code/main.py

@@ -16,16 +16,16 @@ def plt_append(sp, x: list[float], y: list[float], label: str, format: str):
    sp.plot(x, y, format, label=label)
 
 
+def generate_array(min, max, density=10):
+   point_count = int(m.fabs(max-min)*density)
+   x = np.linspace(min, max, point_count)
+   return list(x.tolist())
+
+
 class NonLinear:
    bisect_exp = "x**2 * np.sin(x)"
    newton_exp = "np.sin(x) * np.sqrt(np.abs(x))"
 
-   @staticmethod
-   def generate_array(min, max):
-      point_count = int(m.fabs(max-min))*10
-      x = np.linspace(min, max, point_count)
-      return list(x.tolist())
-
    @staticmethod
    def slice_array(range: list[float], val_min, val_max):
       def index_search(range: list[float], val):
@@ -54,7 +54,7 @@ class NonLinear:
    def plot_bisect():
       bounds = 0, 6
       split_val = 1
-      x1 = NonLinear.generate_array(bounds[0], bounds[1])
+      x1 = generate_array(bounds[0], bounds[1])
       x2 = NonLinear.slice_array(x1, split_val, None)
 
       sp = create_subplot()
@@ -65,9 +65,9 @@ class NonLinear:
       plt_append(
           sp, x1, sol1[0], f"Исходные данные (y={NonLinear.bisect_exp})", "-b")
       plt_append(
-          sp, *(sol1[1]), f"bisect at [{bounds[0]},{bounds[1]}]", "or")
+          sp, *(sol1[1]), f"bisect на [{bounds[0]},{bounds[1]}]", "or")
       plt_append(
-          sp, *(sol2[1]), f"bisect at [{split_val},{bounds[1]}]", "og")
+          sp, *(sol2[1]), f"bisect на [{split_val},{bounds[1]}]", "og")
 
       sp.set_title("scipy.optimize.bisect")
       sp.legend(loc='lower left')
@@ -84,7 +84,7 @@ class NonLinear:
    def plot_newton():
       bounds = -2, 7
       split_l, split_r = 2, 5
-      x1 = NonLinear.generate_array(bounds[0], bounds[1])
+      x1 = generate_array(bounds[0], bounds[1])
       x2 = NonLinear.slice_array(x1, split_l, split_r)
       x0_1, x0_2 = 1/100, 4
       sp = create_subplot()
@@ -95,9 +95,9 @@ class NonLinear:
       plt_append(
           sp, x1, sol1[0], f"Исходные данные (y={NonLinear.newton_exp})", "-b")
       plt_append(
-          sp, *(sol1[1]), f"newton at [{bounds[0]},{bounds[1]}]", "or")
+          sp, *(sol1[1]), f"newton на отрезке [{bounds[0]},{bounds[1]}]", "or")
       plt_append(
-          sp, *(sol2[1]), f"newton at [{split_l},{bounds[1]}]", "og")
+          sp, *(sol2[1]), f"newton на отрезке [{split_l},{bounds[1]}]", "og")
 
       sp.set_title("scipy.optimize.newton")
       sp.legend(loc='lower left')
@@ -137,7 +137,8 @@ class SLE:
          new_data = []
          new_len = len(data[0][0])
          zipped = list(zip(*tuple(data[0])))
-         zipped[len(zipped)-1] = (zipped[len(zipped)-1][0],zipped[len(zipped)-2][1])
+         zipped[len(zipped)-1] = (zipped[len(zipped)-1]
+                                  [0], zipped[len(zipped)-2][1])
          complement_to = new_len - len(zipped[0])
          for i, val in enumerate(zipped):
             zero_r = complement_to - i
@@ -159,7 +160,7 @@ class SLE:
             if coef != 0:
                print(f"({coef}{SLE.var_str(i_coef)}) + ", end='')
             else:
-               print(f"  {coef}   + ",end='')
+               print(f"  {coef}   + ", end='')
          print(f"({val[-1]}{SLE.var_str(len(val)-1)})", end='')
          print(f" = {data[1][i]}")
 
@@ -213,12 +214,215 @@ class SLE:
       if method in ["banded", "all"]:
          SLE.print_tridiagonal()
 
+
 class Approx:
-   function = "np.sin(x) * np.sqrt(np.abs(x))"
+   function_exp = "np.sin(x) * np.sqrt(np.abs(x))"
+   least_sq_exp = "np.sin(x) * np.abs(x)"
+
+   @staticmethod
+   def get_function_exp_der(*args):
+      function_der_exp = "(x * np.sin(x) + 2 * x**2 * np.cos(x)) / (2 * np.sqrt(np.abs(x)) ** 3)"
+      result = ()
+      for i in args:
+         array = []
+         for x in i:
+            array.append(eval(function_der_exp))
+
+         result = result + (array,)
+      return result
+
+   @staticmethod
+   def generate_y(x_array, function):
+      result = []
+      for x in x_array:
+         result.append(eval(function))
+      return result
+
+   @staticmethod
+   def lagrange(x, y):
+      return sitp.lagrange(x, y)
+
+   @staticmethod
+   def get_approx_data(function=function_exp, bounds=[-6, 6]):
+      x1 = generate_array(bounds[0], bounds[1], 1/2)
+      x2 = generate_array(bounds[0], bounds[1], 1)
+      y1 = Approx.generate_y(x1, function)
+      y2 = Approx.generate_y(x2, function)
+      x_real = generate_array(bounds[0], bounds[1])
+      y_real = Approx.generate_y(x_real, function)
+      return x1, x2, y1, y2, x_real, y_real
+
+   @staticmethod
+   def plot_lagrange():
+      x1, x2, y1, y2, x_real, y_real = Approx.get_approx_data()
+
+      sp = create_subplot()
+      sol1 = np.polynomial.polynomial.Polynomial(
+          Approx.lagrange(x1, y1).coef[::-1])
+      sol2 = np.polynomial.polynomial.Polynomial(
+          Approx.lagrange(x2, y2).coef[::-1])
+
+      plt_append(
+          sp, x_real, y_real, f"Исходные данные (y={Approx.function_exp})", "--b")
+      plt_append(
+          sp, x_real, sol1(np.array(x_real)), f"f1 = lagrange, кол-во точек = {len(x1)}", "-m")
+      plt_append(
+          sp, x_real, sol2(np.array(x_real)), f"f2 = lagrange, кол-во точек = {len(x2)}", "-r")
+      plt_append(
+          sp, x1, y1, f"Исходные точки для f1", ".m")
+      plt_append(
+          sp, x2, y2, f"Исходные точки для f2", ".r")
+
+      sp.set_title("scipy.interpolate.lagrange")
+      sp.legend(loc='lower left')
+
+   @staticmethod
+   def plot_spline():
+      x1, x2, y1, y2, x_real, y_real = Approx.get_approx_data()
+      d1, d2 = Approx.get_function_exp_der(x1, x2)
+
+      for interpolator in [sitp.CubicSpline,
+                           sitp.PchipInterpolator,
+                           sitp.CubicHermiteSpline,
+                           sitp.Akima1DInterpolator]:
+         sp = create_subplot()
+
+         if interpolator.__name__ != "CubicHermiteSpline":
+            args1 = x1, y1
+            args2 = x2, y2
+         else:
+            args1 = x1, y1, d1
+            args2 = x2, y2, d2
+
+         sol1 = interpolator(*args1)
+         sol2 = interpolator(*args2)
+         plt_append(
+             sp, x_real, y_real, f"Исходные данные (y={Approx.function_exp})", "--b")
+         plt_append(
+             sp, x_real, sol1(np.array(x_real)), f"f1 = {interpolator.__name__}, кол-во точек = {len(x1)}", "-m")
+         plt_append(
+             sp, x_real, sol2(np.array(x_real)), f"f2 = {interpolator.__name__}, кол-во точек = {len(x2)}", "-r")
+         plt_append(
+             sp, x1, y1, f"Исходные точки для f1", ".m")
+         plt_append(
+             sp, x2, y2, f"Исходные точки для f2", ".r")
+
+         sp.set_title(f"scipy.interpolate.{interpolator.__name__}")
+         sp.legend(loc='lower left')
+
+   @staticmethod
+   def linear(x, a, b):
+      return a*x + b
+
+   @staticmethod
+   def quadratic(x, a, b, c):
+      return a * (x**2) + (b*x) + c
+
+   @staticmethod
+   def fract(x, a, b, c):
+      return x / (a * x + b) - c
+
+   @staticmethod
+   def noise_y(y, rng):
+      diff = max(y) - min(y)
+      noise_coeff = diff*(10/100)
+      return y + (noise_coeff * rng.normal(size=len(y)))
+
+   @staticmethod
+   def plot_least_squares_curvefit():
+      rng = np.random.default_rng()
+      bounds = [3, 6]
+      x1, x2, y1, y2, x_real, y_real = Approx.get_approx_data(
+          Approx.least_sq_exp, bounds)
+      x_real = np.array(x_real)
+
+      y_real = Approx.noise_y(y_real, rng)
+      base_functions = [Approx.linear,
+                        Approx.quadratic, (Approx.fract, "x/(ax+b)")]
+
+      sp = create_subplot()
+      plt_append(
+          sp, x_real, y_real, f"y={Approx.least_sq_exp} на [{bounds[0]};{bounds[1]}], с шумом", ".b")
+      for bf in base_functions:
+         if isinstance(bf, tuple):
+            bf, desc = bf[0], bf[1]
+         else:
+            bf, desc = bf, None
+         optimal_params, _ = sopt.curve_fit(bf, x_real, y_real)
+         desc_str = f" ({desc}) " if desc is not None else ""
+         plt_append(
+             sp, x_real, bf(np.array(x_real), *optimal_params),
+             f"МНК, вид функции - {bf.__name__}{desc_str}", "-")
+      sp.set_title(f"scipy.optimize.curve_fit")
+      sp.legend(loc='lower left')
+
+   @staticmethod
+   def plot_least_squares():
+      rng = np.random.default_rng()
+
+      def exponential(x, a, b, c):
+         return np.sin(x) * np.sqrt(np.abs(x))
+      exponential.str = "np.sin(x) * np.sqrt(np.abs(x))"
+
+      def gen_y(x, a, b, c, noise=0., n_outliers=0):
+         y = exponential(x, a, b, c)
+         error = noise * rng.standard_normal(x.size)
+         outliers = rng.integers(0, x.size, n_outliers)
+         error[outliers] *= 10
+         return y + error
+
+      def loss(params, x, y):
+         return (exponential(x, params[0], params[1], params[2])) - y
+      params0 = np.array([0.1, 1, 0])
+      bounds = [-5, 3]
+      params_real = (3, 1, 5)
+      x_approx = np.array(generate_array(bounds[0], bounds[1], 4))
+      y_approx = np.array(gen_y(x_approx, *params_real,
+                                noise=0.3, n_outliers=4))
+
+      params_lsq = sopt.least_squares(
+          loss, params0, loss='linear', args=(x_approx, y_approx)).x
+      params_soft_l1 = sopt.least_squares(
+          loss, params0, loss='soft_l1', args=(x_approx, y_approx),f_scale=0.1).x
+      params_cauchy = sopt.least_squares(
+          loss, params0, loss='cauchy', args=(x_approx, y_approx), f_scale=2).x
+
+      x_real = np.array(generate_array(bounds[0], bounds[1]))
+      y_real = np.array(gen_y(x_real, *params_real, 0, 0))
+
+      sp = create_subplot()
+      sp.plot(x_real, y_real, "-b",
+              label=f"y={exponential.str} на [{bounds[0]};{bounds[1]}]")
+      sp.plot(x_approx, y_approx, ".r", label=f"Табличные значения с шумом")
+      sp.plot(x_real, gen_y(x_real, *params_lsq), color="green",
+              label=f"loss=\"linear\"", linestyle=(0, (5, 10)))
+      sp.plot(x_real, gen_y(x_real, *params_soft_l1), color="magenta",
+              label=f"loss=\"soft_l1\"", linestyle=(5, (5, 10)))
+      sp.plot(x_real, gen_y(x_real, *params_cauchy), color="black",
+              label=f"loss=\"cauchy\"", linestyle=(7, (5, 10)))
+
+      sp.set_title(f"scipy.optimize.least_squares")
+      sp.legend(loc='lower left')
+
+   @staticmethod
+   def plot(method: str = "all"):
+      if method in ["lagrange", "all"]:
+         Approx.plot_lagrange()
+      if method in ["spline", "all"]:
+         Approx.plot_spline()
+      if method in ["least_squares_curvefit", "all"]:
+         Approx.plot_least_squares_curvefit()
+      if method in ["least_squares", "all"]:
+         Approx.plot_least_squares()
+      plt.ylabel("y")
+      plt.xlabel("x")
+      plt.show()
+
 
 def main():
-   # NonLinear.plot()
+   NonLinear.plot()
    SLE.print()
+   Approx.plot()
 
 
 if __name__ == "__main__":