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// Copyright 2005,2013 Michael E. Stillman
#include "exceptions.hpp"
#include "error.h"
#include "mat-linalg.hpp"
////////////////////////////////////////////////////////////////////////////
// dmat code that might have alternate implementations, depending of type //
////////////////////////////////////////////////////////////////////////////
namespace MatrixOps {
void addMultipleTo(DMatZZpFFPACK& C,
const DMatZZpFFPACK::ElementType& a,
const DMatZZpFFPACK& A,
const DMatZZpFFPACK& B)
{
// Compute C := C + a*A*B
// Both DMat, and FFPACK store dense matrices in row major order.
// Note that the leading dimension in gemm arguments is #columns,
// as the matrix is in row-major order
FFLAS::FFLAS_TRANSPOSE tA = FFLAS::FflasNoTrans;
FFLAS::FFLAS_TRANSPOSE tB = FFLAS::FflasNoTrans;
size_t m = A.numRows();
size_t k = A.numColumns();
assert(A.numColumns() == B.numRows());
size_t n = B.numColumns();
assert(C.numRows() == m);
assert(C.numColumns() == n);
DMatZZpFFPACK::ElementType b;
C.ring().init(b);
C.ring().set_from_long(b, 1);
FFLAS::fgemm(C.ring().field(),
tB,
tA,
m,
n,
k,
a,
A.array(),
A.numColumns(),
B.array(),
B.numColumns(),
b,
C.array(),
C.numColumns());
}
void addMultipleTo(DMatZZpFFPACK& C,
const DMatZZpFFPACK& A,
const DMatZZpFFPACK& B)
{
DMatZZpFFPACK::ElementType one;
A.ring().set_from_long(one, 1);
addMultipleTo(C, one, A, B);
}
void subtractMultipleTo(DMatZZpFFPACK& C,
const DMatZZpFFPACK& A,
const DMatZZpFFPACK& B)
{
DMatZZpFFPACK::ElementType minus_one;
A.ring().set_from_long(minus_one, -1);
addMultipleTo(C, minus_one, A, B);
}
void mult(const DMatZZpFFPACK& A, const DMatZZpFFPACK& B, DMatZZpFFPACK& C)
{
// We assume that C is set to the correct size, and is the zero matrix here.
addMultipleTo(C, A, B);
}
}; // namespace MatrixOps
namespace ffpackInterface {
size_t rank(const DMatZZpFFPACK& mat)
{
/// @note 1. matrix data (N) is modified by FFPACK
DMatZZpFFPACK N(mat); // copy of matrix mat.
size_t result = FFPACK::Rank(mat.ring().field(),
mat.numRows(),
mat.numColumns(),
N.array(),
mat.numColumns());
return result;
}
void determinant(const DMatZZpFFPACK& mat, ZZpFFPACK::ElementType& result_det)
{
/// @note 1. matrix data (N) is modified by FFPACK
if (mat.numRows() == 0)
{
// 26 April 2014: this branch is needed as FFPACK gives answer of 0 in
// this case.
mat.ring().set_from_long(result_det, 1);
}
else
{
DMatZZpFFPACK N(mat);
ZZpFFPACK::ElementType det = 0;
result_det = FFPACK::Det(mat.ring().field(),
det,
mat.numRows(),
N.array(),
mat.numColumns());
}
}
bool inverse(const DMatZZpFFPACK& mat, DMatZZpFFPACK& result_inv)
{
assert(mat.numRows() == mat.numColumns());
result_inv.resize(mat.numRows(), mat.numRows());
assert(result_inv.numRows() == mat.numRows());
assert(result_inv.numColumns() == mat.numRows());
if (mat.numRows() == 0)
{
// 26 April 2014: this branch is needed as FFPACK gives answer of 0 in
// this case.
return true;
}
DMatZZpFFPACK N(mat);
size_t n = mat.numRows();
int nullspacedim;
FFPACK::Invert2(
mat.ring().field(), n, N.array(), n, result_inv.array(), n, nullspacedim);
return (nullspacedim == 0);
}
size_t nullSpace(const DMatZZpFFPACK& mat, DMatZZpFFPACK& nullspace)
{
bool right_side = true; // This function is written so that one could set
// right_side to false.
// (It used to be a parameter).
DMatZZpFFPACK N(mat); // copy of mat
size_t nr = mat.numRows();
size_t nc = mat.numColumns();
DMatZZpFFPACK::ElementType* nullspaceFFPACK = 0;
size_t nullspace_dim;
size_t nullspace_leading_dim;
FFPACK::NullSpaceBasis(mat.ring().field(),
(right_side ? FFLAS::FflasRight : FFLAS::FflasLeft),
nr,
nc,
N.array(),
nc,
nullspaceFFPACK,
nullspace_leading_dim,
nullspace_dim);
// std::cerr << "leading dim = " << nullspace_leading_dim << " and dim = "
// << nullspace_dim << std::endl;
if (right_side && nullspace_dim != nullspace_leading_dim)
{
std::cerr << "error: this should not happen!" << std::endl;
}
else if (!right_side && nullspace_leading_dim != nc)
{
std::cerr << "error: this should not happen either!" << std::endl;
}
if (right_side)
nullspace.resize(nc, nullspace_dim);
else
nullspace.resize(nullspace_dim, nr);
std::swap(nullspace.array(), nullspaceFFPACK);
delete[] nullspaceFFPACK;
return nullspace_dim;
}
bool solveLinear(const DMatZZpFFPACK& A,
const DMatZZpFFPACK& B,
bool right_side,
DMatZZpFFPACK& X,
bool declare_A_is_invertible) // this parameter is unused
{
// std::cerr << "inside FFpackSolveLinear" << std::endl;
size_t a_rows = A.numRows();
size_t a_cols = A.numColumns();
size_t b_rows = B.numRows();
size_t b_cols = B.numColumns();
DMatZZpFFPACK copyA(A);
DMatZZpFFPACK copyB(B);
// preallocate the space for the solutions:
size_t x_rows = (right_side ? a_cols : b_rows);
size_t x_cols = (right_side ? b_cols : a_rows);
X.resize(x_rows, x_cols); // sets it to 0 too.
int info = 0; // >0 if the system is inconsistent, ==0 means success
FFPACK::fgesv(A.ring().field(),
(right_side ? FFLAS::FflasLeft : FFLAS::FflasRight),
a_rows,
a_cols,
(right_side ? b_cols : b_rows),
copyA.array(),
a_cols, // leading dim of A
X.array(),
x_cols,
copyB.array(),
b_cols,
&info);
if (info > 0)
{
// the system is inconsistent
return false;
}
return true;
}
bool solveLinear(const DMatZZpFFPACK& A,
const DMatZZpFFPACK& B,
DMatZZpFFPACK& X)
{
return solveLinear(A, B, true, X, false);
}
M2_arrayintOrNull rankProfile(const DMatZZpFFPACK& mat, bool row_profile)
{
DMatZZpFFPACK N(mat);
size_t* prof; // this is where the result will be placed
size_t rk;
if (row_profile)
rk = FFPACK::RowRankProfile(mat.ring().field(),
mat.numRows(),
mat.numColumns(),
N.array(),
mat.numColumns(),
prof);
else
rk = FFPACK::ColumnRankProfile(mat.ring().field(),
mat.numRows(),
mat.numColumns(),
N.array(),
mat.numColumns(),
prof);
M2_arrayint profile = M2_makearrayint(static_cast<int>(rk));
for (size_t i = 0; i < rk; i++) profile->array[i] = static_cast<int>(prof[i]);
delete[] prof;
return profile;
}
void rankProfile(const DMatZZpFFPACK& mat,
bool row_profile,
std::vector<size_t>& result_profile)
{
DMatZZpFFPACK N(mat);
size_t* prof; // this is where the result will be placed
size_t rk;
if (row_profile)
rk = FFPACK::RowRankProfile(mat.ring().field(),
mat.numRows(),
mat.numColumns(),
N.array(),
mat.numColumns(),
prof);
else
rk = FFPACK::ColumnRankProfile(mat.ring().field(),
mat.numRows(),
mat.numColumns(),
N.array(),
mat.numColumns(),
prof);
result_profile.resize(0);
for (size_t i = 0; i < rk; i++) result_profile.push_back(prof[i]);
delete[] prof;
}
}; // namespace ffpackInterface
// Local Variables:
// compile-command: "make -C $M2BUILDDIR/Macaulay2/e "
// indent-tabs-mode: nil
// End:
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