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Restrict tensor dot ot vectors and matrices only. Introduce bdot to Double TensorAlgebra for broadcasting operations.

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Alexander Nozik 2022-08-03 18:10:44 +03:00
parent 9456217935
commit 5402ba47c9
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5 changed files with 52 additions and 24 deletions
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3
CHANGELOG.md
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@ -7,8 +7,9 @@
- Algebra now has an obligatory `bufferFactory` (#477).
### Changed
- Kotlin 1.7
- Kotlin 1.7.20
- `LazyStructure` `deffered` -> `async` to comply with coroutines code style
- Default `dot` operation in tensor algebra no longer support broadcasting. Instead `bdot` operation is added to `DoubleTensorAlgebra`.
### Deprecated

11
kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/TensorAlgebra.kt
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@ -213,16 +213,7 @@ public interface TensorAlgebra<T, A : Ring<T>> : RingOpsND<T, A> {
* 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 broadcast (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
* Otherwise, throw an exception.
*
* @param other tensor to be multiplied.
* @return a mathematical product of two tensors.

46
kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt
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@ -381,7 +381,36 @@ public open class DoubleTensorAlgebra :
override fun Tensor<Double>.viewAs(other: StructureND<Double>): DoubleTensor =
tensor.view(other.shape)
override infix fun StructureND<Double>.dot(other: StructureND<Double>): DoubleTensor {
/**
* Broadcasting 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, depending on the implementation the prepended dimension might be 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 broadcast (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 a mathematical product of two tensors.
*/
public infix fun StructureND<Double>.bdot(other: StructureND<Double>): DoubleTensor {
if (tensor.shape.size == 1 && other.shape.size == 1) {
return DoubleTensor(intArrayOf(1), doubleArrayOf(tensor.times(other).tensor.mutableBuffer.array().sum()))
}
@ -430,6 +459,11 @@ public open class DoubleTensorAlgebra :
}
}
override fun StructureND<Double>.dot(other: StructureND<Double>): DoubleTensor {
return if (dimension in 0..2 && other.dimension in 0..2) bdot(other)
else error("Only vectors and matrices are allowed in non-broadcasting dot operation")
}
override fun diagonalEmbedding(
diagonalEntries: Tensor<Double>,
offset: Int,
@ -587,7 +621,8 @@ public open class DoubleTensorAlgebra :
val resNumElements = resShape.reduce(Int::times)
val init = foldFunction(DoubleArray(1) { 0.0 })
val resTensor = BufferedTensor(resShape,
MutableBuffer.auto(resNumElements) { init }, 0)
MutableBuffer.auto(resNumElements) { init }, 0
)
for (index in resTensor.indices) {
val prefix = index.take(dim).toIntArray()
val suffix = index.takeLast(dimension - dim - 1).toIntArray()
@ -882,7 +917,8 @@ public open class DoubleTensorAlgebra :
return Triple(uTensor.transpose(), sTensor, vTensor.transpose())
}
override fun StructureND<Double>.symEig(): Pair<DoubleTensor, DoubleTensor> = symEigJacobi(maxIteration = 50, epsilon = 1e-15)
override fun StructureND<Double>.symEig(): Pair<DoubleTensor, DoubleTensor> =
symEigJacobi(maxIteration = 50, epsilon = 1e-15)
/**
* Returns eigenvalues and eigenvectors of a real symmetric matrix input or a batch of real symmetric matrices,
@ -909,7 +945,7 @@ public open class DoubleTensorAlgebra :
val (u, s, v) = tensor.svd(epsilon)
val shp = s.shape + intArrayOf(1)
val utv = u.transpose() dot v
val utv = u.transpose() bdot v
val n = s.shape.last()
for (matrix in utv.matrixSequence()) {
matrix.as2D().cleanSym(n)
@ -951,7 +987,7 @@ public open class DoubleTensorAlgebra :
private fun MutableStructure2D<Double>.jacobiHelper(
maxIteration: Int,
epsilon: Double
epsilon: Double,
): Pair<Structure1D<Double>, Structure2D<Double>> {
val n = this.shape[0]
val A_ = this.copy()

12
kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleLinearOpsAlgebra.kt
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@ -115,7 +115,7 @@ internal class TestDoubleLinearOpsTensorAlgebra {
assertTrue { q.shape contentEquals shape }
assertTrue { r.shape contentEquals shape }
assertTrue((q dot r).eq(tensor))
assertTrue((q bdot r).eq(tensor))
}
@ -136,17 +136,17 @@ internal class TestDoubleLinearOpsTensorAlgebra {
assertTrue { l.shape contentEquals shape }
assertTrue { u.shape contentEquals shape }
assertTrue((p dot tensor).eq(l dot u))
assertTrue((p bdot tensor).eq(l bdot u))
}
@Test
fun testCholesky() = DoubleTensorAlgebra {
val tensor = randomNormal(intArrayOf(2, 5, 5), 0)
val sigma = (tensor dot tensor.transpose()) + diagonalEmbedding(
val sigma = (tensor bdot tensor.transpose()) + diagonalEmbedding(
fromArray(intArrayOf(2, 5), DoubleArray(10) { 0.1 })
)
val low = sigma.cholesky()
val sigmChol = low dot low.transpose()
val sigmChol = low bdot low.transpose()
assertTrue(sigma.eq(sigmChol))
}
@ -171,7 +171,7 @@ internal class TestDoubleLinearOpsTensorAlgebra {
fun testBatchedSVD() = DoubleTensorAlgebra {
val tensor = randomNormal(intArrayOf(2, 5, 3), 0)
val (tensorU, tensorS, tensorV) = tensor.svd()
val tensorSVD = tensorU dot (diagonalEmbedding(tensorS) dot tensorV.transpose())
val tensorSVD = tensorU bdot (diagonalEmbedding(tensorS) bdot tensorV.transpose())
assertTrue(tensor.eq(tensorSVD))
}
@ -180,7 +180,7 @@ internal class TestDoubleLinearOpsTensorAlgebra {
val tensor = randomNormal(shape = intArrayOf(2, 3, 3), 0)
val tensorSigma = tensor + tensor.transpose()
val (tensorS, tensorV) = tensorSigma.symEig()
val tensorSigmaCalc = tensorV dot (diagonalEmbedding(tensorS) dot tensorV.transpose())
val tensorSigmaCalc = tensorV bdot (diagonalEmbedding(tensorS) bdot tensorV.transpose())
assertTrue(tensorSigma.eq(tensorSigmaCalc))
}

4
kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleTensorAlgebra.kt
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@ -114,7 +114,7 @@ internal class TestDoubleTensorAlgebra {
assertTrue(res12.mutableBuffer.array() contentEquals doubleArrayOf(140.0, 320.0))
assertTrue(res12.shape contentEquals intArrayOf(2))
val res32 = tensor3.dot(tensor2)
val res32 = tensor3.bdot(tensor2)
assertTrue(res32.mutableBuffer.array() contentEquals doubleArrayOf(-140.0))
assertTrue(res32.shape contentEquals intArrayOf(1, 1))
@ -126,7 +126,7 @@ internal class TestDoubleTensorAlgebra {
assertTrue(res11.mutableBuffer.array() contentEquals doubleArrayOf(22.0, 28.0, 49.0, 64.0))
assertTrue(res11.shape contentEquals intArrayOf(2, 2))
val res45 = tensor4.dot(tensor5)
val res45 = tensor4.bdot(tensor5)
assertTrue(res45.mutableBuffer.array() contentEquals doubleArrayOf(
36.0, 42.0, 48.0, 81.0, 96.0, 111.0, 126.0, 150.0, 174.0,
468.0, 501.0, 534.0, 594.0, 636.0, 678.0, 720.0, 771.0, 822.0