mikera.matrixx.impl
Class ZeroMatrix
- java.lang.Object
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- mikera.arrayz.impl.AbstractArray<AVector>
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- mikera.matrixx.AMatrix
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- mikera.matrixx.impl.ARectangularMatrix
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- mikera.matrixx.impl.ZeroMatrix
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- All Implemented Interfaces:
- java.io.Serializable, java.lang.Cloneable, java.lang.Comparable<INDArray>, java.lang.Iterable<AVector>, INDArray, ISparse, IMatrix, IFastColumns, IFastRows
public final class ZeroMatrix extends ARectangularMatrix implements IFastRows, IFastColumns, ISparse
Lightweight, sparse immutable zero matrix class. Can be any shape, including empty shapes.- See Also:
- Serialized Form
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Method Summary
All Methods Static Methods Instance Methods Concrete Methods Modifier and Type Method and Description AMatrixaddCopy(AMatrix a)Adds another matrix to this matrix, returning a new matrixvoidaddSparse(double c)Adds to the non-sparse elements of this arrayvoidaddToArray(double[] dest, int offset)Adds all the elements of this array to a double array at the specified offset, in row-major orderAVectorasVector()Returns the matrix values as a single reference Vector in the form [row0 row1 row2....]AMatrixclone()Returns a clone of the array data, as a new array which will be fully mutable and may be of a different class to the original.voidcopyColumnTo(int col, double[] dest, int destOffset)Copies the elements in a selected row of this matrix to a double arrayvoidcopyRowTo(int row, double[] dest, int destOffset)Copies the elements in a selected row of this matrix to a double arraystatic ZeroMatrixcreate(int rows, int columns)Create a ZeroMatrix of the specified sizedoubledeterminant()Calculates the determinant of the matrix.doublediagonalProduct()Computes the product of entries on the main diagonal of a matrixdoubleelementAbsPowSum(double p)Returns the sum of the absolute values of all the elements raised to a specified powerjava.util.Iterator<java.lang.Double>elementIterator()Returns an iterator over all elements in this array, in row-major orderdoubleelementMax()Returns the maximum element value in this array.doubleelementMin()Returns the maximum element value in this array.doubleelementPowSum(double p)Returns the sum of all the elements raised to a specified powerdoubleelementSum()Returns the sum of all elements in this matrixbooleanequals(AMatrix m)Returns true if this matrix is exactly equal to another matrixbooleanequalsArray(double[] data, int offset)Returns true if the elements in this array exactly match the elements in the given array, in row-major orderZeroMatrixexactClone()Creates a deep clone of an array, using the same class implementation as the original arraydoubleget(int i, int j)Returns the double value at the specified position in a 2D matrixAVectorgetBand(int band)Gets a specific band of the matrix, as a view vector.AVectorgetColumnClone(int col)Returns a column of the matrix as a new cloned, mutable vector The cloned column may be modified without affecting the original matrix.AVectorgetColumnView(int col)Returns a column of the matrix as a vector view.voidgetElements(double[] dest, int destOffset)Copies all elements of this array a double array at the specified offsetAVectorgetLeadingDiagonal()Returns a vector view of the leading diagonal values of the matrixAVectorgetRowClone(int row)Returns a row of the matrix as a new cloned, mutable vector.AVectorgetRowView(int row)Returns a row of the matrix as a vector view.ZeroMatrixgetTranspose()Returns the transpose of this array.ZeroMatrixgetTransposeView()Returns a transposed view of the array.inthashCode()booleanhasUncountable()Checks to see if any element in the matrix is NaN of Infinite.AMatrixinnerProduct(AMatrix m)Computes the inner product of this matrix with another.booleanisBoolean()Returns true if the array is boolean (contains only 0.0 or 1.0 values)booleanisDiagonal()Returns true iff this matrix is a square diagonal matrixbooleanisFullyMutable()If this method returns true, the INDArray is guaranteed to be fully mutable in all positions i.e.booleanisInvertible()Checks if this is an invertible matrix (i.e.booleanisLowerTriangular()Returns true if a matrix is lower triangular.booleanisMutable()Returns true if the INDArray is mutable (at least partially)booleanisSparse()Returns true if the array is in a sparse formatbooleanisSymmetric()Returns true if a matrix is symmetricbooleanisUpperTriangular()Returns true if a matrix is upper triangular An upper triangular matrix is defined as having all elements equal to 0.0 where i > jbooleanisZero()Returns true if the matrix is the zero matrix (all components zero)intlowerBandwidthLimit()A limit on the lower bandwidth of the banded matrix.voidmultiply(AMatrix m)Multiplies this matrix in-place by another in an entrywise manner (Hadamard product).ZeroMatrixmultiplyCopy(double a)Returns a copy of the array with all elements multiplied by a single constant valuelongnonZeroCount()Returns the number of non-zero elements in the array.intrank()Calculate the rank of a matrix.doublereduce(Op2 op)Reduces over all elements of the array in row-major order.doublereduce(Op2 op, double init)Reduces over all elements of the array in row-major order.doublerowDotProduct(int i, AVector v)Returns the dot product of a specific row with a vector.voidsetSparse(AMatrix a)Sets the non-sparse elements in this matrix to the corresponding values in the source matrixAMatrixsparseClone()Creates a fully mutable clone of this array.AMatrixsubMatrix(int rowStart, int rows, int colStart, int cols)Gets a rectangular submatrix view of part of a matrixdouble[]toDoubleArray()Copies the elements of this array to a new double[] array.MatrixtoMatrix()Coerces the matrix to the standard mutable Matrix type in row major order.MatrixtoMatrixTranspose()Coerces the transpose of a matrix to the standard mutable Matrix type in row major order.doubletrace()Computes the trace of a matrix, i.e.voidtransform(AVector input, AVector output)Transforms a source vector into a destination vector, using matrix multiplication (inner product).voidtransform(Vector input, Vector output)doubleunsafeGet(int row, int column)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.voidunsafeSet(int row, int column, double value)Sets an element value in the matrix in an unsafe fashion, without performing bound checks The result is undefined if the row and column are out of bounds.intupperBandwidthLimit()A limit on the upper bandwidth of the banded matrix.-
Methods inherited from class mikera.matrixx.impl.ARectangularMatrix
bandLength, checkColumn, checkRow, checkSquare, columnCount, elementCount, getElement, getShape, getShape, getShapeClone, isSameShape, isSameShape, isSameShape, isSquare, rowCount, set
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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, addOuterProductSparse, addRowMultiple, addSparse, addSparse, applyOp, applyOp, applyOp, applyOp, applyOp, applyOp, applyOpCopy, asDoubleArray, asElementList, bandIndex, bandPosition, bandStartColumn, bandStartRow, broadcast, broadcastCloneLike, broadcastCopyLike, broadcastLike, broadcastLike, clamp, composeWith, copy, dense, denseClone, dimensionality, divide, divide, divide, divide, divideCopy, elementsEqual, elementSquaredSum, ensureMutable, epsilonEquals, epsilonEquals, epsilonEquals, equals, equals, equalsTranspose, exp, fill, get, get, get, get, getBandWrapped, getColumn, getColumns, getLongShape, getRow, getRows, getSlices, getSlices, getSliceViews, getTransposeCopy, hasOrthonormalColumns, hasOrthonormalRows, immutable, innerProduct, innerProduct, innerProduct, innerProduct, innerProduct, inputDimensions, inverse, isElementConstrained, isHermitian, isIdentity, isOrthogonal, isOrthogonal, isPositiveDefinite, isRectangularDiagonal, isView, iterator, join, log, lowerBandwidth, mul, multiply, multiply, multiply, multiplyRow, mutable, negate, outerProduct, outputDimensions, pow, reciprocal, 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, signum, slice, slice, sliceCount, sparse, sqrt, square, sub, sub, sub, subArray, subCopy, swapColumns, swapRows, toAffineTransform, toDoubleBuffer, toMutableMatrix, toNestedDoubleArrays, toSliceArray, toString, toStringFull, toVector, transformInPlace, transformInPlace, transposeInnerProduct, transposeInnerProduct, transposeInPlace, upperBandwidth, validate
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Methods inherited from class mikera.arrayz.impl.AbstractArray
absCopy, absDiff, absDiffCopy, add, addApplyOp, addAt, addCopy, addInnerProduct, addInnerProduct, addMultipleSparse, addPower, addPower, broadcastLike, compareTo, componentCount, density, divideCopy, elementMaxAbs, elementProduct, epsilonEquals, equals, equalsArray, get, get, get, get, getComponent, getComponents, getElements, getElements, getElements, isDense, join, multiplyCopy, negateCopy, reciprocalCopy, scale, scaleCopy, setElements, setInnerProduct, setSparse, signumCopy, sliceValue, squareCopy, sub, sub, subCopy, withComponents
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Methods inherited from interface mikera.matrixx.impl.IFastColumns
getColumn
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Methods inherited from interface mikera.matrixx.IMatrix
add2, addAt, addCopy, columnCount, getColumns, getRows, innerProduct, innerProduct, inverse, isIdentity, isRectangularDiagonal, isSquare, rowCount, set, toNestedDoubleArrays, transformInPlace, transposeInPlace
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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, applyOp, applyOp, applyOp, applyOp, applyOpCopy, asDoubleArray, asElementList, broadcast, broadcastCloneLike, broadcastCopyLike, broadcastLike, broadcastLike, broadcastLike, clamp, componentCount, copy, dense, denseClone, dimensionality, divide, divide, divideCopy, divideCopy, elementCount, elementMaxAbs, elementProduct, elementsEqual, elementSquaredSum, ensureMutable, epsilonEquals, epsilonEquals, equals, equalsArray, exp, fill, get, get, get, get, get, get, get, get, getComponent, getComponents, getElement, getElements, getElements, getElements, getLongShape, getShape, getShape, getShapeClone, getSlices, getSlices, getSliceViews, getTransposeCopy, immutable, innerProduct, innerProduct, innerProduct, isDense, isElementConstrained, isSameShape, isView, join, join, log, multiply, multiply, multiplyCopy, mutable, negate, negateCopy, outerProduct, pow, reciprocal, reciprocalCopy, 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, sqrt, square, squareCopy, sub, sub, subArray, subCopy, toDoubleBuffer, toSliceArray, toVector, validate, withComponents
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Method Detail
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isFullyMutable
public boolean isFullyMutable()
Description copied from interface:INDArrayIf this method returns true, the INDArray is guaranteed to be fully mutable in all positions i.e. every position can store any valid double value- Specified by:
isFullyMutablein interfaceINDArray- Specified by:
isFullyMutablein classAMatrix
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create
public static ZeroMatrix create(int rows, int columns)
Create a ZeroMatrix of the specified size- Parameters:
rows-columns-- Returns:
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isSparse
public boolean isSparse()
Description copied from interface:INDArrayReturns true if the array is in a sparse format- Specified by:
isSparsein interfaceINDArray- Overrides:
isSparsein classAbstractArray<AVector>
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isMutable
public boolean isMutable()
Description copied from interface:INDArrayReturns true if the INDArray is mutable (at least partially)
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isSymmetric
public boolean isSymmetric()
Description copied from class:AMatrixReturns true if a matrix is symmetric- Specified by:
isSymmetricin interfaceIMatrix- Overrides:
isSymmetricin classAMatrix- Returns:
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isDiagonal
public boolean isDiagonal()
Description copied from interface:IMatrixReturns true iff this matrix is a square diagonal matrix- Specified by:
isDiagonalin interfaceIMatrix- Overrides:
isDiagonalin classAMatrix
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isUpperTriangular
public boolean isUpperTriangular()
Description copied from class:AMatrixReturns true if a matrix is upper triangular An upper triangular matrix is defined as having all elements equal to 0.0 where i > j- Overrides:
isUpperTriangularin classAMatrix
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isLowerTriangular
public boolean isLowerTriangular()
Description copied from class:AMatrixReturns true if a matrix is lower triangular. A lower triangular matrix is defined as having all elements equal to 0.0 where i < j- Overrides:
isLowerTriangularin classAMatrix
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isBoolean
public boolean isBoolean()
Description copied from interface:INDArrayReturns true if the array is boolean (contains only 0.0 or 1.0 values)
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upperBandwidthLimit
public int upperBandwidthLimit()
Description copied from class:AMatrixA limit on the upper bandwidth of the banded matrix. Actual upper bandwidth is guaranteed to be less than or equal to this value. Implementation should be O(1).- Overrides:
upperBandwidthLimitin classAMatrix- Returns:
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lowerBandwidthLimit
public int lowerBandwidthLimit()
Description copied from class:AMatrixA limit on the lower bandwidth of the banded matrix. Actual lower bandwidth is guaranteed to be less than or equal to this value. Implementation should be O(1).- Overrides:
lowerBandwidthLimitin classAMatrix- Returns:
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getRowView
public AVector getRowView(int row)
Description copied from interface:IMatrixReturns a row of the matrix as a vector view. May be used to modify the original matrix.- Specified by:
getRowViewin interfaceIMatrix- Overrides:
getRowViewin classAMatrix
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getColumnView
public AVector getColumnView(int col)
Description copied from interface:IMatrixReturns a column of the matrix as a vector view. May be used to modify the original matrix.- Specified by:
getColumnViewin interfaceIMatrix- Overrides:
getColumnViewin classAMatrix
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getRowClone
public AVector getRowClone(int row)
Description copied from interface:IMatrixReturns a row of the matrix as a new cloned, mutable vector. The cloned row may be modified without affecting the original matrix.- Specified by:
getRowClonein interfaceIMatrix- Overrides:
getRowClonein classAMatrix
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getColumnClone
public AVector getColumnClone(int col)
Description copied from interface:IMatrixReturns a column of the matrix as a new cloned, mutable vector The cloned column may be modified without affecting the original matrix.- Specified by:
getColumnClonein interfaceIMatrix- Overrides:
getColumnClonein classAMatrix
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copyRowTo
public void copyRowTo(int row, double[] dest, int destOffset)Description copied from class:AMatrixCopies the elements in a selected row of this matrix to a double array
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copyColumnTo
public void copyColumnTo(int col, double[] dest, int destOffset)Description copied from class:AMatrixCopies the elements in a selected row of this matrix to a double array- Overrides:
copyColumnToin classAMatrixdest- Destination double[] array
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addToArray
public void addToArray(double[] dest, int offset)Description copied from interface:INDArrayAdds all the elements of this array to a double array at the specified offset, in row-major order- Specified by:
addToArrayin interfaceINDArray- Overrides:
addToArrayin classAMatrix
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addSparse
public void addSparse(double c)
Description copied from interface:INDArrayAdds to the non-sparse elements of this array- Specified by:
addSparsein interfaceINDArray- Overrides:
addSparsein classAbstractArray<AVector>
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setSparse
public void setSparse(AMatrix a)
Description copied from class:AMatrixSets the non-sparse elements in this matrix to the corresponding values in the source matrix
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reduce
public double reduce(Op2 op, double init)
Description copied from interface:INDArrayReduces over all elements of the array in row-major order. Applies the operator to the initial/previous result at each step. Returns the final result.
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reduce
public double reduce(Op2 op)
Description copied from interface:INDArrayReduces over all elements of the array in row-major order. Applies the operator to the previous result at each step. Returns the final result.
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addCopy
public AMatrix addCopy(AMatrix a)
Description copied from interface:IMatrixAdds another matrix to this matrix, returning a new matrix
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getElements
public void getElements(double[] dest, int destOffset)Description copied from interface:INDArrayCopies all elements of this array a double array at the specified offset- Specified by:
getElementsin interfaceINDArray- Overrides:
getElementsin classAMatrix
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determinant
public double determinant()
Description copied from class:AMatrixCalculates the determinant of the matrix.- Overrides:
determinantin classAMatrix
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rank
public int rank()
Description copied from class:AMatrixCalculate the rank of a matrix. This is equivalent to the maximum number of linearly independent rows or columns.
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trace
public double trace()
Description copied from interface:IMatrixComputes the trace of a matrix, i.e. the sum of all elements on the leading diagonal
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diagonalProduct
public double diagonalProduct()
Description copied from class:AMatrixComputes the product of entries on the main diagonal of a matrix- Specified by:
diagonalProductin interfaceIMatrix- Overrides:
diagonalProductin classAMatrix- Returns:
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rowDotProduct
public double rowDotProduct(int i, AVector v)Description copied from class:AMatrixReturns the dot product of a specific row with a vector. Unsafe operation: performs no bounds checking- Overrides:
rowDotProductin classAMatrix- Returns:
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get
public double get(int i, int j)Description copied from interface:INDArrayReturns the double value at the specified position in a 2D matrix
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unsafeGet
public double unsafeGet(int row, int column)Description copied from class:AMatrixGets 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.
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unsafeSet
public void unsafeSet(int row, int column, double value)Description copied from class:AMatrixSets an element value in the matrix in an unsafe fashion, without performing bound checks The result is undefined if the row and column are out of bounds.
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clone
public AMatrix clone()
Description copied from interface:INDArrayReturns a clone of the array data, as a new array which will be fully mutable and may be of a different class to the original. Clone should attempt to return the most efficient possible array type. Clone should preserve sparsity property where possible, but this is not guaranteed.
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isZero
public boolean isZero()
Description copied from class:AMatrixReturns true if the matrix is the zero matrix (all components zero)
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elementSum
public double elementSum()
Description copied from class:AMatrixReturns the sum of all elements in this matrix- Specified by:
elementSumin interfaceINDArray- Overrides:
elementSumin classAMatrix
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elementMax
public double elementMax()
Description copied from interface:INDArrayReturns the maximum element value in this array. Throws an error if there are no elements.- Specified by:
elementMaxin interfaceINDArray- Overrides:
elementMaxin classAbstractArray<AVector>
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elementMin
public double elementMin()
Description copied from interface:INDArrayReturns the maximum element value in this array. Throws an error if there are no elements.- Specified by:
elementMinin interfaceINDArray- Overrides:
elementMinin classAbstractArray<AVector>
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nonZeroCount
public long nonZeroCount()
Description copied from interface:INDArrayReturns the number of non-zero elements in the array.- Specified by:
nonZeroCountin interfaceINDArray- Overrides:
nonZeroCountin classAMatrix
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transform
public void transform(AVector input, AVector output)
Description copied from interface:IMatrixTransforms a source vector into a destination vector, using matrix multiplication (inner product). The destination vector is overwritten.
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isInvertible
public boolean isInvertible()
Description copied from interface:IMatrixChecks if this is an invertible matrix (i.e. a square matrix with a non-zero determinant)- Specified by:
isInvertiblein interfaceIMatrix- Overrides:
isInvertiblein classAMatrix- Returns:
- true if invertible, false otherwise
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asVector
public AVector asVector()
Description copied from class:AMatrixReturns the matrix values as a single reference Vector in the form [row0 row1 row2....]
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innerProduct
public AMatrix innerProduct(AMatrix m)
Description copied from interface:IMatrixComputes the inner product of this matrix with another. Equivalent to matrix x matrix multiplication- Specified by:
innerProductin interfaceIMatrix- Overrides:
innerProductin classAMatrix- Returns:
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multiplyCopy
public ZeroMatrix multiplyCopy(double a)
Description copied from interface:INDArrayReturns a copy of the array with all elements multiplied by a single constant value- Specified by:
multiplyCopyin interfaceINDArray- Overrides:
multiplyCopyin classAMatrix- Parameters:
a- A scalar factor- Returns:
- A new array, with all element values scaled by the given factor
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multiply
public void multiply(AMatrix m)
Description copied from class:AMatrixMultiplies this matrix in-place by another in an entrywise manner (Hadamard product).
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equals
public boolean equals(AMatrix m)
Description copied from class:AMatrixReturns true if this matrix is exactly equal to another matrix
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equalsArray
public boolean equalsArray(double[] data, int offset)Description copied from interface:INDArrayReturns true if the elements in this array exactly match the elements in the given array, in row-major order- Specified by:
equalsArrayin interfaceINDArray- Overrides:
equalsArrayin classAMatrix- Parameters:
data- Array of double element values to check for equalityoffset- Offset into the data array- Returns:
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getTranspose
public ZeroMatrix getTranspose()
Description copied from interface:INDArrayReturns the transpose of this array. A transpose of an array is equivalent to reversing the order of dimensions. May or may not return a view depending on the array type.- Specified by:
getTransposein interfaceINDArray- Specified by:
getTransposein interfaceIMatrix- Overrides:
getTransposein classAMatrix- Returns:
- the transpose of this matrix
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getTransposeView
public ZeroMatrix getTransposeView()
Description copied from interface:INDArrayReturns a transposed view of the array. May throw UnsupportedOperationException if the array type does not support this capability- Specified by:
getTransposeViewin interfaceINDArray- Specified by:
getTransposeViewin interfaceIMatrix- Overrides:
getTransposeViewin classAMatrix- Returns:
- the transpose of this matrix, as a view
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toMatrix
public Matrix toMatrix()
Description copied from class:AMatrixCoerces the matrix to the standard mutable Matrix type in row major order. Performs a copy if necessary.
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toDoubleArray
public double[] toDoubleArray()
Description copied from interface:INDArrayCopies the elements of this array to a new double[] array.- Specified by:
toDoubleArrayin interfaceINDArray- Overrides:
toDoubleArrayin classAMatrix
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sparseClone
public AMatrix sparseClone()
Description copied from interface:INDArrayCreates a fully mutable clone of this array. Will use a sparse format if possible.- Specified by:
sparseClonein interfaceINDArray- Overrides:
sparseClonein classAMatrix
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toMatrixTranspose
public Matrix toMatrixTranspose()
Description copied from class:AMatrixCoerces the transpose of a matrix to the standard mutable Matrix type in row major order. Performs a copy if necessary.- Overrides:
toMatrixTransposein classAMatrix
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getLeadingDiagonal
public AVector getLeadingDiagonal()
Description copied from class:AMatrixReturns a vector view of the leading diagonal values of the matrix- Overrides:
getLeadingDiagonalin classAMatrix- Returns:
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getBand
public AVector getBand(int band)
Description copied from class:AMatrixGets a specific band of the matrix, as a view vector. The band is truncated at the edges of the matrix, i.e. it does not wrap around the matrix.
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subMatrix
public AMatrix subMatrix(int rowStart, int rows, int colStart, int cols)
Description copied from interface:IMatrixGets a rectangular submatrix view of part of a matrix
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elementIterator
public java.util.Iterator<java.lang.Double> elementIterator()
Description copied from interface:INDArrayReturns an iterator over all elements in this array, in row-major order- Specified by:
elementIteratorin interfaceINDArray- Overrides:
elementIteratorin classAMatrix
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exactClone
public ZeroMatrix exactClone()
Description copied from interface:INDArrayCreates a deep clone of an array, using the same class implementation as the original array- Specified by:
exactClonein interfaceINDArray- Specified by:
exactClonein classAMatrix- Returns:
- A clone of the original array
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hasUncountable
public boolean hasUncountable()
Description copied from class:AMatrixChecks to see if any element in the matrix is NaN of Infinite.- Specified by:
hasUncountablein interfaceINDArray- Overrides:
hasUncountablein classAMatrix- Returns:
- True if any element in the matrix is NaN of Infinite.
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elementPowSum
public double elementPowSum(double p)
Returns the sum of all the elements raised to a specified power- Specified by:
elementPowSumin interfaceINDArray- Overrides:
elementPowSumin classAbstractArray<AVector>- Returns:
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elementAbsPowSum
public double elementAbsPowSum(double p)
Returns the sum of the absolute values of all the elements raised to a specified power- Specified by:
elementAbsPowSumin interfaceINDArray- Overrides:
elementAbsPowSumin classAbstractArray<AVector>- Returns:
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