forked from kscience/kmath
add README and documentation for the main functions of tensor algebra
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README.md
12
README.md
@ -230,6 +230,18 @@ One can still use generic algebras though.
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> **Maturity**: EXPERIMENTAL
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> **Maturity**: EXPERIMENTAL
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<hr/>
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<hr/>
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* ### [kmath-tensors](kmath-tensors)
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>
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>
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> **Maturity**: PROTOTYPE
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>
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> **Features:**
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> - [tensor algebra](kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/TensorAlgebra.kt) : Basic linear algebra operations on tensors (plus, dot, etc.)
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> - [tensor algebra with broadcasting](kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/algebras/BroadcastDoubleTensorAlgebra.kt) : Basic linear algebra operations implemented with broadcasting.
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> - [linear algebra operations](kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/LinearOpsTensorAlgebra.kt) : Advanced linear algebra operations like LU decomposition, SVD, etc.
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<hr/>
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* ### [kmath-viktor](kmath-viktor)
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* ### [kmath-viktor](kmath-viktor)
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>
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>
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>
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>
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37
kmath-tensors/README.md
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37
kmath-tensors/README.md
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@ -0,0 +1,37 @@
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# Module kmath-tensors
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Common linear algebra operations on tensors.
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- [tensor algebra](src/commonMain/kotlin/space/kscience/kmath/tensors/api/TensorAlgebra.kt) : Basic linear algebra operations on tensors (plus, dot, etc.)
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- [tensor algebra with broadcasting](src/commonMain/kotlin/space/kscience/kmath/tensors/core/algebras/BroadcastDoubleTensorAlgebra.kt) : Basic linear algebra operations implemented with broadcasting.
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- [linear algebra operations](src/commonMain/kotlin/space/kscience/kmath/tensors/api/LinearOpsTensorAlgebra.kt) : Advanced linear algebra operations like LU decomposition, SVD, etc.
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## Artifact:
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The Maven coordinates of this project are `space.kscience:kmath-tensors:0.3.0-dev-7`.
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**Gradle:**
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```gradle
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repositories {
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maven { url 'https://repo.kotlin.link' }
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maven { url 'https://dl.bintray.com/hotkeytlt/maven' }
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maven { url "https://dl.bintray.com/kotlin/kotlin-eap" } // include for builds based on kotlin-eap
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}
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dependencies {
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implementation 'space.kscience:kmath-tensors:0.3.0-dev-7'
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}
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```
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**Gradle Kotlin DSL:**
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```kotlin
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repositories {
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maven("https://repo.kotlin.link")
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maven("https://dl.bintray.com/kotlin/kotlin-eap") // include for builds based on kotlin-eap
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maven("https://dl.bintray.com/hotkeytlt/maven") // required for a
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}
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dependencies {
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implementation("space.kscience:kmath-tensors:0.3.0-dev-7")
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}
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```
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@ -11,6 +11,30 @@ kotlin.sourceSets {
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}
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}
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}
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}
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readme {
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tasks.dokkaHtml {
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maturity = ru.mipt.npm.gradle.Maturity.EXPERIMENTAL
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dependsOn(tasks.build)
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}
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readme {
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maturity = ru.mipt.npm.gradle.Maturity.PROTOTYPE
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propertyByTemplate("artifact", rootProject.file("docs/templates/ARTIFACT-TEMPLATE.md"))
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feature(
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id = "tensor algebra",
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description = "Basic linear algebra operations on tensors (plus, dot, etc.)",
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ref = "src/commonMain/kotlin/space/kscience/kmath/tensors/api/TensorAlgebra.kt"
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)
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feature(
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id = "tensor algebra with broadcasting",
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description = "Basic linear algebra operations implemented with broadcasting.",
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ref = "src/commonMain/kotlin/space/kscience/kmath/tensors/core/algebras/BroadcastDoubleTensorAlgebra.kt"
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)
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feature(
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id = "linear algebra operations",
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description = "Advanced linear algebra operations like LU decomposition, SVD, etc.",
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ref = "src/commonMain/kotlin/space/kscience/kmath/tensors/api/LinearOpsTensorAlgebra.kt"
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)
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}
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}
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7
kmath-tensors/docs/README-TEMPLATE.md
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7
kmath-tensors/docs/README-TEMPLATE.md
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# Module kmath-tensors
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Common linear algebra operations on tensors.
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${features}
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${artifact}
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@ -5,33 +5,99 @@
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package space.kscience.kmath.tensors.api
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package space.kscience.kmath.tensors.api
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/**
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* Common linear algebra operations. Operates on [TensorStructure].
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*
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* @param T the type of items in the tensors.
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*/
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public interface LinearOpsTensorAlgebra<T> :
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public interface LinearOpsTensorAlgebra<T> :
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TensorPartialDivisionAlgebra<T> {
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TensorPartialDivisionAlgebra<T> {
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//https://pytorch.org/docs/stable/linalg.html#torch.linalg.det
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/**
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* Computes the determinant of a square matrix input, or of each square matrix in a batched input.
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* For more information: https://pytorch.org/docs/stable/linalg.html#torch.linalg.det
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*
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* @return the determinant.
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*/
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public fun TensorStructure<T>.det(): TensorStructure<T>
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public fun TensorStructure<T>.det(): TensorStructure<T>
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//https://pytorch.org/docs/stable/linalg.html#torch.linalg.inv
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/**
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* Computes the multiplicative inverse matrix of a square matrix input, or of each square matrix in a batched input.
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* Given a square matrix `a`, return the matrix `aInv` satisfying
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* ``a.dot(aInv) = aInv.dot(a) = eye(a.shape[0])``.
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* For more information: https://pytorch.org/docs/stable/linalg.html#torch.linalg.inv
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*
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* @return the multiplicative inverse of a matrix.
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*/
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public fun TensorStructure<T>.inv(): TensorStructure<T>
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public fun TensorStructure<T>.inv(): TensorStructure<T>
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//https://pytorch.org/docs/stable/linalg.html#torch.linalg.cholesky
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/**
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* Cholesky decomposition.
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*
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* Computes the Cholesky decomposition of a Hermitian (or symmetric for real-valued matrices)
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* positive-definite matrix or the Cholesky decompositions for a batch of such matrices.
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* Each decomposition has the form:
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* Given a tensor `input`, return the tensor `L` satisfying ``input = L * L.H``,
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* where L is a lower-triangular matrix and L.H is the conjugate transpose of L,
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* which is just a transpose for the case of real-valued input matrices.
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* For more information: https://pytorch.org/docs/stable/linalg.html#torch.linalg.cholesky
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*
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* @return the batch of L matrices.
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*/
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public fun TensorStructure<T>.cholesky(): TensorStructure<T>
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public fun TensorStructure<T>.cholesky(): TensorStructure<T>
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//https://pytorch.org/docs/stable/linalg.html#torch.linalg.qr
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/**
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* QR decomposition.
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*
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* Computes the QR decomposition of a matrix or a batch of matrices, and returns a namedtuple `(Q, R)` of tensors.
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* Given a tensor `input`, return tensors (Q, R) satisfying ``input = Q * R``,
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* with `Q` being an orthogonal matrix or batch of orthogonal matrices
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* and `R` being an upper triangular matrix or batch of upper triangular matrices.
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* For more information: https://pytorch.org/docs/stable/linalg.html#torch.linalg.qr
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*
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* @return tuple of Q and R tensors.
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*/
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public fun TensorStructure<T>.qr(): Pair<TensorStructure<T>, TensorStructure<T>>
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public fun TensorStructure<T>.qr(): Pair<TensorStructure<T>, TensorStructure<T>>
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//https://pytorch.org/docs/stable/generated/torch.lu.html
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/**
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* TODO('Andrew')
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* For more information: https://pytorch.org/docs/stable/generated/torch.lu.html
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*
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* @return ...
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*/
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public fun TensorStructure<T>.lu(): Pair<TensorStructure<T>, TensorStructure<Int>>
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public fun TensorStructure<T>.lu(): Pair<TensorStructure<T>, TensorStructure<Int>>
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//https://pytorch.org/docs/stable/generated/torch.lu_unpack.html
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/**
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* TODO('Andrew')
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* For more information: https://pytorch.org/docs/stable/generated/torch.lu_unpack.html
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*
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* @param luTensor ...
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* @param pivotsTensor ...
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* @return ...
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*/
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public fun luPivot(luTensor: TensorStructure<T>, pivotsTensor: TensorStructure<Int>):
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public fun luPivot(luTensor: TensorStructure<T>, pivotsTensor: TensorStructure<Int>):
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Triple<TensorStructure<T>, TensorStructure<T>, TensorStructure<T>>
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Triple<TensorStructure<T>, TensorStructure<T>, TensorStructure<T>>
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//https://pytorch.org/docs/stable/linalg.html#torch.linalg.svd
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/**
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* Singular Value Decomposition.
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*
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* Computes the singular value decomposition of either a matrix or batch of matrices `input`.
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* The singular value decomposition is represented as a namedtuple `(U, S, V)`,
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* such that ``input = U.dot(diagonalEmbedding(S).dot(V.T))``.
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* If input is a batch of tensors, then U, S, and Vh are also batched with the same batch dimensions as input.
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* For more information: https://pytorch.org/docs/stable/linalg.html#torch.linalg.svd
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*
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* @return the determinant.
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*/
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public fun TensorStructure<T>.svd(): Triple<TensorStructure<T>, TensorStructure<T>, TensorStructure<T>>
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public fun TensorStructure<T>.svd(): Triple<TensorStructure<T>, TensorStructure<T>, TensorStructure<T>>
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//https://pytorch.org/docs/stable/generated/torch.symeig.html
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/**
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* Returns eigenvalues and eigenvectors of a real symmetric matrix input or a batch of real symmetric matrices,
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* represented by a namedtuple (eigenvalues, eigenvectors).
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* For more information: https://pytorch.org/docs/stable/generated/torch.symeig.html
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*
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* @return a namedtuple (eigenvalues, eigenvectors)
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*/
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public fun TensorStructure<T>.symEig(): Pair<TensorStructure<T>, TensorStructure<T>>
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public fun TensorStructure<T>.symEig(): Pair<TensorStructure<T>, TensorStructure<T>>
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}
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}
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package space.kscience.kmath.tensors.api
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package space.kscience.kmath.tensors.api
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// https://proofwiki.org/wiki/Definition:Algebra_over_Ring
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/**
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* Basic linear algebra operations on [TensorStructure].
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* For more information: https://proofwiki.org/wiki/Definition:Algebra_over_Ring
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*
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* @param T the type of items in the tensors.
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*/
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public interface TensorAlgebra<T> {
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public interface TensorAlgebra<T> {
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/**
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* Returns a single tensor value of unit dimension. The tensor shape must be equal to [1].
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*
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* @return the value of a scalar tensor.
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*/
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public fun TensorStructure<T>.value(): T
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public fun TensorStructure<T>.value(): T
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/**
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* Each element of the tensor [other] is added to this value.
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* The resulting tensor is returned.
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*
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* @param other tensor to be added.
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* @return the sum of this value and tensor [other].
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*/
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public operator fun T.plus(other: TensorStructure<T>): TensorStructure<T>
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public operator fun T.plus(other: TensorStructure<T>): TensorStructure<T>
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/**
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* Adds the scalar [value] to each element of this tensor and returns a new resulting tensor.
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*
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* @param value the number to be added to each element of this tensor.
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* @return the sum of this tensor and [value].
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*/
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public operator fun TensorStructure<T>.plus(value: T): TensorStructure<T>
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public operator fun TensorStructure<T>.plus(value: T): TensorStructure<T>
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/**
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* Each element of the tensor [other] is added to each element of this tensor.
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* The resulting tensor is returned.
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*
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* @param other tensor to be added.
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* @return the sum of this tensor and [other].
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*/
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public operator fun TensorStructure<T>.plus(other: TensorStructure<T>): TensorStructure<T>
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public operator fun TensorStructure<T>.plus(other: TensorStructure<T>): TensorStructure<T>
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/**
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* Adds the scalar [value] to each element of this tensor.
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*
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* @param value the number to be added to each element of this tensor.
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*/
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public operator fun TensorStructure<T>.plusAssign(value: T): Unit
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public operator fun TensorStructure<T>.plusAssign(value: T): Unit
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/**
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* Each element of the tensor [other] is added to each element of this tensor.
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*
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* @param other tensor to be added.
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*/
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public operator fun TensorStructure<T>.plusAssign(other: TensorStructure<T>): Unit
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public operator fun TensorStructure<T>.plusAssign(other: TensorStructure<T>): Unit
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/**
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* Each element of the tensor [other] is subtracted from this value.
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* The resulting tensor is returned.
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*
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* @param other tensor to be subtracted.
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* @return the difference between this value and tensor [other].
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*/
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public operator fun T.minus(other: TensorStructure<T>): TensorStructure<T>
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public operator fun T.minus(other: TensorStructure<T>): TensorStructure<T>
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/**
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* Subtracts the scalar [value] from each element of this tensor and returns a new resulting tensor.
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*
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* @param value the number to be subtracted from each element of this tensor.
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* @return the difference between this tensor and [value].
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*/
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public operator fun TensorStructure<T>.minus(value: T): TensorStructure<T>
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public operator fun TensorStructure<T>.minus(value: T): TensorStructure<T>
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/**
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* Each element of the tensor [other] is subtracted from each element of this tensor.
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* The resulting tensor is returned.
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*
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* @param other tensor to be subtracted.
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* @return the difference between this tensor and [other].
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*/
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public operator fun TensorStructure<T>.minus(other: TensorStructure<T>): TensorStructure<T>
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public operator fun TensorStructure<T>.minus(other: TensorStructure<T>): TensorStructure<T>
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/**
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* Subtracts the scalar [value] from each element of this tensor.
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*
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* @param value the number to be subtracted from each element of this tensor.
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*/
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public operator fun TensorStructure<T>.minusAssign(value: T): Unit
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public operator fun TensorStructure<T>.minusAssign(value: T): Unit
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/**
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* Each element of the tensor [other] is subtracted from each element of this tensor.
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*
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* @param other tensor to be subtracted.
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*/
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public operator fun TensorStructure<T>.minusAssign(other: TensorStructure<T>): Unit
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public operator fun TensorStructure<T>.minusAssign(other: TensorStructure<T>): Unit
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/**
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* Each element of the tensor [other] is multiplied by this value.
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* The resulting tensor is returned.
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*
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* @param other tensor to be multiplied.
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* @return the product of this value and tensor [other].
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*/
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public operator fun T.times(other: TensorStructure<T>): TensorStructure<T>
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public operator fun T.times(other: TensorStructure<T>): TensorStructure<T>
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/**
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* Multiplies the scalar [value] by each element of this tensor and returns a new resulting tensor.
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*
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* @param value the number to be multiplied by each element of this tensor.
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* @return the product of this tensor and [value].
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*/
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public operator fun TensorStructure<T>.times(value: T): TensorStructure<T>
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public operator fun TensorStructure<T>.times(value: T): TensorStructure<T>
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/**
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* Each element of the tensor [other] is multiplied by each element of this tensor.
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* The resulting tensor is returned.
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*
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* @param other tensor to be multiplied.
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* @return the product of this tensor and [other].
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*/
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public operator fun TensorStructure<T>.times(other: TensorStructure<T>): TensorStructure<T>
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public operator fun TensorStructure<T>.times(other: TensorStructure<T>): TensorStructure<T>
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/**
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* Multiplies the scalar [value] by each element of this tensor.
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*
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* @param value the number to be multiplied by each element of this tensor.
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*/
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public operator fun TensorStructure<T>.timesAssign(value: T): Unit
|
public operator fun TensorStructure<T>.timesAssign(value: T): Unit
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Each element of the tensor [other] is multiplied by each element of this tensor.
|
||||||
|
*
|
||||||
|
* @param other tensor to be multiplied.
|
||||||
|
*/
|
||||||
public operator fun TensorStructure<T>.timesAssign(other: TensorStructure<T>): Unit
|
public operator fun TensorStructure<T>.timesAssign(other: TensorStructure<T>): Unit
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Numerical negative, element-wise.
|
||||||
|
*
|
||||||
|
* @return tensor - negation of the original tensor.
|
||||||
|
*/
|
||||||
public operator fun TensorStructure<T>.unaryMinus(): TensorStructure<T>
|
public operator fun TensorStructure<T>.unaryMinus(): TensorStructure<T>
|
||||||
|
|
||||||
//https://pytorch.org/cppdocs/notes/tensor_indexing.html
|
/**
|
||||||
|
* Returns the tensor at index i
|
||||||
|
* For more information: https://pytorch.org/cppdocs/notes/tensor_indexing.html
|
||||||
|
*
|
||||||
|
* @param i index of the extractable tensor
|
||||||
|
* @return subtensor of the original tensor with index [i]
|
||||||
|
*/
|
||||||
public operator fun TensorStructure<T>.get(i: Int): TensorStructure<T>
|
public operator fun TensorStructure<T>.get(i: Int): TensorStructure<T>
|
||||||
|
|
||||||
//https://pytorch.org/docs/stable/generated/torch.transpose.html
|
/**
|
||||||
|
* Returns a tensor that is a transposed version of this tensor. The given dimensions [i] and [j] are swapped.
|
||||||
|
* For more information: https://pytorch.org/docs/stable/generated/torch.transpose.html
|
||||||
|
*
|
||||||
|
* @param i the first dimension to be transposed
|
||||||
|
* @param j the second dimension to be transposed
|
||||||
|
* @return transposed tensor
|
||||||
|
*/
|
||||||
public fun TensorStructure<T>.transpose(i: Int = -2, j: Int = -1): TensorStructure<T>
|
public fun TensorStructure<T>.transpose(i: Int = -2, j: Int = -1): TensorStructure<T>
|
||||||
|
|
||||||
//https://pytorch.org/docs/stable/tensor_view.html
|
/**
|
||||||
|
* Returns a new tensor with the same data as the self tensor but of a different shape.
|
||||||
|
* The returned tensor shares the same data and must have the same number of elements, but may have a different size
|
||||||
|
* For more information: https://pytorch.org/docs/stable/tensor_view.html
|
||||||
|
*
|
||||||
|
* @param shape the desired size
|
||||||
|
* @return tensor with new shape
|
||||||
|
*/
|
||||||
public fun TensorStructure<T>.view(shape: IntArray): TensorStructure<T>
|
public fun TensorStructure<T>.view(shape: IntArray): TensorStructure<T>
|
||||||
|
|
||||||
|
/**
|
||||||
|
* View this tensor as the same size as [other].
|
||||||
|
* ``this.viewAs(other) is equivalent to this.view(other.shape)``.
|
||||||
|
* For more information: https://pytorch.org/cppdocs/notes/tensor_indexing.html
|
||||||
|
*
|
||||||
|
* @param other the result tensor has the same size as other.
|
||||||
|
* @return the result tensor with the same size as other.
|
||||||
|
*/
|
||||||
public fun TensorStructure<T>.viewAs(other: TensorStructure<T>): TensorStructure<T>
|
public fun TensorStructure<T>.viewAs(other: TensorStructure<T>): TensorStructure<T>
|
||||||
|
|
||||||
//https://pytorch.org/docs/stable/generated/torch.matmul.html
|
/**
|
||||||
|
* Matrix product of two tensors.
|
||||||
|
*
|
||||||
|
* The behavior depends on the dimensionality of the tensors as follows:
|
||||||
|
* 1. If both tensors are 1-dimensional, the dot product (scalar) is returned.
|
||||||
|
*
|
||||||
|
* 2. If both arguments are 2-dimensional, the matrix-matrix product is returned.
|
||||||
|
*
|
||||||
|
* 3. If the first argument is 1-dimensional and the second argument is 2-dimensional,
|
||||||
|
* a 1 is prepended to its dimension for the purpose of the matrix multiply.
|
||||||
|
* After the matrix multiply, the prepended dimension is removed.
|
||||||
|
*
|
||||||
|
* 4. If the first argument is 2-dimensional and the second argument is 1-dimensional,
|
||||||
|
* the matrix-vector product is returned.
|
||||||
|
*
|
||||||
|
* 5. If both arguments are at least 1-dimensional and at least one argument is N-dimensional (where N > 2),
|
||||||
|
* then a batched matrix multiply is returned. If the first argument is 1-dimensional,
|
||||||
|
* a 1 is prepended to its dimension for the purpose of the batched matrix multiply and removed after.
|
||||||
|
* If the second argument is 1-dimensional, a 1 is appended to its dimension for the purpose of the batched matrix
|
||||||
|
* multiple and removed after.
|
||||||
|
* The non-matrix (i.e. batch) dimensions are broadcasted (and thus must be broadcastable).
|
||||||
|
* For example, if `input` is a (j \times 1 \times n \times n) tensor and `other` is a
|
||||||
|
* (k \times n \times n) tensor, out will be a (j \times k \times n \times n) tensor.
|
||||||
|
*
|
||||||
|
* For more information: https://pytorch.org/docs/stable/generated/torch.matmul.html
|
||||||
|
*
|
||||||
|
* @param other tensor to be multiplied
|
||||||
|
* @return mathematical product of two tensors
|
||||||
|
*/
|
||||||
public infix fun TensorStructure<T>.dot(other: TensorStructure<T>): TensorStructure<T>
|
public infix fun TensorStructure<T>.dot(other: TensorStructure<T>): TensorStructure<T>
|
||||||
|
|
||||||
//https://pytorch.org/docs/stable/generated/torch.diag_embed.html
|
/**
|
||||||
|
* Creates a tensor whose diagonals of certain 2D planes (specified by [dim1] and [dim2])
|
||||||
|
* are filled by [diagonalEntries].
|
||||||
|
* To facilitate creating batched diagonal matrices,
|
||||||
|
* the 2D planes formed by the last two dimensions of the returned tensor are chosen by default.
|
||||||
|
*
|
||||||
|
* The argument [offset] controls which diagonal to consider:
|
||||||
|
* 1. If [offset] = 0, it is the main diagonal.
|
||||||
|
* 2. If [offset] > 0, it is above the main diagonal.
|
||||||
|
* 3. If [offset] < 0, it is below the main diagonal.
|
||||||
|
*
|
||||||
|
* The size of the new matrix will be calculated
|
||||||
|
* to make the specified diagonal of the size of the last input dimension.
|
||||||
|
* For more information: https://pytorch.org/docs/stable/generated/torch.diag_embed.html
|
||||||
|
*
|
||||||
|
* @param diagonalEntries - the input tensor. Must be at least 1-dimensional.
|
||||||
|
* @param offset - which diagonal to consider. Default: 0 (main diagonal).
|
||||||
|
* @param dim1 - first dimension with respect to which to take diagonal. Default: -2.
|
||||||
|
* @param dim2 - second dimension with respect to which to take diagonal. Default: -1.
|
||||||
|
*
|
||||||
|
* @return tensor whose diagonals of certain 2D planes (specified by [dim1] and [dim2])
|
||||||
|
* are filled by [diagonalEntries]
|
||||||
|
*/
|
||||||
public fun diagonalEmbedding(
|
public fun diagonalEmbedding(
|
||||||
diagonalEntries: TensorStructure<T>,
|
diagonalEntries: TensorStructure<T>,
|
||||||
offset: Int = 0,
|
offset: Int = 0,
|
||||||
|
@ -10,6 +10,10 @@ import space.kscience.kmath.tensors.core.*
|
|||||||
import space.kscience.kmath.tensors.core.broadcastTensors
|
import space.kscience.kmath.tensors.core.broadcastTensors
|
||||||
import space.kscience.kmath.tensors.core.broadcastTo
|
import space.kscience.kmath.tensors.core.broadcastTo
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Basic linear algebra operations implemented with broadcasting.
|
||||||
|
* For more information: https://pytorch.org/docs/stable/notes/broadcasting.html
|
||||||
|
*/
|
||||||
public class BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
|
public class BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
|
||||||
|
|
||||||
override fun TensorStructure<Double>.plus(other: TensorStructure<Double>): DoubleTensor {
|
override fun TensorStructure<Double>.plus(other: TensorStructure<Double>): DoubleTensor {
|
||||||
|
Loading…
Reference in New Issue
Block a user