added stejskal tanner plane model and test

dmipy/signal_models/plane_models.py

@@ -11,6 +11,67 @@
 ]
 
 
+class P2PlaneStejskalTannerApproximation(ModelProperties):
+    r""" Stejskal-Tanner approximation of diffusion between two infinitely
+    large parallel planes. Assumes short-gradient pulse (SGP) approximation
+    (pulse length towards zero) and the long diffusion time limit (pulse
+    separation towards infinity). We follow the notation of Balinov [1]_.
+
+    References
+    ----------
+    .. [1] Balinov, Balin, et al. "The NMR self-diffusion method applied to
+        restricted diffusion. Simulation of echo attenuation from molecules in
+        spheres and between planes." Journal of Magnetic Resonance, Series A
+        104.1 (1993): 17-25.
+    """
+    _parameter_ranges = {
+        'diameter': (1e-2, 20)
+    }
+
+    _parameter_scales = {
+        'diameter': DIAMETER_SCALING
+    }
+
+    _parameter_types = {
+        'diameter': 'plane'
+    }
+    _model_type = 'NMRModel'
+
+    def __init__(self, diameter=None):
+        self.diameter = diameter
+
+    def plane_attenuation(self, q, diameter):
+        "Equation 6 in Balinov et al. (1993)."
+        q_argument = 2 * np.pi * q * diameter
+        return 2 * (1 - np.cos(q_argument)) / q_argument ** 2
+
+    def __call__(self, acquisition_scheme, **kwargs):
+        r'''
+        Calculates the signal attenuation.
+
+        Parameters
+        ----------
+        acquisition_scheme : DmipyAcquisitionScheme instance,
+            An acquisition scheme that has been instantiated using dMipy.
+        kwargs: keyword arguments to the model parameter values,
+            Is internally given as **parameter_dictionary.
+
+        Returns
+        -------
+        attenuation : float or array, shape(N),
+            signal attenuation
+        '''
+        q = acquisition_scheme.qvalues
+        diameter = kwargs.get('diameter', self.diameter)
+
+        E_plane = np.ones_like(q)
+        q_nonzero = q > 0
+        E_plane[q_nonzero] = self.plane_attenuation(
+            q[q_nonzero], diameter
+        )
+        return E_plane
+
+
 class P3PlaneCallaghanApproximation(ModelProperties):
     r"""
     The Callaghan model [1]_ of diffusion between two parallel infinite plates.

dmipy/signal_models/tests/test_soderman.py

@@ -1,10 +1,36 @@
 from numpy.testing import assert_almost_equal
 import numpy as np
-from dmipy.signal_models import cylinder_models, sphere_models
+from dmipy.signal_models import plane_models, cylinder_models, sphere_models
 from dmipy.core.acquisition_scheme import (
     acquisition_scheme_from_qvalues,)
 
 
+def test_RTPP_to_diameter_soderman(samples=1000):
+    """This tests if the RTPP of the plane relates correctly to the diameter
+    of the plane."""
+    diameter = 10e-6
+
+    delta = np.tile(1e-10, samples)  # delta towards zero
+    Delta = np.tile(1e10, samples)  # Delta towards infinity
+    qvals_perp = np.linspace(0, 10e6, samples)
+    n_perp = np.tile(np.r_[1., 0., 0.], (samples, 1))
+    scheme = acquisition_scheme_from_qvalues(
+        qvals_perp, n_perp, delta, Delta)
+
+    soderman = plane_models.P2PlaneStejskalTannerApproximation(
+        diameter=diameter)
+
+    E_soderman = soderman(scheme)
+
+    rtpp_soderman = 2 * np.trapz(
+        E_soderman, x=qvals_perp
+    )
+
+    diameter_soderman = 1 / rtpp_soderman
+
+    assert_almost_equal(diameter_soderman, diameter, 7)
+
+
 def test_RTAP_to_diameter_soderman(samples=1000):
     """This tests if the RTAP of the cylinder relates correctly to the diameter
     of the cylinder."""