libraries
/
libmatricxx
1
0
Fork 0
Code Issues Pull Requests Releases Activity

inverse tested

Browse Source
master
Marc Wäckerlin 8 years ago
parent 549db697b7
commit 2f35c1e3a0
4 changed files with 210 additions and 62 deletions
Whitespace
Show all changes Ignore whitespace when comparing lines Ignore changes in amount of whitespace Ignore changes in whitespace at EOL
Split View
Diff Options
Show Stats Download Patch File Download Diff File
  1. 2
      COPYING
  2. 2
      INSTALL
  3. 144
      src/matrix.hxx
  4. 74
      test/basic.cxx

2
COPYING
Unescape View File

@ -1 +1 @@
/usr/share/automake-1.15/COPYING
/usr/share/automake-1.14/COPYING

2
INSTALL
Unescape View File

@ -1 +1 @@
/usr/share/automake-1.15/INSTALL
/usr/share/automake-1.14/INSTALL

144
src/matrix.hxx
Unescape View File

@ -9,6 +9,42 @@
#include <cstring>
#include <cassert>
#include <type_traits>
#include <limits>
namespace math {
template<typename TYPE>
bool almostEqual(TYPE a, TYPE b) {
if (a<0)
if (b<0) {
a = -a;
b = -b;
} else return a==b; // different signs
else if (b<0) return a==b; // different signs
TYPE diff(abs(a-b));
a = abs(a);
b = abs(b);
TYPE max(a>b?a:b);
if (max<1) return diff<=std::numeric_limits<TYPE>::epsilon();
return diff<=max*std::numeric_limits<TYPE>::epsilon();
}
template<typename TYPE>
bool equal(const TYPE& a, const TYPE& b) {
return a==b;
}
template<>
bool equal(const double& a, const double& b) {
return almostEqual(a, b);
}
template<>
bool equal(const float& a, const float& b) {
return almostEqual(a, b);
}
}
template<typename TYPE, typename ARRAY=TYPE*> class MatrixBase {
@ -137,7 +173,7 @@ template<typename TYPE, typename ARRAY=TYPE*> class MatrixBase {
bool operator==(const MatrixBase& o) const {
if (!check(o)) return false;
TYPE *to((TYPE*)(_c)+SIZE), *from((TYPE*)(o._c)+SIZE);
while (to>(TYPE*)(_c)) if (*--to != *--from) return false;
while (to>(TYPE*)(_c)) if (!math::equal(*--to, *--from)) return false;
return true;
}
@ -176,6 +212,13 @@ template<typename TYPE, typename ARRAY=TYPE*> class MatrixBase {
/// @name special operations
///{
bool similar(const MatrixBase& o, const TYPE& diff) const {
if (!check(o)) return false;
TYPE *to((TYPE*)(_c)+SIZE), *from((TYPE*)(o._c)+SIZE);
while (to>(TYPE*)(_c)) if (abs(*--to - *--from)>diff) return false;
return true;
}
TYPE det() {
TYPE res(gauss());
for (TYPE *p((TYPE*)(_c)+SIZE); --p>=(TYPE*)(_c); p-=COLUMNS) res *= *p;
@ -302,27 +345,45 @@ template<typename TYPE, size_t TROWS=0, size_t TCOLUMNS=0> class Matrix:
Matrix o(*this); // left side
*this = i(); // right side
/// 1. lower left part
for (size_t row(0); row<this->ROWS; ++row)
if (rows<this->COLUMNS) {
/// 2. normalize first line to first value
TYPE pivot(o(row, row));
for (size_t column(0); column<this->COLUMNS; ++column) {
if (column<this->ROWS) {
/// 2. normalize pivot to one
TYPE pivot(o(column, column));
if (pivot!=1) {
o(row, row) = 1;
for (size_t column(row+1); column<this->COLUMNS; ++column) o(row, column)/=pivot;
for (size_t column(row); column<this->COLUMNS; ++column) this->at(row, column)/=pivot;
o(column, column) = 1;
for (size_t pos(column+1); pos<this->COLUMNS; ++pos)
o(column, pos)/=pivot;
for (size_t pos(0); pos<this->COLUMNS; ++pos)
this->at(column, pos)/=pivot;
}
/// 3. nullify lower triangle
for (size_t row(column+1); row<this->ROWS; ++row) {
TYPE pivot(o(row, column));
if (pivot!=0) {
o(row, column) = 0;
for (size_t pos(column+1); pos<this->COLUMNS; ++pos) o(row, pos) -= pivot*o(0, pos);
for (size_t pos(column); pos<this->COLUMNS; ++pos) this->at(row, pos) -= pivot*this->at(0, pos);
for (size_t pos(column+1); pos<this->COLUMNS; ++pos)
o(row, pos) -= pivot*o(column, pos);
for (size_t pos(0); pos<this->COLUMNS; ++pos)
this->at(row, pos) -= pivot*this->at(column, pos);
}
}
}
}
/// 4. nullify the upper triangle
const size_t LASTCOL(this->COLUMNS-1);
const size_t LASTROW(this->ROWS-1);
for (size_t column(1); column<this->COLUMNS; ++column) {
for (size_t row(0); row<column && row<LASTROW; ++row) {
TYPE pivot(o(row, column));
if (pivot!=0) {
o(row, column) = 0;
for (size_t pos(column+1); pos<this->COLUMNS; ++pos)
o(row, pos) -= pivot*o(column, pos);
for (size_t pos(0); pos<this->COLUMNS; ++pos)
this->at(row, pos) -= pivot*this->at(column, pos);
}
}
}
return *this;
}
@ -379,18 +440,6 @@ template<typename TYPE> class Matrix<TYPE, 0, 0>: public MatrixBase<TYPE> {
/// @name operators
///{
Matrix& operator=(const Matrix& o) {
if (o.ROWS!=Parent::ROWS&&o.COLUMNS!=Parent::COLUMNS) {
delete[] Parent::_c;
Parent::ROWS = o.ROWS;
Parent::COLUMNS = o.COLUMNS;
Parent::SIZE = o.SIZE;
Parent::MEM_SIZE = o.MEM_SIZE;
Parent::_c = new TYPE[Parent::SIZE];
}
return Parent::operator=(o);
}
Matrix operator-() const {
Matrix res(Parent::COLUMNS, Parent::ROWS);
for (TYPE *to((TYPE*)(res._c)+Parent::SIZE); to>(TYPE*)(Parent::_c); --to)
@ -428,6 +477,54 @@ template<typename TYPE> class Matrix<TYPE, 0, 0>: public MatrixBase<TYPE> {
return res;
}
Matrix& inv() {
/// calculate using gauss-jordan algorithmus
/// @see http://www.mathebibel.de/inverse-matrix-berechnen-nach-gauss-jordan
Matrix o(*this); // left side
*this = i(); // right side
/// 1. lower left part
for (size_t column(0); column<this->COLUMNS; ++column) {
if (column<this->ROWS) {
/// 2. normalize pivot to one
TYPE pivot(o(column, column));
if (pivot!=1) {
o(column, column) = 1;
for (size_t pos(column+1); pos<this->COLUMNS; ++pos)
o(column, pos)/=pivot;
for (size_t pos(0); pos<this->COLUMNS; ++pos)
this->at(column, pos)/=pivot;
}
/// 3. nullify lower triangle
for (size_t row(column+1); row<this->ROWS; ++row) {
TYPE pivot(o(row, column));
if (pivot!=0) {
o(row, column) = 0;
for (size_t pos(column+1); pos<this->COLUMNS; ++pos)
o(row, pos) -= pivot*o(column, pos);
for (size_t pos(0); pos<this->COLUMNS; ++pos)
this->at(row, pos) -= pivot*this->at(column, pos);
}
}
}
}
/// 4. nullify the upper triangle
const size_t LASTCOL(this->COLUMNS-1);
const size_t LASTROW(this->ROWS-1);
for (size_t column(1); column<this->COLUMNS; ++column) {
for (size_t row(0); row<column && row<LASTROW; ++row) {
TYPE pivot(o(row, column));
if (pivot!=0) {
o(row, column) = 0;
for (size_t pos(column+1); pos<this->COLUMNS; ++pos)
o(row, pos) -= pivot*o(column, pos);
for (size_t pos(0); pos<this->COLUMNS; ++pos)
this->at(row, pos) -= pivot*this->at(column, pos);
}
}
}
return *this;
}
///}
//................................................................methods
@ -494,4 +591,3 @@ template<typename TYPE, size_t ROWS, size_t COLUMNS>
s<<'\n';
}
}

74
test/basic.cxx
Unescape View File

@ -204,17 +204,41 @@ class TemplateMatrixTest: public CppUnit::TestFixture {
}
template<typename T>
void inv() {
Matrix<T,3,3> m(2, -1, 0,
1, 2, -2,
0, -1, 1);
const Matrix<T,3,3> res(0.5, 0, 0,
-0.2, 0.4, 0,
-1, 2, 5);
// const Matrix<T,3,3> res(0, 1, 2,
// -1, 2, 4,
// -1, 2, 5);
m.inv();
CPPUNIT_ASSERT_EQUAL(res, m);
{
Matrix<T,3,3> m(2, -1, 0,
1, 2, -2,
0, -1, 1);
const Matrix<T,3,3> res(0, 1, 2,
-1, 2, 4,
-1, 2, 5);
m.inv();
CPPUNIT_ASSERT(m.similar(res, 0.0001));
} {
Matrix<T,3,3> m(1, 2, 3,
0, 1, 4,
5, 6, 0);
const Matrix<T,3,3> res(-24, 18, 5,
20, -15, -4,
-5, 4, 1);
m.inv();
CPPUNIT_ASSERT_EQUAL(res, m);
} {
Matrix<T,3,3> m(1, 2, 3,
0, 4, 5,
1, 0, 6);
const Matrix<T,3,3> res((T)12/11, (T)-6/11, (T)-1/11,
(T)5/22, (T)3/22, (T)-5/22,
(T)-2/11, (T)1/11, (T)2/11);
m.inv();
CPPUNIT_ASSERT_EQUAL(res, m);
} {
Matrix<T,2,2> m(4, 3,
3, 2);
const Matrix<T,2,2> res(-2, 3,
3, -4);
m.inv();
CPPUNIT_ASSERT_EQUAL(res, m);
}
}
CPPUNIT_TEST_SUITE(TemplateMatrixTest);
CPPUNIT_TEST(initFromArray1<int>);
@ -502,6 +526,32 @@ class VariableMatrixTest: public CppUnit::TestFixture {
CPPUNIT_ASSERT_EQUAL(m2, m2.i());
CPPUNIT_ASSERT_EQUAL(m3, m3.i());
}
template<typename T>
void inv() {
{
Matrix<T> m(3, 3,
2, -1, 0,
1, 2, -2,
0, -1, 1);
const Matrix<T> res(3, 3,
0, 1, 2,
-1, 2, 4,
-1, 2, 5);
m.inv();
CPPUNIT_ASSERT(m.similar(res, 0.0001));
} {
Matrix<T> m(3, 3,
1, 2, 3,
0, 1, 4,
5, 6, 0);
const Matrix<T> res(3, 3,
-24, 18, 5,
20, -15, -4,
-5, 4, 1);
m.inv();
CPPUNIT_ASSERT_EQUAL(res, m);
}
}
CPPUNIT_TEST_SUITE(VariableMatrixTest);
CPPUNIT_TEST(initFromArray1<int>);
CPPUNIT_TEST(initFromArray1<long>);
@ -583,6 +633,8 @@ class VariableMatrixTest: public CppUnit::TestFixture {
CPPUNIT_TEST(i<unsigned long>);
CPPUNIT_TEST(i<float>);
CPPUNIT_TEST(i<double>);
CPPUNIT_TEST(inv<float>);
CPPUNIT_TEST(inv<double>);
CPPUNIT_TEST_SUITE_END();
};
CPPUNIT_TEST_SUITE_REGISTRATION(VariableMatrixTest);

Write Preview
Loading…
Cancel
Save