|
|||
|
|
}
|
|||
|
|
return kahan.sum();
|
|||
|
|
#else
|
|||
|
|
float sum = 0.0f;
|
|||
|
|
for (uint i = 0; i < h; i++)
|
|||
|
|
{
|
|||
|
|
sum += A.getCoefficient(y, i) * B.getCoefficient(x, i);
|
|||
|
|
}
|
|||
|
|
return sum;
|
|||
|
|
#endif
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
|
|||
|
|
void nv::transpose(const SparseMatrix & A, SparseMatrix & B)
|
|||
|
|
{
|
|||
|
|
nvDebugCheck(A.width() == B.height());
|
|||
|
|
nvDebugCheck(B.width() == A.height());
|
|||
|
|
|
|||
|
|
const uint w = A.width();
|
|||
|
|
for (uint x = 0; x < w; x++)
|
|||
|
|
{
|
|||
|
|
B.clearRow(x);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
const uint h = A.height();
|
|||
|
|
for (uint y = 0; y < h; y++)
|
|||
|
|
{
|
|||
|
|
const Array<SparseMatrix::Coefficient> & row = A.getRow(y);
|
|||
|
|
|
|||
|
|
const uint count = row.count();
|
|||
|
|
for (uint i = 0; i < count; i++)
|
|||
|
|
{
|
|||
|
|
const SparseMatrix::Coefficient & c = row[i];
|
|||
|
|
nvDebugCheck(c.x < w);
|
|||
|
|
|
|||
|
|
B.setCoefficient(y, c.x, c.v);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// C = A * B
|
|||
|
|
void nv::mult(const SparseMatrix & A, const SparseMatrix & B, SparseMatrix & C)
|
|||
|
|
{
|
|||
|
|
mult(NoTransposed, A, NoTransposed, B, C);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
void nv::mult(Transpose TA, const SparseMatrix & A, Transpose TB, const SparseMatrix & B, SparseMatrix & C)
|
|||
|
|
{
|
|||
|
|
sgemm(1.0f, TA, A, TB, B, 0.0f, C);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// C = alpha*A*B + beta*C
|
|||
|
|
void nv::sgemm(float alpha, const SparseMatrix & A, const SparseMatrix & B, float beta, SparseMatrix & C)
|
|||
|
|
{
|
|||
|
|
sgemm(alpha, NoTransposed, A, NoTransposed, B, beta, C);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
void nv::sgemm(float alpha, Transpose TA, const SparseMatrix & A, Transpose TB, const SparseMatrix & B, float beta, SparseMatrix & C)
|
|||
|
|
{
|
|||
|
|
const uint w = C.width();
|
|||
|
|
const uint h = C.height();
|
|||
|
|
|
|||
|
|
uint aw = (TA == NoTransposed) ? A.width() : A.height();
|
|||
|
|
uint ah = (TA == NoTransposed) ? A.height() : A.width();
|
|||
|
|
uint bw = (TB == NoTransposed) ? B.width() : B.height();
|
|||
|
|
uint bh = (TB == NoTransposed) ? B.height() : B.width();
|
|||
|
|
|
|||
|
|
nvDebugCheck(aw == bh);
|
|||
|
|
nvDebugCheck(bw == ah);
|
|||
|
|
nvDebugCheck(w == bw);
|
|||
|
|
nvDebugCheck(h == ah);
|
|||
|
|
|
|||
|
|
|
|||
|
|
for (uint y = 0; y < h; y++)
|
|||
|
|
{
|
|||
|
|
for (uint x = 0; x < w; x++)
|
|||
|
|
{
|
|||
|
|
float c = beta * C.getCoefficient(x, y);
|
|||
|
|
|
|||
|
|
if (TA == NoTransposed && TB == NoTransposed)
|
|||
|
|
{
|
|||
|
|
// dot y-row of A by x-column of B.
|
|||
|
|
c += alpha * dotRowColumn(y, A, x, B);
|
|||
|
|
}
|
|||
|
|
else if (TA == Transposed && TB == Transposed)
|
|||
|
|
{
|
|||
|
|
// dot y-column of A by x-row of B.
|
|||
|
|
c += alpha * dotRowColumn(x, B, y, A);
|
|||
|
|
}
|
|||
|
|
else if (TA == Transposed && TB == NoTransposed)
|
|||
|
|
{
|
|||
|
|
// dot y-column of A by x-column of B.
|
|||
|
|
c += alpha * dotColumnColumn(y, A, x, B);
|
|||
|
|
}
|
|||
|
|
else if (TA == NoTransposed && TB == Transposed)
|
|||
|
|
{
|
|||
|
|
// dot y-row of A by x-row of B.
|
|||
|
|
c += alpha * dotRowRow(y, A, x, B);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
C.setCoefficient(x, y, c);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// C = At * A
|
|||
|
|
void nv::sqm(const SparseMatrix & A, SparseMatrix & C)
|
|||
|
|
{
|
|||
|
|
// This is quite expensive...
|
|||
|
|
mult(Transposed, A, NoTransposed, A, C);
|
|||
|
|
}
|