Changeset cbd37a7 in sasmodels

Timestamp:

Mar 18, 2016 12:10:44 AM (8 years ago)

Author:

Paul Kienzle <pkienzle@…>

Branches:

master, core_shell_microgels, costrafo411, magnetic_model, release_v0.94, release_v0.95, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests

Children:

c094758

Parents:

c515b1b

Message:

compare cephes bessel function against multiprecision math

Files:

• explore/J1c.py (modified) (5 diffs)
• sasmodels/models/bessel.py (modified) (2 diffs)

explore/J1c.py

@@ -9 +9 @@
 
 
-SHOW_DIFF = True  # True if show diff rather than function value
+SHOW_DIFF = True # True if show diff rather than function value
+#SHOW_DIFF = False # True if show diff rather than function value
 LINEAR_X = False  # True if q is linearly spaced instead of log spaced
+#LINEAR_X = True # True if q is linearly spaced instead of log spaced
+FUNCTION = "2*J1(x)/x"
 
-def mp_J1c(vec, bits=500):
+def mp_fn(vec, bits=500):
     """
     Direct calculation using sympy multiprecision library.
     """
     with mp.workprec(bits):
-        return [_mp_J1c(mp.mpf(x)) for x in vec]
+        return [_mp_fn(mp.mpf(x)) for x in vec]
 
-def _mp_J1c(x):
+def _mp_fn(x):
     """
-    Helper funciton for mp_j1c
+    Actual function that gets evaluated.  The caller just vectorizes.
     """
     return mp.mpf(2)*mp.j1(x)/x
 
-def np_J1c(x, dtype):
+def np_fn(x, dtype):
     """
     Direct calculation using scipy.
@@ -33 +36 @@
     return np.asarray(2, dtype)*J1(x)/x
 
-def cephes_J1c(x, dtype, n):
+def sasmodels_fn(x, dtype, platform='ocl'):
     """
     Calculation using pade approximant.
     """
-    f = np.float64 if np.dtype(dtype) == np.float64 else np.float32
-    x = np.asarray(x, dtype)
-    ans = np.empty_like(x)
-    ax = abs(x)
-
-    # Branch a
-    a_idx = ax < f(8.0)
-    a_xsq = x[a_idx]**2
-    a_coeff1 = list(reversed((72362614232.0, -7895059235.0, 242396853.1, -2972611.439, 15704.48260, -30.16036606)))
-    a_coeff2 = list(reversed((144725228442.0, 2300535178.0, 18583304.74, 99447.43394, 376.9991397, 1.0)))
-    a_ans1 = np.polyval(np.asarray(a_coeff1[n:], dtype), a_xsq)
-    a_ans2 = np.polyval(np.asarray(a_coeff2[n:], dtype), a_xsq)
-    ans[a_idx] = f(2.0)*a_ans1/a_ans2
-
-    # Branch b
-    b_idx = ~a_idx
-    b_ax = ax[b_idx]
-    b_x = x[b_idx]
-
-    b_y = f(64.0)/(b_ax**2)
-    b_xx = b_ax - f(2.356194491)
-    b_coeff1 = list(reversed((1.0, 0.183105e-2, -0.3516396496e-4, 0.2457520174e-5, -0.240337019e-6)))
-    b_coeff2 = list(reversed((0.04687499995, -0.2002690873e-3, 0.8449199096e-5, -0.88228987e-6, 0.105787412e-6)))
-    b_ans1 = np.polyval(np.asarray(b_coeff1[n:], dtype),b_y)
-    b_ans2 = np.polyval(np.asarray(b_coeff2[n:], dtype), b_y)
-    b_sn, b_cn = np.sin(b_xx), np.cos(b_xx)
-    ans[b_idx] = np.sign(b_x)*np.sqrt(f(0.636619772)/b_ax) * (b_cn*b_ans1 - (f(8.0)/b_ax)*b_sn*b_ans2)*f(2.0)/b_x
-
-    return ans
-
-def div_J1c(x, dtype):
-    f = np.float64 if np.dtype(dtype) == np.float64 else np.float32
-    x = np.asarray(x, dtype)
-    return f(2.0)*np.asarray([_J1(xi, f)/xi for xi in x], dtype)
-
-def _J1(x, f):
-    ax = abs(x)
-    if ax < f(8.0):
-        y = x*x
-        ans1 = x*(f(72362614232.0)
-                  + y*(f(-7895059235.0)
-                  + y*(f(242396853.1)
-                  + y*(f(-2972611.439)
-                  + y*(f(15704.48260)
-                  + y*(f(-30.16036606)))))))
-        ans2 = (f(144725228442.0)
-                  + y*(f(2300535178.0)
-                  + y*(f(18583304.74)
-                  + y*(f(99447.43394)
-                  + y*(f(376.9991397)
-                  + y)))))
-        return ans1/ans2
-    else:
-        y = f(64.0)/(ax*ax)
-        xx = ax - f(2.356194491)
-        ans1 = (f(1.0)
-                  + y*(f(0.183105e-2)
-                  + y*(f(-0.3516396496e-4)
-                  + y*(f(0.2457520174e-5)
-                  + y*f(-0.240337019e-6)))))
-        ans2 = (f(0.04687499995)
-                  + y*(f(-0.2002690873e-3)
-                  + y*(f(0.8449199096e-5)
-                  + y*(f(-0.88228987e-6)
-                  + y*f(0.105787412e-6)))))
-        sn, cn = np.sin(xx), np.cos(xx)
-        ans = np.sqrt(f(0.636619772)/ax) * (cn*ans1 - (f(8.0)/ax)*sn*ans2)
-        return -ans if (x < f(0.0)) else ans
+    from sasmodels import core, data, direct_model
+    model = core.load_model('bessel', dtype=dtype)
+    calculator = direct_model.DirectModel(data.empty_data1D(x), model)
+    return calculator(background=0)
 
 def plotdiff(x, target, actual, label):
@@ -113 +52 @@
     """
     if SHOW_DIFF:
-        err = np.clip(abs((target-actual)/target), 0, 1)
+        err = abs((target-actual)/target)
+        #err = np.clip(err, 0, 1)
         pylab.loglog(x, err, '-', label=label)
     else:
@@ -119 +59 @@
         pylab.semilogx(x, np.clip(actual,*limits),  '-', label=label)
 
-def compare(x, precision):
+def compare(x, precision, target):
     r"""
     Compare the different computation methods using the given precision.
     """
-    target = np.asarray(mp_J1c(x), 'double')
-    #plotdiff(x, target, mp_J1c(x, 11), 'mp 11 bits')
-    plotdiff(x, target, np_J1c(x, precision), 'direct '+precision)
-    plotdiff(x, target, cephes_J1c(x, precision, 0), 'cephes '+precision)
-    #plotdiff(x, target, cephes_J1c(x, precision, 1), 'cephes '+precision)
-    #plotdiff(x, target, div_J1c(x, precision), 'cephes 2 J1(x)/x '+precision)
+    #plotdiff(x, target, mp_fn(x, 11), 'mp 11 bits')
+    plotdiff(x, target, np_fn(x, precision), 'numpy '+precision)
+    plotdiff(x, target, sasmodels_fn(x, precision, 0), 'sasmodels '+precision)
     pylab.xlabel("qr (1/Ang)")
     if SHOW_DIFF:
         pylab.ylabel("relative error")
     else:
-        pylab.ylabel("2 J1(x)/x")
+        pylab.ylabel(FUNCTION)
         pylab.semilogx(x, target,  '-', label="true value")
     if LINEAR_X:
@@ -147 +84 @@
     else:
         qr = np.logspace(-3,5,400)
+    target = np.asarray(mp_fn(qr), 'double')
     pylab.subplot(121)
-    compare(qr, 'single')
+    compare(qr, 'single', target)
     pylab.legend(loc='best')
     pylab.subplot(122)
-    compare(qr, 'double')
+    compare(qr, 'double', target)
     pylab.legend(loc='best')
-    pylab.suptitle('2 J1(x)/x')
+    pylab.suptitle(FUNCTION)
 
 if __name__ == "__main__":

sasmodels/models/bessel.py

@@ -67 +67 @@
 #Bessel
 parameters = [
+    ["ignored", "", 0.0, [-inf, inf], "", "no parameterless functions"],
              ]
 
-source = ["lib/polevl.c", "lib/j1d.c"]
+source = ["lib/polevl.c", "lib/j1_cephes.c"]
 
 # No volume normalization despite having a volume parameter
@@ -77 +78 @@
 
 Iq = """
-    return j1(q);
+    return 2.0*j1(q)/q;
     """