diff --git a/core/MultiplePortQR.py b/core/MultiplePortQR.py
new file mode 100644
index 0000000..0f67eaa
--- /dev/null
+++ b/core/MultiplePortQR.py
@@ -0,0 +1,360 @@
+import numpy as np
+from core.sk_iter import generate_starting_poles
+from scipy.linalg import block_diag
+import skrf as rf
+from skrf import VectorFitting
+from core.freqency import auto_select
+import random as rnd
+
+class MultiplePortQR:
+    def __init__(self,H,freqs,poles,weights=None,passivity=True,dc_enforce=True,fit_constant=True,fit_proportional=False):
+        self.least_squares_rms_error  = None
+        self.least_squares_condition = None
+        self.eigenval_condition = None
+        self.eigenval_rms_error = None
+
+        self.dc_tol = 1e-18
+
+        self.dc_enforce = dc_enforce
+        self.fit_constant = fit_constant
+        self.fit_proportional = fit_proportional
+        
+        # self.H = H
+        # self.freqs = freqs
+        self.freqs = freqs
+        self.H = H
+        self.s = self.freqs * 2j * np.pi
+        self.P = len(poles)
+        self.poles = poles
+        self.Phi = self.generate_basis(self.s, self.poles)
+        self.A = self.matrix_A(self.poles)
+        self.B = self.vector_B(self.poles)
+        self.Cw,self.w0,self.e = self.fit_denominator(self.H, weights=weights)
+        self.D = self.w0
+
+        self.Cr = None
+        
+        z = np.linalg.eigvals(self.A - self.B @ self.Cw)
+        p_next = -z
+
+        if passivity:
+            self.next_poles = self.passivity_enforce(p_next)
+        else:
+            self.next_poles = p_next
+        # z = np.where(np.real(z) < 0, z, -np.conj(z))  # enforce LHP
+        # self.next_poles = np.sort_complex(z)
+        self.eigenval_condition = np.linalg.cond(self.A - self.B @ self.Cw)
+        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))
+
+        self.Dt = self.eval_Dt_state_space()
+        self.delta = self.Dt / weights if weights is not None else self.Dt
+        pass
+
+    def passivity_enforce(self,poles):
+        """enforce poles' real parts to be negative"""
+        enforced_poles = []
+        for pole in poles:
+            if pole.real > 0:
+                pole = -np.conj(pole)
+            enforced_poles.append(pole)
+        return enforced_poles
+
+    def eval_Dt_state_space(self):
+        """Return D(s_k)=C(s_k I - A)^(-1)B + D for all k (complex 1D array)."""
+        s = 1j * 2*np.pi * np.asarray(self.freqs, float).ravel()
+        A = np.asarray(self.A, np.complex128); n = A.shape[0]
+        B = np.asarray(self.B, np.complex128).reshape(n, 1)
+        C = np.asarray(self.Cw, float).reshape(1, n)
+        D = self.D
+        I = np.eye(n, dtype=np.complex128)
+        out = np.empty_like(s, dtype=np.complex128)
+        for k, sk in enumerate(s):
+            DS = D + (C @ np.linalg.inv(sk*I - A) @ B)
+            out[k] = DS[0, 0]
+        return out
+    
+
+    def generate_basis(self,s, poles):
+        """Real basis of (15)-(16); returns Φ(s) and a layout for packing C."""
+        cols = []
+        i = 0
+        while i < len(poles):
+            p = poles[i]
+            if p.real > 0:
+                raise ValueError("poles must be in the LHP")
+            if i+1 < len(poles) and np.isclose(poles[i+1], np.conj(p)):
+                pc = poles[i+1]
+                phi1 = 1/(s - p) + 1/(s - pc)                 # eq (15)generate_basis
+                phi2 = 1j*(1/(s - p) - 1/(s - pc))            # eq (16)  (fixed sign)
+                cols += [phi1, phi2]
+                i += 2
+            else:
+                cols.append(1/(s - p))
+                i += 1
+        Phi = np.column_stack(cols).astype(np.complex128)
+        return Phi
+
+    def matrix_A(self, poles):
+        def A_block(p):
+            if abs(p.imag) < 1e-14:
+                return np.array([[p.real]], float)                  # A_p = [ p ]
+            return np.array([[p.real,  p.imag],                     # A_p = [[Re p, Im p],
+                              [-p.imag, p.real]], float)            #         [-Im p, Re p]]
+        A = None; i = 0
+        while i < len(poles):
+            p = poles[i]
+            Ab = A_block(p)
+            if i+1 < len(poles) and np.isclose(poles[i+1], np.conj(p)): i += 2
+            else: i += 1
+            A = Ab if A is None else block_diag(A, Ab)
+        return A
+    
+    def vector_B(self, poles):
+        def B_block(p):
+            return np.array([[1.0]], float) if abs(p.imag)<1e-14 else np.array([[2.0],[0.0]], float)
+        B = None; i = 0
+        while i < len(poles):
+            p = poles[i]
+            Bb = B_block(p)
+            if i+1 < len(poles) and np.isclose(poles[i+1], np.conj(p)): i += 2
+            else: i += 1
+            B = Bb if B is None else np.vstack([B, Bb])
+        return B
+    
+    def fit_denominator(self, H, weights=None, d0 = 1.0):
+        """
+        Solve formula (70) on the real basis Φ to obtain:
+          - d (real)  → packs into C for this state's block structure
+          - gamma (complex)
+        Optional 'weights' (K,) apply row scaling: SK weighting if 1/|D_prev|.
+        """
+        H = np.asarray(H, np.complex128).reshape(-1,1)
+        K, N = self.Phi.shape
+        one  = np.ones((K, 1), np.complex128)
+        Phi   = self.Phi
+        dc_tol = 1e-18
+        has_dc = self.dc_enforce and self.freqs[0] < dc_tol
+        keep = np.ones(K, dtype=bool)
+
+        # SK weighting (applied only to the (73) rows we keep in LS)
+        if weights is None:
+            weights = np.diag(np.ones(len(H), np.complex128))
+        else:
+            weights = np.diag([1/res for res in weights])
+
+        if self.fit_constant:  
+            Phi_w = np.hstack([one, Phi]) 
+            M     = np.hstack([Phi, -(H * Phi_w)])    # (K, 2N+1), complex
+        else:
+            M     = np.hstack([Phi, -(H * Phi)])       # (K, 2N),   complex
+
+        if has_dc:
+            # Enforce DC response exactly:
+            k0   = int(np.argmin(np.abs(self.freqs)))
+            keep[k0] = False
+            M_w     = weights @ M
+            A_re  = np.real(M_w[keep, :])
+            A_im  = np.imag(M_w[keep, :])
+            mask    = np.ones(K, dtype=bool); mask[k0] = False
+            # exact (unweighted) DC rows:
+            A_dc_re = np.real(M[k0, :]).reshape(1, -1)
+            A_dc_im = np.imag(M[k0, :]).reshape(1, -1)
+        else:
+            M_w    = weights @ M
+            A_re = np.real(M_w)
+            A_im = np.imag(M_w)
+            A_dc_re = A_dc_im = None
+
+        A_blocks = [A_re, A_im]
+
+        if self.fit_constant:
+            beta     = float(np.sqrt(np.sum(np.abs(H)**2)))
+            mean_row = (beta / K) * np.sum(Phi_w, axis=0)
+            A_w0      = np.concatenate([np.zeros(N, float),
+                                np.real(mean_row).astype(float)]
+                                ).reshape(1, -1)
+            b_w0      = np.array([beta], float)
+
+            A_blocks += [A_w0]
+            m = A_re.shape[0] + A_im.shape[0]
+            b = np.zeros(m, float)
+            b = np.concatenate([b, b_w0])
+        else:
+            H_kp = (weights @ H)[keep,:]
+            b_re = np.real(d0 * H_kp)
+            b_im = np.imag(d0 * H_kp)
+            b = np.concatenate([b_re.ravel(), b_im.ravel()]).astype(float)
+
+        # ---- build final stacked-real system ----
+        
+
+        # if A_dc_re is not None:
+        #     A_blocks += [A_dc_re, A_dc_im]
+        #     b = np.concatenate([b, np.zeros(2, float)])   # DC rows → 0
+
+        # ---- QR solve for x = [c_H (N); c_w (N+1)] ----
+        A = np.vstack(A_blocks).astype(float)
+        Q, R = np.linalg.qr(A, mode="reduced")
+        
+        if self.fit_constant:
+            Q2 = Q[:,A.shape[1]//2:]
+            R22 = R[A.shape[1]//2:,A.shape[1]//2:]
+        else:
+            Q2 = Q[:,A.shape[1]//2:]
+            R22 = R[A.shape[1]//2:,A.shape[1]//2:]
+
+        x = np.linalg.solve(R22, Q2.T @ b)
+
+        # diagnostics
+        resid = Q2 @ R22 @ x - b
+        self.least_squares_rms_error = float(np.sqrt(np.mean(resid**2)))
+        self.least_squares_condition = float(np.linalg.cond(R))
+
+        # split cw and return
+        # cw = x[N:]                     # last (N+1) entries = [w0, w_1..w_N]
+        # w0 = float(cw[0])
+        # Cw = cw[1:].reshape(1, N)      # row vector (1, N)
+        return self.extract_Cw_d_e(x,N,d0)
+    
+    def extract_Cw_d_e(self,C,N,d0=1.0):
+        if self.fit_proportional and self.fit_constant:
+            d = C[1]
+            e = C[0]
+            return C[2:].reshape(1, -1), d, e
+        elif self.fit_proportional and not self.fit_constant:
+            d = 0.0
+            e = C[0]
+            return C[1:].reshape(1, -1), d, e
+        elif not self.fit_proportional and self.fit_constant:
+            d = C[0]
+            e = 0.0
+            return C[1:].reshape(1, -1), d, e
+        else:
+            return C.reshape(1, -1), d0, 0.0
+    
+    
+    def non_bias_Cr(self,w0):
+        A = np.asarray(self.Phi)
+        den = np.diag((w0 + self.Phi @ self.Cw.T).ravel())
+        b = np.asarray(den) @ self.H.reshape(-1,1)
+        Cr, residuals, rank, s = np.linalg.lstsq(A, b, rcond=None)
+        return Cr
+    
+    def evaluate(self,freqs, w0):
+        s = 1j * 2*np.pi * np.asarray(freqs, float).ravel()
+        phi = self.generate_basis(s, self.poles)
+        den = w0 + phi @ self.Cw.T
+        if self.Cr is None:
+            self.Cr = self.non_bias_Cr(w0=w0)
+        num = phi @ self.Cr
+        H = num / den
+        return H.ravel()
+    
+def noise(n:complex,coeff:float=0.05):
+    noise_r = rnd.gauss(-coeff * n.real, coeff * n.real)
+    noise_i = rnd.gauss(-coeff * n.imag, coeff * n.imag)
+    return complex(n.real + noise_r, n.imag + noise_i)
+
+if __name__ == "__main__":
+    start_point = 0
+    network = rf.Network("/tmp/paramer/simulation/3000/3000.s2p")
+    K = 10
+
+    full_freqences = network.f[start_point:]
+    noised_sampled_points = [(network.y[i][0][0]) for i in range(start_point,len(network.y))]
+    sampled_points = [network.y[i][0][0] for i in range(start_point,len(network.y))]
+
+    H11,freqs = auto_select(noised_sampled_points,full_freqences,max_points=20)
+    poles = generate_starting_poles(2,beta_min=1e4,beta_max=freqs[-1]*1.1)
+    
+    Dt_1 = np.ones((len(freqs),1),np.complex128)
+    # Levi step (no weighting):
+    basis = MultiplePortQR(H11,freqs,poles=poles)
+    Dt = basis.Dt
+    poles = basis.next_poles
+
+    print("Levi step (no weighting):")
+    print("A:",basis.A)
+    print("B:",basis.B)
+    print("C:",basis.Cw)
+    print("D:",basis.D)
+    print("next_pozles:",basis.next_poles)
+    print("Dt:",Dt, "norm:",np.linalg.norm(Dt))
+
+    # SK weighting (optional, after first pass):
+    least_squares_condition = []
+    least_squares_rms_error = []
+    eigenval_condition = []
+    eigenval_rms_error = []
+    for i in range(K):
+        basis = MultiplePortQR(H11,freqs,poles=poles,weights=Dt)
+        Dt_1 = Dt
+        Dt = basis.Dt
+        poles = basis.next_poles
+        print(f"SK Iteration {i+1}/{K}")
+        print("A:",basis.A)
+        print("B:",basis.B)
+        print("C:",basis.Cw)
+        print("D:",basis.D)
+        print("z:",basis.next_poles)
+        print("Dt:",Dt)
+        print("Dt/Dt-1",np.linalg.norm(Dt) / np.linalg.norm(Dt_1))
+        least_squares_condition.append(basis.least_squares_condition)
+        least_squares_rms_error.append(basis.least_squares_rms_error)
+        eigenval_condition.append(basis.eigenval_condition)
+        eigenval_rms_error.append(basis.eigenval_rms_error)
+
+    # H11_evaluated = basis.evaluate_pole_residue(network.f[1:],poles,basis.C[0])
+    H11_evaluated = basis.evaluate(network.f[start_point:], w0=basis.w0)
+    import matplotlib.pyplot as plt
+    fig, axes = plt.subplots(3, 2, figsize=(15, 16), sharex=False)
+
+    ax00 = axes[0][0]
+    fitted_points = H11_evaluated
+    sliced_freqences = freqs
+
+    input_points = H11
+    ax00.plot(full_freqences, np.abs(sampled_points), 'o', ms=4, color='red', label='Samples')
+    ax00.plot(full_freqences, np.abs(fitted_points), '-', lw=2, color='k', label='Fit')
+    ax00.plot(sliced_freqences, np.abs(input_points), 'x', ms=4, color='blue', label='Input Samples')
+    ax00.set_title("Response i=0, j=0")
+    ax00.set_ylabel("Magnitude")
+    ax00.legend(loc="best")
+
+    ax01 = axes[0][1]
+    ax01.set_title("Response i=0, j=0")
+    ax01.set_ylabel("Phase (deg)")
+    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')
+    ax01.plot(network.f[start_point:], np.angle(H11_evaluated,deg=True), '-', lw=2, color='k', label='Fit')
+    ax01.plot(freqs, np.angle(H11,deg=True), 'x', ms=4, color='blue', label='Input Samples')
+    ax01.legend(loc="best")
+
+    ax10 = axes[1][0]
+    ax10.plot(least_squares_condition, label='Least Squares Condition')
+    ax10.set_title("least_squares_condition")
+    ax10.set_ylabel("Magnitude")
+    ax10.legend(loc="best")
+
+    ax11 = axes[1][1]
+    ax11.plot(least_squares_rms_error, label='Least Squares RMS Error')
+    ax11.set_title("least_squares_rms_error")
+    ax11.set_ylabel("Magnitude")
+    ax11.legend(loc="best")
+
+    ax20 = axes[2][0]
+    ax20.plot(eigenval_condition, label='Eigenvalue Condition')
+    ax20.set_title("eigenval_condition")
+    ax20.set_ylabel("Magnitude")
+    ax20.legend(loc="best")
+
+    ax21 = axes[2][1]
+    ax21.plot(eigenval_rms_error, label='Eigenvalue RMS Error')
+    ax21.set_title("eigenval_rms_error")
+    ax21.set_ylabel("Magnitude")
+    ax21.legend(loc="best")
+    fig.tight_layout()
+    plt.savefig(f"relaxed_basic_basis_QR.png")
+
+    
+
+