refactored standard and neural network state space estimators

.gitignore

 *.ini
+*.ipynb
 pytorchbridge.egg-info
-__pycache__/
\ No newline at end of file
+__pycache__/
+.vscode/
+.ipynb_checkpoints/
\ No newline at end of file

README.md

@@ -34,7 +34,7 @@ Three classes are defined:
 
 ### `Trapezoid`
 
-Uses trapezoid integration rule to integrate `(1)`. The `dxdt` and `y` methods need to be overridden.
+Uses trapezoid integration rule to integrate `(1)`. `dxdt` and `y` methods can be overridden or provided as arguments.
 
 ### `LTISystem`
 

pystatespace/__init__.py

+from .standard import Trapezoid
+from .standard import LTISystem
+from .standard import SS_ODE

pystatespace/neural.py

+from typing import Union, Callable, Tuple
+from numbers import Number
+
+import numpy as np
+import torch
+from torch import Tensor
+import torch.nn as nn
+
+
+
+class Trapezoid(nn.Module):
+    """
+    A state-space model that uses trapezoid integration to predict state variables.
+    `dxdt` and `y` methods need to be overridden.
+    """
+
+
+    def __init__(self, dims: int, outputs: int, dx: Union[Callable, nn.Module]=None,
+        out: Union[Callable, nn.Module]=None, tstep: float=1e-4):
+        """ 
+        Arguments:
+            dims {int} -- Number of state-space variables.
+            outputs {int} -- Number of output variables.
+            dx {Callable} -- A function with a signature (time, x, u) -> np.ndarray
+                that returns dx/dt. `x, u` are vectors. `time` is a float.
+            out {Callable} -- A function with a signature (time, x, u) -> np.ndarray
+                that returns y. `x, u` are vectors. `time` is a float.
+        
+        Keyword Arguments:
+            tstep {float} -- Minimum size of simulation step (default: {1e-4})
+        """
+        super().__init__()
+        self.dims = dims
+        self.outputs = outputs
+        self.dx = dx
+        self.out = out
+        self.tstep = tstep
+
+
+    def create_parameters(self):
+        self.b_ux = nn.Parameter(Tensor(self.dims, 1))
+        self.w_ux = nn.Parameter(Tensor(self.dims, self.dims))
+        self.w_xx = nn.Parameter(Tensor(self.dims, self.dims))
+
+
+    def reset_parameters(self):
+        self.b_ux.data = torch.zeros(self.dims, 1)
+        self.w_ux.data = torch.eye(self.dims) * self.tstep
+        self.w_xx.data = torch.eye(self.dims)
+
+
+    def dxdt(self, t: float, x: np.ndarray, u: np.ndarray) -> np.ndarray:
+        if self.dxdt is not None:
+            return self.dx(t, x, u)
+        raise NotImplementedError
+
+
+    def y(self, t: float, x: np.ndarray, u: np.ndarray) -> np.ndarray:
+        if self.out is not None:
+            return self.out(t, x, u)
+        raise NotImplementedError
+
+
+    def _init(self, x0, u):
+        self.create_parameters()
+        self.reset_parameters()
+        if isinstance(self.dx, nn.Module):
+            self.dx_ = self.dx.forward
+        if isinstance(self.out, nn.Module):
+            self.out_ = self.out.forward
+        
+        if isinstance(x0, torch.Tensor):
+            type_x0 = x0.dtype
+        elif isinstance(x0, np.ndarray):
+            type_x0 = torch.float32 if x0.dtype == np.float32 else torch.float64
+        else:
+            type_u = torch.float32
+
+        if isinstance(u, torch.Tensor):
+            type_u = u.dtype
+        elif isinstance(u, np.ndarray):
+            type_u = torch.float32 if u.dtype == np.float32 else torch.float64
+        else:
+            type_u = torch.float32
+        
+        if type_u == torch.float64 or type_x0 == torch.float64:
+            self.type_ = torch.float64
+        else:
+            self.type_ = torch.float32
+
+        self.to(self.type_)
+
+
+    def predict(self, t: np.ndarray, x0: np.ndarray=None, u: np.ndarray=None) \
+        -> Tuple[Tensor, Tensor]:
+        """
+        Generate system response to inputs. The system response is calculated through
+        trapezoid rule.
+
+        Arguments:
+            t {np.ndarray} -- The end time (float) or an array of time stamps for
+                the corresponding element in `u`.
+            x0 {np.ndarray} -- The initial state of the system.
+            u {np.ndarray} -- An `N x Inputs` array of inputs,
+
+        Returns:
+            np.ndarray -- array of shape `N x Outputs`,
+        """
+        self._init(x0, u)
+        xdim = self.dims
+        if isinstance(t, Number):
+            t = torch.from_numpy(np.linspace(0, t, len(u) + 1, endpoint=True)).to(self.type_)
+
+        xt = (torch.zeros(xdim) if x0 is None else torch.tensor(x0)).to(self.type_)
+        X = torch.zeros((len(t), self.dims)).to(self.type_)
+        X[0] = xt
+        Y = torch.zeros((len(t), self.outputs)).to(self.type_)
+        Y[0] = self.y(t[0], X[0], u[0])
+
+        for i in range(1, len(t)):
+            Dt = t[i] - t[i - 1]        # Time step in supplied data
+            dt = min(Dt, self.tstep)    # Time step to take per calculation
+            while True:
+                dx = torch.tensor(self.dxdt(t[i] - Dt, xt, u[i - 1])).to(self.type_)
+                xt = self.w_xx @ xt + (self.w_ux * dt) @ dx
+
+                Dt -= dt
+                dt = min(Dt, self.tstep)
+                if dt == 0: break
+            X[i] = xt
+            Y[i] = self.y(t[i], xt, u[i - 1])
+        return X, Y

pystatespace/state_space.py → pystatespace/standard.py

@@ -2,7 +2,7 @@
 Defines state space class for rough linear system modelling.
 """
 from numbers import Number
-from typing import Callable, Tuple, Any
+from typing import Callable, Tuple, Union
 
 import numpy as np
 from scipy.integrate import odeint
@@ -16,25 +16,36 @@ class Trapezoid:
     """
 
 
-    def __init__(self, dims: int, outputs: int, tstep: float=1e-4):
-        """ 
+    def __init__(self, dims: int, outputs: int, dx: Callable=None, out: Callable=None,
+                 tstep: float=1e-4):
+        """
         Arguments:
             dims {int} -- Number of state-space variables.
             outputs {int} -- Number of output variables.
+            dx {Callable} -- A function with a signature (time, x, u) -> np.ndarray
+                that returns dx/dt. `x, u` are vectors. `time` is a float.
+            out {Callable} -- A function with a signature (time, x, u) -> np.ndarray
+                that returns y. `x, u` are vectors. `time` is a float.
         
         Keyword Arguments:
             tstep {float} -- Minimum size of simulation step (default: {1e-4})
         """
         self.dims = dims
         self.outputs = outputs
+        self.dx = dx
+        self.out = out
         self.tstep = tstep
 
 
     def dxdt(self, t: float, x: np.ndarray, u: np.ndarray) -> np.ndarray:
+        if self.dxdt is not None:
+            return self.dx(t, x, u)
         raise NotImplementedError
 
 
     def y(self, t: float, x: np.ndarray, u: np.ndarray) -> np.ndarray:
+        if self.out is not None:
+            return self.out(t, x, u)
         raise NotImplementedError
 
 
@@ -53,11 +64,15 @@ class Trapezoid:
         Returns:
             np.ndarray -- array of shape `N x Outputs`,
         """
+        # t:    0   1   2   3   4   5
+        # x:    x0  (                   )
+        # u:        u   u   u   u   u   u
+        #
         xdim = self.dims
         if isinstance(t, Number):
-            t = np.linspace(0, t, len(u), endpoint=False)
+            t = np.linspace(0, t, len(u) + 1, endpoint=True)
 
-        xt = np.zeros(xdim) if x0 is None else x0
+        xt = np.zeros(xdim) if x0 is None else np.copy(x0)
         X = np.zeros((len(t), self.dims))
         X[0] = xt
         Y = np.zeros((len(t), self.outputs))
@@ -68,7 +83,7 @@ class Trapezoid:
             Dt = t[i] - t[i - 1]        # Time step in supplied data
             dt = min(Dt, self.tstep)    # Time step to take per calculation
             while True:
-                dx = self.dxdt(t[i] - Dt, xt, u[i])
+                dx = self.dxdt(t[i] - Dt, xt, u[i - 1])
                 # xt += 0.5 * dt * (dx + dxprev)
                 xt += dt * dx
 
@@ -76,7 +91,8 @@ class Trapezoid:
                 dt = min(Dt, self.tstep)
                 if dt == 0: break
             X[i] = xt
-            Y[i] = self.y(t[i], xt, u[i])
+            Y[i] = self.y(t[i], xt, u[i - 1])
+        # return X[1:], Y
         return X, Y
 
 
@@ -117,39 +133,10 @@ class LTISystem(Trapezoid):
 
 
 
-class SS_ODE:
-
-
-    def __init__(self, dims: int, outputs: int, dx: Callable, out: Callable,
-        tstep: float=1e-4):
-        """
-        Arguments:
-            dims {int} -- Number of state-space variables.
-            outputs {int} -- Number of output variables.
-            dx {Callable} -- A function with a signature (time, x, u) -> np.ndarray
-                that returns dx/dt. `x, u` are vectors. `time` is a float.
-            out {Callable} -- A function with a signature (time, x, u) -> np.ndarray
-                that returns y. `x, u` are vectors. `time` is a float.
-        
-        Keyword Arguments:
-            tstep {float} -- Maximum size of integration step (default: {1e-4})
-        """
-        self.dx = dx
-        self.out = out
-        self.tstep = tstep
-        self.dims = dims
-        self.outputs = outputs
-
-
-    def dxdt(self, t: float, x: np.ndarray, u: np.ndarray) -> np.ndarray:
-        return self.dx(t, x, u)
-
-
-    def y(self, t: float, x: np.ndarray, u: np.ndarray) -> np.ndarray:
-        return self.out(t, x, u)
+class SS_ODE(Trapezoid):
 
 
-    def predict(self, t: Any[float, np.ndarray], x0: np.ndarray, u: np.ndarray) \
+    def predict(self, t: Union[float, np.ndarray], x0: np.ndarray, u: np.ndarray) \
         -> Tuple[np.ndarray, np.ndarray]:
         if isinstance(t, Number):
             t = np.linspace(0, t, len(u), endpoint=False)
@@ -157,7 +144,7 @@ class SS_ODE:
         u = np.concatenate(([u[0]-u[0]], u), axis=0)
         X = np.zeros((len(t), self.dims))
         Y = np.zeros((len(t), self.outputs))
-        X[0] = np.zeros(self.dims) if x0 is None else x0
+        X[0] = np.zeros(self.dims) if x0 is None else np.copy(x0)
         Y[0] = self.y(t[0], X[0], u[0])
         for idx in range(1, len(t)):
             X[idx] = odeint(func=self.dxdt,

pystatespace/test.py

@@ -18,7 +18,7 @@ class TestTrapezoid(TestCase):
     def setUp(self):
         class _Trapezoid(Trapezoid):
             def dxdt(self, t, x, u):
-                return np.asarray([1., 1.])
+                return np.asarray([1., 1.]) + u
             def y(self, t, x, u):
                 return 1*x
         self.solver = _Trapezoid(dims=2, outputs=2, tstep=0.5)
@@ -26,7 +26,7 @@ class TestTrapezoid(TestCase):
 
     def test_integration(self):
         u = np.zeros(10)
-        t = np.arange(10) * 2
+        t = np.arange(10).astype(np.float32)
         x, y = self.solver.predict(t, np.asarray([0., 0.]), u)
         self.assertEqual(len(y), len(t), 'Input/output length mismatch.')
 
@@ -37,7 +37,7 @@ class TestSS_ODE(TestTrapezoid):
 
     def setUp(self):
         self.solver = SS_ODE(dims=2, outputs=2,
-                             dx=lambda t, x, u: np.asarray([1., 1.]),
+                             dx=lambda t, x, u: np.asarray([1., 1.]) + u,
                              out=lambda t, x, u: 1*x,
                              tstep=1.0)
 

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