mikera.matrixx.impl

Class IdentityMatrix

java.lang.Object

mikera.arrayz.impl.AbstractArray<AVector>

mikera.matrixx.AMatrix

mikera.matrixx.impl.ABandedMatrix

mikera.matrixx.impl.ASingleBandMatrix

mikera.matrixx.impl.ADiagonalMatrix

mikera.matrixx.impl.IdentityMatrix

All Implemented Interfaces:

java.io.Serializable, java.lang.Cloneable, java.lang.Comparable<INDArray>, java.lang.Iterable<AVector>, INDArray, ISparse, IMatrix, IFastBands, IFastColumns, IFastRows

public class IdentityMatrix
extends ADiagonalMatrix
implements IFastRows, IFastColumns

Specialised identity matrix class. Immutable.

See Also:

Serialized Form

Method Summary

Modifier and Type	Method and Description
AMatrix	addCopy(AMatrix m) Adds another matrix to this matrix, returning a new matrix
static IdentityMatrix	create(int i)
double	determinant() Calculates the determinant of the matrix.
double	diagonalProduct() Computes the product of entries on the main diagonal of a matrix
double	elementAbsPowSum(double p) Returns the sum of the absolute values of all the elements raised to a specified power
double	elementMax() Returns the maximum element value in this array.
double	elementMin() Returns the maximum element value in this array.
double	elementPowSum(double p) Returns the sum of all the elements raised to a specified power
double	elementSum() Returns the sum of all elements in this matrix
IdentityMatrix	exactClone() Creates a deep clone of an array, using the same class implementation as the original array
double	get(int i, int j) Returns the double value at the specified position in a 2D matrix
AxisVector	getColumn(int j) Returns a column of the matrix.
AxisVector	getColumnView(int column) Returns a column of the matrix as a vector view.
double	getDiagonalValue(int i)
AVector	getLeadingDiagonal() Returns a vector view of the leading diagonal values of the matrix
AxisVector	getRow(int i) Returns a row of the matrix.
AxisVector	getRowView(int row) Returns a row of the matrix as a vector view.
IdentityMatrix	getTransposeView() Returns a transposed view of the array.
boolean	hasUncountable() Checks to see if any element in the matrix is NaN of Infinite.
AMatrix	innerProduct(ADiagonalMatrix a) Computes the inner product of this matrix with another diagonal matrix of the same shape.
AMatrix	innerProduct(AMatrix a) Computes the inner product of this matrix with another.
AVector	innerProduct(AVector v) Computes the inner product of this array with a vector
AMatrix	inverse() Computes the inverse of a matrix.
boolean	isBoolean() Returns true if the array is boolean (contains only 0.0 or 1.0 values)
boolean	isIdentity() Checks if this is an identity matrix (i.e.
boolean	isMutable() Returns true if the INDArray is mutable (at least partially)
boolean	isOrthogonal() Check to see if the matrix is orthogonal (default tolerance: 1e-8)
boolean	isOrthogonal(double tolerance) Check to see if the matrix is orthogonal
boolean	isZero() Returns true if the matrix is the zero matrix (all components zero)
ScalarMatrix	multiplyCopy(double d) Returns a copy of the array with all elements multiplied by a single constant value
long	nonZeroCount() Returns the number of non-zero elements in the array.
int	rank() Calculate the rank of a matrix.
double	rowDotProduct(int i, AVector v) Returns the dot product of a specific row with a vector.
void	set(int row, int column, double value) Sets a value at a given position in a mutable 2D array
double	trace() Computes the trace of a matrix, i.e.
void	transform(AVector source, AVector dest) Transforms a source vector into a destination vector, using matrix multiplication (inner product).
void	transformInPlace(ADenseArrayVector v)
void	transformInPlace(AVector v)
double	unsafeGet(int i, int j) Gets an element in the matrix in an unsafe fashion, without performing bound checks The result is undefined if the row and column are out of bounds.
double	unsafeGetDiagonalValue(int i)

Methods inherited from class mikera.matrixx.impl.ADiagonalMatrix

addOuterProductSparse, addToArray, checkSquare, clone, columnCount, copyColumnTo, copyRowTo, dimensions, elementSquaredSum, equalsTranspose, getBand, getNonZeroBand, getTranspose, isDiagonal, isFullyMutable, isLowerTriangular, isRectangularDiagonal, isSameShape, isSameShape, isSquare, isSymmetric, isUpperTriangular, lowerBandwidthLimit, nonZeroBand, rowCount, setSparse, toDoubleArray, toMatrix, toMatrixTranspose, transform, transposeInnerProduct, transposeInPlace, upperBandwidthLimit, validate

Methods inherited from class mikera.matrixx.impl.ASingleBandMatrix

isSparse, subMatrix

Methods inherited from class mikera.matrixx.impl.ABandedMatrix

density, fill, lowerBandwidth, multiply, upperBandwidth

Methods inherited from class mikera.matrixx.AMatrix

abs, add, add, add, add, add2, addAt, addCopy, addCopy, addCopy, addCopy, addInnerProduct, addInnerProduct, addInnerProduct, addMultiple, addMultiple, addMultiple, addOuterProduct, addOuterProduct, addOuterProductSparse, addRowMultiple, addSparse, addSparse, applyOp, applyOp, applyOp, applyOp, applyOp, applyOp, applyOpCopy, asDoubleArray, asElementList, asVector, bandIndex, bandLength, bandPosition, bandStartColumn, bandStartRow, broadcast, broadcastCloneLike, broadcastCopyLike, broadcastLike, broadcastLike, checkColumn, checkRow, clamp, composeWith, copy, dense, denseClone, dimensionality, divide, divide, divide, divide, divideCopy, elementCount, elementIterator, elementsEqual, ensureMutable, epsilonEquals, epsilonEquals, epsilonEquals, equals, equals, equals, equalsArray, exp, get, get, get, get, getBandWrapped, getColumnClone, getColumns, getElement, getElements, getLongShape, getRowClone, getRows, getShape, getShape, getShapeClone, getSlices, getSlices, getSliceViews, getTransposeCopy, hashCode, hasOrthonormalColumns, hasOrthonormalRows, immutable, innerProduct, innerProduct, innerProduct, innerProduct, inputDimensions, isElementConstrained, isHermitian, isInvertible, isPositiveDefinite, isSameShape, isView, iterator, join, log, mul, multiply, multiply, multiply, multiplyRow, mutable, negate, outerProduct, outputDimensions, pow, reciprocal, reduce, reduce, reduceSlices, reduceSlices, reorder, reorder, replaceColumn, replaceRow, reshape, reshape, rotateView, scaleAdd, scaleAdd, set, set, set, set, set, set, set, set, setApplyOp, setApplyOp, setColumn, setElements, setElements, setMultiple, setMultiple, setMultiple, setMultiple, setMultiple, setRow, setSparse, setSparse, signum, slice, slice, sliceCount, sparse, sparseClone, sqrt, square, sub, sub, sub, subArray, subCopy, swapColumns, swapRows, toAffineTransform, toDoubleBuffer, toMutableMatrix, toNestedDoubleArrays, toSliceArray, toString, toStringFull, toVector, transposeInnerProduct, unsafeSet

Methods inherited from class mikera.arrayz.impl.AbstractArray

absCopy, absDiff, absDiffCopy, add, addApplyOp, addAt, addCopy, addInnerProduct, addInnerProduct, addMultipleSparse, addPower, addPower, addSparse, broadcastLike, compareTo, componentCount, divideCopy, elementMaxAbs, elementProduct, epsilonEquals, equals, equalsArray, get, get, get, get, getComponent, getComponents, getElements, getElements, getElements, isDense, join, multiplyCopy, negateCopy, reciprocalCopy, scale, scaleCopy, setElements, setInnerProduct, signumCopy, sliceValue, squareCopy, sub, sub, subCopy, withComponents

Methods inherited from class java.lang.Object

getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface mikera.matrixx.IMatrix

add2, addAt, addCopy, columnCount, getBand, getColumnClone, getColumns, getRowClone, getRows, getTranspose, innerProduct, isDiagonal, isInvertible, isRectangularDiagonal, isSquare, isSymmetric, rowCount, subMatrix, toNestedDoubleArrays, transposeInPlace

Methods inherited from interface mikera.arrayz.INDArray

abs, absCopy, absDiff, absDiffCopy, add, add, addApplyOp, addAt, addCopy, addCopy, addInnerProduct, addInnerProduct, addMultiple, addMultipleSparse, addOuterProduct, addOuterProductSparse, addPower, addPower, addSparse, addSparse, addToArray, applyOp, applyOp, applyOp, applyOp, applyOpCopy, asDoubleArray, asElementList, asVector, broadcast, broadcastCloneLike, broadcastCopyLike, broadcastLike, broadcastLike, broadcastLike, clamp, clone, componentCount, copy, dense, denseClone, dimensionality, divide, divide, divideCopy, divideCopy, elementCount, elementIterator, elementMaxAbs, elementProduct, elementsEqual, elementSquaredSum, ensureMutable, epsilonEquals, epsilonEquals, equals, equalsArray, equalsArray, exp, fill, get, get, get, get, get, get, get, get, getComponent, getComponents, getElement, getElements, getElements, getElements, getElements, getLongShape, getShape, getShape, getShapeClone, getSlices, getSlices, getSliceViews, getTransposeCopy, immutable, innerProduct, innerProduct, innerProduct, isDense, isElementConstrained, isFullyMutable, isSameShape, isSparse, isView, join, join, log, multiply, multiply, multiplyCopy, mutable, negate, negateCopy, outerProduct, pow, reciprocal, reciprocalCopy, reduce, reduce, reduceSlices, reduceSlices, reorder, reorder, reshape, rotateView, scale, scaleAdd, scaleAdd, scaleCopy, set, set, set, set, set, set, setApplyOp, setElements, setElements, setElements, setInnerProduct, setMultiple, setMultiple, setSparse, setSparse, signum, signumCopy, slice, slice, sliceCount, sliceValue, sparse, sparseClone, sqrt, square, squareCopy, sub, sub, subArray, subCopy, toDoubleArray, toDoubleBuffer, toSliceArray, toVector, validate, withComponents

Methods inherited from interface java.lang.Comparable

compareTo

Methods inherited from interface mikera.arrayz.ISparse

density

Methods inherited from interface java.lang.Iterable

forEach, spliterator

Method Detail

create

public static IdentityMatrix create(int i)

isMutable

public boolean isMutable()

Description copied from interface: INDArray

Returns true if the INDArray is mutable (at least partially)

Specified by:

isMutable in interface INDArray

Specified by:

isMutable in class ADiagonalMatrix

isBoolean

public boolean isBoolean()

Description copied from interface: INDArray

Returns true if the array is boolean (contains only 0.0 or 1.0 values)

Specified by:

isBoolean in interface INDArray

Overrides:

isBoolean in class ADiagonalMatrix

isZero

public boolean isZero()

Description copied from class: AMatrix

Returns true if the matrix is the zero matrix (all components zero)

Specified by:

isZero in interface INDArray

Overrides:

isZero in class ADiagonalMatrix

rowDotProduct

public double rowDotProduct(int i,
                            AVector v)

Description copied from class: AMatrix

Returns the dot product of a specific row with a vector. Unsafe operation: performs no bounds checking

Overrides:

rowDotProduct in class ADiagonalMatrix

Returns:

get

public double get(int i,
                  int j)

Description copied from interface: INDArray

Returns the double value at the specified position in a 2D matrix

Specified by:

get in interface INDArray

Specified by:

get in interface IMatrix

Specified by:

get in class AMatrix

unsafeGet

public double unsafeGet(int i,
                        int j)

Description copied from class: AMatrix

Gets an element in the matrix in an unsafe fashion, without performing bound checks The result is undefined if the row and column are out of bounds.

Overrides:

unsafeGet in class AMatrix

Returns:

getRow

public AxisVector getRow(int i)

Description copied from interface: IMatrix

Returns a row of the matrix. May or may not be a view, depending on matrix type. Intended for the fastest possible read access of the row. This often means a view, but might not be (e.g. getRow on a Matrix33 returns a Vector3).

Specified by:

getRow in interface IMatrix

Specified by:

getRow in interface IFastRows

Overrides:

getRow in class ADiagonalMatrix

getColumn

public AxisVector getColumn(int j)

Description copied from interface: IMatrix

Returns a column of the matrix. May or may not be a view, depending on matrix type. Intended for the fastest possible read access of the column. This often means a view, but might not be (e.g. getColumn on a Matrix33 returns a Vector3).

Specified by:

getColumn in interface IMatrix

Specified by:

getColumn in interface IFastColumns

Overrides:

getColumn in class ADiagonalMatrix

getRowView

public AxisVector getRowView(int row)

Description copied from interface: IMatrix

Returns a row of the matrix as a vector view. May be used to modify the original matrix.

Specified by:

getRowView in interface IMatrix

Overrides:

getRowView in class ABandedMatrix

getColumnView

public AxisVector getColumnView(int column)

Description copied from interface: IMatrix

Returns a column of the matrix as a vector view. May be used to modify the original matrix.

Specified by:

getColumnView in interface IMatrix

Overrides:

getColumnView in class AMatrix

getDiagonalValue

public double getDiagonalValue(int i)

Overrides:

getDiagonalValue in class ADiagonalMatrix

unsafeGetDiagonalValue

public double unsafeGetDiagonalValue(int i)

Overrides:

unsafeGetDiagonalValue in class ADiagonalMatrix

set

public void set(int row,
                int column,
                double value)

Description copied from interface: INDArray

Sets a value at a given position in a mutable 2D array

Specified by:

set in interface INDArray

Specified by:

set in interface IMatrix

Overrides:

set in class ADiagonalMatrix

transform

public void transform(AVector source,
                      AVector dest)

Description copied from interface: IMatrix

Transforms a source vector into a destination vector, using matrix multiplication (inner product). The destination vector is overwritten.

Specified by:

transform in interface IMatrix

Overrides:

transform in class AMatrix

transformInPlace

public void transformInPlace(AVector v)

Specified by:

transformInPlace in interface IMatrix

Overrides:

transformInPlace in class ADiagonalMatrix

transformInPlace

public void transformInPlace(ADenseArrayVector v)

Overrides:

transformInPlace in class ADiagonalMatrix

getLeadingDiagonal

public AVector getLeadingDiagonal()

Description copied from class: AMatrix

Returns a vector view of the leading diagonal values of the matrix

Specified by:

getLeadingDiagonal in class ADiagonalMatrix

Returns:

isIdentity

public boolean isIdentity()

Description copied from interface: IMatrix

Checks if this is an identity matrix (i.e. 1.0 in leading diagonal, 0.0 elsewhere)

Specified by:

isIdentity in interface IMatrix

Overrides:

isIdentity in class ADiagonalMatrix

Returns:

true if this matrix is a square identity matrix, false otherwise.

isOrthogonal

public boolean isOrthogonal()

Description copied from class: AMatrix

Check to see if the matrix is orthogonal (default tolerance: 1e-8)

Overrides:

isOrthogonal in class AMatrix

Returns:

isOrthogonal

public boolean isOrthogonal(double tolerance)

Description copied from class: AMatrix

Check to see if the matrix is orthogonal

Overrides:

isOrthogonal in class AMatrix

Parameters:

tolerance - inner product of a column with all of the next columns should be less than tolerance

Returns:

inverse

public AMatrix inverse()

Description copied from class: AMatrix

Computes the inverse of a matrix. Returns null if the matrix is singular. Throws an Exception is the matrix is not square

Specified by:

inverse in interface IMatrix

Overrides:

inverse in class AMatrix

Returns:

A matrix which is the inverse of this matrix, or null if the inverse does not exist.

determinant

public double determinant()

Description copied from class: AMatrix

Calculates the determinant of the matrix.

Overrides:

determinant in class ADiagonalMatrix

rank

public int rank()

Description copied from class: AMatrix

Calculate the rank of a matrix. This is equivalent to the maximum number of linearly independent rows or columns.

Overrides:

rank in class ADiagonalMatrix

nonZeroCount

public long nonZeroCount()

Description copied from interface: INDArray

Returns the number of non-zero elements in the array.

Specified by:

nonZeroCount in interface INDArray

Overrides:

nonZeroCount in class ADiagonalMatrix

elementSum

public double elementSum()

Description copied from class: AMatrix

Returns the sum of all elements in this matrix

Specified by:

elementSum in interface INDArray

Overrides:

elementSum in class ADiagonalMatrix

elementMin

public double elementMin()

Description copied from interface: INDArray

Returns the maximum element value in this array. Throws an error if there are no elements.

Specified by:

elementMin in interface INDArray

Overrides:

elementMin in class ADiagonalMatrix

elementMax

public double elementMax()

Description copied from interface: INDArray

Returns the maximum element value in this array. Throws an error if there are no elements.

Specified by:

elementMax in interface INDArray

Overrides:

elementMax in class ADiagonalMatrix

trace

public double trace()

Description copied from interface: IMatrix

Computes the trace of a matrix, i.e. the sum of all elements on the leading diagonal

Specified by:

trace in interface IMatrix

Overrides:

trace in class ADiagonalMatrix

Returns:

diagonalProduct

public double diagonalProduct()

Description copied from class: AMatrix

Computes the product of entries on the main diagonal of a matrix

Specified by:

diagonalProduct in interface IMatrix

Overrides:

diagonalProduct in class ADiagonalMatrix

Returns:

innerProduct

public AMatrix innerProduct(ADiagonalMatrix a)

Description copied from class: ADiagonalMatrix

Computes the inner product of this matrix with another diagonal matrix of the same shape. The result will be a diagnonal matrix of the same shape.

Overrides:

innerProduct in class ADiagonalMatrix

Returns:

innerProduct

public AMatrix innerProduct(AMatrix a)

Description copied from interface: IMatrix

Computes the inner product of this matrix with another. Equivalent to matrix x matrix multiplication

Specified by:

innerProduct in interface IMatrix

Overrides:

innerProduct in class ADiagonalMatrix

Returns:

innerProduct

public AVector innerProduct(AVector v)

Description copied from interface: INDArray

Computes the inner product of this array with a vector

Specified by:

innerProduct in interface INDArray

Specified by:

innerProduct in interface IMatrix

Overrides:

innerProduct in class AMatrix

Parameters:

v - A vector

Returns:

A new array representing the inner product

multiplyCopy

public ScalarMatrix multiplyCopy(double d)

Description copied from interface: INDArray

Returns a copy of the array with all elements multiplied by a single constant value

Specified by:

multiplyCopy in interface INDArray

Overrides:

multiplyCopy in class AMatrix

Parameters:

d - A scalar factor

Returns:

A new array, with all element values scaled by the given factor

addCopy

public AMatrix addCopy(AMatrix m)

Description copied from interface: IMatrix

Adds another matrix to this matrix, returning a new matrix

Specified by:

addCopy in interface IMatrix

Overrides:

addCopy in class ADiagonalMatrix

Returns:

getTransposeView

public IdentityMatrix getTransposeView()

Description copied from interface: INDArray

Returns a transposed view of the array. May throw UnsupportedOperationException if the array type does not support this capability

Specified by:

getTransposeView in interface INDArray

Specified by:

getTransposeView in interface IMatrix

Overrides:

getTransposeView in class ADiagonalMatrix

Returns:

the transpose of this matrix, as a view

exactClone

public IdentityMatrix exactClone()

Description copied from interface: INDArray

Creates a deep clone of an array, using the same class implementation as the original array

Specified by:

exactClone in interface INDArray

Specified by:

exactClone in class ADiagonalMatrix

Returns:

A clone of the original array

hasUncountable

public boolean hasUncountable()

Description copied from class: AMatrix

Checks to see if any element in the matrix is NaN of Infinite.

Specified by:

hasUncountable in interface INDArray

Overrides:

hasUncountable in class ADiagonalMatrix

Returns:

True if any element in the matrix is NaN of Infinite.

elementPowSum

public double elementPowSum(double p)

Returns the sum of all the elements raised to a specified power

Specified by:

elementPowSum in interface INDArray

Overrides:

elementPowSum in class ADiagonalMatrix

Returns:

elementAbsPowSum

public double elementAbsPowSum(double p)

Returns the sum of the absolute values of all the elements raised to a specified power

Specified by:

elementAbsPowSum in interface INDArray

Overrides:

elementAbsPowSum in class ADiagonalMatrix

Returns: