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petercorke · petercorke · commit 2f4ef0a3588f · 2021-04-02T15:28:17.000+10:00
diff --git a/spatialmath/base/matrix.py b/spatialmath/base/matrix.py
@@ -0,0 +1,50 @@
+import numpy as np
+from spatialmath import base
+
+def numjac(f, x, dx=1e-8, tN=0, rN=0):
+    r"""
+    Numerically compute Jacobian of function
+
+    :param f: the function, returns an m-vector
+    :type f: callable
+    :param x: function argument
+    :type x: ndarray(n)
+    :param dx: the numerical perturbation, defaults to 1e-8
+    :type dx: float, optional
+    :param N: function returns SE(N) matrix, defaults to 0
+    :type N: int, optional
+    :return: Jacobian matrix
+    :rtype: ndarray(m,n)
+
+    Computes a numerical approximation to the Jacobian for ``f(x)`` where 
+    :math:`f: \mathbb{R}^n \mapsto \mathbb{R}^m`.
+
+    Uses first-order difference :math:`J[:,i] = (f(x + dx) - f(x)) / dx`.
+
+    If ``N`` is 2 or 3, then it is assumed that the function returns
+    an SE(N) matrix which is converted into a Jacobian column comprising the
+    translational Jacobian followed by the rotational Jacobian.
+    """
+    x = np.array(x)
+    Jcol = []
+    J0 = f(x)
+    I = np.eye(len(x))
+    f0 = np.array(f(x))
+    for i in range(len(x)):
+        fi = np.array(f(x + I[:,i] * dx))
+        Ji = (fi - f0) / dx
+
+        if tN > 0:
+            t = Ji[:tN,tN]
+            r = base.vex(Ji[:tN,:tN] @ J0[:tN,:tN].T)
+            Jcol.append(np.r_[t, r])
+        elif rN > 0:
+            R = Ji[:rN,:rN]
+            r = base.vex(R @ J0[:rN,:rN].T)
+            Jcol.append(r)
+        else:
+            Jcol.append(Ji)
+        # print(Ji)
+
+    return np.c_[Jcol].T
+
