added examples and tests

examples/src/main/kotlin/space/kscience/kmath/tensors/LevenbergMarquardt/StaticLm/staticDifficultTest.kt

@@ -0,0 +1,92 @@
+/*
+ * 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.LevenbergMarquardt.StaticLm
+
+import space.kscience.kmath.nd.ShapeND
+import space.kscience.kmath.nd.as2D
+import space.kscience.kmath.nd.component1
+import space.kscience.kmath.tensors.LevenbergMarquardt.funcDifficultForLm
+import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra
+import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.div
+import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
+import space.kscience.kmath.tensors.core.internal.LMSettings
+import kotlin.math.roundToInt
+
+fun main() {
+    val NData = 200
+    var t_example = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(NData, 1))).as2D()
+    for (i in 0 until NData) {
+        t_example[i, 0] = t_example[i, 0] * (i + 1) - 104
+    }
+
+    val Nparams = 15
+    var p_example = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(Nparams, 1))).as2D()
+    for (i in 0 until Nparams) {
+        p_example[i, 0] = p_example[i, 0] + i - 25
+    }
+
+    val settings = LMSettings(0, 0, 1)
+
+    var y_hat =  funcDifficultForLm(t_example, p_example, settings)
+
+    var p_init = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(Nparams, 1))).as2D()
+    for (i in 0 until Nparams) {
+        p_init[i, 0] = (p_example[i, 0] + 0.9)
+    }
+
+    var t = t_example
+    val y_dat = y_hat
+    val weight = BroadcastDoubleTensorAlgebra.fromArray(
+        ShapeND(intArrayOf(1, 1)), DoubleArray(1) { 1.0 / Nparams * 1.0 - 0.085 }
+    ).as2D()
+    val dp = BroadcastDoubleTensorAlgebra.fromArray(
+        ShapeND(intArrayOf(1, 1)), DoubleArray(1) { -0.01 }
+    ).as2D()
+    var p_min = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(Nparams, 1)))
+    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, 10000.0, 1e-2, 0.015, 1e-2, 1e-2, 1e-2, 11.0, 9.0, 1.0)
+//    val opts = doubleArrayOf(3.0, 10000.0, 1e-5, 1e-5, 1e-5, 1e-5, 1e-3, 11.0, 9.0, 1.0)
+
+    val result = DoubleTensorAlgebra.lm(
+        ::funcDifficultForLm,
+        p_init.as2D(),
+        t,
+        y_dat,
+        weight,
+        dp,
+        p_min.as2D(),
+        p_max.as2D(),
+        consts,
+        opts,
+        10,
+        1
+    )
+
+    println("Parameters:")
+    for (i in 0 until result.result_parameters.shape.component1()) {
+        val x = (result.result_parameters[i, 0] * 10000).roundToInt() / 10000.0
+        print("$x ")
+    }
+    println()
+
+    println("Y true and y received:")
+    var y_hat_after =  funcDifficultForLm(t_example, result.result_parameters, settings)
+    for (i in 0 until y_hat.shape.component1()) {
+        val x = (y_hat[i, 0] * 10000).roundToInt() / 10000.0
+        val y = (y_hat_after[i, 0] * 10000).roundToInt() / 10000.0
+        println("$x $y")
+    }
+
+    println("Сhi_sq:")
+    println(result.result_chi_sq)
+    println("Number of iterations:")
+    println(result.iterations)
+}

examples/src/main/kotlin/space/kscience/kmath/tensors/LevenbergMarquardt/StaticLm/staticEasyTest.kt

@@ -0,0 +1,56 @@
+/*
+ * 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.LevenbergMarquardt.StaticLm
+
+import space.kscience.kmath.nd.ShapeND
+import space.kscience.kmath.nd.as2D
+import space.kscience.kmath.nd.component1
+import space.kscience.kmath.tensors.LevenbergMarquardt.funcDifficultForLm
+import space.kscience.kmath.tensors.LevenbergMarquardt.funcEasyForLm
+import space.kscience.kmath.tensors.LevenbergMarquardt.getStartDataForFuncEasy
+import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra
+import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
+import space.kscience.kmath.tensors.core.internal.LMSettings
+import kotlin.math.roundToInt
+
+fun main() {
+    val startedData = getStartDataForFuncEasy()
+
+    val result = DoubleTensorAlgebra.lm(
+        ::funcEasyForLm,
+        DoubleTensorAlgebra.ones(ShapeND(intArrayOf(4, 1))).as2D(),
+        startedData.t,
+        startedData.y_dat,
+        startedData.weight,
+        startedData.dp,
+        startedData.p_min,
+        startedData.p_max,
+        startedData.consts,
+        startedData.opts,
+        10,
+        startedData.example_number
+    )
+
+    println("Parameters:")
+    for (i in 0 until result.result_parameters.shape.component1()) {
+        val x = (result.result_parameters[i, 0] * 10000).roundToInt() / 10000.0
+        print("$x ")
+    }
+    println()
+
+    println("Y true and y received:")
+    var y_hat_after =  funcDifficultForLm(startedData.t, result.result_parameters, LMSettings(0, 0, startedData.example_number))
+    for (i in 0 until startedData.y_dat.shape.component1()) {
+        val x = (startedData.y_dat[i, 0] * 10000).roundToInt() / 10000.0
+        val y = (y_hat_after[i, 0] * 10000).roundToInt() / 10000.0
+        println("$x $y")
+    }
+
+    println("Сhi_sq:")
+    println(result.result_chi_sq)
+    println("Number of iterations:")
+    println(result.iterations)
+}

examples/src/main/kotlin/space/kscience/kmath/tensors/LevenbergMarquardt/StaticLm/staticMiddleTest.kt

@@ -0,0 +1,91 @@
+/*
+ * 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.LevenbergMarquardt.StaticLm
+
+import space.kscience.kmath.nd.ShapeND
+import space.kscience.kmath.nd.as2D
+import space.kscience.kmath.nd.component1
+import space.kscience.kmath.tensors.LevenbergMarquardt.funcMiddleForLm
+import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra
+import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.div
+import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
+import space.kscience.kmath.tensors.core.internal.LMSettings
+import kotlin.math.roundToInt
+fun main() {
+    val NData = 100
+    var t_example = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(NData, 1))).as2D()
+    for (i in 0 until NData) {
+        t_example[i, 0] = t_example[i, 0] * (i + 1)
+    }
+
+    val Nparams = 20
+    var p_example = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(Nparams, 1))).as2D()
+    for (i in 0 until Nparams) {
+        p_example[i, 0] = p_example[i, 0] + i - 25
+    }
+
+    val settings = LMSettings(0, 0, 1)
+
+    var y_hat =  funcMiddleForLm(t_example, p_example, settings)
+
+    var p_init = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(Nparams, 1))).as2D()
+    for (i in 0 until Nparams) {
+        p_init[i, 0] = (p_example[i, 0] + 0.9)
+    }
+//    val p_init = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(Nparams, 1)))
+//    val p_init = p_example
+    var t = t_example
+    val y_dat = y_hat
+    val weight = BroadcastDoubleTensorAlgebra.fromArray(
+        ShapeND(intArrayOf(1, 1)), DoubleArray(1) { 1.0 }
+    ).as2D()
+    val dp = BroadcastDoubleTensorAlgebra.fromArray(
+        ShapeND(intArrayOf(1, 1)), DoubleArray(1) { -0.01 }
+    ).as2D()
+    var p_min = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(Nparams, 1)))
+    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, 10000.0, 1e-5, 1e-5, 1e-5, 1e-5, 1e-5, 11.0, 9.0, 1.0)
+
+    val result = DoubleTensorAlgebra.lm(
+        ::funcMiddleForLm,
+        p_init.as2D(),
+        t,
+        y_dat,
+        weight,
+        dp,
+        p_min.as2D(),
+        p_max.as2D(),
+        consts,
+        opts,
+        10,
+        1
+    )
+
+    println("Parameters:")
+    for (i in 0 until result.result_parameters.shape.component1()) {
+        val x = (result.result_parameters[i, 0] * 10000).roundToInt() / 10000.0
+        print("$x ")
+    }
+    println()
+
+    println("Y true and y received:")
+    var y_hat_after =  funcMiddleForLm(t_example, result.result_parameters, settings)
+    for (i in 0 until y_hat.shape.component1()) {
+        val x = (y_hat[i, 0] * 10000).roundToInt() / 10000.0
+        val y = (y_hat_after[i, 0] * 10000).roundToInt() / 10000.0
+        println("$x $y")
+    }
+
+    println("Сhi_sq:")
+    println(result.result_chi_sq)
+    println("Number of iterations:")
+    println(result.iterations)
+}

examples/src/main/kotlin/space/kscience/kmath/tensors/LevenbergMarquardt/StreamingLm/streamLm.kt

@@ -3,20 +3,20 @@
  * 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.StreamingLm
+package space.kscience.kmath.tensors.LevenbergMarquardt.StreamingLm
 
 import kotlinx.coroutines.delay
 import kotlinx.coroutines.flow.*
 import space.kscience.kmath.nd.*
+import space.kscience.kmath.tensors.LevenbergMarquardt.StartDataLm
 import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.zeros
 import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
 import space.kscience.kmath.tensors.core.internal.LMSettings
-import kotlin.math.roundToInt
 import kotlin.random.Random
 import kotlin.reflect.KFunction3
 
 fun streamLm(lm_func: KFunction3<MutableStructure2D<Double>, MutableStructure2D<Double>, LMSettings, MutableStructure2D<Double>>,
-             startData: StartDataLm, launchFrequencyInMs: Long): Flow<MutableStructure2D<Double>> = flow{
+             startData: StartDataLm, launchFrequencyInMs: Long, numberOfLaunches: Int): Flow<MutableStructure2D<Double>> = flow{
 
     var example_number = startData.example_number
     var p_init = startData.p_init
@@ -29,7 +29,10 @@ fun streamLm(lm_func: KFunction3<MutableStructure2D<Double>, MutableStructure2D<
     val consts = startData.consts
     val opts = startData.opts
 
-    while (true) {
+    var steps = numberOfLaunches
+    val isEndless = (steps <= 0)
+
+    while (isEndless || steps > 0) {
         val result = DoubleTensorAlgebra.lm(
             lm_func,
             p_init,
@@ -48,6 +51,7 @@ fun streamLm(lm_func: KFunction3<MutableStructure2D<Double>, MutableStructure2D<
         delay(launchFrequencyInMs)
         p_init = result.result_parameters
         y_dat = generateNewYDat(y_dat, 0.1)
+        if (!isEndless) steps -= 1
     }
 }
 
@@ -59,18 +63,4 @@ fun generateNewYDat(y_dat: MutableStructure2D<Double>, delta: Double): MutableSt
         y_dat_new[i, 0] = y_dat[i, 0] + randomEps
     }
     return y_dat_new
-}
-
-suspend fun main(){
-    val startData = getStartDataForFunc1()
-    // Создание потока:
-    val lmFlow = streamLm(::func1ForLm, startData, 1000)
-    // Запуск потока
-    lmFlow.collect { parameters ->
-        for (i in 0 until parameters.shape.component1()) {
-            val x = (parameters[i, 0] * 10000).roundToInt() / 10000.0
-            print("$x ")
-            if (i == parameters.shape.component1() - 1) println()
-        }
-    }
 }

examples/src/main/kotlin/space/kscience/kmath/tensors/LevenbergMarquardt/StreamingLm/streamingLmTest.kt

@@ -0,0 +1,25 @@
+/*
+ * 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.LevenbergMarquardt.StreamingLm
+
+import space.kscience.kmath.nd.*
+import space.kscience.kmath.tensors.LevenbergMarquardt.funcEasyForLm
+import space.kscience.kmath.tensors.LevenbergMarquardt.getStartDataForFuncEasy
+import kotlin.math.roundToInt
+
+suspend fun main(){
+    val startData = getStartDataForFuncEasy()
+    // Создание потока:
+    val lmFlow = streamLm(::funcEasyForLm, startData, 1000,  10)
+    // Запуск потока
+    lmFlow.collect { parameters ->
+        for (i in 0 until parameters.shape.component1()) {
+            val x = (parameters[i, 0] * 10000).roundToInt() / 10000.0
+            print("$x ")
+            if (i == parameters.shape.component1() - 1) println()
+        }
+    }
+}

examples/src/main/kotlin/space/kscience/kmath/tensors/LevenbergMarquardt/functionsToOptimize.kt

@@ -3,7 +3,7 @@
  * 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.StreamingLm
+package space.kscience.kmath.tensors.LevenbergMarquardt
 
 import space.kscience.kmath.nd.MutableStructure2D
 import space.kscience.kmath.nd.ShapeND
@@ -15,6 +15,7 @@ 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.asDoubleTensor
 import space.kscience.kmath.tensors.core.internal.LMSettings
 
 public data class StartDataLm (
@@ -31,7 +32,39 @@ public data class StartDataLm (
     var opts: DoubleArray
 )
 
-fun func1ForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> {
+fun funcDifficultForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> {
+    val m = t.shape.component1()
+    var y_hat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf (m, 1)))
+
+    val mt = t.max()
+    for(i in 0 until p.shape.component1()){
+        y_hat = y_hat.plus( (t.times(1.0 / mt)).times(p[i, 0]) )
+    }
+
+    for(i in 0 until 4){
+        y_hat = funcEasyForLm((y_hat.as2D() + t).as2D(), p, settings).asDoubleTensor()
+    }
+
+    return y_hat.as2D()
+}
+
+fun funcMiddleForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> {
+    val m = t.shape.component1()
+    var y_hat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf (m, 1)))
+
+    val mt = t.max()
+    for(i in 0 until p.shape.component1()){
+        y_hat += (t.times(1.0 / mt)).times(p[i, 0])
+    }
+
+    for(i in 0 until 5){
+        y_hat = funcEasyForLm(y_hat.as2D(), p, settings).asDoubleTensor()
+    }
+
+    return y_hat.as2D()
+}
+
+fun funcEasyForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> {
     val m = t.shape.component1()
     var y_hat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf (m, 1)))
 
@@ -55,7 +88,7 @@ fun func1ForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, set
     return y_hat.as2D()
 }
 
-fun getStartDataForFunc1(): StartDataLm {
+fun getStartDataForFuncEasy(): StartDataLm {
     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,

kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt

@@ -765,12 +765,12 @@ public open class DoubleTensorAlgebra :
 
         var weight = weight_input
         if (nargin <  5) {
-            weight = fromArray(ShapeND(intArrayOf(1, 1)), doubleArrayOf((y_dat.transpose().dot(y_dat)).as1D()[0])).as2D()
+            fromArray(ShapeND(intArrayOf(1, 1)), doubleArrayOf(1.0)).as2D()
         }
 
         var dp = dp_input
         if (nargin < 6) {
-            dp = fromArray(ShapeND(intArrayOf(1, 1)), doubleArrayOf(0.001)).as2D()
+            dp = fromArray(ShapeND(intArrayOf(1, 1)), doubleArrayOf(-0.001)).as2D()
         }
 
         var p_min = p_min_input
@@ -1023,6 +1023,8 @@ public open class DoubleTensorAlgebra :
 //                println(" !! Maximum Number of Iterations Reached Without Convergence !!")
                 resultInfo.typeOfConvergence = LinearOpsTensorAlgebra.TypeOfConvergence.noConvergence
                 resultInfo.epsilon = 0.0
+                print("noConvergence, MaxIter = ")
+                println(MaxIter)
                 stop = true
             }
         }  // --- End of Main Loop

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

@@ -0,0 +1,267 @@
+/*
+ * 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.nd.MutableStructure2D
+import space.kscience.kmath.nd.ShapeND
+import space.kscience.kmath.nd.as2D
+import space.kscience.kmath.nd.component1
+import space.kscience.kmath.operations.invoke
+import space.kscience.kmath.tensors.api.LinearOpsTensorAlgebra
+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
+
+class TestLmAlgorithm {
+    companion object {
+        fun funcEasyForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> {
+            val m = t.shape.component1()
+            var y_hat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(m, 1)))
+
+            if (settings.example_number == 1) {
+                y_hat = DoubleTensorAlgebra.exp((t.times(-1.0 / p[1, 0]))).times(p[0, 0]) + t.times(p[2, 0]).times(
+                    DoubleTensorAlgebra.exp((t.times(-1.0 / p[3, 0])))
+                )
+            }
+            else if (settings.example_number == 2) {
+                val mt = t.max()
+                y_hat = (t.times(1.0 / mt)).times(p[0, 0]) +
+                        (t.times(1.0 / mt)).pow(2).times(p[1, 0]) +
+                        (t.times(1.0 / mt)).pow(3).times(p[2, 0]) +
+                        (t.times(1.0 / mt)).pow(4).times(p[3, 0])
+            }
+            else if (settings.example_number == 3) {
+                y_hat = DoubleTensorAlgebra.exp((t.times(-1.0 / p[1, 0])))
+                    .times(p[0, 0]) + DoubleTensorAlgebra.sin((t.times(1.0 / p[3, 0]))).times(p[2, 0])
+            }
+
+            return y_hat.as2D()
+        }
+
+        fun funcMiddleForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> {
+            val m = t.shape.component1()
+            var y_hat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf (m, 1)))
+
+            val mt = t.max()
+            for(i in 0 until p.shape.component1()){
+                y_hat += (t.times(1.0 / mt)).times(p[i, 0])
+            }
+
+            for(i in 0 until 5){
+                y_hat = funcEasyForLm(y_hat.as2D(), p, settings).asDoubleTensor()
+            }
+
+            return y_hat.as2D()
+        }
+
+        fun funcDifficultForLm(t: MutableStructure2D<Double>, p: MutableStructure2D<Double>, settings: LMSettings): MutableStructure2D<Double> {
+            val m = t.shape.component1()
+            var y_hat = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf (m, 1)))
+
+            val mt = t.max()
+            for(i in 0 until p.shape.component1()){
+                y_hat = y_hat.plus( (t.times(1.0 / mt)).times(p[i, 0]) )
+            }
+
+            for(i in 0 until 4){
+                y_hat = funcEasyForLm((y_hat.as2D() + t).as2D(), p, settings).asDoubleTensor()
+            }
+
+            return y_hat.as2D()
+        }
+
+    }
+    @Test
+    fun testLMEasy() = DoubleTensorAlgebra {
+        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(::funcEasyForLm, 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])
+    }
+
+    @Test
+    fun TestLMMiddle() = DoubleTensorAlgebra {
+        val NData = 100
+        var t_example = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(NData, 1))).as2D()
+        for (i in 0 until NData) {
+            t_example[i, 0] = t_example[i, 0] * (i + 1)
+        }
+
+        val Nparams = 20
+        var p_example = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(Nparams, 1))).as2D()
+        for (i in 0 until Nparams) {
+            p_example[i, 0] = p_example[i, 0] + i - 25
+        }
+
+        val settings = LMSettings(0, 0, 1)
+
+        var y_hat =  funcMiddleForLm(t_example, p_example, settings)
+
+        var p_init = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(Nparams, 1))).as2D()
+        for (i in 0 until Nparams) {
+            p_init[i, 0] = (p_example[i, 0] + 0.9)
+        }
+
+        var t = t_example
+        val y_dat = y_hat
+        val weight = BroadcastDoubleTensorAlgebra.fromArray(
+            ShapeND(intArrayOf(1, 1)), DoubleArray(1) { 1.0 }
+        ).as2D()
+        val dp = BroadcastDoubleTensorAlgebra.fromArray(
+            ShapeND(intArrayOf(1, 1)), DoubleArray(1) { -0.01 }
+        ).as2D()
+        var p_min = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(Nparams, 1)))
+        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(
+            ::funcMiddleForLm,
+            p_init.as2D(),
+            t,
+            y_dat,
+            weight,
+            dp,
+            p_min.as2D(),
+            p_max.as2D(),
+            consts,
+            opts,
+            10,
+            1
+        )
+    }
+
+    @Test
+    fun TestLMDifficult() = DoubleTensorAlgebra {
+        val NData = 200
+        var t_example = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(NData, 1))).as2D()
+        for (i in 0 until NData) {
+            t_example[i, 0] = t_example[i, 0] * (i + 1) - 104
+        }
+
+        val Nparams = 15
+        var p_example = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(Nparams, 1))).as2D()
+        for (i in 0 until Nparams) {
+            p_example[i, 0] = p_example[i, 0] + i - 25
+        }
+
+        val settings = LMSettings(0, 0, 1)
+
+        var y_hat =  funcDifficultForLm(t_example, p_example, settings)
+
+        var p_init = DoubleTensorAlgebra.zeros(ShapeND(intArrayOf(Nparams, 1))).as2D()
+        for (i in 0 until Nparams) {
+            p_init[i, 0] = (p_example[i, 0] + 0.9)
+        }
+
+        var t = t_example
+        val y_dat = y_hat
+        val weight = BroadcastDoubleTensorAlgebra.fromArray(
+            ShapeND(intArrayOf(1, 1)), DoubleArray(1) { 1.0 / Nparams * 1.0 - 0.085 }
+        ).as2D()
+        val dp = BroadcastDoubleTensorAlgebra.fromArray(
+            ShapeND(intArrayOf(1, 1)), DoubleArray(1) { -0.01 }
+        ).as2D()
+        var p_min = DoubleTensorAlgebra.ones(ShapeND(intArrayOf(Nparams, 1)))
+        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-1, 1e-2, 1e-2, 1e-2, 11.0, 9.0, 1.0)
+
+        val result = DoubleTensorAlgebra.lm(
+            ::funcDifficultForLm,
+            p_init.as2D(),
+            t,
+            y_dat,
+            weight,
+            dp,
+            p_min.as2D(),
+            p_max.as2D(),
+            consts,
+            opts,
+            10,
+            1
+        )
+
+//        assertEquals(1.15, (result.result_chi_sq * 1e2).roundToLong() / 1e2)
+    }
+}