debugmsg("matrix ctor from unsigned,unsigned,exvector",LOGLEVEL_CONSTRUCT);
}
+/** Construct matrix from (flat) list of elements. If the list has fewer
+ * elements than the matrix, the remaining matrix elements are set to zero.
+ * If the list has more elements than the matrix, the excessive elements are
+ * thrown away. */
+matrix::matrix(unsigned r, unsigned c, const lst & l)
+ : inherited(TINFO_matrix), row(r), col(c)
+{
+ debugmsg("matrix ctor from unsigned,unsigned,lst",LOGLEVEL_CONSTRUCT);
+ m.resize(r*c, _ex0());
+
+ for (unsigned i=0; i<l.nops(); i++) {
+ unsigned x = i % c;
+ unsigned y = i / c;
+ if (y >= r)
+ break; // matrix smaller than list: throw away excessive elements
+ m[y*c+x] = l.op(i);
+ }
+}
+
//////////
// archiving
//////////
return i.hold();
}
-/** Contraction of an indexed matrix with something else. */
-bool matrix::contract_with(ex & self, ex & other) const
+/** Sum of two indexed matrices. */
+ex matrix::add_indexed(const ex & self, const ex & other) const
{
GINAC_ASSERT(is_ex_of_type(self, indexed));
+ GINAC_ASSERT(is_ex_of_type(self.op(0), matrix));
GINAC_ASSERT(is_ex_of_type(other, indexed));
GINAC_ASSERT(self.nops() == 2 || self.nops() == 3);
+
+ // Only add two matrices
+ 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));
+
+ if (self.nops() == 2 && other.nops() == 2) { // vector + vector
+
+ if (self_matrix.row == other_matrix.row)
+ return indexed(self_matrix.add(other_matrix), self.op(1));
+ else if (self_matrix.row == other_matrix.col)
+ return indexed(self_matrix.add(other_matrix.transpose()), self.op(1));
+
+ } else if (self.nops() == 3 && other.nops() == 3) { // matrix + matrix
+
+ if (self.op(1).is_equal(other.op(1)) && self.op(2).is_equal(other.op(2)))
+ return indexed(self_matrix.add(other_matrix), self.op(1), self.op(2));
+ else if (self.op(1).is_equal(other.op(2)) && self.op(2).is_equal(other.op(1)))
+ return indexed(self_matrix.add(other_matrix.transpose()), self.op(1), self.op(2));
+
+ }
+ }
+
+ // Don't know what to do, return unevaluated sum
+ return self + other;
+}
+
+/** Product of an indexed matrix with a number. */
+ex matrix::scalar_mul_indexed(const ex & self, const numeric & other) const
+{
+ GINAC_ASSERT(is_ex_of_type(self, indexed));
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));
+
+ if (self.nops() == 2)
+ return indexed(self_matrix.mul(other), self.op(1));
+ else // self.nops() == 3
+ return indexed(self_matrix.mul(other), self.op(1), self.op(2));
+}
+
+/** Contraction of an indexed matrix with something else. */
+bool matrix::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
+{
+ GINAC_ASSERT(is_ex_of_type(*self, indexed));
+ GINAC_ASSERT(is_ex_of_type(*other, indexed));
+ GINAC_ASSERT(self->nops() == 2 || self->nops() == 3);
+ GINAC_ASSERT(is_ex_of_type(self->op(0), matrix));
// Only contract with other matrices
- if (!is_ex_of_type(other.op(0), matrix))
+ if (!is_ex_of_type(other->op(0), matrix))
return false;
- GINAC_ASSERT(other.nops() == 2 || other.nops() == 3);
+ 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) {
+ 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)
+ 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) {
// Column vector * column vector, transpose first vector
- self = self_matrix.transpose().mul(other_matrix)(0, 0);
+ *self = self_matrix.transpose().mul(other_matrix)(0, 0);
} else {
// Column vector * row vector, swap factors
- self = other_matrix.mul(self_matrix)(0, 0);
+ *self = other_matrix.mul(self_matrix)(0, 0);
}
} else {
if (other_matrix.col == 1) {
// Row vector * column vector, perfect
- self = self_matrix.mul(other_matrix)(0, 0);
+ *self = self_matrix.mul(other_matrix)(0, 0);
} else {
// Row vector * row vector, transpose second vector
- self = self_matrix.mul(other_matrix.transpose())(0, 0);
+ *self = self_matrix.mul(other_matrix.transpose())(0, 0);
}
}
- other = _ex1();
+ *other = _ex1();
return true;
} else { // vector * matrix
- GINAC_ASSERT(other.nops() == 3);
-
// B_i * A_ij = (B*A)_j (B is row vector)
- if (is_dummy_pair(self.op(1), other.op(1))) {
+ if (is_dummy_pair(self->op(1), other->op(1))) {
if (self_matrix.row == 1)
- self = indexed(self_matrix.mul(other_matrix), other.op(2));
+ *self = indexed(self_matrix.mul(other_matrix), other->op(2));
else
- self = indexed(self_matrix.transpose().mul(other_matrix), other.op(2));
- other = _ex1();
+ *self = indexed(self_matrix.transpose().mul(other_matrix), other->op(2));
+ *other = _ex1();
return true;
}
// B_j * A_ij = (A*B)_i (B is column vector)
- if (is_dummy_pair(self.op(1), other.op(2))) {
+ if (is_dummy_pair(self->op(1), other->op(2))) {
if (self_matrix.col == 1)
- self = indexed(other_matrix.mul(self_matrix), other.op(1));
+ *self = indexed(other_matrix.mul(self_matrix), other->op(1));
else
- self = indexed(other_matrix.mul(self_matrix.transpose()), other.op(1));
- other = _ex1();
+ *self = indexed(other_matrix.mul(self_matrix.transpose()), other->op(1));
+ *other = _ex1();
return true;
}
}
- } else if (other.nops() == 3) { // matrix * matrix
-
- GINAC_ASSERT(self.nops() == 3);
- GINAC_ASSERT(other.nops() == 3);
+ } else if (other->nops() == 3) { // matrix * matrix
// A_ij * B_jk = (A*B)_ik
- if (is_dummy_pair(self.op(2), other.op(1))) {
- self = indexed(self_matrix.mul(other_matrix), self.op(1), other.op(2));
- other = _ex1();
+ if (is_dummy_pair(self->op(2), other->op(1))) {
+ *self = indexed(self_matrix.mul(other_matrix), self->op(1), other->op(2));
+ *other = _ex1();
return true;
}
// A_ij * B_kj = (A*Btrans)_ik
- if (is_dummy_pair(self.op(2), other.op(2))) {
- self = indexed(self_matrix.mul(other_matrix.transpose()), self.op(1), other.op(1));
- other = _ex1();
+ if (is_dummy_pair(self->op(2), other->op(2))) {
+ *self = indexed(self_matrix.mul(other_matrix.transpose()), self->op(1), other->op(1));
+ *other = _ex1();
return true;
}
// A_ji * B_jk = (Atrans*B)_ik
- if (is_dummy_pair(self.op(1), other.op(1))) {
- self = indexed(self_matrix.transpose().mul(other_matrix), self.op(2), other.op(2));
- other = _ex1();
+ if (is_dummy_pair(self->op(1), other->op(1))) {
+ *self = indexed(self_matrix.transpose().mul(other_matrix), self->op(2), other->op(2));
+ *other = _ex1();
return true;
}
// A_ji * B_kj = (B*A)_ki
- if (is_dummy_pair(self.op(1), other.op(2))) {
- self = indexed(other_matrix.mul(self_matrix), other.op(1), self.op(2));
- other = _ex1();
+ if (is_dummy_pair(self->op(1), other->op(2))) {
+ *self = indexed(other_matrix.mul(self_matrix), other->op(1), self->op(2));
+ *other = _ex1();
return true;
}
}
}
+/** Product of matrix and scalar. */
+matrix matrix::mul(const numeric & other) const
+{
+ 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);
+}
+
+
/** operator() to access elements.
*
* @param ro row of element
return k;
}
-/** Convert list of lists to matrix. */
-ex lst_to_matrix(const ex &l)
+ex lst_to_matrix(const lst & l)
{
- if (!is_ex_of_type(l, lst))
- throw(std::invalid_argument("argument to lst_to_matrix() must be a lst"));
-
// Find number of rows and columns
unsigned rows = l.nops(), cols = 0, i, j;
for (i=0; i<rows; i++)
return m;
}
+ex diag_matrix(const lst & l)
+{
+ unsigned dim = l.nops();
+
+ matrix &m = *new matrix(dim, dim);
+ for (unsigned i=0; i<dim; i++)
+ m.set(i, i, l.op(i));
+
+ return m;
+}
+
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff