我们从Python开源项目中，提取了以下50个代码示例，用于说明如何使用numpy.sin()。
def deriveKernel(self, params, i): self.checkParamsI(params, i) ell = np.exp(params[0]) p = np.exp(params[1]) #compute d2 if (self.K_sq is None): d2 = sq_dist(self.X_scaled.T / ell) #precompute squared distances else: d2 = self.K_sq / ell**2 #compute dp dp = self.dp/p K = np.exp(-d2 / 2.0) if (i==0): return d2*K*np.cos(2*np.pi*dp) elif (i==1): return 2*np.pi*dp*np.sin(2*np.pi*dp)*K else: raise Exception('invalid parameter index:' + str(i))
def _generate_data(): """ ????? ????u(k-1) ? y(k-1)?????y(k) """ # u = np.random.uniform(-1,1,200) # y=[] # former_y_value = 0 # for i in np.arange(0,200): # y.append(former_y_value) # next_y_value = (29.0 / 40) * np.sin( # (16.0 * u[i] + 8 * former_y_value) / (3.0 + 4.0 * (u[i] ** 2) + 4 * (former_y_value ** 2))) \ # + (2.0 / 10) * u[i] + (2.0 / 10) * former_y_value # former_y_value = next_y_value # return u,y u1 = np.random.uniform(-np.pi,np.pi,200) u2 = np.random.uniform(-1,1,200) y = np.zeros(200) for i in range(200): value = np.sin(u1[i]) + u2[i] y[i] = value return u1, u2, y
def rotate_point_cloud(batch_data): """ Randomly rotate the point clouds to augument the dataset rotation is per shape based along up direction Input: BxNx3 array, original batch of point clouds Return: BxNx3 array, rotated batch of point clouds """ rotated_data = np.zeros(batch_data.shape, dtype=np.float32) for k in range(batch_data.shape[0]): rotation_angle = np.random.uniform() * 2 * np.pi cosval = np.cos(rotation_angle) sinval = np.sin(rotation_angle) rotation_matrix = np.array([[cosval, 0, sinval], [0, 1, 0], [-sinval, 0, cosval]]) shape_pc = batch_data[k, ...] rotated_data[k, ...] = np.dot(shape_pc.reshape((-1, 3)), rotation_matrix) return rotated_data
def rotate_point_cloud_by_angle(batch_data, rotation_angle): """ Rotate the point cloud along up direction with certain angle. Input: BxNx3 array, original batch of point clouds Return: BxNx3 array, rotated batch of point clouds """ rotated_data = np.zeros(batch_data.shape, dtype=np.float32) for k in range(batch_data.shape[0]): #rotation_angle = np.random.uniform() * 2 * np.pi cosval = np.cos(rotation_angle) sinval = np.sin(rotation_angle) rotation_matrix = np.array([[cosval, 0, sinval], [0, 1, 0], [-sinval, 0, cosval]]) shape_pc = batch_data[k, ...] rotated_data[k, ...] = np.dot(shape_pc.reshape((-1, 3)), rotation_matrix) return rotated_data
def monotoneTFosc(f): """Maps [-inf,inf] to [-inf,inf] with different constants for positive and negative part. """ if np.isscalar(f): if f > 0.: f = np.log(f) / 0.1 f = np.exp(f + 0.49 * (np.sin(f) + np.sin(0.79 * f))) ** 0.1 elif f < 0.: f = np.log(-f) / 0.1 f = -np.exp(f + 0.49 * (np.sin(0.55 * f) + np.sin(0.31 * f))) ** 0.1 return f else: f = np.asarray(f) g = f.copy() idx = (f > 0) g[idx] = np.log(f[idx]) / 0.1 g[idx] = np.exp(g[idx] + 0.49 * (np.sin(g[idx]) + np.sin(0.79 * g[idx])))**0.1 idx = (f < 0) g[idx] = np.log(-f[idx]) / 0.1 g[idx] = -np.exp(g[idx] + 0.49 * (np.sin(0.55 * g[idx]) + np.sin(0.31 * g[idx])))**0.1 return g
def test_pitch_estimation(self): """ test pitch estimation algo with contrived small example if pitch is within 5 Hz, then say its good (for this small example, since the algorithm wasn't made for this type of synthesized signal) """ cfg = ExperimentConfig(pitch_strength_thresh=-np.inf) # the next 3 variables are in Hz tolerance = 5 fs = 48000 f = 150 # create a sine wave of f Hz freq sampled at fs Hz x = np.sin(2*np.pi * f/fs * np.arange(2**10)) # estimate the pitch, it should be close to f p, t, s = pest.pitch_estimation(x, fs, cfg) self.assertTrue(np.all(np.abs(p - f) < tolerance))
def make_wafer(self,wafer_r,frame,label,labelloc,labelwidth): """ Generate wafer with primary flat on the left. From https://coresix.com/products/wafers/ I estimated that the angle defining the wafer flat to arctan(flat/2 / radius) """ angled = 18 angle = angled*np.pi/180 circ = cad.shapes.Circle((0,0), wafer_r, width=self.boxwidth, initial_angle=180+angled, final_angle=360+180-angled, layer=self.layer_box) flat = cad.core.Path([(-wafer_r*np.cos(angle),wafer_r*np.sin(angle)),(-wafer_r*np.cos(angle),-wafer_r*np.sin(angle))], width=self.boxwidth, layer=self.layer_box) date = time.strftime("%d/%m/%Y") if labelloc==(0,0): labelloc=(-2e3,wafer_r-1e3) # The label is added 100 um on top of the main cell label_grid_chip = cad.shapes.LineLabel( self.name + " " +\ date,500,position=labelloc, line_width=labelwidth, layer=self.layer_label) if frame==True: self.add(circ) self.add(flat) if label==True: self.add(label_grid_chip)
def ani_update(arg, ii=[0]): i = ii[0] # don't ask... if np.isclose(t_arr[i], np.around(t_arr[i], 1)): fig2.suptitle('Evolution (Time: {})'.format(t_arr[i]), fontsize=24) graphic_floor[0].set_data([-floor_lim*np.cos(incline_history[i]) + radius*np.sin(incline_history[i]), floor_lim*np.cos(incline_history[i]) + radius*np.sin(incline_history[i])], [-floor_lim*np.sin(incline_history[i])-radius*np.cos(incline_history[i]), floor_lim*np.sin(incline_history[i])-radius*np.cos(incline_history[i])]) graphic_wheel.center = (x_history[i], y_history[i]) graphic_ind[0].set_data([x_history[i], x_history[i] + radius*np.sin(w_history[i])], [y_history[i], y_history[i] + radius*np.cos(w_history[i])]) graphic_pend[0].set_data([x_history[i], x_history[i] - cw_to_cm[1]*np.sin(q_history[i, 2])], [y_history[i], y_history[i] + cw_to_cm[1]*np.cos(q_history[i, 2])]) graphic_dist[0].set_data([x_history[i] - cw_to_cm[1]*np.sin(q_history[i, 2]), x_history[i] - cw_to_cm[1]*np.sin(q_history[i, 2]) - pscale*p_history[i]*np.cos(q_history[i, 2])], [y_history[i] + cw_to_cm[1]*np.cos(q_history[i, 2]), y_history[i] + cw_to_cm[1]*np.cos(q_history[i, 2]) - pscale*p_history[i]*np.sin(q_history[i, 2])]) ii[0] += int(1 / (timestep * framerate)) if ii[0] >= len(t_arr): print("Resetting animation!") ii[0] = 0 return [graphic_floor, graphic_wheel, graphic_ind, graphic_pend, graphic_dist] # Run animation
def solveIter(mu,e): """__solvIter returns an iterative solution for Ek Mk = Ek - e sin(Ek) """ thisStart = np.asarray(mu-1.01*e) thisEnd = np.asarray(mu + 1.01*e) bestGuess = np.zeros(mu.shape) for i in range(5): minErr = 10000*np.ones(mu.shape) for j in range(5): thisGuess = thisStart + j*(thisEnd-thisStart)/10.0 thisErr = np.asarray(abs(mu - thisGuess + e*np.sin(thisGuess))) mask = thisErr<minErr minErr[mask] = thisErr[mask] bestGuess[mask] = thisGuess[mask] # reset for next loop thisRange = thisEnd - thisStart thisStart = bestGuess - thisRange/10.0 thisEnd = bestGuess + thisRange/10.0 return(bestGuess)
def great_circle_dist(p1, p2): """Return the distance (in km) between two points in geographical coordinates. """ lon0, lat0 = p1 lon1, lat1 = p2 EARTH_R = 6372.8 lat0 = np.radians(float(lat0)) lon0 = np.radians(float(lon0)) lat1 = np.radians(float(lat1)) lon1 = np.radians(float(lon1)) dlon = lon0 - lon1 y = np.sqrt( (np.cos(lat1) * np.sin(dlon)) ** 2 + (np.cos(lat0) * np.sin(lat1) - np.sin(lat0) * np.cos(lat1) * np.cos(dlon)) ** 2) x = np.sin(lat0) * np.sin(lat1) + \ np.cos(lat0) * np.cos(lat1) * np.cos(dlon) c = np.arctan2(y, x) return EARTH_R * c
def x_axis_rotation(theta): """Generates a 3x3 rotation matrix for a rotation of angle theta about the x axis. Parameters ---------- theta : float amount to rotate, in radians Returns ------- :obj:`numpy.ndarray` of float A random 3x3 rotation matrix. """ R = np.array([[1, 0, 0,], [0, np.cos(theta), -np.sin(theta)], [0, np.sin(theta), np.cos(theta)]]) return R
def y_axis_rotation(theta): """Generates a 3x3 rotation matrix for a rotation of angle theta about the y axis. Parameters ---------- theta : float amount to rotate, in radians Returns ------- :obj:`numpy.ndarray` of float A random 3x3 rotation matrix. """ R = np.array([[np.cos(theta), 0, np.sin(theta)], [0, 1, 0], [-np.sin(theta), 0, np.cos(theta)]]) return R
def z_axis_rotation(theta): """Generates a 3x3 rotation matrix for a rotation of angle theta about the z axis. Parameters ---------- theta : float amount to rotate, in radians Returns ------- :obj:`numpy.ndarray` of float A random 3x3 rotation matrix. """ R = np.array([[np.cos(theta), -np.sin(theta), 0], [np.sin(theta), np.cos(theta), 0], [0, 0, 1]]) return R
def sph2cart(r, az, elev): """ Convert spherical to cartesian coordinates. Attributes ---------- r : float radius az : float aziumth (angle about z axis) elev : float elevation from xy plane Returns ------- float x-coordinate float y-coordinate float z-coordinate """ x = r * np.cos(az) * np.sin(elev) y = r * np.sin(az) * np.sin(elev) z = r * np.cos(elev) return x, y, z
def mdst(x, odd=True): """ Calculate modified discrete sine transform of input signal in an inefficient pure-Python method. Use only for testing. Parameters ---------- X : array_like The input signal odd : boolean, optional Switch to oddly stacked transform. Defaults to :code:`True`. Returns ------- out : array_like The output signal """ return trans(x, func=numpy.sin, odd=odd) * numpy.sqrt(2)
def imdst(X, odd=True): """ Calculate inverse modified discrete sine transform of input signal in an inefficient pure-Python method. Use only for testing. Parameters ---------- X : array_like The input signal odd : boolean, optional Switch to oddly stacked transform. Defaults to :code:`True`. Returns ------- out : array_like The output signal """ return itrans(X, func=numpy.sin, odd=odd) * numpy.sqrt(2)
def cmdct(x, odd=True): """ Calculate complex modified discrete cosine transform of input inefficient pure-Python method. Use only for testing. Parameters ---------- X : array_like The input signal odd : boolean, optional Switch to oddly stacked transform. Defaults to :code:`True`. Returns ------- out : array_like The output signal """ return trans(x, func=lambda x: numpy.cos(x) - 1j * numpy.sin(x), odd=odd)
def icmdct(X, odd=True): """ Calculate inverse complex modified discrete cosine transform of input signal in an inefficient pure-Python method. Use only for testing. Parameters ---------- X : array_like The input signal odd : boolean, optional Switch to oddly stacked transform. Defaults to :code:`True`. Returns ------- out : array_like The output signal """ return itrans(X, func=lambda x: numpy.cos(x) + 1j * numpy.sin(x), odd=odd)
def test_with_fake_log_prob(self): np.random.seed(42) def grad_log_prob(x): return -(x/2.0 + np.sin(x))*(1.0/2.0 + np.cos(x)) def fake_log_prob(x): return -(x/5.0 + np.sin(x) )**2.0/2.0 generator = mh_generator(log_density=fake_log_prob,x_start=1.0) tester = GaussianSteinTest(grad_log_prob,41) selector = SampleSelector(generator, sample_size=1000,thinning=20,tester=tester, max_iterations=5) data,converged = selector.points_from_stationary() assert converged is False
def test_with_ugly(self): np.random.seed(42) def grad_log_prob(x): return -(x/5.0 + np.sin(x))*(1.0/5.0 + np.cos(x)) def log_prob(x): return -(x/5.0 + np.sin(x) )**2.0/2.0 generator = mh_generator(log_density=log_prob,x_start=1.0) tester = GaussianSteinTest(grad_log_prob,41) selector = SampleSelector(generator, sample_size=1000,thinning=20,tester=tester, max_iterations=5) data,converged = selector.points_from_stationary() tester = GaussianSteinTest(grad_log_prob,41) assert tester.compute_pvalue(data)>0.05 assert converged is True
def bandpass(self, rin, sin, rout, sout): ''' To create a band pass two circle images are created, one inverted and pasted into dthe other''' # if radius zero dont create the inner circle if rin != 0: self.create_circle_mask(rin, sin) else: self.data = np.zeros(self.data.shape) # create the outer circle bigcircle = deepcopy(self) bigcircle.create_circle_mask(rout, sout) bigcircle.invert() # sum the two pictures m = (self + bigcircle) # limit fro 0 to 1 and invert m.limit(1) m.invert() self.data = m.data
def random_points_in_circle(n,xx,yy,rr): """ get n random points in a circle. """ rnd = random(size=(n,3)) t = TWOPI*rnd[:,0] u = rnd[:,1:].sum(axis=1) r = zeros(n,'float') mask = u>1. xmask = logical_not(mask) r[mask] = 2.-u[mask] r[xmask] = u[xmask] xyp = reshape(rr*r,(n,1))*column_stack( (cos(t),sin(t)) ) dartsxy = xyp + array([xx,yy]) return dartsxy
def get_data(filename,headers,ph_units): # Importation des données .DAT dat_file = np.loadtxt("%s"%(filename),skiprows=headers,delimiter=',') labels = ["freq", "amp", "pha", "amp_err", "pha_err"] data = {l:dat_file[:,i] for (i,l) in enumerate(labels)} if ph_units == "mrad": data["pha"] = data["pha"]/1000 # mrad to rad data["pha_err"] = data["pha_err"]/1000 # mrad to rad if ph_units == "deg": data["pha"] = np.radians(data["pha"]) # deg to rad data["pha_err"] = np.radians(data["pha_err"]) # deg to rad data["phase_range"] = abs(max(data["pha"])-min(data["pha"])) # Range of phase measurements (used in NRMS error calculation) data["Z"] = data["amp"]*(np.cos(data["pha"]) + 1j*np.sin(data["pha"])) EI = np.sqrt(((data["amp"]*np.cos(data["pha"])*data["pha_err"])**2)+(np.sin(data["pha"])*data["amp_err"])**2) ER = np.sqrt(((data["amp"]*np.sin(data["pha"])*data["pha_err"])**2)+(np.cos(data["pha"])*data["amp_err"])**2) data["Z_err"] = ER + 1j*EI # Normalization of amplitude data["Z_max"] = max(abs(data["Z"])) # Maximum amplitude zn, zn_e = data["Z"]/data["Z_max"], data["Z_err"]/data["Z_max"] # Normalization of impedance by max amplitude data["zn"] = np.array([zn.real, zn.imag]) # 2D array with first column = real values, second column = imag values data["zn_err"] = np.array([zn_e.real, zn_e.imag]) # 2D array with first column = real values, second column = imag values return data
def genSphCoords(): """ Generates cartesian (x,y,z) and spherical (theta, phi) coordinates of a sphere Returns ------- coords : named tuple holds cartesian (x,y,z) and spherical (theta, phi) coordinates """ coords = namedtuple('coords', ['x', 'y', 'z', 'az', 'el']) az = _np.linspace(0, 2 * _np.pi, 360) el = _np.linspace(0, _np.pi, 181) coords.x = _np.outer(_np.cos(az), _np.sin(el)) coords.y = _np.outer(_np.sin(az), _np.sin(el)) coords.z = _np.outer(_np.ones(360), _np.cos(el)) coords.el, coords.az = _np.meshgrid(_np.linspace(0, _np.pi, 181), _np.linspace(0, 2 * _np.pi, 360)) return coords
def sph2cartMTX(vizMTX): """ Converts the spherical vizMTX data to named tuple contaibubg .xs/.ys/.zs Parameters ---------- vizMTX : array_like [180 x 360] matrix that hold amplitude information over phi and theta Returns ------- V : named_tuple Contains .xs, .ys, .zs cartesian coordinates """ rs = _np.abs(vizMTX.reshape((181, -1)).T) coords = genSphCoords() V = namedtuple('V', ['xs', 'ys', 'zs']) V.xs = rs * _np.sin(coords.el) * _np.cos(coords.az) V.ys = rs * _np.sin(coords.el) * _np.sin(coords.az) V.zs = rs * _np.cos(coords.el) return V
def convert_cof_mag2mass(t0, te, u0, alpha, s, q): """ function to convert from center of magnification to center of mass coordinates. Note that this function is for illustration only. It has not been tested and may have sign errors. """ if s <= 1.0: return t0, u0 else: delta = q / (1. + q) / s delta_u0 = delta * np.sin(alpha * np.pi / 180.) delta_tau = delta * np.cos(alpha * np.pi / 180.) t0_prime = t0 + delta_tau * te u0_prime = u0 + delta_u0 return t0_prime, u0_prime #Define model parameters in CoMAGN system
def _B_0_function(self, z): """ calculate B_0(z) function defined in: Gould A. 1994 ApJ 421L, 71 "Proper motions of MACHOs http://adsabs.harvard.edu/abs/1994ApJ...421L..71G Yoo J. et al. 2004 ApJ 603, 139 "OGLE-2003-BLG-262: Finite-Source Effects from a Point-Mass Lens" http://adsabs.harvard.edu/abs/2004ApJ...603..139Y """ out = 4. * z / np.pi function = lambda x: (1.-value**2*np.sin(x)**2)**.5 for (i, value) in enumerate(z): if value < 1.: out[i] *= ellipe(value*value) else: out[i] *= integrate.quad(function, 0., np.arcsin(1./value))[0] return out
def get_orientation_sector(dx,dy): # rotate (dx,dy) by pi/8 rotation = np.array([[np.cos(np.pi/8), -np.sin(np.pi/8)], [np.sin(np.pi/8), np.cos(np.pi/8)]]) rotated = np.dot(rotation, np.array([[dx], [dy]])) if rotated[1] < 0: rotated[0] = -rotated[0] rotated[1] = -rotated[1] s_theta = -1 if rotated[0] >= 0 and rotated[0] >= rotated[1]: s_theta = 0 elif rotated[0] >= 0 and rotated[0] < rotated[1]: s_theta = 1 elif rotated[0] < 0 and -rotated[0] < rotated[1]: s_theta = 2 elif rotated[0] < 0 and -rotated[0] >= rotated[1]: s_theta = 3 return s_theta
def to_radec(coords, xc=0, yc=0): """ Convert the generated coordinates to (ra, dec) (unit: degree). xc, yc: the center coordinate (ra, dec) """ results = [] for r, theta in coords: # FIXME: spherical algebra should be used!!! dx = r * np.cos(theta*np.pi/180) dy = r * np.sin(theta*np.pi/180) x = xc + dx y = yc + dy results.append((x, y)) if len(results) == 1: return results[0] else: return results
def plotArc(start_angle, stop_angle, radius, width, **kwargs): """ write a docstring for this function""" numsegments = 100 theta = np.radians(np.linspace(start_angle+90, stop_angle+90, numsegments)) centerx = 0 centery = 0 x1 = -np.cos(theta) * (radius) y1 = np.sin(theta) * (radius) stack1 = np.column_stack([x1, y1]) x2 = -np.cos(theta) * (radius + width) y2 = np.sin(theta) * (radius + width) stack2 = np.column_stack([np.flip(x2, axis=0), np.flip(y2,axis=0)]) #add the first values from the first set to close the polygon np.append(stack2, [[x1[0],y1[0]]], axis=0) arcArray = np.concatenate((stack1,stack2), axis=0) return patches.Polygon(arcArray, True, **kwargs), ((x1, y1), (x2, y2))
def ct2lg(dX, dY, dZ, lat, lon): n = dX.size R = np.zeros((3, 3, n)) R[0, 0, :] = -np.multiply(np.sin(np.deg2rad(lat)), np.cos(np.deg2rad(lon))) R[0, 1, :] = -np.multiply(np.sin(np.deg2rad(lat)), np.sin(np.deg2rad(lon))) R[0, 2, :] = np.cos(np.deg2rad(lat)) R[1, 0, :] = -np.sin(np.deg2rad(lon)) R[1, 1, :] = np.cos(np.deg2rad(lon)) R[1, 2, :] = np.zeros((1, n)) R[2, 0, :] = np.multiply(np.cos(np.deg2rad(lat)), np.cos(np.deg2rad(lon))) R[2, 1, :] = np.multiply(np.cos(np.deg2rad(lat)), np.sin(np.deg2rad(lon))) R[2, 2, :] = np.sin(np.deg2rad(lat)) dxdydz = np.column_stack((np.column_stack((dX, dY)), dZ)) RR = np.reshape(R[0, :, :], (3, n)) dx = np.sum(np.multiply(RR, dxdydz.transpose()), axis=0) RR = np.reshape(R[1, :, :], (3, n)) dy = np.sum(np.multiply(RR, dxdydz.transpose()), axis=0) RR = np.reshape(R[2, :, :], (3, n)) dz = np.sum(np.multiply(RR, dxdydz.transpose()), axis=0) return dx, dy, dz
def distance(self, lon1, lat1, lon2, lat2): """ Calculate the great circle distance between two points on the earth (specified in decimal degrees) """ # convert decimal degrees to radians lon1 = lon1*pi/180 lat1 = lat1*pi/180 lon2 = lon2*pi/180 lat2 = lat2*pi/180 # haversine formula dlon = lon2 - lon1 dlat = lat2 - lat1 a = np.sin(dlat/2)**2 + np.cos(lat1) * np.cos(lat2) * np.sin(dlon/2)**2 c = 2 * np.arcsin(np.sqrt(a)) km = 6371 * c return km
def distance(self, lon1, lat1, lon2, lat2): """ Calculate the great circle distance between two points on the earth (specified in decimal degrees) """ # convert decimal degrees to radians lon1 = lon1*pi/180 lat1 = lat1*pi/180 lon2 = lon2*pi/180 lat2 = lat2*pi/180 # haversine formula dlon = lon2 - lon1 dlat = lat2 - lat1 a = numpy.sin(dlat/2)**2 + numpy.cos(lat1) * numpy.cos(lat2) * numpy.sin(dlon/2)**2 c = 2 * numpy.arcsin(numpy.sqrt(a)) km = 6371 * c return km
def distance(lon1, lat1, lon2, lat2): """ Calculate the great circle distance between two points on the earth (specified in decimal degrees) """ # convert decimal degrees to radians lon1 = lon1*pi/180 lat1 = lat1*pi/180 lon2 = lon2*pi/180 lat2 = lat2*pi/180 # haversine formula dlon = lon2 - lon1 dlat = lat2 - lat1 a = np.sin(dlat/2)**2 + np.cos(lat1) * np.cos(lat2) * np.sin(dlon/2)**2 c = 2 * np.arcsin(np.sqrt(a)) km = 6371 * c return km
def todictionary(self, time_series=False): # convert the ETM adjustment into a dirtionary # optionally, output the whole time series as well # start with the parameters etm = dict() etm['Linear'] = {'tref': self.Linear.tref, 'params': self.Linear.values.tolist()} etm['Jumps'] = [{'type':jump.type, 'year': jump.year, 'a': jump.a.tolist(), 'b': jump.b.tolist(), 'T': jump.T} for jump in self.Jumps.table] etm['Periodic'] = {'frequencies': self.Periodic.frequencies, 'sin': self.Periodic.sin.tolist(), 'cos': self.Periodic.cos.tolist()} if time_series: ts = dict() ts['t'] = self.ppp_soln.t.tolist() ts['x'] = self.ppp_soln.x.tolist() ts['y'] = self.ppp_soln.y.tolist() ts['z'] = self.ppp_soln.z.tolist() etm['time_series'] = ts return etm
def ct2lg(self, dX, dY, dZ, lat, lon): n = dX.size R = numpy.zeros((3, 3, n)) R[0, 0, :] = -numpy.multiply(numpy.sin(numpy.deg2rad(lat)), numpy.cos(numpy.deg2rad(lon))) R[0, 1, :] = -numpy.multiply(numpy.sin(numpy.deg2rad(lat)), numpy.sin(numpy.deg2rad(lon))) R[0, 2, :] = numpy.cos(numpy.deg2rad(lat)) R[1, 0, :] = -numpy.sin(numpy.deg2rad(lon)) R[1, 1, :] = numpy.cos(numpy.deg2rad(lon)) R[1, 2, :] = numpy.zeros((1, n)) R[2, 0, :] = numpy.multiply(numpy.cos(numpy.deg2rad(lat)), numpy.cos(numpy.deg2rad(lon))) R[2, 1, :] = numpy.multiply(numpy.cos(numpy.deg2rad(lat)), numpy.sin(numpy.deg2rad(lon))) R[2, 2, :] = numpy.sin(numpy.deg2rad(lat)) dxdydz = numpy.column_stack((numpy.column_stack((dX, dY)), dZ)) RR = numpy.reshape(R[0, :, :], (3, n)) dx = numpy.sum(numpy.multiply(RR, dxdydz.transpose()), axis=0) RR = numpy.reshape(R[1, :, :], (3, n)) dy = numpy.sum(numpy.multiply(RR, dxdydz.transpose()), axis=0) RR = numpy.reshape(R[2, :, :], (3, n)) dz = numpy.sum(numpy.multiply(RR, dxdydz.transpose()), axis=0) return dx, dy, dz
def orthogonalization_matrix(lengths, angles): """Return orthogonalization matrix for crystallographic cell coordinates. Angles are expected in degrees. The de-orthogonalization matrix is the inverse. >>> O = orthogonalization_matrix([10, 10, 10], [90, 90, 90]) >>> numpy.allclose(O[:3, :3], numpy.identity(3, float) * 10) True >>> O = orthogonalization_matrix([9.8, 12.0, 15.5], [87.2, 80.7, 69.7]) >>> numpy.allclose(numpy.sum(O), 43.063229) True """ a, b, c = lengths angles = numpy.radians(angles) sina, sinb, _ = numpy.sin(angles) cosa, cosb, cosg = numpy.cos(angles) co = (cosa * cosb - cosg) / (sina * sinb) return numpy.array([ [ a*sinb*math.sqrt(1.0-co*co), 0.0, 0.0, 0.0], [-a*sinb*co, b*sina, 0.0, 0.0], [ a*cosb, b*cosa, c, 0.0], [ 0.0, 0.0, 0.0, 1.0]])
def plotPlaceTxRxSphereXY(Ax,xtx,ytx,xrx,yrx,x0,y0,a): Xlim = Ax.get_xlim() Ylim = Ax.get_ylim() FS = 20 Ax.scatter(xtx,ytx,s=100,color='k') Ax.text(xtx-0.75,ytx+1.5,'$\mathbf{Tx}$',fontsize=FS+6) Ax.scatter(xrx,yrx,s=100,color='k') Ax.text(xrx-0.75,yrx-4,'$\mathbf{Rx}$',fontsize=FS+6) xs = x0 + a*np.cos(np.linspace(0,2*np.pi,41)) ys = y0 + a*np.sin(np.linspace(0,2*np.pi,41)) Ax.plot(xs,ys,ls=':',color='k',linewidth=3) Ax.set_xbound(Xlim) Ax.set_ybound(Ylim) return Ax
def calc_IndCurrent_cos_range(self,f,t): """Induced current over a range of times""" Bpx = self.Bpx Bpz = self.Bpz a2 = self.a2 azm = np.pi*self.azm/180. R = self.R L = self.L w = 2*np.pi*f Ax = np.pi*a2**2*np.sin(azm) Az = np.pi*a2**2*np.cos(azm) Phi = (Ax*Bpx + Az*Bpz) phi = np.arctan(R/(w*L))-np.pi # This is the phase and not phase lag Is = -(w*Phi/(R*np.sin(phi) + w*L*np.cos(phi)))*np.cos(w*t + phi) Ire = -(w*Phi/(R*np.sin(phi) + w*L*np.cos(phi)))*np.cos(w*t)*np.cos(phi) Iim = (w*Phi/(R*np.sin(phi) + w*L*np.cos(phi)))*np.sin(w*t)*np.sin(phi) return Ire,Iim,Is,phi
def is_grid(self, grid, image): """ Checks the "gridness" by analyzing the results of a hough transform. :param grid: binary image :return: wheter the object in the image might be a grid or not """ # - Distance resolution = 1 pixel # - Angle resolution = 1° degree for high line density # - Threshold = 144 hough intersections # 8px digit + 3*2px white + 2*1px border = 16px per cell # => 144x144 grid # 144 - minimum number of points on the same line # (but due to imperfections in the binarized image it's highly # improbable to detect a 144x144 grid) lines = cv2.HoughLines(grid, 1, np.pi / 180, 144) if lines is not None and np.size(lines) >= 20: lines = lines.reshape((lines.size / 2), 2) # theta in [0, pi] (theta > pi => rho < 0) # normalise theta in [-pi, pi] and negatives rho lines[lines[:, 0] < 0, 1] -= np.pi lines[lines[:, 0] < 0, 0] *= -1 criteria = (cv2.TERM_CRITERIA_EPS, 0, 0.01) # split lines into 2 groups to check whether they're perpendicular if cv2.__version__[0] == '2': density, clmap, centers = cv2.kmeans( lines[:, 1], 2, criteria, 5, cv2.KMEANS_RANDOM_CENTERS) else: density, clmap, centers = cv2.kmeans( lines[:, 1], 2, None, criteria, 5, cv2.KMEANS_RANDOM_CENTERS) if self.debug: self.save_hough(lines, clmap) # Overall variance from respective centers var = density / np.size(clmap) sin = abs(np.sin(centers[0] - centers[1])) # It is probably a grid only if: # - centroids difference is almost a 90° angle (+-15° limit) # - variance is less than 5° (keeping in mind surface distortions) return sin > 0.99 and var <= (5*np.pi / 180) ** 2 else: return False
def save_hough(self, lines, clmap): """ :param lines: (rho, theta) pairs :param clmap: clusters assigned to lines :return: None """ height, width = self.image.shape ratio = 600. * (self.step+1) / min(height, width) temp = cv2.resize(self.image, None, fx=ratio, fy=ratio, interpolation=cv2.INTER_CUBIC) temp = cv2.cvtColor(temp, cv2.COLOR_GRAY2BGR) colors = [(0, 127, 255), (255, 0, 127)] for i in range(0, np.size(lines) / 2): rho = lines[i, 0] theta = lines[i, 1] color = colors[clmap[i, 0]] if theta < np.pi / 4 or theta > 3 * np.pi / 4: pt1 = (rho / np.cos(theta), 0) pt2 = (rho - height * np.sin(theta) / np.cos(theta), height) else: pt1 = (0, rho / np.sin(theta)) pt2 = (width, (rho - width * np.cos(theta)) / np.sin(theta)) pt1 = (int(pt1[0]), int(pt1[1])) pt2 = (int(pt2[0]), int(pt2[1])) cv2.line(temp, pt1, pt2, color, 5) self.save2image(temp)
def is_grid(self, grid, image): """ Checks the "gridness" by analyzing the results of a hough transform. :param grid: binary image :return: wheter the object in the image might be a grid or not """ # - Distance resolution = 1 pixel # - Angle resolution = 1° degree for high line density # - Threshold = 144 hough intersections # 8px digit + 3*2px white + 2*1px border = 16px per cell # => 144x144 grid # 144 - minimum number of points on the same line # (but due to imperfections in the binarized image it's highly # improbable to detect a 144x144 grid) lines = cv2.HoughLines(grid, 1, np.pi / 180, 144) if lines is not None and np.size(lines) >= 20: lines = lines.reshape((lines.size/2), 2) # theta in [0, pi] (theta > pi => rho < 0) # normalise theta in [-pi, pi] and negatives rho lines[lines[:, 0] < 0, 1] -= np.pi lines[lines[:, 0] < 0, 0] *= -1 criteria = (cv2.TERM_CRITERIA_EPS, 0, 0.01) # split lines into 2 groups to check whether they're perpendicular if cv2.__version__[0] == '2': density, clmap, centers = cv2.kmeans( lines[:, 1], 2, criteria, 5, cv2.KMEANS_RANDOM_CENTERS) else: density, clmap, centers = cv2.kmeans( lines[:, 1], 2, None, criteria, 5, cv2.KMEANS_RANDOM_CENTERS) # Overall variance from respective centers var = density / np.size(clmap) sin = abs(np.sin(centers[0] - centers[1])) # It is probably a grid only if: # - centroids difference is almost a 90° angle (+-15° limit) # - variance is less than 5° (keeping in mind surface distortions) return sin > 0.99 and var <= (5*np.pi / 180) ** 2 else: return False
def build_2D_cov_matrix(sigmax,sigmay,angle,verbose=True): """ Build a covariance matrix for a 2D multivariate Gaussian --- INPUT --- sigmax Standard deviation of the x-compoent of the multivariate Gaussian sigmay Standard deviation of the y-compoent of the multivariate Gaussian angle Angle to rotate matrix by in degrees (clockwise) to populate covariance cross terms verbose Toggle verbosity --- EXAMPLE OF USE --- import tdose_utilities as tu covmatrix = tu.build_2D_cov_matrix(3,1,35) """ if verbose: print ' - Build 2D covariance matrix with varinaces (x,y)=('+str(sigmax)+','+str(sigmay)+\ ') and then rotated '+str(angle)+' degrees' cov_orig = np.zeros([2,2]) cov_orig[0,0] = sigmay**2.0 cov_orig[1,1] = sigmax**2.0 angle_rad = (180.0-angle) * np.pi/180.0 # The (90-angle) makes sure the same convention as DS9 is used c, s = np.cos(angle_rad), np.sin(angle_rad) rotmatrix = np.matrix([[c, -s], [s, c]]) cov_rot = np.dot(np.dot(rotmatrix,cov_orig),np.transpose(rotmatrix)) # performing rot * cov * rot^T return cov_rot # = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
def residual(r,theta,u,d): out = np.empty_like(u) out[0] = (2*np.sin(theta)*r*d(u[0],1,0) + r*r*np.sin(theta)*d(u[0],2,0) + np.cos(theta)*d(u[0],0,1) + np.sin(theta)*d(u[1],0,2)) out[1] = (2*np.sin(theta)*r*d(u[1],1,0) + r*r*np.sin(theta)*d(u[1],2,0) + np.cos(theta)*d(u[1],0,1) + np.sin(theta)*d(u[1],0,2)) return out
def residual(r,theta,u,d): u = u[0] out = (2*np.sin(theta)*r*d(u,1,0) + r*r*np.sin(theta)*d(u,2,0) + np.cos(theta)*d(u,0,1) + np.sin(theta)*d(u,0,2)) out = out.reshape(tuple([1]) + out.shape) return out
