DOC: math notations for mono sources

Author: hagenw

doc/math-definitions.rst

@@ -8,3 +8,6 @@
     \newcommand{\scalarprod}[2]{\left\langle#1,#2\right\rangle}
     \renewcommand{\vec}[1]{\mathbf{#1}}
     \newcommand{\wc}{\frac{\omega}{c}}
+    \newcommand{\w}{\omega}
+    \newcommand{\x}{\vec{x}}
+    \newcommand{\n}{\vec{n}}

sfs/mono/source.py

@@ -1,5 +1,7 @@
 """Compute the sound field generated by a sound source.
 
+.. include:: math-definitions.rst
+
 .. plot::
     :context: reset
 
@@ -31,7 +33,7 @@
 
 
 def point(omega, x0, n0, grid, c=None):
-    """Sound pressure of a point source.
+    r"""Sound pressure of a point source.
 
     Parameters
     ----------
@@ -54,11 +56,9 @@ def point(omega, x0, n0, grid, c=None):
 
     Notes
     -----
-    ::
+    .. math::
 
-                      1  e^(-j w/c |x-x0|)
-        G(x-x0, w) = --- -----------------
-                     4pi      |x-x0|
+        G(\x-\x_0,\w) = \frac{1}{4\pi} \frac{\e{-\i\wc|\x-\x_0|}}{|\x-\x_0|}
 
     Examples
     --------
@@ -188,11 +188,11 @@ def point_dipole(omega, x0, n0, grid, c=None):
 
     Notes
     -----
-    ::
+    .. math::
 
-         d                1   / iw       1    \   (x-x0) n0
-        ---- G(x-x0,w) = --- | ----- + ------- | ----------- e^(-i w/c |x-x0|)
-        d ns             4pi  \  c     |x-x0| /   |x-x0|^2
+        G(\x-\x_0,\w) = \frac{1}{4\pi} \left(\i\wc + \frac{1}{|\x-\x_0|}\right)
+            \frac{\scalarprod{\x-\x_0}{\n_\text{s}}}{|\x-\x_0|^2}
+            \e{-\i\wc|\x-\x_0}
 
     Examples
     --------
@@ -406,16 +406,15 @@ def point_image_sources(omega, x0, n0, grid, L, max_order, coeffs=None,
 
 
 def line(omega, x0, n0, grid, c=None):
-    """Line source parallel to the z-axis.
+    r"""Line source parallel to the z-axis.
 
     Note: third component of x0 is ignored.
 
     Notes
     -----
-    ::
+    .. math::
 
-                           (2)
-        G(x-x0, w) = -j/4 H0  (w/c |x-x0|)
+        G(\x-\x_0,\w) = -\frac{\i}{4} \Hankel{2}{0}{\wc|\x-\x_0|}
 
     Examples
     --------
@@ -486,17 +485,15 @@ def line_velocity(omega, x0, n0, grid, c=None):
 
 
 def line_dipole(omega, x0, n0, grid, c=None):
-    """Line source with dipole characteristics parallel to the z-axis.
+    r"""Line source with dipole characteristics parallel to the z-axis.
 
     Note: third component of x0 is ignored.
 
     Notes
     -----
-    ::
-
-                           (2)
-        G(x-x0, w) = jk/4 H1  (w/c |x-x0|) cos(phi)
+    .. math::
 
+        G(\x-\x_0,\w) = \frac{\i k}{4} \Hankel{2}{1}{\wc|\x-\x_0|} \cos{\phi}
 
     """
     k = util.wavenumber(omega, c)
@@ -577,7 +574,7 @@ def line_dirichlet_edge(omega, x0, grid, alpha=3/2*np.pi, Nc=None, c=None):
 
 
 def plane(omega, x0, n0, grid, c=None):
-    """Plane wave.
+    r"""Plane wave.
 
     Parameters
     ----------
@@ -600,9 +597,9 @@ def plane(omega, x0, n0, grid, c=None):
 
     Notes
     -----
-    ::
+    .. math::
 
-        G(x, w) = e^(-i w/c n x)
+        G(\x,\w) = \e{-\i\wc\n\x}
 
     Examples
     --------
@@ -624,7 +621,7 @@ def plane(omega, x0, n0, grid, c=None):
 
 
 def plane_velocity(omega, x0, n0, grid, c=None):
-    """Velocity of a plane wave.
+    r"""Velocity of a plane wave.
 
     Parameters
     ----------
@@ -647,9 +644,9 @@ def plane_velocity(omega, x0, n0, grid, c=None):
 
     Notes
     -----
-    ::
+    .. math::
 
-        V(x, w) = 1/(rho c) e^(-i w/c n x) n
+        V(\x,\w) = \frac{1}{\rho c} \e{-\i\wc\n\x} \n
 
     Examples
     --------
@@ -671,7 +668,7 @@ def plane_velocity(omega, x0, n0, grid, c=None):
 
 
 def plane_averaged_intensity(omega, x0, n0, grid, c=None):
-    """Averaged intensity of a plane wave.
+    r"""Averaged intensity of a plane wave.
 
     Parameters
     ----------
@@ -694,9 +691,9 @@ def plane_averaged_intensity(omega, x0, n0, grid, c=None):
 
     Notes
     -----
-    ::
+    .. math::
 
-        I(x, w) = 1/(2 rho c) n
+        I(\x,\w) = \frac{1}{2\rho c} \n
 
     """
     if c is None: