362 lines
13 KiB
Python
362 lines
13 KiB
Python
import numpy as np
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from core.sk_iter import generate_starting_poles
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from scipy.linalg import block_diag
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import skrf as rf
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from skrf import VectorFitting
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from core.freqency import auto_select
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import random as rnd
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class RelaxedBasicBasisQR:
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def __init__(self,H,freqs,poles,weights=None,passivity=True,dc_enforce=True,fit_constant=True,fit_proportional=False):
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self.least_squares_rms_error = None
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self.least_squares_condition = None
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self.eigenval_condition = None
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self.eigenval_rms_error = None
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self.dc_tol = 1e-18
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self.dc_enforce = dc_enforce
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self.fit_constant = fit_constant
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self.fit_proportional = fit_proportional
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# self.H = H
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# self.freqs = freqs
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self.freqs = freqs
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self.H = H
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self.s = self.freqs * 2j * np.pi
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self.P = len(poles)
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self.poles = poles
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self.Phi = self.generate_basis(self.s, self.poles)
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self.A = self.matrix_A(self.poles)
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self.B = self.vector_B(self.poles)
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self.Cw,self.w0,self.e = self.fit_denominator(self.H, weights=weights)
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self.D = self.w0
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self.Cr = None
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z = np.linalg.eigvals(self.A - self.B @ self.Cw)
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p_next = -z
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if passivity:
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self.next_poles = self.passivity_enforce(p_next)
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else:
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self.next_poles = p_next
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# z = np.where(np.real(z) < 0, z, -np.conj(z)) # enforce LHP
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# self.next_poles = np.sort_complex(z)
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self.eigenval_condition = np.linalg.cond(self.A - self.B @ self.Cw)
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self.eigenval_rms_error = np.sqrt(np.mean(np.abs(np.real(z) - np.real(poles))**2 + np.abs(np.imag(z) - np.imag(poles))**2))
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self.Dt = self.eval_Dt_state_space()
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self.delta = self.Dt / weights if weights is not None else self.Dt
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pass
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def passivity_enforce(self,poles):
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"""enforce poles' real parts to be negative"""
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enforced_poles = []
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for pole in poles:
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if pole.real > 0:
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pole = -np.conj(pole)
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enforced_poles.append(pole)
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return enforced_poles
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def eval_Dt_state_space(self):
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"""Return D(s_k)=C(s_k I - A)^(-1)B + D for all k (complex 1D array)."""
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s = 1j * 2*np.pi * np.asarray(self.freqs, float).ravel()
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A = np.asarray(self.A, np.complex128); n = A.shape[0]
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B = np.asarray(self.B, np.complex128).reshape(n, 1)
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C = np.asarray(self.Cw, float).reshape(1, n)
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D = self.D
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I = np.eye(n, dtype=np.complex128)
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out = np.empty_like(s, dtype=np.complex128)
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for k, sk in enumerate(s):
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DS = D + (C @ np.linalg.inv(sk*I - A) @ B)
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out[k] = DS[0, 0]
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return out
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def generate_basis(self,s, poles):
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"""Real basis of (15)-(16); returns Φ(s) and a layout for packing C."""
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cols = []
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i = 0
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while i < len(poles):
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p = poles[i]
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if p.real > 0:
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raise ValueError("poles must be in the LHP")
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if i+1 < len(poles) and np.isclose(poles[i+1], np.conj(p)):
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pc = poles[i+1]
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phi1 = 1/(s - p) + 1/(s - pc) # eq (15)generate_basis
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phi2 = 1j*(1/(s - p) - 1/(s - pc)) # eq (16) (fixed sign)
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cols += [phi1, phi2]
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i += 2
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else:
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cols.append(1/(s - p))
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i += 1
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Phi = np.column_stack(cols).astype(np.complex128)
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return Phi
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def matrix_A(self, poles):
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def A_block(p):
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if abs(p.imag) < 1e-14:
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return np.array([[p.real]], float) # A_p = [ p ]
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return np.array([[p.real, p.imag], # A_p = [[Re p, Im p],
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[-p.imag, p.real]], float) # [-Im p, Re p]]
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A = None; i = 0
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while i < len(poles):
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p = poles[i]
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Ab = A_block(p)
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if i+1 < len(poles) and np.isclose(poles[i+1], np.conj(p)): i += 2
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else: i += 1
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A = Ab if A is None else block_diag(A, Ab)
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return A
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def vector_B(self, poles):
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def B_block(p):
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return np.array([[1.0]], float) if abs(p.imag)<1e-14 else np.array([[2.0],[0.0]], float)
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B = None; i = 0
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while i < len(poles):
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p = poles[i]
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Bb = B_block(p)
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if i+1 < len(poles) and np.isclose(poles[i+1], np.conj(p)): i += 2
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else: i += 1
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B = Bb if B is None else np.vstack([B, Bb])
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return B
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def fit_denominator(self, H, weights=None, d0 = 1.0):
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"""
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Solve formula (70) on the real basis Φ to obtain:
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- d (real) → packs into C for this state's block structure
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- gamma (complex)
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Optional 'weights' (K,) apply row scaling: SK weighting if 1/|D_prev|.
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"""
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H = np.asarray(H, np.complex128).reshape(-1,1)
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K, N = self.Phi.shape
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one = np.ones((K, 1), np.complex128)
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Phi = self.Phi
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dc_tol = 1e-18
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has_dc = self.dc_enforce and self.freqs[0] < dc_tol
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keep = np.ones(K, dtype=bool)
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# SK weighting (applied only to the (73) rows we keep in LS)
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if weights is None:
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weights = np.diag(np.ones(len(H), np.complex128))
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else:
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weights = np.diag([1/res for res in weights])
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if self.fit_constant:
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Phi_w = np.hstack([one, Phi])
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M = np.hstack([Phi, -(H * Phi_w)]) # (K, 2N+1), complex
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else:
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M = np.hstack([Phi, -(H * Phi)]) # (K, 2N), complex
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if has_dc:
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# Enforce DC response exactly:
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k0 = int(np.argmin(np.abs(self.freqs)))
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keep[k0] = False
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M_w = weights @ M
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A_re = np.real(M_w[keep, :])
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A_im = np.imag(M_w[keep, :])
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mask = np.ones(K, dtype=bool); mask[k0] = False
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# exact (unweighted) DC rows:
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A_dc_re = np.real(M[k0, :]).reshape(1, -1)
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A_dc_im = np.imag(M[k0, :]).reshape(1, -1)
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else:
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M_w = weights @ M
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A_re = np.real(M_w)
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A_im = np.imag(M_w)
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A_dc_re = A_dc_im = None
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A_blocks = [A_re, A_im]
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if self.fit_constant:
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beta = float(np.sqrt(np.sum(np.abs(H)**2)))
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mean_row = (beta / K) * np.sum(Phi_w, axis=0)
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A_w0 = np.concatenate([np.zeros(N, float),
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np.real(mean_row).astype(float)]
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).reshape(1, -1)
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b_w0 = np.array([beta], float)
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A_blocks += [A_w0]
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m = A_re.shape[0] + A_im.shape[0]
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b = np.zeros(m, float)
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b = np.concatenate([b, b_w0])
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else:
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H_kp = (weights @ H)[keep,:]
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b_re = np.real(d0 * H_kp)
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b_im = np.imag(d0 * H_kp)
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b = np.concatenate([b_re.ravel(), b_im.ravel()]).astype(float)
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# ---- build final stacked-real system ----
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# if A_dc_re is not None:
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# A_blocks += [A_dc_re, A_dc_im]
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# b = np.concatenate([b, np.zeros(2, float)]) # DC rows → 0
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# ---- QR solve for x = [c_H (N); c_w (N+1)] ----
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A = np.vstack(A_blocks).astype(float)
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Q, R = np.linalg.qr(A, mode="reduced")
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if self.fit_constant:
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Q2 = Q[:,A.shape[1]//2:]
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R22 = R[A.shape[1]//2:,A.shape[1]//2:]
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else:
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Q2 = Q[:,A.shape[1]//2:]
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R22 = R[A.shape[1]//2:,A.shape[1]//2:]
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x = np.linalg.solve(R22, Q2.T @ b)
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# diagnostics
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resid = Q2 @ R22 @ x - b
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self.least_squares_rms_error = float(np.sqrt(np.mean(resid**2)))
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self.least_squares_condition = float(np.linalg.cond(R))
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# split cw and return
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# cw = x[N:] # last (N+1) entries = [w0, w_1..w_N]
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# w0 = float(cw[0])
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# Cw = cw[1:].reshape(1, N) # row vector (1, N)
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return self.extract_Cw_d_e(x,N,d0)
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def extract_Cw_d_e(self,C,N,d0=1.0):
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if self.fit_proportional and self.fit_constant:
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d = C[1]
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e = C[0]
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return C[2:].reshape(1, -1), d, e
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elif self.fit_proportional and not self.fit_constant:
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d = 0.0
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e = C[0]
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return C[1:].reshape(1, -1), d, e
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elif not self.fit_proportional and self.fit_constant:
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d = C[0]
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e = 0.0
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return C[1:].reshape(1, -1), d, e
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else:
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return C.reshape(1, -1), d0, 0.0
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def non_bias_Cr(self,w0):
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A = np.asarray(self.Phi)
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den = np.diag((w0 + self.Phi @ self.Cw.T).ravel())
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b = np.asarray(den) @ self.H.reshape(-1,1)
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Cr, residuals, rank, s = np.linalg.lstsq(A, b, rcond=None)
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return Cr
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def evaluate(self,freqs, w0):
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s = 1j * 2*np.pi * np.asarray(freqs, float).ravel()
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phi = self.generate_basis(s, self.poles)
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den = w0 + phi @ self.Cw.T
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if self.Cr is None:
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self.Cr = self.non_bias_Cr(w0=w0)
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num = phi @ self.Cr
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H = num / den
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return H.ravel()
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def noise(n:complex,coeff:float=0.05):
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noise_r = rnd.gauss(-coeff * n.real, coeff * n.real)
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noise_i = rnd.gauss(-coeff * n.imag, coeff * n.imag)
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return complex(n.real + noise_r, n.imag + noise_i)
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if __name__ == "__main__":
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start_point = 0
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network = rf.Network("/tmp/paramer/simulation/3000/3000.s2p")
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K = 50
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full_freqences = network.f[start_point:]
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noised_sampled_points = [(network.y[i][0][0]) for i in range(start_point,len(network.y))]
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sampled_points = [network.y[i][0][0] for i in range(start_point,len(network.y))]
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H11,freqs = auto_select(noised_sampled_points,full_freqences,max_points=20)
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poles = generate_starting_poles(2,beta_min=1e4,beta_max=freqs[-1]*1.1)
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Dt_1 = np.ones((len(freqs),1),np.complex128)
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# Levi step (no weighting):
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basis = RelaxedBasicBasisQR(H11,freqs,poles=poles)
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Dt = basis.Dt
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poles = basis.next_poles
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print("Levi step (no weighting):")
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print("A:",basis.A)
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print("B:",basis.B)
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print("C:",basis.Cw)
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print("D:",basis.D)
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print("next_pozles:",basis.next_poles)
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print("Dt:",Dt, "norm:",np.linalg.norm(Dt))
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# SK weighting (optional, after first pass):
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least_squares_condition = []
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least_squares_rms_error = []
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eigenval_condition = []
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eigenval_rms_error = []
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for i in range(K):
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basis = RelaxedBasicBasisQR(H11,freqs,poles=poles,weights=Dt)
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Dt_1 = Dt
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Dt = basis.Dt
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poles = basis.next_poles
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print(f"SK Iteration {i+1}/{K}")
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print("A:",basis.A)
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print("B:",basis.B)
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print("C:",basis.Cw)
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print("D:",basis.D)
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print("z:",basis.next_poles)
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print("Dt:",Dt)
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print("Dt/Dt-1",np.linalg.norm(Dt) / np.linalg.norm(Dt_1))
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least_squares_condition.append(basis.least_squares_condition)
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least_squares_rms_error.append(basis.least_squares_rms_error)
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eigenval_condition.append(basis.eigenval_condition)
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eigenval_rms_error.append(basis.eigenval_rms_error)
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# H11_evaluated = basis.evaluate_pole_residue(network.f[1:],poles,basis.C[0])
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H11_evaluated = basis.evaluate(network.f[start_point:], w0=basis.w0)
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import matplotlib.pyplot as plt
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fig, axes = plt.subplots(3, 2, figsize=(15, 16), sharex=False)
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ax00 = axes[0][0]
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fitted_points = H11_evaluated
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sliced_freqences = freqs
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input_points = H11
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ax00.plot(full_freqences, np.abs(sampled_points), 'o', ms=4, color='red', label='Samples')
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ax00.plot(full_freqences, np.abs(fitted_points), '-', lw=2, color='k', label='Fit')
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ax00.plot(sliced_freqences, np.abs(input_points), 'x', ms=4, color='blue', label='Input Samples')
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ax00.set_title("Response i=0, j=0")
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ax00.set_ylabel("Magnitude")
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ax00.legend(loc="best")
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ax01 = axes[0][1]
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ax01.set_title("Response i=0, j=0")
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ax01.set_ylabel("Phase (deg)")
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ax01.plot(network.f[start_point:], np.angle([network.y[i][0][0] for i in range(start_point,len(network.y))],deg=True), 'o', ms=4, color='red', label='Samples')
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ax01.plot(network.f[start_point:], np.angle(H11_evaluated,deg=True), '-', lw=2, color='k', label='Fit')
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ax01.plot(freqs, np.angle(H11,deg=True), 'x', ms=4, color='blue', label='Input Samples')
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ax01.legend(loc="best")
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ax10 = axes[1][0]
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ax10.plot(least_squares_condition, label='Least Squares Condition')
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ax10.set_title("least_squares_condition")
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ax10.set_ylabel("Magnitude")
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ax10.legend(loc="best")
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ax11 = axes[1][1]
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ax11.plot(least_squares_rms_error, label='Least Squares RMS Error')
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ax11.set_title("least_squares_rms_error")
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ax11.set_ylabel("Magnitude")
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ax11.legend(loc="best")
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ax20 = axes[2][0]
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ax20.plot(eigenval_condition, label='Eigenvalue Condition')
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ax20.set_title("eigenval_condition")
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ax20.set_ylabel("Magnitude")
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ax20.legend(loc="best")
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ax21 = axes[2][1]
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ax21.plot(eigenval_rms_error, label='Eigenvalue RMS Error')
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ax21.set_title("eigenval_rms_error")
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ax21.set_ylabel("Magnitude")
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ax21.legend(loc="best")
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fig.tight_layout()
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plt.savefig(f"relaxed_basic_basis_QR.png")
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print("Saved relaxed_basic_basis_QR.png")
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