Add tests.

2 files changed, 153 insertions, 1 deletions

diff --git a/Makefile b/Makefile
index 75de828..aec6c0b 100644
--- a/Makefile
+++ b/Makefile
@@ -13,4 +13,7 @@ $(TARGET): $(OBJECTS)
 clean:
 	-rm $(OBJECTS) $(TARGET)
 
-.PHONY: clean
+test: $(TARGET)
+	LD_LIBRARY_PATH=. ./test.py
+
+.PHONY: clean test
diff --git a/test.py b/test.py
new file mode 100755
index 0000000..5af80bc
--- /dev/null
+++ b/test.py
@@ -0,0 +1,149 @@
+#!/usr/bin/python
+
+import brill_data
+import numpy as np
+import sys
+
+def eval_residual_coeffs(bd, x, z):
+    X, Z = np.meshgrid(x, z)
+
+    psi     = bd.eval_psi(x, z)
+    d2psi_x = bd.eval_psi(x, z, (2, 0))
+    d2psi_z = bd.eval_psi(x, z, (0, 2))
+    dpsi_x  = bd.eval_psi(x, z, (1, 0))
+
+    d2psi_y = np.where(np.abs(X) < 1e-12, d2psi_x, dpsi_x / X)
+
+    d2q = bd.eval_q(x, z, (2, 0)) + bd.eval_q(x, z, (0, 2))
+
+    d2psi = d2psi_x + d2psi_y + d2psi_z
+
+    return d2psi + 0.25 * psi * d2q
+
+coeffs     = (10, 15, 20, 25, 30, 40, 50, 60, 80, 100)
+amplitudes = (1, 2, 4, 6)
+
+x  = np.linspace(0, 10, 100)
+z    = np.linspace(0, 10, 100)
+
+err_coeffs = [
+    [ 1, 0.01, 0.001, 5e-7, 1e-8, 1e-11, 1e-12, 5e-13, 1e-13, 1e-13 ], # amplitude 1
+    [ 5, 0.1,  5e-4,  5e-7, 5e-8, 5e-11, 5e-12, 5e-11, 1e-13, 1e-13 ], # amplitude 2
+    [ 5, 1,    5e-3,  1e-6, 5e-8, 1e-10, 1e-11, 5e-12, 5e-13, 5e-13 ], # amplitude 4
+    [ 5, 15,   1e-2,  1e-5, 1e-7, 5e-10, 5e-11, 5e-12, 5e-13, 1e-12 ], # amplitude 6
+]
+
+sys.stderr.write('Testing convergence of the residual calculated by spectral derivatives\n')
+for amplitude, err_row in zip(amplitudes, err_coeffs):
+    sys.stderr.write('amplitude: %d\n' % amplitude)
+
+    for coeff, err_ref in zip(coeffs, err_row):
+        sys.stderr.write('coeffs: %dx%d ' % (coeff, coeff))
+
+        BD = brill_data.BrillData(nb_coeffs_rho = coeff, amplitude = amplitude)
+
+        error = np.max(np.abs(eval_residual_coeffs(BD, x, z)))
+        sys.stderr.write('calculated error %g, reference %g\n' % (error, err_ref))
+        if error > err_ref:
+            sys.stderr.write('Test FAILED\n')
+            sys.exit(1)
+
+
+def eval_residual_fd(bd, x, y, z):
+    Z, Y, X = np.meshgrid(z, y, x, indexing = 'ij')
+
+    psi = np.empty_like(Z)
+    d2q = np.empty_like(Z)
+    for i, yy in enumerate(y):
+        rho = np.sqrt(x ** 2 + yy ** 2)
+        stuff = bd.eval_psi(rho, z)
+        psi[:, i] = bd.eval_psi(rho, z)
+        d2q[:, i] = bd.eval_q(rho, z, (2, 0)) + bd.eval_q(rho, z, (0, 2))
+
+    dpsi_z, dpsi_y, dpsi_x = np.gradient(psi, z[1] - z[0], y[1] - y[0], x[1] - x[0])
+    d2psi_z, foo, foo = np.gradient(dpsi_z, z[1] - z[0], y[1] - y[0], x[1] - x[0])
+    foo, d2psi_y, foo = np.gradient(dpsi_y, z[1] - z[0], y[1] - y[0], x[1] - x[0])
+    foo, foo, d2psi_x = np.gradient(dpsi_x, z[1] - z[0], y[1] - y[0], x[1] - x[0])
+
+    d2psi = d2psi_x + d2psi_y + d2psi_z
+
+    return (d2psi + 0.25 * psi * d2q)[2:-2, 2:-2, 2:-2]
+    return (d2psi + 0.25 * psi * d2q)[2:-2, 2:-2, 2:-2]
+
+points = [ 100,  500,  1000 ]
+err_fd = [ 1e-2, 5e-4, 1e-4 ]
+sys.stderr.write('Testing convergence of the residual calculated by finite difference derivatives\n')
+BD = brill_data.BrillData(nb_coeffs_rho = 50, amplitude = 5)
+for point, err_ref in zip(points, err_fd):
+    x    = np.linspace(-1, 1, point)
+    y    = np.linspace(-3 * (x[1] - x[0]), 3 * (x[1] - x[0]), 7)
+    z    = np.linspace(-1, 1, point)
+    sys.stderr.write('number of points: %d\n' % point)
+
+    error = np.max(np.abs(eval_residual_fd(BD, x, y, z)))
+    sys.stderr.write('calculated error %g, reference %g\n' % (error, err_ref))
+    if error > err_ref:
+        sys.stderr.write('Test FAILED\n')
+        sys.exit(1)
+
+sys.stderr.write('Testing metric evaluation\n')
+
+rho  = np.linspace(0, 1, 100)
+z    = np.linspace(0, 1, 100)
+
+err_metric = [
+    [ 5e-3, 5e-4, 1e-2, 5e-3, 1e-3 ],    # component 00
+    [ 5e-3, 5e-4, 1e-2, 5e-3, 1e-3 ],    # component 11
+    [ 5e-4, 5e-5, 5e-4, 1e-4, 1e-4 ],    # component 22
+]
+
+BD = brill_data.BrillData(nb_coeffs_rho = 40, amplitude = 3)
+for c, err_row in zip(xrange(3), err_metric):
+    sys.stderr.write('component %d%d\n' % (c, c))
+
+    metric  = BD.eval_metric(rho, z, (c, c))
+
+    dmetric_rho      = BD.eval_metric(rho, z, (c, c), (1, 0))
+    dmetric_z        = BD.eval_metric(rho, z, (c, c), (0, 1))
+    d2metric_rho_z   = BD.eval_metric(rho, z, (c, c), (1, 1))
+    d2metric_rho     = BD.eval_metric(rho, z, (c, c), (2, 0))
+    d2metric_z       = BD.eval_metric(rho, z, (c, c), (0, 2))
+
+    emetric_z, emetric_rho       = np.gradient(metric,      z[1] - z[0], rho[1] - rho[0])
+    e2metric_rho_z, e2metric_rho = np.gradient(dmetric_rho, z[1] - z[0], rho[1] - rho[0])
+    e2metric_z, foo              = np.gradient(dmetric_z,   z[1] - z[0], rho[1] - rho[0])
+
+    err = np.max(np.abs((dmetric_rho - emetric_rho)[3:-3, 3:-3]))
+    err_ref = err_row[0]
+    sys.stderr.write('calculated error for d/drho %g, reference %g\n' % (err, err_ref))
+    if err > err_ref:
+        sys.stderr.write('Test FAILED\n')
+        sys.exit(1)
+
+    err = np.max(np.abs((dmetric_z - emetric_z)[3:-3, 3:-3]))
+    err_ref = err_row[1]
+    sys.stderr.write('calculated error for d/dz %g, reference %g\n' % (err, err_ref))
+    if err > err_ref:
+        sys.stderr.write('Test FAILED\n')
+        sys.exit(1)
+
+    err = np.max(np.abs((d2metric_rho - e2metric_rho)[3:-3, 3:-3]))
+    err_ref = err_row[2]
+    sys.stderr.write('calculated error for d2/drho2 %g, reference %g\n' % (err, err_ref))
+    if err > err_ref:
+        sys.stderr.write('Test FAILED\n')
+        sys.exit(1)
+
+    err = np.max(np.abs((d2metric_z - e2metric_z)[3:-3, 3:-3]))
+    err_ref = err_row[3]
+    sys.stderr.write('calculated error for d2/dz2 %g, reference %g\n' % (err, err_ref))
+    if err > err_ref:
+        sys.stderr.write('Test FAILED\n')
+        sys.exit(1)
+
+    err = np.max(np.abs((d2metric_rho_z - e2metric_rho_z)[3:-3, 3:-3]))
+    err_ref = err_row[4]
+    sys.stderr.write('calculated error for d2/drhodz %g, reference %g\n' % (err, err_ref))
+    if err > err_ref:
+        sys.stderr.write('Test FAILED\n')
+        sys.exit(1)