void subtractMultipleTo(DMat<RT>& C,
const DMat<RT>& A,
const DMat<RT>& B)
// C = C - A*B
{
typedef typename RT::ElementType ElementType;
typedef typename DMat<RT>::ConstIterator ConstIterator;
M2_ASSERT(A.numColumns() == B.numRows());
M2_ASSERT(A.numRows() == C.numRows());
M2_ASSERT(B.numColumns() == C.numColumns());
ElementType* result = C.array();
ElementType tmp;
A.ring().init(tmp);
// WARNING: this routine expects the result matrix to be in ROW MAJOR ORDER
for (size_t i = 0; i<A.numRows(); i++)
for (size_t j = 0; j<B.numColumns(); j++)
{
ConstIterator i1 = A.rowBegin(i);
ConstIterator iend = A.rowEnd(i);
ConstIterator j1 = B.columnBegin(j);
while (i1 != iend)
{
A.ring().mult(tmp, *i1, *j1);
A.ring().subtract(*result, *result, tmp);
++i1;
++j1;
}
result++;
}
A.ring().clear(tmp);
}
void mult(const DMat<RT>& A,
const DMat<RT>& B,
DMat<RT>& result_product)
{
//printf("entering dmat mult\n");
typedef typename RT::ElementType ElementType;
typedef typename DMat<RT>::ConstIterator ConstIterator;
M2_ASSERT(A.numColumns() == B.numRows());
M2_ASSERT(A.numRows() == result_product.numRows());
M2_ASSERT(B.numColumns() == result_product.numColumns());
ElementType* result = result_product.array();
ElementType tmp;
A.ring().init(tmp);
// WARNING: this routine expects the result matrix to be in ROW MAJOR ORDER
for (size_t i = 0; i<A.numRows(); i++)
for (size_t j = 0; j<B.numColumns(); j++)
{
ConstIterator i1 = A.rowBegin(i);
ConstIterator iend = A.rowEnd(i);
ConstIterator j1 = B.columnBegin(j);
while (i1 != iend)
{
A.ring().mult(tmp, *i1, *j1);
A.ring().add(*result, *result, tmp);
++i1;
++j1;
}
result++;
}
A.ring().clear(tmp);
}
bool isEqual(const DMat<RT>& A, const DMat<RT>& B)
{
assert(&A.ring() == &B.ring());
if (B.numRows() != A.numRows()) return false;
if (B.numColumns() != A.numColumns()) return false;
size_t top = A.numRows() * A.numColumns();
auto elemsA = A.array();
auto elemsB = B.array();
for (size_t i = 0; i < top; i++)
if (!A.ring().is_equal(*elemsA++, *elemsB++)) return false;
return true;
}
void subtractInPlace(DMat<RT>& A, const DMat<RT>& B)
// A -= B
{
M2_ASSERT(&B.ring() == &A.ring());
M2_ASSERT(B.numRows() == A.numRows());
M2_ASSERT(B.numColumns() == A.numColumns());
size_t len = A.numRows() * A.numColumns();
for (size_t i=0; i<len; i++)
{
A.ring().subtract(A.array()[i], A.array()[i], B.array()[i]);
}
}
void addInPlace(DMat<RT>& A, const DMat<RT>& B)
// A += B.
{
assert(&B.ring() == &A.ring());
assert(B.numRows() == A.numRows());
assert(B.numColumns() == A.numColumns());
size_t len = A.numRows() * A.numColumns();
for (size_t i = 0; i < len; i++)
{
A.ring().add(A.array()[i], A.array()[i], B.array()[i]);
}
}
void scalarMultInPlace(DMat<RT>& A, const typename RT::ElementType &f)
{
for (size_t i=0; i<A.numRows()*A.numColumns(); i++)
{
A.ring().mult(A.array()[i], f, A.array()[i]);
}
}
bool isZero(const DMat<RT>& A)
{
size_t len = A.numRows() * A.numColumns();
if (len == 0) return true;
for (auto t = A.array() + len - 1; t >= A.array(); t--)
if (!A.ring().is_zero(*t)) return false;
return true;
}
void negateInPlace(DMat<RT>& A)
// A = -A
{
size_t len = A.numRows() * A.numColumns();
for (size_t i=0; i<len; i++)
{
A.ring().negate(A.array()[i], A.array()[i]);
}
}
void addMultipleTo(DMat<RT>& A, MatrixWindow wA, const typename RT::ElementType& c, const DMat<RT>& B, MatrixWindow wB)
{
M2_ASSERT(wA.sameSize(wB));
typename RT::ElementType tmp;
A.ring().init(tmp);
long rA = wA.begin_row;
long rB = wB.begin_row;
for ( ; rA < wA.end_row; ++rA, ++rB)
{
long cA = wA.begin_column;
long cB = wB.begin_column;
for ( ; cA < wA.end_column; ++cA, ++cB)
{
A.ring().mult(tmp, c, B.entry(rB,cB));
auto& a = A.entry(rA,cA);
A.ring().add(a, a, tmp);
}
}
A.ring().clear(tmp);
}
void transpose(const DMat<RT>& A, DMat<RT>& result)
{
assert(&A != &result); // these cannot be aliased!
assert(result.numRows() == A.numColumns());
assert(result.numColumns() == A.numRows());
for (size_t c = 0; c < A.numColumns(); ++c)
{
auto i = A.columnBegin(c);
auto j = result.rowBegin(c);
auto end = A.columnEnd(c);
for (; i != end; ++i, ++j) A.ring().set(*j, *i);
}
}
void set(DMat<RT>& A, MatrixWindow wA, const DMat<RT>& B, MatrixWindow wB)
{
M2_ASSERT(wA.sameSize(wB));
long rA = wA.begin_row;
long rB = wB.begin_row;
for ( ; rA < wA.end_row; ++rA, ++rB)
{
long cA = wA.begin_column;
long cB = wB.begin_column;
for ( ; cA < wA.end_column; ++cA, ++cB)
A.ring().set(A.entry(rA,cA), B.entry(rB,cB));
}
}
inline void norm2(const DMat<RT>& M, size_t n, typename RT::RealElementType& result)
{
const auto& C = M.ring();
const auto& R = C.real_ring();
typename RT::RealElementType c;
R.init(c);
R.set_zero(result);
for(size_t i=0; i<n; i++) {
C.abs_squared(c,M.entry(0,i));
R.add(result,result,c);
}
R.clear(c);
}
void scalarMultInPlace(DMat<RT>& A, MatrixWindow wA, const typename RT::ElementType& c)
{
M2_ASSERT(wA.sameSize(wB));
long rA = wA.begin_row;
for ( ; rA < wA.end_row; ++rA)
{
long cA = wA.begin_column;
for ( ; cA < wA.end_column; ++cA)
{
auto& a = A.entry(rA,cA);
A.ring().mult(a, a, c);
}
}
}
void scalarMult(DMat<RT>& A, MatrixWindow wA, const typename RT::ElementType& c, const DMat<RT>& B, MatrixWindow wB)
{
M2_ASSERT(wA.sameSize(wB));
long rA = wA.begin_row;
long rB = wB.begin_row;
for ( ; rA < wA.end_row; ++rA, ++rB)
{
long cA = wA.begin_column;
long cB = wB.begin_column;
for ( ; cA < wA.end_column; ++cA, ++cB)
{
A.ring().mult(A.entry(rA,cA), c, B.entry(rB,cB));
}
}
}
void addTo(DMat<RT>& A, MatrixWindow wA, const DMat<RT>& B, MatrixWindow wB)
{
assert(wA.sameSize(wB));
long rA = wA.begin_row;
long rB = wB.begin_row;
for (; rA < wA.end_row; ++rA, ++rB)
{
long cA = wA.begin_column;
long cB = wB.begin_column;
for (; cA < wA.end_column; ++cA, ++cB)
{
auto& a = A.entry(rA, cA);
A.ring().add(a, a, B.entry(rB, cB));
}
}
}
engine_RawArrayIntPairOrNull rawLQUPFactorizationInPlace(MutableMatrix *A, M2_bool transpose)
{
#ifdef HAVE_FFLAS_FFPACK
// Suppose A is m x n
// then we get A = LQUP = LSP, see e.g. http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2006/RR2006-28.pdf
// P and Q are permutation info using LAPACK's convention:, see
// http://www.netlib.org/lapack/explore-html/d0/d39/_v_a_r_i_a_n_t_s_2lu_2_r_e_c_2dgetrf_8f.html
// P is n element permutation on column: size(P)=min(m,n);
// for 1 <= i <= min(m,n), col i of the matrix was interchanged with col P(i).
// Qt is m element permutation on rows (inverse permutation)
// for 1 <= i <= min(m,n), col i of the matrix was interchanged with col P(i).
A->transpose();
DMat<M2::ARingZZpFFPACK> *mat = A->coerce< DMat<M2::ARingZZpFFPACK> >();
if (mat == 0)
{
throw exc::engine_error("LUDivine not defined for this ring");
// ERROR("LUDivine not defined for this ring");
// return 0;
}
size_t nelems = mat->numColumns();
if (mat->numRows() < mat->numColumns()) nelems = mat->numRows();
std::vector<size_t> P(nelems, -1);
std::vector<size_t> Qt(nelems, -1);
// ignore return value (rank) of:
LUdivine(mat->ring().field(),
FFLAS::FflasNonUnit,
(transpose ? FFLAS::FflasTrans : FFLAS::FflasNoTrans),
mat->numRows(),
mat->numColumns(),
mat->array(),
mat->numColumns(),
&P[0],
&Qt[0]);
engine_RawArrayIntPairOrNull result = new engine_RawArrayIntPair_struct;
result->a = stdvector_to_M2_arrayint(Qt);
result->b = stdvector_to_M2_arrayint(P);
return result;
#endif
return 0;
}
inline M2_arrayintOrNull rankProfile(const DMat<RT>& A,
bool row_profile)
{
std::vector<size_t> profile;
if (row_profile)
{
// First transpose A
DMat<RT> B(A.ring(), A.numColumns(), A.numRows());
MatrixOps::transpose(A,B);
DMatLinAlg<RT> LUdecomp(B);
LUdecomp.columnRankProfile(profile);
return stdvector_to_M2_arrayint(profile);
}
else
{
DMatLinAlg<RT> LUdecomp(A);
LUdecomp.columnRankProfile(profile);
return stdvector_to_M2_arrayint(profile);
}
}
DMat(const DMat<ACoeffRing>& M) : mRing(&M.ring())
{
fmpz_mat_init_set(mArray, M.mArray);
}
DMat(const DMat<ACoeffRing>& M)
: mRing(& M.ring())
{
fmpq_mat_init(mArray, M.numRows(), M.numColumns());
fmpq_mat_set(mArray, M.mArray);
}
void setZero(DMat<RT>& A, MatrixWindow wA)
{
for (long rA = wA.begin_row; rA < wA.end_row; ++rA)
for (size_t cA = wA.begin_column; cA < wA.end_column; ++cA)
A.ring().set_zero(A.entry(rA,cA));
}
void determinantRRR(const DMat<M2::ARingRRR> &M, M2::ARingRRR::elem &result) { M.ring().set_zero(result); }
double ResF4toM2Interface::setDegreeZeroMap(SchreyerFrame& C,
DMat<RingType>& result,
int slanted_degree,
int lev)
// 'result' should be previously initialized, but will be resized.
// return value: -1 means (slanted_degree, lev) is out of range, and the zero matrix was returned.
// otherwise: the fraction of non-zero elements is returned.
{
// As above, get the size of the matrix, and 'newcols'
// Now we loop through the elements of degree 'slanted_degree + lev' at level 'lev'
const RingType& R = result.ring();
if (not (lev > 0 and lev <= C.maxLevel()))
{
result.resize(0,0);
return -1;
}
assert(lev > 0 and lev <= C.maxLevel());
int degree = slanted_degree + lev;
auto& thislevel = C.level(lev);
int ncols = 0;
for (auto p=thislevel.begin(); p != thislevel.end(); ++p)
{
if (p->mDegree == degree) ncols++;
}
auto& prevlevel = C.level(lev-1);
int* newcomps = new int[prevlevel.size()];
int nrows = 0;
for (int i=0; i<prevlevel.size(); i++)
if (prevlevel[i].mDegree == degree)
newcomps[i] = nrows++;
else
newcomps[i] = -1;
result.resize(nrows, ncols);
int col = 0;
long nnonzeros = 0;
for (auto p=thislevel.begin(); p != thislevel.end(); ++p)
{
if (p->mDegree != degree) continue;
auto& f = p->mSyzygy;
auto end = poly_iter(C.ring(), f, 1);
auto i = poly_iter(C.ring(), f);
for ( ; i != end; ++i)
{
long comp = C.monoid().get_component(i.monomial());
if (newcomps[comp] >= 0)
{
R.set_from_long(result.entry(newcomps[comp], col), C.gausser().coeff_to_int(i.coefficient()));
nnonzeros++;
}
}
++col;
}
double frac_nonzero = (nrows*ncols);
frac_nonzero = static_cast<double>(nnonzeros) / frac_nonzero;
delete[] newcomps;
return frac_nonzero;
}
DMat(const DMat<ACoeffRing>& M)
: mRing(& M.ring())
{
fq_nmod_mat_init_set(mArray, M.mArray, ring().flintContext());
}