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Roland Grinis
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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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Common operations on tensors, the API consists of:
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- [TensorAlgebra](src/commonMain/kotlin/space/kscience/kmath/tensors/api/TensorAlgebra.kt) : Basic algebra operations on tensors (plus, dot, etc.)
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- [TensorPartialDivisionAlgebra](src/commonMain/kotlin/space/kscience/kmath/tensors/api/TensorPartialDivisionAlgebra.kt) : Emulates an algebra over a field
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- [LinearOpsTensorAlgebra](src/commonMain/kotlin/space/kscience/kmath/tensors/api/LinearOpsTensorAlgebra.kt) : Linear algebra operations including LU, QR, Cholesky LL and SVD decompositions
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- [AnalyticTensorAlgebra](src/commonMain/kotlin/space/kscience/kmath/tensors/api/AnalyticTensorAlgebra.kt) : Element-wise analytic operations
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The library offers a multiplatform implementation for this interface over the `Double`'s. As the highlight, the user can find:
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- [BroadcastDoubleTensorAlgebra](src/commonMain/kotlin/space/kscience/kmath/tensors/core/algebras/BroadcastDoubleTensorAlgebra.kt) : Basic algebra operations implemented with broadcasting.
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- [DoubleLinearOpsTensorAlgebra](src/commonMain/kotlin/space/kscience/kmath/tensors/core/algebras/DoubleLinearOpsTensorAlgebra.kt) : Includes the power method for SVD and the spectrum of symmetric matrices.
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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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@ -5,59 +5,63 @@
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package space.kscience.kmath.tensors.api
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/**
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* Element-wise analytic operations on [TensorStructure].
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*
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* @param T the type of items closed under analytic functions in the tensors.
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*/
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public interface AnalyticTensorAlgebra<T> :
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TensorPartialDivisionAlgebra<T> {
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//https://pytorch.org/docs/stable/generated/torch.exp.html
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//For information: https://pytorch.org/docs/stable/generated/torch.exp.html
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public fun TensorStructure<T>.exp(): TensorStructure<T>
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//https://pytorch.org/docs/stable/generated/torch.log.html
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//For information: https://pytorch.org/docs/stable/generated/torch.log.html
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public fun TensorStructure<T>.log(): TensorStructure<T>
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//https://pytorch.org/docs/stable/generated/torch.sqrt.html
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//For information: https://pytorch.org/docs/stable/generated/torch.sqrt.html
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public fun TensorStructure<T>.sqrt(): TensorStructure<T>
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//https://pytorch.org/docs/stable/generated/torch.acos.html#torch.cos
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//For information: https://pytorch.org/docs/stable/generated/torch.acos.html#torch.cos
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public fun TensorStructure<T>.cos(): TensorStructure<T>
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//https://pytorch.org/docs/stable/generated/torch.acos.html#torch.acos
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//For information: https://pytorch.org/docs/stable/generated/torch.acos.html#torch.acos
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public fun TensorStructure<T>.acos(): TensorStructure<T>
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//https://pytorch.org/docs/stable/generated/torch.acosh.html#torch.cosh
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//For information: https://pytorch.org/docs/stable/generated/torch.acosh.html#torch.cosh
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public fun TensorStructure<T>.cosh(): TensorStructure<T>
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//https://pytorch.org/docs/stable/generated/torch.acosh.html#torch.acosh
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//For information: https://pytorch.org/docs/stable/generated/torch.acosh.html#torch.acosh
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public fun TensorStructure<T>.acosh(): TensorStructure<T>
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//https://pytorch.org/docs/stable/generated/torch.asin.html#torch.sin
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//For information: https://pytorch.org/docs/stable/generated/torch.asin.html#torch.sin
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public fun TensorStructure<T>.sin(): TensorStructure<T>
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//https://pytorch.org/docs/stable/generated/torch.asin.html#torch.asin
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//For information: https://pytorch.org/docs/stable/generated/torch.asin.html#torch.asin
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public fun TensorStructure<T>.asin(): TensorStructure<T>
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//https://pytorch.org/docs/stable/generated/torch.asin.html#torch.sinh
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//For information: https://pytorch.org/docs/stable/generated/torch.asin.html#torch.sinh
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public fun TensorStructure<T>.sinh(): TensorStructure<T>
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//https://pytorch.org/docs/stable/generated/torch.asin.html#torch.asinh
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//For information: https://pytorch.org/docs/stable/generated/torch.asin.html#torch.asinh
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public fun TensorStructure<T>.asinh(): TensorStructure<T>
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//https://pytorch.org/docs/stable/generated/torch.atan.html#torch.tan
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//For information: https://pytorch.org/docs/stable/generated/torch.atan.html#torch.tan
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public fun TensorStructure<T>.tan(): TensorStructure<T>
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//https://pytorch.org/docs/stable/generated/torch.atan.html#torch.atan
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public fun TensorStructure<T>.atan(): TensorStructure<T>
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//https://pytorch.org/docs/stable/generated/torch.atanh.html#torch.tanh
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//For information: https://pytorch.org/docs/stable/generated/torch.atanh.html#torch.tanh
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public fun TensorStructure<T>.tanh(): TensorStructure<T>
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//https://pytorch.org/docs/stable/generated/torch.atanh.html#torch.atanh
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//For information: https://pytorch.org/docs/stable/generated/torch.atanh.html#torch.atanh
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public fun TensorStructure<T>.atanh(): TensorStructure<T>
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//https://pytorch.org/docs/stable/generated/torch.ceil.html#torch.ceil
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//For information: https://pytorch.org/docs/stable/generated/torch.ceil.html#torch.ceil
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public fun TensorStructure<T>.ceil(): TensorStructure<T>
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//https://pytorch.org/docs/stable/generated/torch.floor.html#torch.floor
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//For information: https://pytorch.org/docs/stable/generated/torch.floor.html#torch.floor
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public fun TensorStructure<T>.floor(): TensorStructure<T>
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}
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@ -8,7 +8,7 @@ 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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* @param T the type of items closed under division in the tensors.
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*/
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public interface LinearOpsTensorAlgebra<T> :
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TensorPartialDivisionAlgebra<T> {
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@ -6,7 +6,7 @@
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package space.kscience.kmath.tensors.api
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/**
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* Basic linear algebra operations on [TensorStructure].
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* Algebra over a ring 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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@ -5,12 +5,52 @@
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package space.kscience.kmath.tensors.api
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// https://proofwiki.org/wiki/Definition:Division_Algebra
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/**
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* Algebra over a field with partial division on [TensorStructure].
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* For more information: https://proofwiki.org/wiki/Definition:Division_Algebra
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*
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* @param T the type of items closed under division in the tensors.
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*/
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public interface TensorPartialDivisionAlgebra<T> :
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TensorAlgebra<T> {
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/**
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* Each element of the tensor [other] is divided by this value.
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* The resulting tensor is returned.
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*
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* @param other tensor to divide by.
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* @return the division of this value by the tensor [other].
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*/
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public operator fun T.div(other: TensorStructure<T>): TensorStructure<T>
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/**
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* Divide by the scalar [value] each element of this tensor returns a new resulting tensor.
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*
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* @param value the number to divide by each element of this tensor.
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* @return the division of this tensor by the [value].
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*/
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public operator fun TensorStructure<T>.div(value: T): TensorStructure<T>
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/**
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* Each element of the tensor [other] is divided 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 divided by.
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* @return the division of this tensor by [other].
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*/
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public operator fun TensorStructure<T>.div(other: TensorStructure<T>): TensorStructure<T>
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/**
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* Divides by the scalar [value] each element of this tensor.
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*
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* @param value the number to divide by each element of this tensor.
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*/
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public operator fun TensorStructure<T>.divAssign(value: T)
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/**
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* Each element of this tensor is divided by each element of the [other] tensor.
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*
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* @param other tensor to be divide by.
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*/
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public operator fun TensorStructure<T>.divAssign(other: TensorStructure<T>)
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}
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