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dense_matrix.cpp
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2100 lines (1809 loc) · 62.4 KB
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#include <symengine/matrix.h>
#include <symengine/number.h>
#include <symengine/add.h>
#include <symengine/functions.h>
#include <symengine/pow.h>
#include <symengine/subs.h>
#include <symengine/symengine_exception.h>
#include <symengine/polys/uexprpoly.h>
#include <symengine/solve.h>
#include <symengine/test_visitors.h>
#if HAVE_SYMENGINE_RTTI
#include <symengine/serialize-cereal.h>
#endif
namespace SymEngine
{
// Constructors
DenseMatrix::DenseMatrix() {}
DenseMatrix::DenseMatrix(unsigned row, unsigned col) : row_(row), col_(col)
{
m_ = std::vector<RCP<const Basic>>(row * col);
}
DenseMatrix::DenseMatrix(unsigned row, unsigned col, const vec_basic &l)
: m_{l}, row_(row), col_(col){SYMENGINE_ASSERT(m_.size() == row * col)}
DenseMatrix::DenseMatrix(const vec_basic &column_elements)
: m_(column_elements), row_(static_cast<unsigned>(column_elements.size())),
col_(1)
{
}
// Resize the Matrix
void DenseMatrix::resize(unsigned row, unsigned col)
{
row_ = row;
col_ = col;
m_.resize(row * col);
}
// Get and set elements
RCP<const Basic> DenseMatrix::get(unsigned i, unsigned j) const
{
SYMENGINE_ASSERT(i < row_ and j < col_);
return m_[i * col_ + j];
}
void DenseMatrix::set(unsigned i, unsigned j, const RCP<const Basic> &e)
{
SYMENGINE_ASSERT(i < row_ and j < col_);
m_[i * col_ + j] = e;
}
// Flat (row major) view of Matrix
vec_basic DenseMatrix::as_vec_basic() const
{
return m_;
}
RCP<const Basic> DenseMatrix::trace() const
{
SYMENGINE_ASSERT(row_ == col_);
unsigned offset = 0;
vec_basic diag;
for (unsigned i = 0; i < row_; i++) {
diag.push_back(m_[offset]);
offset += row_ + 1;
}
auto sum = add(diag);
return sum;
}
unsigned DenseMatrix::rank() const
{
throw NotImplementedError("Not Implemented");
}
bool DenseMatrix::is_lower() const
{
auto A = *this;
unsigned n = A.nrows();
for (unsigned i = 1; i < n; ++i) {
for (unsigned j = 0; j < i; ++j) {
if (not is_number_and_zero(*A.get(i, j))) {
return false;
}
}
}
return true;
}
bool DenseMatrix::is_upper() const
{
auto A = *this;
unsigned n = A.nrows();
for (unsigned i = 0; i < n - 1; ++i) {
for (unsigned j = i + 1; j < n; ++j) {
if (not is_number_and_zero(*A.get(i, j))) {
return false;
}
}
}
return true;
}
tribool DenseMatrix::is_zero() const
{
auto A = *this;
tribool cur = tribool::tritrue;
for (auto &e : m_) {
cur = and_tribool(cur, SymEngine::is_zero(*e));
if (is_false(cur)) {
return cur;
}
}
return cur;
}
tribool DenseMatrix::is_diagonal() const
{
auto A = *this;
if (not A.is_square()) {
return tribool::trifalse;
}
unsigned ncols = A.ncols();
unsigned offset;
tribool cur = tribool::tritrue;
for (unsigned i = 0; i < ncols; i++) {
offset = i * ncols;
for (unsigned j = 0; j < ncols; j++) {
if (j != i) {
auto &e = m_[offset];
cur = and_tribool(cur, SymEngine::is_zero(*e));
if (is_false(cur)) {
return cur;
}
}
offset++;
}
}
return cur;
}
tribool DenseMatrix::is_real(const Assumptions *assumptions) const
{
RealVisitor visitor(assumptions);
tribool cur = tribool::tritrue;
for (auto &e : m_) {
cur = and_tribool(cur, visitor.apply(*e));
if (is_false(cur)) {
return cur;
}
}
return cur;
}
tribool DenseMatrix::is_symmetric() const
{
auto A = *this;
if (not A.is_square()) {
return tribool::trifalse;
}
unsigned ncols = A.ncols();
tribool cur = tribool::tritrue;
for (unsigned i = 0; i < ncols; i++) {
for (unsigned j = 0; j <= i; j++) {
if (j != i) {
auto &e = m_[i * ncols + j];
auto &e2 = m_[j * ncols + i];
cur = and_tribool(cur, SymEngine::is_zero(*sub(e, e2)));
}
if (is_false(cur)) {
return cur;
}
}
}
return cur;
}
tribool DenseMatrix::is_hermitian() const
{
auto A = *this;
if (not A.is_square()) {
return tribool::trifalse;
}
unsigned ncols = A.ncols();
tribool cur = tribool::tritrue;
for (unsigned i = 0; i < ncols; i++) {
for (unsigned j = 0; j <= i; j++) {
auto &e = m_[i * ncols + j];
if (j != i) {
auto &e2 = m_[j * ncols + i];
cur = and_tribool(
cur, SymEngine::is_zero(*sub(e, SymEngine::conjugate(e2))));
} else {
cur = and_tribool(cur, SymEngine::is_real(*e));
}
if (is_false(cur)) {
return cur;
}
}
}
return cur;
}
tribool DenseMatrix::is_weakly_diagonally_dominant() const
{
auto A = *this;
if (not A.is_square()) {
return tribool::trifalse;
}
unsigned ncols = A.ncols();
RCP<const Basic> diag;
RCP<const Basic> sum;
tribool diagdom = tribool::tritrue;
for (unsigned i = 0; i < ncols; i++) {
sum = zero;
for (unsigned j = 0; j < ncols; j++) {
auto &e = m_[i * ncols + j];
if (i == j) {
diag = abs(e);
} else {
sum = add(sum, abs(e));
}
}
diagdom = and_tribool(diagdom, is_nonnegative(*sub(diag, sum)));
if (is_false(diagdom)) {
return diagdom;
}
}
return diagdom;
}
tribool DenseMatrix::is_strictly_diagonally_dominant() const
{
auto A = *this;
if (not A.is_square()) {
return tribool::trifalse;
}
unsigned ncols = A.ncols();
RCP<const Basic> diag;
RCP<const Basic> sum;
tribool diagdom = tribool::tritrue;
for (unsigned i = 0; i < ncols; i++) {
sum = zero;
for (unsigned j = 0; j < ncols; j++) {
auto &e = m_[i * ncols + j];
if (i == j) {
diag = abs(e);
} else {
sum = add(sum, abs(e));
}
}
diagdom = and_tribool(diagdom, is_positive(*sub(diag, sum)));
if (is_false(diagdom)) {
return diagdom;
}
}
return diagdom;
}
tribool DenseMatrix::shortcut_to_posdef() const
{
tribool is_diagonal_positive = tribool::tritrue;
unsigned offset = 0;
for (unsigned i = 0; i < row_; i++) {
is_diagonal_positive
= and_tribool(is_diagonal_positive, is_positive(*m_[offset]));
if (is_false(is_diagonal_positive))
return is_diagonal_positive;
offset += row_ + 1;
}
if (is_true(and_tribool(is_diagonal_positive,
this->is_strictly_diagonally_dominant())))
return tribool::tritrue;
return tribool::indeterminate;
}
tribool DenseMatrix::is_positive_definite_GE()
{
auto size = row_;
for (unsigned i = 0; i < size; i++) {
auto ispos = is_positive(*m_[i * size + i]);
if (!is_true(ispos))
return ispos;
for (unsigned j = i + 1; j < size; j++) {
for (unsigned k = i + 1; k < size; k++) {
m_[j * size + k] = sub(mul(m_[i * size + i], m_[j * size + k]),
mul(m_[j * size + i], m_[i * size + k]));
}
}
}
return tribool::tritrue;
}
tribool DenseMatrix::is_positive_definite() const
{
auto A = *this;
std::unique_ptr<DenseMatrix> B;
const DenseMatrix *H;
if (!is_true(A.is_hermitian())) {
if (!A.is_square())
return tribool::trifalse;
DenseMatrix tmp1 = DenseMatrix(A.row_, A.col_);
B = std::unique_ptr<DenseMatrix>(new DenseMatrix(A.row_, A.col_));
A.conjugate_transpose(tmp1);
add_dense_dense(A, tmp1, *B.get());
H = B.get();
} else {
H = this;
}
tribool shortcut = H->shortcut_to_posdef();
if (!is_indeterminate(shortcut))
return shortcut;
if (!B) {
B = std::unique_ptr<DenseMatrix>(new DenseMatrix(A));
}
return B->is_positive_definite_GE();
}
tribool DenseMatrix::is_negative_definite() const
{
auto res = DenseMatrix(row_, col_);
mul_dense_scalar(*this, integer(-1), res);
return res.is_positive_definite();
}
RCP<const Basic> DenseMatrix::det() const
{
return det_bareis(*this);
}
void DenseMatrix::inv(MatrixBase &result) const
{
if (is_a<DenseMatrix>(result)) {
DenseMatrix &r = down_cast<DenseMatrix &>(result);
inverse_pivoted_LU(*this, r);
}
}
void DenseMatrix::add_matrix(const MatrixBase &other, MatrixBase &result) const
{
SYMENGINE_ASSERT(row_ == result.nrows() and col_ == result.ncols());
if (is_a<DenseMatrix>(other) and is_a<DenseMatrix>(result)) {
const DenseMatrix &o = down_cast<const DenseMatrix &>(other);
DenseMatrix &r = down_cast<DenseMatrix &>(result);
add_dense_dense(*this, o, r);
}
}
void DenseMatrix::mul_matrix(const MatrixBase &other, MatrixBase &result) const
{
SYMENGINE_ASSERT(row_ == result.nrows()
and other.ncols() == result.ncols());
if (is_a<DenseMatrix>(other) and is_a<DenseMatrix>(result)) {
const DenseMatrix &o = down_cast<const DenseMatrix &>(other);
DenseMatrix &r = down_cast<DenseMatrix &>(result);
mul_dense_dense(*this, o, r);
}
}
void DenseMatrix::elementwise_mul_matrix(const MatrixBase &other,
MatrixBase &result) const
{
SYMENGINE_ASSERT(row_ == result.nrows() and col_ == result.ncols()
and row_ == other.nrows() and col_ == other.ncols());
if (is_a<DenseMatrix>(other) and is_a<DenseMatrix>(result)) {
const DenseMatrix &o = down_cast<const DenseMatrix &>(other);
DenseMatrix &r = down_cast<DenseMatrix &>(result);
elementwise_mul_dense_dense(*this, o, r);
}
}
// Add a scalar
void DenseMatrix::add_scalar(const RCP<const Basic> &k,
MatrixBase &result) const
{
if (is_a<DenseMatrix>(result)) {
DenseMatrix &r = down_cast<DenseMatrix &>(result);
add_dense_scalar(*this, k, r);
}
}
// Multiply by a scalar
void DenseMatrix::mul_scalar(const RCP<const Basic> &k,
MatrixBase &result) const
{
if (is_a<DenseMatrix>(result)) {
DenseMatrix &r = down_cast<DenseMatrix &>(result);
mul_dense_scalar(*this, k, r);
}
}
// Matrix conjugate
void DenseMatrix::conjugate(MatrixBase &result) const
{
if (is_a<DenseMatrix>(result)) {
DenseMatrix &r = down_cast<DenseMatrix &>(result);
conjugate_dense(*this, r);
}
}
// Matrix transpose
void DenseMatrix::transpose(MatrixBase &result) const
{
if (is_a<DenseMatrix>(result)) {
DenseMatrix &r = down_cast<DenseMatrix &>(result);
transpose_dense(*this, r);
}
}
// Matrix conjugate transpose
void DenseMatrix::conjugate_transpose(MatrixBase &result) const
{
if (is_a<DenseMatrix>(result)) {
DenseMatrix &r = down_cast<DenseMatrix &>(result);
conjugate_transpose_dense(*this, r);
}
}
// Extract out a submatrix
void DenseMatrix::submatrix(MatrixBase &result, unsigned row_start,
unsigned col_start, unsigned row_end,
unsigned col_end, unsigned row_step,
unsigned col_step) const
{
if (is_a<DenseMatrix>(result)) {
DenseMatrix &r = down_cast<DenseMatrix &>(result);
submatrix_dense(*this, r, row_start, col_start, row_end, col_end,
row_step, col_step);
}
}
// LU factorization
void DenseMatrix::LU(MatrixBase &L, MatrixBase &U) const
{
if (is_a<DenseMatrix>(L) and is_a<DenseMatrix>(U)) {
DenseMatrix &L_ = down_cast<DenseMatrix &>(L);
DenseMatrix &U_ = down_cast<DenseMatrix &>(U);
SymEngine::LU(*this, L_, U_);
}
}
// LDL factorization
void DenseMatrix::LDL(MatrixBase &L, MatrixBase &D) const
{
if (is_a<DenseMatrix>(L) and is_a<DenseMatrix>(D)) {
DenseMatrix &L_ = down_cast<DenseMatrix &>(L);
DenseMatrix &D_ = down_cast<DenseMatrix &>(D);
SymEngine::LDL(*this, L_, D_);
}
}
// Solve Ax = b using LU factorization
void DenseMatrix::LU_solve(const MatrixBase &b, MatrixBase &x) const
{
if (is_a<DenseMatrix>(b) and is_a<DenseMatrix>(x)) {
const DenseMatrix &b_ = down_cast<const DenseMatrix &>(b);
DenseMatrix &x_ = down_cast<DenseMatrix &>(x);
SymEngine::LU_solve(*this, b_, x_);
}
}
// Fraction free LU factorization
void DenseMatrix::FFLU(MatrixBase &LU) const
{
if (is_a<DenseMatrix>(LU)) {
DenseMatrix &LU_ = down_cast<DenseMatrix &>(LU);
fraction_free_LU(*this, LU_);
}
}
// Fraction free LDU factorization
void DenseMatrix::FFLDU(MatrixBase &L, MatrixBase &D, MatrixBase &U) const
{
if (is_a<DenseMatrix>(L) and is_a<DenseMatrix>(D)
and is_a<DenseMatrix>(U)) {
DenseMatrix &L_ = down_cast<DenseMatrix &>(L);
DenseMatrix &D_ = down_cast<DenseMatrix &>(D);
DenseMatrix &U_ = down_cast<DenseMatrix &>(U);
fraction_free_LDU(*this, L_, D_, U_);
}
}
// QR factorization
void DenseMatrix::QR(MatrixBase &Q, MatrixBase &R) const
{
if (is_a<DenseMatrix>(Q) and is_a<DenseMatrix>(R)) {
DenseMatrix &Q_ = down_cast<DenseMatrix &>(Q);
DenseMatrix &R_ = down_cast<DenseMatrix &>(R);
SymEngine::QR(*this, Q_, R_);
}
}
// Cholesky decomposition
void DenseMatrix::cholesky(MatrixBase &L) const
{
if (is_a<DenseMatrix>(L)) {
DenseMatrix &L_ = down_cast<DenseMatrix &>(L);
SymEngine::cholesky(*this, L_);
}
}
// ---------------------------- Jacobian -------------------------------------//
void jacobian(const DenseMatrix &A, const DenseMatrix &x, DenseMatrix &result,
bool diff_cache)
{
SYMENGINE_ASSERT(A.col_ == 1);
SYMENGINE_ASSERT(x.col_ == 1);
SYMENGINE_ASSERT(A.row_ == result.nrows() and x.row_ == result.ncols());
bool error = false;
#pragma omp parallel for
for (unsigned i = 0; i < result.row_; i++) {
for (unsigned j = 0; j < result.col_; j++) {
if (is_a<Symbol>(*(x.m_[j]))) {
const RCP<const Symbol> x_
= rcp_static_cast<const Symbol>(x.m_[j]);
result.m_[i * result.col_ + j] = A.m_[i]->diff(x_, diff_cache);
} else {
error = true;
break;
}
}
}
if (error) {
throw SymEngineException(
"'x' must contain Symbols only. "
"Use sjacobian for SymPy style differentiation");
}
}
void sjacobian(const DenseMatrix &A, const DenseMatrix &x, DenseMatrix &result,
bool diff_cache)
{
SYMENGINE_ASSERT(A.col_ == 1);
SYMENGINE_ASSERT(x.col_ == 1);
SYMENGINE_ASSERT(A.row_ == result.nrows() and x.row_ == result.ncols());
#pragma omp parallel for
for (unsigned i = 0; i < result.row_; i++) {
for (unsigned j = 0; j < result.col_; j++) {
if (is_a<Symbol>(*(x.m_[j]))) {
const RCP<const Symbol> x_
= rcp_static_cast<const Symbol>(x.m_[j]);
result.m_[i * result.col_ + j] = A.m_[i]->diff(x_, diff_cache);
} else {
// TODO: Use a dummy symbol
const RCP<const Symbol> x_ = symbol("x_");
result.m_[i * result.col_ + j] = ssubs(
ssubs(A.m_[i], {{x.m_[j], x_}})->diff(x_, diff_cache),
{{x_, x.m_[j]}});
}
}
}
}
// ---------------------------- Diff -------------------------------------//
void diff(const DenseMatrix &A, const RCP<const Symbol> &x, DenseMatrix &result,
bool diff_cache)
{
SYMENGINE_ASSERT(A.row_ == result.nrows() and A.col_ == result.ncols());
#pragma omp parallel for
for (unsigned i = 0; i < result.row_; i++) {
for (unsigned j = 0; j < result.col_; j++) {
result.m_[i * result.col_ + j]
= A.m_[i * result.col_ + j]->diff(x, diff_cache);
}
}
}
void sdiff(const DenseMatrix &A, const RCP<const Basic> &x, DenseMatrix &result,
bool diff_cache)
{
SYMENGINE_ASSERT(A.row_ == result.nrows() and A.col_ == result.ncols());
#pragma omp parallel for
for (unsigned i = 0; i < result.row_; i++) {
for (unsigned j = 0; j < result.col_; j++) {
if (is_a<Symbol>(*x)) {
const RCP<const Symbol> x_ = rcp_static_cast<const Symbol>(x);
result.m_[i * result.col_ + j]
= A.m_[i * result.col_ + j]->diff(x_, diff_cache);
} else {
// TODO: Use a dummy symbol
const RCP<const Symbol> x_ = symbol("_x");
result.m_[i * result.col_ + j]
= ssubs(ssubs(A.m_[i * result.col_ + j], {{x, x_}})
->diff(x_, diff_cache),
{{x_, x}});
}
}
}
}
// ----------------------------- Matrix Conjugate ----------------------------//
void conjugate_dense(const DenseMatrix &A, DenseMatrix &B)
{
SYMENGINE_ASSERT(B.col_ == A.col_ and B.row_ == A.row_);
for (unsigned i = 0; i < A.row_; i++)
for (unsigned j = 0; j < A.col_; j++)
B.m_[i * B.col_ + j] = conjugate(A.m_[i * A.col_ + j]);
}
// ----------------------------- Matrix Transpose ----------------------------//
void transpose_dense(const DenseMatrix &A, DenseMatrix &B)
{
SYMENGINE_ASSERT(B.row_ == A.col_ and B.col_ == A.row_);
for (unsigned i = 0; i < A.row_; i++)
for (unsigned j = 0; j < A.col_; j++)
B.m_[j * B.col_ + i] = A.m_[i * A.col_ + j];
}
// ----------------------------- Matrix Conjugate Transpose -----------------//
void conjugate_transpose_dense(const DenseMatrix &A, DenseMatrix &B)
{
SYMENGINE_ASSERT(B.row_ == A.col_ and B.col_ == A.row_);
for (unsigned i = 0; i < A.row_; i++)
for (unsigned j = 0; j < A.col_; j++)
B.m_[j * B.col_ + i] = conjugate(A.m_[i * A.col_ + j]);
}
// ------------------------------- Submatrix ---------------------------------//
void submatrix_dense(const DenseMatrix &A, DenseMatrix &B, unsigned row_start,
unsigned col_start, unsigned row_end, unsigned col_end,
unsigned row_step, unsigned col_step)
{
SYMENGINE_ASSERT(row_end >= row_start and col_end >= col_start);
SYMENGINE_ASSERT(row_end < A.row_);
SYMENGINE_ASSERT(col_end < A.col_);
SYMENGINE_ASSERT(B.row_ == row_end - row_start + 1
and B.col_ == col_end - col_start + 1);
unsigned row = B.row_, col = B.col_;
for (unsigned i = 0; i < row; i += row_step)
for (unsigned j = 0; j < col; j += col_step)
B.m_[i * col + j] = A.m_[(row_start + i) * A.col_ + col_start + j];
}
// ------------------------------- Matrix Addition ---------------------------//
void add_dense_dense(const DenseMatrix &A, const DenseMatrix &B, DenseMatrix &C)
{
SYMENGINE_ASSERT(A.row_ == B.row_ and A.col_ == B.col_ and A.row_ == C.row_
and A.col_ == C.col_);
unsigned row = A.row_, col = A.col_;
for (unsigned i = 0; i < row; i++) {
for (unsigned j = 0; j < col; j++) {
C.m_[i * col + j] = add(A.m_[i * col + j], B.m_[i * col + j]);
}
}
}
void add_dense_scalar(const DenseMatrix &A, const RCP<const Basic> &k,
DenseMatrix &B)
{
SYMENGINE_ASSERT(A.row_ == B.row_ and A.col_ == B.col_);
unsigned row = A.row_, col = A.col_;
for (unsigned i = 0; i < row; i++) {
for (unsigned j = 0; j < col; j++) {
B.m_[i * col + j] = add(A.m_[i * col + j], k);
}
}
}
// ------------------------------- Matrix Multiplication ---------------------//
void mul_dense_dense(const DenseMatrix &A, const DenseMatrix &B, DenseMatrix &C)
{
SYMENGINE_ASSERT(A.col_ == B.row_ and C.row_ == A.row_
and C.col_ == B.col_);
unsigned row = A.row_, col = B.col_;
if (&A != &C and &B != &C) {
for (unsigned r = 0; r < row; r++) {
for (unsigned c = 0; c < col; c++) {
C.m_[r * col + c] = zero; // Integer Zero
for (unsigned k = 0; k < A.col_; k++)
C.m_[r * col + c]
= add(C.m_[r * col + c],
mul(A.m_[r * A.col_ + k], B.m_[k * col + c]));
}
}
} else {
DenseMatrix tmp = DenseMatrix(A.row_, B.col_);
mul_dense_dense(A, B, tmp);
C = tmp;
}
}
void elementwise_mul_dense_dense(const DenseMatrix &A, const DenseMatrix &B,
DenseMatrix &C)
{
SYMENGINE_ASSERT(A.row_ == B.row_ and A.col_ == B.col_ and A.row_ == C.row_
and A.col_ == C.col_);
unsigned row = A.row_, col = A.col_;
for (unsigned i = 0; i < row; i++) {
for (unsigned j = 0; j < col; j++) {
C.m_[i * col + j] = mul(A.m_[i * col + j], B.m_[i * col + j]);
}
}
}
void mul_dense_scalar(const DenseMatrix &A, const RCP<const Basic> &k,
DenseMatrix &B)
{
SYMENGINE_ASSERT(A.col_ == B.col_ and A.row_ == B.row_);
unsigned row = A.row_, col = A.col_;
for (unsigned i = 0; i < row; i++) {
for (unsigned j = 0; j < col; j++) {
B.m_[i * col + j] = mul(A.m_[i * col + j], k);
}
}
}
// ---------------------------- Joining Operations ---------------------------//
void DenseMatrix::row_join(const DenseMatrix &B)
{
this->col_insert(B, col_);
}
void DenseMatrix::col_join(const DenseMatrix &B)
{
this->row_insert(B, row_);
}
void DenseMatrix::row_insert(const DenseMatrix &B, unsigned pos)
{
SYMENGINE_ASSERT(col_ == B.col_ and pos <= row_)
unsigned row = row_, col = col_;
this->resize(row_ + B.row_, col_);
for (unsigned i = row; i-- > pos;) {
for (unsigned j = col; j-- > 0;) {
this->m_[(i + B.row_) * col + j] = this->m_[i * col + j];
}
}
for (unsigned i = 0; i < B.row_; i++) {
for (unsigned j = 0; j < col; j++) {
this->m_[(i + pos) * col + j] = B.m_[i * col + j];
}
}
}
void DenseMatrix::col_insert(const DenseMatrix &B, unsigned pos)
{
SYMENGINE_ASSERT(row_ == B.row_ and pos <= col_)
unsigned row = row_, col = col_;
this->resize(row_, col_ + B.col_);
for (unsigned i = row; i-- > 0;) {
for (unsigned j = col; j-- > 0;) {
if (j >= pos) {
this->m_[i * (col + B.col_) + j + B.col_]
= this->m_[i * col + j];
} else {
this->m_[i * (col + B.col_) + j] = this->m_[i * col + j];
}
}
}
for (unsigned i = 0; i < row; i++) {
for (unsigned j = 0; j < B.col_; j++) {
this->m_[i * (col + B.col_) + j + pos] = B.m_[i * B.col_ + j];
}
}
}
void DenseMatrix::row_del(unsigned k)
{
SYMENGINE_ASSERT(k < row_)
if (row_ == 1)
this->resize(0, 0);
else {
for (unsigned i = k; i < row_ - 1; i++) {
row_exchange_dense(*this, i, i + 1);
}
this->resize(row_ - 1, col_);
}
}
void DenseMatrix::col_del(unsigned k)
{
SYMENGINE_ASSERT(k < col_)
if (col_ == 1)
this->resize(0, 0);
else {
unsigned row = row_, col = col_, m = 0;
for (unsigned i = 0; i < row; i++) {
for (unsigned j = 0; j < col; j++) {
if (j != k) {
this->m_[m] = this->m_[i * col + j];
m++;
}
}
}
this->resize(row_, col_ - 1);
}
}
// -------------------------------- Row Operations ---------------------------//
void row_exchange_dense(DenseMatrix &A, unsigned i, unsigned j)
{
SYMENGINE_ASSERT(i != j and i < A.row_ and j < A.row_);
unsigned col = A.col_;
for (unsigned k = 0; k < A.col_; k++)
std::swap(A.m_[i * col + k], A.m_[j * col + k]);
}
void row_mul_scalar_dense(DenseMatrix &A, unsigned i, RCP<const Basic> &c)
{
SYMENGINE_ASSERT(i < A.row_);
unsigned col = A.col_;
for (unsigned j = 0; j < A.col_; j++)
A.m_[i * col + j] = mul(c, A.m_[i * col + j]);
}
void row_add_row_dense(DenseMatrix &A, unsigned i, unsigned j,
RCP<const Basic> &c)
{
SYMENGINE_ASSERT(i != j and i < A.row_ and j < A.row_);
unsigned col = A.col_;
for (unsigned k = 0; k < A.col_; k++)
A.m_[i * col + k] = add(A.m_[i * col + k], mul(c, A.m_[j * col + k]));
}
void permuteFwd(DenseMatrix &A, permutelist &pl)
{
for (auto &p : pl) {
row_exchange_dense(A, p.first, p.second);
}
}
// ----------------------------- Column Operations ---------------------------//
void column_exchange_dense(DenseMatrix &A, unsigned i, unsigned j)
{
SYMENGINE_ASSERT(i != j and i < A.col_ and j < A.col_);
unsigned col = A.col_;
for (unsigned k = 0; k < A.row_; k++)
std::swap(A.m_[k * col + i], A.m_[k * col + j]);
}
// ------------------------------ Gaussian Elimination -----------------------//
void pivoted_gaussian_elimination(const DenseMatrix &A, DenseMatrix &B,
permutelist &pl)
{
SYMENGINE_ASSERT(A.row_ == B.row_ and A.col_ == B.col_);
unsigned row = A.row_, col = A.col_;
unsigned index = 0, i, j, k;
B.m_ = A.m_;
RCP<const Basic> scale;
for (i = 0; i < col - 1; i++) {
if (index == row)
break;
k = pivot(B, index, i);
if (k == row)
continue;
if (k != index) {
row_exchange_dense(B, k, index);
pl.push_back({k, index});
}
scale = div(one, B.m_[index * col + i]);
row_mul_scalar_dense(B, index, scale);
for (j = i + 1; j < row; j++) {
for (k = i + 1; k < col; k++)
B.m_[j * col + k]
= sub(B.m_[j * col + k],
mul(B.m_[j * col + i], B.m_[i * col + k]));
B.m_[j * col + i] = zero;
}
index++;
}
}
// Algorithm 1, page 12, Nakos, G. C., Turner, P. R., Williams, R. M. (1997).
// Fraction-free algorithms for linear and polynomial equations.
// ACM SIGSAM Bulletin, 31(3), 11–19. doi:10.1145/271130.271133.
void fraction_free_gaussian_elimination(const DenseMatrix &A, DenseMatrix &B)
{
SYMENGINE_ASSERT(A.row_ == B.row_ and A.col_ == B.col_);
unsigned col = A.col_;
B.m_ = A.m_;
for (unsigned i = 0; i < col - 1; i++)
for (unsigned j = i + 1; j < A.row_; j++) {
for (unsigned k = i + 1; k < col; k++) {
B.m_[j * col + k]
= sub(mul(B.m_[i * col + i], B.m_[j * col + k]),
mul(B.m_[j * col + i], B.m_[i * col + k]));
if (i > 0)
B.m_[j * col + k]
= div(B.m_[j * col + k], B.m_[i * col - col + i - 1]);
}
B.m_[j * col + i] = zero;
}
}
// Pivoted version of `fraction_free_gaussian_elimination`
void pivoted_fraction_free_gaussian_elimination(const DenseMatrix &A,
DenseMatrix &B, permutelist &pl)
{
SYMENGINE_ASSERT(A.row_ == B.row_ and A.col_ == B.col_);
unsigned col = A.col_, row = A.row_;
unsigned index = 0, i, k, j;
B.m_ = A.m_;
for (i = 0; i < col - 1; i++) {
if (index == row)
break;
k = pivot(B, index, i);
if (k == row)
continue;
if (k != index) {
row_exchange_dense(B, k, index);
pl.push_back({k, index});
}
for (j = i + 1; j < row; j++) {
for (k = i + 1; k < col; k++) {
B.m_[j * col + k]
= sub(mul(B.m_[i * col + i], B.m_[j * col + k]),
mul(B.m_[j * col + i], B.m_[i * col + k]));
if (i > 0)
B.m_[j * col + k]
= div(B.m_[j * col + k], B.m_[i * col - col + i - 1]);
}
B.m_[j * col + i] = zero;
}
index++;
}
}
void pivoted_gauss_jordan_elimination(const DenseMatrix &A, DenseMatrix &B,
permutelist &pl)
{
SYMENGINE_ASSERT(A.row_ == B.row_ and A.col_ == B.col_);
unsigned row = A.row_, col = A.col_;
unsigned index = 0, i, j, k;
RCP<const Basic> scale;
B.m_ = A.m_;
for (i = 0; i < col; i++) {
if (index == row)
break;
k = pivot(B, index, i);
if (k == row)
continue;
if (k != index) {
row_exchange_dense(B, k, index);
pl.push_back({k, index});
}
scale = div(one, B.m_[index * col + i]);