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Added Levenberg-Marquardt algorithm and svd Golub-Kahan #513

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margarita0303 merged 35 commits from dev into dev 2023-06-19 16:11:59 +03:00
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7 changed files with 125 additions and 128 deletions
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13
examples/src/main/kotlin/space/kscience/kmath/tensors/LevenbergMarquardt/StaticLm/staticDifficultTest.kt
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@ -12,7 +12,6 @@ import space.kscience.kmath.tensors.LevenbergMarquardt.funcDifficultForLm
import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra
import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.div import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.div
import space.kscience.kmath.tensors.core.DoubleTensorAlgebra import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
import space.kscience.kmath.tensors.core.LMSettings
import space.kscience.kmath.tensors.core.lm import space.kscience.kmath.tensors.core.lm
import kotlin.math.roundToInt import kotlin.math.roundToInt
@ -29,9 +28,9 @@ fun main() {
p_example[i, 0] = p_example[i, 0] + i - 25 p_example[i, 0] = p_example[i, 0] + i - 25
} }
val settings = LMSettings(0, 0, 1) val exampleNumber = 1
var y_hat = funcDifficultForLm(t_example, p_example, settings) var y_hat = funcDifficultForLm(t_example, p_example, exampleNumber)
var p_init = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(Nparams, 1))).as2D() var p_init = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(Nparams, 1))).as2D()
for (i in 0 until Nparams) { for (i in 0 until Nparams) {
@ -72,14 +71,14 @@ fun main() {
) )
println("Parameters:") println("Parameters:")
for (i in 0 until result.result_parameters.shape.component1()) { for (i in 0 until result.resultParameters.shape.component1()) {
val x = (result.result_parameters[i, 0] * 10000).roundToInt() / 10000.0 val x = (result.resultParameters[i, 0] * 10000).roundToInt() / 10000.0
print("$x ") print("$x ")
} }
println() println()
println("Y true and y received:") println("Y true and y received:")
var y_hat_after = funcDifficultForLm(t_example, result.result_parameters, settings) var y_hat_after = funcDifficultForLm(t_example, result.resultParameters, exampleNumber)
for (i in 0 until y_hat.shape.component1()) { for (i in 0 until y_hat.shape.component1()) {
val x = (y_hat[i, 0] * 10000).roundToInt() / 10000.0 val x = (y_hat[i, 0] * 10000).roundToInt() / 10000.0
val y = (y_hat_after[i, 0] * 10000).roundToInt() / 10000.0 val y = (y_hat_after[i, 0] * 10000).roundToInt() / 10000.0
@ -87,7 +86,7 @@ fun main() {
} }
println("Сhi_sq:") println("Сhi_sq:")
println(result.result_chi_sq) println(result.resultChiSq)
println("Number of iterations:") println("Number of iterations:")
println(result.iterations) println(result.iterations)
} }

9
examples/src/main/kotlin/space/kscience/kmath/tensors/LevenbergMarquardt/StaticLm/staticEasyTest.kt
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@ -12,7 +12,6 @@ import space.kscience.kmath.tensors.LevenbergMarquardt.funcDifficultForLm
import space.kscience.kmath.tensors.LevenbergMarquardt.funcEasyForLm import space.kscience.kmath.tensors.LevenbergMarquardt.funcEasyForLm
import space.kscience.kmath.tensors.LevenbergMarquardt.getStartDataForFuncEasy import space.kscience.kmath.tensors.LevenbergMarquardt.getStartDataForFuncEasy
import space.kscience.kmath.tensors.core.DoubleTensorAlgebra import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
import space.kscience.kmath.tensors.core.LMSettings
import space.kscience.kmath.tensors.core.lm import space.kscience.kmath.tensors.core.lm
import kotlin.math.roundToInt import kotlin.math.roundToInt
@ -35,14 +34,14 @@ fun main() {
) )
println("Parameters:") println("Parameters:")
for (i in 0 until result.result_parameters.shape.component1()) { for (i in 0 until result.resultParameters.shape.component1()) {
val x = (result.result_parameters[i, 0] * 10000).roundToInt() / 10000.0 val x = (result.resultParameters[i, 0] * 10000).roundToInt() / 10000.0
print("$x ") print("$x ")
} }
println() println()
println("Y true and y received:") println("Y true and y received:")
var y_hat_after = funcDifficultForLm(startedData.t, result.result_parameters, LMSettings(0, 0, startedData.example_number)) var y_hat_after = funcDifficultForLm(startedData.t, result.resultParameters, startedData.example_number)
for (i in 0 until startedData.y_dat.shape.component1()) { for (i in 0 until startedData.y_dat.shape.component1()) {
val x = (startedData.y_dat[i, 0] * 10000).roundToInt() / 10000.0 val x = (startedData.y_dat[i, 0] * 10000).roundToInt() / 10000.0
val y = (y_hat_after[i, 0] * 10000).roundToInt() / 10000.0 val y = (y_hat_after[i, 0] * 10000).roundToInt() / 10000.0
@ -50,7 +49,7 @@ fun main() {
} }
println("Сhi_sq:") println("Сhi_sq:")
println(result.result_chi_sq) println(result.resultChiSq)
println("Number of iterations:") println("Number of iterations:")
println(result.iterations) println(result.iterations)
} }

19
examples/src/main/kotlin/space/kscience/kmath/tensors/LevenbergMarquardt/StaticLm/staticMiddleTest.kt
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@ -12,8 +12,6 @@ import space.kscience.kmath.tensors.LevenbergMarquardt.funcMiddleForLm
import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra
import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.div import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.div
import space.kscience.kmath.tensors.core.DoubleTensorAlgebra import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
import space.kscience.kmath.tensors.core.DoubleTensorAlgebra.Companion.times
import space.kscience.kmath.tensors.core.LMSettings
import space.kscience.kmath.tensors.core.lm import space.kscience.kmath.tensors.core.lm
import kotlin.math.roundToInt import kotlin.math.roundToInt
fun main() { fun main() {
@ -29,16 +27,15 @@ fun main() {
p_example[i, 0] = p_example[i, 0] + i - 25 p_example[i, 0] = p_example[i, 0] + i - 25
} }
val settings = LMSettings(0, 0, 1) val exampleNumber = 1
var y_hat = funcMiddleForLm(t_example, p_example, settings) var y_hat = funcMiddleForLm(t_example, p_example, exampleNumber)
var p_init = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(Nparams, 1))).as2D() var p_init = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(Nparams, 1))).as2D()
for (i in 0 until Nparams) { for (i in 0 until Nparams) {
p_init[i, 0] = (p_example[i, 0] + 0.9) p_init[i, 0] = (p_example[i, 0] + 0.9)
} }
// val p_init = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(Nparams, 1)))
// val p_init = p_example
var t = t_example var t = t_example
val y_dat = y_hat val y_dat = y_hat
val weight = BroadcastDoubleTensorAlgebra.fromArray( val weight = BroadcastDoubleTensorAlgebra.fromArray(
@ -54,7 +51,7 @@ fun main() {
val consts = BroadcastDoubleTensorAlgebra.fromArray( val consts = BroadcastDoubleTensorAlgebra.fromArray(
ShapeND(intArrayOf(1, 1)), doubleArrayOf(0.0) ShapeND(intArrayOf(1, 1)), doubleArrayOf(0.0)
).as2D() ).as2D()
val opts = doubleArrayOf(3.0, 10000.0, 1e-3, 1e-3, 1e-3, 1e-3, 1e-15, 11.0, 9.0, 1.0) val opts = doubleArrayOf(3.0, 7000.0, 1e-5, 1e-5, 1e-5, 1e-5, 1e-5, 11.0, 9.0, 1.0)
val result = DoubleTensorAlgebra.lm( val result = DoubleTensorAlgebra.lm(
::funcMiddleForLm, ::funcMiddleForLm,
@ -72,14 +69,14 @@ fun main() {
) )
println("Parameters:") println("Parameters:")
for (i in 0 until result.result_parameters.shape.component1()) { for (i in 0 until result.resultParameters.shape.component1()) {
val x = (result.result_parameters[i, 0] * 10000).roundToInt() / 10000.0 val x = (result.resultParameters[i, 0] * 10000).roundToInt() / 10000.0
print("$x ") print("$x ")
} }
println() println()
var y_hat_after = funcMiddleForLm(t_example, result.result_parameters, settings) var y_hat_after = funcMiddleForLm(t_example, result.resultParameters, exampleNumber)
for (i in 0 until y_hat.shape.component1()) { for (i in 0 until y_hat.shape.component1()) {
val x = (y_hat[i, 0] * 10000).roundToInt() / 10000.0 val x = (y_hat[i, 0] * 10000).roundToInt() / 10000.0
val y = (y_hat_after[i, 0] * 10000).roundToInt() / 10000.0 val y = (y_hat_after[i, 0] * 10000).roundToInt() / 10000.0
@ -87,7 +84,7 @@ fun main() {
} }
println("Сhi_sq:") println("Сhi_sq:")
println(result.result_chi_sq) println(result.resultChiSq)
println("Number of iterations:") println("Number of iterations:")
println(result.iterations) println(result.iterations)
} }

7
examples/src/main/kotlin/space/kscience/kmath/tensors/LevenbergMarquardt/StreamingLm/streamLm.kt
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@ -11,12 +11,11 @@ import space.kscience.kmath.nd.*
import space.kscience.kmath.tensors.LevenbergMarquardt.StartDataLm import space.kscience.kmath.tensors.LevenbergMarquardt.StartDataLm
import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.zeros import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.zeros
import space.kscience.kmath.tensors.core.DoubleTensorAlgebra import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
import space.kscience.kmath.tensors.core.LMSettings
import space.kscience.kmath.tensors.core.lm import space.kscience.kmath.tensors.core.lm
import kotlin.random.Random import kotlin.random.Random
import kotlin.reflect.KFunction3 import kotlin.reflect.KFunction3
fun streamLm(lm_func: KFunction3<MutableStructure2D<Double>, MutableStructure2D<Double>, LMSettings, MutableStructure2D<Double>>, fun streamLm(lm_func: KFunction3<MutableStructure2D<Double>, MutableStructure2D<Double>, Int, MutableStructure2D<Double>>,
startData: StartDataLm, launchFrequencyInMs: Long, numberOfLaunches: Int): Flow<MutableStructure2D<Double>> = flow{ startData: StartDataLm, launchFrequencyInMs: Long, numberOfLaunches: Int): Flow<MutableStructure2D<Double>> = flow{
var example_number = startData.example_number var example_number = startData.example_number
@ -48,9 +47,9 @@ fun streamLm(lm_func: KFunction3<MutableStructure2D<Double>, MutableStructure2D<
10, 10,
example_number example_number
) )
emit(result.result_parameters) emit(result.resultParameters)
delay(launchFrequencyInMs) delay(launchFrequencyInMs)
p_init = result.result_parameters p_init = result.resultParameters
y_dat = generateNewYDat(y_dat, 0.1) y_dat = generateNewYDat(y_dat, 0.1)
if (!isEndless) steps -= 1 if (!isEndless) steps -= 1
} }

60
examples/src/main/kotlin/space/kscience/kmath/tensors/LevenbergMarquardt/functionsToOptimize.kt
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@ -16,7 +16,6 @@ import space.kscience.kmath.tensors.core.DoubleTensorAlgebra.Companion.max
import space.kscience.kmath.tensors.core.DoubleTensorAlgebra.Companion.plus import space.kscience.kmath.tensors.core.DoubleTensorAlgebra.Companion.plus
import space.kscience.kmath.tensors.core.DoubleTensorAlgebra.Companion.pow import space.kscience.kmath.tensors.core.DoubleTensorAlgebra.Companion.pow
import space.kscience.kmath.tensors.core.DoubleTensorAlgebra.Companion.times import space.kscience.kmath.tensors.core.DoubleTensorAlgebra.Companion.times
import space.kscience.kmath.tensors.core.LMSettings
import space.kscience.kmath.tensors.core.asDoubleTensor import space.kscience.kmath.tensors.core.asDoubleTensor
public data class StartDataLm ( public data class StartDataLm (
@ -33,23 +32,31 @@ public data class StartDataLm (
var opts: DoubleArray var opts: DoubleArray
) )
fun funcDifficultForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> { fun funcEasyForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, exampleNumber: Int): MutableStructure2D<Double> {
val m = t.shape.component1() val m = t.shape.component1()
var y_hat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf (m, 1))) var y_hat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(m, 1)))
val mt = t.max() if (exampleNumber == 1) {
for(i in 0 until p.shape.component1()){ y_hat = DoubleTensorAlgebra.exp((t.times(-1.0 / p[1, 0]))).times(p[0, 0]) + t.times(p[2, 0]).times(
y_hat = y_hat.plus( (t.times(1.0 / mt)).times(p[i, 0]) ) DoubleTensorAlgebra.exp((t.times(-1.0 / p[3, 0])))
)
} }
else if (exampleNumber == 2) {
for(i in 0 until 4){ val mt = t.max()
y_hat = funcEasyForLm((y_hat.as2D() + t).as2D(), p, settings).asDoubleTensor() y_hat = (t.times(1.0 / mt)).times(p[0, 0]) +
(t.times(1.0 / mt)).pow(2).times(p[1, 0]) +
(t.times(1.0 / mt)).pow(3).times(p[2, 0]) +
(t.times(1.0 / mt)).pow(4).times(p[3, 0])
}
else if (exampleNumber == 3) {
y_hat = DoubleTensorAlgebra.exp((t.times(-1.0 / p[1, 0])))
.times(p[0, 0]) + DoubleTensorAlgebra.sin((t.times(1.0 / p[3, 0]))).times(p[2, 0])
} }
return y_hat.as2D() return y_hat.as2D()
} }
fun funcMiddleForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> { fun funcMiddleForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, exampleNumber: Int): MutableStructure2D<Double> {
val m = t.shape.component1() val m = t.shape.component1()
var y_hat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf (m, 1))) var y_hat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf (m, 1)))
@ -59,36 +66,29 @@ fun funcMiddleForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>
} }
for(i in 0 until 5){ for(i in 0 until 5){
y_hat = funcEasyForLm(y_hat.as2D(), p, settings).asDoubleTensor() y_hat = funcEasyForLm(y_hat.as2D(), p, exampleNumber).asDoubleTensor()
} }
return y_hat.as2D() return y_hat.as2D()
} }
fun funcEasyForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> { fun funcDifficultForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, exampleNumber: Int): MutableStructure2D<Double> {
val m = t.shape.component1() val m = t.shape.component1()
var y_hat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf (m, 1))) var y_hat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf (m, 1)))
if (settings.example_number == 1) { val mt = t.max()
y_hat = DoubleTensorAlgebra.exp((t.times(-1.0 / p[1, 0]))).times(p[0, 0]) + t.times(p[2, 0]).times( for(i in 0 until p.shape.component1()){
DoubleTensorAlgebra.exp((t.times(-1.0 / p[3, 0]))) y_hat = y_hat.plus( (t.times(1.0 / mt)).times(p[i, 0]) )
)
} }
else if (settings.example_number == 2) {
val mt = t.max() for(i in 0 until 4){
y_hat = (t.times(1.0 / mt)).times(p[0, 0]) + y_hat = funcEasyForLm((y_hat.as2D() + t).as2D(), p, exampleNumber).asDoubleTensor()
(t.times(1.0 / mt)).pow(2).times(p[1, 0]) +
(t.times(1.0 / mt)).pow(3).times(p[2, 0]) +
(t.times(1.0 / mt)).pow(4).times(p[3, 0])
}
else if (settings.example_number == 3) {
y_hat = DoubleTensorAlgebra.exp((t.times(-1.0 / p[1, 0])))
.times(p[0, 0]) + DoubleTensorAlgebra.sin((t.times(1.0 / p[3, 0]))).times(p[2, 0])
} }
return y_hat.as2D() return y_hat.as2D()
} }
fun getStartDataForFuncDifficult(): StartDataLm { fun getStartDataForFuncDifficult(): StartDataLm {
val NData = 200 val NData = 200
var t_example = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(NData, 1))).as2D() var t_example = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(NData, 1))).as2D()
@ -102,9 +102,9 @@ fun getStartDataForFuncDifficult(): StartDataLm {
p_example[i, 0] = p_example[i, 0] + i - 25 p_example[i, 0] = p_example[i, 0] + i - 25
} }
val settings = LMSettings(0, 0, 1) val exampleNumber = 1
var y_hat = funcDifficultForLm(t_example, p_example, settings) var y_hat = funcDifficultForLm(t_example, p_example, exampleNumber)
var p_init = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(Nparams, 1))).as2D() var p_init = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(Nparams, 1))).as2D()
for (i in 0 until Nparams) { for (i in 0 until Nparams) {
@ -144,9 +144,9 @@ fun getStartDataForFuncMiddle(): StartDataLm {
p_example[i, 0] = p_example[i, 0] + i - 25 p_example[i, 0] = p_example[i, 0] + i - 25
} }
val settings = LMSettings(0, 0, 1) val exampleNumber = 1
var y_hat = funcMiddleForLm(t_example, p_example, settings) var y_hat = funcMiddleForLm(t_example, p_example, exampleNumber)
var p_init = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(Nparams, 1))).as2D() var p_init = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(Nparams, 1))).as2D()
for (i in 0 until Nparams) { for (i in 0 until Nparams) {

107
kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/LevenbergMarquardtAlgorithm.kt
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@ -40,36 +40,39 @@ public enum class TypeOfConvergence{
NoConvergence NoConvergence
} }
/**
* Class for the data obtained as a result of the execution of the Levenberg-Marquardt algorithm
*
* iterations: number of completed iterations
* funcCalls: the number of evaluations of the input function during execution
* resultChiSq: chi squared value on final parameters
* resultLambda: final lambda parameter used to calculate the offset
* resultParameters: final parameters
* typeOfConvergence: type of convergence
*/
public data class LMResultInfo ( public data class LMResultInfo (
var iterations:Int, var iterations:Int,
var func_calls: Int, var funcCalls: Int,
var example_number: Int, var resultChiSq: Double,
var result_chi_sq: Double, var resultLambda: Double,
var result_lambda: Double, var resultParameters: MutableStructure2D<Double>,
var result_parameters: MutableStructure2D<Double>,
var typeOfConvergence: TypeOfConvergence, var typeOfConvergence: TypeOfConvergence,
var epsilon: Double
)
public data class LMSettings (
var iteration:Int,
var func_calls: Int,
var example_number:Int
) )
public fun DoubleTensorAlgebra.lm( public fun DoubleTensorAlgebra.lm(
func: KFunction3<MutableStructure2D<Double>, MutableStructure2D<Double>, LMSettings, MutableStructure2D<Double>>, func: KFunction3<MutableStructure2D<Double>, MutableStructure2D<Double>, Int, MutableStructure2D<Double>>,
p_input: MutableStructure2D<Double>, t_input: MutableStructure2D<Double>, y_dat_input: MutableStructure2D<Double>, p_input: MutableStructure2D<Double>, t_input: MutableStructure2D<Double>, y_dat_input: MutableStructure2D<Double>,
weight_input: MutableStructure2D<Double>, dp_input: MutableStructure2D<Double>, p_min_input: MutableStructure2D<Double>, p_max_input: MutableStructure2D<Double>, weight_input: MutableStructure2D<Double>, dp_input: MutableStructure2D<Double>, p_min_input: MutableStructure2D<Double>, p_max_input: MutableStructure2D<Double>,
c_input: MutableStructure2D<Double>, opts_input: DoubleArray, nargin: Int, example_number: Int): LMResultInfo { c_input: MutableStructure2D<Double>, opts_input: DoubleArray, nargin: Int, example_number: Int): LMResultInfo {
val resultInfo = LMResultInfo(0, 0, example_number, 0.0,
0.0, p_input, TypeOfConvergence.NoConvergence, 0.0) val resultInfo = LMResultInfo(0, 0, 0.0,
0.0, p_input, TypeOfConvergence.NoConvergence)
val eps:Double = 2.2204e-16 val eps:Double = 2.2204e-16
val settings = LMSettings(0, 0, example_number) val settings = LMSettings(0, 0, example_number)
settings.func_calls = 0 // running count of function evaluations settings.funcCalls = 0 // running count of function evaluations
var p = p_input var p = p_input
val y_dat = y_dat_input val y_dat = y_dat_input
@ -160,7 +163,7 @@ public fun DoubleTensorAlgebra.lm(
val idx = get_zero_indices(dp) // indices of the parameters to be fit val idx = get_zero_indices(dp) // indices of the parameters to be fit
val Nfit = idx?.shape?.component1() // number of parameters to fit val Nfit = idx?.shape?.component1() // number of parameters to fit
var stop = false // termination flag var stop = false // termination flag
val y_init = feval(func, t, p, settings) // residual error using p_try val y_init = feval(func, t, p, example_number) // residual error using p_try
if (weight.shape.component1() == 1 || variance(weight) == 0.0) { // identical weights vector if (weight.shape.component1() == 1 || variance(weight) == 0.0) { // identical weights vector
weight = ones(ShapeND(intArrayOf(Npnt, 1))).div(1 / kotlin.math.abs(weight[0, 0])).as2D() weight = ones(ShapeND(intArrayOf(Npnt, 1))).div(1 / kotlin.math.abs(weight[0, 0])).as2D()
@ -219,7 +222,7 @@ public fun DoubleTensorAlgebra.lm(
var p_try = (p + h).as2D() // update the [idx] elements var p_try = (p + h).as2D() // update the [idx] elements
p_try = smallest_element_comparison(largest_element_comparison(p_min, p_try.as2D()), p_max) // apply constraints p_try = smallest_element_comparison(largest_element_comparison(p_min, p_try.as2D()), p_max) // apply constraints
var delta_y = y_dat.minus(feval(func, t, p_try, settings)) // residual error using p_try var delta_y = y_dat.minus(feval(func, t, p_try, example_number)) // residual error using p_try
for (i in 0 until delta_y.shape.component1()) { // floating point error; break for (i in 0 until delta_y.shape.component1()) { // floating point error; break
for (j in 0 until delta_y.shape.component2()) { for (j in 0 until delta_y.shape.component2()) {
@ -230,7 +233,7 @@ public fun DoubleTensorAlgebra.lm(
} }
} }
settings.func_calls += 1 settings.funcCalls += 1
val tmp = delta_y.times(weight) val tmp = delta_y.times(weight)
var X2_try = delta_y.as2D().transpose().dot(tmp) // Chi-squared error criteria var X2_try = delta_y.as2D().transpose().dot(tmp) // Chi-squared error criteria
@ -244,8 +247,8 @@ public fun DoubleTensorAlgebra.lm(
p_try = p.plus(h).as2D() // update only [idx] elements p_try = p.plus(h).as2D() // update only [idx] elements
p_try = smallest_element_comparison(largest_element_comparison(p_min, p_try), p_max) // apply constraints p_try = smallest_element_comparison(largest_element_comparison(p_min, p_try), p_max) // apply constraints
var delta_y = y_dat.minus(feval(func, t, p_try, settings)) // residual error using p_try var delta_y = y_dat.minus(feval(func, t, p_try, example_number)) // residual error using p_try
settings.func_calls += 1 settings.funcCalls += 1
val tmp = delta_y.times(weight) val tmp = delta_y.times(weight)
X2_try = delta_y.as2D().transpose().dot(tmp) // Chi-squared error criteria X2_try = delta_y.as2D().transpose().dot(tmp) // Chi-squared error criteria
@ -320,10 +323,10 @@ public fun DoubleTensorAlgebra.lm(
if (prnt > 1) { if (prnt > 1) {
val chi_sq = X2 / DoF val chi_sq = X2 / DoF
resultInfo.iterations = settings.iteration resultInfo.iterations = settings.iteration
resultInfo.func_calls = settings.func_calls resultInfo.funcCalls = settings.funcCalls
resultInfo.result_chi_sq = chi_sq resultInfo.resultChiSq = chi_sq
resultInfo.result_lambda = lambda resultInfo.resultLambda = lambda
resultInfo.result_parameters = p resultInfo.resultParameters = p
} }
// update convergence history ... save _reduced_ Chi-square // update convergence history ... save _reduced_ Chi-square
@ -331,30 +334,32 @@ public fun DoubleTensorAlgebra.lm(
if (abs(JtWdy).max()!! < epsilon_1 && settings.iteration > 2) { if (abs(JtWdy).max()!! < epsilon_1 && settings.iteration > 2) {
resultInfo.typeOfConvergence = TypeOfConvergence.InGradient resultInfo.typeOfConvergence = TypeOfConvergence.InGradient
resultInfo.epsilon = epsilon_1
stop = true stop = true
} }
if ((abs(h.as2D()).div(abs(p) + 1e-12)).max() < epsilon_2 && settings.iteration > 2) { if ((abs(h.as2D()).div(abs(p) + 1e-12)).max() < epsilon_2 && settings.iteration > 2) {
resultInfo.typeOfConvergence = TypeOfConvergence.InParameters resultInfo.typeOfConvergence = TypeOfConvergence.InParameters
resultInfo.epsilon = epsilon_2
stop = true stop = true
} }
if (X2 / DoF < epsilon_3 && settings.iteration > 2) { if (X2 / DoF < epsilon_3 && settings.iteration > 2) {
resultInfo.typeOfConvergence = TypeOfConvergence.InReducedChiSquare resultInfo.typeOfConvergence = TypeOfConvergence.InReducedChiSquare
resultInfo.epsilon = epsilon_3
stop = true stop = true
} }
if (settings.iteration == MaxIter) { if (settings.iteration == MaxIter) {
resultInfo.typeOfConvergence = TypeOfConvergence.NoConvergence resultInfo.typeOfConvergence = TypeOfConvergence.NoConvergence
resultInfo.epsilon = 0.0
stop = true stop = true
} }
} }
return resultInfo return resultInfo
} }
private data class LMSettings (
var iteration:Int,
var funcCalls: Int,
var exampleNumber:Int
)
/* matrix -> column of all elemnets */ /* matrix -> column of all elemnets */
public fun make_column(tensor: MutableStructure2D<Double>) : MutableStructure2D<Double> { private fun make_column(tensor: MutableStructure2D<Double>) : MutableStructure2D<Double> {
val shape = intArrayOf(tensor.shape.component1() * tensor.shape.component2(), 1) val shape = intArrayOf(tensor.shape.component1() * tensor.shape.component2(), 1)
val buffer = DoubleArray(tensor.shape.component1() * tensor.shape.component2()) val buffer = DoubleArray(tensor.shape.component1() * tensor.shape.component2())
for (i in 0 until tensor.shape.component1()) { for (i in 0 until tensor.shape.component1()) {
@ -367,11 +372,11 @@ public fun make_column(tensor: MutableStructure2D<Double>) : MutableStructure2D<
} }
/* column length */ /* column length */
public fun length(column: MutableStructure2D<Double>) : Int { private fun length(column: MutableStructure2D<Double>) : Int {
return column.shape.component1() return column.shape.component1()
} }
public fun MutableStructure2D<Double>.abs() { private fun MutableStructure2D<Double>.abs() {
for (i in 0 until this.shape.component1()) { for (i in 0 until this.shape.component1()) {
for (j in 0 until this.shape.component2()) { for (j in 0 until this.shape.component2()) {
this[i, j] = kotlin.math.abs(this[i, j]) this[i, j] = kotlin.math.abs(this[i, j])
@ -379,7 +384,7 @@ public fun MutableStructure2D<Double>.abs() {
} }
} }
public fun abs(input: MutableStructure2D<Double>): MutableStructure2D<Double> { private fun abs(input: MutableStructure2D<Double>): MutableStructure2D<Double> {
val tensor = BroadcastDoubleTensorAlgebra.ones( val tensor = BroadcastDoubleTensorAlgebra.ones(
ShapeND( ShapeND(
intArrayOf( intArrayOf(
@ -396,7 +401,7 @@ public fun abs(input: MutableStructure2D<Double>): MutableStructure2D<Double> {
return tensor return tensor
} }
public fun diag(input: MutableStructure2D<Double>): MutableStructure2D<Double> { private fun diag(input: MutableStructure2D<Double>): MutableStructure2D<Double> {
val tensor = BroadcastDoubleTensorAlgebra.ones(ShapeND(intArrayOf(input.shape.component1(), 1))).as2D() val tensor = BroadcastDoubleTensorAlgebra.ones(ShapeND(intArrayOf(input.shape.component1(), 1))).as2D()
for (i in 0 until tensor.shape.component1()) { for (i in 0 until tensor.shape.component1()) {
tensor[i, 0] = input[i, i] tensor[i, 0] = input[i, i]
@ -404,7 +409,7 @@ public fun diag(input: MutableStructure2D<Double>): MutableStructure2D<Double> {
return tensor return tensor
} }
public fun make_matrx_with_diagonal(column: MutableStructure2D<Double>): MutableStructure2D<Double> { private fun make_matrx_with_diagonal(column: MutableStructure2D<Double>): MutableStructure2D<Double> {
val size = column.shape.component1() val size = column.shape.component1()
val tensor = BroadcastDoubleTensorAlgebra.zeros(ShapeND(intArrayOf(size, size))).as2D() val tensor = BroadcastDoubleTensorAlgebra.zeros(ShapeND(intArrayOf(size, size))).as2D()
for (i in 0 until size) { for (i in 0 until size) {
@ -413,12 +418,12 @@ public fun make_matrx_with_diagonal(column: MutableStructure2D<Double>): Mutable
return tensor return tensor
} }
public fun lm_eye(size: Int): MutableStructure2D<Double> { private fun lm_eye(size: Int): MutableStructure2D<Double> {
val column = BroadcastDoubleTensorAlgebra.ones(ShapeND(intArrayOf(size, 1))).as2D() val column = BroadcastDoubleTensorAlgebra.ones(ShapeND(intArrayOf(size, 1))).as2D()
return make_matrx_with_diagonal(column) return make_matrx_with_diagonal(column)
} }
public fun largest_element_comparison(a: MutableStructure2D<Double>, b: MutableStructure2D<Double>): MutableStructure2D<Double> { private fun largest_element_comparison(a: MutableStructure2D<Double>, b: MutableStructure2D<Double>): MutableStructure2D<Double> {
val a_sizeX = a.shape.component1() val a_sizeX = a.shape.component1()
val a_sizeY = a.shape.component2() val a_sizeY = a.shape.component2()
val b_sizeX = b.shape.component1() val b_sizeX = b.shape.component1()
@ -440,7 +445,7 @@ public fun largest_element_comparison(a: MutableStructure2D<Double>, b: MutableS
return tensor return tensor
} }
public fun smallest_element_comparison(a: MutableStructure2D<Double>, b: MutableStructure2D<Double>): MutableStructure2D<Double> { private fun smallest_element_comparison(a: MutableStructure2D<Double>, b: MutableStructure2D<Double>): MutableStructure2D<Double> {
val a_sizeX = a.shape.component1() val a_sizeX = a.shape.component1()
val a_sizeY = a.shape.component2() val a_sizeY = a.shape.component2()
val b_sizeX = b.shape.component1() val b_sizeX = b.shape.component1()
@ -462,7 +467,7 @@ public fun smallest_element_comparison(a: MutableStructure2D<Double>, b: Mutable
return tensor return tensor
} }
public fun get_zero_indices(column: MutableStructure2D<Double>, epsilon: Double = 0.000001): MutableStructure2D<Double>? { private fun get_zero_indices(column: MutableStructure2D<Double>, epsilon: Double = 0.000001): MutableStructure2D<Double>? {
var idx = emptyArray<Double>() var idx = emptyArray<Double>()
for (i in 0 until column.shape.component1()) { for (i in 0 until column.shape.component1()) {
if (kotlin.math.abs(column[i, 0]) > epsilon) { if (kotlin.math.abs(column[i, 0]) > epsilon) {
@ -475,14 +480,14 @@ public fun get_zero_indices(column: MutableStructure2D<Double>, epsilon: Double
return null return null
} }
public fun feval(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, LMSettings) -> MutableStructure2D<Double>, private fun feval(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, Int) -> MutableStructure2D<Double>,
t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, settings: LMSettings) t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, exampleNumber: Int)
: MutableStructure2D<Double> : MutableStructure2D<Double>
{ {
return func(t, p, settings) return func(t, p, exampleNumber)
} }
public fun lm_matx(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, LMSettings) -> MutableStructure2D<Double>, private fun lm_matx(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, Int) -> MutableStructure2D<Double>,
t: MutableStructure2D<Double>, p_old: MutableStructure2D<Double>, y_old: MutableStructure2D<Double>, t: MutableStructure2D<Double>, p_old: MutableStructure2D<Double>, y_old: MutableStructure2D<Double>,
dX2: Int, J_input: MutableStructure2D<Double>, p: MutableStructure2D<Double>, dX2: Int, J_input: MutableStructure2D<Double>, p: MutableStructure2D<Double>,
y_dat: MutableStructure2D<Double>, weight: MutableStructure2D<Double>, dp:MutableStructure2D<Double>, settings:LMSettings) : Array<MutableStructure2D<Double>> y_dat: MutableStructure2D<Double>, weight: MutableStructure2D<Double>, dp:MutableStructure2D<Double>, settings:LMSettings) : Array<MutableStructure2D<Double>>
@ -492,8 +497,8 @@ public fun lm_matx(func: (MutableStructure2D<Double>, MutableStructure2D<Double>
val Npnt = length(y_dat) // number of data points val Npnt = length(y_dat) // number of data points
val Npar = length(p) // number of parameters val Npar = length(p) // number of parameters
val y_hat = feval(func, t, p, settings) // evaluate model using parameters 'p' val y_hat = feval(func, t, p, settings.exampleNumber) // evaluate model using parameters 'p'
settings.func_calls += 1 settings.funcCalls += 1
var J = J_input var J = J_input
@ -513,7 +518,7 @@ public fun lm_matx(func: (MutableStructure2D<Double>, MutableStructure2D<Double>
return arrayOf(JtWJ,JtWdy,Chi_sq,y_hat,J) return arrayOf(JtWJ,JtWdy,Chi_sq,y_hat,J)
} }
public fun lm_Broyden_J(p_old: MutableStructure2D<Double>, y_old: MutableStructure2D<Double>, J_input: MutableStructure2D<Double>, private fun lm_Broyden_J(p_old: MutableStructure2D<Double>, y_old: MutableStructure2D<Double>, J_input: MutableStructure2D<Double>,
p: MutableStructure2D<Double>, y: MutableStructure2D<Double>): MutableStructure2D<Double> { p: MutableStructure2D<Double>, y: MutableStructure2D<Double>): MutableStructure2D<Double> {
var J = J_input.copyToTensor() var J = J_input.copyToTensor()
@ -524,7 +529,7 @@ public fun lm_Broyden_J(p_old: MutableStructure2D<Double>, y_old: MutableStructu
return J.as2D() return J.as2D()
} }
public fun lm_FD_J(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, settings: LMSettings) -> MutableStructure2D<Double>, private fun lm_FD_J(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, exampleNumber: Int) -> MutableStructure2D<Double>,
t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, y: MutableStructure2D<Double>, t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, y: MutableStructure2D<Double>,
dp: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> { dp: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> {
// default: dp = 0.001 * ones(1,n) // default: dp = 0.001 * ones(1,n)
@ -543,8 +548,8 @@ public fun lm_FD_J(func: (MutableStructure2D<Double>, MutableStructure2D<Double>
val epsilon = 0.0000001 val epsilon = 0.0000001
if (kotlin.math.abs(del[j, 0]) > epsilon) { if (kotlin.math.abs(del[j, 0]) > epsilon) {
val y1 = feval(func, t, p, settings) val y1 = feval(func, t, p, settings.exampleNumber)
settings.func_calls += 1 settings.funcCalls += 1
if (dp[j, 0] < 0) { // backwards difference if (dp[j, 0] < 0) { // backwards difference
for (i in 0 until J.shape.component1()) { for (i in 0 until J.shape.component1()) {
@ -556,9 +561,9 @@ public fun lm_FD_J(func: (MutableStructure2D<Double>, MutableStructure2D<Double>
println("Potential mistake") println("Potential mistake")
p[j, 0] = ps[j, 0] - del[j, 0] // central difference, additional func call p[j, 0] = ps[j, 0] - del[j, 0] // central difference, additional func call
for (i in 0 until J.shape.component1()) { for (i in 0 until J.shape.component1()) {
J[i, j] = (y1.as2D().minus(feval(func, t, p, settings)).as2D())[i, 0] / (2 * del[j, 0]) J[i, j] = (y1.as2D().minus(feval(func, t, p, settings.exampleNumber)).as2D())[i, 0] / (2 * del[j, 0])
} }
settings.func_calls += 1 settings.funcCalls += 1
} }
} }

38
kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestLmAlgorithm.kt
View File

@ -20,23 +20,23 @@ import kotlin.test.assertEquals
class TestLmAlgorithm { class TestLmAlgorithm {
companion object { companion object {
fun funcEasyForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> { fun funcEasyForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, exampleNumber: Int): MutableStructure2D<Double> {
val m = t.shape.component1() val m = t.shape.component1()
var y_hat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(m, 1))) var y_hat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(m, 1)))
if (settings.example_number == 1) { if (exampleNumber == 1) {
y_hat = DoubleTensorAlgebra.exp((t.times(-1.0 / p[1, 0]))).times(p[0, 0]) + t.times(p[2, 0]).times( y_hat = DoubleTensorAlgebra.exp((t.times(-1.0 / p[1, 0]))).times(p[0, 0]) + t.times(p[2, 0]).times(
DoubleTensorAlgebra.exp((t.times(-1.0 / p[3, 0]))) DoubleTensorAlgebra.exp((t.times(-1.0 / p[3, 0])))
) )
} }
else if (settings.example_number == 2) { else if (exampleNumber == 2) {
val mt = t.max() val mt = t.max()
y_hat = (t.times(1.0 / mt)).times(p[0, 0]) + y_hat = (t.times(1.0 / mt)).times(p[0, 0]) +
(t.times(1.0 / mt)).pow(2).times(p[1, 0]) + (t.times(1.0 / mt)).pow(2).times(p[1, 0]) +
(t.times(1.0 / mt)).pow(3).times(p[2, 0]) + (t.times(1.0 / mt)).pow(3).times(p[2, 0]) +
(t.times(1.0 / mt)).pow(4).times(p[3, 0]) (t.times(1.0 / mt)).pow(4).times(p[3, 0])
} }
else if (settings.example_number == 3) { else if (exampleNumber == 3) {
y_hat = DoubleTensorAlgebra.exp((t.times(-1.0 / p[1, 0]))) y_hat = DoubleTensorAlgebra.exp((t.times(-1.0 / p[1, 0])))
.times(p[0, 0]) + DoubleTensorAlgebra.sin((t.times(1.0 / p[3, 0]))).times(p[2, 0]) .times(p[0, 0]) + DoubleTensorAlgebra.sin((t.times(1.0 / p[3, 0]))).times(p[2, 0])
} }
@ -44,7 +44,7 @@ class TestLmAlgorithm {
return y_hat.as2D() return y_hat.as2D()
} }
fun funcMiddleForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> { fun funcMiddleForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, exampleNumber: Int): MutableStructure2D<Double> {
val m = t.shape.component1() val m = t.shape.component1()
var y_hat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf (m, 1))) var y_hat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf (m, 1)))
@ -54,13 +54,13 @@ class TestLmAlgorithm {
} }
for(i in 0 until 5){ for(i in 0 until 5){
y_hat = funcEasyForLm(y_hat.as2D(), p, settings).asDoubleTensor() y_hat = funcEasyForLm(y_hat.as2D(), p, exampleNumber).asDoubleTensor()
} }
return y_hat.as2D() return y_hat.as2D()
} }
fun funcDifficultForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> { fun funcDifficultForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, exampleNumber: Int): MutableStructure2D<Double> {
val m = t.shape.component1() val m = t.shape.component1()
var y_hat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf (m, 1))) var y_hat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf (m, 1)))
@ -70,12 +70,11 @@ class TestLmAlgorithm {
} }
for(i in 0 until 4){ for(i in 0 until 4){
y_hat = funcEasyForLm((y_hat.as2D() + t).as2D(), p, settings).asDoubleTensor() y_hat = funcEasyForLm((y_hat.as2D() + t).as2D(), p, exampleNumber).asDoubleTensor()
} }
return y_hat.as2D() return y_hat.as2D()
} }
} }
@Test @Test
fun testLMEasy() = DoubleTensorAlgebra { fun testLMEasy() = DoubleTensorAlgebra {
@ -130,18 +129,17 @@ class TestLmAlgorithm {
val result = lm(::funcEasyForLm, p_init, t, y_dat, weight, dp, p_min, p_max, consts, opts, 10, example_number) val result = lm(::funcEasyForLm, p_init, t, y_dat, weight, dp, p_min, p_max, consts, opts, 10, example_number)
assertEquals(13, result.iterations) assertEquals(13, result.iterations)
assertEquals(31, result.func_calls) assertEquals(31, result.funcCalls)
assertEquals(1, result.example_number) assertEquals(0.9131368192633, (result.resultChiSq * 1e13).roundToLong() / 1e13)
assertEquals(0.9131368192633, (result.result_chi_sq * 1e13).roundToLong() / 1e13) assertEquals(3.7790980 * 1e-7, (result.resultLambda * 1e13).roundToLong() / 1e13)
assertEquals(3.7790980 * 1e-7, (result.result_lambda * 1e13).roundToLong() / 1e13)
assertEquals(result.typeOfConvergence, TypeOfConvergence.InParameters) assertEquals(result.typeOfConvergence, TypeOfConvergence.InParameters)
val expectedParameters = BroadcastDoubleTensorAlgebra.fromArray( val expectedParameters = BroadcastDoubleTensorAlgebra.fromArray(
ShapeND(intArrayOf(4, 1)), doubleArrayOf(20.527230909086, 9.833627103230, 0.997571256572, 50.174445822506) ShapeND(intArrayOf(4, 1)), doubleArrayOf(20.527230909086, 9.833627103230, 0.997571256572, 50.174445822506)
).as2D() ).as2D()
result.result_parameters = result.result_parameters.map { x -> (x * 1e12).toLong() / 1e12}.as2D() result.resultParameters = result.resultParameters.map { x -> (x * 1e12).toLong() / 1e12}.as2D()
val receivedParameters = BroadcastDoubleTensorAlgebra.fromArray( val receivedParameters = BroadcastDoubleTensorAlgebra.fromArray(
ShapeND(intArrayOf(4, 1)), doubleArrayOf(result.result_parameters[0, 0], result.result_parameters[1, 0], ShapeND(intArrayOf(4, 1)), doubleArrayOf(result.resultParameters[0, 0], result.resultParameters[1, 0],
result.result_parameters[2, 0], result.result_parameters[3, 0]) result.resultParameters[2, 0], result.resultParameters[3, 0])
).as2D() ).as2D()
assertEquals(expectedParameters[0, 0], receivedParameters[0, 0]) assertEquals(expectedParameters[0, 0], receivedParameters[0, 0])
assertEquals(expectedParameters[1, 0], receivedParameters[1, 0]) assertEquals(expectedParameters[1, 0], receivedParameters[1, 0])
@ -163,9 +161,9 @@ class TestLmAlgorithm {
p_example[i, 0] = p_example[i, 0] + i - 25 p_example[i, 0] = p_example[i, 0] + i - 25
} }
val settings = LMSettings(0, 0, 1) val exampleNumber = 1
var y_hat = funcMiddleForLm(t_example, p_example, settings) var y_hat = funcMiddleForLm(t_example, p_example, exampleNumber)
var p_init = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(Nparams, 1))).as2D() var p_init = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(Nparams, 1))).as2D()
for (i in 0 until Nparams) { for (i in 0 until Nparams) {
@ -219,9 +217,9 @@ class TestLmAlgorithm {
p_example[i, 0] = p_example[i, 0] + i - 25 p_example[i, 0] = p_example[i, 0] + i - 25
} }
val settings = LMSettings(0, 0, 1) val exampleNumber = 1
var y_hat = funcDifficultForLm(t_example, p_example, settings) var y_hat = funcDifficultForLm(t_example, p_example, exampleNumber)
var p_init = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(Nparams, 1))).as2D() var p_init = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(Nparams, 1))).as2D()
for (i in 0 until Nparams) { for (i in 0 until Nparams) {