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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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6 changed files with 554 additions and 706 deletions
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14
kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/LinearOpsTensorAlgebra.kt
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@ -7,15 +7,7 @@ package space.kscience.kmath.tensors.api
import space.kscience.kmath.nd.MutableStructure2D
import space.kscience.kmath.nd.StructureND
import space.kscience.kmath.nd.as2D
import space.kscience.kmath.operations.Field
import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra
import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.dot
import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.map
import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.transposed
import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
import space.kscience.kmath.tensors.core.internal.LMSettings
import kotlin.reflect.KFunction3
/**
* Common linear algebra operations. Operates on [Tensor].
@ -137,10 +129,4 @@ public interface LinearOpsTensorAlgebra<T, A : Field<T>> : TensorPartialDivision
var typeOfConvergence: TypeOfConvergence,
var epsilon: Double
)
public fun lm(
func: KFunction3<MutableStructure2D<Double>, MutableStructure2D<Double>, LMSettings, 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>,
c_input: MutableStructure2D<Double>, opts_input: DoubleArray, nargin: Int, example_number: Int): LMResultInfo
}

363
kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt
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@ -9,7 +9,6 @@
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.operations.DoubleBufferOps
import space.kscience.kmath.operations.DoubleField
@ -19,7 +18,6 @@ import space.kscience.kmath.tensors.api.LinearOpsTensorAlgebra
import space.kscience.kmath.tensors.api.Tensor
import space.kscience.kmath.tensors.core.internal.*
import kotlin.math.*
import kotlin.reflect.KFunction3
/**
* Implementation of basic operations over double tensors and basic algebra operations on them.
@ -716,367 +714,6 @@ public open class DoubleTensorAlgebra :
val aInverse = aSvd.third.dot(s).dot(aSvd.first.transposed())
return aInverse.dot(b).as2D()
}
override fun lm(
func: KFunction3<MutableStructure2D<Double>, MutableStructure2D<Double>, LMSettings, 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>,
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, LinearOpsTensorAlgebra.TypeOfConvergence.noConvergence, 0.0)
val eps:Double = 2.2204e-16
var settings = LMSettings(0, 0, example_number)
settings.func_calls = 0 // running count of function evaluations
var p = p_input
val y_dat = y_dat_input
val t = t_input
val Npar = length(p) // number of parameters
val Npnt = length(y_dat) // number of data points
var p_old = zeros(ShapeND(intArrayOf(Npar, 1))).as2D() // previous set of parameters
var y_old = 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 X2_old = 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
var corr_p = 0
var sigma_p = 0
var sigma_y = 0
var R_sq = 0
var cvg_hist = 0
if (length(t) != length(y_dat)) {
// println("lm.m error: the length of t must equal the length of y_dat")
val length_t = length(t)
val length_y_dat = length(y_dat)
X2 = 0.0
corr_p = 0
sigma_p = 0
sigma_y = 0
R_sq = 0
cvg_hist = 0
}
var weight = weight_input
if (nargin < 5) {
fromArray(ShapeND(intArrayOf(1, 1)), doubleArrayOf(1.0)).as2D()
}
var dp = dp_input
if (nargin < 6) {
dp = fromArray(ShapeND(intArrayOf(1, 1)), doubleArrayOf(-0.001)).as2D()
}
var p_min = p_min_input
if (nargin < 7) {
p_min = p
p_min.abs()
p_min = p_min.div(-100.0).as2D()
}
var p_max = p_max_input
if (nargin < 8) {
p_max = p
p_max.abs()
p_max = p_max.div(100.0).as2D()
}
var c = c_input
if (nargin < 9) {
c = fromArray(ShapeND(intArrayOf(1, 1)), doubleArrayOf(1.0)).as2D()
}
var opts = opts_input
if (nargin < 10) {
opts = doubleArrayOf(3.0, 10.0 * Npar, 1e-3, 1e-3, 1e-1, 1e-1, 1e-2, 11.0, 9.0, 1.0)
}
val prnt = opts[0] // >1 intermediate results; >2 plots
val MaxIter = opts[1].toInt() // maximum number of iterations
val epsilon_1 = opts[2] // convergence tolerance for gradient
val epsilon_2 = opts[3] // convergence tolerance for parameters
val epsilon_3 = opts[4] // convergence tolerance for Chi-square
val epsilon_4 = opts[5] // determines acceptance of a L-M step
val lambda_0 = opts[6] // initial value of damping paramter, lambda
val lambda_UP_fac = opts[7] // factor for increasing lambda
val lambda_DN_fac = opts[8] // factor for decreasing lambda
val Update_Type = opts[9].toInt() // 1: Levenberg-Marquardt lambda update
// 2: Quadratic update
// 3: Nielsen's lambda update equations
p_min = make_column(p_min)
p_max = make_column(p_max)
if (length(make_column(dp)) == 1) {
dp = ones(ShapeND(intArrayOf(Npar, 1))).div(1 / dp[0, 0]).as2D()
}
val idx = get_zero_indices(dp) // indices of the parameters to be fit
val Nfit = idx?.shape?.component1() // number of parameters to fit
var stop = false // termination flag
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
weight = ones(ShapeND(intArrayOf(Npnt, 1))).div(1 / abs(weight[0, 0])).as2D()
// println("using uniform weights for error analysis")
}
else {
weight = make_column(weight)
weight.abs()
}
// initialize Jacobian with finite difference calculation
var lm_matx_ans = lm_matx(func, t, p_old, y_old,1, J, p, y_dat, weight, dp, settings)
var JtWJ = lm_matx_ans[0]
var JtWdy = lm_matx_ans[1]
X2 = lm_matx_ans[2][0, 0]
var y_hat = lm_matx_ans[3]
J = lm_matx_ans[4]
if ( abs(JtWdy).max()!! < epsilon_1 ) {
// println(" *** Your Initial Guess is Extremely Close to Optimal ***\n")
// println(" *** epsilon_1 = %e\n$epsilon_1")
stop = true
}
var lambda = 1.0
var nu = 1
when (Update_Type) {
1 -> lambda = lambda_0 // Marquardt: init'l lambda
else -> { // Quadratic and Nielsen
lambda = lambda_0 * (diag(JtWJ)).max()!!
nu = 2
}
}
X2_old = X2 // previous value of X2
var cvg_hst = ones(ShapeND(intArrayOf(MaxIter, Npar + 3))) // initialize convergence history
var h: DoubleTensor
var dX2 = X2
while (!stop && settings.iteration <= MaxIter) { //--- Start Main Loop
settings.iteration += 1
// incremental change in parameters
h = when (Update_Type) {
1 -> { // Marquardt
val solve = solve(JtWJ.plus(make_matrx_with_diagonal(diag(JtWJ)).div(1 / lambda)).as2D(), JtWdy)
solve.asDoubleTensor()
}
else -> { // Quadratic and Nielsen
val solve = solve(JtWJ.plus(lm_eye(Npar).div(1 / lambda)).as2D(), JtWdy)
solve.asDoubleTensor()
}
}
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
var delta_y = y_dat.minus(feval(func, t, p_try, settings)) // residual error using p_try
for (i in 0 until delta_y.shape.component1()) { // floating point error; break
for (j in 0 until delta_y.shape.component2()) {
if (delta_y[i, j] == Double.POSITIVE_INFINITY || delta_y[i, j] == Double.NEGATIVE_INFINITY) {
stop = true
break
}
}
}
settings.func_calls += 1
val tmp = delta_y.times(weight)
var X2_try = delta_y.as2D().transpose().dot(tmp) // Chi-squared error criteria
val alpha = 1.0
if (Update_Type == 2) { // Quadratic
// One step of quadratic line update in the h direction for minimum X2
val alpha = JtWdy.transpose().dot(h) / ( (X2_try.minus(X2)).div(2.0).plus(2 * JtWdy.transpose().dot(h)) )
h = h.dot(alpha)
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
var delta_y = y_dat.minus(feval(func, t, p_try, settings)) // residual error using p_try
settings.func_calls += 1
val tmp = delta_y.times(weight)
X2_try = delta_y.as2D().transpose().dot(tmp) // Chi-squared error criteria
}
val rho = when (Update_Type) { // Nielsen
1 -> {
val tmp = h.transposed().dot(make_matrx_with_diagonal(diag(JtWJ)).div(1 / lambda).dot(h).plus(JtWdy))
X2.minus(X2_try).as2D()[0, 0] / abs(tmp.as2D()).as2D()[0, 0]
}
else -> {
val tmp = h.transposed().dot(h.div(1 / lambda).plus(JtWdy))
X2.minus(X2_try).as2D()[0, 0] / abs(tmp.as2D()).as2D()[0, 0]
}
}
if (rho > epsilon_4) { // it IS significantly better
val dX2 = X2.minus(X2_old)
X2_old = X2
p_old = p.copyToTensor().as2D()
y_old = y_hat.copyToTensor().as2D()
p = make_column(p_try) // accept p_try
lm_matx_ans = lm_matx(func, t, p_old, y_old, dX2.toInt(), J, p, y_dat, weight, dp, settings)
// decrease lambda ==> Gauss-Newton method
JtWJ = lm_matx_ans[0]
JtWdy = lm_matx_ans[1]
X2 = lm_matx_ans[2][0, 0]
y_hat = lm_matx_ans[3]
J = lm_matx_ans[4]
lambda = when (Update_Type) {
1 -> { // Levenberg
max(lambda / lambda_DN_fac, 1e-7);
}
2 -> { // Quadratic
max( lambda / (1 + alpha) , 1e-7 );
}
else -> { // Nielsen
nu = 2
lambda * max( 1.0 / 3, 1 - (2 * rho - 1).pow(3) )
}
}
}
else { // it IS NOT better
X2 = X2_old // do not accept p_try
if (settings.iteration % (2 * Npar) == 0 ) { // rank-1 update of Jacobian
lm_matx_ans = lm_matx(func, t, p_old, y_old,-1, J, p, y_dat, weight, dp, settings)
JtWJ = lm_matx_ans[0]
JtWdy = lm_matx_ans[1]
dX2 = lm_matx_ans[2][0, 0]
y_hat = lm_matx_ans[3]
J = lm_matx_ans[4]
}
// increase lambda ==> gradient descent method
lambda = when (Update_Type) {
1 -> { // Levenberg
min(lambda * lambda_UP_fac, 1e7)
}
2 -> { // Quadratic
lambda + abs(((X2_try.as2D()[0, 0] - X2) / 2) / alpha)
}
else -> { // Nielsen
nu *= 2
lambda * (nu / 2)
}
}
}
if (prnt > 1) {
val chi_sq = X2 / DoF
// println("Iteration $settings | chi_sq=$chi_sq | lambda=$lambda")
// print("param: ")
// for (pn in 0 until Npar) {
// print(p[pn, 0].toString() + " ")
// }
// print("\ndp/p: ")
// for (pn in 0 until Npar) {
// print((h.as2D()[pn, 0] / p[pn, 0]).toString() + " ")
// }
resultInfo.iterations = settings.iteration
resultInfo.func_calls = settings.func_calls
resultInfo.result_chi_sq = chi_sq
resultInfo.result_lambda = lambda
resultInfo.result_parameters = p
}
// update convergence history ... save _reduced_ Chi-square
// cvg_hst(iteration,:) = [ func_calls p' X2/DoF lambda ];
if (abs(JtWdy).max()!! < epsilon_1 && settings.iteration > 2) {
// println(" **** Convergence in r.h.s. (\"JtWdy\") ****")
// println(" **** epsilon_1 = $epsilon_1")
resultInfo.typeOfConvergence = LinearOpsTensorAlgebra.TypeOfConvergence.inRHS_JtWdy
resultInfo.epsilon = epsilon_1
stop = true
}
if ((abs(h.as2D()).div(abs(p) + 1e-12)).max() < epsilon_2 && settings.iteration > 2) {
// println(" **** Convergence in Parameters ****")
// println(" **** epsilon_2 = $epsilon_2")
resultInfo.typeOfConvergence = LinearOpsTensorAlgebra.TypeOfConvergence.inParameters
resultInfo.epsilon = epsilon_2
stop = true
}
if (X2 / DoF < epsilon_3 && settings.iteration > 2) {
// println(" **** Convergence in reduced Chi-square **** ")
// println(" **** epsilon_3 = $epsilon_3")
resultInfo.typeOfConvergence = LinearOpsTensorAlgebra.TypeOfConvergence.inReducedChi_square
resultInfo.epsilon = epsilon_3
stop = true
}
if (settings.iteration == MaxIter) {
// println(" !! Maximum Number of Iterations Reached Without Convergence !!")
resultInfo.typeOfConvergence = LinearOpsTensorAlgebra.TypeOfConvergence.noConvergence
resultInfo.epsilon = 0.0
print("noConvergence, MaxIter = ")
println(MaxIter)
stop = true
}
} // --- End of Main Loop
// --- convergence achieved, find covariance and confidence intervals
// ---- Error Analysis ----
// if (weight.shape.component1() == 1 || weight.variance() == 0.0) {
// weight = DoF / (delta_y.transpose().dot(delta_y)) * ones(intArrayOf(Npt, 1))
// }
// if (nargout > 1) {
// val redX2 = X2 / DoF
// }
//
// lm_matx_ans = lm_matx(func, t, p_old, y_old, -1, J, p, y_dat, weight, dp)
// JtWJ = lm_matx_ans[0]
// JtWdy = lm_matx_ans[1]
// X2 = lm_matx_ans[2][0, 0]
// y_hat = lm_matx_ans[3]
// J = lm_matx_ans[4]
//
// if (nargout > 2) { // standard error of parameters
// covar_p = inv(JtWJ);
// siif nagma_p = sqrt(diag(covar_p));
// }
//
// if (nargout > 3) { // standard error of the fit
// /// sigma_y = sqrt(diag(J * covar_p * J')); // slower version of below
// sigma_y = zeros(Npnt,1);
// for i=1:Npnt
// sigma_y(i) = J(i,:) * covar_p * J(i,:)';
// end
// sigma_y = sqrt(sigma_y);
// }
//
// if (nargout > 4) { // parameter correlation matrix
// corr_p = covar_p ./ [sigma_p*sigma_p'];
// }
//
// if (nargout > 5) { // coefficient of multiple determination
// R_sq = corr([y_dat y_hat]);
// R_sq = R_sq(1,2).^2;
// }
//
// if (nargout > 6) { // convergence history
// cvg_hst = cvg_hst(1:iteration,:);
// }
return resultInfo
}
}
public val Double.Companion.tensorAlgebra: DoubleTensorAlgebra get() = DoubleTensorAlgebra

553
kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/LevenbergMarquardtAlgorithm.kt Normal file
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@ -0,0 +1,553 @@
/*
* Copyright 2018-2023 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.tensors.core
import space.kscience.kmath.linear.transpose
import space.kscience.kmath.nd.*
import space.kscience.kmath.tensors.api.LinearOpsTensorAlgebra
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.max
import kotlin.math.min
import kotlin.math.pow
import kotlin.reflect.KFunction3
public fun DoubleTensorAlgebra.lm(
func: KFunction3<MutableStructure2D<Double>, MutableStructure2D<Double>, LMSettings, 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>,
c_input: MutableStructure2D<Double>, opts_input: DoubleArray, nargin: Int, example_number: Int): LinearOpsTensorAlgebra.LMResultInfo {
val resultInfo = LinearOpsTensorAlgebra.LMResultInfo(0, 0, example_number, 0.0,
0.0, p_input, LinearOpsTensorAlgebra.TypeOfConvergence.noConvergence, 0.0)
val eps:Double = 2.2204e-16
val settings = LMSettings(0, 0, example_number)
settings.func_calls = 0 // running count of function evaluations
var p = p_input
val y_dat = y_dat_input
val t = t_input
val Npar = length(p) // number of parameters
val Npnt = length(y_dat) // number of data points
var p_old = zeros(ShapeND(intArrayOf(Npar, 1))).as2D() // previous set of parameters
var y_old = 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 X2_old = 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
var corr_p = 0
var sigma_p = 0
var sigma_y = 0
var R_sq = 0
var cvg_hist = 0
if (length(t) != length(y_dat)) {
// println("lm.m error: the length of t must equal the length of y_dat")
val length_t = length(t)
val length_y_dat = length(y_dat)
X2 = 0.0
corr_p = 0
sigma_p = 0
sigma_y = 0
R_sq = 0
cvg_hist = 0
}
var weight = weight_input
if (nargin < 5) {
weight = fromArray(ShapeND(intArrayOf(1, 1)), doubleArrayOf((y_dat.transpose().dot(y_dat)).as1D()[0])).as2D()
}
var dp = dp_input
if (nargin < 6) {
dp = fromArray(ShapeND(intArrayOf(1, 1)), doubleArrayOf(0.001)).as2D()
}
var p_min = p_min_input
if (nargin < 7) {
p_min = p
p_min.abs()
p_min = p_min.div(-100.0).as2D()
}
var p_max = p_max_input
if (nargin < 8) {
p_max = p
p_max.abs()
p_max = p_max.div(100.0).as2D()
}
var c = c_input
if (nargin < 9) {
c = fromArray(ShapeND(intArrayOf(1, 1)), doubleArrayOf(1.0)).as2D()
}
var opts = opts_input
if (nargin < 10) {
opts = doubleArrayOf(3.0, 10.0 * Npar, 1e-3, 1e-3, 1e-1, 1e-1, 1e-2, 11.0, 9.0, 1.0)
}
val prnt = opts[0] // >1 intermediate results; >2 plots
val MaxIter = opts[1].toInt() // maximum number of iterations
val epsilon_1 = opts[2] // convergence tolerance for gradient
val epsilon_2 = opts[3] // convergence tolerance for parameters
val epsilon_3 = opts[4] // convergence tolerance for Chi-square
val epsilon_4 = opts[5] // determines acceptance of a L-M step
val lambda_0 = opts[6] // initial value of damping paramter, lambda
val lambda_UP_fac = opts[7] // factor for increasing lambda
val lambda_DN_fac = opts[8] // factor for decreasing lambda
val Update_Type = opts[9].toInt() // 1: Levenberg-Marquardt lambda update
// 2: Quadratic update
// 3: Nielsen's lambda update equations
p_min = make_column(p_min)
p_max = make_column(p_max)
if (length(make_column(dp)) == 1) {
dp = ones(ShapeND(intArrayOf(Npar, 1))).div(1 / dp[0, 0]).as2D()
}
val idx = get_zero_indices(dp) // indices of the parameters to be fit
val Nfit = idx?.shape?.component1() // number of parameters to fit
var stop = false // termination flag
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
weight = ones(ShapeND(intArrayOf(Npnt, 1))).div(1 / kotlin.math.abs(weight[0, 0])).as2D()
// println("using uniform weights for error analysis")
}
else {
weight = make_column(weight)
weight.abs()
}
// initialize Jacobian with finite difference calculation
var lm_matx_ans = lm_matx(func, t, p_old, y_old,1, J, p, y_dat, weight, dp, settings)
var JtWJ = lm_matx_ans[0]
var JtWdy = lm_matx_ans[1]
X2 = lm_matx_ans[2][0, 0]
var y_hat = lm_matx_ans[3]
J = lm_matx_ans[4]
if ( abs(JtWdy).max()!! < epsilon_1 ) {
// println(" *** Your Initial Guess is Extremely Close to Optimal ***\n")
// println(" *** epsilon_1 = %e\n$epsilon_1")
stop = true
}
var lambda = 1.0
var nu = 1
when (Update_Type) {
1 -> lambda = lambda_0 // Marquardt: init'l lambda
else -> { // Quadratic and Nielsen
lambda = lambda_0 * (diag(JtWJ)).max()!!
nu = 2
}
}
X2_old = X2 // previous value of X2
var cvg_hst = ones(ShapeND(intArrayOf(MaxIter, Npar + 3))) // initialize convergence history
var h: DoubleTensor
var dX2 = X2
while (!stop && settings.iteration <= MaxIter) { //--- Start Main Loop
settings.iteration += 1
// incremental change in parameters
h = when (Update_Type) {
1 -> { // Marquardt
val solve = solve(JtWJ.plus(make_matrx_with_diagonal(diag(JtWJ)).div(1 / lambda)).as2D(), JtWdy)
solve.asDoubleTensor()
}
else -> { // Quadratic and Nielsen
val solve = solve(JtWJ.plus(lm_eye(Npar).div(1 / lambda)).as2D(), JtWdy)
solve.asDoubleTensor()
}
}
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
var delta_y = y_dat.minus(feval(func, t, p_try, settings)) // residual error using p_try
for (i in 0 until delta_y.shape.component1()) { // floating point error; break
for (j in 0 until delta_y.shape.component2()) {
if (delta_y[i, j] == Double.POSITIVE_INFINITY || delta_y[i, j] == Double.NEGATIVE_INFINITY) {
stop = true
break
}
}
}
settings.func_calls += 1
val tmp = delta_y.times(weight)
var X2_try = delta_y.as2D().transpose().dot(tmp) // Chi-squared error criteria
val alpha = 1.0
if (Update_Type == 2) { // Quadratic
// One step of quadratic line update in the h direction for minimum X2
val alpha = JtWdy.transpose().dot(h) / ( (X2_try.minus(X2)).div(2.0).plus(2 * JtWdy.transpose().dot(h)) )
h = h.dot(alpha)
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
var delta_y = y_dat.minus(feval(func, t, p_try, settings)) // residual error using p_try
settings.func_calls += 1
val tmp = delta_y.times(weight)
X2_try = delta_y.as2D().transpose().dot(tmp) // Chi-squared error criteria
}
val rho = when (Update_Type) { // Nielsen
1 -> {
val tmp = h.transposed().dot(make_matrx_with_diagonal(diag(JtWJ)).div(1 / lambda).dot(h).plus(JtWdy))
X2.minus(X2_try).as2D()[0, 0] / abs(tmp.as2D()).as2D()[0, 0]
}
else -> {
val tmp = h.transposed().dot(h.div(1 / lambda).plus(JtWdy))
X2.minus(X2_try).as2D()[0, 0] / abs(tmp.as2D()).as2D()[0, 0]
}
}
if (rho > epsilon_4) { // it IS significantly better
val dX2 = X2.minus(X2_old)
X2_old = X2
p_old = p.copyToTensor().as2D()
y_old = y_hat.copyToTensor().as2D()
p = make_column(p_try) // accept p_try
lm_matx_ans = lm_matx(func, t, p_old, y_old, dX2.toInt(), J, p, y_dat, weight, dp, settings)
// decrease lambda ==> Gauss-Newton method
JtWJ = lm_matx_ans[0]
JtWdy = lm_matx_ans[1]
X2 = lm_matx_ans[2][0, 0]
y_hat = lm_matx_ans[3]
J = lm_matx_ans[4]
lambda = when (Update_Type) {
1 -> { // Levenberg
max(lambda / lambda_DN_fac, 1e-7);
}
2 -> { // Quadratic
max( lambda / (1 + alpha) , 1e-7 );
}
else -> { // Nielsen
nu = 2
lambda * max( 1.0 / 3, 1 - (2 * rho - 1).pow(3) )
}
}
}
else { // it IS NOT better
X2 = X2_old // do not accept p_try
if (settings.iteration % (2 * Npar) == 0 ) { // rank-1 update of Jacobian
lm_matx_ans = lm_matx(func, t, p_old, y_old,-1, J, p, y_dat, weight, dp, settings)
JtWJ = lm_matx_ans[0]
JtWdy = lm_matx_ans[1]
dX2 = lm_matx_ans[2][0, 0]
y_hat = lm_matx_ans[3]
J = lm_matx_ans[4]
}
// increase lambda ==> gradient descent method
lambda = when (Update_Type) {
1 -> { // Levenberg
min(lambda * lambda_UP_fac, 1e7)
}
2 -> { // Quadratic
lambda + kotlin.math.abs(((X2_try.as2D()[0, 0] - X2) / 2) / alpha)
}
else -> { // Nielsen
nu *= 2
lambda * (nu / 2)
}
}
}
if (prnt > 1) {
val chi_sq = X2 / DoF
// println("Iteration $settings | chi_sq=$chi_sq | lambda=$lambda")
// print("param: ")
// for (pn in 0 until Npar) {
// print(p[pn, 0].toString() + " ")
// }
// print("\ndp/p: ")
// for (pn in 0 until Npar) {
// print((h.as2D()[pn, 0] / p[pn, 0]).toString() + " ")
// }
resultInfo.iterations = settings.iteration
resultInfo.func_calls = settings.func_calls
resultInfo.result_chi_sq = chi_sq
resultInfo.result_lambda = lambda
resultInfo.result_parameters = p
}
// update convergence history ... save _reduced_ Chi-square
// cvg_hst(iteration,:) = [ func_calls p' X2/DoF lambda ];
if (abs(JtWdy).max()!! < epsilon_1 && settings.iteration > 2) {
// println(" **** Convergence in r.h.s. (\"JtWdy\") ****")
// println(" **** epsilon_1 = $epsilon_1")
resultInfo.typeOfConvergence = LinearOpsTensorAlgebra.TypeOfConvergence.inRHS_JtWdy
resultInfo.epsilon = epsilon_1
stop = true
}
if ((abs(h.as2D()).div(abs(p) + 1e-12)).max() < epsilon_2 && settings.iteration > 2) {
// println(" **** Convergence in Parameters ****")
// println(" **** epsilon_2 = $epsilon_2")
resultInfo.typeOfConvergence = LinearOpsTensorAlgebra.TypeOfConvergence.inParameters
resultInfo.epsilon = epsilon_2
stop = true
}
if (X2 / DoF < epsilon_3 && settings.iteration > 2) {
// println(" **** Convergence in reduced Chi-square **** ")
// println(" **** epsilon_3 = $epsilon_3")
resultInfo.typeOfConvergence = LinearOpsTensorAlgebra.TypeOfConvergence.inReducedChi_square
resultInfo.epsilon = epsilon_3
stop = true
}
if (settings.iteration == MaxIter) {
// println(" !! Maximum Number of Iterations Reached Without Convergence !!")
resultInfo.typeOfConvergence = LinearOpsTensorAlgebra.TypeOfConvergence.noConvergence
resultInfo.epsilon = 0.0
stop = true
}
} // --- End of Main Loop
return resultInfo
}
public data class LMSettings (
var iteration:Int,
var func_calls: Int,
var example_number:Int
)
/* matrix -> column of all elemnets */
public fun make_column(tensor: MutableStructure2D<Double>) : MutableStructure2D<Double> {
val shape = intArrayOf(tensor.shape.component1() * tensor.shape.component2(), 1)
val buffer = DoubleArray(tensor.shape.component1() * tensor.shape.component2())
for (i in 0 until tensor.shape.component1()) {
for (j in 0 until tensor.shape.component2()) {
buffer[i * tensor.shape.component2() + j] = tensor[i, j]
}
}
val column = BroadcastDoubleTensorAlgebra.fromArray(ShapeND(shape), buffer).as2D()
return column
}
/* column length */
public fun length(column: MutableStructure2D<Double>) : Int {
return column.shape.component1()
}
public 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])
}
}
}
public fun abs(input: MutableStructure2D<Double>): MutableStructure2D<Double> {
val tensor = BroadcastDoubleTensorAlgebra.ones(
ShapeND(
intArrayOf(
input.shape.component1(),
input.shape.component2()
)
)
).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])
}
}
return tensor
}
public fun diag(input: MutableStructure2D<Double>): MutableStructure2D<Double> {
val tensor = BroadcastDoubleTensorAlgebra.ones(ShapeND(intArrayOf(input.shape.component1(), 1))).as2D()
for (i in 0 until tensor.shape.component1()) {
tensor[i, 0] = input[i, i]
}
return tensor
}
public fun make_matrx_with_diagonal(column: MutableStructure2D<Double>): MutableStructure2D<Double> {
val size = column.shape.component1()
val tensor = BroadcastDoubleTensorAlgebra.zeros(ShapeND(intArrayOf(size, size))).as2D()
for (i in 0 until size) {
tensor[i, i] = column[i, 0]
}
return tensor
}
public fun lm_eye(size: Int): MutableStructure2D<Double> {
val column = BroadcastDoubleTensorAlgebra.ones(ShapeND(intArrayOf(size, 1))).as2D()
return make_matrx_with_diagonal(column)
}
public fun largest_element_comparison(a: MutableStructure2D<Double>, b: MutableStructure2D<Double>): MutableStructure2D<Double> {
val a_sizeX = a.shape.component1()
val a_sizeY = a.shape.component2()
val b_sizeX = b.shape.component1()
val b_sizeY = b.shape.component2()
val tensor = BroadcastDoubleTensorAlgebra.zeros(ShapeND(intArrayOf(max(a_sizeX, b_sizeX), max(a_sizeY, b_sizeY)))).as2D()
for (i in 0 until tensor.shape.component1()) {
for (j in 0 until tensor.shape.component2()) {
if (i < a_sizeX && i < b_sizeX && j < a_sizeY && j < b_sizeY) {
tensor[i, j] = max(a[i, j], b[i, j])
}
else if (i < a_sizeX && j < a_sizeY) {
tensor[i, j] = a[i, j]
}
else {
tensor[i, j] = b[i, j]
}
}
}
return tensor
}
public fun smallest_element_comparison(a: MutableStructure2D<Double>, b: MutableStructure2D<Double>): MutableStructure2D<Double> {
val a_sizeX = a.shape.component1()
val a_sizeY = a.shape.component2()
val b_sizeX = b.shape.component1()
val b_sizeY = b.shape.component2()
val tensor = BroadcastDoubleTensorAlgebra.zeros(ShapeND(intArrayOf(max(a_sizeX, b_sizeX), max(a_sizeY, b_sizeY)))).as2D()
for (i in 0 until tensor.shape.component1()) {
for (j in 0 until tensor.shape.component2()) {
if (i < a_sizeX && i < b_sizeX && j < a_sizeY && j < b_sizeY) {
tensor[i, j] = min(a[i, j], b[i, j])
}
else if (i < a_sizeX && j < a_sizeY) {
tensor[i, j] = a[i, j]
}
else {
tensor[i, j] = b[i, j]
}
}
}
return tensor
}
public fun get_zero_indices(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) {
idx += (i + 1.0)
}
}
if (idx.size > 0) {
return BroadcastDoubleTensorAlgebra.fromArray(ShapeND(intArrayOf(idx.size, 1)), idx.toDoubleArray()).as2D()
}
return null
}
public fun feval(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, LMSettings) -> MutableStructure2D<Double>,
t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, settings: LMSettings)
: MutableStructure2D<Double>
{
return func(t, p, settings)
}
public fun lm_matx(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, LMSettings) -> MutableStructure2D<Double>,
t: MutableStructure2D<Double>, p_old: MutableStructure2D<Double>, y_old: 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>>
{
// default: dp = 0.001
val Npnt = length(y_dat) // number of data points
val Npar = length(p) // number of parameters
val y_hat = feval(func, t, p, settings) // evaluate model using parameters 'p'
settings.func_calls += 1
var J = J_input
if (settings.iteration % (2 * Npar) == 0 || dX2 > 0) {
J = lm_FD_J(func, t, p, y_hat, dp, settings).as2D() // finite difference
}
else {
J = lm_Broyden_J(p_old, y_old, J, p, y_hat).as2D() // rank-1 update
}
val delta_y = y_dat.minus(y_hat)
val Chi_sq = delta_y.transposed().dot( delta_y.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(delta_y) ).as2D()
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>,
p: MutableStructure2D<Double>, y: MutableStructure2D<Double>): MutableStructure2D<Double> {
var J = J_input.copyToTensor()
val h = p.minus(p_old)
val increase = y.minus(y_old).minus( J.dot(h) ).dot(h.transposed()).div( (h.transposed().dot(h)).as2D()[0, 0] )
J = J.plus(increase)
return J.as2D()
}
public fun lm_FD_J(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, settings: LMSettings) -> MutableStructure2D<Double>,
t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, y: MutableStructure2D<Double>,
dp: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> {
// 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()
for (j in 0 until n) {
del[j, 0] = dp[j, 0] * (1 + kotlin.math.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) {
val y1 = feval(func, t, p, settings)
settings.func_calls += 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]
}
}
else {
// Do tests for it
println("Potential mistake")
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(feval(func, t, p, settings)).as2D())[i, 0] / (2 * del[j, 0])
}
settings.func_calls += 1
}
}
p[j, 0] = ps[j, 0] // restore p(j)
}
return J.as2D()
}

229
kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/linUtils.kt
View File

@ -9,12 +9,6 @@ import space.kscience.kmath.nd.*
import space.kscience.kmath.operations.invoke
import space.kscience.kmath.structures.*
import space.kscience.kmath.tensors.core.*
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
@ -607,225 +601,4 @@ internal fun MutableStructure2D<Double>.svdGolubKahanHelper(u: MutableStructure2
u[j, i] = this[j, i]
}
}
}
data class LMSettings (
var iteration:Int,
var func_calls: Int,
var example_number:Int
)
/* matrix -> column of all elemnets */
fun make_column(tensor: MutableStructure2D<Double>) : MutableStructure2D<Double> {
val shape = intArrayOf(tensor.shape.component1() * tensor.shape.component2(), 1)
var buffer = DoubleArray(tensor.shape.component1() * tensor.shape.component2())
for (i in 0 until tensor.shape.component1()) {
for (j in 0 until tensor.shape.component2()) {
buffer[i * tensor.shape.component2() + j] = tensor[i, j]
}
}
var column = BroadcastDoubleTensorAlgebra.fromArray(ShapeND(shape), buffer).as2D()
return column
}
/* column length */
fun length(column: MutableStructure2D<Double>) : Int {
return column.shape.component1()
}
fun MutableStructure2D<Double>.abs() {
for (i in 0 until this.shape.component1()) {
for (j in 0 until this.shape.component2()) {
this[i, j] = abs(this[i, j])
}
}
}
fun abs(input: MutableStructure2D<Double>): MutableStructure2D<Double> {
val tensor = BroadcastDoubleTensorAlgebra.ones(
ShapeND(
intArrayOf(
input.shape.component1(),
input.shape.component2()
)
)
).as2D()
for (i in 0 until tensor.shape.component1()) {
for (j in 0 until tensor.shape.component2()) {
tensor[i, j] = abs(input[i, j])
}
}
return tensor
}
fun diag(input: MutableStructure2D<Double>): MutableStructure2D<Double> {
val tensor = BroadcastDoubleTensorAlgebra.ones(ShapeND(intArrayOf(input.shape.component1(), 1))).as2D()
for (i in 0 until tensor.shape.component1()) {
tensor[i, 0] = input[i, i]
}
return tensor
}
fun make_matrx_with_diagonal(column: MutableStructure2D<Double>): MutableStructure2D<Double> {
val size = column.shape.component1()
val tensor = BroadcastDoubleTensorAlgebra.zeros(ShapeND(intArrayOf(size, size))).as2D()
for (i in 0 until size) {
tensor[i, i] = column[i, 0]
}
return tensor
}
fun lm_eye(size: Int): MutableStructure2D<Double> {
val column = BroadcastDoubleTensorAlgebra.ones(ShapeND(intArrayOf(size, 1))).as2D()
return make_matrx_with_diagonal(column)
}
fun largest_element_comparison(a: MutableStructure2D<Double>, b: MutableStructure2D<Double>): MutableStructure2D<Double> {
val a_sizeX = a.shape.component1()
val a_sizeY = a.shape.component2()
val b_sizeX = b.shape.component1()
val b_sizeY = b.shape.component2()
val tensor = BroadcastDoubleTensorAlgebra.zeros(ShapeND(intArrayOf(max(a_sizeX, b_sizeX), max(a_sizeY, b_sizeY)))).as2D()
for (i in 0 until tensor.shape.component1()) {
for (j in 0 until tensor.shape.component2()) {
if (i < a_sizeX && i < b_sizeX && j < a_sizeY && j < b_sizeY) {
tensor[i, j] = max(a[i, j], b[i, j])
}
else if (i < a_sizeX && j < a_sizeY) {
tensor[i, j] = a[i, j]
}
else {
tensor[i, j] = b[i, j]
}
}
}
return tensor
}
fun smallest_element_comparison(a: MutableStructure2D<Double>, b: MutableStructure2D<Double>): MutableStructure2D<Double> {
val a_sizeX = a.shape.component1()
val a_sizeY = a.shape.component2()
val b_sizeX = b.shape.component1()
val b_sizeY = b.shape.component2()
val tensor = BroadcastDoubleTensorAlgebra.zeros(ShapeND(intArrayOf(max(a_sizeX, b_sizeX), max(a_sizeY, b_sizeY)))).as2D()
for (i in 0 until tensor.shape.component1()) {
for (j in 0 until tensor.shape.component2()) {
if (i < a_sizeX && i < b_sizeX && j < a_sizeY && j < b_sizeY) {
tensor[i, j] = min(a[i, j], b[i, j])
}
else if (i < a_sizeX && j < a_sizeY) {
tensor[i, j] = a[i, j]
}
else {
tensor[i, j] = b[i, j]
}
}
}
return tensor
}
fun get_zero_indices(column: MutableStructure2D<Double>, epsilon: Double = 0.000001): MutableStructure2D<Double>? {
var idx = emptyArray<Double>()
for (i in 0 until column.shape.component1()) {
if (abs(column[i, 0]) > epsilon) {
idx += (i + 1.0)
}
}
if (idx.size > 0) {
return BroadcastDoubleTensorAlgebra.fromArray(ShapeND(intArrayOf(idx.size, 1)), idx.toDoubleArray()).as2D()
}
return null
}
fun feval(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, LMSettings) -> MutableStructure2D<Double>,
t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, settings: LMSettings)
: MutableStructure2D<Double>
{
return func(t, p, settings)
}
fun lm_matx(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, LMSettings) -> MutableStructure2D<Double>,
t: MutableStructure2D<Double>, p_old: MutableStructure2D<Double>, y_old: 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>>
{
// default: dp = 0.001
val Npnt = length(y_dat) // number of data points
val Npar = length(p) // number of parameters
val y_hat = feval(func, t, p, settings) // evaluate model using parameters 'p'
settings.func_calls += 1
var J = J_input
if (settings.iteration % (2 * Npar) == 0 || dX2 > 0) {
J = lm_FD_J(func, t, p, y_hat, dp, settings).as2D() // finite difference
}
else {
J = lm_Broyden_J(p_old, y_old, J, p, y_hat).as2D() // rank-1 update
}
val delta_y = y_dat.minus(y_hat)
val Chi_sq = delta_y.transposed().dot( delta_y.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(delta_y) ).as2D()
return arrayOf(JtWJ,JtWdy,Chi_sq,y_hat,J)
}
fun lm_Broyden_J(p_old: MutableStructure2D<Double>, y_old: MutableStructure2D<Double>, J_input: MutableStructure2D<Double>,
p: MutableStructure2D<Double>, y: MutableStructure2D<Double>): MutableStructure2D<Double> {
var J = J_input.copyToTensor()
val h = p.minus(p_old)
val increase = y.minus(y_old).minus( J.dot(h) ).dot(h.transposed()).div( (h.transposed().dot(h)).as2D()[0, 0] )
J = J.plus(increase)
return J.as2D()
}
fun lm_FD_J(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, settings: LMSettings) -> MutableStructure2D<Double>,
t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, y: MutableStructure2D<Double>,
dp: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> {
// 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()
for (j in 0 until n) {
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) {
val y1 = feval(func, t, p, settings)
settings.func_calls += 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]
}
}
else {
// Do tests for it
println("Potential mistake")
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(feval(func, t, p, settings)).as2D())[i, 0] / (2 * del[j, 0])
}
settings.func_calls += 1
}
}
p[j, 0] = ps[j, 0] // restore p(j)
}
return J.as2D()
}
}

100
kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleTensorAlgebra.kt
View File

@ -8,11 +8,7 @@ package space.kscience.kmath.tensors.core
import space.kscience.kmath.nd.*
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.testutils.assertBufferEquals
import kotlin.math.roundToInt
import kotlin.math.roundToLong
import kotlin.test.Test
import kotlin.test.assertEquals
import kotlin.test.assertFalse
@ -209,100 +205,4 @@ internal class TestDoubleTensorAlgebra {
assertTrue { ShapeND(5, 5) contentEquals res.shape }
assertEquals(2.0, res[4, 4])
}
@Test
fun testLM() = DoubleTensorAlgebra {
fun lm_func(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> {
val m = t.shape.component1()
var y_hat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(m, 1)))
if (settings.example_number == 1) {
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])))
)
}
else if (settings.example_number == 2) {
val mt = t.max()
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 (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()
}
val lm_matx_y_dat = doubleArrayOf(
19.6594, 18.6096, 17.6792, 17.2747, 16.3065, 17.1458, 16.0467, 16.7023, 15.7809, 15.9807,
14.7620, 15.1128, 16.0973, 15.1934, 15.8636, 15.4763, 15.6860, 15.1895, 15.3495, 16.6054,
16.2247, 15.9854, 16.1421, 17.0960, 16.7769, 17.1997, 17.2767, 17.5882, 17.5378, 16.7894,
17.7648, 18.2512, 18.1581, 16.7037, 17.8475, 17.9081, 18.3067, 17.9632, 18.2817, 19.1427,
18.8130, 18.5658, 18.0056, 18.4607, 18.5918, 18.2544, 18.3731, 18.7511, 19.3181, 17.3066,
17.9632, 19.0513, 18.7528, 18.2928, 18.5967, 17.8567, 17.7859, 18.4016, 18.9423, 18.4959,
17.8000, 18.4251, 17.7829, 17.4645, 17.5221, 17.3517, 17.4637, 17.7563, 16.8471, 17.4558,
17.7447, 17.1487, 17.3183, 16.8312, 17.7551, 17.0942, 15.6093, 16.4163, 15.3755, 16.6725,
16.2332, 16.2316, 16.2236, 16.5361, 15.3721, 15.3347, 15.5815, 15.6319, 14.4538, 14.6044,
14.7665, 13.3718, 15.0587, 13.8320, 14.7873, 13.6824, 14.2579, 14.2154, 13.5818, 13.8157
)
var example_number = 1
val p_init = BroadcastDoubleTensorAlgebra.fromArray(
ShapeND(intArrayOf(4, 1)), doubleArrayOf(5.0, 2.0, 0.2, 10.0)
).as2D()
var t = ones(ShapeND(intArrayOf(100, 1))).as2D()
for (i in 0 until 100) {
t[i, 0] = t[i, 0] * (i + 1)
}
val y_dat = BroadcastDoubleTensorAlgebra.fromArray(
ShapeND(intArrayOf(100, 1)), lm_matx_y_dat
).as2D()
val weight = BroadcastDoubleTensorAlgebra.fromArray(
ShapeND(intArrayOf(1, 1)), DoubleArray(1) { 4.0 }
).as2D()
val dp = BroadcastDoubleTensorAlgebra.fromArray(
ShapeND(intArrayOf(1, 1)), DoubleArray(1) { -0.01 }
).as2D()
val p_min = BroadcastDoubleTensorAlgebra.fromArray(
ShapeND(intArrayOf(4, 1)), doubleArrayOf(-50.0, -20.0, -2.0, -100.0)
).as2D()
val p_max = BroadcastDoubleTensorAlgebra.fromArray(
ShapeND(intArrayOf(4, 1)), doubleArrayOf(50.0, 20.0, 2.0, 100.0)
).as2D()
val consts = BroadcastDoubleTensorAlgebra.fromArray(
ShapeND(intArrayOf(1, 1)), doubleArrayOf(0.0)
).as2D()
val opts = doubleArrayOf(3.0, 100.0, 1e-3, 1e-3, 1e-1, 1e-1, 1e-2, 11.0, 9.0, 1.0)
val result = lm(::lm_func, p_init, t, y_dat, weight, dp, p_min, p_max, consts, opts, 10, example_number)
assertEquals(13, result.iterations)
assertEquals(31, result.func_calls)
assertEquals(1, result.example_number)
assertEquals(0.9131368192633, (result.result_chi_sq * 1e13).roundToLong() / 1e13)
assertEquals(3.7790980 * 1e-7, (result.result_lambda * 1e13).roundToLong() / 1e13)
assertEquals(result.typeOfConvergence, LinearOpsTensorAlgebra.TypeOfConvergence.inParameters)
val expectedParameters = BroadcastDoubleTensorAlgebra.fromArray(
ShapeND(intArrayOf(4, 1)), doubleArrayOf(20.527230909086, 9.833627103230, 0.997571256572, 50.174445822506)
).as2D()
result.result_parameters = result.result_parameters.map { x -> (x * 1e12).toLong() / 1e12}.as2D()
val receivedParameters = BroadcastDoubleTensorAlgebra.fromArray(
ShapeND(intArrayOf(4, 1)), doubleArrayOf(result.result_parameters[0, 0], result.result_parameters[1, 0],
result.result_parameters[2, 0], result.result_parameters[3, 0])
).as2D()
assertEquals(expectedParameters[0, 0], receivedParameters[0, 0])
assertEquals(expectedParameters[1, 0], receivedParameters[1, 0])
assertEquals(expectedParameters[2, 0], receivedParameters[2, 0])
assertEquals(expectedParameters[3, 0], receivedParameters[3, 0])
}
}

1
kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestLmAlgorithm.kt
View File

@ -15,7 +15,6 @@ 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.pow
import space.kscience.kmath.tensors.core.DoubleTensorAlgebra.Companion.times
import space.kscience.kmath.tensors.core.internal.LMSettings
import kotlin.math.roundToLong
import kotlin.test.Test
import kotlin.test.assertEquals