Merge branch 'qgaussian_derivative' into release/v0.21.3

contributors_and_credits.txt

@@ -11,5 +11,6 @@ CERN contributors:
  - K. Paraschou
  - M. Schwinzerl
  - F. Soubelet
+ - E. Waagaard
 
 The Particle In Cell implementation is largely based on the PyPIC package (https://github.com/pycomplete/pypic)

examples/longitudinal_kick_in_spacecharge/004_qgaussian_derivative.py

@@ -0,0 +1,63 @@
+# copyright ################################# #
+# This file is part of the Xfields Package.   #
+# Copyright (c) CERN, 2021.                   #
+# ########################################### #
+
+import numpy as np
+from xfields import LongitudinalProfileQGaussian
+import xobjects as xo
+import matplotlib.pyplot as plt
+
+plt.rcParams.update(
+    {
+        "font.family": "serif",
+        "font.size": 20,
+        "axes.titlesize": 20,
+        "axes.labelsize": 18,
+        "xtick.labelsize": 18,
+        "ytick.labelsize": 18,
+        "legend.fontsize": 15,
+        "figure.titlesize": 20,
+    }
+)
+
+# Longitudinal example parameters
+z0 = 0.1
+sigma_z = 0.2
+npart = 1e11
+
+test_context = xo.ContextCpu()
+#test_context = xo.ContextCupy()
+
+for qq in [0.0, 0.5, 0.95, 1.05, 1.3]:
+    lprofile = LongitudinalProfileQGaussian(
+            _context=test_context,
+            number_of_particles=npart,
+            sigma_z=sigma_z,
+            z0=z0,
+            q_parameter=qq)
+
+    # Select range relevant for derivative continuity
+    if qq < 1:
+        z = np.linspace(-0.347, 0.5, 1_000_000)
+    else:
+        z = np.linspace(-3., 3., 1_000_000)
+    z_dev = test_context.nparray_to_context_array(z)
+    lden_dev = lprofile.line_density(z_dev)
+    lden = test_context.nparray_from_context_array(lden_dev)
+
+    lderivative_dev = lprofile.line_derivative(z_dev)
+    lderivative = test_context.nparray_from_context_array(lderivative_dev)
+
+    numerical_derivative = np.gradient(lden, z)
+
+    print('q = {:.2f} max relative difference anal. vs num. : {:.3e}'.format(qq, max((lderivative - numerical_derivative) / numerical_derivative)))
+
+    fig, ax = plt.subplots(1, 1, figsize=(8, 6))
+    ax.plot(z, lderivative, label='Analytical derivative')
+    ax.plot(z, numerical_derivative, ls='--', label='Numerical derivative')
+    ax.text(0.83, 0.92, 'q={:.2f}'.format(qq), color='k', fontsize=15.5, transform=ax.transAxes)
+    ax.set_ylabel('Function value')
+    ax.set_xlabel('Zeta [m]')
+    ax.legend(loc='lower left')
+    plt.show()

tests/test_profiles.py

@@ -34,3 +34,33 @@ def test_qgauss(test_context):
         assert np.isclose(area, npart)
         assert np.isclose(z_mean, z0)
         assert np.isclose(z_std, sigma_z)
+
+@for_all_test_contexts
+def test_qgauss_derivative(test_context):
+    z0 = 0.1
+    sigma_z = 0.2
+    npart = 1e11
+
+    for qq in [0, 0.5, 0.95, 1.05, 1.3]:
+        lprofile = LongitudinalProfileQGaussian(
+                _context=test_context,
+                number_of_particles=npart,
+                sigma_z=sigma_z,
+                z0=z0,
+                q_parameter=qq)
+
+        # Select range relevant for derivative continuity
+        if qq < 1:
+            z = np.linspace(-0.347, 0.5, 1_000_000)
+        else:
+            z = np.linspace(-3., 3., 1_000_000)
+        z_dev = test_context.nparray_to_context_array(z)
+        lden_dev = lprofile.line_density(z_dev)
+        lden = test_context.nparray_from_context_array(lden_dev)
+
+        lderivative_dev = lprofile.line_derivative(z_dev)
+        lderivative = test_context.nparray_from_context_array(lderivative_dev)
+
+        numerical_derivative = np.gradient(lden, z)
+
+        assert np.isclose(lderivative, numerical_derivative, rtol=1e-5, atol=1e3).all()

xfields/longitudinal_profiles/qgaussian.py

@@ -32,6 +32,12 @@ class LongitudinalProfileQGaussian(xo.HybridClass):
         ]
 
     _kernels = {'line_density_qgauss':
+        xo.Kernel(args=[xo.Arg(xo.ThisClass, name='prof'),
+                        xo.Arg(xo.Int64, name='n'),
+                        xo.Arg(xo.Float64, pointer=True, name='z'),
+                        xo.Arg(xo.Float64, pointer=True, name='res')],
+                  n_threads='n'),
+                  'line_derivative_qgauss':
         xo.Kernel(args=[xo.Arg(xo.ThisClass, name='prof'),
                         xo.Arg(xo.Int64, name='n'),
                         xo.Arg(xo.Float64, pointer=True, name='z'),
@@ -177,4 +183,15 @@ def line_density(self, z):
         context.kernels.line_density_qgauss(prof=self._xobject, n=len(z), z=z, res=res)
 
         return res
+
+    def line_derivative(self, z):
+        context = self._buffer.context
+        res = context.zeros(len(z), dtype=np.float64)
+
+        if 'line_derivative_qgauss' not in context.kernels.keys():
+            self.compile_kernels()
+
+        context.kernels.line_derivative_qgauss(prof=self._xobject, n=len(z), z=z, res=res)
+
+        return res
 

xfields/longitudinal_profiles/qgaussian_src/qgaussian.h

@@ -80,7 +80,10 @@ double LongitudinalProfileQGaussian_line_density_derivative_scalar(
     else{
     	double exponent = 1./(1.-q);
 	if (z<z_max && z>z_min){
-		return -9999.0;
+	    double z_m_z0 = z - z0;
+    		double q_exp_arg =  -(beta_param*z_m_z0*z_m_z0 );
+    		double q_exp_res = pow((1.+(1.-q)*q_exp_arg), exponent-1.);
+    		return -2*factor*beta_param*z_m_z0*q_exp_res;
 	}
 	else{
 		return 0;
@@ -104,4 +107,19 @@ void line_density_qgauss(LongitudinalProfileQGaussianData prof,
    }//end_vectorize
 }
 
+
+/*gpukern*/
+void line_derivative_qgauss(LongitudinalProfileQGaussianData prof,
+		               const int64_t n,
+		  /*gpuglmem*/ const double* z, 
+		  /*gpuglmem*/       double* res){
+
+   #pragma omp parallel for //only_for_context cpu_openmp 
+   for(int ii; ii<n; ii++){ //vectorize_over ii n 
+
+       res[ii] = LongitudinalProfileQGaussian_line_density_derivative_scalar(prof, z[ii]);
+
+   }//end_vectorize
+}
+
 #endif