X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fmatrix.cpp;h=8daa11db0fab78332effeec157ed16fb17b4294f;hp=e9c68175897daa5222ee8b0750fcc85333cb05cd;hb=7e7beee2c946694130a484c923f6af8391867495;hpb=2862087ce55d944c1ac5d37283944b2b37507fd2

diff --git a/ginac/matrix.cpp b/ginac/matrix.cpp
index e9c68175..8daa11db 100644
--- a/ginac/matrix.cpp
+++ b/ginac/matrix.cpp
@@ -3,7 +3,7 @@
  *  Implementation of symbolic matrices */
 
 /*
- *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2002 Johannes Gutenberg University Mainz, Germany
  *
  *  This program is free software; you can redistribute it and/or modify
  *  it under the terms of the GNU General Public License as published by
@@ -20,6 +20,7 @@
  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  */
 
+#include <iostream>
 #include <algorithm>
 #include <map>
 #include <stdexcept>
@@ -35,7 +36,6 @@
 #include "print.h"
 #include "archive.h"
 #include "utils.h"
-#include "debugmsg.h"
 
 namespace GiNaC {
 
@@ -48,8 +48,7 @@ GINAC_IMPLEMENT_REGISTERED_CLASS(matrix, basic)
 /** Default ctor.  Initializes to 1 x 1-dimensional zero-matrix. */
 matrix::matrix() : inherited(TINFO_matrix), row(1), col(1)
 {
-	debugmsg("matrix default ctor",LOGLEVEL_CONSTRUCT);
-	m.push_back(_ex0());
+	m.push_back(_ex0);
 }
 
 void matrix::copy(const matrix & other)
@@ -75,18 +74,14 @@ DEFAULT_DESTROY(matrix)
 matrix::matrix(unsigned r, unsigned c)
   : inherited(TINFO_matrix), row(r), col(c)
 {
-	debugmsg("matrix ctor from unsigned,unsigned",LOGLEVEL_CONSTRUCT);
-	m.resize(r*c, _ex0());
+	m.resize(r*c, _ex0);
 }
 
 // protected
 
 /** Ctor from representation, for internal use only. */
 matrix::matrix(unsigned r, unsigned c, const exvector & m2)
-  : inherited(TINFO_matrix), row(r), col(c), m(m2)
-{
-	debugmsg("matrix ctor from unsigned,unsigned,exvector",LOGLEVEL_CONSTRUCT);
-}
+  : inherited(TINFO_matrix), row(r), col(c), m(m2) {}
 
 /** Construct matrix from (flat) list of elements. If the list has fewer
  *  elements than the matrix, the remaining matrix elements are set to zero.
@@ -95,8 +90,7 @@ matrix::matrix(unsigned r, unsigned c, const exvector & m2)
 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());
+	m.resize(r*c, _ex0);
 
 	for (unsigned i=0; i<l.nops(); i++) {
 		unsigned x = i % c;
@@ -113,7 +107,6 @@ matrix::matrix(unsigned r, unsigned c, const lst & l)
 
 matrix::matrix(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 {
-	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);
@@ -148,31 +141,50 @@ DEFAULT_UNARCHIVE(matrix)
 
 void matrix::print(const print_context & c, unsigned level) const
 {
-	debugmsg("matrix print", LOGLEVEL_PRINT);
-
-	if (is_of_type(c, print_tree)) {
+	if (is_a<print_tree>(c)) {
 
 		inherited::print(c, level);
 
 	} else {
 
-		c.s << "[";
-		for (unsigned y=0; y<row-1; ++y) {
+		if (is_a<print_python_repr>(c))
+			c.s << class_name() << '(';
+
+		if (is_a<print_latex>(c))
+			c.s << "\\left(\\begin{array}{" << std::string(col,'c') << "}";
+		else
 			c.s << "[";
-			for (unsigned x=0; x<col-1; ++x) {
-				m[y*col+x].print(c);
-				c.s << ",";
+
+		for (unsigned ro=0; ro<row; ++ro) {
+			if (!is_a<print_latex>(c))
+				c.s << "[";
+			for (unsigned co=0; co<col; ++co) {
+				m[ro*col+co].print(c);
+				if (co<col-1) {
+					if (is_a<print_latex>(c))
+						c.s << "&";
+					else
+						c.s << ",";
+				} else {
+					if (!is_a<print_latex>(c))
+						c.s << "]";
+				}
+			}
+			if (ro<row-1) {
+				if (is_a<print_latex>(c))
+					c.s << "\\\\";
+				else
+					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 << "]]";
+
+		if (is_a<print_latex>(c))
+			c.s << "\\end{array}\\right)";
+		else
+			c.s << "]";
+
+		if (is_a<print_python_repr>(c))
+			c.s << ')';
 
 	}
 }
@@ -201,8 +213,6 @@ ex & matrix::let_op(int i)
 /** Evaluate matrix entry by entry. */
 ex matrix::eval(int level) const
 {
-	debugmsg("matrix eval",LOGLEVEL_MEMBER_FUNCTION);
-	
 	// check if we have to do anything at all
 	if ((level==1)&&(flags & status_flags::evaluated))
 		return *this;
@@ -236,8 +246,8 @@ ex matrix::subs(const lst & ls, const lst & lr, bool no_pattern) const
 
 int matrix::compare_same_type(const basic & other) const
 {
-	GINAC_ASSERT(is_exactly_of_type(other, matrix));
-	const matrix & o = static_cast<const matrix &>(other);
+	GINAC_ASSERT(is_exactly_a<matrix>(other));
+	const matrix &o = static_cast<const matrix &>(other);
 	
 	// compare number of rows
 	if (row != o.rows())
@@ -261,7 +271,7 @@ int matrix::compare_same_type(const basic & other) const
 
 bool matrix::match_same_type(const basic & other) const
 {
-	GINAC_ASSERT(is_exactly_of_type(other, matrix));
+	GINAC_ASSERT(is_exactly_a<matrix>(other));
 	const matrix & o = static_cast<const matrix &>(other);
 	
 	// The number of rows and columns must be the same. This is necessary to
@@ -272,8 +282,8 @@ bool matrix::match_same_type(const basic & other) const
 /** 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));
+	GINAC_ASSERT(is_a<indexed>(i));
+	GINAC_ASSERT(is_a<matrix>(i.op(0)));
 
 	bool all_indices_unsigned = static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint);
 
@@ -349,9 +359,9 @@ ex matrix::eval_indexed(const basic & i) 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(is_a<indexed>(self));
+	GINAC_ASSERT(is_a<matrix>(self.op(0)));
+	GINAC_ASSERT(is_a<indexed>(other));
 	GINAC_ASSERT(self.nops() == 2 || self.nops() == 3);
 
 	// Only add two matrices
@@ -385,8 +395,8 @@ ex matrix::add_indexed(const ex & self, const ex & other) const
 /** 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(is_a<indexed>(self));
+	GINAC_ASSERT(is_a<matrix>(self.op(0)));
 	GINAC_ASSERT(self.nops() == 2 || self.nops() == 3);
 
 	const matrix &self_matrix = ex_to<matrix>(self.op(0));
@@ -400,10 +410,10 @@ ex matrix::scalar_mul_indexed(const ex & self, const numeric & other) const
 /** 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(is_a<indexed>(*self));
+	GINAC_ASSERT(is_a<indexed>(*other));
 	GINAC_ASSERT(self->nops() == 2 || self->nops() == 3);
-	GINAC_ASSERT(is_ex_of_type(self->op(0), matrix));
+	GINAC_ASSERT(is_a<matrix>(self->op(0)));
 
 	// Only contract with other matrices
 	if (!is_ex_of_type(other->op(0), matrix))
@@ -435,7 +445,7 @@ bool matrix::contract_with(exvector::iterator self, exvector::iterator other, ex
 					*self = self_matrix.mul(other_matrix.transpose())(0, 0);
 				}
 			}
-			*other = _ex1();
+			*other = _ex1;
 			return true;
 
 		} else { // vector * matrix
@@ -446,7 +456,7 @@ bool matrix::contract_with(exvector::iterator self, exvector::iterator other, ex
 					*self = indexed(self_matrix.mul(other_matrix), other->op(2));
 				else
 					*self = indexed(self_matrix.transpose().mul(other_matrix), other->op(2));
-				*other = _ex1();
+				*other = _ex1;
 				return true;
 			}
 
@@ -456,7 +466,7 @@ bool matrix::contract_with(exvector::iterator self, exvector::iterator other, ex
 					*self = indexed(other_matrix.mul(self_matrix), other->op(1));
 				else
 					*self = indexed(other_matrix.mul(self_matrix.transpose()), other->op(1));
-				*other = _ex1();
+				*other = _ex1;
 				return true;
 			}
 		}
@@ -466,28 +476,28 @@ bool matrix::contract_with(exvector::iterator self, exvector::iterator other, ex
 		// 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();
+			*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();
+			*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();
+			*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();
+			*other = _ex1;
 			return true;
 		}
 	}
@@ -609,18 +619,20 @@ matrix matrix::pow(const ex & expn) const
 			}
 			matrix C(row,col);
 			for (unsigned r=0; r<row; ++r)
-				C(r,r) = _ex1();
+				C(r,r) = _ex1;
+			if (b.is_zero())
+				return C;
 			// 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) {
+			while (b!=_num1) {
 				if (b.is_odd()) {
 					C = C.mul(A);
-					b -= 1;
+					--b;
 				}
-				b *= _num1_2();  // b /= 2, still integer.
+				b /= _num2;  // still integer.
 				A = A.mul(A);
 			}
 			return A.mul(C);
@@ -760,7 +772,7 @@ ex matrix::determinant(unsigned algo) const
 			int sign;
 			sign = tmp.division_free_elimination(true);
 			if (sign==0)
-				return _ex0();
+				return _ex0;
 			ex det = tmp.m[row*col-1];
 			// factor out accumulated bogus slag
 			for (unsigned d=0; d<row-2; ++d)
@@ -772,10 +784,13 @@ ex matrix::determinant(unsigned algo) const
 		default: {
 			// This is the minor expansion scheme.  We always develop such
 			// that the smallest minors (i.e, the trivial 1x1 ones) are on the
-			// rightmost column.  For this to be efficient it turns out that
-			// the emptiest columns (i.e. the ones with most zeros) should be
-			// the ones on the right hand side.  Therefore we presort the
-			// columns of the matrix:
+			// rightmost column.  For this to be efficient, empirical tests
+			// have shown that the emptiest columns (i.e. the ones with most
+			// zeros) should be the ones on the right hand side -- although
+			// this might seem counter-intuitive (and in contradiction to some
+			// literature like the FORM manual).  Please go ahead and test it
+			// if you don't believe me!  Therefore we presort the columns of
+			// the matrix:
 			typedef std::pair<unsigned,unsigned> uintpair;
 			std::vector<uintpair> c_zeros;  // number of zeros in column
 			for (unsigned c=0; c<col; ++c) {
@@ -785,7 +800,7 @@ ex matrix::determinant(unsigned algo) const
 						++acc;
 				c_zeros.push_back(uintpair(acc,c));
 			}
-			sort(c_zeros.begin(),c_zeros.end());
+			std::sort(c_zeros.begin(),c_zeros.end());
 			std::vector<unsigned> pre_sort;
 			for (std::vector<uintpair>::const_iterator i=c_zeros.begin(); i!=c_zeros.end(); ++i)
 				pre_sort.push_back(i->second);
@@ -900,7 +915,7 @@ matrix matrix::inverse(void) const
 	// First populate the identity matrix supposed to become the right hand side.
 	matrix identity(row,col);
 	for (unsigned i=0; i<row; ++i)
-		identity(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
@@ -1111,7 +1126,7 @@ ex matrix::determinant_minor(void) const
 			Pkey.push_back(i);
 		unsigned fc = 0;  // controls logic for our strange flipper counter
 		do {
-			det = _ex0();
+			det = _ex0;
 			for (unsigned r=0; r<n-c; ++r) {
 				// maybe there is nothing to do?
 				if (m[Pkey[r]*n+c].is_zero())
@@ -1191,12 +1206,12 @@ int matrix::gauss_elimination(const bool det)
 				}
 				// fill up left hand side with zeros
 				for (unsigned c=0; c<=r1; ++c)
-					this->m[r2*n+c] = _ex0();
+					this->m[r2*n+c] = _ex0;
 			}
 			if (det) {
 				// save space by deleting no longer needed elements
 				for (unsigned c=r0+1; c<n; ++c)
-					this->m[r0*n+c] = _ex0();
+					this->m[r0*n+c] = _ex0;
 			}
 			++r0;
 		}
@@ -1238,12 +1253,12 @@ int matrix::division_free_elimination(const bool det)
 					this->m[r2*n+c] = (this->m[r0*n+r1]*this->m[r2*n+c] - this->m[r2*n+r1]*this->m[r0*n+c]).expand();
 				// fill up left hand side with zeros
 				for (unsigned c=0; c<=r1; ++c)
-					this->m[r2*n+c] = _ex0();
+					this->m[r2*n+c] = _ex0;
 			}
 			if (det) {
 				// save space by deleting no longer needed elements
 				for (unsigned c=r0+1; c<n; ++c)
-					this->m[r0*n+c] = _ex0();
+					this->m[r0*n+c] = _ex0;
 			}
 			++r0;
 		}
@@ -1351,7 +1366,7 @@ int matrix::fraction_free_elimination(const bool det)
 				}
 				// fill up left hand side with zeros
 				for (unsigned c=0; c<=r1; ++c)
-					tmp_n.m[r2*n+c] = _ex0();
+					tmp_n.m[r2*n+c] = _ex0;
 			}
 			if ((r1<n-1)&&(r0<m-1)) {
 				// compute next iteration's divisor
@@ -1360,8 +1375,8 @@ int matrix::fraction_free_elimination(const bool det)
 				if (det) {
 					// save space by deleting no longer needed elements
 					for (unsigned c=0; c<n; ++c) {
-						tmp_n.m[r0*n+c] = _ex0();
-						tmp_d.m[r0*n+c] = _ex1();
+						tmp_n.m[r0*n+c] = _ex0;
+						tmp_d.m[r0*n+c] = _ex1;
 					}
 				}
 			}
@@ -1401,11 +1416,11 @@ int matrix::pivot(unsigned ro, unsigned co, bool symbolic)
 			++k;
 	} else {
 		// search largest element in column co beginning at row ro
-		GINAC_ASSERT(is_ex_of_type(this->m[k*col+co],numeric));
+		GINAC_ASSERT(is_a<numeric>(this->m[k*col+co]));
 		unsigned kmax = k+1;
 		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));
+			GINAC_ASSERT(is_a<numeric>(this->m[kmax*col+co]));
 			numeric tmp = ex_to<numeric>(this->m[kmax*col+co]);
 			if (abs(tmp) > mmax) {
 				mmax = tmp;
@@ -1446,7 +1461,7 @@ ex lst_to_matrix(const lst & l)
 			if (l.op(i).nops() > j)
 				m(i, j) = l.op(i).op(j);
 			else
-				m(i, j) = _ex0();
+				m(i, j) = _ex0;
 	return m;
 }
 
@@ -1462,4 +1477,12 @@ ex diag_matrix(const lst & l)
 	return m;
 }
 
+ex unit_matrix(unsigned r, unsigned c)
+{
+	matrix Id(r,c);
+	for (unsigned i=0; i<r && i<c; ++i)
+		Id(i,i) = _ex1;
+	return Id;
+}
+
 } // namespace GiNaC