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// license:GPL-2.0+
// copyright-holders:Couriersud
/*
* nld_ms_direct.h
*
*
* Sherman-Morrison Solver
*
* Computes the updated inverse of A given that the change in A is
*
* A <- A + (u x v) u,v vectors
*
* In this specific implementation, u is a unit vector specifying the row which
* changed. Thus v contains the changed column.
*
* Than z = A^-1 u , w = transpose(A^-1) v , lambda = v z
*
* A^-1 <- 1.0 / (1.0 + lambda) * (z x w)
*
* The approach is iterative and applied for each row changed.
*
* The performance for a typical circuit like kidniki compared to Gaussian
* elimination is poor:
*
* a) The code needs to be run for each row change.
* b) The inverse of A typically is fully occupied.
*
* It may have advantages for circuits with a high number of elements and only
* few dynamic/active components.
*
*/
#ifndef NLD_MS_SM_H_
#define NLD_MS_SM_H_
#include <algorithm>
#include "nld_solver.h"
#include "nld_matrix_solver.h"
#include "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 <std::size_t m_N, std::size_t storage_N>
class matrix_solver_sm_t: public matrix_solver_t
{
friend class matrix_solver_t;
public:
matrix_solver_sm_t(netlist_t &anetlist, const pstring &name,
const solver_parameters_t *params, const std::size_t size);
virtual ~matrix_solver_sm_t() override;
virtual void vsetup(analog_net_t::list_t &nets) override;
virtual void reset() override { matrix_solver_t::reset(); }
protected:
virtual unsigned vsolve_non_dynamic(const bool newton_raphson) override;
unsigned solve_non_dynamic(const bool newton_raphson);
constexpr std::size_t N() const { return (m_N == 0) ? m_dim : m_N; }
void LE_invert();
template <typename T>
void LE_compute_x(T * RESTRICT x);
template <typename T1, typename T2>
nl_ext_double &A(const T1 &r, const T2 &c) { return m_A[r][c]; }
template <typename T1, typename T2>
nl_ext_double &W(const T1 &r, const T2 &c) { return m_W[r][c]; }
template <typename T1, typename T2>
nl_ext_double &Ainv(const T1 &r, const T2 &c) { return m_Ainv[r][c]; }
template <typename T1>
nl_ext_double &RHS(const T1 &r) { return m_RHS[r]; }
template <typename T1, typename T2>
nl_ext_double &lA(const T1 &r, const T2 &c) { return m_lA[r][c]; }
template <typename T1, typename T2>
nl_ext_double &lAinv(const T1 &r, const T2 &c) { return m_lAinv[r][c]; }
nl_double m_last_RHS[storage_N]; // right hand side - contains currents
private:
static constexpr 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];
nl_ext_double m_lAinv[storage_N][m_pitch];
//nl_ext_double m_RHSx[storage_N];
const std::size_t m_dim;
std::size_t m_cnt;
};
// ----------------------------------------------------------------------------------------
// matrix_solver_direct
// ----------------------------------------------------------------------------------------
template <std::size_t m_N, std::size_t storage_N>
matrix_solver_sm_t<m_N, storage_N>::~matrix_solver_sm_t()
{
}
template <std::size_t m_N, std::size_t storage_N>
void matrix_solver_sm_t<m_N, storage_N>::vsetup(analog_net_t::list_t &nets)
{
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 <std::size_t m_N, std::size_t storage_N>
void matrix_solver_sm_t<m_N, storage_N>::LE_invert()
{
const std::size_t kN = N();
for (std::size_t i = 0; i < kN; i++)
{
for (std::size_t 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 (std::size_t 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 std::size_t 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 std::size_t eb = m_terms[i]->m_nzbd.size();
for (std::size_t jb = 0; jb < eb; jb++)
{
const unsigned j = pb[jb];
const nl_double f1 = - W(j,i) * f;
if (f1 != 0.0)
{
for (std::size_t k = 0; k < e; k++)
W(j,p[k]) += W(i,p[k]) * f1;
for (std::size_t k = 0; k <= i; k ++)
Ainv(j,k) += Ainv(i,k) * f1;
}
}
}
/* up */
for (std::size_t i = kN; i-- > 0; )
{
/* FIXME: Singular matrix? */
const nl_double f = 1.0 / W(i,i);
for (std::size_t j = i; j-- > 0; )
{
const nl_double f1 = - W(j,i) * f;
if (f1 != 0.0)
{
for (std::size_t k = i; k < kN; k++)
W(j,k) += W(i,k) * f1;
for (std::size_t k = 0; k < kN; k++)
Ainv(j,k) += Ainv(i,k) * f1;
}
}
for (std::size_t k = 0; k < kN; k++)
{
Ainv(i,k) *= f;
lAinv(i,k) = Ainv(i,k);
}
}
}
template <std::size_t m_N, std::size_t storage_N>
template <typename T>
void matrix_solver_sm_t<m_N, storage_N>::LE_compute_x(
T * RESTRICT x)
{
const std::size_t kN = N();
for (std::size_t i=0; i<kN; i++)
x[i] = 0.0;
for (std::size_t k=0; k<kN; k++)
{
const nl_double f = RHS(k);
for (std::size_t i=0; i<kN; i++)
x[i] += Ainv(i,k) * f;
}
}
template <std::size_t m_N, std::size_t storage_N>
unsigned matrix_solver_sm_t<m_N, storage_N>::solve_non_dynamic(const bool newton_raphson)
{
static constexpr const bool incremental = true;
const std::size_t iN = N();
nl_double new_V[storage_N]; // = { 0.0 };
if ((m_cnt % 50) == 0)
{
/* complete calculation */
this->LE_invert();
}
else
{
if (!incremental)
{
for (std::size_t row = 0; row < iN; row ++)
for (std::size_t k = 0; k < iN; k++)
Ainv(row,k) = lAinv(row, k);
}
for (std::size_t row = 0; row < iN; row ++)
{
nl_double v[m_pitch] = {0};
std::size_t cols[m_pitch];
std::size_t colcount = 0;
auto &nz = m_terms[row]->m_nz;
for (unsigned & col : nz)
{
v[col] = A(row,col) - lA(row,col);
if (incremental)
lA(row,col) = A(row,col);
if (v[col] != 0.0)
cols[colcount++] = col;
}
if (colcount > 0)
{
nl_double lamba = 0.0;
nl_double w[m_pitch] = {0};
nl_double z[m_pitch];
/* compute w and lamba */
for (std::size_t i = 0; i < iN; i++)
z[i] = Ainv(i, row); /* u is row'th column */
for (std::size_t j = 0; j < colcount; j++)
lamba += v[cols[j]] * z[cols[j]];
for (std::size_t j=0; j<colcount; j++)
{
std::size_t col = cols[j];
nl_double f = v[col];
for (std::size_t k = 0; k < iN; k++)
w[k] += Ainv(col,k) * f; /* Transpose(Ainv) * v */
}
lamba = -1.0 / (1.0 + lamba);
for (std::size_t i=0; i<iN; i++)
{
const nl_double f = lamba * z[i];
if (f != 0.0)
for (std::size_t k = 0; k < iN; k++)
Ainv(i,k) += f * w[k];
}
}
}
}
m_cnt++;
this->LE_compute_x(new_V);
const nl_double err = (newton_raphson ? delta(new_V) : 0.0);
store(new_V);
return (err > this->m_params.m_accuracy) ? 2 : 1;
}
template <std::size_t m_N, std::size_t storage_N>
inline unsigned matrix_solver_sm_t<m_N, storage_N>::vsolve_non_dynamic(const bool newton_raphson)
{
build_LE_A<matrix_solver_sm_t>();
build_LE_RHS<matrix_solver_sm_t>();
for (std::size_t 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 <std::size_t m_N, std::size_t storage_N>
matrix_solver_sm_t<m_N, storage_N>::matrix_solver_sm_t(netlist_t &anetlist, const pstring &name,
const solver_parameters_t *params, const std::size_t size)
: matrix_solver_t(anetlist, name, NOSORT, params)
, m_dim(size)
, m_cnt(0)
{
for (std::size_t k = 0; k < N(); k++)
{
m_last_RHS[k] = 0.0;
}
}
} //namespace devices
} // namespace netlist
#endif /* NLD_MS_DIRECT_H_ */
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