480 lines
14 KiB
C++
480 lines
14 KiB
C++
/**
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* @file Vector.cpp
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* @brief typedef and functions to augment Boost's ublas::vector<double>
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* @author Kai Ni
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* @author Frank Dellaert
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*/
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#include <stdarg.h>
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#include <limits>
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#include <iostream>
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#include <fstream>
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#include <sstream>
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#include <iomanip>
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#include <cmath>
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#include <boost/foreach.hpp>
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#include <boost/optional.hpp>
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#include <stdio.h>
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#ifdef WIN32
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#include <Windows.h>
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#endif
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#include <boost/numeric/ublas/io.hpp>
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#include <boost/numeric/ublas/vector_proxy.hpp>
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#include <boost/random/normal_distribution.hpp>
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#include <boost/random/variate_generator.hpp>
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#include <gtsam/base/Vector.h>
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using namespace std;
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namespace ublas = boost::numeric::ublas;
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namespace gtsam {
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/* ************************************************************************* */
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void odprintf_(const char *format, ostream& stream, ...) {
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char buf[4096], *p = buf;
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int n;
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va_list args;
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va_start(args, stream);
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#ifdef WIN32
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n = _vsnprintf(p, sizeof buf - 3, format, args); // buf-3 is room for CR/LF/NUL
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#else
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n = vsnprintf(p, sizeof buf - 3, format, args); // buf-3 is room for CR/LF/NUL
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#endif
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va_end(args);
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#ifdef WIN32
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OutputDebugString(buf);
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#else
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stream << buf;
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#endif
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}
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/* ************************************************************************* */
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// copy and paste from above, as two functions can not be easily merged
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void odprintf(const char *format, ...)
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{
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char buf[4096], *p = buf;
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int n;
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va_list args;
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va_start(args, format);
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#ifdef WIN32
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n = _vsnprintf(p, sizeof buf - 3, format, args); // buf-3 is room for CR/LF/NUL
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#else
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n = vsnprintf(p, sizeof buf - 3, format, args); // buf-3 is room for CR/LF/NUL
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#endif
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va_end(args);
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#ifdef WIN32
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OutputDebugString(buf);
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#else
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cout << buf;
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#endif
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}
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/* ************************************************************************* */
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Vector Vector_( size_t m, const double* const data) {
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Vector v(m);
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copy(data, data+m, v.data().begin());
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return v;
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}
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/* ************************************************************************* */
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Vector Vector_(size_t m, ...) {
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Vector v(m);
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va_list ap;
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va_start(ap, m);
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for( size_t i = 0 ; i < m ; i++) {
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double value = va_arg(ap, double);
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v(i) = value;
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}
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va_end(ap);
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return v;
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}
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/* ************************************************************************* */
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bool zero(const Vector& v) {
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bool result = true;
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size_t n = v.size();
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for( size_t j = 0 ; j < n ; j++)
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result = result && (v(j) == 0.0);
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return result;
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}
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/* ************************************************************************* */
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Vector repeat(size_t n, double value) {
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Vector v(n, value);
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return v;
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}
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/* ************************************************************************* */
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Vector delta(size_t n, size_t i, double value) {
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Vector v = zero(n);
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v(i) = value;
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return v;
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}
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/* ************************************************************************* */
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void print(const Vector& v, const string& s, ostream& stream) {
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size_t n = v.size();
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odprintf_("%s [", stream, s.c_str());
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for(size_t i=0; i<n; i++)
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odprintf_("%g%s", stream, v[i], (i<n-1 ? "; " : ""));
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odprintf_("];\n", stream);
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}
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/* ************************************************************************* */
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void save(const Vector& v, const string &s, const string& filename) {
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fstream stream(filename.c_str(), fstream::out | fstream::app);
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print(v, s + "=", stream);
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stream.close();
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}
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/* ************************************************************************* */
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bool operator==(const Vector& vec1,const Vector& vec2) {
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Vector::const_iterator it1 = vec1.begin();
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Vector::const_iterator it2 = vec2.begin();
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size_t m = vec1.size();
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for(size_t i=0; i<m; i++)
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if(it1[i] != it2[i])
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return false;
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return true;
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}
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/* ************************************************************************* */
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bool greaterThanOrEqual(const Vector& vec1, const Vector& vec2) {
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Vector::const_iterator it1 = vec1.begin();
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Vector::const_iterator it2 = vec2.begin();
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size_t m = vec1.size();
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for(size_t i=0; i<m; i++)
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if(!(it1[i] >= it2[i]))
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return false;
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return true;
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}
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/* ************************************************************************* */
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bool equal_with_abs_tol(const Vector& vec1, const Vector& vec2, double tol) {
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Vector::const_iterator it1 = vec1.begin();
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Vector::const_iterator it2 = vec2.begin();
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if (vec1.size()!=vec2.size()) return false;
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for(size_t i=0; i<vec1.size(); i++) {
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if(isnan(it1[i]) xor isnan(it2[i]))
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return false;
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if(fabs(it1[i] - it2[i]) > tol)
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return false;
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}
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return true;
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}
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/* ************************************************************************* */
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bool assert_equal(const Vector& expected, const Vector& actual, double tol) {
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if (equal_with_abs_tol(expected,actual,tol)) return true;
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cout << "not equal:" << endl;
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print(expected, "expected");
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print(actual, "actual");
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return false;
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}
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/* ************************************************************************* */
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bool assert_equal(SubVector expected, SubVector actual, double tol) {
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if (equal_with_abs_tol(expected,actual,tol)) return true;
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cout << "not equal:" << endl;
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print(expected, "expected");
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print(actual, "actual");
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return false;
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}
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/* ************************************************************************* */
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bool assert_equal(ConstSubVector expected, ConstSubVector actual, double tol) {
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if (equal_with_abs_tol(expected,actual,tol)) return true;
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cout << "not equal:" << endl;
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print(expected, "expected");
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print(actual, "actual");
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return false;
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}
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/* ************************************************************************* */
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bool linear_dependent(const Vector& vec1, const Vector& vec2, double tol) {
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if (vec1.size()!=vec2.size()) return false;
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Vector::const_iterator it1 = vec1.begin();
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Vector::const_iterator it2 = vec2.begin();
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boost::optional<double> scale;
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for(size_t i=0; i<vec1.size(); i++) {
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if((fabs(it1[i])>tol&&fabs(it2[i])<tol) || (fabs(it1[i])<tol&&fabs(it2[i])>tol))
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return false;
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if(it1[i] == 0 && it2[i] == 0)
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continue;
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if (!scale)
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scale = it1[i] / it2[i];
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else if (fabs(it1[i] - it2[i] * (*scale)) > tol)
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return false;
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}
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return scale.is_initialized();
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}
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/* ************************************************************************* */
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Vector sub(const Vector &v, size_t i1, size_t i2) {
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size_t n = i2-i1;
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Vector v_return(n);
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for( size_t i = 0; i < n; i++ )
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v_return(i) = v(i1 + i);
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return v_return;
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}
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/* ************************************************************************* */
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void subInsert(Vector& big, const Vector& small, size_t i) {
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ublas::vector_range<Vector> colsubproxy(big, ublas::range (i, i+small.size()));
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colsubproxy = small;
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}
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/* ************************************************************************* */
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Vector emul(const Vector &a, const Vector &b) {
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size_t n = a.size();
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assert (b.size()==n);
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Vector c(n);
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for( size_t i = 0; i < n; i++ )
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c(i) = a(i)*b(i);
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return c;
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}
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/* ************************************************************************* */
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Vector ediv(const Vector &a, const Vector &b) {
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size_t n = a.size();
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assert (b.size()==n);
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Vector c(n);
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for( size_t i = 0; i < n; i++ )
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c(i) = a(i)/b(i);
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return c;
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}
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/* ************************************************************************* */
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Vector ediv_(const Vector &a, const Vector &b) {
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size_t n = a.size();
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assert (b.size()==n);
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Vector c(n);
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for( size_t i = 0; i < n; i++ ) {
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double ai = a(i), bi = b(i);
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c(i) = (bi==0.0 && ai==0.0) ? 0.0 : a(i)/b(i);
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}
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return c;
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}
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/* ************************************************************************* */
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double sum(const Vector &a) {
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double result = 0.0;
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size_t n = a.size();
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for( size_t i = 0; i < n; i++ )
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result += a(i);
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return result;
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}
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/* ************************************************************************* */
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Vector reciprocal(const Vector &a) {
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size_t n = a.size();
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Vector b(n);
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for( size_t i = 0; i < n; i++ )
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b(i) = 1.0/a(i);
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return b;
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}
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/* ************************************************************************* */
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Vector esqrt(const Vector& v) {
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Vector s(v.size());
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transform(v.begin(), v.end(), s.begin(), ::sqrt);
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return s;
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}
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/* ************************************************************************* */
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Vector abs(const Vector& v) {
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Vector s(v.size());
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transform(v.begin(), v.end(), s.begin(), ::fabs);
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return s;
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}
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/* ************************************************************************* */
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double max(const Vector &a) {
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return *(std::max_element(a.begin(), a.end()));
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}
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/* ************************************************************************* */
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double dot(const Vector& a, const Vector& b) {
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size_t n = a.size();
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assert (b.size()==n);
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double result = 0.0;
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for (size_t i = 0; i < n; i++)
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result += a[i] * b[i];
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return result;
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}
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/* ************************************************************************* */
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void scal(double alpha, Vector& x) {
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size_t n = x.size();
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for (size_t i = 0; i < n; i++)
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x[i] *= alpha;
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}
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/* ************************************************************************* */
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void axpy(double alpha, const Vector& x, Vector& y) {
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size_t n = x.size();
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assert (y.size()==n);
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for (size_t i = 0; i < n; i++)
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y[i] += alpha * x[i];
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}
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/* ************************************************************************* */
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void axpy(double alpha, const Vector& x, SubVector y) {
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size_t n = x.size();
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assert (y.size()==n);
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for (size_t i = 0; i < n; i++)
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y[i] += alpha * x[i];
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}
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/* ************************************************************************* */
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Vector operator/(double s, const Vector& v) {
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Vector result(v.size());
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for(size_t i = 0; i < v.size(); i++)
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result[i] = s / v[i];
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return result;
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}
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/* ************************************************************************* */
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// imperative version, pass in x
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double houseInPlace(Vector &v) {
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const double x0 = v(0);
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const double x02 = x0*x0;
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// old code - GSL verison was actually a bit slower
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const double sigma = inner_prod(v,v) - x02;
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v(0) = 1.0;
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if( sigma == 0.0 )
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return 0.0;
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else {
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double mu = sqrt(x02 + sigma);
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if( x0 <= 0.0 )
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v(0) = x0 - mu;
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else
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v(0) = -sigma / (x0 + mu);
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const double v02 = v(0)*v(0);
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v = v / v(0);
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return 2.0 * v02 / (sigma + v02);
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}
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}
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/* ************************************************************************* */
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pair<double, Vector > house(const Vector &x) {
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Vector v(x);
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double beta = houseInPlace(v);
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return make_pair(beta, v);
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}
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/* ************************************************************************* */
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// Fast version *no error checking* !
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// Pass in initialized vector of size m or will crash !
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double weightedPseudoinverse(const Vector& a, const Vector& weights,
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Vector& pseudo) {
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size_t m = weights.size();
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static const double inf = std::numeric_limits<double>::infinity();
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// Check once for zero entries of a. TODO: really needed ?
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vector<bool> isZero;
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for (size_t i = 0; i < m; ++i) isZero.push_back(fabs(a[i]) < 1e-9);
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// If there is a valid (a!=0) constraint (sigma==0) return the first one
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for (size_t i = 0; i < m; ++i)
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if (weights[i] == inf && !isZero[i]) {
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pseudo = delta(m, i, 1 / a[i]);
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return inf;
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}
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// Form psuedo-inverse inv(a'inv(Sigma)a)a'inv(Sigma)
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// For diagonal Sigma, inv(Sigma) = diag(precisions)
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double precision = 0;
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for (size_t i = 0; i < m; i++) {
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double ai = a[i];
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if (!isZero[i]) // also catches remaining sigma==0 rows
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precision += weights[i] * (ai * ai);
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}
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// precision = a'inv(Sigma)a
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if (precision < 1e-9)
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for (size_t i = 0; i < m; i++)
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pseudo[i] = 0;
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else {
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// emul(precisions,a)/precision
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double variance = 1.0 / precision;
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for (size_t i = 0; i < m; i++)
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pseudo[i] = isZero[i] ? 0 : variance * weights[i] * a[i];
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}
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return precision; // sum of weights
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}
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/* ************************************************************************* */
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// Slow version with error checking
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pair<Vector, double>
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weightedPseudoinverse(const Vector& a, const Vector& weights) {
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size_t m = weights.size();
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if (a.size() != m)
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throw invalid_argument("a and weights have different sizes!");
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Vector pseudo(m);
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double precision = weightedPseudoinverse(a, weights, pseudo);
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return make_pair(pseudo, precision);
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}
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/* ************************************************************************* */
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Vector concatVectors(const std::list<Vector>& vs)
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{
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size_t dim = 0;
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BOOST_FOREACH(Vector v, vs)
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dim += v.size();
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Vector A(dim);
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size_t index = 0;
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BOOST_FOREACH(Vector v, vs) {
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for(size_t d = 0; d < v.size(); d++)
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A(d+index) = v(d);
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index += v.size();
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}
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return A;
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}
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/* ************************************************************************* */
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Vector concatVectors(size_t nrVectors, ...)
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{
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va_list ap;
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list<Vector> vs;
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va_start(ap, nrVectors);
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for( size_t i = 0 ; i < nrVectors ; i++) {
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Vector* V = va_arg(ap, Vector*);
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vs.push_back(*V);
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}
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va_end(ap);
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return concatVectors(vs);
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}
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/* ************************************************************************* */
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Vector rand_vector_norm(size_t dim, double mean, double sigma)
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{
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boost::normal_distribution<double> norm_dist(mean, sigma);
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boost::variate_generator<boost::minstd_rand&, boost::normal_distribution<double> > norm(generator, norm_dist);
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Vector v(dim);
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Vector::iterator it_v;
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for(it_v=v.begin(); it_v!=v.end(); it_v++)
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*it_v = norm();
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return v;
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}
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/* ************************************************************************* */
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} // namespace gtsam
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