vigra - vigra::linalg Namespace Reference

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| vigra::linalg Namespace Reference Linear Algebra |

Linear algebra functions. More...

## Classes
class | LeastAngleRegressionOptions
| Pass options to leastAngleRegression(). More...
class | Matrix

## Functions
template<class T , class C >
linalg::TemporaryMatrix< T > | abs (MultiArrayView< 2, T, C > const &v)
template<class T , class C >
linalg::TemporaryMatrix< T > | acos (MultiArrayView< 2, T, C > const &v)
template<class T , class C1 , class C2 , class C3 >
void | add (const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b, MultiArrayView< 2, T, C3 > &r)
template<class T , class C >
int | argMax (MultiArrayView< 2, T, C > const &a)
| Find the index of the maximum element in a matrix. More...
template<class T , class C , class UnaryFunctor >
int | argMaxIf (MultiArrayView< 2, T, C > const &a, UnaryFunctor condition)
| Find the index of the maximum element in a matrix subject to a condition. More...
template<class T , class C >
int | argMin (MultiArrayView< 2, T, C > const &a)
| Find the index of the minimum element in a matrix. More...
template<class T , class C , class UnaryFunctor >
int | argMinIf (MultiArrayView< 2, T, C > const &a, UnaryFunctor condition)
| Find the index of the minimum element in a matrix subject to a condition. More...
template<class T , class C >
linalg::TemporaryMatrix< T > | asin (MultiArrayView< 2, T, C > const &v)
template<class T , class C >
linalg::TemporaryMatrix< T > | atan (MultiArrayView< 2, T, C > const &v)
template<class T , class C >
linalg::TemporaryMatrix< T > | ceil (MultiArrayView< 2, T, C > const &v)
template<class T , class C1 , class C2 >
bool | choleskyDecomposition (MultiArrayView< 2, T, C1 > const &A, MultiArrayView< 2, T, C2 > &L)
template<class T , class C1 , class C2 , class C3 >
void | choleskySolve (MultiArrayView< 2, T, C1 > const &L, MultiArrayView< 2, T, C2 > const &b, MultiArrayView< 2, T, C3 > &x)
template<class T , class C >
MultiArrayIndex | columnCount (const MultiArrayView< 2, T, C > &x)
template<... >
void | columnStatistics (...)
template<class T , class C >
MultiArrayView< 2, T, C > | columnVector (MultiArrayView< 2, T, C > const &m, MultiArrayIndex d)
template<class T , class C >
MultiArrayView< 2, T, C > | columnVector (MultiArrayView< 2, T, C > const &m, MultiArrayShape< 2 >::type first, int end)
template<class T , class C >
linalg::TemporaryMatrix< T > | cos (MultiArrayView< 2, T, C > const &v)
template<class T1 , class C1 , class T2 , class C2 >
void | covarianceMatrixOfColumns (MultiArrayView< 2, T1, C1 > const &features, MultiArrayView< 2, T2, C2 > &covariance)
| Compute the covariance matrix between the columns of a matrix features. More...
template<class T , class C >
TemporaryMatrix< T > | covarianceMatrixOfColumns (MultiArrayView< 2, T, C > const &features)
| Compute the covariance matrix between the columns of a matrix features. More...
template<class T1 , class C1 , class T2 , class C2 >
void | covarianceMatrixOfRows (MultiArrayView< 2, T1, C1 > const &features, MultiArrayView< 2, T2, C2 > &covariance)
| Compute the covariance matrix between the rows of a matrix features. More...
template<class T , class C >
TemporaryMatrix< T > | covarianceMatrixOfRows (MultiArrayView< 2, T, C > const &features)
| Compute the covariance matrix between the rows of a matrix features. More...
template<class T , class C1 , class C2 , class C3 >
void | cross (const MultiArrayView< 1, T, C1 > &x, const MultiArrayView< 1, T, C2 > &y, MultiArrayView< 1, T, C3 > &r)
template<class T , class C1 , class C2 , class C3 >
void | cross (const MultiArrayView< 2, T, C1 > &x, const MultiArrayView< 2, T, C2 > &y, MultiArrayView< 2, T, C3 > &r)
template<class T , class C1 , class C2 >
TemporaryMatrix< T > | cross (const MultiArrayView< 2, T, C1 > &x, const MultiArrayView< 2, T, C2 > &y)
template<class T , class C1 >
NumericTraits< T >::Promote | determinant (MultiArrayView< 2, T, C1 > const &a, std::string method="default")
template<class T , class C1 , class C2 >
void | diagonalMatrix (MultiArrayView< 2, T, C1 > const &v, MultiArrayView< 2, T, C2 > &r)
template<class T , class C >
TemporaryMatrix< T > | diagonalMatrix (MultiArrayView< 2, T, C > const &v)
template<class T , class C1 , class C2 >
NormTraits< T >::SquaredNormType | dot (const MultiArrayView< 2, T, C1 > &x, const MultiArrayView< 2, T, C2 > &y)
template<class T , class C1 , class C2 >
NormTraits< T >::SquaredNormType | dot (const MultiArrayView< 1, T, C1 > &x, const MultiArrayView< 1, T, C2 > &y)
template<class T , class C >
linalg::TemporaryMatrix< T > | exp (MultiArrayView< 2, T, C > const &v)
template<class T , class C >
linalg::TemporaryMatrix< T > | floor (MultiArrayView< 2, T, C > const &v)
template<class T , class C >
void | identityMatrix (MultiArrayView< 2, T, C > &r)
template<class T >
TemporaryMatrix< T > | identityMatrix (MultiArrayIndex size)
template<class T , class C1 , class C2 >
bool | inverse (const MultiArrayView< 2, T, C1 > &v, MultiArrayView< 2, T, C2 > &res)
template<class T , class C >
TemporaryMatrix< T > | inverse (const MultiArrayView< 2, T, C > &v)
template<class T , class C >
bool | isSymmetric (const MultiArrayView< 2, T, C > &v)
template<class T , class C1 , class C2 >
TemporaryMatrix< T > | joinHorizontally (const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b)
template<class T , class C1 , class C2 >
TemporaryMatrix< T > | joinVertically (const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b)
template<... >
unsigned int | leastAngleRegression (...)
template<class T , class C1 , class C2 , class C3 >
bool | leastSquares (MultiArrayView< 2, T, C1 > const &A, MultiArrayView< 2, T, C2 > const &b, MultiArrayView< 2, T, C3 > &x, std::string method="QR")
template<... >
bool | linearSolve (...)
template<class T , class C1 , class C2 , class C3 >
bool | linearSolveLowerTriangular (const MultiArrayView< 2, T, C1 > &l, const MultiArrayView< 2, T, C2 > &b, MultiArrayView< 2, T, C3 > x)
template<class T , class C1 , class C2 , class C3 >
bool | linearSolveUpperTriangular (const MultiArrayView< 2, T, C1 > &r, const MultiArrayView< 2, T, C2 > &b, MultiArrayView< 2, T, C3 > x)
template<class T , class C >
linalg::TemporaryMatrix< T > | log (MultiArrayView< 2, T, C > const &v)
template<class T , class C >
linalg::TemporaryMatrix< T > | log10 (MultiArrayView< 2, T, C > const &v)
template<class T , class C1 >
T | logDeterminant (MultiArrayView< 2, T, C1 > const &a)
template<class T , class C1 , class C2 , class C3 >
void | mmul (const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b, MultiArrayView< 2, T, C3 > &r)
template<class T , class C1 , class C2 >
TemporaryMatrix< T > | mmul (const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b)
template<... >
unsigned int | nonnegativeLeastSquares (...)
template<class T , class C1 , class C2 , class C3 >
bool | nonsymmetricEigensystem (MultiArrayView< 2, T, C1 > const &a, MultiArrayView< 2, std::complex< T >, C2 > &ew, MultiArrayView< 2, T, C3 > &ev)
template<class T , class ALLOC >
Matrix< T, ALLLOC >::NormType | norm (const Matrix< T, ALLLOC > &a)
template<class T >
TemporaryMatrix< T > | ones (MultiArrayIndex rows, MultiArrayIndex cols)
template<class T , class C , class U >
TemporaryMatrix< T > | operator* (const MultiArrayView< 2, T, C > &a, PointWise< U > b)
template<class T , class C >
TemporaryMatrix< T > | operator* (const MultiArrayView< 2, T, C > &a, T b)
template<class T , class C >
TemporaryMatrix< T > | operator* (T a, const MultiArrayView< 2, T, C > &b)
template<class T , class A , int N, class DATA , class DERIVED >
TinyVector< T, N > | operator* (const Matrix< T, A > &a, const TinyVectorBase< T, N, DATA, DERIVED > &b)
template<class T , int N, class DATA , class DERIVED , class A >
TinyVector< T, N > | operator* (const TinyVectorBase< T, N, DATA, DERIVED > &a, const Matrix< T, A > &b)
template<class T , class C1 , class C2 >
TemporaryMatrix< T > | operator* (const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b)
template<class T , class C1 , class C2 >
TemporaryMatrix< T > | operator+ (const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b)
template<class T , class C >
TemporaryMatrix< T > | operator+ (const MultiArrayView< 2, T, C > &a, T b)
template<class T , class C >
TemporaryMatrix< T > | operator+ (T a, const MultiArrayView< 2, T, C > &b)
template<class T , class C1 , class C2 >
TemporaryMatrix< T > | operator- (const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b)
template<class T , class C >
TemporaryMatrix< T > | operator- (const MultiArrayView< 2, T, C > &a)
template<class T , class C >
TemporaryMatrix< T > | operator- (const MultiArrayView< 2, T, C > &a, T b)
template<class T , class C >
TemporaryMatrix< T > | operator- (T a, const MultiArrayView< 2, T, C > &b)
template<class T , class C , class U >
TemporaryMatrix< T > | operator/ (const MultiArrayView< 2, T, C > &a, PointWise< U > b)
template<class T , class C >
TemporaryMatrix< T > | operator/ (const MultiArrayView< 2, T, C > &a, T b)
template<class T , class C >
TemporaryMatrix< T > | operator/ (T a, const MultiArrayView< 2, T, C > &b)
template<class T , class C1 , class C2 , class C3 >
void | outer (const MultiArrayView< 2, T, C1 > &x, const MultiArrayView< 2, T, C2 > &y, MultiArrayView< 2, T, C3 > &r)
template<class T , class C1 , class C2 >
TemporaryMatrix< T > | outer (const MultiArrayView< 2, T, C1 > &x, const MultiArrayView< 2, T, C2 > &y)
template<class T , class C >
TemporaryMatrix< T > | outer (const MultiArrayView< 2, T, C > &x)
template<class T , int N>
TemporaryMatrix< T > | outer (const TinyVector< T, N > &x)
template<class T , class C1 , class C2 , class C3 >
void | pdiv (const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b, MultiArrayView< 2, T, C3 > &r)
template<class T , class C1 , class C2 >
TemporaryMatrix< T > | pdiv (const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b)
template<class T , class C1 , class C2 , class C3 >
void | pmul (const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b, MultiArrayView< 2, T, C3 > &r)
template<class T , class C1 , class C2 >
TemporaryMatrix< T > | pmul (const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b)
template<class POLYNOMIAL , class VECTOR >
bool | polynomialRealRootsEigenvalueMethod (POLYNOMIAL const &p, VECTOR &roots, bool)
template<class POLYNOMIAL , class VECTOR >
bool | polynomialRootsEigenvalueMethod (POLYNOMIAL const &poly, VECTOR &roots, bool polishRoots)
template<class T , class C >
linalg::TemporaryMatrix< T > | pow (MultiArrayView< 2, T, C > const &v, T exponent)
template<... >
void | prepareColumns (...)
| Standardize the columns of a matrix according to given `DataPreparationGoals`. More...
template<... >
void | prepareRows (...)
| Standardize the rows of a matrix according to given `DataPreparationGoals`. More...
template<class T , class C1 , class C2 , class C3 >
bool | qrDecomposition (MultiArrayView< 2, T, C1 > const &a, MultiArrayView< 2, T, C2 > &q, MultiArrayView< 2, T, C3 > &r, double epsilon=0.0)
template<class T , class C1 , class C2 >
void | repeatMatrix (MultiArrayView< 2, T, C1 > const &v, MultiArrayView< 2, T, C2 > &r, unsigned int verticalCount, unsigned int horizontalCount)
template<class T , class C >
TemporaryMatrix< T > | repeatMatrix (MultiArrayView< 2, T, C > const &v, unsigned int verticalCount, unsigned int horizontalCount)
template<class T , class C1 , class C2 , class C3 >
bool | reverseElimination (const MultiArrayView< 2, T, C1 > &r, const MultiArrayView< 2, T, C2 > &b, MultiArrayView< 2, T, C3 > x)
template<class T , class C1 , class C2 , class C3 >
bool | ridgeRegression (MultiArrayView< 2, T, C1 > const &A, MultiArrayView< 2, T, C2 > const &b, MultiArrayView< 2, T, C3 > &x, double lambda)
template<class T , class C1 , class C2 , class C3 , class Array >
bool | ridgeRegressionSeries (MultiArrayView< 2, T, C1 > const &A, MultiArrayView< 2, T, C2 > const &b, MultiArrayView< 2, T, C3 > &x, Array const &lambda)
template<class T , class C >
linalg::TemporaryMatrix< T > | round (MultiArrayView< 2, T, C > const &v)
template<class T , class C >
MultiArrayIndex | rowCount (const MultiArrayView< 2, T, C > &x)
template<... >
void | rowStatistics (...)
template<class T , class C >
MultiArrayView< 2, T, C > | rowVector (MultiArrayView< 2, T, C > const &m, MultiArrayIndex d)
template<class T , class C >
MultiArrayView< 2, T, C > | rowVector (MultiArrayView< 2, T, C > const &m, MultiArrayShape< 2 >::type first, MultiArrayIndex end)
template<class T , class C1 , class C2 >
void | sdiv (const MultiArrayView< 2, T, C1 > &a, T b, MultiArrayView< 2, T, C2 > &r)
template<class T , class C >
linalg::TemporaryMatrix< T > | sign (MultiArrayView< 2, T, C > const &v)
template<class T , class C >
linalg::TemporaryMatrix< T > | sin (MultiArrayView< 2, T, C > const &v)
template<class T , class C1 , class C2 , class C3 , class C4 >
unsigned int | singularValueDecomposition (MultiArrayView< 2, T, C1 > const &A, MultiArrayView< 2, T, C2 > &U, MultiArrayView< 2, T, C3 > &S, MultiArrayView< 2, T, C4 > &V)
template<class T , class C1 , class C2 >
void | smul (const MultiArrayView< 2, T, C1 > &a, T b, MultiArrayView< 2, T, C2 > &r)
template<class T , class C2 , class C3 >
void | smul (T a, const MultiArrayView< 2, T, C2 > &b, MultiArrayView< 2, T, C3 > &r)
template<class T , class C >
linalg::TemporaryMatrix< T > | sq (MultiArrayView< 2, T, C > const &v)
template<class T , class C >
linalg::TemporaryMatrix< T > | sqrt (MultiArrayView< 2, T, C > const &v)
template<class T , class ALLOC >
Matrix< T, ALLLOC > ::SquaredNormType | squaredNorm (const Matrix< T, ALLLOC > &a)
template<class T , class C1 , class C2 , class C3 >
void | sub (const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b, MultiArrayView< 2, T, C3 > &r)
template<class T , class C >
MultiArrayView< 2, T, C > | subVector (MultiArrayView< 2, T, C > const &m, int first, int end)
template<class T , class C1 , class C2 , class C3 >
bool | symmetricEigensystem (MultiArrayView< 2, T, C1 > const &a, MultiArrayView< 2, T, C2 > &ew, MultiArrayView< 2, T, C3 > &ev)
template<class T , class C1 , class C2 , class C3 >
bool | symmetricEigensystemNoniterative (MultiArrayView< 2, T, C1 > const &a, MultiArrayView< 2, T, C2 > &ew, MultiArrayView< 2, T, C3 > &ev)
template<class T , class C >
linalg::TemporaryMatrix< T > | tan (MultiArrayView< 2, T, C > const &v)
template<class T , class C >
NumericTraits< T >::Promote | trace (MultiArrayView< 2, T, C > const &m)
template<class T , class C1 , class C2 >
void | transpose (const MultiArrayView< 2, T, C1 > &v, MultiArrayView< 2, T, C2 > &r)
template<class T , class C >
MultiArrayView< 2, T, StridedArrayTag > | transpose (MultiArrayView< 2, T, C > const &v)
template<class T , class C1 , class C2 , class C3 , class C4 >
bool | weightedLeastSquares (MultiArrayView< 2, T, C1 > const &A, MultiArrayView< 2, T, C2 > const &b, MultiArrayView< 2, T, C3 > const &weights, MultiArrayView< 2, T, C4 > &x, std::string method="QR")
template<class T , class C1 , class C2 , class C3 , class C4 >
bool | weightedRidgeRegression (MultiArrayView< 2, T, C1 > const &A, MultiArrayView< 2, T, C2 > const &b, MultiArrayView< 2, T, C3 > const &weights, MultiArrayView< 2, T, C4 > &x, double lambda)

## Detailed Description

Linear algebra functions.

Namespace `vigra/linalg` hold VIGRA's linear algebra functionality. But most of its contents is exported into namespace `vigra` via `using` directives.

© Ullrich Köthe (ullrich.koethe@iwr.uni-heidelberg.de) Heidelberg Collaboratory for Image Processing, University of Heidelberg, Germany | html generated using doxygen and Python vigra 1.11.1 (Fri May 19 2017)