forked from kscience/kmath
levenbergMarquardt cleanup
This commit is contained in:
parent
14f0fa1a6f
commit
1e2a8a40e5
@ -15,7 +15,7 @@ allprojects {
|
||||
}
|
||||
|
||||
group = "space.kscience"
|
||||
version = "0.3.1"
|
||||
version = "0.3.2-dev-1"
|
||||
}
|
||||
|
||||
subprojects {
|
||||
|
||||
@ -5,18 +5,13 @@
|
||||
|
||||
package space.kscience.kmath.tensors.core
|
||||
|
||||
import space.kscience.kmath.PerformancePitfall
|
||||
import space.kscience.kmath.linear.transpose
|
||||
import space.kscience.kmath.nd.*
|
||||
import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.div
|
||||
import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.dot
|
||||
import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.minus
|
||||
import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.times
|
||||
import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.transposed
|
||||
import space.kscience.kmath.tensors.core.DoubleTensorAlgebra.Companion.plus
|
||||
import kotlin.math.abs
|
||||
import kotlin.math.max
|
||||
import kotlin.math.min
|
||||
import kotlin.math.pow
|
||||
import kotlin.reflect.KFunction3
|
||||
|
||||
/**
|
||||
* Type of convergence achieved as a result of executing the Levenberg-Marquardt algorithm.
|
||||
@ -101,7 +96,7 @@ public data class LMInput (
|
||||
var lambdas: DoubleArray,
|
||||
var updateType: Int,
|
||||
var nargin: Int,
|
||||
var exampleNumber: Int
|
||||
var exampleNumber: Int,
|
||||
)
|
||||
|
||||
|
||||
@ -120,8 +115,10 @@ public data class LMInput (
|
||||
* @return the 'output'.
|
||||
*/
|
||||
public fun DoubleTensorAlgebra.levenbergMarquardt(inputData: LMInput): LMResultInfo {
|
||||
val resultInfo = LMResultInfo(0, 0, 0.0,
|
||||
0.0, inputData.startParameters, TypeOfConvergence.NoConvergence)
|
||||
val resultInfo = LMResultInfo(
|
||||
0, 0, 0.0,
|
||||
0.0, inputData.startParameters, TypeOfConvergence.NoConvergence
|
||||
)
|
||||
|
||||
val eps = 2.2204e-16
|
||||
|
||||
@ -131,18 +128,21 @@ public fun DoubleTensorAlgebra.levenbergMarquardt(inputData: LMInput): LMResultI
|
||||
var p = inputData.startParameters
|
||||
val t = inputData.independentVariables
|
||||
|
||||
val Npar = length(p) // number of parameters
|
||||
val Npnt = length(inputData.realValues) // number of data points
|
||||
var pOld = zeros(ShapeND(intArrayOf(Npar, 1))).as2D() // previous set of parameters
|
||||
var yOld = zeros(ShapeND(intArrayOf(Npnt, 1))).as2D() // previous model, y_old = y_hat(t;p_old)
|
||||
var X2 = 1e-3 / eps // a really big initial Chi-sq value
|
||||
var X2Old = 1e-3 / eps // a really big initial Chi-sq value
|
||||
var J = zeros(ShapeND(intArrayOf(Npnt, Npar))).as2D() // Jacobian matrix
|
||||
val DoF = Npnt - Npar // statistical degrees of freedom
|
||||
val nPar = length(p) // number of parameters
|
||||
val nPoints = length(inputData.realValues) // number of data points
|
||||
var pOld = zeros(ShapeND(intArrayOf(nPar, 1))).as2D() // previous set of parameters
|
||||
var yOld = zeros(ShapeND(intArrayOf(nPoints, 1))).as2D() // previous model, y_old = y_hat(t;p_old)
|
||||
var x2: Double // a really big initial Chi-sq value
|
||||
var x2Old: Double // a really big initial Chi-sq value
|
||||
var jacobian = zeros(ShapeND(intArrayOf(nPoints, nPar))).as2D() // Jacobian matrix
|
||||
val dof = nPoints - nPar // statistical degrees of freedom
|
||||
|
||||
var weight = fromArray(ShapeND(intArrayOf(1, 1)), doubleArrayOf(inputData.weight)).as2D()
|
||||
if (inputData.nargin < 5) {
|
||||
weight = fromArray(ShapeND(intArrayOf(1, 1)), doubleArrayOf((inputData.realValues.transpose().dot(inputData.realValues)).as1D()[0])).as2D()
|
||||
weight = fromArray(
|
||||
ShapeND(intArrayOf(1, 1)),
|
||||
doubleArrayOf((inputData.realValues.transpose().dot(inputData.realValues)).as1D()[0])
|
||||
).as2D()
|
||||
}
|
||||
|
||||
var dp = inputData.pDelta
|
||||
@ -175,7 +175,7 @@ public fun DoubleTensorAlgebra.levenbergMarquardt(inputData: LMInput): LMResultI
|
||||
var updateType = inputData.updateType
|
||||
|
||||
if (inputData.nargin < 9) {
|
||||
maxIterations = 10 * Npar
|
||||
maxIterations = 10 * nPar
|
||||
epsilon1 = 1e-3
|
||||
epsilon2 = 1e-3
|
||||
epsilon3 = 1e-1
|
||||
@ -190,28 +190,27 @@ public fun DoubleTensorAlgebra.levenbergMarquardt(inputData: LMInput): LMResultI
|
||||
maxParameters = makeColumn(maxParameters)
|
||||
|
||||
if (length(makeColumn(dp)) == 1) {
|
||||
dp = ones(ShapeND(intArrayOf(Npar, 1))).div(1 / dp[0, 0]).as2D()
|
||||
dp = ones(ShapeND(intArrayOf(nPar, 1))).div(1 / dp[0, 0]).as2D()
|
||||
}
|
||||
|
||||
var stop = false // termination flag
|
||||
|
||||
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()
|
||||
}
|
||||
else {
|
||||
weight = ones(ShapeND(intArrayOf(nPoints, 1))).div(1 / abs(weight[0, 0])).as2D()
|
||||
} else {
|
||||
weight = makeColumn(weight)
|
||||
weight.abs()
|
||||
}
|
||||
|
||||
// initialize Jacobian with finite difference calculation
|
||||
var lmMatxAns = lmMatx(inputData.func, t, pOld, yOld, 1, J, p, inputData.realValues, weight, dp, settings)
|
||||
var JtWJ = lmMatxAns[0]
|
||||
var JtWdy = lmMatxAns[1]
|
||||
X2 = lmMatxAns[2][0, 0]
|
||||
var lmMatxAns = lmMatx(inputData.func, t, pOld, yOld, 1, jacobian, p, inputData.realValues, weight, dp, settings)
|
||||
var jtWJ = lmMatxAns[0]
|
||||
var jtWdy = lmMatxAns[1]
|
||||
x2 = lmMatxAns[2][0, 0]
|
||||
var yHat = lmMatxAns[3]
|
||||
J = lmMatxAns[4]
|
||||
jacobian = lmMatxAns[4]
|
||||
|
||||
if ( abs(JtWdy).max() < epsilon1 ) {
|
||||
if (abs(jtWdy).max() < epsilon1) {
|
||||
stop = true
|
||||
}
|
||||
|
||||
@ -220,13 +219,12 @@ public fun DoubleTensorAlgebra.levenbergMarquardt(inputData: LMInput): LMResultI
|
||||
|
||||
if (updateType == 1) {
|
||||
lambda = lambda0 // Marquardt: init'l lambda
|
||||
}
|
||||
else {
|
||||
lambda = lambda0 * (makeColumnFromDiagonal(JtWJ)).max()
|
||||
} else {
|
||||
lambda = lambda0 * (makeColumnFromDiagonal(jtWJ)).max()
|
||||
nu = 2
|
||||
}
|
||||
|
||||
X2Old = X2 // previous value of X2
|
||||
x2Old = x2 // previous value of X2
|
||||
|
||||
var h: DoubleTensor
|
||||
|
||||
@ -235,20 +233,31 @@ public fun DoubleTensorAlgebra.levenbergMarquardt(inputData: LMInput): LMResultI
|
||||
|
||||
// incremental change in parameters
|
||||
h = if (updateType == 1) { // Marquardt
|
||||
val solve = solve(JtWJ.plus(makeMatrixWithDiagonal(makeColumnFromDiagonal(JtWJ)).div(1 / lambda)).as2D(), JtWdy)
|
||||
val solve =
|
||||
solve((jtWJ + makeMatrixWithDiagonal(makeColumnFromDiagonal(jtWJ)) / (1 / lambda)).as2D(), jtWdy)
|
||||
solve.asDoubleTensor()
|
||||
} else { // Quadratic and Nielsen
|
||||
val solve = solve(JtWJ.plus(lmEye(Npar).div(1 / lambda)).as2D(), JtWdy)
|
||||
val solve = solve(jtWJ.plus(lmEye(nPar) * lambda).as2D(), jtWdy)
|
||||
solve.asDoubleTensor()
|
||||
}
|
||||
|
||||
var pTry = (p + h).as2D() // update the [idx] elements
|
||||
pTry = smallestElementComparison(largestElementComparison(minParameters, pTry.as2D()), maxParameters) // apply constraints
|
||||
pTry = smallestElementComparison(
|
||||
largestElementComparison(minParameters, pTry),
|
||||
maxParameters
|
||||
) // apply constraints
|
||||
|
||||
var deltaY = inputData.realValues.minus(evaluateFunction(inputData.func, t, pTry, inputData.exampleNumber)) // residual error using p_try
|
||||
var deltaY = inputData.realValues.minus(
|
||||
evaluateFunction(
|
||||
inputData.func,
|
||||
t,
|
||||
pTry,
|
||||
inputData.exampleNumber
|
||||
)
|
||||
) // residual error using p_try
|
||||
|
||||
for (i in 0 until deltaY.shape.component1()) { // floating point error; break
|
||||
for (j in 0 until deltaY.shape.component2()) {
|
||||
for (i in 0 until deltaY.shape[0]) { // floating point error; break
|
||||
for (j in 0 until deltaY.shape[1]) {
|
||||
if (deltaY[i, j] == Double.POSITIVE_INFINITY || deltaY[i, j] == Double.NEGATIVE_INFINITY) {
|
||||
stop = true
|
||||
break
|
||||
@ -258,49 +267,72 @@ public fun DoubleTensorAlgebra.levenbergMarquardt(inputData: LMInput): LMResultI
|
||||
|
||||
settings.funcCalls += 1
|
||||
|
||||
val tmp = deltaY.times(weight)
|
||||
var X2Try = deltaY.as2D().transpose().dot(tmp) // Chi-squared error criteria
|
||||
// val tmp = deltaY.times(weight)
|
||||
var X2Try = deltaY.as2D().transpose().dot(deltaY.times(weight)) // Chi-squared error criteria
|
||||
|
||||
val alpha = 1.0
|
||||
if (updateType == 2) { // Quadratic
|
||||
// One step of quadratic line update in the h direction for minimum X2
|
||||
val alpha = JtWdy.transpose().dot(h) / ((X2Try.minus(X2)).div(2.0).plus(2 * JtWdy.transpose().dot(h)))
|
||||
h = h.dot(alpha)
|
||||
pTry = p.plus(h).as2D() // update only [idx] elements
|
||||
pTry = smallestElementComparison(largestElementComparison(minParameters, pTry), maxParameters) // apply constraints
|
||||
val alpha = (jtWdy.transpose() dot h) / ((X2Try - x2) / 2.0 + 2 * (jtWdy.transpose() dot h))
|
||||
h = h dot alpha
|
||||
pTry = (p + h).as2D() // update only [idx] elements
|
||||
pTry = smallestElementComparison(
|
||||
largestElementComparison(minParameters, pTry),
|
||||
maxParameters
|
||||
) // apply constraints
|
||||
|
||||
deltaY = inputData.realValues.minus(evaluateFunction(inputData.func, t, pTry, inputData.exampleNumber)) // residual error using p_try
|
||||
deltaY = inputData.realValues.minus(
|
||||
evaluateFunction(
|
||||
inputData.func,
|
||||
t,
|
||||
pTry,
|
||||
inputData.exampleNumber
|
||||
)
|
||||
) // residual error using p_try
|
||||
settings.funcCalls += 1
|
||||
|
||||
X2Try = deltaY.as2D().transpose().dot(deltaY.times(weight)) // Chi-squared error criteria
|
||||
X2Try = deltaY.as2D().transpose() dot deltaY * weight // Chi-squared error criteria
|
||||
}
|
||||
|
||||
val rho = when (updateType) { // Nielsen
|
||||
1 -> {
|
||||
val tmp = h.transposed()
|
||||
.dot(makeMatrixWithDiagonal(makeColumnFromDiagonal(JtWJ)).div(1 / lambda).dot(h).plus(JtWdy))
|
||||
X2.minus(X2Try).as2D()[0, 0] / abs(tmp.as2D()).as2D()[0, 0]
|
||||
.dot((makeMatrixWithDiagonal(makeColumnFromDiagonal(jtWJ)) * lambda dot h) + jtWdy)
|
||||
(x2 - X2Try)[0, 0] / abs(tmp.as2D())[0, 0]
|
||||
}
|
||||
|
||||
else -> {
|
||||
val tmp = h.transposed().dot(h.div(1 / lambda).plus(JtWdy))
|
||||
X2.minus(X2Try).as2D()[0, 0] / abs(tmp.as2D()).as2D()[0, 0]
|
||||
val tmp = h.transposed().dot((h * lambda) + jtWdy)
|
||||
x2.minus(X2Try).as2D()[0, 0] / abs(tmp.as2D()).as2D()[0, 0]
|
||||
}
|
||||
}
|
||||
|
||||
if (rho > epsilon4) { // it IS significantly better
|
||||
val dX2 = X2.minus(X2Old)
|
||||
X2Old = X2
|
||||
val dX2 = x2.minus(x2Old)
|
||||
x2Old = x2
|
||||
pOld = p.copyToTensor().as2D()
|
||||
yOld = yHat.copyToTensor().as2D()
|
||||
p = makeColumn(pTry) // accept p_try
|
||||
|
||||
lmMatxAns = lmMatx(inputData.func, t, pOld, yOld, dX2.toInt(), J, p, inputData.realValues, weight, dp, settings)
|
||||
lmMatxAns = lmMatx(
|
||||
inputData.func,
|
||||
t,
|
||||
pOld,
|
||||
yOld,
|
||||
dX2.toInt(),
|
||||
jacobian,
|
||||
p,
|
||||
inputData.realValues,
|
||||
weight,
|
||||
dp,
|
||||
settings
|
||||
)
|
||||
// decrease lambda ==> Gauss-Newton method
|
||||
JtWJ = lmMatxAns[0]
|
||||
JtWdy = lmMatxAns[1]
|
||||
X2 = lmMatxAns[2][0, 0]
|
||||
jtWJ = lmMatxAns[0]
|
||||
jtWdy = lmMatxAns[1]
|
||||
x2 = lmMatxAns[2][0, 0]
|
||||
yHat = lmMatxAns[3]
|
||||
J = lmMatxAns[4]
|
||||
jacobian = lmMatxAns[4]
|
||||
|
||||
lambda = when (updateType) {
|
||||
1 -> { // Levenberg
|
||||
@ -317,13 +349,14 @@ public fun DoubleTensorAlgebra.levenbergMarquardt(inputData: LMInput): LMResultI
|
||||
}
|
||||
}
|
||||
} else { // it IS NOT better
|
||||
X2 = X2Old // do not accept p_try
|
||||
if (settings.iteration % (2 * Npar) == 0) { // rank-1 update of Jacobian
|
||||
lmMatxAns = lmMatx(inputData.func, t, pOld, yOld, -1, J, p, inputData.realValues, weight, dp, settings)
|
||||
JtWJ = lmMatxAns[0]
|
||||
JtWdy = lmMatxAns[1]
|
||||
x2 = x2Old // do not accept p_try
|
||||
if (settings.iteration % (2 * nPar) == 0) { // rank-1 update of Jacobian
|
||||
lmMatxAns =
|
||||
lmMatx(inputData.func, t, pOld, yOld, -1, jacobian, p, inputData.realValues, weight, dp, settings)
|
||||
jtWJ = lmMatxAns[0]
|
||||
jtWdy = lmMatxAns[1]
|
||||
yHat = lmMatxAns[3]
|
||||
J = lmMatxAns[4]
|
||||
jacobian = lmMatxAns[4]
|
||||
}
|
||||
|
||||
// increase lambda ==> gradient descent method
|
||||
@ -333,7 +366,7 @@ public fun DoubleTensorAlgebra.levenbergMarquardt(inputData: LMInput): LMResultI
|
||||
}
|
||||
|
||||
2 -> { // Quadratic
|
||||
lambda + kotlin.math.abs(((X2Try.as2D()[0, 0] - X2) / 2) / alpha)
|
||||
lambda + abs(((X2Try.as2D()[0, 0] - x2) / 2) / alpha)
|
||||
}
|
||||
|
||||
else -> { // Nielsen
|
||||
@ -343,7 +376,7 @@ public fun DoubleTensorAlgebra.levenbergMarquardt(inputData: LMInput): LMResultI
|
||||
}
|
||||
}
|
||||
|
||||
val chiSq = X2 / DoF
|
||||
val chiSq = x2 / dof
|
||||
resultInfo.iterations = settings.iteration
|
||||
resultInfo.funcCalls = settings.funcCalls
|
||||
resultInfo.resultChiSq = chiSq
|
||||
@ -351,7 +384,7 @@ public fun DoubleTensorAlgebra.levenbergMarquardt(inputData: LMInput): LMResultI
|
||||
resultInfo.resultParameters = p
|
||||
|
||||
|
||||
if (abs(JtWdy).max() < epsilon1 && settings.iteration > 2) {
|
||||
if (abs(jtWdy).max() < epsilon1 && settings.iteration > 2) {
|
||||
resultInfo.typeOfConvergence = TypeOfConvergence.InGradient
|
||||
stop = true
|
||||
}
|
||||
@ -359,7 +392,7 @@ public fun DoubleTensorAlgebra.levenbergMarquardt(inputData: LMInput): LMResultI
|
||||
resultInfo.typeOfConvergence = TypeOfConvergence.InParameters
|
||||
stop = true
|
||||
}
|
||||
if (X2 / DoF < epsilon3 && settings.iteration > 2) {
|
||||
if (x2 / dof < epsilon3 && settings.iteration > 2) {
|
||||
resultInfo.typeOfConvergence = TypeOfConvergence.InReducedChiSquare
|
||||
stop = true
|
||||
}
|
||||
@ -374,7 +407,7 @@ public fun DoubleTensorAlgebra.levenbergMarquardt(inputData: LMInput): LMResultI
|
||||
private data class LMSettings(
|
||||
var iteration: Int,
|
||||
var funcCalls: Int,
|
||||
var exampleNumber:Int
|
||||
var exampleNumber: Int,
|
||||
)
|
||||
|
||||
/* matrix -> column of all elements */
|
||||
@ -395,9 +428,9 @@ private fun length(column: MutableStructure2D<Double>) : Int {
|
||||
}
|
||||
|
||||
private fun MutableStructure2D<Double>.abs() {
|
||||
for (i in 0 until this.shape.component1()) {
|
||||
for (j in 0 until this.shape.component2()) {
|
||||
this[i, j] = kotlin.math.abs(this[i, j])
|
||||
for (i in 0 until this.shape[0]) {
|
||||
for (j in 0 until this.shape[1]) {
|
||||
this[i, j] = abs(this[i, j])
|
||||
}
|
||||
}
|
||||
}
|
||||
@ -413,7 +446,7 @@ private fun abs(input: MutableStructure2D<Double>): MutableStructure2D<Double> {
|
||||
).as2D()
|
||||
for (i in 0 until tensor.shape.component1()) {
|
||||
for (j in 0 until tensor.shape.component2()) {
|
||||
tensor[i, j] = kotlin.math.abs(input[i, j])
|
||||
tensor[i, j] = abs(input[i, j])
|
||||
}
|
||||
}
|
||||
return tensor
|
||||
@ -441,21 +474,23 @@ private fun lmEye(size: Int): MutableStructure2D<Double> {
|
||||
return makeMatrixWithDiagonal(column)
|
||||
}
|
||||
|
||||
private fun largestElementComparison(a: MutableStructure2D<Double>, b: MutableStructure2D<Double>): MutableStructure2D<Double> {
|
||||
private fun largestElementComparison(
|
||||
a: MutableStructure2D<Double>,
|
||||
b: MutableStructure2D<Double>,
|
||||
): MutableStructure2D<Double> {
|
||||
val aSizeX = a.shape.component1()
|
||||
val aSizeY = a.shape.component2()
|
||||
val bSizeX = b.shape.component1()
|
||||
val bSizeY = b.shape.component2()
|
||||
val tensor = BroadcastDoubleTensorAlgebra.zeros(ShapeND(intArrayOf(max(aSizeX, bSizeX), max(aSizeY, bSizeY)))).as2D()
|
||||
val tensor =
|
||||
BroadcastDoubleTensorAlgebra.zeros(ShapeND(intArrayOf(max(aSizeX, bSizeX), max(aSizeY, bSizeY)))).as2D()
|
||||
for (i in 0 until tensor.shape.component1()) {
|
||||
for (j in 0 until tensor.shape.component2()) {
|
||||
if (i < aSizeX && i < bSizeX && j < aSizeY && j < bSizeY) {
|
||||
tensor[i, j] = max(a[i, j], b[i, j])
|
||||
}
|
||||
else if (i < aSizeX && j < aSizeY) {
|
||||
} else if (i < aSizeX && j < aSizeY) {
|
||||
tensor[i, j] = a[i, j]
|
||||
}
|
||||
else {
|
||||
} else {
|
||||
tensor[i, j] = b[i, j]
|
||||
}
|
||||
}
|
||||
@ -463,21 +498,23 @@ private fun largestElementComparison(a: MutableStructure2D<Double>, b: MutableSt
|
||||
return tensor
|
||||
}
|
||||
|
||||
private fun smallestElementComparison(a: MutableStructure2D<Double>, b: MutableStructure2D<Double>): MutableStructure2D<Double> {
|
||||
private fun smallestElementComparison(
|
||||
a: MutableStructure2D<Double>,
|
||||
b: MutableStructure2D<Double>,
|
||||
): MutableStructure2D<Double> {
|
||||
val aSizeX = a.shape.component1()
|
||||
val aSizeY = a.shape.component2()
|
||||
val bSizeX = b.shape.component1()
|
||||
val bSizeY = b.shape.component2()
|
||||
val tensor = BroadcastDoubleTensorAlgebra.zeros(ShapeND(intArrayOf(max(aSizeX, bSizeX), max(aSizeY, bSizeY)))).as2D()
|
||||
val tensor =
|
||||
BroadcastDoubleTensorAlgebra.zeros(ShapeND(intArrayOf(max(aSizeX, bSizeX), max(aSizeY, bSizeY)))).as2D()
|
||||
for (i in 0 until tensor.shape.component1()) {
|
||||
for (j in 0 until tensor.shape.component2()) {
|
||||
if (i < aSizeX && i < bSizeX && j < aSizeY && j < bSizeY) {
|
||||
tensor[i, j] = min(a[i, j], b[i, j])
|
||||
}
|
||||
else if (i < aSizeX && j < aSizeY) {
|
||||
} else if (i < aSizeX && j < aSizeY) {
|
||||
tensor[i, j] = a[i, j]
|
||||
}
|
||||
else {
|
||||
} else {
|
||||
tensor[i, j] = b[i, j]
|
||||
}
|
||||
}
|
||||
@ -485,10 +522,13 @@ private fun smallestElementComparison(a: MutableStructure2D<Double>, b: MutableS
|
||||
return tensor
|
||||
}
|
||||
|
||||
private fun getZeroIndices(column: MutableStructure2D<Double>, epsilon: Double = 0.000001): MutableStructure2D<Double>? {
|
||||
private fun getZeroIndices(
|
||||
column: MutableStructure2D<Double>,
|
||||
epsilon: Double = 0.000001,
|
||||
): MutableStructure2D<Double>? {
|
||||
var idx = emptyArray<Double>()
|
||||
for (i in 0 until column.shape.component1()) {
|
||||
if (kotlin.math.abs(column[i, 0]) > epsilon) {
|
||||
if (abs(column[i, 0]) > epsilon) {
|
||||
idx += (i + 1.0)
|
||||
}
|
||||
}
|
||||
@ -498,18 +538,27 @@ private fun getZeroIndices(column: MutableStructure2D<Double>, epsilon: Double =
|
||||
return null
|
||||
}
|
||||
|
||||
private fun evaluateFunction(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, Int) -> MutableStructure2D<Double>,
|
||||
t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, exampleNumber: Int)
|
||||
: MutableStructure2D<Double>
|
||||
{
|
||||
private fun evaluateFunction(
|
||||
func: (MutableStructure2D<Double>, MutableStructure2D<Double>, Int) -> MutableStructure2D<Double>,
|
||||
t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, exampleNumber: Int,
|
||||
)
|
||||
: MutableStructure2D<Double> {
|
||||
return func(t, p, exampleNumber)
|
||||
}
|
||||
|
||||
private fun lmMatx(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, Int) -> MutableStructure2D<Double>,
|
||||
t: MutableStructure2D<Double>, pOld: MutableStructure2D<Double>, yOld: MutableStructure2D<Double>,
|
||||
dX2: Int, JInput: MutableStructure2D<Double>, p: MutableStructure2D<Double>,
|
||||
yDat: MutableStructure2D<Double>, weight: MutableStructure2D<Double>, dp:MutableStructure2D<Double>, settings:LMSettings) : Array<MutableStructure2D<Double>>
|
||||
{
|
||||
private fun lmMatx(
|
||||
func: (MutableStructure2D<Double>, MutableStructure2D<Double>, Int) -> MutableStructure2D<Double>,
|
||||
t: MutableStructure2D<Double>,
|
||||
pOld: MutableStructure2D<Double>,
|
||||
yOld: MutableStructure2D<Double>,
|
||||
dX2: Int,
|
||||
JInput: MutableStructure2D<Double>,
|
||||
p: MutableStructure2D<Double>,
|
||||
yDat: MutableStructure2D<Double>,
|
||||
weight: MutableStructure2D<Double>,
|
||||
dp: MutableStructure2D<Double>,
|
||||
settings: LMSettings,
|
||||
): Array<MutableStructure2D<Double>> = with(DoubleTensorAlgebra) {
|
||||
// default: dp = 0.001
|
||||
val Npar = length(p) // number of parameters
|
||||
|
||||
@ -520,63 +569,70 @@ private fun lmMatx(func: (MutableStructure2D<Double>, MutableStructure2D<Double>
|
||||
|
||||
J = if (settings.iteration % (2 * Npar) == 0 || dX2 > 0) {
|
||||
lmFdJ(func, t, p, yHat, dp, settings).as2D() // finite difference
|
||||
}
|
||||
else {
|
||||
} else {
|
||||
lmBroydenJ(pOld, yOld, J, p, yHat).as2D() // rank-1 update
|
||||
}
|
||||
|
||||
val deltaY = yDat.minus(yHat)
|
||||
|
||||
val chiSq = deltaY.transposed().dot(deltaY.times(weight)).as2D()
|
||||
val JtWJ = J.transposed().dot ( J.times( weight.dot(BroadcastDoubleTensorAlgebra.ones(ShapeND(intArrayOf(1, Npar)))) ) ).as2D()
|
||||
val JtWdy = J.transposed().dot( weight.times(deltaY) ).as2D()
|
||||
val JtWJ =
|
||||
(J.transposed() dot J * (weight dot ones(ShapeND(intArrayOf(1, Npar))))).as2D()
|
||||
val JtWdy = (J.transposed() dot weight * deltaY).as2D()
|
||||
|
||||
return arrayOf(JtWJ, JtWdy, chiSq, yHat, J)
|
||||
}
|
||||
|
||||
private fun lmBroydenJ(pOld: MutableStructure2D<Double>, yOld: MutableStructure2D<Double>, JInput: MutableStructure2D<Double>,
|
||||
p: MutableStructure2D<Double>, y: MutableStructure2D<Double>): MutableStructure2D<Double> {
|
||||
private fun lmBroydenJ(
|
||||
pOld: MutableStructure2D<Double>, yOld: MutableStructure2D<Double>, JInput: MutableStructure2D<Double>,
|
||||
p: MutableStructure2D<Double>, y: MutableStructure2D<Double>,
|
||||
): MutableStructure2D<Double> = with(DoubleTensorAlgebra) {
|
||||
var J = JInput.copyToTensor()
|
||||
|
||||
val h = p.minus(pOld)
|
||||
val increase = y.minus(yOld).minus( J.dot(h) ).dot(h.transposed()).div( (h.transposed().dot(h)).as2D()[0, 0] )
|
||||
val increase = ((y - yOld - (J dot h)) dot h.transposed()) / (h.transposed() dot h)[0, 0]
|
||||
J = J.plus(increase)
|
||||
|
||||
return J.as2D()
|
||||
}
|
||||
|
||||
private fun lmFdJ(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, exampleNumber: Int) -> MutableStructure2D<Double>,
|
||||
t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, y: MutableStructure2D<Double>,
|
||||
dp: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> {
|
||||
@OptIn(PerformancePitfall::class)
|
||||
private fun lmFdJ(
|
||||
func: (MutableStructure2D<Double>, MutableStructure2D<Double>, exampleNumber: Int) -> MutableStructure2D<Double>,
|
||||
t: MutableStructure2D<Double>,
|
||||
p: MutableStructure2D<Double>,
|
||||
y: MutableStructure2D<Double>,
|
||||
dp: MutableStructure2D<Double>,
|
||||
settings: LMSettings,
|
||||
): MutableStructure2D<Double> = with(DoubleTensorAlgebra) {
|
||||
// default: dp = 0.001 * ones(1,n)
|
||||
|
||||
val m = length(y) // number of data points
|
||||
val n = length(p) // number of parameters
|
||||
|
||||
val ps = p.copyToTensor().as2D()
|
||||
val J = BroadcastDoubleTensorAlgebra.zeros(ShapeND(intArrayOf(m, n))).as2D() // initialize Jacobian to Zero
|
||||
val del = BroadcastDoubleTensorAlgebra.zeros(ShapeND(intArrayOf(n, 1))).as2D()
|
||||
val ps = p.copyToTensor()
|
||||
val J = zero(m, n) // initialize Jacobian to Zero
|
||||
val del = zero(n, 1)
|
||||
|
||||
for (j in 0 until n) {
|
||||
|
||||
del[j, 0] = dp[j, 0] * (1 + kotlin.math.abs(p[j, 0])) // parameter perturbation
|
||||
del[j, 0] = dp[j, 0] * (1 + abs(p[j, 0])) // parameter perturbation
|
||||
p[j, 0] = ps[j, 0] + del[j, 0] // perturb parameter p(j)
|
||||
|
||||
val epsilon = 0.0000001
|
||||
if (kotlin.math.abs(del[j, 0]) > epsilon) {
|
||||
if (abs(del[j, 0]) > epsilon) {
|
||||
val y1 = evaluateFunction(func, t, p, settings.exampleNumber)
|
||||
settings.funcCalls += 1
|
||||
|
||||
if (dp[j, 0] < 0) { // backwards difference
|
||||
for (i in 0 until J.shape.component1()) {
|
||||
J[i, j] = (y1.as2D().minus(y).as2D())[i, 0] / del[j, 0]
|
||||
for (i in 0 until J.shape.first()) {
|
||||
J[i, j] = (y1 - y)[i, 0] / del[j, 0]
|
||||
}
|
||||
}
|
||||
else {
|
||||
} else {
|
||||
// Do tests for it
|
||||
p[j, 0] = ps[j, 0] - del[j, 0] // central difference, additional func call
|
||||
for (i in 0 until J.shape.component1()) {
|
||||
J[i, j] = (y1.as2D().minus(evaluateFunction(func, t, p, settings.exampleNumber)).as2D())[i, 0] / (2 * del[j, 0])
|
||||
for (i in 0 until J.shape.first()) {
|
||||
J[i, j] = (y1 - evaluateFunction(func, t, p, settings.exampleNumber))[i, 0] / (2 * del[j, 0])
|
||||
}
|
||||
settings.funcCalls += 1
|
||||
}
|
||||
|
||||
@ -5,52 +5,53 @@
|
||||
|
||||
package space.kscience.kmath.tensors.core
|
||||
|
||||
import space.kscience.kmath.nd.MutableStructure2D
|
||||
import space.kscience.kmath.nd.ShapeND
|
||||
import space.kscience.kmath.nd.as2D
|
||||
import space.kscience.kmath.nd.component1
|
||||
import space.kscience.kmath.PerformancePitfall
|
||||
import space.kscience.kmath.nd.*
|
||||
import space.kscience.kmath.operations.invoke
|
||||
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.pow
|
||||
import space.kscience.kmath.tensors.core.DoubleTensorAlgebra.Companion.times
|
||||
import kotlin.math.roundToLong
|
||||
import space.kscience.kmath.structures.DoubleBuffer
|
||||
import kotlin.test.Test
|
||||
import kotlin.test.assertEquals
|
||||
|
||||
@PerformancePitfall
|
||||
class TestLmAlgorithm {
|
||||
companion object {
|
||||
fun funcEasyForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, exampleNumber: Int): MutableStructure2D<Double> {
|
||||
fun funcEasyForLm(
|
||||
t: MutableStructure2D<Double>,
|
||||
p: MutableStructure2D<Double>,
|
||||
exampleNumber: Int,
|
||||
): MutableStructure2D<Double> = with(DoubleTensorAlgebra) {
|
||||
val m = t.shape.component1()
|
||||
var yHat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(m, 1)))
|
||||
val yHat = when (exampleNumber) {
|
||||
1 -> exp((t * (-1.0 / p[1, 0]))) * p[0, 0] + (t * p[2, 0]) * exp((t * (-1.0 / p[3, 0])))
|
||||
|
||||
if (exampleNumber == 1) {
|
||||
yHat = 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])))
|
||||
)
|
||||
}
|
||||
else if (exampleNumber == 2) {
|
||||
2 -> {
|
||||
val mt = t.max()
|
||||
yHat = (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])
|
||||
(t * (1.0 / mt)) * p[0, 0] +
|
||||
(t * (1.0 / mt)).pow(2) * p[1, 0] +
|
||||
(t * (1.0 / mt)).pow(3) * p[2, 0] +
|
||||
(t * (1.0 / mt)).pow(4) * p[3, 0]
|
||||
}
|
||||
else if (exampleNumber == 3) {
|
||||
yHat = 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])
|
||||
|
||||
3 -> exp(t * (-1.0 / p[1, 0])) * p[0, 0] +
|
||||
sin((t * (1.0 / p[3, 0]))) * p[2, 0]
|
||||
|
||||
else -> zeros(ShapeND(intArrayOf(m, 1)))
|
||||
}
|
||||
|
||||
return yHat.as2D()
|
||||
}
|
||||
|
||||
fun funcMiddleForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, exampleNumber: Int): MutableStructure2D<Double> {
|
||||
fun funcMiddleForLm(
|
||||
t: MutableStructure2D<Double>,
|
||||
p: MutableStructure2D<Double>,
|
||||
exampleNumber: Int,
|
||||
): MutableStructure2D<Double> = with(DoubleTensorAlgebra) {
|
||||
val m = t.shape.component1()
|
||||
var yHat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf (m, 1)))
|
||||
var yHat = zeros(ShapeND(intArrayOf(m, 1)))
|
||||
|
||||
val mt = t.max()
|
||||
for (i in 0 until p.shape.component1()) {
|
||||
yHat += (t.times(1.0 / mt)).times(p[i, 0])
|
||||
yHat.plusAssign(t * (1.0 / mt) * p[i, 0])
|
||||
}
|
||||
|
||||
for (i in 0 until 5) {
|
||||
@ -60,13 +61,17 @@ class TestLmAlgorithm {
|
||||
return yHat.as2D()
|
||||
}
|
||||
|
||||
fun funcDifficultForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, exampleNumber: Int): MutableStructure2D<Double> {
|
||||
fun funcDifficultForLm(
|
||||
t: MutableStructure2D<Double>,
|
||||
p: MutableStructure2D<Double>,
|
||||
exampleNumber: Int,
|
||||
): MutableStructure2D<Double> = with(DoubleTensorAlgebra) {
|
||||
val m = t.shape.component1()
|
||||
var yHat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf (m, 1)))
|
||||
var yHat = zeros(ShapeND(intArrayOf(m, 1)))
|
||||
|
||||
val mt = t.max()
|
||||
for (i in 0 until p.shape.component1()) {
|
||||
yHat = yHat.plus( (t.times(1.0 / mt)).times(p[i, 0]) )
|
||||
yHat = yHat + (t * (1.0 / mt)) * p[i, 0]
|
||||
}
|
||||
|
||||
for (i in 0 until 4) {
|
||||
@ -76,6 +81,7 @@ class TestLmAlgorithm {
|
||||
return yHat.as2D()
|
||||
}
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testLMEasy() = DoubleTensorAlgebra {
|
||||
val lmMatxYDat = doubleArrayOf(
|
||||
@ -91,12 +97,12 @@ class TestLmAlgorithm {
|
||||
14.7665, 13.3718, 15.0587, 13.8320, 14.7873, 13.6824, 14.2579, 14.2154, 13.5818, 13.8157
|
||||
)
|
||||
|
||||
var exampleNumber = 1
|
||||
val p_init = BroadcastDoubleTensorAlgebra.fromArray(
|
||||
val exampleNumber = 1
|
||||
val pInit = fromArray(
|
||||
ShapeND(intArrayOf(4, 1)), doubleArrayOf(5.0, 2.0, 0.2, 10.0)
|
||||
).as2D()
|
||||
|
||||
var t = ones(ShapeND(intArrayOf(100, 1))).as2D()
|
||||
val t = ones(ShapeND(intArrayOf(100, 1))).as2D()
|
||||
for (i in 0 until 100) {
|
||||
t[i, 0] = t[i, 0] * (i + 1)
|
||||
}
|
||||
@ -119,22 +125,26 @@ class TestLmAlgorithm {
|
||||
ShapeND(intArrayOf(4, 1)), doubleArrayOf(50.0, 20.0, 2.0, 100.0)
|
||||
).as2D()
|
||||
|
||||
val inputData = LMInput(::funcEasyForLm, p_init, t, yDat, weight, dp, pMin, pMax, 100,
|
||||
doubleArrayOf(1e-3, 1e-3, 1e-1, 1e-1), doubleArrayOf(1e-2, 11.0, 9.0), 1, 10, exampleNumber)
|
||||
val inputData = LMInput(
|
||||
Companion::funcEasyForLm, pInit, t, yDat, weight, dp, pMin, pMax, 100,
|
||||
doubleArrayOf(1e-3, 1e-3, 1e-1, 1e-1), doubleArrayOf(1e-2, 11.0, 9.0), 1, 10, exampleNumber
|
||||
)
|
||||
|
||||
val result = levenbergMarquardt(inputData)
|
||||
assertEquals(13, result.iterations)
|
||||
assertEquals(31, result.funcCalls)
|
||||
assertEquals(0.9131368192633, (result.resultChiSq * 1e13).roundToLong() / 1e13)
|
||||
assertEquals(3.7790980 * 1e-7, (result.resultLambda * 1e13).roundToLong() / 1e13)
|
||||
assertEquals(0.9131368192633, result.resultChiSq, 1e-13)
|
||||
assertEquals(3.7790980 * 1e-7, result.resultLambda, 1e-13)
|
||||
assertEquals(result.typeOfConvergence, TypeOfConvergence.InParameters)
|
||||
val expectedParameters = BroadcastDoubleTensorAlgebra.fromArray(
|
||||
ShapeND(intArrayOf(4, 1)), doubleArrayOf(20.527230909086, 9.833627103230, 0.997571256572, 50.174445822506)
|
||||
).as2D()
|
||||
result.resultParameters = result.resultParameters.map { x -> (x * 1e12).toLong() / 1e12 }.as2D()
|
||||
val receivedParameters = BroadcastDoubleTensorAlgebra.fromArray(
|
||||
ShapeND(intArrayOf(4, 1)), doubleArrayOf(result.resultParameters[0, 0], result.resultParameters[1, 0],
|
||||
result.resultParameters[2, 0], result.resultParameters[3, 0])
|
||||
ShapeND(intArrayOf(4, 1)), doubleArrayOf(
|
||||
result.resultParameters[0, 0], result.resultParameters[1, 0],
|
||||
result.resultParameters[2, 0], result.resultParameters[3, 0]
|
||||
)
|
||||
).as2D()
|
||||
assertEquals(expectedParameters[0, 0], receivedParameters[0, 0])
|
||||
assertEquals(expectedParameters[1, 0], receivedParameters[1, 0])
|
||||
@ -143,16 +153,16 @@ class TestLmAlgorithm {
|
||||
}
|
||||
|
||||
@Test
|
||||
fun TestLMMiddle() = DoubleTensorAlgebra {
|
||||
val NData = 100
|
||||
val tExample = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(NData, 1))).as2D()
|
||||
for (i in 0 until NData) {
|
||||
fun testLMMiddle() = DoubleTensorAlgebra {
|
||||
val nData = 100
|
||||
val tExample = one(nData, 1).as2D()
|
||||
for (i in 0 until nData) {
|
||||
tExample[i, 0] = tExample[i, 0] * (i + 1)
|
||||
}
|
||||
|
||||
val Nparams = 20
|
||||
val pExample = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(Nparams, 1))).as2D()
|
||||
for (i in 0 until Nparams) {
|
||||
val nParams = 20
|
||||
val pExample = one(nParams, 1).as2D()
|
||||
for (i in 0 until nParams) {
|
||||
pExample[i, 0] = pExample[i, 0] + i - 25
|
||||
}
|
||||
|
||||
@ -160,8 +170,8 @@ class TestLmAlgorithm {
|
||||
|
||||
val yHat = funcMiddleForLm(tExample, pExample, exampleNumber)
|
||||
|
||||
val pInit = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(Nparams, 1))).as2D()
|
||||
for (i in 0 until Nparams) {
|
||||
val pInit = zeros(ShapeND(intArrayOf(nParams, 1))).as2D()
|
||||
for (i in 0 until nParams) {
|
||||
pInit[i, 0] = (pExample[i, 0] + 0.9)
|
||||
}
|
||||
|
||||
@ -171,13 +181,14 @@ class TestLmAlgorithm {
|
||||
val dp = BroadcastDoubleTensorAlgebra.fromArray(
|
||||
ShapeND(intArrayOf(1, 1)), DoubleArray(1) { -0.01 }
|
||||
).as2D()
|
||||
var pMin = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(Nparams, 1)))
|
||||
pMin = pMin.div(1.0 / -50.0)
|
||||
val pMax = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(Nparams, 1)))
|
||||
pMin = pMin.div(1.0 / 50.0)
|
||||
var pMin = ones(ShapeND(intArrayOf(nParams, 1)))
|
||||
pMin = pMin * (-50.0)
|
||||
val pMax = ones(ShapeND(intArrayOf(nParams, 1)))
|
||||
pMin = pMin * 50.0
|
||||
val opts = doubleArrayOf(3.0, 7000.0, 1e-5, 1e-5, 1e-5, 1e-5, 1e-5, 11.0, 9.0, 1.0)
|
||||
|
||||
val inputData = LMInput(::funcMiddleForLm,
|
||||
val inputData = LMInput(
|
||||
Companion::funcMiddleForLm,
|
||||
pInit.as2D(),
|
||||
t,
|
||||
yDat,
|
||||
@ -190,63 +201,67 @@ class TestLmAlgorithm {
|
||||
doubleArrayOf(opts[6], opts[7], opts[8]),
|
||||
opts[9].toInt(),
|
||||
10,
|
||||
1)
|
||||
1
|
||||
)
|
||||
|
||||
val result = DoubleTensorAlgebra.levenbergMarquardt(inputData)
|
||||
|
||||
assertEquals(46, result.iterations)
|
||||
assertEquals(113, result.funcCalls)
|
||||
assertEquals(0.000005977, (result.resultChiSq * 1e9).roundToLong() / 1e9)
|
||||
assertEquals(1.0 * 1e-7, (result.resultLambda * 1e13).roundToLong() / 1e13)
|
||||
assertEquals(0.000005977, result.resultChiSq, 1e-9)
|
||||
assertEquals(1.0 * 1e-7, result.resultLambda, 1e-13)
|
||||
assertEquals(result.typeOfConvergence, TypeOfConvergence.InReducedChiSquare)
|
||||
val expectedParameters = BroadcastDoubleTensorAlgebra.fromArray(
|
||||
ShapeND(intArrayOf(Nparams, 1)), doubleArrayOf( -23.9717, -18.6686, -21.7971,
|
||||
val expectedParameters = fromArray(
|
||||
ShapeND(intArrayOf(nParams, 1)), doubleArrayOf(
|
||||
-23.9717, -18.6686, -21.7971,
|
||||
-20.9681, -22.086, -20.5859, -19.0384, -17.4957, -15.9991, -14.576, -13.2441, -
|
||||
12.0201, -10.9256, -9.9878, -9.2309, -8.6589, -8.2365, -7.8783, -7.4598, -6.8511)).as2D()
|
||||
result.resultParameters = result.resultParameters.map { x -> (x * 1e4).roundToLong() / 1e4}.as2D()
|
||||
val receivedParameters = zeros(ShapeND(intArrayOf(Nparams, 1))).as2D()
|
||||
for (i in 0 until Nparams) {
|
||||
12.0201, -10.9256, -9.9878, -9.2309, -8.6589, -8.2365, -7.8783, -7.4598, -6.8511
|
||||
)
|
||||
)
|
||||
val receivedParameters = zero(nParams, 1)
|
||||
for (i in 0 until nParams) {
|
||||
receivedParameters[i, 0] = result.resultParameters[i, 0]
|
||||
assertEquals(expectedParameters[i, 0], result.resultParameters[i, 0])
|
||||
assertEquals(expectedParameters[i, 0], result.resultParameters[i, 0], 1e-2)
|
||||
}
|
||||
}
|
||||
|
||||
@Test
|
||||
fun TestLMDifficult() = DoubleTensorAlgebra {
|
||||
val NData = 200
|
||||
var tExample = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(NData, 1))).as2D()
|
||||
for (i in 0 until NData) {
|
||||
val nData = 200
|
||||
val tExample = ones(ShapeND(intArrayOf(nData, 1))).as2D()
|
||||
for (i in 0 until nData) {
|
||||
tExample[i, 0] = tExample[i, 0] * (i + 1) - 104
|
||||
}
|
||||
|
||||
val Nparams = 15
|
||||
var pExample = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(Nparams, 1))).as2D()
|
||||
for (i in 0 until Nparams) {
|
||||
val nParams = 15
|
||||
val pExample = ones(ShapeND(intArrayOf(nParams, 1))).as2D()
|
||||
for (i in 0 until nParams) {
|
||||
pExample[i, 0] = pExample[i, 0] + i - 25
|
||||
}
|
||||
|
||||
val exampleNumber = 1
|
||||
|
||||
var yHat = funcDifficultForLm(tExample, pExample, exampleNumber)
|
||||
val yHat = funcDifficultForLm(tExample, pExample, exampleNumber)
|
||||
|
||||
var pInit = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(Nparams, 1))).as2D()
|
||||
for (i in 0 until Nparams) {
|
||||
val pInit = zeros(ShapeND(intArrayOf(nParams, 1))).as2D()
|
||||
for (i in 0 until nParams) {
|
||||
pInit[i, 0] = (pExample[i, 0] + 0.9)
|
||||
}
|
||||
|
||||
var t = tExample
|
||||
val t = tExample
|
||||
val yDat = yHat
|
||||
val weight = 1.0 / Nparams * 1.0 - 0.085
|
||||
val dp = BroadcastDoubleTensorAlgebra.fromArray(
|
||||
val weight = 1.0 / nParams * 1.0 - 0.085
|
||||
val dp = fromArray(
|
||||
ShapeND(intArrayOf(1, 1)), DoubleArray(1) { -0.01 }
|
||||
).as2D()
|
||||
var pMin = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(Nparams, 1)))
|
||||
pMin = pMin.div(1.0 / -50.0)
|
||||
val pMax = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(Nparams, 1)))
|
||||
pMin = pMin.div(1.0 / 50.0)
|
||||
var pMin = ones(ShapeND(intArrayOf(nParams, 1)))
|
||||
pMin = pMin * (-50.0)
|
||||
val pMax = ones(ShapeND(intArrayOf(nParams, 1)))
|
||||
pMin = pMin * (50.0)
|
||||
val opts = doubleArrayOf(3.0, 7000.0, 1e-2, 1e-3, 1e-2, 1e-2, 1e-2, 11.0, 9.0, 1.0)
|
||||
|
||||
val inputData = LMInput(::funcDifficultForLm,
|
||||
val inputData = LMInput(
|
||||
Companion::funcDifficultForLm,
|
||||
pInit.as2D(),
|
||||
t,
|
||||
yDat,
|
||||
@ -259,22 +274,37 @@ class TestLmAlgorithm {
|
||||
doubleArrayOf(opts[6], opts[7], opts[8]),
|
||||
opts[9].toInt(),
|
||||
10,
|
||||
1)
|
||||
1
|
||||
)
|
||||
|
||||
val result = DoubleTensorAlgebra.levenbergMarquardt(inputData)
|
||||
|
||||
assertEquals(2375, result.iterations)
|
||||
assertEquals(4858, result.funcCalls)
|
||||
assertEquals(5.14347, (result.resultLambda * 1e5).roundToLong() / 1e5)
|
||||
assertEquals(5.14347, result.resultLambda, 1e-5)
|
||||
assertEquals(result.typeOfConvergence, TypeOfConvergence.InParameters)
|
||||
val expectedParameters = BroadcastDoubleTensorAlgebra.fromArray(
|
||||
ShapeND(intArrayOf(Nparams, 1)), doubleArrayOf(-23.6412, -16.7402, -21.5705, -21.0464,
|
||||
-17.2852, -17.2959, -17.298, 0.9999, -17.2885, -17.3008, -17.2941, -17.2923, -17.2976, -17.3028, -17.2891)).as2D()
|
||||
result.resultParameters = result.resultParameters.map { x -> (x * 1e4).roundToLong() / 1e4}.as2D()
|
||||
val receivedParameters = zeros(ShapeND(intArrayOf(Nparams, 1))).as2D()
|
||||
for (i in 0 until Nparams) {
|
||||
val expectedParameters = DoubleBuffer(
|
||||
-23.6412,
|
||||
-16.7402,
|
||||
-21.5705,
|
||||
-21.0464,
|
||||
-17.2852,
|
||||
-17.2959,
|
||||
-17.298,
|
||||
0.9999,
|
||||
-17.2885,
|
||||
-17.3008,
|
||||
-17.2941,
|
||||
-17.2923,
|
||||
-17.2976,
|
||||
-17.3028,
|
||||
-17.2891
|
||||
)
|
||||
|
||||
val receivedParameters = zeros(ShapeND(intArrayOf(nParams, 1))).as2D()
|
||||
for (i in 0 until nParams) {
|
||||
receivedParameters[i, 0] = result.resultParameters[i, 0]
|
||||
assertEquals(expectedParameters[i, 0], result.resultParameters[i, 0])
|
||||
assertEquals(expectedParameters[i], result.resultParameters[i, 0], 1e-2)
|
||||
}
|
||||
}
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user