GSparseMatrix* GSparseMatrix::subMatrix(int row, int col, int height, int width)
{
if(row < 0 || col < 0 || row + height >= (int)m_rows || col + width >= (int)m_cols || height < 0 || width < 0)
ThrowError("out of range");
GSparseMatrix* pSub = new GSparseMatrix(height, width);
for(int y = 0; y < height; y++)
{
for(int x = 0; x < width; x++)
pSub->set(y, x, get(row + y, col + x));
}
return pSub;
}
GSparseMatrix* GRecommenderLib::loadSparseData(const char* szFilename)
{
// Load the dataset by extension
PathData pd;
GFile::parsePath(szFilename, &pd);
if(_stricmp(szFilename + pd.extStart, ".arff") == 0)
{
// Convert a 3-column dense ARFF file to a sparse matrix
GMatrix data;
data.loadArff(szFilename);
if(data.cols() != 3)
throw Ex("Expected 3 columns: 0) user or row-index, 1) item or col-index, 2) value or rating");
double m0 = data.columnMin(0);
double r0 = data.columnMax(0) - m0;
double m1 = data.columnMin(1);
double r1 = data.columnMax(1) - m1;
if(m0 < 0 || m0 > 1e10 || r0 < 2 || r0 > 1e10)
throw Ex("Invalid row indexes");
if(m1 < 0 || m1 > 1e10 || r1 < 2 || r1 > 1e10)
throw Ex("Invalid col indexes");
GSparseMatrix* pMatrix = new GSparseMatrix(size_t(m0 + r0) + 1, size_t(m1 + r1) + 1, UNKNOWN_REAL_VALUE);
std::unique_ptr<GSparseMatrix> hMatrix(pMatrix);
for(size_t i = 0; i < data.rows(); i++)
{
GVec& row = data.row(i);
pMatrix->set(size_t(row[0]), size_t(row[1]), row[2]);
}
return hMatrix.release();
}
else if(_stricmp(szFilename + pd.extStart, ".sparse") == 0)
{
GDom doc;
doc.loadJson(szFilename);
return new GSparseMatrix(doc.root());
}
throw Ex("Unsupported file format: ", szFilename + pd.extStart);
return NULL;
}
GSparseMatrix* loadSparseData(const char* szFilename)
{
// Load the dataset by extension
PathData pd;
GFile::parsePath(szFilename, &pd);
if(_stricmp(szFilename + pd.extStart, ".arff") == 0)
{
// Convert a 3-column dense ARFF file to a sparse matrix
GMatrix* pData = GMatrix::loadArff(szFilename);
if(pData->cols() != 3)
ThrowError("Expected 3 columns: 0) user or row-index, 1) item or col-index, 2) value or rating");
double m0, r0, m1, r1;
pData->minAndRange(0, &m0, &r0);
pData->minAndRange(1, &m1, &r1);
if(m0 < 0 || m0 > 1e10 || r0 < 2 || r0 > 1e10)
ThrowError("Invalid row indexes");
if(m1 < 0 || m1 > 1e10 || r1 < 2 || r1 > 1e10)
ThrowError("Invalid col indexes");
GSparseMatrix* pMatrix = new GSparseMatrix(size_t(m0 + r0) + 1, size_t(m1 + r1) + 1, UNKNOWN_REAL_VALUE);
Holder<GSparseMatrix> hMatrix(pMatrix);
for(size_t i = 0; i < pData->rows(); i++)
{
double* pRow = pData->row(i);
pMatrix->set(size_t(pRow[0]), size_t(pRow[1]), pRow[2]);
}
return hMatrix.release();
}
else if(_stricmp(szFilename + pd.extStart, ".sparse") == 0)
{
GDom doc;
doc.loadJson(szFilename);
return new GSparseMatrix(doc.root());
}
ThrowError("Unsupported file format: ", szFilename + pd.extStart);
return NULL;
}
void GSparseMatrix::singularValueDecompositionHelper(GSparseMatrix** ppU, double** ppDiag, GSparseMatrix** ppV, int maxIters)
{
int m = rows();
int n = cols();
if(m < n)
ThrowError("Expected at least as many rows as columns");
int i, j, k;
int l = 0;
int q, iter;
double c, f, h, s, x, y, z;
double norm = 0.0;
double g = 0.0;
double scale = 0.0;
GSparseMatrix* pU = new GSparseMatrix(m, m);
Holder<GSparseMatrix> hU(pU);
pU->copyFrom(this);
double* pSigma = new double[n];
ArrayHolder<double> hSigma(pSigma);
GSparseMatrix* pV = new GSparseMatrix(n, n);
Holder<GSparseMatrix> hV(pV);
GTEMPBUF(double, temp, n + m);
double* temp2 = temp + n;
// Householder reduction to bidiagonal form
for(int i = 0; i < n; i++)
{
// Left-hand reduction
temp[i] = scale * g;
l = i + 1;
g = 0.0;
s = 0.0;
scale = 0.0;
if(i < m)
{
Iter kend = pU->colEnd(i);
for(Iter kk = pU->colBegin(i); kk != kend; kk++)
{
if(kk->first >= (unsigned int)i)
scale += ABS(kk->second);
}
if(scale != 0.0)
{
for(Iter kk = pU->colBegin(i); kk != kend; kk++)
{
if(kk->first >= (unsigned int)i)
{
double t = kk->second / scale;
pU->set(kk->first, i, t);
s += (t * t);
}
}
f = pU->get(i, i);
g = -GSparseMatrix_takeSign(sqrt(s), f);
h = f * g - s;
pU->set(i, i, f - g);
if(i != n - 1)
{
for(j = l; j < n; j++)
{
s = 0.0;
for(Iter kk = pU->colBegin(i); kk != kend; kk++)
{
if(kk->first >= (unsigned int)i)
s += kk->second * pU->get(kk->first, j);
}
f = s / h;
for(Iter kk = pU->colBegin(i); kk != kend; kk++)
{
if(kk->first >= (unsigned int)i)
pU->set(kk->first, j, pU->get(kk->first, j) + f * kk->second);
}
}
}
for(Iter kk = pU->colBegin(i); kk != kend; kk++)
{
if(kk->first >= (unsigned int)i)
pU->set(kk->first, i, pU->get(kk->first, i) * scale);
}
}
}
pSigma[i] = scale * g;
// Right-hand reduction
g = 0.0;
s = 0.0;
scale = 0.0;
if(i < m && i != n - 1)
{
Iter kend = pU->rowEnd(i);
for(Iter kk = pU->rowBegin(i); kk != kend; kk++)
{
if(kk->first >= (unsigned int)n)
break;
if(kk->first >= (unsigned int)l)
scale += ABS(kk->second);
}
if(scale != 0.0)
{
for(Iter kk = pU->rowBegin(i); kk != kend; kk++)
{
if(kk->first >= (unsigned int)n)
break;
if(kk->first >= (unsigned int)l)
{
double t = kk->second / scale;
pU->set(i, kk->first, t);
s += (t * t);
}
}
f = pU->get(i, l);
g = -GSparseMatrix_takeSign(sqrt(s), f);
h = f * g - s;
pU->set(i, l, f - g);
for(k = l; k < n; k++)
temp[k] = pU->get(i, k) / h;
if(i != m - 1)
{
for(j = l; j < m; j++)
{
s = 0.0;
for(Iter kk = pU->rowBegin(i); kk != kend; kk++)
{
if(kk->first >= (unsigned int)n)
break;
if(kk->first >= (unsigned int)l)
s += pU->get(j, kk->first) * kk->second;
}
Iter kend2 = pU->rowEnd(j);
for(Iter kk = pU->rowBegin(j); kk != kend2; kk++)
{
if(kk->first >= (unsigned int)n)
break;
if(kk->first >= (unsigned int)l)
pU->set(j, kk->first, pU->get(j, kk->first) + s * temp[kk->first]);
}
}
}
for(Iter kk = pU->rowBegin(i); kk != kend; kk++)
{
if(kk->first >= (unsigned int)n)
break;
if(kk->first >= (unsigned int)l)
pU->set(i, kk->first, kk->second * scale);
}
}
}
norm = MAX(norm, ABS(pSigma[i]) + ABS(temp[i]));
}
// Accumulate right-hand transform
for(int i = n - 1; i >= 0; i--)
{
if(i < n - 1)
{
if(g != 0.0)
{
Iter jend = pU->rowEnd(i);
for(Iter jj = pU->rowBegin(i); jj != jend; jj++)
{
if(jj->first >= (unsigned int)n)
break;
if(jj->first >= (unsigned int)l)
pV->set(i, jj->first, (jj->second / pU->get(i, l)) / g); // (double-division to avoid underflow)
}
for(j = l; j < n; j++)
{
s = 0.0;
Iter kend = pU->rowEnd(i);
for(Iter kk = pU->rowBegin(i); kk != kend; kk++)
{
if(kk->first >= (unsigned int)n)
break;
if(kk->first >= (unsigned int)l)
s += kk->second * pV->get(j, kk->first);
}
kend = pV->rowEnd(i);
for(Iter kk = pV->rowBegin(i); kk != kend; kk++)
{
if(kk->first >= (unsigned int)n)
break;
if(kk->first >= (unsigned int)l)
pV->set(j, kk->first, pV->get(j, kk->first) + s * kk->second);
}
}
}
for(j = l; j < n; j++)
{
pV->set(i, j, 0.0);
pV->set(j, i, 0.0);
}
}
pV->set(i, i, 1.0);
g = temp[i];
l = i;
}
// Accumulate left-hand transform
for(i = n - 1; i >= 0; i--)
{
l = i + 1;
g = pSigma[i];
if(i < n - 1)
{
for(j = l; j < n; j++)
pU->set(i, j, 0.0);
}
if(g != 0.0)
{
g = 1.0 / g;
if(i != n - 1)
{
for(j = l; j < n; j++)
{
s = 0.0;
Iter kend = pU->colEnd(i);
for(Iter kk = pU->colBegin(i); kk != kend; kk++)
{
if(kk->first >= (unsigned int)l)
s += kk->second * pU->get(kk->first, j);
}
f = (s / pU->get(i, i)) * g;
if(f != 0.0)
{
for(Iter kk = pU->colBegin(i); kk != kend; kk++)
{
if(kk->first >= (unsigned int)i)
pU->set(kk->first, j, pU->get(kk->first, j) + f * kk->second);
}
}
}
}
for(j = i; j < m; j++)
pU->set(j, i, pU->get(j, i) * g);
}
else
{
for(j = i; j < m; j++)
pU->set(j, i, 0.0);
}
pU->set(i, i, pU->get(i, i) + 1.0);
}
// Diagonalize the bidiagonal matrix
for(k = n - 1; k >= 0; k--) // For each singular value
{
for(iter = 1; iter <= maxIters; iter++)
{
// Test for splitting
bool flag = true;
for(l = k; l >= 0; l--)
{
q = l - 1;
if(ABS(temp[l]) + norm == norm)
{
flag = false;
break;
}
if(ABS(pSigma[q]) + norm == norm)
break;
}
if(flag)
{
c = 0.0;
s = 1.0;
for(i = l; i <= k; i++)
{
f = s * temp[i];
temp[i] *= c;
if(ABS(f) + norm == norm)
break;
g = pSigma[i];
h = GSparseMatrix_pythag(f, g);
pSigma[i] = h;
h = 1.0 / h;
c = g * h;
s = -f * h;
Iter jendi = pU->colEnd(i);
Iter jendq = pU->colEnd(q);
Iter jji = pU->colBegin(i);
Iter jjq = pU->colBegin(q);
int tpos;
for(tpos = 0; jji != jendi || jjq != jendq; tpos++)
{
if(jjq == jendq || (jji != jendi && jji->first < jjq->first))
{
temp2[tpos] = jji->first;
jji++;
}
else
{
temp2[tpos] = jjq->first;
if(jji != jendi && jjq->first == jji->first)
jji++;
jjq++;
}
}
for(int tpos2 = 0; tpos2 < tpos; tpos2++)
{
y = pU->get((unsigned int)temp2[tpos2], q);
z = pU->get((unsigned int)temp2[tpos2], i);
pU->set((unsigned int)temp2[tpos2], q, y * c + z * s);
pU->set((unsigned int)temp2[tpos2], i, z * c - y * s);
}
}
}
z = pSigma[k];
if(l == k)
{
// Detect convergence
if(z < 0.0)
{
// Singular value should be positive
pSigma[k] = -z;
for(j = 0; j < n; j++)
pV->set(k, j, pV->get(k, j) * -1.0);
}
break;
}
if(iter >= maxIters)
ThrowError("failed to converge");
// Shift from bottom 2x2 minor
x = pSigma[l];
q = k - 1;
y = pSigma[q];
g = temp[q];
h = temp[k];
f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y);
g = GSparseMatrix_pythag(f, 1.0);
f = ((x - z) * (x + z) + h * ((y / (f + GSparseMatrix_takeSign(g, f))) - h)) / x;
// QR transform
c = 1.0;
s = 1.0;
for(j = l; j <= q; j++)
{
i = j + 1;
g = temp[i];
y = pSigma[i];
h = s * g;
g = c * g;
z = GSparseMatrix_pythag(f, h);
temp[j] = z;
c = f / z;
s = h / z;
f = x * c + g * s;
g = g * c - x * s;
h = y * s;
y = y * c;
Iter pendi = pV->rowEnd(i);
Iter pendj = pV->rowEnd(j);
Iter ppi = pV->rowBegin(i);
Iter ppj = pV->rowBegin(j);
int tpos;
for(tpos = 0; ppi != pendi || ppj != pendj; tpos++)
{
if(ppj == pendj || (ppi != pendi && ppi->first < ppj->first))
{
temp2[tpos] = ppi->first;
ppi++;
}
else
{
temp2[tpos] = ppj->first;
if(ppi != pendi && ppj->first == ppi->first)
ppi++;
ppj++;
}
}
for(int tpos2 = 0; tpos2 < tpos; tpos2++)
{
x = pV->get(j, (unsigned int)temp2[tpos2]);
z = pV->get(i, (unsigned int)temp2[tpos2]);
pV->set(j, (unsigned int)temp2[tpos2], x * c + z * s);
pV->set(i, (unsigned int)temp2[tpos2], z * c - x * s);
}
z = GSparseMatrix_pythag(f, h);
pSigma[j] = z;
if(z != 0.0)
{
z = 1.0 / z;
c = f * z;
s = h * z;
}
f = c * g + s * y;
x = c * y - s * g;
pendi = pU->colEnd(i);
pendj = pU->colEnd(j);
ppi = pU->colBegin(i);
ppj = pU->colBegin(j);
for(tpos = 0; ppi != pendi || ppj != pendj; tpos++)
{
if(ppj == pendj || (ppi != pendi && ppi->first < ppj->first))
{
temp2[tpos] = ppi->first;
ppi++;
}
else
{
temp2[tpos] = ppj->first;
if(ppi != pendi && ppj->first == ppi->first)
ppi++;
ppj++;
}
}
for(int tpos2 = 0; tpos2 < tpos; tpos2++)
{
y = pU->get((unsigned int)temp2[tpos2], j);
z = pU->get((unsigned int)temp2[tpos2], i);
pU->set((unsigned int)temp2[tpos2], j, y * c + z * s);
pU->set((unsigned int)temp2[tpos2], i, z * c - y * s);
}
}
temp[l] = 0.0;
temp[k] = f;
pSigma[k] = x;
}
}
// Sort the singular values from largest to smallest
for(i = 1; i < n; i++)
{
for(j = i; j > 0; j--)
{
if(pSigma[j - 1] >= pSigma[j])
break;
pU->swapColumns(j - 1, j);
pV->swapRows(j - 1, j);
std::swap(pSigma[j - 1], pSigma[j]);
}
}
// Return results
*ppU = hU.release();
*ppDiag = hSigma.release();
*ppV = hV.release();
}
