forked from kscience/kmath
removed extra comments, unnecessary variables, renaming variables and secondary functions
This commit is contained in:
Margarita Lashina
parent
cac5b513f3
commit
162e37cb2f
@ -49,9 +49,6 @@ fun main() {
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p_min = p_min.div(1.0 / -50.0)
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val p_max = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(Nparams, 1)))
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p_min = p_min.div(1.0 / 50.0)
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val consts = BroadcastDoubleTensorAlgebra.fromArray(
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ShapeND(intArrayOf(1, 1)), doubleArrayOf(0.0)
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).as2D()
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val opts = doubleArrayOf(3.0, 10000.0, 1e-6, 1e-6, 1e-6, 1e-6, 1e-2, 11.0, 9.0, 1.0)
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// val opts = doubleArrayOf(3.0, 10000.0, 1e-6, 1e-6, 1e-6, 1e-6, 1e-3, 11.0, 9.0, 1.0)
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@ -64,7 +61,6 @@ fun main() {
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dp,
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p_min.as2D(),
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p_max.as2D(),
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consts,
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opts,
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10,
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1
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@ -27,7 +27,6 @@ fun main() {
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startedData.dp,
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startedData.p_min,
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startedData.p_max,
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startedData.consts,
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startedData.opts,
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10,
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startedData.example_number
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@ -48,9 +48,6 @@ fun main() {
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p_min = p_min.div(1.0 / -50.0)
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val p_max = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(Nparams, 1)))
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p_min = p_min.div(1.0 / 50.0)
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val consts = BroadcastDoubleTensorAlgebra.fromArray(
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ShapeND(intArrayOf(1, 1)), doubleArrayOf(0.0)
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).as2D()
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val opts = doubleArrayOf(3.0, 7000.0, 1e-5, 1e-5, 1e-5, 1e-5, 1e-5, 11.0, 9.0, 1.0)
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val result = DoubleTensorAlgebra.lm(
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@ -62,7 +59,6 @@ fun main() {
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dp,
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p_min.as2D(),
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p_max.as2D(),
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consts,
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opts,
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10,
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1
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@ -26,7 +26,6 @@ fun streamLm(lm_func: KFunction3<MutableStructure2D<Double>, MutableStructure2D<
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val dp = startData.dp
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val p_min = startData.p_min
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val p_max = startData.p_max
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val consts = startData.consts
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val opts = startData.opts
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var steps = numberOfLaunches
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@ -42,7 +41,6 @@ fun streamLm(lm_func: KFunction3<MutableStructure2D<Double>, MutableStructure2D<
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dp,
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p_min,
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p_max,
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consts,
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opts,
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10,
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example_number
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@ -31,7 +31,7 @@ import kotlin.reflect.KFunction3
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* InReducedChiSquare: chi-squared convergence achieved
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* (chi squared value divided by (m - n + 1) < epsilon2 = opts[4],
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* where n - number of parameters, m - amount of points
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* NoConvergence: the maximum number of iterations has been reached without reaching convergence
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* NoConvergence: the maximum number of iterations has been reached without reaching any convergence
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*/
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public enum class TypeOfConvergence{
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InGradient,
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@ -61,172 +61,141 @@ public data class LMResultInfo (
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public fun DoubleTensorAlgebra.lm(
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func: KFunction3<MutableStructure2D<Double>, MutableStructure2D<Double>, Int, 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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pInput: MutableStructure2D<Double>, tInput: MutableStructure2D<Double>, yDatInput: MutableStructure2D<Double>,
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weightInput: MutableStructure2D<Double>, dpInput: MutableStructure2D<Double>, pMinInput: MutableStructure2D<Double>,
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pMaxInput: MutableStructure2D<Double>, optsInput: DoubleArray, nargin: Int, exampleNumber: Int): LMResultInfo {
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val resultInfo = LMResultInfo(0, 0, 0.0,
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0.0, p_input, TypeOfConvergence.NoConvergence)
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0.0, pInput, TypeOfConvergence.NoConvergence)
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val eps:Double = 2.2204e-16
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val eps = 2.2204e-16
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val settings = LMSettings(0, 0, example_number)
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val settings = LMSettings(0, 0, exampleNumber)
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settings.funcCalls = 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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var p = pInput
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val t = tInput
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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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val Npnt = length(yDatInput) // number of data points
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var pOld = zeros(ShapeND(intArrayOf(Npar, 1))).as2D() // previous set of parameters
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var yOld = 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 X2Old = 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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var weight = weightInput
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if (nargin < 5) {
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weight = fromArray(ShapeND(intArrayOf(1, 1)), doubleArrayOf((y_dat.transpose().dot(y_dat)).as1D()[0])).as2D()
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weight = fromArray(ShapeND(intArrayOf(1, 1)), doubleArrayOf((yDatInput.transpose().dot(yDatInput)).as1D()[0])).as2D()
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}
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var dp = dp_input
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var dp = dpInput
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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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var pMin = pMinInput
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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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pMin = p
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pMin.abs()
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pMin = pMin.div(-100.0).as2D()
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}
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var p_max = p_max_input
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var pMax = pMaxInput
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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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pMax = p
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pMax.abs()
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pMax = pMax.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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var opts = optsInput
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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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val maxIterations = opts[1].toInt() // maximum number of iterations
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val epsilon1 = opts[2] // convergence tolerance for gradient
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val epsilon2 = opts[3] // convergence tolerance for parameters
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val epsilon3 = opts[4] // convergence tolerance for Chi-square
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val epsilon4 = opts[5] // determines acceptance of a L-M step
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val lambda0 = opts[6] // initial value of damping paramter, lambda
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val lambdaUpFac = opts[7] // factor for increasing lambda
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val lambdaDnFac = opts[8] // factor for decreasing lambda
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val updateType = 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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pMin = makeColumn(pMin)
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pMax = makeColumn(pMax)
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if (length(make_column(dp)) == 1) {
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if (length(makeColumn(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, example_number) // 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 / kotlin.math.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 = makeColumn(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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var lmMatxAns = lmMatx(func, t, pOld, yOld, 1, J, p, yDatInput, weight, dp, settings)
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var JtWJ = lmMatxAns[0]
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var JtWdy = lmMatxAns[1]
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X2 = lmMatxAns[2][0, 0]
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var yHat = lmMatxAns[3]
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J = lmMatxAns[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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if ( abs(JtWdy).max() < epsilon1 ) {
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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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when (updateType) {
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1 -> lambda = lambda0 // 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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lambda = lambda0 * (makeColumnFromDiagonal(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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X2Old = X2 // previous value of X2
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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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while (!stop && settings.iteration <= maxIterations) { //--- 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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h = when (updateType) {
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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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val solve =
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solve(JtWJ.plus(makeMatrixWithDiagonal(makeColumnFromDiagonal(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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val solve = solve(JtWJ.plus(lmEye(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 pTry = (p + h).as2D() // update the [idx] elements
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pTry = smallestElementComparison(largestElementComparison(pMin, pTry.as2D()), pMax) // apply constraints
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var delta_y = y_dat.minus(feval(func, t, p_try, example_number)) // residual error using p_try
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var deltaY = yDatInput.minus(evaluateFunction(func, t, pTry, exampleNumber)) // 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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for (i in 0 until deltaY.shape.component1()) { // floating point error; break
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for (j in 0 until deltaY.shape.component2()) {
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if (deltaY[i, j] == Double.POSITIVE_INFINITY || deltaY[i, j] == Double.NEGATIVE_INFINITY) {
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stop = true
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break
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}
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@ -235,84 +204,87 @@ public fun DoubleTensorAlgebra.lm(
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settings.funcCalls += 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 tmp = deltaY.times(weight)
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var X2Try = deltaY.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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if (updateType == 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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val alpha = JtWdy.transpose().dot(h) / ((X2Try.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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pTry = p.plus(h).as2D() // update only [idx] elements
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pTry = smallestElementComparison(largestElementComparison(pMin, pTry), pMax) // apply constraints
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var delta_y = y_dat.minus(feval(func, t, p_try, example_number)) // residual error using p_try
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deltaY = yDatInput.minus(evaluateFunction(func, t, pTry, exampleNumber)) // residual error using p_try
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settings.funcCalls += 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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X2Try = deltaY.as2D().transpose().dot(deltaY.times(weight)) // Chi-squared error criteria
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}
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val rho = when (Update_Type) { // Nielsen
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val rho = when (updateType) { // 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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val tmp = h.transposed()
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.dot(makeMatrixWithDiagonal(makeColumnFromDiagonal(JtWJ)).div(1 / lambda).dot(h).plus(JtWdy))
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X2.minus(X2Try).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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X2.minus(X2Try).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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if (rho > epsilon4) { // it IS significantly better
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val dX2 = X2.minus(X2Old)
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X2Old = X2
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pOld = p.copyToTensor().as2D()
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yOld = yHat.copyToTensor().as2D()
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p = makeColumn(pTry) // 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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lmMatxAns = lmMatx(func, t, pOld, yOld, dX2.toInt(), J, p, yDatInput, 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]
|
||||
J = lm_matx_ans[4]
|
||||
JtWJ = lmMatxAns[0]
|
||||
JtWdy = lmMatxAns[1]
|
||||
X2 = lmMatxAns[2][0, 0]
|
||||
yHat = lmMatxAns[3]
|
||||
J = lmMatxAns[4]
|
||||
|
||||
lambda = when (Update_Type) {
|
||||
lambda = when (updateType) {
|
||||
1 -> { // Levenberg
|
||||
max(lambda / lambda_DN_fac, 1e-7);
|
||||
max(lambda / lambdaDnFac, 1e-7);
|
||||
}
|
||||
|
||||
2 -> { // Quadratic
|
||||
max( lambda / (1 + alpha) , 1e-7 );
|
||||
max(lambda / (1 + alpha), 1e-7);
|
||||
}
|
||||
|
||||
else -> { // Nielsen
|
||||
nu = 2
|
||||
lambda * max( 1.0 / 3, 1 - (2 * rho - 1).pow(3) )
|
||||
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]
|
||||
} else { // it IS NOT better
|
||||
X2 = X2Old // do not accept p_try
|
||||
if (settings.iteration % (2 * Npar) == 0) { // rank-1 update of Jacobian
|
||||
lmMatxAns = lmMatx(func, t, pOld, yOld, -1, J, p, yDatInput, weight, dp, settings)
|
||||
JtWJ = lmMatxAns[0]
|
||||
JtWdy = lmMatxAns[1]
|
||||
yHat = lmMatxAns[3]
|
||||
J = lmMatxAns[4]
|
||||
}
|
||||
|
||||
// increase lambda ==> gradient descent method
|
||||
lambda = when (Update_Type) {
|
||||
lambda = when (updateType) {
|
||||
1 -> { // Levenberg
|
||||
min(lambda * lambda_UP_fac, 1e7)
|
||||
min(lambda * lambdaUpFac, 1e7)
|
||||
}
|
||||
|
||||
2 -> { // Quadratic
|
||||
lambda + kotlin.math.abs(((X2_try.as2D()[0, 0] - X2) / 2) / alpha)
|
||||
lambda + kotlin.math.abs(((X2Try.as2D()[0, 0] - X2) / 2) / alpha)
|
||||
}
|
||||
|
||||
else -> { // Nielsen
|
||||
nu *= 2
|
||||
lambda * (nu / 2)
|
||||
@ -321,30 +293,27 @@ public fun DoubleTensorAlgebra.lm(
|
||||
}
|
||||
|
||||
if (prnt > 1) {
|
||||
val chi_sq = X2 / DoF
|
||||
val chiSq = X2 / DoF
|
||||
resultInfo.iterations = settings.iteration
|
||||
resultInfo.funcCalls = settings.funcCalls
|
||||
resultInfo.resultChiSq = chi_sq
|
||||
resultInfo.resultChiSq = chiSq
|
||||
resultInfo.resultLambda = lambda
|
||||
resultInfo.resultParameters = 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) {
|
||||
if (abs(JtWdy).max() < epsilon1 && settings.iteration > 2) {
|
||||
resultInfo.typeOfConvergence = TypeOfConvergence.InGradient
|
||||
stop = true
|
||||
}
|
||||
if ((abs(h.as2D()).div(abs(p) + 1e-12)).max() < epsilon_2 && settings.iteration > 2) {
|
||||
if ((abs(h.as2D()).div(abs(p) + 1e-12)).max() < epsilon2 && settings.iteration > 2) {
|
||||
resultInfo.typeOfConvergence = TypeOfConvergence.InParameters
|
||||
stop = true
|
||||
}
|
||||
if (X2 / DoF < epsilon_3 && settings.iteration > 2) {
|
||||
if (X2 / DoF < epsilon3 && settings.iteration > 2) {
|
||||
resultInfo.typeOfConvergence = TypeOfConvergence.InReducedChiSquare
|
||||
stop = true
|
||||
}
|
||||
if (settings.iteration == MaxIter) {
|
||||
if (settings.iteration == maxIterations) {
|
||||
resultInfo.typeOfConvergence = TypeOfConvergence.NoConvergence
|
||||
stop = true
|
||||
}
|
||||
@ -358,8 +327,8 @@ private data class LMSettings (
|
||||
var exampleNumber:Int
|
||||
)
|
||||
|
||||
/* matrix -> column of all elemnets */
|
||||
private fun make_column(tensor: MutableStructure2D<Double>) : MutableStructure2D<Double> {
|
||||
/* matrix -> column of all elements */
|
||||
private fun makeColumn(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()) {
|
||||
@ -367,8 +336,7 @@ private fun make_column(tensor: MutableStructure2D<Double>) : MutableStructure2D
|
||||
buffer[i * tensor.shape.component2() + j] = tensor[i, j]
|
||||
}
|
||||
}
|
||||
val column = BroadcastDoubleTensorAlgebra.fromArray(ShapeND(shape), buffer).as2D()
|
||||
return column
|
||||
return BroadcastDoubleTensorAlgebra.fromArray(ShapeND(shape), buffer).as2D()
|
||||
}
|
||||
|
||||
/* column length */
|
||||
@ -401,7 +369,7 @@ private fun abs(input: MutableStructure2D<Double>): MutableStructure2D<Double> {
|
||||
return tensor
|
||||
}
|
||||
|
||||
private fun diag(input: MutableStructure2D<Double>): MutableStructure2D<Double> {
|
||||
private fun makeColumnFromDiagonal(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]
|
||||
@ -409,7 +377,7 @@ private fun diag(input: MutableStructure2D<Double>): MutableStructure2D<Double>
|
||||
return tensor
|
||||
}
|
||||
|
||||
private fun make_matrx_with_diagonal(column: MutableStructure2D<Double>): MutableStructure2D<Double> {
|
||||
private fun makeMatrixWithDiagonal(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) {
|
||||
@ -418,23 +386,23 @@ private fun make_matrx_with_diagonal(column: MutableStructure2D<Double>): Mutabl
|
||||
return tensor
|
||||
}
|
||||
|
||||
private fun lm_eye(size: Int): MutableStructure2D<Double> {
|
||||
private fun lmEye(size: Int): MutableStructure2D<Double> {
|
||||
val column = BroadcastDoubleTensorAlgebra.ones(ShapeND(intArrayOf(size, 1))).as2D()
|
||||
return make_matrx_with_diagonal(column)
|
||||
return makeMatrixWithDiagonal(column)
|
||||
}
|
||||
|
||||
private 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()
|
||||
private fun largestElementComparison(a: MutableStructure2D<Double>, b: MutableStructure2D<Double>): MutableStructure2D<Double> {
|
||||
val aSizeX = a.shape.component1()
|
||||
val aSizeY = a.shape.component2()
|
||||
val bSizeX = b.shape.component1()
|
||||
val bSizeY = b.shape.component2()
|
||||
val tensor = BroadcastDoubleTensorAlgebra.zeros(ShapeND(intArrayOf(max(aSizeX, bSizeX), max(aSizeY, bSizeY)))).as2D()
|
||||
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) {
|
||||
if (i < aSizeX && i < bSizeX && j < aSizeY && j < bSizeY) {
|
||||
tensor[i, j] = max(a[i, j], b[i, j])
|
||||
}
|
||||
else if (i < a_sizeX && j < a_sizeY) {
|
||||
else if (i < aSizeX && j < aSizeY) {
|
||||
tensor[i, j] = a[i, j]
|
||||
}
|
||||
else {
|
||||
@ -445,18 +413,18 @@ private fun largest_element_comparison(a: MutableStructure2D<Double>, b: Mutable
|
||||
return tensor
|
||||
}
|
||||
|
||||
private 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()
|
||||
private fun smallestElementComparison(a: MutableStructure2D<Double>, b: MutableStructure2D<Double>): MutableStructure2D<Double> {
|
||||
val aSizeX = a.shape.component1()
|
||||
val aSizeY = a.shape.component2()
|
||||
val bSizeX = b.shape.component1()
|
||||
val bSizeY = b.shape.component2()
|
||||
val tensor = BroadcastDoubleTensorAlgebra.zeros(ShapeND(intArrayOf(max(aSizeX, bSizeX), max(aSizeY, bSizeY)))).as2D()
|
||||
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) {
|
||||
if (i < aSizeX && i < bSizeX && j < aSizeY && j < bSizeY) {
|
||||
tensor[i, j] = min(a[i, j], b[i, j])
|
||||
}
|
||||
else if (i < a_sizeX && j < a_sizeY) {
|
||||
else if (i < aSizeX && j < aSizeY) {
|
||||
tensor[i, j] = a[i, j]
|
||||
}
|
||||
else {
|
||||
@ -467,71 +435,69 @@ private fun smallest_element_comparison(a: MutableStructure2D<Double>, b: Mutabl
|
||||
return tensor
|
||||
}
|
||||
|
||||
private fun get_zero_indices(column: MutableStructure2D<Double>, epsilon: Double = 0.000001): MutableStructure2D<Double>? {
|
||||
private fun getZeroIndices(column: MutableStructure2D<Double>, epsilon: Double = 0.000001): MutableStructure2D<Double>? {
|
||||
var idx = emptyArray<Double>()
|
||||
for (i in 0 until column.shape.component1()) {
|
||||
if (kotlin.math.abs(column[i, 0]) > epsilon) {
|
||||
idx += (i + 1.0)
|
||||
}
|
||||
}
|
||||
if (idx.size > 0) {
|
||||
if (idx.isNotEmpty()) {
|
||||
return BroadcastDoubleTensorAlgebra.fromArray(ShapeND(intArrayOf(idx.size, 1)), idx.toDoubleArray()).as2D()
|
||||
}
|
||||
return null
|
||||
}
|
||||
|
||||
private fun feval(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, Int) -> MutableStructure2D<Double>,
|
||||
t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, exampleNumber: Int)
|
||||
private fun evaluateFunction(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, Int) -> MutableStructure2D<Double>,
|
||||
t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, exampleNumber: Int)
|
||||
: MutableStructure2D<Double>
|
||||
{
|
||||
return func(t, p, exampleNumber)
|
||||
}
|
||||
|
||||
private fun lm_matx(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, Int) -> 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>>
|
||||
private fun lmMatx(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, Int) -> MutableStructure2D<Double>,
|
||||
t: MutableStructure2D<Double>, pOld: MutableStructure2D<Double>, yOld: MutableStructure2D<Double>,
|
||||
dX2: Int, JInput: MutableStructure2D<Double>, p: MutableStructure2D<Double>,
|
||||
yDat: MutableStructure2D<Double>, weight: MutableStructure2D<Double>, dp:MutableStructure2D<Double>, settings:LMSettings) : Array<MutableStructure2D<Double>>
|
||||
{
|
||||
// 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.exampleNumber) // evaluate model using parameters 'p'
|
||||
val yHat = evaluateFunction(func, t, p, settings.exampleNumber) // evaluate model using parameters 'p'
|
||||
settings.funcCalls += 1
|
||||
|
||||
var J = J_input
|
||||
var J = JInput
|
||||
|
||||
if (settings.iteration % (2 * Npar) == 0 || dX2 > 0) {
|
||||
J = lm_FD_J(func, t, p, y_hat, dp, settings).as2D() // finite difference
|
||||
J = if (settings.iteration % (2 * Npar) == 0 || dX2 > 0) {
|
||||
lmFdJ(func, t, p, yHat, dp, settings).as2D() // finite difference
|
||||
}
|
||||
else {
|
||||
J = lm_Broyden_J(p_old, y_old, J, p, y_hat).as2D() // rank-1 update
|
||||
lmBroydenJ(pOld, yOld, J, p, yHat).as2D() // rank-1 update
|
||||
}
|
||||
|
||||
val delta_y = y_dat.minus(y_hat)
|
||||
val deltaY = yDat.minus(yHat)
|
||||
|
||||
val Chi_sq = delta_y.transposed().dot( delta_y.times(weight) ).as2D()
|
||||
val chiSq = deltaY.transposed().dot( deltaY.times(weight) ).as2D()
|
||||
val JtWJ = J.transposed().dot ( J.times( weight.dot(BroadcastDoubleTensorAlgebra.ones(ShapeND(intArrayOf(1, Npar)))) ) ).as2D()
|
||||
val JtWdy = J.transposed().dot( weight.times(delta_y) ).as2D()
|
||||
val JtWdy = J.transposed().dot( weight.times(deltaY) ).as2D()
|
||||
|
||||
return arrayOf(JtWJ,JtWdy,Chi_sq,y_hat,J)
|
||||
return arrayOf(JtWJ,JtWdy,chiSq,yHat,J)
|
||||
}
|
||||
|
||||
private fun lm_Broyden_J(p_old: MutableStructure2D<Double>, y_old: MutableStructure2D<Double>, J_input: MutableStructure2D<Double>,
|
||||
p: MutableStructure2D<Double>, y: MutableStructure2D<Double>): MutableStructure2D<Double> {
|
||||
var J = J_input.copyToTensor()
|
||||
private fun lmBroydenJ(pOld: MutableStructure2D<Double>, yOld: MutableStructure2D<Double>, JInput: MutableStructure2D<Double>,
|
||||
p: MutableStructure2D<Double>, y: MutableStructure2D<Double>): MutableStructure2D<Double> {
|
||||
var J = JInput.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] )
|
||||
val h = p.minus(pOld)
|
||||
val increase = y.minus(yOld).minus( J.dot(h) ).dot(h.transposed()).div( (h.transposed().dot(h)).as2D()[0, 0] )
|
||||
J = J.plus(increase)
|
||||
|
||||
return J.as2D()
|
||||
}
|
||||
|
||||
private fun lm_FD_J(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, exampleNumber: Int) -> MutableStructure2D<Double>,
|
||||
t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, y: MutableStructure2D<Double>,
|
||||
dp: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> {
|
||||
private fun lmFdJ(func: (MutableStructure2D<Double>, MutableStructure2D<Double>, exampleNumber: Int) -> MutableStructure2D<Double>,
|
||||
t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, y: MutableStructure2D<Double>,
|
||||
dp: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> {
|
||||
// default: dp = 0.001 * ones(1,n)
|
||||
|
||||
val m = length(y) // number of data points
|
||||
@ -548,7 +514,7 @@ private fun lm_FD_J(func: (MutableStructure2D<Double>, MutableStructure2D<Double
|
||||
|
||||
val epsilon = 0.0000001
|
||||
if (kotlin.math.abs(del[j, 0]) > epsilon) {
|
||||
val y1 = feval(func, t, p, settings.exampleNumber)
|
||||
val y1 = evaluateFunction(func, t, p, settings.exampleNumber)
|
||||
settings.funcCalls += 1
|
||||
|
||||
if (dp[j, 0] < 0) { // backwards difference
|
||||
@ -558,10 +524,9 @@ private fun lm_FD_J(func: (MutableStructure2D<Double>, MutableStructure2D<Double
|
||||
}
|
||||
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.exampleNumber)).as2D())[i, 0] / (2 * del[j, 0])
|
||||
J[i, j] = (y1.as2D().minus(evaluateFunction(func, t, p, settings.exampleNumber)).as2D())[i, 0] / (2 * del[j, 0])
|
||||
}
|
||||
settings.funcCalls += 1
|
||||
}
|
||||
|
||||
@ -121,13 +121,9 @@ class TestLmAlgorithm {
|
||||
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(::funcEasyForLm, p_init, t, y_dat, weight, dp, p_min, p_max, consts, opts, 10, example_number)
|
||||
val result = lm(::funcEasyForLm, p_init, t, y_dat, weight, dp, p_min, p_max, opts, 10, example_number)
|
||||
assertEquals(13, result.iterations)
|
||||
assertEquals(31, result.funcCalls)
|
||||
assertEquals(0.9131368192633, (result.resultChiSq * 1e13).roundToLong() / 1e13)
|
||||
@ -182,9 +178,6 @@ class TestLmAlgorithm {
|
||||
p_min = p_min.div(1.0 / -50.0)
|
||||
val p_max = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(Nparams, 1)))
|
||||
p_min = p_min.div(1.0 / 50.0)
|
||||
val consts = BroadcastDoubleTensorAlgebra.fromArray(
|
||||
ShapeND(intArrayOf(1, 1)), doubleArrayOf(0.0)
|
||||
).as2D()
|
||||
val opts = doubleArrayOf(3.0, 7000.0, 1e-5, 1e-5, 1e-5, 1e-5, 1e-5, 11.0, 9.0, 1.0)
|
||||
|
||||
val result = DoubleTensorAlgebra.lm(
|
||||
@ -196,7 +189,6 @@ class TestLmAlgorithm {
|
||||
dp,
|
||||
p_min.as2D(),
|
||||
p_max.as2D(),
|
||||
consts,
|
||||
opts,
|
||||
10,
|
||||
1
|
||||
@ -238,9 +230,6 @@ class TestLmAlgorithm {
|
||||
p_min = p_min.div(1.0 / -50.0)
|
||||
val p_max = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(Nparams, 1)))
|
||||
p_min = p_min.div(1.0 / 50.0)
|
||||
val consts = BroadcastDoubleTensorAlgebra.fromArray(
|
||||
ShapeND(intArrayOf(1, 1)), doubleArrayOf(0.0)
|
||||
).as2D()
|
||||
val opts = doubleArrayOf(3.0, 7000.0, 1e-2, 1e-3, 1e-2, 1e-2, 1e-2, 11.0, 9.0, 1.0)
|
||||
|
||||
val result = DoubleTensorAlgebra.lm(
|
||||
@ -252,7 +241,6 @@ class TestLmAlgorithm {
|
||||
dp,
|
||||
p_min.as2D(),
|
||||
p_max.as2D(),
|
||||
consts,
|
||||
opts,
|
||||
10,
|
||||
1
|
||||
|
||||
Loading…
Reference in New Issue
Block a user