import numpy as np
from polsartools.utils.plot_utils import pol_sign, pol_sign2d, poincare_plot,poincare_sphere
def prepare_data(S2):
A0 = (1/4)*np.abs(S2[0,0]+S2[1,1])**2
B0 = (1/4)*np.abs(S2[0,0]-S2[1,1])**2 + np.abs(S2[0,1])**2
B_psi = (1/4)*np.abs(S2[0,0]-S2[1,1])**2 - np.abs(S2[0,1])**2
# C_psi = (1/2)*np.abs(S2[0,0]-S2[1,1])**2
# di-hedral fix convert real part of vv to positive
C_psi = (1/2) * np.abs(S2[0,0] - (np.real(S2[1,1]) * (1 if np.real(S2[1,1]) >= 0 else -1) + 1j * np.imag(S2[1,1])))**2
D_psi = np.imag(S2[0,0]*np.conjugate(S2[1,1]))
E_psi = np.real(np.conjugate(S2[0,1])*(S2[0,0]-S2[1,1]))
F_psi = np.imag(np.conjugate(S2[0,1])*(S2[0,0]-S2[1,1]))
G_psi = np.imag(np.conjugate(S2[0,1])*(S2[0,0]+S2[1,1]))
H_psi = np.real(np.conjugate(S2[0,1])*(S2[0,0]+S2[1,1]))
K_mat = np.array([
[A0+B0,C_psi,H_psi,F_psi],
[C_psi,A0+B_psi,E_psi,G_psi],
[H_psi,E_psi,A0-B_psi,D_psi],
[F_psi,G_psi,D_psi,-A0+B0]
])
XX_POL = []
cp_sign = np.zeros((181,91))
xp_sign = np.zeros((181,91))
x, y = np.mgrid[-90: 91 : 1, -45 : 46 : 1]
xx = 0
for tilt in np.arange(-90,91,1):
yy=0
for elep in np.arange(-45,46,1):
psi = tilt*np.pi/180
tau = elep*np.pi/180
S_co = np.array([1,
np.cos(2*psi)*np.cos(2*tau),
np.sin(2*psi)*np.cos(2*tau),
np.sin(2*tau)
])
stc = np.conjugate(S_co.T)
temp_pow_c = np.matmul(stc,np.matmul(K_mat,S_co))
S_cross = np.array([1,
-np.cos(2*psi)*np.cos(2*tau),
-np.sin(2*psi)*np.cos(2*tau),
-np.sin(2*tau)
])
stx = np.conjugate(S_cross.T)
temp_pow_x = np.matmul(stx,np.matmul(K_mat,S_co))
XX_POL.append([tilt,elep,temp_pow_c,temp_pow_x])
cp_sign[xx,yy] = temp_pow_c
xp_sign[xx,yy] = temp_pow_x
yy=yy+1
# print(xx,yy)
xx=xx+1
# cp_sign[cp_sign==0]=np.nan
# xp_sign[xp_sign==0]=np.nan
cp_sign = cp_sign/np.nanmax(cp_sign)
xp_sign = xp_sign/np.nanmax(xp_sign)
return cp_sign, xp_sign
def prepare_dataT3(T3):
# Define angular grids
phi_deg = np.linspace(-90, 90, 181)
tau_deg = np.linspace(-45, 45, 91)
phi = np.deg2rad(phi_deg)
tau = np.deg2rad(tau_deg)
# Create output arrays
cp_sign = np.zeros((len(phi), len(tau)))
xp_sign = np.zeros((len(phi), len(tau)))
T11 = T3[0, 0].real
T12_re = T3[0, 1].real
T12_im = T3[0, 1].imag
T13_re = T3[0, 2].real
T13_im = T3[0, 2].imag
T22 = T3[1, 1].real
T23_re = T3[1, 2].real
T23_im = T3[1, 2].imag
T33 = T3[2, 2].real
for i_phi, Phi in enumerate(phi):
cos2P, sin2P, sin4P, cos4P = np.cos(2*Phi), np.sin(2*Phi), np.sin(4*Phi), np.cos(4*Phi)
# Phi rotation
T12_re_phi = T12_re * cos2P + T13_re * sin2P
# T12_im_phi = T12_im * cos2P + T13_im * sin2P
# T13_re_phi = -T12_re * sin2P + T13_re * cos2P
T13_im_phi = -T12_im * sin2P + T13_im * cos2P
T22_phi = T22 * cos2P**2 + T23_re * sin4P + T33 * sin2P**2
# T23_re_phi = 0.5 * (T33 - T22) * sin4P + T23_re * cos4P
T23_im_phi = T23_im
T33_phi = T22 * sin2P**2 - T23_re * sin4P + T33 * cos2P**2
for j_tau, Tau in enumerate(tau):
cos2T, sin2T, sin4T, cos4T = np.cos(2*Tau), np.sin(2*Tau), np.sin(4*Tau), np.cos(4*Tau)
# Tau rotation
T311 = T11 * cos2T**2 + T13_im_phi * sin4T + T33_phi * sin2T**2
T312_re = T12_re_phi * cos2T + T23_im_phi * sin2T
T322 = T22_phi
T333 = T11 * sin2T**2 - T13_im_phi * sin4T + T33_phi * cos2T**2
# Output values
cp_sign[i_phi, j_tau] = (T311 + 2 * T312_re + T322) / 2.0
xp_sign[i_phi, j_tau] = T333 / 2.0
cp_sign = cp_sign/np.nanmax(cp_sign)
xp_sign = xp_sign/np.nanmax(xp_sign)
return cp_sign, xp_sign
[docs]
def signature_fp(mat=None, title='',ppath='',cmap='jet',plotType = 1,
fig=None, axes=None, start_index=0):
"""
Generates and visualizes polarimetric signatures from a 2x2 scattering matrix (S2) or a 3x3 coherency matrix (T3).
Examples
--------
>>> mat = np.array([[1, 0], [0, 1]]) # Trihedral
>>> signature_fp(mat, title='Trihedral', plotType=1)
Parameters
----------
mat : np.ndarray (2x2 or 3x3) or None
Input matrix. If shape is (2, 2), treated as S2. If (3, 3), treated as T3.
If None, only theoretical/canonical plots will be generated.
title : str, optional
Title of the plot. Default is an empty string.
ppath : str, optional
Name of the output file (*.png). Default is an empty string.
cmap : str, optional
Colormap used for visualizing the data. Default is 'jet'.
plotType : int, optional
Determines the type of plot to generate:
- 1: Standard polarimetric signature via `pol_sign`.
- 2: 2D polarimetric signature via `pol_sign2d`.
- 3: Poincaré sphere mapping via `poincare_plot`.
- 4: Render empty or canonical Poincaré sphere via `poincare_sphere` (S2 not required).
"""
if mat is not None:
if mat.shape == (2, 2):
cp_sign, xp_sign = prepare_data(mat) # From S2
elif mat.shape == (3, 3):
if not np.allclose(mat, mat.conj().T, atol=1e-8):
print("Warning: Input matrix is not Hermitian. Results may be inaccurate.")
cp_sign, xp_sign = prepare_dataT3(mat) # From T3
else:
raise ValueError("Input matrix must be either 2x2 (S2) or 3x3 (T3).")
# Choose visualization method
if plotType == 4:
poincare_sphere(ppath=ppath)
elif mat is not None and plotType == 3:
poincare_plot(cp_sign, xp_sign, title=title, ppath=ppath, cmap=cmap)
elif mat is not None and plotType == 2:
pol_sign2d(cp_sign, xp_sign, title=title, ppath=ppath, cmap=cmap)
else:
figout, axesout = pol_sign(cp_sign, xp_sign, title=title, ppath=ppath,
cmap=cmap, fig=fig, axes=axes, start_index=start_index)
return figout, axesout
# S2 = np.array([[1,0],
# [0,1]])
# T3 = np.array([
# [2.0, 0.0, 0.0],
# [0.0, 0.0, 0.0],
# [0.0, 0.0, 0.0]
# ])
# # fix this oriented dihedral
# S2 = np.array([[1, 0],
# [0,-1]])
# S2 = np.array([[0,1],
# [1,0]])
# S2 = np.array([[0,0],
# [0,1]])
# S2 = np.array([[1,-1],
# [-1,1]])
# array([[2248.6506 -5218.124j , -4.0451455 -46.991398j],
# [ -11.6204195 -27.771238j, 800.1831 -5830.6836j ]],
# dtype=complex64)
# fp_sign(S2, plotType = 3)
