Merge pull request #486 from margarita0303/feature/tensors-performance
added partial implementation of svd calculation with divide-by-near-zero error
This commit is contained in:
Roland Grinis
GitHub
commit
13fe078304
@ -0,0 +1,65 @@
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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.tensorAlgebra
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import kotlin.math.*
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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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)
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val tensor = fromArray(shape, buffer).as2D()
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val v = fromArray(intArrayOf(3, 3), buffer2).as2D()
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val w_shape = intArrayOf(3, 1)
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var w_buffer = doubleArrayOf(0.000000)
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for (i in 0 until 3 - 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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tensor.print()
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var ans = Pair(w, v)
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tensor.svdGolabKahan(v, w)
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println("u")
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tensor.print()
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println("w")
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w.print()
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println("v")
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v.print()
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}
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325
examples/src/main/kotlin/space/kscience/kmath/tensors/svdcmp.kt
Normal file
325
examples/src/main/kotlin/space/kscience/kmath/tensors/svdcmp.kt
Normal file
@ -0,0 +1,325 @@
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package space.kscience.kmath.tensors
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import space.kscience.kmath.nd.*
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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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// matrix v is not transposed at the output
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internal fun MutableStructure2D<Double>.svdGolabKahan(v: MutableStructure2D<Double>, w: MutableStructure2D<Double>) {
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val shape = this.shape
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val m = shape.component1()
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val n = shape.component2()
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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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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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} 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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} 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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// до этого момента все правильно считается
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// дальше - нет
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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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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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// !!!!! вот тут деление на почти ноль
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g = 1.0 / 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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} 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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}
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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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this[0, 2] = 0.522117
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this[1, 2] = -0.245388
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this[2, 2] = -0.527383
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this[3, 2] = -0.297540
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this[4, 2] = 0.548193
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// задала правильные значения, чтобы проверить правильность кода дальше
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// дальше - все корректно
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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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var x = 0.0
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for (k in n - 1 downTo 0) {
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for (its in 1 until 30) {
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flag = 1
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for (newl in k downTo 0) {
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nm = newl - 1
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if (abs(rv1[newl]) + anorm == anorm) {
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flag = 0
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l = newl
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break
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}
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if (abs(w[nm, 0]) + anorm == anorm) {
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l = newl
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break
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}
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}
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if (flag != 0) {
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c = 0.0
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s = 1.0
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for (i in l until k) {
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f = s * rv1[i]
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rv1[i] = c * rv1[i]
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if (abs(f) + anorm == anorm) {
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break
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}
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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) {
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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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z = w[k, 0]
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if (l == k) {
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if (z < 0.0) {
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w[k, 0] = -z
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for (j in 0 until n)
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v[j, k] = -v[j, k]
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}
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break
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}
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// надо придумать, что сделать - выкинуть ошибку?
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// if (its == 30) {
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// return
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// }
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x = w[l, 0]
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nm = k - 1
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y = w[nm, 0]
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g = rv1[nm]
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h = rv1[k]
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f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y)
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g = pythag(f, 1.0)
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f = ((x - z) * (x + z) + h * ((y / (f + SIGN(g, f))) - h)) / x
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c = 1.0
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s = 1.0
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var i = 0
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for (j in l until nm + 1) {
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i = j + 1
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g = rv1[i]
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y = w[i, 0]
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h = s * g
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g = c * g
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z = pythag(f, h)
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rv1[j] = z
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c = f / z
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s = h / z
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f = x * c + g * s
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g = g * c - x * s
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h = y * s
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y *= c
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for (jj in 0 until n) {
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x = v[jj, j];
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z = v[jj, i];
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v[jj, j] = x * c + z * s;
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v[jj, i] = z * c - x * s;
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}
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z = pythag(f, h)
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w[j, 0] = z
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if (z != 0.0) {
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z = 1.0 / z
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c = f * z
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s = h * z
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}
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f = c * g + s * y
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x = c * y - s * g
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for (jj in 0 until m) {
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y = this[jj, j]
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z = this[jj, i]
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this[jj, j] = y * c + z * s
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this[jj, i] = z * c - y * s
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}
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}
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rv1[l] = 0.0
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rv1[k] = f
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w[k, 0] = x
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}
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}
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}
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@ -132,6 +132,27 @@ internal class TestDoubleTensorAlgebra {
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468.0, 501.0, 534.0, 594.0, 636.0, 678.0, 720.0, 771.0, 822.0
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))
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assertTrue(res45.shape contentEquals intArrayOf(2, 3, 3))
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val oneDimTensor1 = fromArray(intArrayOf(3), doubleArrayOf(1.0, 2.0, 3.0))
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val oneDimTensor2 = fromArray(intArrayOf(3), doubleArrayOf(4.0, 5.0, 6.0))
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val resOneDimTensors = oneDimTensor1.dot(oneDimTensor2)
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assertTrue(resOneDimTensors.mutableBuffer.array() contentEquals doubleArrayOf(32.0))
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assertTrue(resOneDimTensors.shape contentEquals intArrayOf(1))
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val twoDimTensor1 = fromArray(intArrayOf(2, 2), doubleArrayOf(1.0, 2.0, 3.0, 4.0))
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val twoDimTensor2 = fromArray(intArrayOf(2, 2), doubleArrayOf(5.0, 6.0, 7.0, 8.0))
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val resTwoDimTensors = twoDimTensor1.dot(twoDimTensor2)
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assertTrue(resTwoDimTensors.mutableBuffer.array() contentEquals doubleArrayOf(19.0, 22.0, 43.0, 50.0))
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assertTrue(resTwoDimTensors.shape contentEquals intArrayOf(2, 2))
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val oneDimTensor3 = fromArray(intArrayOf(2), doubleArrayOf(1.0, 2.0))
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val resOneDimTensorOnTwoDimTensor = oneDimTensor3.dot(twoDimTensor1)
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assertTrue(resOneDimTensorOnTwoDimTensor.mutableBuffer.array() contentEquals doubleArrayOf(7.0, 10.0))
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assertTrue(resOneDimTensorOnTwoDimTensor.shape contentEquals intArrayOf(2))
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val resTwoDimTensorOnOneDimTensor = twoDimTensor1.dot(oneDimTensor3)
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assertTrue(resTwoDimTensorOnOneDimTensor.mutableBuffer.array() contentEquals doubleArrayOf(5.0, 11.0))
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assertTrue(resTwoDimTensorOnOneDimTensor.shape contentEquals intArrayOf(2))
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}
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@Test
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