DEFAULT_UNARCHIVE(matrix)
//////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
//////////
// public
} else {
- c.s << "[[ ";
+ c.s << "[";
for (unsigned y=0; y<row-1; ++y) {
- c.s << "[[";
+ c.s << "[";
for (unsigned x=0; x<col-1; ++x) {
m[y*col+x].print(c);
c.s << ",";
}
m[col*(y+1)-1].print(c);
- c.s << "]], ";
+ c.s << "],";
}
- c.s << "[[";
+ c.s << "[";
for (unsigned x=0; x<col-1; ++x) {
m[(row-1)*col+x].print(c);
c.s << ",";
}
m[row*col-1].print(c);
- c.s << "]] ]]";
+ c.s << "]]";
}
}
return m[i];
}
-/** expands the elements of a matrix entry by entry. */
-ex matrix::expand(unsigned options) const
-{
- exvector tmp(row*col);
- for (unsigned i=0; i<row*col; ++i)
- tmp[i] = m[i].expand(options);
-
- return matrix(row, col, tmp);
-}
-
-/** Search ocurrences. A matrix 'has' an expression if it is the expression
- * itself or one of the elements 'has' it. */
-bool matrix::has(const ex & other) const
-{
- GINAC_ASSERT(other.bp!=0);
-
- // tautology: it is the expression itself
- if (is_equal(*other.bp)) return true;
-
- // search all the elements
- for (exvector::const_iterator r=m.begin(); r!=m.end(); ++r)
- if ((*r).has(other)) return true;
-
- return false;
-}
-
/** Evaluate matrix entry by entry. */
ex matrix::eval(int level) const
{
status_flags::evaluated );
}
-/** Evaluate matrix numerically entry by entry. */
-ex matrix::evalf(int level) const
-{
- debugmsg("matrix evalf",LOGLEVEL_MEMBER_FUNCTION);
-
- // check if we have to do anything at all
- if (level==1)
- return *this;
-
- // emergency break
- if (level == -max_recursion_level) {
- throw (std::runtime_error("matrix::evalf(): recursion limit exceeded"));
- }
-
- // evalf() entry by entry
- exvector m2(row*col);
- --level;
- for (unsigned r=0; r<row; ++r)
- for (unsigned c=0; c<col; ++c)
- m2[r*col+c] = m[r*col+c].evalf(level);
-
- return matrix(row, col, m2);
-}
-
-ex matrix::subs(const lst & ls, const lst & lr) const
+ex matrix::subs(const lst & ls, const lst & lr, bool no_pattern) const
{
exvector m2(row * col);
for (unsigned r=0; r<row; ++r)
for (unsigned c=0; c<col; ++c)
- m2[r*col+c] = m[r*col+c].subs(ls, lr);
+ m2[r*col+c] = m[r*col+c].subs(ls, lr, no_pattern);
- return matrix(row, col, m2);
+ return ex(matrix(row, col, m2)).bp->basic::subs(ls, lr, no_pattern);
}
// protected
int matrix::compare_same_type(const basic & other) const
{
GINAC_ASSERT(is_exactly_of_type(other, matrix));
- const matrix & o = static_cast<matrix &>(const_cast<basic &>(other));
+ const matrix & o = static_cast<const matrix &>(other);
// compare number of rows
if (row != o.rows())
return 0;
}
+bool matrix::match_same_type(const basic & other) const
+{
+ GINAC_ASSERT(is_exactly_of_type(other, matrix));
+ const matrix & o = static_cast<const matrix &>(other);
+
+ // The number of rows and columns must be the same. This is necessary to
+ // prevent a 2x3 matrix from matching a 3x2 one.
+ return row == o.rows() && col == o.cols();
+}
+
/** Automatic symbolic evaluation of an indexed matrix. */
ex matrix::eval_indexed(const basic & i) const
{
if (row != 1 && col != 1)
throw (std::runtime_error("matrix::eval_indexed(): vector must have exactly 1 index"));
- const idx & i1 = ex_to_idx(i.op(1));
+ const idx & i1 = ex_to<idx>(i.op(1));
if (col == 1) {
// Index numeric -> return vector element
if (all_indices_unsigned) {
- unsigned n1 = ex_to_numeric(i1.get_value()).to_int();
+ unsigned n1 = ex_to<numeric>(i1.get_value()).to_int();
if (n1 >= row)
throw (std::runtime_error("matrix::eval_indexed(): value of index exceeds number of vector elements"));
return (*this)(n1, 0);
// Index numeric -> return vector element
if (all_indices_unsigned) {
- unsigned n1 = ex_to_numeric(i1.get_value()).to_int();
+ unsigned n1 = ex_to<numeric>(i1.get_value()).to_int();
if (n1 >= col)
throw (std::runtime_error("matrix::eval_indexed(): value of index exceeds number of vector elements"));
return (*this)(0, n1);
} else if (i.nops() == 3) {
// Two indices
- const idx & i1 = ex_to_idx(i.op(1));
- const idx & i2 = ex_to_idx(i.op(2));
+ const idx & i1 = ex_to<idx>(i.op(1));
+ const idx & i2 = ex_to<idx>(i.op(2));
if (!i1.get_dim().is_equal(row))
throw (std::runtime_error("matrix::eval_indexed(): dimension of first index must match number of rows"));
// Both indices numeric -> return matrix element
if (all_indices_unsigned) {
- unsigned n1 = ex_to_numeric(i1.get_value()).to_int(), n2 = ex_to_numeric(i2.get_value()).to_int();
+ unsigned n1 = ex_to<numeric>(i1.get_value()).to_int(), n2 = ex_to<numeric>(i2.get_value()).to_int();
if (n1 >= row)
throw (std::runtime_error("matrix::eval_indexed(): value of first index exceeds number of rows"));
if (n2 >= col)
if (is_ex_of_type(other.op(0), matrix)) {
GINAC_ASSERT(other.nops() == 2 || other.nops() == 3);
- const matrix &self_matrix = ex_to_matrix(self.op(0));
- const matrix &other_matrix = ex_to_matrix(other.op(0));
+ const matrix &self_matrix = ex_to<matrix>(self.op(0));
+ const matrix &other_matrix = ex_to<matrix>(other.op(0));
if (self.nops() == 2 && other.nops() == 2) { // vector + vector
GINAC_ASSERT(is_ex_of_type(self.op(0), matrix));
GINAC_ASSERT(self.nops() == 2 || self.nops() == 3);
- const matrix &self_matrix = ex_to_matrix(self.op(0));
+ const matrix &self_matrix = ex_to<matrix>(self.op(0));
if (self.nops() == 2)
return indexed(self_matrix.mul(other), self.op(1));
GINAC_ASSERT(other->nops() == 2 || other->nops() == 3);
- const matrix &self_matrix = ex_to_matrix(self->op(0));
- const matrix &other_matrix = ex_to_matrix(other->op(0));
+ const matrix &self_matrix = ex_to<matrix>(self->op(0));
+ const matrix &other_matrix = ex_to<matrix>(other->op(0));
if (self->nops() == 2) {
- unsigned self_dim = (self_matrix.col == 1) ? self_matrix.row : self_matrix.col;
if (other->nops() == 2) { // vector * vector (scalar product)
- unsigned other_dim = (other_matrix.col == 1) ? other_matrix.row : other_matrix.col;
if (self_matrix.col == 1) {
if (other_matrix.col == 1) {
matrix matrix::add(const matrix & other) const
{
if (col != other.col || row != other.row)
- throw (std::logic_error("matrix::add(): incompatible matrices"));
+ throw std::logic_error("matrix::add(): incompatible matrices");
exvector sum(this->m);
- exvector::iterator i;
- exvector::const_iterator ci;
- for (i=sum.begin(), ci=other.m.begin(); i!=sum.end(); ++i, ++ci)
- (*i) += (*ci);
+ exvector::iterator i = sum.begin(), end = sum.end();
+ exvector::const_iterator ci = other.m.begin();
+ while (i != end)
+ *i++ += *ci++;
return matrix(row,col,sum);
}
matrix matrix::sub(const matrix & other) const
{
if (col != other.col || row != other.row)
- throw (std::logic_error("matrix::sub(): incompatible matrices"));
+ throw std::logic_error("matrix::sub(): incompatible matrices");
exvector dif(this->m);
- exvector::iterator i;
- exvector::const_iterator ci;
- for (i=dif.begin(), ci=other.m.begin(); i!=dif.end(); ++i, ++ci)
- (*i) -= (*ci);
+ exvector::iterator i = dif.begin(), end = dif.end();
+ exvector::const_iterator ci = other.m.begin();
+ while (i != end)
+ *i++ -= *ci++;
return matrix(row,col,dif);
}
matrix matrix::mul(const matrix & other) const
{
if (this->cols() != other.rows())
- throw (std::logic_error("matrix::mul(): incompatible matrices"));
+ throw std::logic_error("matrix::mul(): incompatible matrices");
exvector prod(this->rows()*other.cols());
}
-/** operator() to access elements.
+/** Product of matrix and scalar expression. */
+matrix matrix::mul_scalar(const ex & other) const
+{
+ if (other.return_type() != return_types::commutative)
+ throw std::runtime_error("matrix::mul_scalar(): non-commutative scalar");
+
+ exvector prod(row * col);
+
+ for (unsigned r=0; r<row; ++r)
+ for (unsigned c=0; c<col; ++c)
+ prod[r*col+c] = m[r*col+c] * other;
+
+ return matrix(row, col, prod);
+}
+
+
+/** Power of a matrix. Currently handles integer exponents only. */
+matrix matrix::pow(const ex & expn) const
+{
+ if (col!=row)
+ throw (std::logic_error("matrix::pow(): matrix not square"));
+
+ if (is_ex_exactly_of_type(expn, numeric)) {
+ // Integer cases are computed by successive multiplication, using the
+ // obvious shortcut of storing temporaries, like A^4 == (A*A)*(A*A).
+ if (expn.info(info_flags::integer)) {
+ numeric b = ex_to<numeric>(expn);
+ matrix A(row,col);
+ if (expn.info(info_flags::negative)) {
+ b *= -1;
+ A = this->inverse();
+ } else {
+ A = *this;
+ }
+ matrix C(row,col);
+ for (unsigned r=0; r<row; ++r)
+ C(r,r) = _ex1();
+ // This loop computes the representation of b in base 2 from right
+ // to left and multiplies the factors whenever needed. Note
+ // that this is not entirely optimal but close to optimal and
+ // "better" algorithms are much harder to implement. (See Knuth,
+ // TAoCP2, section "Evaluation of Powers" for a good discussion.)
+ while (b!=1) {
+ if (b.is_odd()) {
+ C = C.mul(A);
+ b -= 1;
+ }
+ b *= _num1_2(); // b /= 2, still integer.
+ A = A.mul(A);
+ }
+ return A.mul(C);
+ }
+ }
+ throw (std::runtime_error("matrix::pow(): don't know how to handle exponent"));
+}
+
+
+/** operator() to access elements for reading.
*
* @param ro row of element
* @param co column of element
}
-/** Set individual elements manually.
+/** operator() to access elements for writing.
*
+ * @param ro row of element
+ * @param co column of element
* @exception range_error (index out of range) */
-matrix & matrix::set(unsigned ro, unsigned co, ex value)
+ex & matrix::operator() (unsigned ro, unsigned co)
{
if (ro>=row || co>=col)
- throw (std::range_error("matrix::set(): index out of range"));
-
+ throw (std::range_error("matrix::operator(): index out of range"));
+
ensure_if_modifiable();
- m[ro*col+co] = value;
- return *this;
+ return m[ro*col+co];
}
return matrix(this->cols(),this->rows(),trans);
}
-
/** Determinant of square matrix. This routine doesn't actually calculate the
* determinant, it only implements some heuristics about which algorithm to
* run. If all the elements of the matrix are elements of an integral domain
bool numeric_flag = true;
bool normal_flag = false;
unsigned sparse_count = 0; // counts non-zero elements
- for (exvector::const_iterator r=m.begin(); r!=m.end(); ++r) {
+ exvector::const_iterator r = m.begin(), rend = m.end();
+ while (r != rend) {
lst srl; // symbol replacement list
- ex rtest = (*r).to_rational(srl);
+ ex rtest = r->to_rational(srl);
if (!rtest.is_zero())
++sparse_count;
if (!rtest.info(info_flags::numeric))
if (!rtest.info(info_flags::crational_polynomial) &&
rtest.info(info_flags::rational_function))
normal_flag = true;
+ ++r;
}
// Here is the heuristics in case this routine has to decide:
}
sort(c_zeros.begin(),c_zeros.end());
std::vector<unsigned> pre_sort;
- for (std::vector<uintpair>::iterator i=c_zeros.begin(); i!=c_zeros.end(); ++i)
+ for (std::vector<uintpair>::const_iterator i=c_zeros.begin(); i!=c_zeros.end(); ++i)
pre_sort.push_back(i->second);
- int sign = permutation_sign(pre_sort);
+ std::vector<unsigned> pre_sort_test(pre_sort); // permutation_sign() modifies the vector so we make a copy here
+ int sign = permutation_sign(pre_sort_test.begin(), pre_sort_test.end());
exvector result(row*col); // represents sorted matrix
unsigned c = 0;
- for (std::vector<unsigned>::iterator i=pre_sort.begin();
+ for (std::vector<unsigned>::const_iterator i=pre_sort.begin();
i!=pre_sort.end();
++i,++c) {
for (unsigned r=0; r<row; ++r)
throw (std::logic_error("matrix::charpoly(): matrix not square"));
bool numeric_flag = true;
- for (exvector::const_iterator r=m.begin(); r!=m.end(); ++r) {
- if (!(*r).info(info_flags::numeric)) {
+ exvector::const_iterator r = m.begin(), rend = m.end();
+ while (r != rend) {
+ if (!r->info(info_flags::numeric))
numeric_flag = false;
- }
+ ++r;
}
// The pure numeric case is traditionally rather common. Hence, it is
// First populate the identity matrix supposed to become the right hand side.
matrix identity(row,col);
for (unsigned i=0; i<row; ++i)
- identity.set(i,i,_ex1());
+ identity(i,i) = _ex1();
// Populate a dummy matrix of variables, just because of compatibility with
// matrix::solve() which wants this (for compatibility with under-determined
matrix vars(row,col);
for (unsigned r=0; r<row; ++r)
for (unsigned c=0; c<col; ++c)
- vars.set(r,c,symbol());
+ vars(r,c) = symbol();
matrix sol(row,col);
try {
// Gather some statistical information about the augmented matrix:
bool numeric_flag = true;
- for (exvector::const_iterator r=aug.m.begin(); r!=aug.m.end(); ++r) {
- if (!(*r).info(info_flags::numeric))
+ exvector::const_iterator r = aug.m.begin(), rend = aug.m.end();
+ while (r != rend) {
+ if (!r->info(info_flags::numeric))
numeric_flag = false;
+ ++r;
}
// Here is the heuristics in case this routine has to decide:
// assign solutions for vars between fnz+1 and
// last_assigned_sol-1: free parameters
for (unsigned c=fnz; c<last_assigned_sol-1; ++c)
- sol.set(c,co,vars.m[c*p+co]);
+ sol(c,co) = vars.m[c*p+co];
ex e = aug.m[r*(n+p)+n+co];
for (unsigned c=fnz; c<n; ++c)
e -= aug.m[r*(n+p)+c]*sol.m[c*p+co];
- sol.set(fnz-1,co,
- (e/(aug.m[r*(n+p)+(fnz-1)])).normal());
+ sol(fnz-1,co) = (e/(aug.m[r*(n+p)+(fnz-1)])).normal();
last_assigned_sol = fnz;
}
}
// assign solutions for vars between 1 and
// last_assigned_sol-1: free parameters
for (unsigned ro=0; ro<last_assigned_sol-1; ++ro)
- sol.set(ro,co,vars(ro,co));
+ sol(ro,co) = vars(ro,co);
}
return sol;
// for (unsigned r=0; r<minorM.rows(); ++r) {
// for (unsigned c=0; c<minorM.cols(); ++c) {
// if (r<r1)
- // minorM.set(r,c,m[r*col+c+1]);
+ // minorM(r,c) = m[r*col+c+1];
// else
- // minorM.set(r,c,m[(r+1)*col+c+1]);
+ // minorM(r,c) = m[(r+1)*col+c+1];
// }
// }
// // recurse down and care for sign:
matrix tmp_n(*this);
matrix tmp_d(m,n); // for denominators, if needed
lst srl; // symbol replacement list
- exvector::iterator it = this->m.begin();
- exvector::iterator tmp_n_it = tmp_n.m.begin();
- exvector::iterator tmp_d_it = tmp_d.m.begin();
- for (; it!= this->m.end(); ++it, ++tmp_n_it, ++tmp_d_it) {
- (*tmp_n_it) = (*it).normal().to_rational(srl);
- (*tmp_d_it) = (*tmp_n_it).denom();
- (*tmp_n_it) = (*tmp_n_it).numer();
+ exvector::const_iterator cit = this->m.begin(), citend = this->m.end();
+ exvector::iterator tmp_n_it = tmp_n.m.begin(), tmp_d_it = tmp_d.m.begin();
+ while (cit != citend) {
+ ex nd = cit->normal().to_rational(srl).numer_denom();
+ ++cit;
+ *tmp_n_it++ = nd.op(0);
+ *tmp_d_it++ = nd.op(1);
}
unsigned r0 = 0;
}
}
// repopulate *this matrix:
- it = this->m.begin();
+ exvector::iterator it = this->m.begin(), itend = this->m.end();
tmp_n_it = tmp_n.m.begin();
tmp_d_it = tmp_d.m.begin();
- for (; it!= this->m.end(); ++it, ++tmp_n_it, ++tmp_d_it)
- (*it) = ((*tmp_n_it)/(*tmp_d_it)).subs(srl);
+ while (it != itend)
+ *it++ = ((*tmp_n_it++)/(*tmp_d_it++)).subs(srl);
return sign;
}
// search largest element in column co beginning at row ro
GINAC_ASSERT(is_ex_of_type(this->m[k*col+co],numeric));
unsigned kmax = k+1;
- numeric mmax = abs(ex_to_numeric(m[kmax*col+co]));
+ numeric mmax = abs(ex_to<numeric>(m[kmax*col+co]));
while (kmax<row) {
GINAC_ASSERT(is_ex_of_type(this->m[kmax*col+co],numeric));
- numeric tmp = ex_to_numeric(this->m[kmax*col+co]);
+ numeric tmp = ex_to<numeric>(this->m[kmax*col+co]);
if (abs(tmp) > mmax) {
mmax = tmp;
k = kmax;
for (i=0; i<rows; i++)
for (j=0; j<cols; j++)
if (l.op(i).nops() > j)
- m.set(i, j, l.op(i).op(j));
+ m(i, j) = l.op(i).op(j);
else
- m.set(i, j, ex(0));
+ m(i, j) = _ex0();
return m;
}
matrix &m = *new matrix(dim, dim);
m.setflag(status_flags::dynallocated);
for (unsigned i=0; i<dim; i++)
- m.set(i, i, l.op(i));
+ m(i, i) = l.op(i);
return m;
}
git://www.ginac.de / ginac.git / blobdiff