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README and documentation for the main functions of tensor algebra #297

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AlyaNovikova merged 3 commits from feature/tensor-algebra into feature/tensor-algebra 2021-04-29 20:03:49 +03:00
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kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/LinearOpsTensorAlgebra.kt
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@ -49,13 +49,13 @@ public interface LinearOpsTensorAlgebra<T> :
/** /**
* QR decomposition. * QR decomposition.
* *
* Computes the QR decomposition of a matrix or a batch of matrices, and returns a namedtuple `(Q, R)` of tensors. * Computes the QR decomposition of a matrix or a batch of matrices, and returns a pair `(Q, R)` of tensors.
* Given a tensor `input`, return tensors (Q, R) satisfying ``input = Q * R``, * Given a tensor `input`, return tensors (Q, R) satisfying ``input = Q * R``,
* with `Q` being an orthogonal matrix or batch of orthogonal matrices * with `Q` being an orthogonal matrix or batch of orthogonal matrices
* and `R` being an upper triangular matrix or batch of upper triangular matrices. * and `R` being an upper triangular matrix or batch of upper triangular matrices.
* For more information: https://pytorch.org/docs/stable/linalg.html#torch.linalg.qr * For more information: https://pytorch.org/docs/stable/linalg.html#torch.linalg.qr
* *
* @return tuple of Q and R tensors. * @return pair of Q and R tensors.
*/ */
public fun TensorStructure<T>.qr(): Pair<TensorStructure<T>, TensorStructure<T>> public fun TensorStructure<T>.qr(): Pair<TensorStructure<T>, TensorStructure<T>>
@ -82,7 +82,7 @@ public interface LinearOpsTensorAlgebra<T> :
* Singular Value Decomposition. * Singular Value Decomposition.
* *
* Computes the singular value decomposition of either a matrix or batch of matrices `input`. * Computes the singular value decomposition of either a matrix or batch of matrices `input`.
* The singular value decomposition is represented as a namedtuple `(U, S, V)`, * The singular value decomposition is represented as a triple `(U, S, V)`,
* such that ``input = U.dot(diagonalEmbedding(S).dot(V.T))``. * such that ``input = U.dot(diagonalEmbedding(S).dot(V.T))``.
* If input is a batch of tensors, then U, S, and Vh are also batched with the same batch dimensions as input. * If input is a batch of tensors, then U, S, and Vh are also batched with the same batch dimensions as input.
* For more information: https://pytorch.org/docs/stable/linalg.html#torch.linalg.svd * For more information: https://pytorch.org/docs/stable/linalg.html#torch.linalg.svd
@ -93,10 +93,10 @@ public interface LinearOpsTensorAlgebra<T> :
/** /**
* Returns eigenvalues and eigenvectors of a real symmetric matrix input or a batch of real symmetric matrices, * Returns eigenvalues and eigenvectors of a real symmetric matrix input or a batch of real symmetric matrices,
* represented by a namedtuple (eigenvalues, eigenvectors). * represented by a pair (eigenvalues, eigenvectors).
* For more information: https://pytorch.org/docs/stable/generated/torch.symeig.html * For more information: https://pytorch.org/docs/stable/generated/torch.symeig.html
* *
* @return a namedtuple (eigenvalues, eigenvectors) * @return a pair (eigenvalues, eigenvectors)
*/ */
public fun TensorStructure<T>.symEig(): Pair<TensorStructure<T>, TensorStructure<T>> public fun TensorStructure<T>.symEig(): Pair<TensorStructure<T>, TensorStructure<T>>