move lm-algorithm from DoubleTensorAlgebra as extension
This commit is contained in:
Margarita Lashina
parent
2ead722620
commit
8d81d2d8d5
@ -7,15 +7,7 @@ package space.kscience.kmath.tensors.api
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import space.kscience.kmath.nd.MutableStructure2D
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import space.kscience.kmath.nd.StructureND
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import space.kscience.kmath.nd.as2D
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import space.kscience.kmath.operations.Field
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import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra
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import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.dot
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import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.map
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import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.transposed
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import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
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import space.kscience.kmath.tensors.core.internal.LMSettings
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import kotlin.reflect.KFunction3
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/**
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* Common linear algebra operations. Operates on [Tensor].
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@ -137,10 +129,4 @@ public interface LinearOpsTensorAlgebra<T, A : Field<T>> : TensorPartialDivision
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var typeOfConvergence: TypeOfConvergence,
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var epsilon: Double
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)
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public fun lm(
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func: KFunction3<MutableStructure2D<Double>, MutableStructure2D<Double>, LMSettings, MutableStructure2D<Double>>,
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p_input: MutableStructure2D<Double>, t_input: MutableStructure2D<Double>, y_dat_input: MutableStructure2D<Double>,
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weight_input: MutableStructure2D<Double>, dp_input: MutableStructure2D<Double>, p_min_input: MutableStructure2D<Double>, p_max_input: MutableStructure2D<Double>,
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c_input: MutableStructure2D<Double>, opts_input: DoubleArray, nargin: Int, example_number: Int): LMResultInfo
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}
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@ -9,7 +9,6 @@
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package space.kscience.kmath.tensors.core
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import space.kscience.kmath.PerformancePitfall
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import space.kscience.kmath.linear.transpose
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import space.kscience.kmath.nd.*
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import space.kscience.kmath.operations.DoubleBufferOps
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import space.kscience.kmath.operations.DoubleField
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@ -19,7 +18,6 @@ import space.kscience.kmath.tensors.api.LinearOpsTensorAlgebra
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import space.kscience.kmath.tensors.api.Tensor
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import space.kscience.kmath.tensors.core.internal.*
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import kotlin.math.*
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import kotlin.reflect.KFunction3
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/**
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* Implementation of basic operations over double tensors and basic algebra operations on them.
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@ -716,367 +714,6 @@ public open class DoubleTensorAlgebra :
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val aInverse = aSvd.third.dot(s).dot(aSvd.first.transposed())
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return aInverse.dot(b).as2D()
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}
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override fun lm(
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func: KFunction3<MutableStructure2D<Double>, MutableStructure2D<Double>, LMSettings, MutableStructure2D<Double>>,
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p_input: MutableStructure2D<Double>, t_input: MutableStructure2D<Double>, y_dat_input: MutableStructure2D<Double>,
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weight_input: MutableStructure2D<Double>, dp_input: MutableStructure2D<Double>, p_min_input: MutableStructure2D<Double>, p_max_input: MutableStructure2D<Double>,
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c_input: MutableStructure2D<Double>, opts_input: DoubleArray, nargin: Int, example_number: Int): LinearOpsTensorAlgebra.LMResultInfo {
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var resultInfo = LinearOpsTensorAlgebra.LMResultInfo(0, 0, example_number, 0.0,
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0.0, p_input, LinearOpsTensorAlgebra.TypeOfConvergence.noConvergence, 0.0)
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val eps:Double = 2.2204e-16
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var settings = LMSettings(0, 0, example_number)
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settings.func_calls = 0 // running count of function evaluations
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var p = p_input
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val y_dat = y_dat_input
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val t = t_input
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val Npar = length(p) // number of parameters
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val Npnt = length(y_dat) // number of data points
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var p_old = zeros(ShapeND(intArrayOf(Npar, 1))).as2D() // previous set of parameters
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var y_old = zeros(ShapeND(intArrayOf(Npnt, 1))).as2D() // previous model, y_old = y_hat(t;p_old)
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var X2 = 1e-3 / eps // a really big initial Chi-sq value
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var X2_old = 1e-3 / eps // a really big initial Chi-sq value
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var J = zeros(ShapeND(intArrayOf(Npnt, Npar))).as2D() // Jacobian matrix
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val DoF = Npnt - Npar // statistical degrees of freedom
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var corr_p = 0
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var sigma_p = 0
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var sigma_y = 0
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var R_sq = 0
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var cvg_hist = 0
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if (length(t) != length(y_dat)) {
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// println("lm.m error: the length of t must equal the length of y_dat")
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val length_t = length(t)
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val length_y_dat = length(y_dat)
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X2 = 0.0
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corr_p = 0
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sigma_p = 0
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sigma_y = 0
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R_sq = 0
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cvg_hist = 0
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}
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var weight = weight_input
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if (nargin < 5) {
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fromArray(ShapeND(intArrayOf(1, 1)), doubleArrayOf(1.0)).as2D()
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}
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var dp = dp_input
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if (nargin < 6) {
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dp = fromArray(ShapeND(intArrayOf(1, 1)), doubleArrayOf(-0.001)).as2D()
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}
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var p_min = p_min_input
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if (nargin < 7) {
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p_min = p
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p_min.abs()
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p_min = p_min.div(-100.0).as2D()
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}
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var p_max = p_max_input
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if (nargin < 8) {
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p_max = p
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p_max.abs()
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p_max = p_max.div(100.0).as2D()
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}
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var c = c_input
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if (nargin < 9) {
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c = fromArray(ShapeND(intArrayOf(1, 1)), doubleArrayOf(1.0)).as2D()
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}
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var opts = opts_input
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if (nargin < 10) {
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opts = doubleArrayOf(3.0, 10.0 * Npar, 1e-3, 1e-3, 1e-1, 1e-1, 1e-2, 11.0, 9.0, 1.0)
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}
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val prnt = opts[0] // >1 intermediate results; >2 plots
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val MaxIter = opts[1].toInt() // maximum number of iterations
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val epsilon_1 = opts[2] // convergence tolerance for gradient
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val epsilon_2 = opts[3] // convergence tolerance for parameters
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val epsilon_3 = opts[4] // convergence tolerance for Chi-square
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val epsilon_4 = opts[5] // determines acceptance of a L-M step
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val lambda_0 = opts[6] // initial value of damping paramter, lambda
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val lambda_UP_fac = opts[7] // factor for increasing lambda
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val lambda_DN_fac = opts[8] // factor for decreasing lambda
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val Update_Type = opts[9].toInt() // 1: Levenberg-Marquardt lambda update
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// 2: Quadratic update
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// 3: Nielsen's lambda update equations
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p_min = make_column(p_min)
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p_max = make_column(p_max)
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if (length(make_column(dp)) == 1) {
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dp = ones(ShapeND(intArrayOf(Npar, 1))).div(1 / dp[0, 0]).as2D()
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}
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val idx = get_zero_indices(dp) // indices of the parameters to be fit
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val Nfit = idx?.shape?.component1() // number of parameters to fit
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var stop = false // termination flag
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val y_init = feval(func, t, p, settings) // residual error using p_try
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if (weight.shape.component1() == 1 || variance(weight) == 0.0) { // identical weights vector
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weight = ones(ShapeND(intArrayOf(Npnt, 1))).div(1 / abs(weight[0, 0])).as2D()
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// println("using uniform weights for error analysis")
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}
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else {
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weight = make_column(weight)
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weight.abs()
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}
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// initialize Jacobian with finite difference calculation
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var lm_matx_ans = lm_matx(func, t, p_old, y_old,1, J, p, y_dat, weight, dp, settings)
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var JtWJ = lm_matx_ans[0]
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var JtWdy = lm_matx_ans[1]
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X2 = lm_matx_ans[2][0, 0]
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var y_hat = lm_matx_ans[3]
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J = lm_matx_ans[4]
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if ( abs(JtWdy).max()!! < epsilon_1 ) {
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// println(" *** Your Initial Guess is Extremely Close to Optimal ***\n")
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// println(" *** epsilon_1 = %e\n$epsilon_1")
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stop = true
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}
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var lambda = 1.0
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var nu = 1
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when (Update_Type) {
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1 -> lambda = lambda_0 // Marquardt: init'l lambda
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else -> { // Quadratic and Nielsen
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lambda = lambda_0 * (diag(JtWJ)).max()!!
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nu = 2
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}
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}
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X2_old = X2 // previous value of X2
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var cvg_hst = ones(ShapeND(intArrayOf(MaxIter, Npar + 3))) // initialize convergence history
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var h: DoubleTensor
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var dX2 = X2
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while (!stop && settings.iteration <= MaxIter) { //--- Start Main Loop
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settings.iteration += 1
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// incremental change in parameters
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h = when (Update_Type) {
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1 -> { // Marquardt
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val solve = solve(JtWJ.plus(make_matrx_with_diagonal(diag(JtWJ)).div(1 / lambda)).as2D(), JtWdy)
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solve.asDoubleTensor()
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}
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else -> { // Quadratic and Nielsen
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val solve = solve(JtWJ.plus(lm_eye(Npar).div(1 / lambda)).as2D(), JtWdy)
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solve.asDoubleTensor()
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}
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}
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var p_try = (p + h).as2D() // update the [idx] elements
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p_try = smallest_element_comparison(largest_element_comparison(p_min, p_try.as2D()), p_max) // apply constraints
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var delta_y = y_dat.minus(feval(func, t, p_try, settings)) // residual error using p_try
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for (i in 0 until delta_y.shape.component1()) { // floating point error; break
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for (j in 0 until delta_y.shape.component2()) {
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if (delta_y[i, j] == Double.POSITIVE_INFINITY || delta_y[i, j] == Double.NEGATIVE_INFINITY) {
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stop = true
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break
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}
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}
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}
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settings.func_calls += 1
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val tmp = delta_y.times(weight)
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var X2_try = delta_y.as2D().transpose().dot(tmp) // Chi-squared error criteria
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val alpha = 1.0
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if (Update_Type == 2) { // Quadratic
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// One step of quadratic line update in the h direction for minimum X2
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val alpha = JtWdy.transpose().dot(h) / ( (X2_try.minus(X2)).div(2.0).plus(2 * JtWdy.transpose().dot(h)) )
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h = h.dot(alpha)
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p_try = p.plus(h).as2D() // update only [idx] elements
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p_try = smallest_element_comparison(largest_element_comparison(p_min, p_try), p_max) // apply constraints
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var delta_y = y_dat.minus(feval(func, t, p_try, settings)) // residual error using p_try
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settings.func_calls += 1
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val tmp = delta_y.times(weight)
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X2_try = delta_y.as2D().transpose().dot(tmp) // Chi-squared error criteria
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}
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val rho = when (Update_Type) { // Nielsen
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1 -> {
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val tmp = h.transposed().dot(make_matrx_with_diagonal(diag(JtWJ)).div(1 / lambda).dot(h).plus(JtWdy))
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X2.minus(X2_try).as2D()[0, 0] / abs(tmp.as2D()).as2D()[0, 0]
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}
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else -> {
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val tmp = h.transposed().dot(h.div(1 / lambda).plus(JtWdy))
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X2.minus(X2_try).as2D()[0, 0] / abs(tmp.as2D()).as2D()[0, 0]
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}
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}
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if (rho > epsilon_4) { // it IS significantly better
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val dX2 = X2.minus(X2_old)
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X2_old = X2
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p_old = p.copyToTensor().as2D()
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y_old = y_hat.copyToTensor().as2D()
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p = make_column(p_try) // accept p_try
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lm_matx_ans = lm_matx(func, t, p_old, y_old, dX2.toInt(), J, p, y_dat, weight, dp, settings)
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// decrease lambda ==> Gauss-Newton method
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JtWJ = lm_matx_ans[0]
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JtWdy = lm_matx_ans[1]
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X2 = lm_matx_ans[2][0, 0]
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y_hat = lm_matx_ans[3]
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J = lm_matx_ans[4]
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lambda = when (Update_Type) {
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1 -> { // Levenberg
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max(lambda / lambda_DN_fac, 1e-7);
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}
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2 -> { // Quadratic
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max( lambda / (1 + alpha) , 1e-7 );
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}
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else -> { // Nielsen
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nu = 2
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lambda * max( 1.0 / 3, 1 - (2 * rho - 1).pow(3) )
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}
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}
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}
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else { // it IS NOT better
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X2 = X2_old // do not accept p_try
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if (settings.iteration % (2 * Npar) == 0 ) { // rank-1 update of Jacobian
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lm_matx_ans = lm_matx(func, t, p_old, y_old,-1, J, p, y_dat, weight, dp, settings)
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JtWJ = lm_matx_ans[0]
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JtWdy = lm_matx_ans[1]
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dX2 = lm_matx_ans[2][0, 0]
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y_hat = lm_matx_ans[3]
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J = lm_matx_ans[4]
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}
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// increase lambda ==> gradient descent method
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lambda = when (Update_Type) {
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1 -> { // Levenberg
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min(lambda * lambda_UP_fac, 1e7)
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}
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2 -> { // Quadratic
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lambda + abs(((X2_try.as2D()[0, 0] - X2) / 2) / alpha)
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}
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else -> { // Nielsen
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nu *= 2
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lambda * (nu / 2)
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}
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}
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}
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if (prnt > 1) {
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val chi_sq = X2 / DoF
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// println("Iteration $settings | chi_sq=$chi_sq | lambda=$lambda")
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// print("param: ")
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// for (pn in 0 until Npar) {
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// print(p[pn, 0].toString() + " ")
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// }
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// print("\ndp/p: ")
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// for (pn in 0 until Npar) {
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// print((h.as2D()[pn, 0] / p[pn, 0]).toString() + " ")
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// }
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resultInfo.iterations = settings.iteration
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resultInfo.func_calls = settings.func_calls
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resultInfo.result_chi_sq = chi_sq
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resultInfo.result_lambda = lambda
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resultInfo.result_parameters = p
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}
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// update convergence history ... save _reduced_ Chi-square
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// cvg_hst(iteration,:) = [ func_calls p' X2/DoF lambda ];
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if (abs(JtWdy).max()!! < epsilon_1 && settings.iteration > 2) {
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// println(" **** Convergence in r.h.s. (\"JtWdy\") ****")
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// println(" **** epsilon_1 = $epsilon_1")
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resultInfo.typeOfConvergence = LinearOpsTensorAlgebra.TypeOfConvergence.inRHS_JtWdy
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resultInfo.epsilon = epsilon_1
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stop = true
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}
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if ((abs(h.as2D()).div(abs(p) + 1e-12)).max() < epsilon_2 && settings.iteration > 2) {
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// println(" **** Convergence in Parameters ****")
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// println(" **** epsilon_2 = $epsilon_2")
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resultInfo.typeOfConvergence = LinearOpsTensorAlgebra.TypeOfConvergence.inParameters
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resultInfo.epsilon = epsilon_2
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stop = true
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}
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if (X2 / DoF < epsilon_3 && settings.iteration > 2) {
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// println(" **** Convergence in reduced Chi-square **** ")
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// println(" **** epsilon_3 = $epsilon_3")
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resultInfo.typeOfConvergence = LinearOpsTensorAlgebra.TypeOfConvergence.inReducedChi_square
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resultInfo.epsilon = epsilon_3
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stop = true
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}
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if (settings.iteration == MaxIter) {
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// println(" !! Maximum Number of Iterations Reached Without Convergence !!")
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resultInfo.typeOfConvergence = LinearOpsTensorAlgebra.TypeOfConvergence.noConvergence
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resultInfo.epsilon = 0.0
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print("noConvergence, MaxIter = ")
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println(MaxIter)
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stop = true
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}
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} // --- End of Main Loop
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// --- convergence achieved, find covariance and confidence intervals
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// ---- Error Analysis ----
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// if (weight.shape.component1() == 1 || weight.variance() == 0.0) {
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// weight = DoF / (delta_y.transpose().dot(delta_y)) * ones(intArrayOf(Npt, 1))
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// }
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// if (nargout > 1) {
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// val redX2 = X2 / DoF
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// }
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//
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// lm_matx_ans = lm_matx(func, t, p_old, y_old, -1, J, p, y_dat, weight, dp)
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// JtWJ = lm_matx_ans[0]
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// JtWdy = lm_matx_ans[1]
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// X2 = lm_matx_ans[2][0, 0]
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// y_hat = lm_matx_ans[3]
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// J = lm_matx_ans[4]
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//
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// if (nargout > 2) { // standard error of parameters
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// covar_p = inv(JtWJ);
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// siif nagma_p = sqrt(diag(covar_p));
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// }
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//
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// if (nargout > 3) { // standard error of the fit
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// /// sigma_y = sqrt(diag(J * covar_p * J')); // slower version of below
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// sigma_y = zeros(Npnt,1);
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// for i=1:Npnt
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// sigma_y(i) = J(i,:) * covar_p * J(i,:)';
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// end
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// sigma_y = sqrt(sigma_y);
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// }
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//
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// if (nargout > 4) { // parameter correlation matrix
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// corr_p = covar_p ./ [sigma_p*sigma_p'];
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// }
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//
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// if (nargout > 5) { // coefficient of multiple determination
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// R_sq = corr([y_dat y_hat]);
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// R_sq = R_sq(1,2).^2;
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// }
|
||||
//
|
||||
// if (nargout > 6) { // convergence history
|
||||
// cvg_hst = cvg_hst(1:iteration,:);
|
||||
// }
|
||||
|
||||
return resultInfo
|
||||
}
|
||||
}
|
||||
|
||||
public val Double.Companion.tensorAlgebra: DoubleTensorAlgebra get() = DoubleTensorAlgebra
|
||||
|
||||
@ -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()
|
||||
}
|
||||
@ -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()
|
||||
}
|
||||
}
|
||||
@ -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
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import space.kscience.kmath.testutils.assertBufferEquals
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import kotlin.math.roundToInt
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import kotlin.math.roundToLong
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import kotlin.test.Test
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import kotlin.test.assertEquals
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import kotlin.test.assertFalse
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@ -209,100 +205,4 @@ internal class TestDoubleTensorAlgebra {
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assertTrue { ShapeND(5, 5) contentEquals res.shape }
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assertEquals(2.0, res[4, 4])
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}
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@Test
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fun testLM() = DoubleTensorAlgebra {
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fun lm_func(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> {
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val m = t.shape.component1()
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var y_hat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(m, 1)))
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if (settings.example_number == 1) {
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y_hat = DoubleTensorAlgebra.exp((t.times(-1.0 / p[1, 0]))).times(p[0, 0]) + t.times(p[2, 0]).times(
|
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DoubleTensorAlgebra.exp((t.times(-1.0 / p[3, 0])))
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)
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}
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else if (settings.example_number == 2) {
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val mt = t.max()
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y_hat = (t.times(1.0 / mt)).times(p[0, 0]) +
|
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(t.times(1.0 / mt)).pow(2).times(p[1, 0]) +
|
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(t.times(1.0 / mt)).pow(3).times(p[2, 0]) +
|
||||
(t.times(1.0 / mt)).pow(4).times(p[3, 0])
|
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}
|
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else if (settings.example_number == 3) {
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y_hat = DoubleTensorAlgebra.exp((t.times(-1.0 / p[1, 0])))
|
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.times(p[0, 0]) + DoubleTensorAlgebra.sin((t.times(1.0 / p[3, 0]))).times(p[2, 0])
|
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}
|
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|
||||
return y_hat.as2D()
|
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}
|
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|
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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])
|
||||
}
|
||||
}
|
||||
|
||||
@ -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
|
||||
|
||||
Loading…
Reference in New Issue
Block a user