Class AbstractCsrRingMatrix<T extends AbstractCsrRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,?,U,W>,W extends Ring<W>>

java.lang.Object

org.flag4j.arrays.backend.AbstractTensor<T,W[],W>

org.flag4j.arrays.backend.semiring_arrays.AbstractCsrSemiringMatrix<T,U,V,W>

org.flag4j.arrays.backend.ring_arrays.AbstractCsrRingMatrix<T,U,V,W>

Type Parameters:

T - Type of this CSR field matrix.

U - Type of dense field matrix equivalent to T.

V - Type of vector equivalent to V.

Y - Type of field element of this matrix.

All Implemented Interfaces:

Serializable, MatrixMixin<T,U,V,W>, RingTensorMixin<T,U,W>, TensorOverRing<T,U,W[],W>, SemiringTensorMixin<T,U,W>, TensorOverSemiring<T,U,W[],W>

Direct Known Subclasses:

AbstractCsrFieldMatrix, CsrRingMatrix

public abstract class AbstractCsrRingMatrix<T extends AbstractCsrRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,?,U,W>,W extends Ring<W>>
extends AbstractCsrSemiringMatrix<T,U,V,W>
implements RingTensorMixin<T,U,W>, MatrixMixin<T,U,V,W>

A sparse matrix stored in compressed sparse row (CSR) format. The AbstractTensor.data of this CSR matrix are elements of a Ring.

The non-zero data and non-zero indices of a CSR matrix are mutable but the AbstractTensor.shape and total number of non-zero data is fixed.

Sparse matrices allow for the efficient storage of and ops on matrices that contain many zero values.

A sparse CSR matrix is stored as:

• The full shape of the matrix.
• The non-zero AbstractTensor.data of the matrix. All other data in the matrix are assumed to be zero. Zero values can also explicitly be stored in AbstractTensor.data.
• The row pointers of the non-zero values in the CSR matrix. Has size numRows + 1

rowPointers[i] indicates the starting index within data and colData of all values in row i.

• The column indices of the non-zero values in the sparse matrix.

Note: many ops assume that the data of the CSR matrix are sorted lexicographically by the row and column indices. (i.e.) by row indices first then column indices. However, this is not explicitly verified. Any ops implemented in this class will preserve the lexicographical sorting.

If indices need to be sorted, call AbstractCsrSemiringMatrix.sortIndices().

See Also:

• Serialized Form

Field Summary

Fields inherited from class org.flag4j.arrays.backend.semiring_arrays.AbstractCsrSemiringMatrix

colIndices, nnz, numCols, numRows, rowPointers, sparsity, zeroElement

Fields inherited from class org.flag4j.arrays.backend.AbstractTensor

data, rank, shape

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	AbstractCsrRingMatrix(Shape shape, W[] entries, int[] rowPointers, int[] colIndices)	Creates a sparse CSR matrix with the specified shape, non-zero data, row pointers, and non-zero column indices.

Method Summary

Modifier and Type	Method	Description
boolean	allClose(T b)	Checks if two sparse CSR ring matrices are element-wise equal within the following tolerance for two entries x and y:
boolean	allClose(T b, double relRol, double absTol)	Checks if two matrices are element-wise equal within the tolerance specified by relTol and absTol.
T	div(T b)	Warning: throws UnsupportedOperationException as division is not defined for general ring matrices.
T	H()	Computes the Hermitian transpose of this matrix.
T	H(int... axes)	Computes the conjugate transpose of this tensor.
T	H(int axis1, int axis2)	Computes the conjugate transpose of a tensor by conjugating and exchanging axis1 and axis2.
T	sub(T b)	Computes the element-wise difference between two tensors of the same shape.

Methods inherited from class org.flag4j.arrays.backend.semiring_arrays.AbstractCsrSemiringMatrix

add, augment, augment, copy, dataLength, density, elemMult, flatten, flatten, get, get, getSlice, getTriL, getTriU, getZeroElement, isHermitian, isI, isOrthogonal, isSymmetric, isTriL, isTriU, makeLikeCooMatrix, makeLikeDenseTensor, makeLikeTensor, makeLikeTensor, mult, multToSparse, multTranspose, numCols, numRows, removeCol, removeCols, removeRow, removeRows, reshape, set, set, setCol, setRow, setSliceCopy, setZeroElement, sortIndices, sparsity, stack, swapCols, swapRows, T, T, T, tensorTr, toCoo, toDense, toTensor, toTensor, toVector, tr

Methods inherited from class org.flag4j.arrays.backend.AbstractTensor

getData, getRank, getShape, makeLikeTensor, reshape, sameShape, totalEntries

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface org.flag4j.arrays.backend.MatrixMixin

accept, add, augment, augment, copy, dataLength, elemMult, fib, get, getCol, getCol, getDiag, getDiag, getRow, getRow, getShape, getSlice, getTriL, getTriL, getTriU, getTriU, isDiag, isHermitian, isI, isOrthogonal, isSquare, isSymmetric, isTri, isTriL, isTriU, isVector, mult, mult, multTranspose, numCols, numRows, removeCol, removeCols, removeRow, removeRows, set, setCol, setRow, setSliceCopy, stack, stack, swapCols, swapRows, T, toVector, tr, trace, vectorType

Methods inherited from interface org.flag4j.arrays.backend.ring_arrays.RingTensorMixin

add, addEq, argmax, argmaxAbs, argmin, argminAbs, conj, isOnes, isZeros, makeEmptyDataArray, max, maxAbs, min, minAbs, mult, multEq, norm, norm, prod, sub, subEq, sum

Methods inherited from interface org.flag4j.arrays.backend.semiring_arrays.SemiringTensorMixin

argmax, argmin, max, min

Methods inherited from interface org.flag4j.arrays.backend.ring_arrays.TensorOverRing

abs

Methods inherited from interface org.flag4j.arrays.backend.semiring_arrays.TensorOverSemiring

add, elemMult, getData, getRank, getShape, makeLikeTensor, tensorDot, tensorDot, tensorDot, tensorDot, tensorTr, tensorTr

Constructor Details

AbstractCsrRingMatrix

protected AbstractCsrRingMatrix(Shape shape,
 W[] entries,
 int[] rowPointers,
 int[] colIndices)

Creates a sparse CSR matrix with the specified shape, non-zero data, row pointers, and non-zero column indices.

Parameters:

shape - Shape of this tensor.

entries - The non-zero data of this CSR matrix.

rowPointers - The row pointers for the non-zero values in the sparse CSR matrix.

rowPointers[i] indicates the starting index within data and colData of all values in row i.

colIndices - Column indices for each non-zero value in this sparse CSR matrix. Must satisfy data.length == colData.length.

Method Details

sub

public T sub(T b)

Computes the element-wise difference between two tensors of the same shape.

Specified by:

sub in interface MatrixMixin<T extends AbstractCsrRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,?,U,W>,W extends Ring<W>>

Specified by:

sub in interface TensorOverRing<T extends AbstractCsrRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,?,U,W>,W extends Ring<W>>

Overrides:

sub in class AbstractCsrSemiringMatrix<T extends AbstractCsrRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,?,U,W>,W extends Ring<W>>

Parameters:

b - Second tensor in the element-wise difference.

Returns:

The difference of this tensor with b.

Throws:

TensorShapeException - If this tensor and b do not have the same shape.

div

public T div(T b)

Warning: throws UnsupportedOperationException as division is not defined for general ring matrices.

Warning: throws UnsupportedOperationException as division is not defined for general semiring matrices.

Computes the element-wise quotient of two matrices.

Specified by:

div in interface MatrixMixin<T extends AbstractCsrRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,?,U,W>,W extends Ring<W>>

Overrides:

div in class AbstractCsrSemiringMatrix<T extends AbstractCsrRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,?,U,W>,W extends Ring<W>>

Parameters:

b - Second matrix in the element-wise quotient.

Returns:

The element-wise quotient of this matrix and b.

H

public T H()

Computes the Hermitian transpose of this matrix.

Specified by:

H in interface MatrixMixin<T extends AbstractCsrRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,?,U,W>,W extends Ring<W>>

Specified by:

H in interface TensorOverRing<T extends AbstractCsrRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,?,U,W>,W extends Ring<W>>

Overrides:

H in class AbstractCsrSemiringMatrix<T extends AbstractCsrRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,?,U,W>,W extends Ring<W>>

Returns:

The Hermitian transpose of this matrix.

See Also:

• TensorOverRing.H(int, int)
• TensorOverRing.H(int...)

H

public T H(int axis1,
 int axis2)

Computes the conjugate transpose of a tensor by conjugating and exchanging axis1 and axis2.

Specified by:

H in interface TensorOverRing<T extends AbstractCsrRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,?,U,W>,W extends Ring<W>>

Parameters:

axis1 - First axis to exchange and conjugate.

axis2 - Second axis to exchange and conjugate.

Returns:

The conjugate transpose of this tensor according to the specified axes.

Throws:

IndexOutOfBoundsException - If either axis1 or axis2 are out of bounds for the rank of this tensor.

See Also:

• H()
• H(int...)

H

public T H(int... axes)

Computes the conjugate transpose of this tensor. That is, conjugates and permutes the axes of this tensor so that it matches the permutation specified by axes.

Specified by:

H in interface TensorOverRing<T extends AbstractCsrRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,?,U,W>,W extends Ring<W>>

Parameters:

axes - Permutation of tensor axis. If the tensor has rank N, then this must be an array of length N which is a permutation of {0, 1, 2, ..., N-1}.

Returns:

The conjugate transpose of this tensor with its axes permuted by the axes array.

Throws:

IndexOutOfBoundsException - If any element of axes is out of bounds for the rank of this tensor.

IllegalArgumentException - If axes is not a permutation of {1, 2, 3, ... N-1}.

See Also:

• H(int, int)
• H()

allClose

public boolean allClose(T b)

Checks if two sparse CSR ring matrices are element-wise equal within the following tolerance for two entries x and y:

  |x-y| <= (1e-08 + 1e-05*|y|)
 

To specify the relative and absolute tolerances use allClose(AbstractCsrRingMatrix, double, double)

Returns:

true if this matrix and b element-wise equal within the tolerance |x-y| <= (1e-08 + 1e-05*|y|).

See Also:

• allClose(AbstractCsrRingMatrix, double, double)

allClose

public boolean allClose(T b,
 double relRol,
 double absTol)

Checks if two matrices are element-wise equal within the tolerance specified by relTol and absTol. Two elements x and y are considered "close" if they satisfy the following:

  |x-y| <= (absTol + relTol*|y|)
 

Parameters:

b - Matrix to compare to this matrix.

absTol - Absolute tolerance.

relTol - Relative tolerance.

Returns:

true if the src1 matrix is the same shape as the src2 matrix and all data are 'close', i.e. elements a and b at the same positions in the two matrices respectively satisfy |a-b| <= (absTol + relTol*|b|). Otherwise, returns false.

See Also:

• allClose(AbstractCsrRingMatrix)