Class PositiveDefiniteMatrix

A subclass of Matrix with extra methods appropriate to positive-definite matrices.

Inheritance
Object
Matrix
PositiveDefiniteMatrix
Inherited Members
Namespace: Microsoft.ML.Probabilistic.Math
Assembly: Microsoft.ML.Probabilistic.dll
Syntax
[Serializable]
[DataContract]
public class PositiveDefiniteMatrix : Matrix, IList<double>, ICollection<double>, IReadOnlyList<double>, IReadOnlyCollection<double>, IEnumerable<double>, IEnumerable, ICloneable, SettableTo<Matrix>, CanSetAllElementsTo<double>

Constructors

PositiveDefiniteMatrix()

Default constructor just used for serialization.

Declaration
protected PositiveDefiniteMatrix()

PositiveDefiniteMatrix(Matrix)

Constructs a positive-definite matrix type which references an existing matrix.

Declaration
public PositiveDefiniteMatrix(Matrix A)
Parameters
Type Name Description
Matrix A

A positive-definite matrix.
Remarks

This method is similar to a typecast, except it creates a new wrapper around the matrix.

PositiveDefiniteMatrix(Double[,])

Constructs a matrix from data in a 2D array.

Declaration
[Construction(new string[]{"ToArray"})]
public PositiveDefiniteMatrix(double[, ] data)
Parameters
Type Name Description
Double[,] data

2D array of elements.
Remarks

The 2D array is copied into new storage. The size of the matrix is taken from the array.

PositiveDefiniteMatrix(Int32, Int32)

Constructs a zero matrix of the given dimensions.

Declaration
public PositiveDefiniteMatrix(int rows, int cols)
Parameters
Type Name Description
Int32 rows

Number of rows >= 0.
Int32 cols

Number of columns >= 0.

PositiveDefiniteMatrix(Int32, Int32, Double[])

Constructs a matrix by referencing an array.

Declaration
public PositiveDefiniteMatrix(int rows, int cols, double[] data)
Parameters
Type Name Description
Int32 rows

Number of rows.
Int32 cols

Number of columns.
Double[] data

Storage for the matrix elements.

Methods

CholeskyInPlace(out Boolean)

Gets the Cholesky decomposition of the matrix (L*L' = A), replacing its contents.

Declaration
public LowerTriangularMatrix CholeskyInPlace(out bool isPosDef)
Parameters
Type Name Description
Boolean isPosDef

True if this is positive definite, otherwise false.
Returns
Type Description
LowerTriangularMatrix

The Cholesky decomposition L. If this is positive semidefinite, then L will satisfy LL' = A. Otherwise, L will only approximately satisfy LL' = A.
Remarks

this must be symmetric, but need not be positive definite.

Clone()

Creates a full clone of this positive-definite matrix

Declaration
public override object Clone()
Returns
Type Description
Object
Overrides

Determinant()

Returns the determinant of this positive-definite matrix.

Declaration
public double Determinant()
Returns
Type Description
Double

The determinant of this.
Remarks

Throws a MatrixSingularException if the matrix is singular.

Identity(Int32)

Creates a positive-definite identity matrix of a given dimension

Declaration
public static PositiveDefiniteMatrix Identity(int dimension)
Parameters
Type Name Description
Int32 dimension
Returns
Type Description
PositiveDefiniteMatrix

IdentityScaledBy(Int32, Double)

Creates a positive-definite identity matrix of a given dimension, scaled by a given value

Declaration
public static PositiveDefiniteMatrix IdentityScaledBy(int dimension, double scale)
Parameters
Type Name Description
Int32 dimension
Double scale
Returns
Type Description
PositiveDefiniteMatrix

Inverse()

Returns the inverse of a positive-definite matrix.

Declaration
public PositiveDefiniteMatrix Inverse()
Returns
Type Description
PositiveDefiniteMatrix

A new matrix which is the inverse of this
Remarks

Because this is positive definite, it must be invertible, so this routine never throws MatrixSingularException.

Exceptions
Type Condition
PositiveDefiniteMatrixException

If this is not positive definite.

LogDeterminant(LowerTriangularMatrix, Boolean)

Returns the natural logarithm of the determinant of this positive-definite matrix where a lower triangular workspace is passed in.

Declaration
public double LogDeterminant(LowerTriangularMatrix L, bool ignoreInfinity = false)
Parameters
Type Name Description
LowerTriangularMatrix L

A temporary workspace, same size as this.
Boolean ignoreInfinity

If true, +infinity on the diagonal is treated as 1.
Returns
Type Description
Double

The log-determinant.
Remarks

Throws a MatrixSingularException if the matrix is singular.

LogDeterminant(Boolean)

Returns the natural logarithm of the determinant of this positive-definite matrix.

Declaration
public double LogDeterminant(bool ignoreInfinity = false)
Parameters
Type Name Description
Boolean ignoreInfinity

If true, +infinity on the diagonal is treated as 1.
Returns
Type Description
Double

The log-determinant of this.

SetToInverse(PositiveDefiniteMatrix)

Sets this positive-definite matrix to inverse of a given positive-definite matrix.

Declaration
public PositiveDefiniteMatrix SetToInverse(PositiveDefiniteMatrix A)
Parameters
Type Name Description
PositiveDefiniteMatrix A

A symmetric positive-definite matrix, same size as this. Can be the same object as this.
Returns
Type Description
PositiveDefiniteMatrix

this
Exceptions
Type Condition
PositiveDefiniteMatrixException

If A is not positive definite.

SetToInverse(PositiveDefiniteMatrix, LowerTriangularMatrix)

Sets this positive-definite matrix to inverse of a given positive-definite matrix where a lower triangular workspace is passed.

Declaration
public PositiveDefiniteMatrix SetToInverse(PositiveDefiniteMatrix A, LowerTriangularMatrix L)
Parameters
Type Name Description
PositiveDefiniteMatrix A

A symmetric positive-definite matrix, same size as this. Can be the same object as this.
LowerTriangularMatrix L

A workspace, same size as A.
Returns
Type Description
PositiveDefiniteMatrix

this
Exceptions
Type Condition
PositiveDefiniteMatrixException

If A is not positive definite.

SetToSum(PositiveDefiniteMatrix, PositiveDefiniteMatrix)

Sets this positive-definite matrix to the sum of two positive-definite matrices. Assumes compatible matrices

Declaration
public PositiveDefiniteMatrix SetToSum(PositiveDefiniteMatrix a, PositiveDefiniteMatrix b)
Parameters
Type Name Description
PositiveDefiniteMatrix a

First matrix, which must have the same size as this.
PositiveDefiniteMatrix b

Second matrix, which must have the same size as this.
Returns
Type Description
PositiveDefiniteMatrix

this
Remarks

this receives the sum, and must already be the correct size. a and/or b may be the same object as this. If this and a/b occupy distinct yet overlapping portions of the same source array, the results are undefined.

Operators

Addition(PositiveDefiniteMatrix, PositiveDefiniteMatrix)

Add two positive-definite matrices.

Declaration
public static PositiveDefiniteMatrix operator +(PositiveDefiniteMatrix a, PositiveDefiniteMatrix b)
Parameters
Type Name Description
PositiveDefiniteMatrix a

First matrix.
PositiveDefiniteMatrix b

Second matrix.
Returns
Type Description
PositiveDefiniteMatrix

Their sum.

Division(PositiveDefiniteMatrix, Double)

Divide matrix by scalar

Declaration
public static PositiveDefiniteMatrix operator /(PositiveDefiniteMatrix a, double b)
Parameters
Type Name Description
PositiveDefiniteMatrix a
Double b
Returns
Type Description
PositiveDefiniteMatrix

A new matrix with entry [i,j] equal to a[i,j]/b

Multiply(PositiveDefiniteMatrix, Double)

Multiply matrix times scalar

Declaration
public static PositiveDefiniteMatrix operator *(PositiveDefiniteMatrix a, double b)
Parameters
Type Name Description
PositiveDefiniteMatrix a
Double b
Returns
Type Description
PositiveDefiniteMatrix

A new matrix with entry [i,j] equal to a[i,j]*b

Multiply(Double, PositiveDefiniteMatrix)

Multiply matrix times scalar

Declaration
public static PositiveDefiniteMatrix operator *(double a, PositiveDefiniteMatrix b)
Parameters
Type Name Description
Double a
PositiveDefiniteMatrix b
Returns
Type Description
PositiveDefiniteMatrix

A new matrix with entry [i,j] equal to a*b[i,j]

Implements

Extension Methods