void Helmholtz( SparseMatrix<F>& H, Int nx, Int ny, F shift )
{
DEBUG_CSE
typedef Base<F> Real;
const Int n = nx*ny;
Zeros( H, n, n );
const Real hxInv = nx+1;
const Real hyInv = ny+1;
const Real hxInvSquared = hxInv*hxInv;
const Real hyInvSquared = hyInv*hyInv;
const F mainTerm = 2*(hxInvSquared+hyInvSquared) - shift;
H.Reserve( 5*n );
for( Int i=0; i<n; ++i )
{
const Int x = i % nx;
const Int y = i/nx;
H.QueueUpdate( i, i, mainTerm );
if( x != 0 )
H.QueueUpdate( i, i-1, -hxInvSquared );
if( x != nx-1 )
H.QueueUpdate( i, i+1, -hxInvSquared );
if( y != 0 )
H.QueueUpdate( i, i-nx, -hyInvSquared );
if( y != ny-1 )
H.QueueUpdate( i, i+nx, -hyInvSquared );
}
H.ProcessQueues();
}
void ShiftDiagonal
( SparseMatrix<T>& A, S alphaPre, Int offset, bool existingDiag )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const T alpha = T(alphaPre);
if( existingDiag )
{
T* valBuf = A.ValueBuffer();
for( Int i=Max(0,-offset); i<Min(m,n-offset); ++i )
{
const Int e = A.Offset( i, i+offset );
valBuf[e] += alpha;
}
}
else
{
const Int diagLength = Min(m,n-offset) - Max(0,-offset);
A.Reserve( diagLength );
for( Int i=Max(0,-offset); i<Min(m,n-offset); ++i )
A.QueueUpdate( i, i+offset, alpha );
A.ProcessQueues();
}
}
void Fill( SparseMatrix<T>& A, T alpha )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
A.Resize( m, n );
Zero( A );
if( alpha != T(0) )
{
A.Reserve( m*n );
for( Int i=0; i<m; ++i )
for( Int j=0; j<n; ++j )
A.QueueUpdate( i, j, alpha );
A.ProcessQueues();
}
}
void JordanCholesky( SparseMatrix<T>& A, Int n )
{
DEBUG_ONLY(CSE cse("JordanCholesky"))
Zeros( A, n, n );
A.Reserve( 3*n );
for( Int e=0; e<n; ++e )
{
if( e == 0 )
A.QueueUpdate( e, e, T(1) );
else
A.QueueUpdate( e, e, T(5) );
if( e > 0 )
A.QueueUpdate( e, e-1, T(2) );
if( e < n-1 )
A.QueueUpdate( e, e+1, T(2) );
}
A.ProcessQueues();
}
void Helmholtz( SparseMatrix<F>& H, Int n, F shift )
{
DEBUG_CSE
typedef Base<F> Real;
Zeros( H, n, n );
const Real hInv = n+1;
const Real hInvSquared = hInv*hInv;
const F mainTerm = 2*hInvSquared - shift;
H.Reserve( 3*n );
for( Int i=0; i<n; ++i )
{
H.QueueUpdate( i, i, mainTerm );
if( i != 0 )
H.QueueUpdate( i, i-1, -hInvSquared );
if( i != n-1 )
H.QueueUpdate( i, i+1, -hInvSquared );
}
H.ProcessQueues();
}
bool LoadMatrixMarketFile(const std::string& file_path,
SparseMatrix<T>& A,
unsigned int& height,
unsigned int& width,
unsigned int& nnz)
{
std::ifstream infile(file_path);
if (!infile)
return false;
char mm_typecode[4];
// read the matrix market banner (header)
if (0 != mm_read_banner(infile, mm_typecode))
return false;
if (!mm_is_valid(mm_typecode))
return false;
// this reader supports these matrix types:
//
// sparse, real/integer/pattern, general/symm/skew
//
if (!mm_is_sparse(mm_typecode))
{
std::cerr << "Only sparse MatrixMarket files are supported." << std::endl;
return false;
}
if (!mm_is_real(mm_typecode) && !mm_is_integer(mm_typecode) && !mm_is_pattern(mm_typecode))
{
std::cerr << "Only real, integer, and pattern MatrixMarket formats are supported." << std::endl;
return false;
}
if (!mm_is_general(mm_typecode) && !mm_is_symmetric(mm_typecode) && !mm_is_skew(mm_typecode))
{
std::cerr << "Only general, symmetric, and skew-symmetric MatrixMarket formats are supported."
<< std::endl;
return false;
}
// read the number of rows, cols, nonzeros
if (0 != mm_read_mtx_crd_size(infile, height, width, nnz))
{
std::cerr << "could not read matrix coordinate information" << std::endl;
height = width = nnz = 0;
return false;
}
// read the data according to the type
bool is_real = mm_is_real(mm_typecode);
bool is_int = mm_is_integer(mm_typecode);
bool is_symmetric = mm_is_symmetric(mm_typecode);
bool is_skew = mm_is_skew(mm_typecode);
std::string line;
unsigned int reserve_size = nnz;
if (is_symmetric || is_skew)
reserve_size *= 2;
A.Clear();
A.Reserve(height, width, reserve_size);
// load num random entries of A
A.BeginLoad();
unsigned int row, col, count;
if (is_real)
{
double val;
for (count=0; count != nnz; ++count)
{
infile >> row; assert(row >= 1);
infile >> col; assert(col >= 1);
infile >> val;
// convert to 0-based indexing
row -= 1;
col -= 1;
A.Load(row, col, val);
if (row != col)
{
if (is_symmetric)
A.Load(col, row, val);
else if (is_skew)
A.Load(col, row, -val);
}
}
}
else if (is_int)
void RLS
( const SparseMatrix<Real>& A,
const Matrix<Real>& b,
Real rho,
Matrix<Real>& x,
const socp::affine::Ctrl<Real>& ctrl )
{
DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
Matrix<Int> orders, firstInds;
Zeros( orders, m+n+3, 1 );
Zeros( firstInds, m+n+3, 1 );
for( Int i=0; i<m+1; ++i )
{
orders.Set( i, 0, m+1 );
firstInds.Set( i, 0, 0 );
}
for( Int i=0; i<n+2; ++i )
{
orders.Set( i+m+1, 0, n+2 );
firstInds.Set( i+m+1, 0, m+1 );
}
// G := | -1 0 0 |
// | 0 0 A |
// | 0 -1 0 |
// | 0 0 -I |
// | 0 0 0 |
SparseMatrix<Real> G;
{
const Int numEntriesA = A.NumEntries();
Zeros( G, m+n+3, n+2 );
G.Reserve( numEntriesA+n+2 );
G.QueueUpdate( 0, 0, -1 );
for( Int e=0; e<numEntriesA; ++e )
G.QueueUpdate( A.Row(e)+1, A.Col(e)+2, A.Value(e) );
G.QueueUpdate( m+1, 1, -1 );
for( Int j=0; j<n; ++j )
G.QueueUpdate( j+m+2, j+2, -1 );
G.ProcessQueues();
}
// h := | 0 |
// | b |
// | 0 |
// | 0 |
// | 1 |
Matrix<Real> h;
Zeros( h, m+n+3, 1 );
auto hb = h( IR(1,m+1), ALL );
hb = b;
h.Set( END, 0, 1 );
// c := [1; rho; 0]
Matrix<Real> c;
Zeros( c, n+2, 1 );
c.Set( 0, 0, 1 );
c.Set( 1, 0, rho );
SparseMatrix<Real> AHat;
Zeros( AHat, 0, n+2 );
Matrix<Real> bHat;
Zeros( bHat, 0, 1 );
Matrix<Real> xHat, y, z, s;
SOCP( AHat, G, bHat, c, h, orders, firstInds, xHat, y, z, s, ctrl );
x = xHat( IR(2,END), ALL );
}
void SparseMatrix<T>::SubMatrixColsCompact(SparseMatrix<T>& result,
const std::vector<unsigned int>& col_indices,
std::vector<unsigned int>& old_to_new_rows,
std::vector<unsigned int>& new_to_old_rows) const
{
const unsigned int UNUSED_ROW = 0xFFFFFFFF;
// extract entire columns from the source matrix to form the dest matrix
unsigned int new_width = col_indices.size();
if (0u == new_width)
throw std::logic_error("SparseMatrix::SubMatrixColsCompact: empty column set");
// need one entry per original row in the row_map
if (old_to_new_rows.size() < height_)
old_to_new_rows.resize(height_);
std::fill(old_to_new_rows.begin(), old_to_new_rows.begin() + height_, UNUSED_ROW);
// no need to fill 'new_to_old_rows'
// check the column indices for validty and count nonzeros
unsigned int new_size = 0;
for (auto it=col_indices.begin(); it != col_indices.end(); ++it)
{
// index of next source column
unsigned int c = *it;
if (c >= width_)
throw std::logic_error("SparseMatrix::SubMatrixColsCompact: column index out of range");
// number of nonzeros in source column c
new_size += (col_offsets_[c+1] - col_offsets_[c]);
}
if (0u == new_size)
throw std::logic_error("SparseMatrix::SubMatrixColsCompact: submatrix is the zero matrix");
// allocate memory in the result; won't allocate if sufficient memory available
result.Reserve(height_, new_width, new_size);
unsigned int* cols_b = result.ColBuffer();
unsigned int* rows_b = result.RowBuffer();
T* data_b = result.DataBuffer();
unsigned int c_dest = 0;
unsigned int elt_count = 0;
for (auto it=col_indices.begin(); it != col_indices.end(); ++it)
{
// index of the next source column
unsigned int c = *it;
// set element offset for the next dest column
cols_b[c_dest] = elt_count;
unsigned int start = col_offsets_[c];
unsigned int end = col_offsets_[c+1];
for (unsigned int offset = start; offset != end; ++offset)
{
unsigned int row = row_indices_[offset];
old_to_new_rows[row] = row;
rows_b[elt_count] = row;
data_b[elt_count] = data_[offset];
++elt_count;
}
// have now completed another column
++c_dest;
}
cols_b[new_width] = elt_count;
assert(new_width == c_dest);
// set the size of the new matrix explicitly, since Load() has been bypassed
result.SetSize(elt_count);
// determine the new height of the submatrix
unsigned int new_height = 0;
for (unsigned int r=0; r != height_; ++r)
{
if (UNUSED_ROW != old_to_new_rows[r])
++new_height;
}
new_to_old_rows.resize(new_height);
// renumber the rows in the submatrix
unsigned int new_r = 0;
for (unsigned int r=0; r<height_; ++r)
{
if (UNUSED_ROW != old_to_new_rows[r])
{
old_to_new_rows[r] = new_r;
new_to_old_rows[new_r] = r;
++new_r;
}
}
// set the height of the new matrix explicitly
assert(new_r == new_height);
result.SetHeight(new_height);
// re-index the rows in the submatrix
for (unsigned int s=0; s != elt_count; ++s)
{
unsigned int old_row_index = rows_b[s];
rows_b[s] = old_to_new_rows[old_row_index];
}
assert(result.Height() == new_height);
assert(new_to_old_rows.size() == new_height);
assert(old_to_new_rows.size() == height_);
}
void SparseMatrix<T>::SubMatrixCols(SparseMatrix<T>& result,
const std::vector<unsigned int>& col_indices) const
{
// extract entire columns from the source matrix to form the dest matrix
unsigned int new_width = col_indices.size();
if (0u == new_width)
throw std::logic_error("SparseMatrix: empty column set");
// check the column indices for validty and count nonzeros
unsigned int new_size = 0;
for (auto it=col_indices.begin(); it != col_indices.end(); ++it)
{
// index of next source column
unsigned int c = *it;
if (c >= width_)
throw std::logic_error("SparseMatrix::SubMatrix: column index out of range");
// number of nonzeros in source column c
new_size += (col_offsets_[c+1] - col_offsets_[c]);
}
if (0u == new_size)
throw std::logic_error("SparseMatrix::SubMatrix: submatrix is the zero matrix");
// allocate memory in the result; won't allocate if sufficient memory available
result.Reserve(height_, new_width, new_size);
unsigned int* cols_b = result.ColBuffer();
unsigned int* rows_b = result.RowBuffer();
T* data_b = result.DataBuffer();
unsigned int c_dest = 0;
unsigned int elt_count = 0;
for (auto it=col_indices.begin(); it != col_indices.end(); ++it)
{
// index of the next source column
unsigned int c = *it;
// set element offset for the next dest column
cols_b[c_dest] = elt_count;
unsigned int start = col_offsets_[c];
unsigned int end = col_offsets_[c+1];
for (unsigned int offset = start; offset != end; ++offset)
{
rows_b[elt_count] = row_indices_[offset];
data_b[elt_count] = data_[offset];
++elt_count;
}
// have now completed another column
++c_dest;
}
cols_b[new_width] = elt_count;
assert(new_width == c_dest);
// set the size of the new matrix explicitly, since Load() has been bypassed
result.SetSize(elt_count);
}
void SparseMatrix<T>::SubMatrix(SparseMatrix<T>& result,
const unsigned int r0,
const unsigned int c0,
const unsigned int new_height,
const unsigned int new_width) const
{
// one past the end of each range
unsigned int r1 = r0 + new_height;
unsigned int c1 = c0 + new_width;
if ( (r0 >= height_) || (r1 > height_))
throw std::logic_error("SubMatrix: invalid row limits");
if ( (c0 >= width_) || (c1 > width_))
throw std::logic_error("SubMatrix: invalid column limits");
// count the number of nonzeros in the submatrix
unsigned int new_size = 0;
for (unsigned int c=c0; c != c1; ++c)
{
// number of nonzeros in source column c
new_size += (col_offsets_[c+1] - col_offsets_[c]);
}
if (0u == new_size)
throw std::logic_error("SparseMatrix::SubMatrix: submatrix is the zero matrix");
// allocate memory in the result; won't allocate if sufficient memory available
result.Reserve(new_height, new_width, new_size);
// Load the elements within the row and column bounds into the new matrix.
// No need to call result.Clear(), since that will result in a new allocation.
unsigned int* cols_b = result.ColBuffer();
unsigned int* rows_b = result.RowBuffer();
T* data_b = result.DataBuffer();
unsigned int count = 0;
for (unsigned int c=c0; c != c1; ++c)
{
cols_b[c-c0] = count;
unsigned int start = col_offsets_[c];
unsigned int end = col_offsets_[c+1];
for (unsigned int offset = start; offset != end; ++offset)
{
unsigned int row = row_indices_[offset];
if ( (row >= r0) && (row < r1))
{
rows_b[count] = row - r0;
data_b[count] = data_[offset];
++count;
}
}
}
cols_b[c1] = count;
//assert(new_size == count);
// set the size of the new matrix explicitly, since Load() has been bypassed
result.SetSize(count);
}
