def local_vector_points(B, x, y, z, dx=None, dy=None, dz=None): """Get B at 6 points surrounding X X = [x, y, z] with spacing [+/-dx, +/-dy, +/-dz] Args: B (VectorField): B field x (float, ndarray, list): x (single value) y (float, ndarray, list): y (single value) z (float, ndarray, list): z (single value) dx (float, optional): dx, one grid cell if None dy (float, optional): dy, one grid cell if None dz (float, optional): dz, one grid cell if None Returns: (bs, pts, dcrd) * bs (ndarary): shape (6, 3) where 0-3 -> Bx,By,Bz and 0-6 -> X-dx, X+dx, X-dy, X+dy, X-dz, X+dz * pts (ndarray): shape (6, 3); the location of the points of the bs, but this time, 0-3 -> x,y,z * dcrd (list): [dx, dy, dz] """ assert has_cython # if a problem, you need to build Viscid assert B.iscentered("Cell") x, y, z = [np.array(c).reshape(1, 1) for c in [x, y, z]] crds = B.get_crds("xyz") inds = [0] * len(crds) dcrd = [0] * len(crds) # This makes points in xyz order pts = np.tile([x, y, z], 6).reshape(3, -1).T for i, crd, loc, d in zip(count(), crds, [x, y, z], [dx, dy, dz]): inds[i] = cycalc.closest_ind(crd, loc) if d is None: dcrd[i] = crd[inds[i] + 1] - crd[inds[i]] else: dcrd[i] = d pts[2 * i + 1, i] += dcrd[i] pts[2 * i + 0, i] -= dcrd[i] bs = cycalc.interp_trilin(B, seed.Point(pts)) # viscid.interact(banner="in local_vector_points") return bs, pts, dcrd
def _follow_fluid_step(i, dt, grid, root_seeds, plot_function, stream_opts, speed_scale): direction = int(dt / np.abs(dt)) if direction >= 0: sl_direction = streamline.DIR_FORWARD else: sl_direction = streamline.DIR_BACKWARD logger.info("working on timestep {0} {1}".format(i, grid.time)) v = grid["v"] logger.debug("finished reading V field") logger.debug("calculating new streamline positions") flow_lines = calc_streamlines(v, root_seeds, output=viscid.OUTPUT_STREAMLINES, stream_dir=sl_direction, **stream_opts)[0] logger.debug("done with that, now i'm plotting...") plot_function(i, grid, v, flow_lines, root_seeds) ############################################################ # now recalculate the seed positions for the next timestep logger.debug("finding new seed positions...") root_pts = root_seeds.genr_points() valid_pt_inds = [] for i in range(root_pts.shape[1]): valid_pt = True # get the index of the root point in teh 2d flow line array # dist = flow_lines[i] - root_pts[:, [i]] # root_ind = np.argmin(np.sum(dist**2, axis=0)) # print("!!!", root_pts[:, i], "==", flow_lines[i][:, root_ind]) # interpolate velocity onto teh flow line, and get speed too v_interp = cycalc.interp_trilin(v, seed.Point(flow_lines[i])) speed = np.sqrt(np.sum(v_interp * v_interp, axis=1)) # this is a super slopy way to integrate velocity # keep marching along the flow line until we get to the next timestep t = 0.0 ind = 0 if direction < 0: flow_lines[i] = flow_lines[i][:, ::-1] speed = speed[::-1] while t < np.abs(dt): ind += 1 if ind >= len(speed): # set valid_pt to True if you want to keep that point for # future time steps, but most likely if we're here, the seed # has gone out of our region of interest ind = len(speed) - 1 valid_pt = False logger.info("OOPS: ran out of streamline, increase " "max_length when tracing flow lines if this " "is unexpected") break t += stream_opts["ds0"] / (speed_scale * speed[ind]) root_pts[:, i] = flow_lines[i][:, ind] if valid_pt: valid_pt_inds.append(i) # remove seeds that have flown out of our region of interest # (aka, beyond the flow line we drew) root_pts = root_pts[:, valid_pt_inds] logger.debug("ok, done with all that :)") return root_pts
def main(): xl, xh, nx = -1.0, 1.0, 41 yl, yh, ny = -1.5, 1.5, 41 zl, zh, nz = -2.0, 2.0, 41 x = np.linspace(xl, xh, nx) y = np.linspace(yl, yh, ny) z = np.linspace(zl, zh, nz) crds = coordinate.wrap_crds("nonuniform_cartesian", [('z', z), ('y', y), ('x', x)]) bx = field.empty(crds, name="$B_x$", center="Node") by = field.empty(crds, name="$B_y$", center="Node") bz = field.empty(crds, name="$B_z$", center="Node") fld = field.empty(crds, name="B", nr_comps=3, center="Node", layout="interlaced") X, Y, Z = crds.get_crds(shaped=True) x01, y01, z01 = 0.5, 0.5, 0.5 x02, y02, z02 = 0.5, 0.5, 0.5 x03, y03, z03 = 0.5, 0.5, 0.5 bx[:] = 0.0 + 1.0 * (X - x01) + 1.0 * (Y - y01) + 1.0 * (Z - z01) + \ 1.0 * (X - x01) * (Y - y01) + 1.0 * (Y - y01) * (Z - z01) + \ 1.0 * (X - x01) * (Y - y01) * (Z - z01) by[:] = 0.0 + 1.0 * (X - x02) - 1.0 * (Y - y02) + 1.0 * (Z - z02) + \ 1.0 * (X - x02) * (Y - y02) + 1.0 * (Y - y02) * (Z - z02) - \ 1.0 * (X - x02) * (Y - y02) * (Z - z02) bz[:] = 0.0 + 1.0 * (X - x03) + 1.0 * (Y - y03) - 1.0 * (Z - z03) + \ 1.0 * (X - x03) * (Y - y03) + 1.0 * (Y - y03) * (Z - z03) + \ 1.0 * (X - x03) * (Y - y03) * (Z - z03) fld[..., 0] = bx fld[..., 1] = by fld[..., 2] = bz fig = mlab.figure(size=(1150, 850), bgcolor=(1.0, 1.0, 1.0), fgcolor=(0.0, 0.0, 0.0)) f1_src = vlab.add_field(bx) f2_src = vlab.add_field(by) f3_src = vlab.add_field(bz) mlab.pipeline.iso_surface(f1_src, contours=[0.0], opacity=1.0, color=(1.0, 0.0, 0.0)) mlab.pipeline.iso_surface(f2_src, contours=[0.0], opacity=1.0, color=(0.0, 1.0, 0.0)) mlab.pipeline.iso_surface(f3_src, contours=[0.0], opacity=1.0, color=(0.0, 0.0, 1.0)) mlab.axes() mlab.show() nullpt = cycalc.interp_trilin(fld, [(0.5, 0.5, 0.5)]) print("f(0.5, 0.5, 0.5):", nullpt) _, axes = plt.subplots(4, 3, sharex=True, sharey=True) all_roots = [] positive_roots = [] ix = iy = iz = 0 for di, d in enumerate([0, -1]): #### XY face a1 = bx[iz + d, iy, ix] b1 = bx[iz + d, iy, ix - 1] - a1 c1 = bx[iz + d, iy - 1, ix] - a1 d1 = bx[iz + d, iy - 1, ix - 1] - c1 - b1 - a1 a2 = by[iz + d, iy, ix] b2 = by[iz + d, iy, ix - 1] - a2 c2 = by[iz + d, iy - 1, ix] - a2 d2 = by[iz + d, iy - 1, ix - 1] - c2 - b2 - a2 a3 = bz[iz + d, iy, ix] b3 = bz[iz + d, iy, ix - 1] - a3 c3 = bz[iz + d, iy - 1, ix] - a3 d3 = bz[iz + d, iy - 1, ix - 1] - c3 - b3 - a3 roots1, roots2 = find_roots_face(a1, b1, c1, d1, a2, b2, c2, d2) # for rt1, rt2 in zip(roots1, roots2): # print("=") # print("fx", a1 + b1 * rt1 + c1 * rt2 + d1 * rt1 * rt2) # print("fy", a2 + b2 * rt1 + c2 * rt2 + d2 * rt1 * rt2) # print("=") # find f3 at the root points f3 = np.empty_like(roots1) markers = [None] * len(f3) for i, rt1, rt2 in zip(count(), roots1, roots2): f3[i] = a3 + b3 * rt1 + c3 * rt2 + d3 * rt1 * rt2 all_roots.append((rt1, rt2, d)) # switch order here if f3[i] >= 0.0: markers[i] = 'k^' positive_roots.append((rt1, rt2, d)) # switch order here else: markers[i] = 'w^' # rescale the roots to the original domain roots1 = (xh - xl) * roots1 + xl roots2 = (yh - yl) * roots2 + yl xp = np.linspace(0.0, 1.0, nx) vlt.plot(fld['x'], "z={0}i".format(d), ax=axes[0 + 2 * di, 0], plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format(xl, xh, yl, yh)) y1 = - (a1 + b1 * xp) / (c1 + d1 * xp) plt.plot(x, (yh - yl) * y1 + yl, 'k') for i, xrt, yrt in zip(count(), roots1, roots2): plt.plot(xrt, yrt, markers[i]) vlt.plot(fld['y'], "z={0}i".format(d), ax=axes[1 + 2 * di, 0], plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format(xl, xh, yl, yh)) y2 = - (a2 + b2 * xp) / (c2 + d2 * xp) plt.plot(x, (yh - yl) * y2 + yl, 'k') for xrt, yrt in zip(roots1, roots2): plt.plot(xrt, yrt, markers[i]) #### YZ face a1 = bx[iz, iy, ix + d] b1 = bx[iz, iy - 1, ix + d] - a1 c1 = bx[iz - 1, iy, ix + d] - a1 d1 = bx[iz - 1, iy - 1, ix + d] - c1 - b1 - a1 a2 = by[iz, iy, ix + d] b2 = by[iz, iy - 1, ix + d] - a2 c2 = by[iz - 1, iy, ix + d] - a2 d2 = by[iz - 1, iy - 1, ix + d] - c2 - b2 - a2 a3 = bz[iz, iy, ix + d] b3 = bz[iz, iy - 1, ix + d] - a3 c3 = bz[iz - 1, iy, ix + d] - a3 d3 = bz[iz - 1, iy - 1, ix + d] - c3 - b3 - a3 roots1, roots2 = find_roots_face(a1, b1, c1, d1, a2, b2, c2, d2) # for rt1, rt2 in zip(roots1, roots2): # print("=") # print("fx", a1 + b1 * rt1 + c1 * rt2 + d1 * rt1 * rt2) # print("fy", a2 + b2 * rt1 + c2 * rt2 + d2 * rt1 * rt2) # print("=") # find f3 at the root points f3 = np.empty_like(roots1) markers = [None] * len(f3) for i, rt1, rt2 in zip(count(), roots1, roots2): f3[i] = a3 + b3 * rt1 + c3 * rt2 + d3 * rt1 * rt2 all_roots.append((d, rt1, rt2)) # switch order here if f3[i] >= 0.0: markers[i] = 'k^' positive_roots.append((d, rt1, rt2)) # switch order here else: markers[i] = 'w^' # rescale the roots to the original domain roots1 = (yh - yl) * roots1 + yl roots2 = (zh - zl) * roots2 + zl yp = np.linspace(0.0, 1.0, ny) # plt.subplot(121) vlt.plot(fld['x'], "x={0}i".format(d), ax=axes[0 + 2 * di, 1], plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format(yl, yh, zl, zh)) z1 = - (a1 + b1 * yp) / (c1 + d1 * yp) plt.plot(y, (zh - zl) * z1 + zl, 'k') for i, yrt, zrt in zip(count(), roots1, roots2): plt.plot(yrt, zrt, markers[i]) # plt.subplot(122) vlt.plot(fld['y'], "x={0}i".format(d), ax=axes[1 + 2 * di, 1], plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format(yl, yh, zl, zh)) z1 = - (a2 + b2 * yp) / (c2 + d2 * yp) plt.plot(y, (zh - zl) * z1 + zl, 'k') for i, yrt, zrt in zip(count(), roots1, roots2): plt.plot(yrt, zrt, markers[i]) #### ZX face a1 = bx[iz, iy + d, ix] b1 = bx[iz - 1, iy + d, ix] - a1 c1 = bx[iz, iy + d, ix - 1] - a1 d1 = bx[iz - 1, iy + d, ix - 1] - c1 - b1 - a1 a2 = by[iz, iy + d, ix] b2 = by[iz - 1, iy + d, ix] - a2 c2 = by[iz, iy + d, ix - 1] - a2 d2 = by[iz - 1, iy + d, ix - 1] - c2 - b2 - a2 a3 = bz[iz, iy + d, ix] b3 = bz[iz - 1, iy + d, ix] - a3 c3 = bz[iz, iy + d, ix - 1] - a3 d3 = bz[iz - 1, iy + d, ix - 1] - c3 - b3 - a3 roots1, roots2 = find_roots_face(a1, b1, c1, d1, a2, b2, c2, d2) # for rt1, rt2 in zip(roots1, roots2): # print("=") # print("fx", a1 + b1 * rt1 + c1 * rt2 + d1 * rt1 * rt2) # print("fy", a2 + b2 * rt1 + c2 * rt2 + d2 * rt1 * rt2) # print("=") # find f3 at the root points f3 = np.empty_like(roots1) markers = [None] * len(f3) for i, rt1, rt2 in zip(count(), roots1, roots2): f3[i] = a3 + b3 * rt1 + c3 * rt2 + d3 * rt1 * rt2 all_roots.append((rt2, d, rt1)) # switch order here if f3[i] >= 0.0: markers[i] = 'k^' positive_roots.append((rt2, d, rt1)) # switch order here else: markers[i] = 'w^' # rescale the roots to the original domain roots1 = (zh - zl) * roots1 + zl roots2 = (xh - xl) * roots2 + xl zp = np.linspace(0.0, 1.0, nz) # plt.subplot(121) vlt.plot(fld['x'], "y={0}i".format(d), ax=axes[0 + 2 * di, 2], plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format(xl, xh, zl, zh)) x1 = - (a1 + b1 * zp) / (c1 + d1 * zp) plt.plot(z, (xh - xl) * x1 + xl, 'k') for i, zrt, xrt in zip(count(), roots1, roots2): plt.plot(xrt, zrt, markers[i]) # plt.subplot(121) vlt.plot(fld['y'], "y={0}i".format(d), ax=axes[1 + 2 * di, 2], plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format(xl, xh, zl, zh)) x1 = - (a2 + b2 * zp) / (c2 + d2 * zp) plt.plot(z, (xh - xl) * x1 + xl, 'k') for i, zrt, xrt in zip(count(), roots1, roots2): plt.plot(xrt, zrt, markers[i]) print("all:", len(all_roots), "positive:", len(positive_roots)) if len(all_roots) % 2 == 1: print("something is fishy, there are an odd number of root points " "on the surface of your cube, there is probably a degenerate " "line or surface of nulls") print("Null Point?", (len(positive_roots) % 2 == 1)) plt.show()
def main(): xl, xh, nx = -1.0, 1.0, 41 yl, yh, ny = -1.5, 1.5, 41 zl, zh, nz = -2.0, 2.0, 41 x = np.linspace(xl, xh, nx) y = np.linspace(yl, yh, ny) z = np.linspace(zl, zh, nz) crds = coordinate.wrap_crds("nonuniform_cartesian", [('z', z), ('y', y), ('x', x)]) bx = field.empty(crds, name="$B_x$", center="Node") by = field.empty(crds, name="$B_y$", center="Node") bz = field.empty(crds, name="$B_z$", center="Node") fld = field.empty(crds, name="B", nr_comps=3, center="Node", layout="interlaced") X, Y, Z = crds.get_crds(shaped=True) x01, y01, z01 = 0.5, 0.5, 0.5 x02, y02, z02 = 0.5, 0.5, 0.5 x03, y03, z03 = 0.5, 0.5, 0.5 bx[:] = 0.0 + 1.0 * (X - x01) + 1.0 * (Y - y01) + 1.0 * (Z - z01) + \ 1.0 * (X - x01) * (Y - y01) + 1.0 * (Y - y01) * (Z - z01) + \ 1.0 * (X - x01) * (Y - y01) * (Z - z01) by[:] = 0.0 + 1.0 * (X - x02) - 1.0 * (Y - y02) + 1.0 * (Z - z02) + \ 1.0 * (X - x02) * (Y - y02) + 1.0 * (Y - y02) * (Z - z02) - \ 1.0 * (X - x02) * (Y - y02) * (Z - z02) bz[:] = 0.0 + 1.0 * (X - x03) + 1.0 * (Y - y03) - 1.0 * (Z - z03) + \ 1.0 * (X - x03) * (Y - y03) + 1.0 * (Y - y03) * (Z - z03) + \ 1.0 * (X - x03) * (Y - y03) * (Z - z03) fld[..., 0] = bx fld[..., 1] = by fld[..., 2] = bz fig = mlab.figure(size=(1150, 850), bgcolor=(1.0, 1.0, 1.0), fgcolor=(0.0, 0.0, 0.0)) f1_src = vlab.add_field(bx) f2_src = vlab.add_field(by) f3_src = vlab.add_field(bz) mlab.pipeline.iso_surface(f1_src, contours=[0.0], opacity=1.0, color=(1.0, 0.0, 0.0)) mlab.pipeline.iso_surface(f2_src, contours=[0.0], opacity=1.0, color=(0.0, 1.0, 0.0)) mlab.pipeline.iso_surface(f3_src, contours=[0.0], opacity=1.0, color=(0.0, 0.0, 1.0)) mlab.axes() mlab.show() nullpt = cycalc.interp_trilin(fld, [(0.5, 0.5, 0.5)]) print("f(0.5, 0.5, 0.5):", nullpt) ax1 = plt.subplot2grid((4, 3), (0, 0)) all_roots = [] positive_roots = [] ix = iy = iz = 0 for di, d in enumerate([0, -1]): #### XY face a1 = bx[iz + d, iy, ix] b1 = bx[iz + d, iy, ix - 1] - a1 c1 = bx[iz + d, iy - 1, ix] - a1 d1 = bx[iz + d, iy - 1, ix - 1] - c1 - b1 - a1 a2 = by[iz + d, iy, ix] b2 = by[iz + d, iy, ix - 1] - a2 c2 = by[iz + d, iy - 1, ix] - a2 d2 = by[iz + d, iy - 1, ix - 1] - c2 - b2 - a2 a3 = bz[iz + d, iy, ix] b3 = bz[iz + d, iy, ix - 1] - a3 c3 = bz[iz + d, iy - 1, ix] - a3 d3 = bz[iz + d, iy - 1, ix - 1] - c3 - b3 - a3 roots1, roots2 = find_roots_face(a1, b1, c1, d1, a2, b2, c2, d2) # for rt1, rt2 in zip(roots1, roots2): # print("=") # print("fx", a1 + b1 * rt1 + c1 * rt2 + d1 * rt1 * rt2) # print("fy", a2 + b2 * rt1 + c2 * rt2 + d2 * rt1 * rt2) # print("=") # find f3 at the root points f3 = np.empty_like(roots1) markers = [None] * len(f3) for i, rt1, rt2 in zip(count(), roots1, roots2): f3[i] = a3 + b3 * rt1 + c3 * rt2 + d3 * rt1 * rt2 all_roots.append((rt1, rt2, d)) # switch order here if f3[i] >= 0.0: markers[i] = 'k^' positive_roots.append((rt1, rt2, d)) # switch order here else: markers[i] = 'w^' # rescale the roots to the original domain roots1 = (xh - xl) * roots1 + xl roots2 = (yh - yl) * roots2 + yl xp = np.linspace(0.0, 1.0, nx) # plt.subplot(121) plt.subplot2grid((4, 3), (0 + 2 * di, 0), sharex=ax1, sharey=ax1) vlt.plot(fld['x'], "z={0}i".format(d), plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format( xl, xh, yl, yh)) y1 = -(a1 + b1 * xp) / (c1 + d1 * xp) plt.plot(x, (yh - yl) * y1 + yl, 'k') for i, xrt, yrt in zip(count(), roots1, roots2): plt.plot(xrt, yrt, markers[i]) # plt.subplot(122) plt.subplot2grid((4, 3), (1 + 2 * di, 0), sharex=ax1, sharey=ax1) vlt.plot(fld['y'], "z={0}i".format(d), plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format( xl, xh, yl, yh)) y2 = -(a2 + b2 * xp) / (c2 + d2 * xp) plt.plot(x, (yh - yl) * y2 + yl, 'k') for xrt, yrt in zip(roots1, roots2): plt.plot(xrt, yrt, markers[i]) #### YZ face a1 = bx[iz, iy, ix + d] b1 = bx[iz, iy - 1, ix + d] - a1 c1 = bx[iz - 1, iy, ix + d] - a1 d1 = bx[iz - 1, iy - 1, ix + d] - c1 - b1 - a1 a2 = by[iz, iy, ix + d] b2 = by[iz, iy - 1, ix + d] - a2 c2 = by[iz - 1, iy, ix + d] - a2 d2 = by[iz - 1, iy - 1, ix + d] - c2 - b2 - a2 a3 = bz[iz, iy, ix + d] b3 = bz[iz, iy - 1, ix + d] - a3 c3 = bz[iz - 1, iy, ix + d] - a3 d3 = bz[iz - 1, iy - 1, ix + d] - c3 - b3 - a3 roots1, roots2 = find_roots_face(a1, b1, c1, d1, a2, b2, c2, d2) # for rt1, rt2 in zip(roots1, roots2): # print("=") # print("fx", a1 + b1 * rt1 + c1 * rt2 + d1 * rt1 * rt2) # print("fy", a2 + b2 * rt1 + c2 * rt2 + d2 * rt1 * rt2) # print("=") # find f3 at the root points f3 = np.empty_like(roots1) markers = [None] * len(f3) for i, rt1, rt2 in zip(count(), roots1, roots2): f3[i] = a3 + b3 * rt1 + c3 * rt2 + d3 * rt1 * rt2 all_roots.append((d, rt1, rt2)) # switch order here if f3[i] >= 0.0: markers[i] = 'k^' positive_roots.append((d, rt1, rt2)) # switch order here else: markers[i] = 'w^' # rescale the roots to the original domain roots1 = (yh - yl) * roots1 + yl roots2 = (zh - zl) * roots2 + zl yp = np.linspace(0.0, 1.0, ny) # plt.subplot(121) plt.subplot2grid((4, 3), (0 + 2 * di, 1), sharex=ax1, sharey=ax1) vlt.plot(fld['x'], "x={0}i".format(d), plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format( yl, yh, zl, zh)) z1 = -(a1 + b1 * yp) / (c1 + d1 * yp) plt.plot(y, (zh - zl) * z1 + zl, 'k') for i, yrt, zrt in zip(count(), roots1, roots2): plt.plot(yrt, zrt, markers[i]) # plt.subplot(122) plt.subplot2grid((4, 3), (1 + 2 * di, 1), sharex=ax1, sharey=ax1) vlt.plot(fld['y'], "x={0}i".format(d), plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format( yl, yh, zl, zh)) z1 = -(a2 + b2 * yp) / (c2 + d2 * yp) plt.plot(y, (zh - zl) * z1 + zl, 'k') for i, yrt, zrt in zip(count(), roots1, roots2): plt.plot(yrt, zrt, markers[i]) #### ZX face a1 = bx[iz, iy + d, ix] b1 = bx[iz - 1, iy + d, ix] - a1 c1 = bx[iz, iy + d, ix - 1] - a1 d1 = bx[iz - 1, iy + d, ix - 1] - c1 - b1 - a1 a2 = by[iz, iy + d, ix] b2 = by[iz - 1, iy + d, ix] - a2 c2 = by[iz, iy + d, ix - 1] - a2 d2 = by[iz - 1, iy + d, ix - 1] - c2 - b2 - a2 a3 = bz[iz, iy + d, ix] b3 = bz[iz - 1, iy + d, ix] - a3 c3 = bz[iz, iy + d, ix - 1] - a3 d3 = bz[iz - 1, iy + d, ix - 1] - c3 - b3 - a3 roots1, roots2 = find_roots_face(a1, b1, c1, d1, a2, b2, c2, d2) # for rt1, rt2 in zip(roots1, roots2): # print("=") # print("fx", a1 + b1 * rt1 + c1 * rt2 + d1 * rt1 * rt2) # print("fy", a2 + b2 * rt1 + c2 * rt2 + d2 * rt1 * rt2) # print("=") # find f3 at the root points f3 = np.empty_like(roots1) markers = [None] * len(f3) for i, rt1, rt2 in zip(count(), roots1, roots2): f3[i] = a3 + b3 * rt1 + c3 * rt2 + d3 * rt1 * rt2 all_roots.append((rt2, d, rt1)) # switch order here if f3[i] >= 0.0: markers[i] = 'k^' positive_roots.append((rt2, d, rt1)) # switch order here else: markers[i] = 'w^' # rescale the roots to the original domain roots1 = (zh - zl) * roots1 + zl roots2 = (xh - xl) * roots2 + xl zp = np.linspace(0.0, 1.0, nz) # plt.subplot(121) plt.subplot2grid((4, 3), (0 + 2 * di, 2), sharex=ax1, sharey=ax1) vlt.plot(fld['x'], "y={0}i".format(d), plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format( xl, xh, zl, zh)) x1 = -(a1 + b1 * zp) / (c1 + d1 * zp) plt.plot(z, (xh - xl) * x1 + xl, 'k') for i, zrt, xrt in zip(count(), roots1, roots2): plt.plot(xrt, zrt, markers[i]) # plt.subplot(121) plt.subplot2grid((4, 3), (1 + 2 * di, 2), sharex=ax1, sharey=ax1) vlt.plot(fld['y'], "y={0}i".format(d), plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format( xl, xh, zl, zh)) x1 = -(a2 + b2 * zp) / (c2 + d2 * zp) plt.plot(z, (xh - xl) * x1 + xl, 'k') for i, zrt, xrt in zip(count(), roots1, roots2): plt.plot(xrt, zrt, markers[i]) print("all:", len(all_roots), "positive:", len(positive_roots)) if len(all_roots) % 2 == 1: print("something is fishy, there are an odd number of root points " "on the surface of your cube, there is probably a degenerate " "line or surface of nulls") print("Null Point?", (len(positive_roots) % 2 == 1)) plt.show()
def main(): parser = argparse.ArgumentParser(description="Streamline a PSC file") parser.add_argument("-t", default="2000", help="which time to plot (finds closest)") parser.add_argument('infile', nargs=1, help='input file') args = vutil.common_argparse(parser) # f = readers.load_file("pfd.020000.xdmf") # ... or ... # using this way of loading files, one probably wants just to give # pfd.xdmf to the command line f = readers.load_file(args.infile[0]) f.activate_time(args.t) jz = f["jz"] # recreate hx as a field of 0 to keep streamlines from moving in # that direction hx = field.zeros_like(jz, name="hx") h1 = field.scalar_fields_to_vector([hx, f["hy"], f["hz"]], name="H", _force_layout="Interlaced", forget_source=True) e = field.scalar_fields_to_vector([f["ex"], f["ey"], f["ez"]], name="E", _force_layout="Interlaced", forget_source=True) # plot magnetic fields, just a sanity check # ax1 = plt.subplot(211) # mpl.plot(f["hy"], flip_plot=True) # ax2 = plt.subplot(212, sharex=ax1, sharey=ax1) # mpl.plot(f["hz"], flip_plot=True) # mpl.mplshow() # make a line of 30 seeds straight along the z axis (x, y, z ordered) seeds1 = seed.Line((0.0, 0.0, 2.0), (1022.0, 0.0, 0.0), 60) # set outer boundary limits for streamlines ds = 0.005 # spatial step along the stream line curve obound0 = np.array([1, -128, -1000], dtype=h1.dtype) obound1 = np.array([1023, 128, 1000], dtype=h1.dtype) # calc the streamlines lines1, topo1 = streamline.streamlines(h1, seeds1, ds0=ds, maxit=200000, obound0=obound0, obound1=obound1, ibound=0.0) # run with -v to see this logger.info("Topology flags: {0}".format(topo1)) # rotate plot puts the z axis along the horizontal flip_plot = True mpl.plot(jz, flip_plot=flip_plot, plot_opts="lin_-.05_.05") # mpl.plot_streamlines2d(lines1, "x", flip_plot=flip_plot, color='k') plt.xlim([0, 1024]) plt.ylim([-128, 128]) plt.show() # interpolate e onto each point of the first field line of lines1 e1 = cycalc.interp_trilin(e, seed.Point(lines1[0])) print(e1.shape, lines1[0].shape) plt.clf() plt.plot(np.linspace(0, ds * e1.shape[0], e1.shape[0]), e1[:, 0]) plt.xlabel("length along field line") plt.ylabel("Ex") plt.show() return 0