//
// Copyright (c) 2010 Athanasios Iliopoulos
//
// Distributed under the Boost Software License, Version 1.0. (See
// accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
//
#include <boost/numeric/ublas/assignment.hpp>
#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/vector_proxy.hpp>
#include <boost/numeric/ublas/matrix_proxy.hpp>
#include <boost/numeric/ublas/vector_sparse.hpp>
#include <boost/numeric/ublas/matrix_sparse.hpp>
#include <boost/numeric/ublas/io.hpp>
#include <boost/numeric/ublas/matrix.hpp>
using namespace boost::numeric::ublas;
int main() {
// Simple vector fill
vector<double> a(3);
a <<= 0, 1, 2;
std::cout << a << std::endl;
// [ 0 1 2]
// Vector from vector
vector<double> b(7);
b <<= a, 10, a;
std::cout << b << std::endl;
// [ 0 1 2 10 0 1 2]
// Simple matrix fill
matrix<double> A(3,3);
A <<= 0, 1, 2,
3, 4, 5,
6, 7, 8;
std::cout << A << std::endl;
// [ 0 1 2 ]
// [ 3 4 5 ]
// [ 6 7 8 ]
// Matrix from vector
A <<= 0, 1, 2,
3, 4, 5,
a;
std::cout << A << std::endl;
// [ 0 1 2 ]
// [ 3 4 5 ]
// [ 0 1 2 ]
// Matrix from vector - column assignment
A <<= move(0,2), traverse_policy::by_column(),
a;
std::cout << A << std::endl;
// [ 0 1 0 ]
// [ 3 4 1 ]
// [ 0 1 2 ]
// Another matrix from vector example (watch the wraping);
vector<double> c(9); c <<= 1, 2, 3, 4, 5, 6, 7, 8, 9;
A <<= c;
std::cout << A << std::endl;
// [ 1 2 3 ]
// [ 4 5 6 ]
// [ 7 8 9 ]
// If for performance(Benchmarks are not definite about that) or consistency reasons you need to disable wraping:
static next_row_manip endr; //This can be defined globally
A <<= traverse_policy::by_row_no_wrap(),
1, 2, 3, endr,
4, 5, 6, endr,
7, 8, 9, endr;
// [ 1 2 3 ]
// [ 4 5 6 ]
// [ 7 8 9 ]
// If by default you need to disable wraping define
// BOOST_UBLAS_DEFAULT_NO_WRAP_POLICY, in the compilation options,
// so that you avoid typing the "traverse_policy::by_row_no_wrap()".
// Plus and minus assign:
A <<= fill_policy::index_plus_assign(),
3,2,1;
std::cout << A << std::endl;
// [ 4 4 4 ]
// [ 4 5 6 ]
// [ 7 8 9 ]
// Matrix from proxy
A <<= 0, 1, 2,
project(b, range(3,6)),
a;
std::cout << A << std::endl;
// [ 0 1 2 ]
// [10 0 1 ]
// [ 6 7 8 ]
// Matrix from matrix
matrix<double> B(6,6);
B <<= A, A,
A, A;
std::cout << B << std::endl;
// [ A A ]
// [ A A ]
// Matrix range (vector is similar)
B = zero_matrix<double>(6,6);
matrix_range<matrix<double> > mrB (B, range (1, 4), range (1, 4));
mrB <<= 1,2,3,4,5,6,7,8,9;
std::cout << B << std::endl;
// [ 0 0 0 0 0 0]
// [ 0 1 2 3 0 0]
// [ 0 4 5 6 0 0]
// [ 0 0 0 0 0 0]
// [ 0 0 0 0 0 0]
// [ 0 0 0 0 0 0]
// Horizontal concatenation can be achieved using this trick:
matrix<double> BH(3,9);
BH <<= A, A, A;
std::cout << BH << std::endl;
// [ A A A]
// Vertical concatenation can be achieved using this trick:
matrix<double> BV(9,3);
BV <<= A,
A,
A;
std::cout << BV << std::endl;
// [ A ]
// [ A ]
// [ A ]
// Watch the difference when assigning matrices for different traverse policies:
matrix<double> BR(9,9, 0);
BR <<= traverse_policy::by_row(), // This is the default, so this might as well be omitted.
A, A, A;
std::cout << BR << std::endl;
// [ A A A]
// [ 0 0 0]
// [ 0 0 0]
matrix<double> BC(9,9, 0);
BC <<= traverse_policy::by_column(),
A, A, A;
std::cout << BC << std::endl;
// [ A 0 0]
// [ A 0 0]
// [ A 0 0]
// The following will throw a run-time exception in debug mode (matrix mid-assignment wrap is not allowed) :
// matrix<double> C(7,7);
// C <<= A, A, A;
// Matrix from matrix with index manipulators
matrix<double> C(6,6,0);
C <<= A, move(3,0), A;
// [ A 0 ]
// [ 0 A ]
// A faster way for to construct this dense matrix.
matrix<double> D(6,6);
D <<= A, zero_matrix<double>(3,3),
zero_matrix<double>(3,3), A;
// [ A 0 ]
// [ 0 A ]
// The next_row and next_column index manipulators:
// note: next_row and next_column functions return
// a next_row_manip and and next_column_manip object.
// This is the manipulator we used earlier when we disabled
// wrapping.
matrix<double> E(2,4,0);
E <<= 1, 2, next_row(),
3, 4, next_column(),5;
std::cout << E << std::endl;
// [ 1 2 0 5 ]
// [ 3 4 0 0 ]
// The begin1 (moves to the begining of the column) index manipulator, begin2 does the same for the row:
matrix<double> F(2,4,0);
F <<= 1, 2, next_row(),
3, 4, begin1(),5;
std::cout << F << std::endl;
// [ 1 2 5 0 ]
// [ 3 4 0 0 ]
// The move (relative) and move_to(absolute) index manipulators (probably the most useful manipulators):
matrix<double> G(2,4,0);
G <<= 1, 2, move(0,1), 3,
move_to(1,3), 4;
std::cout << G << std::endl;
// [ 1 2 0 3 ]
// [ 0 0 0 4 ]
// Static equivallents (faster) when sizes are known at compile time:
matrix<double> Gs(2,4,0);
Gs <<= 1, 2, move<0,1>(), 3,
move_to<1,3>(), 4;
std::cout << Gs << std::endl;
// [ 1 2 0 3 ]
// [ 0 0 0 4 ]
// Choice of traverse policy (default is "row by row" traverse):
matrix<double> H(2,4,0);
H <<= 1, 2, 3, 4,
5, 6, 7, 8;
std::cout << H << std::endl;
// [ 1 2 3 4 ]
// [ 5 6 7 8 ]
H <<= traverse_policy::by_column(),
1, 2, 3, 4,
5, 6, 7, 8;
std::cout << H << std::endl;
// [ 1 3 5 7 ]
// [ 2 4 6 8 ]
// traverse policy can be changed mid assignment if desired.
matrix<double> H1(4,4,0);
H1 <<= 1, 2, 3, traverse_policy::by_column(), 1, 2, 3;
std::cout << H << std::endl;
// [1 2 3 1]
// [0 0 0 2]
// [0 0 0 3]
// [0 0 0 0]
// note: fill_policy and traverse_policy are namespaces, so you can use them
// by a using statement.
// For compressed and coordinate matrix types a push_back or insert fill policy can be chosen for faster assginment:
compressed_matrix<double> I(2, 2);
I <<= fill_policy::sparse_push_back(),
0, 1, 2, 3;
std::cout << I << std::endl;
// [ 0 1 ]
// [ 2 3 ]
coordinate_matrix<double> J(2,2);
J<<=fill_policy::sparse_insert(),
1, 2, 3, 4;
std::cout << J << std::endl;
// [ 1 2 ]
// [ 3 4 ]
// A sparse matrix from another matrix works as with other types.
coordinate_matrix<double> K(3,3);
K<<=fill_policy::sparse_insert(),
J;
std::cout << K << std::endl;
// [ 1 2 0 ]
// [ 3 4 0 ]
// [ 0 0 0 ]
// Be careful this will not work:
//compressed_matrix<double> J2(4,4);
//J2<<=fill_policy::sparse_push_back(),
// J,J;
// That's because the second J2's elements
// are attempted to be assigned at positions
// that come before the elements already pushed.
// Unfortunatelly that's the only thing you can do in this case
// (or of course make a custom agorithm):
compressed_matrix<double> J2(4,4);
J2<<=fill_policy::sparse_push_back(),
J, fill_policy::sparse_insert(),
J;
std::cout << J2 << std::endl;
// [ J J ]
// [ 0 0 0 0 ]
// [ 0 0 0 0 ]
// A different traverse policy doesn't change the result, only they order it is been assigned.
coordinate_matrix<double> L(3,3);
L<<=fill_policy::sparse_insert(), traverse_policy::by_column(),
J;
std::cout << L << std::endl;
// (same as previous)
// [ 1 2 0 ]
// [ 3 4 0 ]
// [ 0 0 0 ]
typedef coordinate_matrix<double>::size_type cmst;
const cmst size = 30;
//typedef fill_policy::sparse_push_back spb;
// Although the above could have been used the following is may be faster if
// you use the policy often and for relatively small containers.
static fill_policy::sparse_push_back spb;
// A block diagonal sparse using a loop:
compressed_matrix<double> M(size, size, 4*15);
for (cmst i=0; i!=size; i+=J.size1())
M <<= spb, move_to(i,i), J;
// If typedef was used above the last expression should start
// with M <<= spb()...
// Displaying so that blocks can be easily seen:
for (unsigned int i=0; i!=M.size1(); i++) {
std::cout << M(i,0);
for (unsigned int j=1; j!=M.size2(); j++) std::cout << ", " << M(i,j);
std::cout << "\n";
}
// [ J 0 0 0 ... 0]
// [ 0 J 0 0 ... 0]
// [ 0 . . . ... 0]
// [ 0 0 ... 0 0 J]
// A "repeat" trasverser may by provided so that this becomes faster and an on-liner like:
// M <<= spb, repeat(0, size, J.size1(), 0, size, J.size1()), J;
// An alternate would be to create a :repeater" matrix and vector expression that can be used in other places as well. The latter is probably better,
return 0;
}
