Golub-Kahan SVD algorithm for KMP tensors #499
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/*
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* Copyright 2018-2021 KMath contributors.
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* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
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*/
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package space.kscience.kmath.tensors
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import space.kscience.kmath.linear.transpose
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import space.kscience.kmath.misc.PerformancePitfall
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import space.kscience.kmath.nd.MutableStructure2D
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import space.kscience.kmath.nd.Structure2D
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import space.kscience.kmath.nd.as2D
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import space.kscience.kmath.tensors.core.*
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import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.dot
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import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.mapIndexed
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import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.zeros
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import space.kscience.kmath.tensors.core.DoubleTensorAlgebra.Companion.minus
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import space.kscience.kmath.tensors.core.DoubleTensorAlgebra.Companion.sum
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import space.kscience.kmath.tensors.core.tensorAlgebra
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import kotlin.math.*
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fun DoubleArray.fmap(transform: (Double) -> Double): DoubleArray {
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return this.map(transform).toDoubleArray()
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}
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fun scalarProduct(v1: Structure2D<Double>, v2: Structure2D<Double>): Double {
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return v1.mapIndexed { index, d -> d * v2[index] }.sum()
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}
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internal fun diagonal(shape: IntArray, v: Double) : DoubleTensor {
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val matrix = zeros(shape)
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return matrix.mapIndexed { index, _ -> if (index.component1() == index.component2()) v else 0.0 }
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}
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fun MutableStructure2D<Double>.print() {
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val n = this.shape.component1()
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val m = this.shape.component2()
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for (i in 0 until n) {
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for (j in 0 until m) {
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val x = (this[i, j] * 100).roundToInt() / 100.0
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print("$x ")
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}
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println()
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}
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println("______________")
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}
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@OptIn(PerformancePitfall::class)
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fun main(): Unit = Double.tensorAlgebra.withBroadcast {
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val shape = intArrayOf(5, 3)
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val buffer = doubleArrayOf(
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1.000000, 2.000000, 3.000000,
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2.000000, 3.000000, 4.000000,
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3.000000, 4.000000, 5.000000,
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4.000000, 5.000000, 6.000000,
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5.000000, 6.000000, 7.000000
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)
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val buffer2 = doubleArrayOf(
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0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000,
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0.000000, 0.000000, 0.000000
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)
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val tensor = fromArray(shape, buffer).as2D()
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val v = fromArray(shape, buffer2).as2D()
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tensor.print()
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tensor.svdcmp(v)
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// tensor.print()
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}
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276
examples/src/main/kotlin/space/kscience/kmath/tensors/svdcmp.kt
Normal file
276
examples/src/main/kotlin/space/kscience/kmath/tensors/svdcmp.kt
Normal file
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package space.kscience.kmath.tensors
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import space.kscience.kmath.nd.*
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import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra
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import kotlin.math.abs
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import kotlin.math.max
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import kotlin.math.min
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import kotlin.math.sqrt
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/*
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* Copyright 2018-2021 KMath contributors.
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* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
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*/
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fun pythag(a: Double, b: Double): Double {
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val at: Double = abs(a)
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val bt: Double = abs(b)
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val ct: Double
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val result: Double
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if (at > bt) {
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ct = bt / at
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result = at * sqrt(1.0 + ct * ct)
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} else if (bt > 0.0) {
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ct = at / bt
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result = bt * sqrt(1.0 + ct * ct)
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} else result = 0.0
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return result
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}
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fun SIGN(a: Double, b: Double): Double {
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if (b >= 0.0)
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return abs(a)
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else
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return -abs(a)
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}
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internal fun MutableStructure2D<Double>.svdcmp(v: MutableStructure2D<Double>) {
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val shape = this.shape
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val n = shape.component2()
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val m = shape.component1()
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var f = 0.0
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val rv1 = DoubleArray(n)
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var s = 0.0
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var scale = 0.0
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var anorm = 0.0
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var g = 0.0
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var l = 0
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val w_shape = intArrayOf(m, 1)
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var w_buffer = doubleArrayOf(0.000000)
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for (i in 0 until m - 1) {
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w_buffer += doubleArrayOf(0.000000)
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}
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val w = BroadcastDoubleTensorAlgebra.fromArray(w_shape, w_buffer).as2D()
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for (i in 0 until n) {
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/* left-hand reduction */
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l = i + 1
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rv1[i] = scale * g
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g = 0.0
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s = 0.0
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scale = 0.0
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if (i < m) {
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for (k in i until m) {
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scale += abs(this[k, i]);
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}
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if (scale != 0.0) {
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for (k in i until m) {
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this[k, i] = (this[k, i] / scale)
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s += this[k, i] * this[k, i]
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}
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f = this[i, i]
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if (f >= 0) {
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g = (-1) * abs(sqrt(s))
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}
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else {
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g = abs(sqrt(s))
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}
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val h = f * g - s
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this[i, i] = f - g
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if (i != n - 1) {
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for (j in l until n) {
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s = 0.0
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for (k in i until m) {
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s += this[k, i] * this[k, j]
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}
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f = s / h
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for (k in i until m) {
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this[k, j] += f * this[k, i]
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}
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}
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}
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for (k in i until m) {
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this[k, i] = this[k, i] * scale
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}
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}
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}
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w[i, 0] = scale * g
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/* right-hand reduction */
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g = 0.0
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s = 0.0
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scale = 0.0
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if (i < m && i != n - 1) {
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for (k in l until n) {
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scale += abs(this[i, k])
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}
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if (scale != 0.0) {
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for (k in l until n) {
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this[i, k] = this[i, k] / scale
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s += this[i, k] * this[i, k]
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}
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f = this[i, l]
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if (f >= 0) {
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g = (-1) * abs(sqrt(s))
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}
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else {
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g = abs(sqrt(s))
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}
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val h = f * g - s
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this[i, l] = f - g
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for (k in l until n) {
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rv1[k] = this[i, k] / h
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}
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if (i != m - 1) {
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for (j in l until m) {
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s = 0.0
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for (k in l until n) {
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s += this[j, k] * this[i, k]
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}
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for (k in l until n) {
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this[j, k] += s * rv1[k]
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}
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}
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}
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for (k in l until n) {
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this[i, k] = this[i, k] * scale
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}
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}
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}
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anorm = max(anorm, (abs(w[i, 0]) + abs(rv1[i])));
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}
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for (i in n - 1 downTo 0) {
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if (i < n - 1) {
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if (g != 0.0) {
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for (j in l until n) {
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v[j, i] = (this[i, j] / this[i, l]) / g
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}
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for (j in l until n) {
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s = 0.0
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for (k in l until n)
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s += this[i, k] * v[k, j]
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for (k in l until n)
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v[k, j] += s * v[k, i]
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}
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}
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for (j in l until n) {
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v[i, j] = 0.0
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v[j, i] = 0.0
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}
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}
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v[i, i] = 1.0
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g = rv1[i]
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l = i
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}
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// тут все правильно считается
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// println("w")
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// w.print()
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//
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val eps = 0.000000001
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// println("1.0 / w[2, 0] " + 1.0 / w[2, 0])
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// println("w[2, 0] " + w[2, 0])
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for (i in min(n, m) - 1 downTo 0) {
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l = i + 1
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g = w[i, 0]
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// println("w[i, 0] " + w[i, 0])
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for (j in l until n) {
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this[i, j] = 0.0
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}
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if (g != 0.0) {
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g = 1.0 / g
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// println("g " + g)
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for (j in l until n) {
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s = 0.0
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for (k in l until m) {
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s += this[k, i] * this[k, j]
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}
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f = (s / this[i, i]) * g
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for (k in i until m) {
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this[k, j] += f * this[k, i]
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}
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}
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for (j in i until m) {
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this[j, i] *= g
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}
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}
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else {
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for (j in i until m) {
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this[j, i] = 0.0
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}
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}
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this[i, i] += 1.0
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// println("matrix")
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// this.print()
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}
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println("matrix")
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this.print()
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// тут матрица должна выглядеть так:
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// 0.134840 -0.762770 0.522117
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// -0.269680 -0.476731 -0.245388
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// -0.404520 -0.190693 -0.527383
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// -0.539360 0.095346 -0.297540
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// -0.674200 0.381385 0.548193
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// var flag = 0
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// var nm = 0
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// var c = 0.0
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// var h = 0.0
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// var y = 0.0
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// var z = 0.0
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// for (k in n - 1 downTo 0) {
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// for (its in 0 until 30) {
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// flag = 0
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// for (l in k downTo 0) {
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// nm = l - 1
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// if (abs(rv1[l]) < eps) {
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// flag = 0
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//// println("break1")
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// break
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// }
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// if (abs(w[nm, 0]) < eps) {
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// println("break2")
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// break
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// }
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// }
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//
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// // l = 1 тут
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//
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// if (flag != 0) {
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// c = 0.0
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// s = 0.0
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// for (i in l until k) { // а точно ли такие границы? там немного отличается
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// f=s*rv1[i]
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// rv1[i]=c*rv1[i]
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// if (abs(f) < eps) {
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// println("break3")
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// break
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// }
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// g=w[i, 0]
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// h=pythag(f,g)
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// w[i, 0]=h
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// h=1.0/h
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// c=g*h
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// s = -f*h
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// for (j in 0 until m) { // точно ли такие границы?
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// y=this[j, nm]
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// z=this[j, i]
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// this[j, nm]=y*c+z*s
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// this[j, i]=z*c-y*s
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// }
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// }
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// }
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//
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//
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// }
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// }
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}
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