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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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3 changed files with 62 additions and 48 deletions
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13
kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/LinearOpsTensorAlgebra.kt
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@ -120,13 +120,22 @@ public interface LinearOpsTensorAlgebra<T, A : Field<T>> : TensorPartialDivision
*/ */
public fun solve(a: MutableStructure2D<Double>, b: MutableStructure2D<Double>): MutableStructure2D<Double> public fun solve(a: MutableStructure2D<Double>, b: MutableStructure2D<Double>): MutableStructure2D<Double>
data class LMResultInfo ( public enum class TypeOfConvergence{
inRHS_JtWdy,
inParameters,
inReducedChi_square,
noConvergence
}
public data class LMResultInfo (
var iterations:Int, var iterations:Int,
var func_calls: Int, var func_calls: Int,
var example_number: Int, var example_number: Int,
var result_chi_sq: Double, var result_chi_sq: Double,
var result_lambda: Double, var result_lambda: Double,
var result_parameters: MutableStructure2D<Double> var result_parameters: MutableStructure2D<Double>,
var typeOfConvergence: TypeOfConvergence,
var epsilon: Double
) )
public fun lm( public fun lm(

95
kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt
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@ -723,9 +723,9 @@ public open class DoubleTensorAlgebra :
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): LinearOpsTensorAlgebra.LMResultInfo { c_input: MutableStructure2D<Double>, opts_input: DoubleArray, nargin: Int, example_number: Int): LinearOpsTensorAlgebra.LMResultInfo {
var resultInfo = LinearOpsTensorAlgebra.LMResultInfo(0, 0, example_number, 0.0, 0.0, p_input) var resultInfo = LinearOpsTensorAlgebra.LMResultInfo(0, 0, example_number, 0.0,
0.0, p_input, LinearOpsTensorAlgebra.TypeOfConvergence.noConvergence, 0.0)
val tensor_parameter = 0
val eps:Double = 2.2204e-16 val eps:Double = 2.2204e-16
var settings = LMSettings(0, 0, example_number) var settings = LMSettings(0, 0, example_number)
@ -751,7 +751,7 @@ public open class DoubleTensorAlgebra :
var cvg_hist = 0 var cvg_hist = 0
if (length(t) != length(y_dat)) { if (length(t) != length(y_dat)) {
println("lm.m error: the length of t must equal the length of y_dat") // println("lm.m error: the length of t must equal the length of y_dat")
val length_t = length(t) val length_t = length(t)
val length_y_dat = length(y_dat) val length_y_dat = length(y_dat)
X2 = 0.0 X2 = 0.0
@ -761,10 +761,6 @@ public open class DoubleTensorAlgebra :
sigma_y = 0 sigma_y = 0
R_sq = 0 R_sq = 0
cvg_hist = 0 cvg_hist = 0
// if (tensor_parameter != 0) { // Зачем эта проверка?
// return
// }
} }
var weight = weight_input var weight = weight_input
@ -827,8 +823,8 @@ public open class DoubleTensorAlgebra :
val y_init = feval(func, t, p, settings) // residual error using p_try val y_init = feval(func, t, p, settings) // 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 / abs(weight[0, 0])).as2D() // !!! need to check weight = ones(ShapeND(intArrayOf(Npnt, 1))).div(1 / abs(weight[0, 0])).as2D()
println("using uniform weights for error analysis") // println("using uniform weights for error analysis")
} }
else { else {
weight = make_column(weight) weight = make_column(weight)
@ -844,8 +840,8 @@ public open class DoubleTensorAlgebra :
J = lm_matx_ans[4] J = lm_matx_ans[4]
if ( abs(JtWdy).max()!! < epsilon_1 ) { if ( abs(JtWdy).max()!! < epsilon_1 ) {
println(" *** Your Initial Guess is Extremely Close to Optimal ***\n") // println(" *** Your Initial Guess is Extremely Close to Optimal ***\n")
println(" *** epsilon_1 = %e\n$epsilon_1") // println(" *** epsilon_1 = %e\n$epsilon_1")
stop = true stop = true
} }
@ -885,11 +881,14 @@ public open class DoubleTensorAlgebra :
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, settings)) // residual error using p_try
// TODO for (i in 0 until delta_y.shape.component1()) { // floating point error; break
//if ~all(isfinite(delta_y)) // floating point error; break for (j in 0 until delta_y.shape.component2()) {
// stop = 1; if (delta_y[i, j] == Double.POSITIVE_INFINITY || delta_y[i, j] == Double.NEGATIVE_INFINITY) {
// break stop = true
//end break
}
}
}
settings.func_calls += 1 settings.func_calls += 1
@ -900,17 +899,16 @@ public open class DoubleTensorAlgebra :
if (Update_Type == 2) { // Quadratic if (Update_Type == 2) { // Quadratic
// One step of quadratic line update in the h direction for minimum X2 // One step of quadratic line update in the h direction for minimum X2
// TODO val alpha = JtWdy.transpose().dot(h) / ( (X2_try.minus(X2)).div(2.0).plus(2 * JtWdy.transpose().dot(h)) )
// val alpha = JtWdy.transpose().dot(h) / ((X2_try.minus(X2)).div(2.0).plus(2 * JtWdy.transpose().dot(h))) h = h.dot(alpha)
// alpha = JtWdy'*h / ( (X2_try - X2)/2 + 2*JtWdy'*h ) ; p_try = p.plus(h).as2D() // update only [idx] elements
// h = alpha * h; p_try = smallest_element_comparison(largest_element_comparison(p_min, p_try), p_max) // apply constraints
//
// p_try = p + h(idx); % update only [idx] elements var delta_y = y_dat.minus(feval(func, t, p_try, settings)) // residual error using p_try
// p_try = min(max(p_min,p_try),p_max); % apply constraints settings.func_calls += 1
//
// delta_y = y_dat - feval(func,t,p_try,c); % residual error using p_try val tmp = delta_y.times(weight)
// func_calls = func_calls + 1; X2_try = delta_y.as2D().transpose().dot(tmp) // Chi-squared error criteria
// тX2_try = delta_y' * ( delta_y .* weight ); % Chi-squared error criteria
} }
val rho = when (Update_Type) { // Nielsen val rho = when (Update_Type) { // Nielsen
@ -924,9 +922,6 @@ public open class DoubleTensorAlgebra :
} }
} }
println()
println("rho = " + rho)
if (rho > epsilon_4) { // it IS significantly better if (rho > epsilon_4) { // it IS significantly better
val dX2 = X2.minus(X2_old) val dX2 = X2.minus(X2_old)
X2_old = X2 X2_old = X2
@ -984,15 +979,15 @@ public open class DoubleTensorAlgebra :
if (prnt > 1) { if (prnt > 1) {
val chi_sq = X2 / DoF val chi_sq = X2 / DoF
println("Iteration $settings | chi_sq=$chi_sq | lambda=$lambda") // println("Iteration $settings | chi_sq=$chi_sq | lambda=$lambda")
print("param: ") // print("param: ")
for (pn in 0 until Npar) { // for (pn in 0 until Npar) {
print(p[pn, 0].toString() + " ") // print(p[pn, 0].toString() + " ")
} // }
print("\ndp/p: ") // print("\ndp/p: ")
for (pn in 0 until Npar) { // for (pn in 0 until Npar) {
print((h.as2D()[pn, 0] / p[pn, 0]).toString() + " ") // print((h.as2D()[pn, 0] / p[pn, 0]).toString() + " ")
} // }
resultInfo.iterations = settings.iteration resultInfo.iterations = settings.iteration
resultInfo.func_calls = settings.func_calls resultInfo.func_calls = settings.func_calls
resultInfo.result_chi_sq = chi_sq resultInfo.result_chi_sq = chi_sq
@ -1004,22 +999,30 @@ public open class DoubleTensorAlgebra :
// cvg_hst(iteration,:) = [ func_calls p' X2/DoF lambda ]; // cvg_hst(iteration,:) = [ func_calls p' X2/DoF lambda ];
if (abs(JtWdy).max()!! < epsilon_1 && settings.iteration > 2) { if (abs(JtWdy).max()!! < epsilon_1 && settings.iteration > 2) {
println(" **** Convergence in r.h.s. (\"JtWdy\") ****") // println(" **** Convergence in r.h.s. (\"JtWdy\") ****")
println(" **** epsilon_1 = $epsilon_1") // println(" **** epsilon_1 = $epsilon_1")
resultInfo.typeOfConvergence = LinearOpsTensorAlgebra.TypeOfConvergence.inRHS_JtWdy
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) {
println(" **** Convergence in Parameters ****") // println(" **** Convergence in Parameters ****")
println(" **** epsilon_2 = $epsilon_2") // println(" **** epsilon_2 = $epsilon_2")
resultInfo.typeOfConvergence = LinearOpsTensorAlgebra.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) {
println(" **** Convergence in reduced Chi-square **** ") // println(" **** Convergence in reduced Chi-square **** ")
println(" **** epsilon_3 = $epsilon_3") // println(" **** epsilon_3 = $epsilon_3")
resultInfo.typeOfConvergence = LinearOpsTensorAlgebra.TypeOfConvergence.inReducedChi_square
resultInfo.epsilon = epsilon_3
stop = true stop = true
} }
if (settings.iteration == MaxIter) { if (settings.iteration == MaxIter) {
println(" !! Maximum Number of Iterations Reached Without Convergence !!") // println(" !! Maximum Number of Iterations Reached Without Convergence !!")
resultInfo.typeOfConvergence = LinearOpsTensorAlgebra.TypeOfConvergence.noConvergence
resultInfo.epsilon = 0.0
stop = true stop = true
} }
} // --- End of Main Loop } // --- End of Main Loop

2
kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleTensorAlgebra.kt
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@ -8,6 +8,7 @@ package space.kscience.kmath.tensors.core
import space.kscience.kmath.nd.* import space.kscience.kmath.nd.*
import space.kscience.kmath.operations.invoke import space.kscience.kmath.operations.invoke
import space.kscience.kmath.tensors.api.LinearOpsTensorAlgebra
import space.kscience.kmath.tensors.core.internal.LMSettings import space.kscience.kmath.tensors.core.internal.LMSettings
import space.kscience.kmath.testutils.assertBufferEquals import space.kscience.kmath.testutils.assertBufferEquals
import kotlin.math.roundToInt import kotlin.math.roundToInt
@ -290,5 +291,6 @@ internal class TestDoubleTensorAlgebra {
assertEquals(1, result.example_number) assertEquals(1, result.example_number)
assertEquals(0.9131368192633, (result.result_chi_sq * 1e13).roundToLong() / 1e13) assertEquals(0.9131368192633, (result.result_chi_sq * 1e13).roundToLong() / 1e13)
assertEquals(3.7790980 * 1e-7, (result.result_lambda * 1e13).roundToLong() / 1e13) assertEquals(3.7790980 * 1e-7, (result.result_lambda * 1e13).roundToLong() / 1e13)
assertEquals(result.typeOfConvergence, LinearOpsTensorAlgebra.TypeOfConvergence.inParameters)
} }
} }