X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fmatrix.cpp;h=65b1254936e0a378eb5ba1760ee9709a3a52c409;hp=0b87ed5d3ba843511e144bc3c316bd99dd0a4d50;hb=df5f8db62815995d87ebd4f97a5dbc0d1a327b94;hpb=e5362a33f72613b324b3714524a8c2e5f7b7f46f

diff --git a/ginac/matrix.cpp b/ginac/matrix.cpp
index 0b87ed5d..65b12549 100644
--- a/ginac/matrix.cpp
+++ b/ginac/matrix.cpp
@@ -25,37 +25,33 @@
 #include <stdexcept>
 
 #include "matrix.h"
-#include "archive.h"
 #include "numeric.h"
 #include "lst.h"
-#include "utils.h"
-#include "debugmsg.h"
+#include "idx.h"
+#include "indexed.h"
 #include "power.h"
 #include "symbol.h"
 #include "normal.h"
+#include "print.h"
+#include "archive.h"
+#include "utils.h"
+#include "debugmsg.h"
 
-#ifndef NO_NAMESPACE_GINAC
 namespace GiNaC {
-#endif // ndef NO_NAMESPACE_GINAC
 
 GINAC_IMPLEMENT_REGISTERED_CLASS(matrix, basic)
 
 //////////
-// default constructor, destructor, copy constructor, assignment operator
-// and helpers:
+// default ctor, dtor, copy ctor, assignment operator and helpers:
 //////////
 
-// public
-
 /** Default ctor.  Initializes to 1 x 1-dimensional zero-matrix. */
 matrix::matrix() : inherited(TINFO_matrix), row(1), col(1)
 {
-	debugmsg("matrix default constructor",LOGLEVEL_CONSTRUCT);
+	debugmsg("matrix default ctor",LOGLEVEL_CONSTRUCT);
 	m.push_back(_ex0());
 }
 
-// protected
-
 void matrix::copy(const matrix & other)
 {
 	inherited::copy(other);
@@ -64,13 +60,10 @@ void matrix::copy(const matrix & other)
 	m = other.m;  // STL's vector copying invoked here
 }
 
-void matrix::destroy(bool call_parent)
-{
-	if (call_parent) inherited::destroy(call_parent);
-}
+DEFAULT_DESTROY(matrix)
 
 //////////
-// other constructors
+// other ctors
 //////////
 
 // public
@@ -82,7 +75,7 @@ void matrix::destroy(bool call_parent)
 matrix::matrix(unsigned r, unsigned c)
   : inherited(TINFO_matrix), row(r), col(c)
 {
-	debugmsg("matrix constructor from unsigned,unsigned",LOGLEVEL_CONSTRUCT);
+	debugmsg("matrix ctor from unsigned,unsigned",LOGLEVEL_CONSTRUCT);
 	m.resize(r*c, _ex0());
 }
 
@@ -92,17 +85,35 @@ matrix::matrix(unsigned r, unsigned c)
 matrix::matrix(unsigned r, unsigned c, const exvector & m2)
   : inherited(TINFO_matrix), row(r), col(c), m(m2)
 {
-	debugmsg("matrix constructor from unsigned,unsigned,exvector",LOGLEVEL_CONSTRUCT);
+	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
 //////////
 
-/** Construct object from archive_node. */
 matrix::matrix(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 {
-	debugmsg("matrix constructor from archive_node", LOGLEVEL_CONSTRUCT);
+	debugmsg("matrix ctor from archive_node", LOGLEVEL_CONSTRUCT);
 	if (!(n.find_unsigned("row", row)) || !(n.find_unsigned("col", col)))
 		throw (std::runtime_error("unknown matrix dimensions in archive"));
 	m.reserve(row * col);
@@ -115,13 +126,6 @@ matrix::matrix(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst
 	}
 }
 
-/** Unarchive the object. */
-ex matrix::unarchive(const archive_node &n, const lst &sym_lst)
-{
-	return (new matrix(n, sym_lst))->setflag(status_flags::dynallocated);
-}
-
-/** Archive the object. */
 void matrix::archive(archive_node &n) const
 {
 	inherited::archive(n);
@@ -134,48 +138,43 @@ void matrix::archive(archive_node &n) const
 	}
 }
 
+DEFAULT_UNARCHIVE(matrix)
+
 //////////
 // functions overriding virtual functions from bases classes
 //////////
 
 // public
 
-basic * matrix::duplicate() const
+void matrix::print(const print_context & c, unsigned level) const
 {
-	debugmsg("matrix duplicate",LOGLEVEL_DUPLICATE);
-	return new matrix(*this);
-}
+	debugmsg("matrix print", LOGLEVEL_PRINT);
 
-void matrix::print(std::ostream & os, unsigned upper_precedence) const
-{
-	debugmsg("matrix print",LOGLEVEL_PRINT);
-	os << "[[ ";
-	for (unsigned r=0; r<row-1; ++r) {
-		os << "[[";
-		for (unsigned c=0; c<col-1; ++c)
-			os << m[r*col+c] << ",";
-		os << m[col*(r+1)-1] << "]], ";
-	}
-	os << "[[";
-	for (unsigned c=0; c<col-1; ++c)
-		os << m[(row-1)*col+c] << ",";
-	os << m[row*col-1] << "]] ]]";
-}
+	if (is_of_type(c, print_tree)) {
+
+		inherited::print(c, level);
+
+	} else {
+
+		c.s << "[[ ";
+		for (unsigned y=0; y<row-1; ++y) {
+			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 << "[[";
+		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 << "]] ]]";
 
-void matrix::printraw(std::ostream & os) const
-{
-	debugmsg("matrix printraw",LOGLEVEL_PRINT);
-	os << "matrix(" << row << "," << col <<",";
-	for (unsigned r=0; r<row-1; ++r) {
-		os << "(";
-		for (unsigned c=0; c<col-1; ++c)
-			os << m[r*col+c] << ",";
-		os << m[col*(r-1)-1] << "),";
 	}
-	os << "(";
-	for (unsigned c=0; c<col-1; ++c)
-		os << m[(row-1)*col+c] << ",";
-	os << m[row*col-1] << "))";
 }
 
 /** nops is defined to be rows x columns. */
@@ -209,23 +208,7 @@ ex matrix::expand(unsigned options) const
 	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. */
+/** Evaluate matrix entry by entry. */
 ex matrix::eval(int level) const
 {
 	debugmsg("matrix eval",LOGLEVEL_MEMBER_FUNCTION);
@@ -249,7 +232,7 @@ ex matrix::eval(int level) const
 											   status_flags::evaluated );
 }
 
-/** evaluate matrix numerically entry by entry. */
+/** Evaluate matrix numerically entry by entry. */
 ex matrix::evalf(int level) const
 {
 	debugmsg("matrix evalf",LOGLEVEL_MEMBER_FUNCTION);
@@ -273,6 +256,16 @@ ex matrix::evalf(int level) const
 	return matrix(row, col, m2);
 }
 
+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, no_pattern);
+
+	return ex(matrix(row, col, m2)).bp->basic::subs(ls, lr, no_pattern);
+}
+
 // protected
 
 int matrix::compare_same_type(const basic & other) const
@@ -300,6 +293,235 @@ int matrix::compare_same_type(const basic & other) const
 	return 0;
 }
 
+/** Automatic symbolic evaluation of an indexed matrix. */
+ex matrix::eval_indexed(const basic & i) const
+{
+	GINAC_ASSERT(is_of_type(i, indexed));
+	GINAC_ASSERT(is_ex_of_type(i.op(0), matrix));
+
+	bool all_indices_unsigned = static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint);
+
+	// Check indices
+	if (i.nops() == 2) {
+
+		// One index, must be one-dimensional vector
+		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));
+
+		if (col == 1) {
+
+			// Column vector
+			if (!i1.get_dim().is_equal(row))
+				throw (std::runtime_error("matrix::eval_indexed(): dimension of index must match number of vector elements"));
+
+			// Index numeric -> return vector element
+			if (all_indices_unsigned) {
+				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);
+			}
+
+		} else {
+
+			// Row vector
+			if (!i1.get_dim().is_equal(col))
+				throw (std::runtime_error("matrix::eval_indexed(): dimension of index must match number of vector elements"));
+
+			// Index numeric -> return vector element
+			if (all_indices_unsigned) {
+				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));
+
+		if (!i1.get_dim().is_equal(row))
+			throw (std::runtime_error("matrix::eval_indexed(): dimension of first index must match number of rows"));
+		if (!i2.get_dim().is_equal(col))
+			throw (std::runtime_error("matrix::eval_indexed(): dimension of second index must match number of columns"));
+
+		// Pair of dummy indices -> compute trace
+		if (is_dummy_pair(i1, i2))
+			return trace();
+
+		// 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();
+			if (n1 >= row)
+				throw (std::runtime_error("matrix::eval_indexed(): value of first index exceeds number of rows"));
+			if (n2 >= col)
+				throw (std::runtime_error("matrix::eval_indexed(): value of second index exceeds number of columns"));
+			return (*this)(n1, n2);
+		}
+
+	} else
+		throw (std::runtime_error("matrix::eval_indexed(): matrix must have exactly 2 indices"));
+
+	return i.hold();
+}
+
+/** 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))
+		return false;
+
+	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) {
+		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) {
+					// Column vector * column vector, transpose first vector
+					*self = self_matrix.transpose().mul(other_matrix)(0, 0);
+				} else {
+					// Column vector * row vector, swap factors
+					*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);
+				} else {
+					// Row vector * row vector, transpose second vector
+					*self = self_matrix.mul(other_matrix.transpose())(0, 0);
+				}
+			}
+			*other = _ex1();
+			return true;
+
+		} else { // vector * matrix
+
+			// B_i * A_ij = (B*A)_j (B is row vector)
+			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));
+				else
+					*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 (self_matrix.col == 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();
+				return true;
+			}
+		}
+
+	} 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();
+			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();
+			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();
+			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();
+			return true;
+		}
+	}
+
+	return false;
+}
+
+
 //////////
 // non-virtual functions in this class
 //////////
@@ -364,6 +586,19 @@ matrix matrix::mul(const matrix & other) const
 }
 
 
+/** 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
@@ -624,50 +859,32 @@ matrix matrix::inverse(void) const
 	if (row != col)
 		throw (std::logic_error("matrix::inverse(): matrix not square"));
 	
-	// NOTE: the Gauss-Jordan elimination used here can in principle be
-	// replaced by two clever calls to gauss_elimination() and some to
-	// transpose().  Wouldn't be more efficient (maybe less?), just more
-	// orthogonal.
-	matrix tmp(row,col);
-	// set tmp to the unit matrix
-	for (unsigned i=0; i<col; ++i)
-		tmp.m[i*col+i] = _ex1();
+	// This routine actually doesn't do anything fancy at all.  We compute the
+	// inverse of the matrix A by solving the system A * A^{-1} == Id.
 	
-	// create a copy of this matrix
-	matrix cpy(*this);
-	for (unsigned r1=0; r1<row; ++r1) {
-		int indx = cpy.pivot(r1, r1);
-		if (indx == -1) {
+	// 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());
+	
+	// Populate a dummy matrix of variables, just because of compatibility with
+	// matrix::solve() which wants this (for compatibility with under-determined
+	// systems of equations).
+	matrix vars(row,col);
+	for (unsigned r=0; r<row; ++r)
+		for (unsigned c=0; c<col; ++c)
+			vars.set(r,c,symbol());
+	
+	matrix sol(row,col);
+	try {
+		sol = this->solve(vars,identity);
+	} catch (const std::runtime_error & e) {
+	    if (e.what()==std::string("matrix::solve(): inconsistent linear system"))
 			throw (std::runtime_error("matrix::inverse(): singular matrix"));
-		}
-		if (indx != 0) {  // swap rows r and indx of matrix tmp
-			for (unsigned i=0; i<col; ++i)
-				tmp.m[r1*col+i].swap(tmp.m[indx*col+i]);
-		}
-		ex a1 = cpy.m[r1*col+r1];
-		for (unsigned c=0; c<col; ++c) {
-			cpy.m[r1*col+c] /= a1;
-			tmp.m[r1*col+c] /= a1;
-		}
-		for (unsigned r2=0; r2<row; ++r2) {
-			if (r2 != r1) {
-				if (!cpy.m[r2*col+r1].is_zero()) {
-					ex a2 = cpy.m[r2*col+r1];
-					// yes, there is something to do in this column
-					for (unsigned c=0; c<col; ++c) {
-						cpy.m[r2*col+c] -= a2 * cpy.m[r1*col+c];
-						if (!cpy.m[r2*col+c].info(info_flags::numeric))
-							cpy.m[r2*col+c] = cpy.m[r2*col+c].normal();
-						tmp.m[r2*col+c] -= a2 * tmp.m[r1*col+c];
-						if (!tmp.m[r2*col+c].info(info_flags::numeric))
-							tmp.m[r2*col+c] = tmp.m[r2*col+c].normal();
-					}
-				}
-			}
-		}
+		else
+			throw;
 	}
-	
-	return tmp;
+	return sol;
 }
 
 
@@ -730,8 +947,10 @@ matrix matrix::solve(const matrix & vars,
 	switch(algo) {
 		case solve_algo::gauss:
 			aug.gauss_elimination();
+			break;
 		case solve_algo::divfree:
 			aug.division_free_elimination();
+			break;
 		case solve_algo::bareiss:
 		default:
 			aug.fraction_free_elimination();
@@ -1175,20 +1394,17 @@ int matrix::pivot(unsigned ro, unsigned co, bool symbolic)
 	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++)
 		if (l.op(i).nops() > cols)
 			cols = l.op(i).nops();
-	
+
 	// Allocate and fill matrix
 	matrix &m = *new matrix(rows, cols);
+	m.setflag(status_flags::dynallocated);
 	for (i=0; i<rows; i++)
 		for (j=0; j<cols; j++)
 			if (l.op(i).nops() > j)
@@ -1198,6 +1414,16 @@ ex lst_to_matrix(const ex &l)
 	return m;
 }
 
-#ifndef NO_NAMESPACE_GINAC
+ex diag_matrix(const lst & l)
+{
+	unsigned dim = l.nops();
+
+	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));
+
+	return m;
+}
+
 } // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC