// license:GPL-2.0+
// copyright-holders:Couriersud
/*
* nld_ms_direct.h
*
*
* Woodbury Solver
*
* Computes the updated solution of A given that the change in A is
*
* A <- A + (U x transpose(V)) U,V matrices
*
* The approach is describes in "Numerical Recipes in C", Second edition, Page 75ff
*
* Whilst the book proposes to invert the matrix R=(I+transpose(V)*Z) we define
*
* w = transpose(V)*y
* a = R⁻¹ * w
*
* and consequently
*
* R * a = w
*
* And solve for a using Gaussian elimination. This is a lot faster.
*
* One fact omitted in the book is the fact that actually the matrix Z which contains
* in it's columns the solutions of
*
* A * zk = uk
*
* for uk being unit vectors for full rank (max(k) == n) is identical to the
* inverse of A.
*
* The approach performs relatively well for matrices up to n ~ 40 (kidniki using frontiers).
* Kidniki without frontiers has n==88. Here, the average number of Newton-Raphson
* loops increase to 20. It looks like that the approach for larger matrices
* introduces numerical instability.
*/
#ifndef NLD_MS_W_H_
#define NLD_MS_W_H_
#include <algorithm>
#include "solver/nld_solver.h"
#include "solver/nld_matrix_solver.h"
#include "solver/vector_base.h"
namespace netlist
{
namespace devices
{
//#define nl_ext_double _float128 // slow, very slow
//#define nl_ext_double long double // slightly slower
#define nl_ext_double nl_double
template <unsigned m_N, unsigned storage_N>
class matrix_solver_w_t: public matrix_solver_t
{
friend class matrix_solver_t;
public:
matrix_solver_w_t(netlist_t &anetlist, const pstring &name, const solver_parameters_t *params, const int size);
virtual ~matrix_solver_w_t();
virtual void vsetup(analog_net_t::list_t &nets) override;
virtual void reset() override { matrix_solver_t::reset(); }
protected:
virtual int vsolve_non_dynamic(const bool newton_raphson) override;
int solve_non_dynamic(const bool newton_raphson);
inline unsigned N() const { if (m_N == 0) return m_dim; else return m_N; }
void LE_invert();
template <typename T>
void LE_compute_x(T * RESTRICT x);
template <typename T1, typename T2>
inline nl_ext_double &A(const T1 &r, const T2 &c) { return m_A[r][c]; }
template <typename T1, typename T2>
inline nl_ext_double &W(const T1 &r, const T2 &c) { return m_W[r][c]; }
/* access to Ainv for fixed columns over row, there store transposed */
template <typename T1, typename T2>
inline nl_ext_double &Ainv(const T1 &r, const T2 &c) { return m_Ainv[c][r]; }
template <typename T1>
inline nl_ext_double &RHS(const T1 &r) { return m_RHS[r]; }
template <typename T1, typename T2>
inline nl_ext_double &lA(const T1 &r, const T2 &c) { return m_lA[r][c]; }
nl_double m_last_RHS[storage_N]; // right hand side - contains currents
private:
static const std::size_t m_pitch = ((( storage_N) + 7) / 8) * 8;
nl_ext_double m_A[storage_N][m_pitch];
nl_ext_double m_Ainv[storage_N][m_pitch];
nl_ext_double m_W[storage_N][m_pitch];
nl_ext_double m_RHS[storage_N]; // right hand side - contains currents
nl_ext_double m_lA[storage_N][m_pitch];
/* temporary */
nl_double H[storage_N][m_pitch] ;
unsigned rows[storage_N];
unsigned cols[storage_N][m_pitch];
unsigned colcount[storage_N];
unsigned m_cnt;
//nl_ext_double m_RHSx[storage_N];
const unsigned m_dim;
};
// ----------------------------------------------------------------------------------------
// matrix_solver_direct
// ----------------------------------------------------------------------------------------
template <unsigned m_N, unsigned storage_N>
matrix_solver_w_t<m_N, storage_N>::~matrix_solver_w_t()
{
}
template <unsigned m_N, unsigned storage_N>
void matrix_solver_w_t<m_N, storage_N>::vsetup(analog_net_t::list_t &nets)
{
if (m_dim < nets.size())
log().fatal("Dimension {1} less than {2}", m_dim, nets.size());
matrix_solver_t::setup_base(nets);
netlist().save(*this, m_last_RHS, "m_last_RHS");
for (unsigned k = 0; k < N(); k++)
netlist().save(*this, RHS(k), plib::pfmt("RHS.{1}")(k));
}
template <unsigned m_N, unsigned storage_N>
void matrix_solver_w_t<m_N, storage_N>::LE_invert()
{
const unsigned kN = N();
for (unsigned i = 0; i < kN; i++)
{
for (unsigned j = 0; j < kN; j++)
{
W(i,j) = lA(i,j) = A(i,j);
Ainv(i,j) = 0.0;
}
Ainv(i,i) = 1.0;
}
/* down */
for (unsigned i = 0; i < kN; i++)
{
/* FIXME: Singular matrix? */
const nl_double f = 1.0 / W(i,i);
const auto * RESTRICT const p = m_terms[i]->m_nzrd.data();
const unsigned e = m_terms[i]->m_nzrd.size();
/* Eliminate column i from row j */
const auto * RESTRICT const pb = m_terms[i]->m_nzbd.data();
const unsigned eb = m_terms[i]->m_nzbd.size();
for (unsigned jb = 0; jb < eb; jb++)
{
const auto j = pb[jb];
const nl_double f1 = - W(j,i) * f;
if (f1 != 0.0)
{
for (unsigned k = 0; k < e; k++)
W(j,p[k]) += W(i,p[k]) * f1;
for (unsigned k = 0; k <= i; k ++)
Ainv(j,k) += Ainv(i,k) * f1;
}
}
}
/* up */
for (int i = kN - 1; i >= 0; i--)
{
/* FIXME: Singular matrix? */
const nl_double f = 1.0 / W(i,i);
for (int j = i - 1; j>=0; j--)
{
const nl_double f1 = - W(j,i) * f;
if (f1 != 0.0)
{
for (unsigned k = i; k < kN; k++)
W(j,k) += W(i,k) * f1;
for (unsigned k = 0; k < kN; k++)
Ainv(j,k) += Ainv(i,k) * f1;
}
}
for (unsigned k = 0; k < kN; k++)
{
Ainv(i,k) *= f;
}
}
}
template <unsigned m_N, unsigned storage_N>
template <typename T>
void matrix_solver_w_t<m_N, storage_N>::LE_compute_x(
T * RESTRICT x)
{
const unsigned kN = N();
for (unsigned i=0; i<kN; i++)
x[i] = 0.0;
for (unsigned k=0; k<kN; k++)
{
const nl_double f = RHS(k);
for (unsigned i=0; i<kN; i++)
x[i] += Ainv(i,k) * f;
}
}
template <unsigned m_N, unsigned storage_N>
int matrix_solver_w_t<m_N, storage_N>::solve_non_dynamic(ATTR_UNUSED const bool newton_raphson)
{
const auto iN = N();
nl_double new_V[storage_N]; // = { 0.0 };
if ((m_cnt % 100) == 0)
{
/* complete calculation */
this->LE_invert();
this->LE_compute_x(new_V);
}
else
{
/* Solve Ay = b for y */
this->LE_compute_x(new_V);
/* determine changed rows */
unsigned rowcount=0;
#define VT(r,c) (A(r,c) - lA(r,c))
for (unsigned row = 0; row < iN; row ++)
{
unsigned cc=0;
auto &nz = m_terms[row]->m_nz;
for (auto & col : nz)
{
if (A(row,col) != lA(row,col))
cols[rowcount][cc++] = col;
}
if (cc > 0)
{
colcount[rowcount] = cc;
rows[rowcount++] = row;
}
}
if (rowcount > 0)
{
/* construct w = transform(V) * y
* dim: rowcount x iN
* */
nl_double w[storage_N];
for (unsigned i = 0; i < rowcount; i++)
{
const unsigned r = rows[i];
double tmp = 0.0;
for (unsigned k = 0; k < iN; k++)
tmp += VT(r,k) * new_V[k];
w[i] = tmp;
}
for (unsigned i = 0; i < rowcount; i++)
for (unsigned k=0; k< rowcount; k++)
H[i][k] = 0.0;
for (unsigned i = 0; i < rowcount; i++)
H[i][i] = 1.0;
/* Construct H = (I + VT*Z) */
for (unsigned i = 0; i < rowcount; i++)
for (unsigned k=0; k< colcount[i]; k++)
{
const unsigned col = cols[i][k];
nl_double f = VT(rows[i],col);
if (f!=0.0)
for (unsigned j= 0; j < rowcount; j++)
H[i][j] += f * Ainv(col,rows[j]);
}
/* Gaussian elimination of H */
for (unsigned i = 0; i < rowcount; i++)
{
if (H[i][i] == 0.0)
printf("%s H singular\n", this->name().cstr());
const nl_double f = 1.0 / H[i][i];
for (unsigned j = i+1; j < rowcount; j++)
{
const nl_double f1 = - f * H[j][i];
if (f1!=0.0)
{
nl_double *pj = &H[j][i+1];
const nl_double *pi = &H[i][i+1];
for (unsigned k = 0; k < rowcount-i-1; k++)
pj[k] += f1 * pi[k];
//H[j][k] += f1 * H[i][k];
w[j] += f1 * w[i];
}
}
}
/* Back substitution */
//inv(H) w = t w = H t
nl_double t[storage_N]; // FIXME: convert to member
for (int j = rowcount - 1; j >= 0; j--)
{
nl_double tmp = 0;
const nl_double *pj = &H[j][j+1];
const nl_double *tj = &t[j+1];
for (unsigned k = 0; k < rowcount-j-1; k++)
tmp += pj[k] * tj[k];
//tmp += H[j][k] * t[k];
t[j] = (w[j] - tmp) / H[j][j];
}
/* x = y - Zt */
for (unsigned i=0; i<iN; i++)
{
nl_double tmp = 0.0;
for (unsigned j=0; j<rowcount;j++)
{
const unsigned row = rows[j];
tmp += Ainv(i,row) * t[j];
}
new_V[i] -= tmp;
}
}
}
m_cnt++;
if (0)
for (unsigned i=0; i<iN; i++)
{
nl_double tmp = 0.0;
for (unsigned j=0; j<iN; j++)
{
tmp += A(i,j) * new_V[j];
}
if (std::abs(tmp-RHS(i)) > 1e-6)
printf("%s failed on row %d: %f RHS: %f\n", this->name().cstr(), i, std::abs(tmp-RHS(i)), RHS(i));
}
if (newton_raphson)
{
nl_double err = delta(new_V);
store(new_V);
return (err > this->m_params.m_accuracy) ? 2 : 1;
}
else
{
store(new_V);
return 1;
}
}
template <unsigned m_N, unsigned storage_N>
inline int matrix_solver_w_t<m_N, storage_N>::vsolve_non_dynamic(const bool newton_raphson)
{
build_LE_A<matrix_solver_w_t>();
build_LE_RHS<matrix_solver_w_t>();
for (unsigned i=0, iN=N(); i < iN; i++)
m_last_RHS[i] = RHS(i);
this->m_stat_calculations++;
return this->solve_non_dynamic(newton_raphson);
}
template <unsigned m_N, unsigned storage_N>
matrix_solver_w_t<m_N, storage_N>::matrix_solver_w_t(netlist_t &anetlist, const pstring &name,
const solver_parameters_t *params, const int size)
: matrix_solver_t(anetlist, name, NOSORT, params)
,m_cnt(0)
, m_dim(size)
{
for (unsigned k = 0; k < N(); k++)
{
m_last_RHS[k] = 0.0;
}
}
} //namespace devices
} // namespace netlist
#endif /* NLD_MS_DIRECT_H_ */