algorithm

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Functions

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Types

type CholeskyDecomposition 

type CholeskyDecomposition struct {
	L     [][]float64 // Array for internal storage of decomposition.
	N     int         // Row and column dimension (square matrix).
	Isspd bool        // Symmetric and positive definite flag.
}
  • Cholesky Decomposition. <P> For a symmetric, positive definite matrix A, the Cholesky decomposition is an lower triangular matrix L so that A = L*L'. <P> If the matrix is not symmetric or positive definite, the constructor returns a partial decomposition and sets an internal flag that may be queried by the isSPD() method.

func NewCholeskyDecomposition 

func NewCholeskyDecomposition(matrix *Matrix) *CholeskyDecomposition

func (*CholeskyDecomposition) GetL 

func (c *CholeskyDecomposition) GetL() *Matrix

func (*CholeskyDecomposition) Solve 

func (c *CholeskyDecomposition) Solve(B *Matrix) *Matrix

* Solve A*X = B @param B A Matrix with as many rows as A and any number of columns. @return X so that L*L'*X = B @exception IllegalArgumentException Matrix row dimensions must agree. @exception RuntimeException Matrix is not symmetric positive definite.

type EigenvalueDecomposition 

type EigenvalueDecomposition struct {
	N           int         // Row and column dimension (square matrix).
	IsSymmetric bool        //  Symmetry flag.
	D           []float64   // Arrays for internal storage of eigenvalues.
	E           []float64   // Array for internal storage of eigenvectors.
	V           [][]float64 // Array for internal storage of eigenvectors.
	H           [][]float64 //  Array for internal storage of nonsymmetric Hessenberg form.
	Ort         []float64   // Working storage for nonsymmetric algorithm.
}

func NewEigenvalueDecomposition 

func NewEigenvalueDecomposition(matrix *Matrix) *EigenvalueDecomposition

func (*EigenvalueDecomposition) Cdiv 

func (e *EigenvalueDecomposition) Cdiv(xr, xi, yr, yi float64)

func (*EigenvalueDecomposition) GetD 

func (e *EigenvalueDecomposition) GetD() *Matrix

func (*EigenvalueDecomposition) GetImagEigenvalues 

func (e *EigenvalueDecomposition) GetImagEigenvalues() []float64

func (*EigenvalueDecomposition) GetRealEigenvalues 

func (e *EigenvalueDecomposition) GetRealEigenvalues() []float64

func (*EigenvalueDecomposition) GetV 

func (e *EigenvalueDecomposition) GetV() *Matrix

func (*EigenvalueDecomposition) Getd 

func (e *EigenvalueDecomposition) Getd() []float64

func (*EigenvalueDecomposition) Hqr2 

func (e *EigenvalueDecomposition) Hqr2()

func (*EigenvalueDecomposition) Orthes 

func (e *EigenvalueDecomposition) Orthes()

Nonsymmetric reduction to Hessenberg form.

func (*EigenvalueDecomposition) Tql2 

func (e *EigenvalueDecomposition) Tql2()

func (*EigenvalueDecomposition) Tred2 

func (e *EigenvalueDecomposition) Tred2()

This is derived from the Algol procedures tred2 by Bowdler, Martin, Reinsch, and Wilkinson, Handbook for Auto. Comp., Vol.ii-Linear Algebra, and the corresponding Fortran subroutine in EISPACK.

type LUDecomposition 

type LUDecomposition struct {
	LU [][]float64 // Array for internal storage of decomposition.
	N  int         /** Row and column dimensions, and pivot sign.
	  column dimension.
	  l row dimension.
	  pivot sign. */
	M       int
	Pivsign int
	Piv     []int //Internal storage of pivot vector.
}

func NewLUDecomposition 

func NewLUDecomposition(a *Matrix) *LUDecomposition

func (*LUDecomposition) Det 

func (lud *LUDecomposition) Det() float64

* Determinant @return det(A)

func (*LUDecomposition) GetDoublePivot 

func (lud *LUDecomposition) GetDoublePivot() []float64

* Return pivot permutation vector as a one-dimensional double array @return (double) piv

func (*LUDecomposition) GetL 

func (lud *LUDecomposition) GetL() *Matrix

* Return lower triangular factor @return L

func (*LUDecomposition) GetPivot 

func (lud *LUDecomposition) GetPivot() []int

func (*LUDecomposition) GetU 

func (lud *LUDecomposition) GetU() *Matrix

* Return upper triangular factor @return U

func (*LUDecomposition) IsNonsingular 

func (lud *LUDecomposition) IsNonsingular() bool

func (*LUDecomposition) Solve 

func (lud *LUDecomposition) Solve(b *Matrix) *Matrix

type Matrix 

type Matrix struct {
	A [][]float64
	M int
	N int
}

* 

Jama = Java Matrix class.

<P> 

The Java Matrix Class provides the fundamental operations of numerical
linear algebra.  Various constructors create Matrices from two dimensional
arrays of double precision floating point numbers.  Various "gets" and
"sets" provide access to submatrices and matrix elements.  Several methods
implement basic matrix arithmetic, including matrix addition and
multiplication, matrix norms, and element-by-element array operations.
Methods for reading and printing matrices are also included.  All the
operations in this version of the Matrix Class involve real matrices.
Complex matrices may be handled in a future version.

<P> 

Five fundamental matrix decompositions, which consist of pairs or triples
of matrices, permutation vectors, and the like, produce results in five
decomposition classes.  These decompositions are accessed by the Matrix
class to compute solutions of simultaneous linear equations, determinants,
inverses and other matrix functions.  The five decompositions are:

<P><UL> 

<LI>Cholesky Decomposition of symmetric, positive definite matrices.
<LI>LU Decomposition of rectangular matrices.
<LI>QR Decomposition of rectangular matrices.
<LI>Singular Value Decomposition of rectangular matrices.
<LI>Eigenvalue Decomposition of both symmetric and nonsymmetric square matrices.

</UL> <DL> <DT><B>Example of use:</B></DT> <P> <DD>Solve a linear system A x = b and compute the residual norm, ||b - A x||. <P><PRE> 

double[][] vals = {{1.,2.,3},{4.,5.,6.},{7.,8.,10.}};
Matrix A = new Matrix(vals);
Matrix b = Matrix.random(3,1);
Matrix x = A.solve(b);
Matrix r = A.times(x).minus(b);
double rnorm = r.normInf();

</PRE></DD> </DL>

@author The MathWorks, Inc. and the National Institute of Standards and Technology. @version 5 August 1998

func NewMatrix 

func NewMatrix(m, n int) *Matrix

func NewMatrixFilled 

func NewMatrixFilled(m, n, s int) *Matrix

func NewMatrixWithArrays 

func NewMatrixWithArrays(a [][]float64) (*Matrix, error)

func NewMatrixWithMatrix 

func NewMatrixWithMatrix(a [][]float64, m, n int) (*Matrix, error)

func (*Matrix) ColumnsDimension 

func (m *Matrix) ColumnsDimension() int

func (*Matrix) Eig 

func (m *Matrix) Eig() *EigenvalueDecomposition

func (*Matrix) GetMatrix 

func (m *Matrix) GetMatrix(r []int, j0, j1 int) *Matrix

func (*Matrix) GetMatrix2 

func (m *Matrix) GetMatrix2(i0, i1 int, c []int) *Matrix

func (*Matrix) GetMatrix3 

func (m *Matrix) GetMatrix3(i0, i1, j0, j1 int) *Matrix

func (*Matrix) Identity 

func (mat *Matrix) Identity(m, n int) *Matrix

func (*Matrix) Inverse 

func (m *Matrix) Inverse() *Matrix

func (*Matrix) Minus 

func (m *Matrix) Minus(b *Matrix) *Matrix

func (*Matrix) Plus 

func (m *Matrix) Plus(b *Matrix) *Matrix

func (*Matrix) PlusEqual 

func (m *Matrix) PlusEqual(b *Matrix)

func (*Matrix) RowsDimension 

func (m *Matrix) RowsDimension() int

func (*Matrix) SetMatrix 

func (m *Matrix) SetMatrix(i0, i1, j0, j1 int, x *Matrix)

func (*Matrix) Solve 

func (m *Matrix) Solve(b *Matrix) *Matrix

func (*Matrix) Times 

func (m *Matrix) Times(s float64) *Matrix

func (*Matrix) TimesMatrix 

func (m *Matrix) TimesMatrix(b *Matrix) *Matrix

func (*Matrix) Tostring 

func (m *Matrix) Tostring() string

func (*Matrix) Transpose 

func (m *Matrix) Transpose() *Matrix

func (*Matrix) UnVectorize 

func (mat *Matrix) UnVectorize(width, height int) *Matrix

func (*Matrix) Vectorize 

func (mat *Matrix) Vectorize() *Matrix

type QRDecomposition 

type QRDecomposition struct {
	QR    [][]float64 // Array for internal storage of decomposition.
	M     int         //column dimension.
	N     int         //row dimension.
	Rdiag []float64   //Array for internal storage of diagonal of R.
}

func NewQRDecomposition 

func NewQRDecomposition(a *Matrix) *QRDecomposition

func (*QRDecomposition) IsFullRank 

func (q *QRDecomposition) IsFullRank() bool

func (*QRDecomposition) Solve 

func (q *QRDecomposition) Solve(b *Matrix) *Matrix

type SingularValueDecomposition 

type SingularValueDecomposition struct {

	/** Arrays for internal storage of U and V.
	@serial internal storage of U.
	@serial internal storage of V.
	*/
	U [][]float64
	V [][]float64
	/** Array for internal storage of singular values.
	@serial internal storage of singular values.
	*/
	S []float64

	/** Row and column dimensions.
	@serial row dimension.
	@serial column dimension.
	*/
	M int
	N int
}

func NewSingularValueDecomposition 

func NewSingularValueDecomposition(matrix *Matrix) *SingularValueDecomposition

func (*SingularValueDecomposition) Cond 

func (s *SingularValueDecomposition) Cond() float64

* Two norm condition number @return max(S)/min(S)

func (*SingularValueDecomposition) GetS 

func (s *SingularValueDecomposition) GetS() *Matrix

* Return the diagonal matrix of singular values @return S

func (*SingularValueDecomposition) GetSingularValues 

func (s *SingularValueDecomposition) GetSingularValues() []float64

func (*SingularValueDecomposition) GetU 

func (s *SingularValueDecomposition) GetU() *Matrix

* Return the left singular vectors @return U

func (*SingularValueDecomposition) GetV 

func (s *SingularValueDecomposition) GetV() *Matrix

* Return the right singular vectors @return V

func (*SingularValueDecomposition) Norm2 

func (s *SingularValueDecomposition) Norm2() float64

* Two norm @return max(S)

func (*SingularValueDecomposition) Rank 

func (s *SingularValueDecomposition) Rank() int

* Effective numerical matrix rank @return Number of nonnegligible singular values.

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