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-rw-r--r--src/lib/netlist/plib/mat_cr.h530
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diff --git a/src/lib/netlist/plib/mat_cr.h b/src/lib/netlist/plib/mat_cr.h
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+// license:GPL-2.0+
+// copyright-holders:Couriersud
+/*
+ * mat_cr.h
+ *
+ * Compressed row format matrices
+ *
+ */
+
+#ifndef MAT_CR_H_
+#define MAT_CR_H_
+
+#include "palloc.h"
+#include "parray.h"
+#include "pconfig.h"
+#include "pomp.h"
+#include "pstate.h"
+#include "ptypes.h"
+#include "putil.h"
+
+#include <algorithm>
+#include <array>
+#include <cmath>
+#include <cstdlib>
+#include <type_traits>
+#include <vector>
+
+namespace plib
+{
+
+ // FIXME: causes a crash with GMRES handler
+ // template<typename T, int N, typename C = std::size_t>
+
+ template<typename T, int N, typename C = uint16_t>
+ struct matrix_compressed_rows_t
+ {
+ using index_type = C;
+ using value_type = T;
+
+ COPYASSIGNMOVE(matrix_compressed_rows_t, default)
+
+ enum constants_e
+ {
+ FILL_INFINITY = 9999999
+ };
+
+ parray<index_type, N> diag; // diagonal index pointer n
+ parray<index_type, (N == 0) ? 0 : (N < 0 ? N - 1 : N + 1)> row_idx; // row index pointer n + 1
+ parray<index_type, N < 0 ? -N * N : N *N> col_idx; // column index array nz_num, initially (n * n)
+ parray<value_type, N < 0 ? -N * N : N *N> A; // Matrix elements nz_num, initially (n * n)
+ //parray<C, N < 0 ? -N * (N-1) / 2 : N * (N+1) / 2 > nzbd; // Support for gaussian elimination
+ parray<std::vector<index_type>, N > nzbd; // Support for gaussian elimination
+ // contains elimination rows below the diagonal
+ // FIXME: convert to pvector
+ std::vector<std::vector<index_type>> m_ge_par;
+
+ index_type nz_num;
+
+ explicit matrix_compressed_rows_t(const index_type n)
+ : diag(n)
+ , row_idx(n+1)
+ , col_idx(n*n)
+ , A(n*n)
+ //, nzbd(n * (n+1) / 2)
+ , nzbd(n)
+ , nz_num(0)
+ , m_size(n)
+ {
+ for (index_type i=0; i<n+1; i++)
+ row_idx[i] = 0;
+ }
+
+ ~matrix_compressed_rows_t() = default;
+
+ constexpr index_type size() const { return static_cast<index_type>((N>0) ? N : m_size); }
+
+ void clear()
+ {
+ nz_num = 0;
+ for (index_type i=0; i < size() + 1; i++)
+ row_idx[i] = 0;
+ }
+
+ void set_scalar(const T scalar)
+ {
+ for (index_type i=0, e=nz_num; i<e; i++)
+ A[i] = scalar;
+ }
+
+ void set(C r, C c, T val)
+ {
+ C ri = row_idx[r];
+ while (ri < row_idx[r+1] && col_idx[ri] < c)
+ ri++;
+ // we have the position now;
+ if (ri < row_idx[r+1] && col_idx[ri] == c)
+ A[ri] = val;
+ else
+ {
+ for (C i = nz_num; i>ri; i--)
+ {
+ A[i] = A[i-1];
+ col_idx[i] = col_idx[i-1];
+ }
+ A[ri] = val;
+ col_idx[ri] = c;
+ for (C i = r + 1; i < size() + 1; i++)
+ row_idx[i]++;
+ nz_num++;
+ if (c==r)
+ diag[r] = ri;
+ }
+ }
+
+ template <typename M>
+ std::pair<std::size_t, std::size_t> gaussian_extend_fill_mat(M &fill)
+ {
+ std::size_t ops = 0;
+ std::size_t fill_max = 0;
+
+ for (std::size_t k = 0; k < fill.size(); k++)
+ {
+ ops++; // 1/A(k,k)
+ for (std::size_t row = k + 1; row < fill.size(); row++)
+ {
+ if (fill[row][k] < FILL_INFINITY)
+ {
+ ops++;
+ for (std::size_t col = k + 1; col < fill[row].size(); col++)
+ //if (fill[k][col] < FILL_INFINITY)
+ {
+ auto f = std::min(fill[row][col], 1 + fill[row][k] + fill[k][col]);
+ if (f < FILL_INFINITY)
+ {
+ if (f > fill_max)
+ fill_max = f;
+ ops += 2;
+ }
+ fill[row][col] = f;
+ }
+ }
+ }
+ }
+ build_parallel_gaussian_execution_scheme(fill);
+ return { fill_max, ops };
+ }
+
+ template <typename M>
+ void build_from_fill_mat(const M &f, std::size_t max_fill = FILL_INFINITY - 1,
+ std::size_t band_width = FILL_INFINITY)
+ {
+ C nz = 0;
+ if (nz_num != 0)
+ throw pexception("build_from_mat only allowed on empty CR matrix");
+ for (std::size_t k=0; k < size(); k++)
+ {
+ row_idx[k] = nz;
+
+ for (std::size_t j=0; j < size(); j++)
+ if (f[k][j] <= max_fill && std::abs(static_cast<int>(k)-static_cast<int>(j)) <= static_cast<int>(band_width))
+ {
+ col_idx[nz] = static_cast<C>(j);
+ if (j == k)
+ diag[k] = nz;
+ nz++;
+ }
+ }
+
+ row_idx[size()] = nz;
+ nz_num = nz;
+ /* build nzbd */
+
+ for (std::size_t k=0; k < size(); k++)
+ {
+ for (std::size_t j=k + 1; j < size(); j++)
+ if (f[j][k] < FILL_INFINITY)
+ nzbd[k].push_back(static_cast<C>(j));
+ nzbd[k].push_back(0); // end of sequence
+ }
+ }
+
+ template <typename V>
+ void gaussian_elimination(V & RHS)
+ {
+ const std::size_t iN = size();
+
+ for (std::size_t i = 0; i < iN - 1; i++)
+ {
+ std::size_t nzbdp = 0;
+ std::size_t pi = diag[i];
+ const value_type f = 1.0 / A[pi++];
+ const std::size_t piie = row_idx[i+1];
+ const auto &nz = nzbd[i];
+
+ while (auto j = nz[nzbdp++])
+ {
+ // proceed to column i
+
+ std::size_t pj = row_idx[j];
+
+ while (col_idx[pj] < i)
+ pj++;
+
+ const value_type f1 = - A[pj++] * f;
+
+ // subtract row i from j
+ // fill-in available assumed, i.e. matrix was prepared
+
+ for (std::size_t pii = pi; pii<piie; pii++)
+ {
+ while (col_idx[pj] < col_idx[pii])
+ pj++;
+ if (col_idx[pj] == col_idx[pii])
+ A[pj++] += A[pii] * f1;
+ }
+
+ RHS[j] += f1 * RHS[i];
+ }
+ }
+ }
+
+ template <typename V>
+ void gaussian_elimination_parallel(V & RHS)
+ {
+ // FIXME: move into solver creation ...
+ plib::omp::set_num_threads(4);
+ for (auto l = 0ul; l < m_ge_par.size(); l++)
+ plib::omp::for_static(0ul, m_ge_par[l].size(), [this, &RHS, &l] (unsigned ll)
+ {
+ auto &i = m_ge_par[l][ll];
+ {
+ std::size_t nzbdp = 0;
+ std::size_t pi = diag[i];
+ const value_type f = 1.0 / A[pi++];
+ const std::size_t piie = row_idx[i+1];
+
+ while (auto j = nzbd[i][nzbdp++])
+ {
+ // proceed to column i
+
+ std::size_t pj = row_idx[j];
+
+ while (col_idx[pj] < i)
+ pj++;
+
+ const value_type f1 = - A[pj++] * f;
+
+ // subtract row i from j
+ // fill-in available assumed, i.e. matrix was prepared
+ for (std::size_t pii = pi; pii<piie; pii++)
+ {
+ while (col_idx[pj] < col_idx[pii])
+ pj++;
+ if (col_idx[pj] == col_idx[pii])
+ A[pj++] += A[pii] * f1;
+ }
+ RHS[j] += f1 * RHS[i];
+ }
+ }
+ });
+ }
+
+ template <typename V1, typename V2>
+ void gaussian_back_substitution(V1 &V, const V2 &RHS)
+ {
+ const std::size_t iN = size();
+ /* row n-1 */
+ V[iN - 1] = RHS[iN - 1] / A[diag[iN - 1]];
+
+ for (std::size_t j = iN - 1; j-- > 0;)
+ {
+ value_type tmp = 0;
+ const auto jdiag = diag[j];
+ const std::size_t e = row_idx[j+1];
+ for (std::size_t pk = jdiag + 1; pk < e; pk++)
+ tmp += A[pk] * V[col_idx[pk]];
+ V[j] = (RHS[j] - tmp) / A[jdiag];
+ }
+ }
+
+ template <typename V1>
+ void gaussian_back_substitution(V1 &V)
+ {
+ const std::size_t iN = size();
+ /* row n-1 */
+ V[iN - 1] = V[iN - 1] / A[diag[iN - 1]];
+
+ for (std::size_t j = iN - 1; j-- > 0;)
+ {
+ value_type tmp = 0;
+ const auto jdiag = diag[j];
+ const std::size_t e = row_idx[j+1];
+ for (std::size_t pk = jdiag + 1; pk < e; pk++)
+ tmp += A[pk] * V[col_idx[pk]];
+ V[j] = (V[j] - tmp) / A[jdiag];
+ }
+ }
+
+
+ template <typename VTV, typename VTR>
+ void mult_vec(VTR & res, const VTV & x)
+ {
+ /*
+ * res = A * x
+ */
+
+ std::size_t row = 0;
+ std::size_t k = 0;
+ const std::size_t oe = nz_num;
+
+ while (k < oe)
+ {
+ T tmp = 0.0;
+ const std::size_t e = row_idx[row+1];
+ for (; k < e; k++)
+ tmp += A[k] * x[col_idx[k]];
+ res[row++] = tmp;
+ }
+ }
+
+ /* throws error if P(source)>P(destination) */
+ template <typename LUMAT>
+ void slim_copy_from(LUMAT & src)
+ {
+ for (std::size_t r=0; r<src.size(); r++)
+ {
+ C dp = row_idx[r];
+ for (C sp = src.row_idx[r]; sp < src.row_idx[r+1]; sp++)
+ {
+ /* advance dp to source column and fill 0s if necessary */
+ while (col_idx[dp] < src.col_idx[sp])
+ A[dp++] = 0;
+ if (row_idx[r+1] <= dp || col_idx[dp] != src.col_idx[sp])
+ throw plib::pexception("slim_copy_from error");
+ A[dp++] = src.A[sp];
+ }
+ /* fill remaining elements in row */
+ while (dp < row_idx[r+1])
+ A[dp++] = 0;
+ }
+ }
+
+ /* only copies common elements */
+ template <typename LUMAT>
+ void reduction_copy_from(LUMAT & src)
+ {
+ C sp = 0;
+ for (std::size_t r=0; r<src.size(); r++)
+ {
+ C dp = row_idx[r];
+ while(sp < src.row_idx[r+1])
+ {
+ /* advance dp to source column and fill 0s if necessary */
+ if (col_idx[dp] < src.col_idx[sp])
+ A[dp++] = 0;
+ else if (col_idx[dp] == src.col_idx[sp])
+ A[dp++] = src.A[sp++];
+ else
+ sp++;
+ }
+ /* fill remaining elements in row */
+ while (dp < row_idx[r+1])
+ A[dp++] = 0;
+ }
+ }
+
+ /* checks at all - may crash */
+ template <typename LUMAT>
+ void raw_copy_from(LUMAT & src)
+ {
+ for (std::size_t k = 0; k < nz_num; k++)
+ A[k] = src.A[k];
+ }
+
+ void incomplete_LU_factorization()
+ {
+ /*
+ * incomplete LU Factorization according to http://de.wikipedia.org/wiki/ILU-Zerlegung
+ *
+ * Result is stored in matrix LU
+ *
+ * For i = 1,...,N-1
+ * For k = 0, ... , i - 1
+ * If a[i,k] != 0
+ * a[i,k] = a[i,k] / a[k,k]
+ * For j = k + 1, ... , N - 1
+ * If a[i,j] != 0
+ * a[i,j] = a[i,j] - a[i,k] * a[k,j]
+ * j=j+1
+ * k=k+1
+ * i=i+1
+ *
+ */
+
+ for (std::size_t i = 1; i < size(); i++) // row i
+ {
+ const std::size_t p_i_end = row_idx[i + 1];
+ // loop over all columns k left of diag in row i
+ for (std::size_t i_k = row_idx[i]; i_k < diag[i]; i_k++)
+ {
+ const std::size_t k = col_idx[i_k];
+ const std::size_t p_k_end = row_idx[k + 1];
+ const T LUp_i_k = A[i_k] = A[i_k] / A[diag[k]];
+
+ std::size_t k_j = diag[k] + 1;
+ std::size_t i_j = i_k + 1;
+
+ while (i_j < p_i_end && k_j < p_k_end ) // pj = (i, j)
+ {
+ // we can assume that within a row ja increases continuously */
+ const std::size_t c_i_j = col_idx[i_j]; // row i, column j
+ const std::size_t c_k_j = col_idx[k_j]; // row i, column j
+ if (c_k_j < c_i_j)
+ k_j++;
+ else if (c_k_j == c_i_j)
+ A[i_j++] -= LUp_i_k * A[k_j++];
+ else
+ i_j++;
+ }
+ }
+ }
+ }
+
+ template <typename R>
+ void solveLUx (R &r)
+ {
+ /*
+ * Solve a linear equation Ax = r
+ * where
+ * A = L*U
+ *
+ * L unit lower triangular
+ * U upper triangular
+ *
+ * ==> LUx = r
+ *
+ * ==> Ux = L⁻¹ r = w
+ *
+ * ==> r = Lw
+ *
+ * This can be solved for w using backwards elimination in L.
+ *
+ * Now Ux = w
+ *
+ * This can be solved for x using backwards elimination in U.
+ *
+ */
+ for (std::size_t i = 1; i < size(); ++i )
+ {
+ T tmp = 0.0;
+ const std::size_t j1 = row_idx[i];
+ const std::size_t j2 = diag[i];
+
+ for (std::size_t j = j1; j < j2; ++j )
+ tmp += A[j] * r[col_idx[j]];
+ r[i] -= tmp;
+ }
+ // i now is equal to n;
+ for (std::size_t i = size(); i-- > 0; )
+ {
+ T tmp = 0.0;
+ const std::size_t di = diag[i];
+ const std::size_t j2 = row_idx[i+1];
+ for (std::size_t j = di + 1; j < j2; j++ )
+ tmp += A[j] * r[col_idx[j]];
+ r[i] = (r[i] - tmp) / A[di];
+ }
+ }
+ private:
+ template <typename M>
+ void build_parallel_gaussian_execution_scheme(const M &fill)
+ {
+ // calculate parallel scheme for gaussian elimination
+ std::vector<std::vector<index_type>> rt(size());
+ for (index_type k = 0; k < size(); k++)
+ {
+ for (index_type j = k+1; j < size(); j++)
+ {
+ if (fill[j][k] < FILL_INFINITY)
+ {
+ rt[k].push_back(j);
+ }
+ }
+ }
+
+ std::vector<index_type> levGE(size(), 0);
+ index_type cl = 0;
+
+ for (index_type k = 0; k < size(); k++ )
+ {
+ if (levGE[k] >= cl)
+ {
+ std::vector<index_type> t = rt[k];
+ for (index_type j = k+1; j < size(); j++ )
+ {
+ bool overlap = false;
+ // is there overlap
+ if (plib::container::contains(t, j))
+ overlap = true;
+ for (auto &x : rt[j])
+ if (plib::container::contains(t, x))
+ {
+ overlap = true;
+ break;
+ }
+ if (overlap)
+ levGE[j] = cl + 1;
+ else
+ {
+ t.push_back(j);
+ for (auto &x : rt[j])
+ t.push_back(x);
+ }
+ }
+ cl++;
+ }
+ }
+
+ m_ge_par.clear();
+ m_ge_par.resize(cl+1);
+ for (index_type k = 0; k < size(); k++)
+ m_ge_par[levGE[k]].push_back(k);
+ }
+
+ index_type m_size;
+ };
+
+} // namespace plib
+
+#endif /* MAT_CR_H_ */