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Refactor/ndalgebra #197

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altavir merged 11 commits from refactor/ndalgebra into dev 2021-01-28 20:13:39 +03:00
Conversation 0 Commits 11 Files Changed 69 +79 -33
9 changed files with 79 additions and 33 deletions
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3
CHANGELOG.md
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@ -32,9 +32,10 @@
- Use `Point<Double>` instead of specialized type in `kmath-for-real`
- Optimized dot product for buffer matrices moved to `kmath-for-real`
- EjmlMatrix context is an object
- Matrix LUP `inverse` renamed to `inverseWithLUP`
- Matrix LUP `inverse` renamed to `inverseWithLup`
- `NumericAlgebra` moved outside of regular algebra chain (`Ring` no longer implements it).
- Features moved to NDStructure and became transparent.
- Capitalization of LUP in many names changed to Lup.
- Refactored `NDStructure` algebra to be more simple, preferring under-the-hood conversion to explicit NDStructure types
### Deprecated

7
examples/src/benchmarks/kotlin/kscience/kmath/benchmarks/LinearAlgebraBenchmark.kt
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@ -8,6 +8,7 @@ import kscience.kmath.commons.linear.inverse
import kscience.kmath.ejml.EjmlMatrixContext
import kscience.kmath.ejml.inverse
import kscience.kmath.operations.invoke
import kscience.kmath.structures.Matrix
import org.openjdk.jmh.annotations.Scope
import org.openjdk.jmh.annotations.State
import kotlin.random.Random
@ -25,10 +26,8 @@ class LinearAlgebraBenchmark {
}
@Benchmark
fun kmathLUPInversion() {
MatrixContext.real{
inverseWithLUP(matrix)
}
fun kmathLupInversion() {
MatrixContext.real.inverseWithLup(matrix)
}
@Benchmark

36
kmath-commons/src/main/kotlin/kscience/kmath/commons/linear/CMMatrix.kt
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@ -2,6 +2,8 @@ package kscience.kmath.commons.linear
import kscience.kmath.linear.*
import kscience.kmath.misc.UnstableKMathAPI
import kscience.kmath.structures.Matrix
import kscience.kmath.structures.RealBuffer
import org.apache.commons.math3.linear.*
import kotlin.reflect.KClass
import kotlin.reflect.cast
@ -13,8 +15,40 @@ public inline class CMMatrix(public val origin: RealMatrix) : Matrix<Double> {
@UnstableKMathAPI
override fun <T : Any> getFeature(type: KClass<T>): T? = when (type) {
DiagonalFeature::class -> if (origin is DiagonalMatrix) DiagonalFeature else null
DeterminantFeature::class, LupDecompositionFeature::class -> object :
DeterminantFeature<Double>,
LupDecompositionFeature<Double> {
private val lup by lazy { LUDecomposition(origin) }
override val determinant: Double by lazy { lup.determinant }
override val l: Matrix<Double> by lazy { CMMatrix(lup.l) + LFeature }
override val u: Matrix<Double> by lazy { CMMatrix(lup.u) + UFeature }
override val p: Matrix<Double> by lazy { CMMatrix(lup.p) }
}
CholeskyDecompositionFeature::class -> object : CholeskyDecompositionFeature<Double> {
override val l: Matrix<Double> by lazy {
val cholesky = CholeskyDecomposition(origin)
CMMatrix(cholesky.l) + LFeature
}
}
QRDecompositionFeature::class -> object : QRDecompositionFeature<Double> {
private val qr by lazy { QRDecomposition(origin) }
override val q: Matrix<Double> by lazy { CMMatrix(qr.q) + OrthogonalFeature }
override val r: Matrix<Double> by lazy { CMMatrix(qr.r) + UFeature }
}
SingularValueDecompositionFeature::class -> object : SingularValueDecompositionFeature<Double> {
private val sv by lazy { SingularValueDecomposition(origin) }
override val u: Matrix<Double> by lazy { CMMatrix(sv.u) }
override val s: Matrix<Double> by lazy { CMMatrix(sv.s) }
override val v: Matrix<Double> by lazy { CMMatrix(sv.v) }
override val singularValues: Point<Double> by lazy { RealBuffer(sv.singularValues) }
}
else -> null
}?.let { type.cast(it) }
}?.let(type::cast)
public override operator fun get(i: Int, j: Int): Double = origin.getEntry(i, j)
}

24
kmath-core/src/commonMain/kotlin/kscience/kmath/linear/LupDecomposition.kt
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@ -152,7 +152,7 @@ public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext
public fun MatrixContext<Double, Matrix<Double>>.lup(matrix: Matrix<Double>): LupDecomposition<Double> =
lup(Buffer.Companion::real, RealField, matrix) { it < 1e-11 }
public fun <T : Any> LupDecomposition<T>.solveWithLUP(
public fun <T : Any> LupDecomposition<T>.solveWithLup(
factory: MutableBufferFactory<T>,
matrix: Matrix<T>,
): Matrix<T> {
@ -200,14 +200,14 @@ public fun <T : Any> LupDecomposition<T>.solveWithLUP(
}
}
public inline fun <reified T : Any> LupDecomposition<T>.solveWithLUP(matrix: Matrix<T>): Matrix<T> =
solveWithLUP(MutableBuffer.Companion::auto, matrix)
public inline fun <reified T : Any> LupDecomposition<T>.solveWithLup(matrix: Matrix<T>): Matrix<T> =
solveWithLup(MutableBuffer.Companion::auto, matrix)
/**
* Solve a linear equation **a*x = b** using LUP decomposition
* Solves a system of linear equations *ax = b** using LUP decomposition.
*/
@OptIn(UnstableKMathAPI::class)
public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F, Matrix<T>>.solveWithLUP(
public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F, Matrix<T>>.solveWithLup(
a: Matrix<T>,
b: Matrix<T>,
noinline bufferFactory: MutableBufferFactory<T> = MutableBuffer.Companion::auto,
@ -215,26 +215,26 @@ public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext
): Matrix<T> {
// Use existing decomposition if it is provided by matrix
val decomposition = a.getFeature() ?: lup(bufferFactory, elementContext, a, checkSingular)
return decomposition.solveWithLUP(bufferFactory, b)
return decomposition.solveWithLup(bufferFactory, b)
}
public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F, Matrix<T>>.inverseWithLUP(
public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F, Matrix<T>>.inverseWithLup(
matrix: Matrix<T>,
noinline bufferFactory: MutableBufferFactory<T> = MutableBuffer.Companion::auto,
noinline checkSingular: (T) -> Boolean,
): Matrix<T> = solveWithLUP(matrix, one(matrix.rowNum, matrix.colNum), bufferFactory, checkSingular)
): Matrix<T> = solveWithLup(matrix, one(matrix.rowNum, matrix.colNum), bufferFactory, checkSingular)
@OptIn(UnstableKMathAPI::class)
public fun RealMatrixContext.solveWithLUP(a: Matrix<Double>, b: Matrix<Double>): Matrix<Double> {
public fun RealMatrixContext.solveWithLup(a: Matrix<Double>, b: Matrix<Double>): Matrix<Double> {
// Use existing decomposition if it is provided by matrix
val bufferFactory: MutableBufferFactory<Double> = MutableBuffer.Companion::real
val decomposition: LupDecomposition<Double> = a.getFeature() ?: lup(bufferFactory, RealField, a) { it < 1e-11 }
return decomposition.solveWithLUP(bufferFactory, b)
return decomposition.solveWithLup(bufferFactory, b)
}
/**
* Inverses a square matrix using LUP decomposition. Non square matrix will throw a error.
*/
public fun RealMatrixContext.inverseWithLUP(matrix: Matrix<Double>): Matrix<Double> =
solveWithLUP(matrix, one(matrix.rowNum, matrix.colNum))
public fun RealMatrixContext.inverseWithLup(matrix: Matrix<Double>): Matrix<Double> =
solveWithLup(matrix, one(matrix.rowNum, matrix.colNum))

2
kmath-core/src/commonMain/kotlin/kscience/kmath/linear/MatrixFeatures.kt
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@ -37,6 +37,8 @@ public interface InverseMatrixFeature<T : Any> : MatrixFeature {
/**
* Matrices with this feature can compute their determinant.
*
* @param T the type of matrices' items.
*/
public interface DeterminantFeature<T : Any> : MatrixFeature {
/**

4
kmath-core/src/commonTest/kotlin/kscience/kmath/linear/RealLUSolverTest.kt
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@ -8,7 +8,7 @@ class RealLUSolverTest {
@Test
fun testInvertOne() {
val matrix = MatrixContext.real.one(2, 2)
val inverted = MatrixContext.real.inverseWithLUP(matrix)
val inverted = MatrixContext.real.inverseWithLup(matrix)
assertEquals(matrix, inverted)
}
@ -36,7 +36,7 @@ class RealLUSolverTest {
1.0, 3.0
)
val inverted = MatrixContext.real.inverseWithLUP(matrix)
val inverted = MatrixContext.real.inverseWithLup(matrix)
val expected = Matrix.square(
0.375, -0.125,

22
kmath-ejml/src/main/kotlin/kscience/kmath/ejml/EjmlMatrix.kt
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@ -15,21 +15,20 @@ import kotlin.reflect.cast
* @property origin the underlying [SimpleMatrix].
* @author Iaroslav Postovalov
*/
public class EjmlMatrix(
public val origin: SimpleMatrix,
) : Matrix<Double> {
public class EjmlMatrix(public val origin: SimpleMatrix) : Matrix<Double> {
public override val rowNum: Int get() = origin.numRows()
public override val colNum: Int get() = origin.numCols()
@UnstableKMathAPI
override fun <T : Any> getFeature(type: KClass<T>): T? = when (type) {
public override fun <T : Any> getFeature(type: KClass<T>): T? = when (type) {
InverseMatrixFeature::class -> object : InverseMatrixFeature<Double> {
override val inverse: Matrix<Double> by lazy { EjmlMatrix(origin.invert()) }
}
DeterminantFeature::class -> object : DeterminantFeature<Double> {
override val determinant: Double by lazy(origin::determinant)
}
SingularValueDecompositionFeature::class -> object : SingularValueDecompositionFeature<Double> {
private val svd by lazy {
DecompositionFactory_DDRM.svd(origin.numRows(), origin.numCols(), true, true, false)
@ -41,14 +40,19 @@ public class EjmlMatrix(
override val v: Matrix<Double> by lazy { EjmlMatrix(SimpleMatrix(svd.getV(null, false))) }
override val singularValues: Point<Double> by lazy { RealBuffer(svd.singularValues) }
}
QRDecompositionFeature::class -> object : QRDecompositionFeature<Double> {
private val qr by lazy {
DecompositionFactory_DDRM.qr().apply { decompose(origin.ddrm.copy()) }
}
override val q: Matrix<Double> by lazy { EjmlMatrix(SimpleMatrix(qr.getQ(null, false))) }
override val r: Matrix<Double> by lazy { EjmlMatrix(SimpleMatrix(qr.getR(null, false))) }
override val q: Matrix<Double> by lazy {
EjmlMatrix(SimpleMatrix(qr.getQ(null, false))) + OrthogonalFeature
}
override val r: Matrix<Double> by lazy { EjmlMatrix(SimpleMatrix(qr.getR(null, false))) + UFeature }
}
CholeskyDecompositionFeature::class -> object : CholeskyDecompositionFeature<Double> {
override val l: Matrix<Double> by lazy {
val cholesky =
@ -57,6 +61,7 @@ public class EjmlMatrix(
EjmlMatrix(SimpleMatrix(cholesky.getT(null))) + LFeature
}
}
LupDecompositionFeature::class -> object : LupDecompositionFeature<Double> {
private val lup by lazy {
DecompositionFactory_DDRM.lu(origin.numRows(), origin.numCols()).apply { decompose(origin.ddrm.copy()) }
@ -72,8 +77,9 @@ public class EjmlMatrix(
override val p: Matrix<Double> by lazy { EjmlMatrix(SimpleMatrix(lup.getRowPivot(null))) }
}
else -> null
}?.let { type.cast(it) }
}?.let(type::cast)
public override operator fun get(i: Int, j: Int): Double = origin[i, j]

8
kmath-for-real/src/commonMain/kotlin/kscience/kmath/real/RealMatrix.kt
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@ -1,8 +1,12 @@
package kscience.kmath.real
import kscience.kmath.linear.*
import kscience.kmath.linear.MatrixContext
import kscience.kmath.linear.VirtualMatrix
import kscience.kmath.linear.inverseWithLup
import kscience.kmath.linear.real
import kscience.kmath.misc.UnstableKMathAPI
import kscience.kmath.structures.Buffer
import kscience.kmath.structures.Matrix
import kscience.kmath.structures.RealBuffer
import kscience.kmath.structures.asIterable
import kotlin.math.pow
@ -148,7 +152,7 @@ public inline fun RealMatrix.map(crossinline transform: (Double) -> Double): Rea
/**
* Inverse a square real matrix using LUP decomposition
*/
public fun RealMatrix.inverseWithLUP(): RealMatrix = MatrixContext.real.inverseWithLUP(this)
public fun RealMatrix.inverseWithLup(): RealMatrix = MatrixContext.real.inverseWithLup(this)
//extended operations