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////////////////////////////////////////////////////////////////////////////////
//
// StairCaseMatrix.cc
//
// produced: 13/03/98 jr
// last change: 13/03/98 jr
//
////////////////////////////////////////////////////////////////////////////////
#include <iostream>
#include <ctype.h>
#include <string.h>
#include "StairCaseMatrix.hh"
namespace topcom {
void StairCaseMatrix::_eliminate(const parameter_type ridx, const parameter_type cidx, const parameter_type cno) {
if (cno == 0) {
return;
}
const parameter_type n = rowdim();
if (is_zero((*this)(ridx,ridx))) {
#ifdef SUPER_VERBOSE
std::cerr << "eraser = " << (*this)(ridx,ridx) << " == FieldConstants::ZERO -> try colperm; row : " << ridx << ", col: " << ridx << std::endl;
#endif
for (parameter_type k = cidx; k < cidx + cno; ++k) {
if (!is_zero((*this)(ridx,k))) {
Matrix::swap_cols(ridx,k);
_coefficient *= FieldConstants::MINUSONE;
#ifdef SUPER_VERBOSE
std::cerr << "eraser = " << (*this)(ridx,ridx) << " == FieldConstants::ZERO -> colperm successful; row : " << ridx << ", col: " << ridx << std::endl;
#endif
break;
}
}
if (is_zero((*this)(ridx,ridx))) {
#ifdef SUPER_VERBOSE
std::cerr << "eraser = " << (*this)(ridx,ridx) << " == FieldConstants::ZERO -> colperm unsuccessful; row : " << ridx << ", col: " << ridx << std::endl;
#endif
return;
}
#ifdef SUPER_VERBOSE
else {
std::cerr << "eraser = " << (*this)(ridx,ridx) << " != FieldConstants::ZERO; row : " << ridx << ", col: " << ridx << std::endl;
}
#endif
}
#ifdef SUPER_VERBOSE
else {
std::cerr << "eraser = " << (*this)(ridx,ridx) << " != FieldConstants::ZERO; row : " << ridx << ", col: " << ridx << std::endl;
}
#endif
const Field& eraser = (*this)(ridx,ridx);
#ifdef SUPER_VERBOSE
std::cerr << "eraser = " << eraser << "; row : " << ridx << ", col: " << ridx << std::endl;
#endif
for (parameter_type j = cidx; j < cidx + cno; ++j) {
const Field& delinquent = (*this)(ridx,j);
#ifdef SUPER_VERBOSE
std::cerr << "delinquent = " << delinquent << "; row : " << ridx << ", col: " << j << std::endl;
#endif
if (is_zero(delinquent)) {
continue;
}
// An alternative division-free elimination step (slightly slower for large numbers):
// if (eraser < FieldConstants::ZERO) {
// _coefficient /= -eraser;
// for (parameter_type k = ridx + 1; k < n; ++k) {
// (*this)(k,j) *= -eraser;
// (*this)(k,j) += delinquent * (*this)(k,ridx);
// }
// }
// else {
// _coefficient /= eraser;
// for (parameter_type k = ridx + 1; k < n; ++k) {
// (*this)(k,j) *= eraser;
// (*this)(k,j) -= delinquent * (*this)(k,ridx);
// }
// }
const Field multiplier = delinquent / eraser;
for (parameter_type k = ridx + 1; k < n; ++k) {
(*this)(k,j) -= multiplier * (*this)(k,ridx);
}
(*this)(ridx,j) = FieldConstants::ZERO;
}
#ifdef SUPER_VERBOSE
std::cerr << "after step " << ridx << " of stair case transformation: " << std::endl;
(*this).pretty_print(std::cerr);
#endif
}
StairCaseMatrix& StairCaseMatrix::augment(const Matrix& matrix, const IntegerSet& ignored_cols) {
// the resulting matrix will have matrix.rowdim() rows;
// note that (*this) may be empty resulting in rowdim() = 0:
if (matrix.coldim() == 0) {
return *this;
}
if (empty()) {
parameter_type j = 0;
while(j < matrix.coldim()) {
if (!ignored_cols.contains(j)) {
this->push_back(matrix.col(j));
return this->augment(matrix, ignored_cols + j);
}
else {
++j;
}
}
return *this;
}
#ifdef INDEX_CHECK
if (coldim() > 0) {
assert(rowdim() == matrix.rowdim());
}
#endif
const parameter_type m = matrix.rowdim();
// so many columns are already in stair-case form:
const parameter_type n = coldim();
// augment the matrix without elimination:
Matrix::augment(matrix, ignored_cols);
// so many columns must be in stair-case form after the transformations:
const parameter_type n_new = coldim();
// cnt1 many column elimination are needed with old pivot columns:
const parameter_type cnt1 = std::min<parameter_type>(n, m);
// cnt2 - cnt1 many column eliminations are needed with already modified new columns:
const parameter_type cnt2 = std::min<parameter_type>(n_new, m);
if (CommandlineOptions::debug()) {
std::lock_guard<std::mutex> lock(IO_sync::mutex);
std::cerr << "before stair case transformation:" << std::endl;
pretty_print(std::cerr);
}
// eliminate new columns using all old columns:
for (parameter_type i = 0; i < cnt1; ++i) {
// use pivot (i, i) to eliminate (n_new - n) many columns starting at column n:
_eliminate(i, n, n_new - n);
if (CommandlineOptions::debug()) {
std::lock_guard<std::mutex> lock(IO_sync::mutex);
std::cerr << "after elimination with pivot " << i
<< ", startcol " << n
<< ", no " << n_new - n << ":" << std::endl;
(*this).pretty_print(std::cerr);
}
}
// eliminate new columns using new columns:
for (parameter_type i = cnt1; i < cnt2; ++i) {
// use pivot (i, i) to eliminate (n_new - i - 1) many columns starting at column i + 1:
_eliminate(i, i + 1, n_new - i - 1);
if (CommandlineOptions::debug()) {
std::lock_guard<std::mutex> lock(IO_sync::mutex);
std::cerr << "after elimination with pivot " << i
<< ", startcol " << i + 1
<< ", no " << n_new - i - 1 << ":" << std::endl;
(*this).pretty_print(std::cerr);
}
}
if (CommandlineOptions::debug()) {
std::lock_guard<std::mutex> lock(IO_sync::mutex);
std::cerr << "after stair case transformation: " << std::endl;
(*this).pretty_print(std::cerr);
}
return *this;
}
// this special form of "det" computes the determinant of the left-top-most
// square matrix:
const Field StairCaseMatrix::left_upper_det() const {
parameter_type n = coldim();
if (coldim() > rowdim()) {
n = rowdim();
}
Field result(FieldConstants::ONE);
for (parameter_type i = 0; i < n; ++i) {
result *= (*this)(i,i);
if (is_zero(result)) {
return result;
}
}
return result * _coefficient;
}
const Field StairCaseMatrix::det() const {
#ifdef INDEX_CHECK
assert(coldim() == rowdim());
#endif
return left_upper_det();
}
std::ostream& StairCaseMatrix::pretty_print(std::ostream& ost) const {
ost << "matrix: " << '\n';
Matrix::pretty_print(ost);
ost << "coefficient: " << _coefficient << '\n';
return ost;
}
std::ostream& operator<<(std::ostream& ost, const StairCaseMatrix& matrix) {
ost << (Matrix)matrix << '/' << matrix._coefficient;
return ost;
}
}; // namespace topcom
// eof StairCaseMatrix.cc
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