move some functions

nom-eme.py

@@ -364,7 +364,7 @@ def generalize_S(
     g = (z0 - r0) / (z0 + r0)
     D = numpy.diag((1 - g) / numpy.abs(1 - g.conj()) * numpy.sqrt(1 - numpy.abs(g * g.conj())))
     G = numpy.diag(g)
-    U = numpy.eye(S.shape[0])
+    U = numpy.eye(S.shape[-1]).reshape((S.ndim - 2) * (1,) + (S.shape[-2], S.shape[-1]))
     S_gen = pinv(D.conj()) @ (S - G.conj()) @ pinv(U - G @ S) @ D
     return S_gen
 
@@ -375,7 +375,7 @@ def change_R0(
         r2: float,
         ) -> NDArray[numpy.complex128]:
     g = (r2 - r1) / (r2 + r1)
-    U = numpy.eye(S.shape[0])
+    U = numpy.eye(S.shape[-1]).reshape((S.ndim - 2) * (1,) + (S.shape[-2], S.shape[-1]))
     G = U * g
     S_r2 = (S - G) @ pinv(U - G @ S)
     return S_r2

spconv.py

@@ -1,6 +1,8 @@
+import scipy
 import numpy
-from numpy import sqrt, real, abs
+from numpy.typing import ArrayLike, NDArray
 from numpy.linalg import pinv
+from numpy import sqrt, real, abs, pi
 
 
 def diag(twod):
@@ -29,7 +31,9 @@ def change_of_zref(
     #  A = inv(G0') @ G0 @ inv(I - rho*)   (diagonal)
     #  rho = (Z0' - Z0) @ inv(Z0' + Z0)    (diagonal)
 
-    I = numpy.eye(SL.shape[-1])[None, :, :]
+    I = numpy.zeros_like(SL)
+    numpy.einsum('...jj->...j', I)[...] = 1
+
     zref_old = numpy.array(zref_old, copy=False)
     zref_new = numpy.array(zref_new, copy=False)
 
@@ -51,10 +55,14 @@ def embedding(
         SL,   # (nf, ni, ni)
         ):
     # Reveyrand, doi:10.1109/INMMIC.2018.8430023
-    I = numpy.eye(SL.shape[-1])[None, :, :]
+
+    I = numpy.zeros_like(SL)
+    numpy.einsum('...jj->...j', I)[...] = 1
+
     S_tot = See + Sei @ pinv(I - SL @ Sii) @ SL @ Sie
     return S_tot
 
+
 def deembedding(
         Sei,  # (nf, ne, ni)
         Sie,  # (nf, ni, ne)
@@ -73,14 +81,188 @@ def thru_with_Zref_change(
         zref0,  # (nf,)
         zref1,  # (nf,)
         ):
-    nf = zref0.shape[0]
+    s = numpy.empty(tuple(zref0.shape) + (2, 2), dtype=complex)
-    s = numpy.empty((nf, 2, 2), dtype=complex)
+    s[..., 0, 0] = zref1 - zref0
-    s[:, 0, 0] = zref1 - zref0
+    s[..., 0, 1] = 2 * sqrt(zref0 * zref1)
-    s[:, 0, 1] = 2 * sqrt(zref0 * zref1)
+    s[..., 1, 0] = s[..., 0, 1]
-    s[:, 1, 0] = s[:, 0, 1]
+    s[..., 1, 1] = -s[..., 0, 0]
-    s[:, 1, 1] = -s[:, 0, 0]
 
     s /= zref0 + zref1
     return s
 
 
+def propagation_matrix(mode_neffs: ArrayLike, wavelength: float, distance: float):
+    eigenv = numpy.array(mode_neffs, copy=False) * 2 * pi / wavelength
+    prop_diag = numpy.diag(numpy.exp(distance * 1j * numpy.hstack((eigenv, eigenv))))
+    prop_matrix = numpy.roll(prop_diag, len(eigenv), axis=0)
+    return prop_matrix
+
+
+def connect_s(
+        A: NDArray[numpy.complex128],
+        k: int,
+        B: NDArray[numpy.complex128],
+        l: int,
+        ) -> NDArray[numpy.complex128]:
+    """
+    TODO
+    freq x ...  x n x n
+
+    Based on skrf implementation
+
+    Connect two n-port networks' s-matrices together.
+
+    Specifically, connect port `k` on network `A` to port `l` on network
+    `B`. The resultant network has nports = (A.rank + B.rank-2); first
+    (A.rank - 1) ports are from `A`, remainder are from B.
+
+    Assumes same reference impedance for both `k` and `l`; may need to
+    connect an "impedance mismatch" thru element first!
+
+    Args:
+        A: S-parameter matrix of `A`, shape is fxnxn
+        k: port index on `A` (port indices start from 0)
+        B: S-parameter matrix of `B`, shape is fxnxn
+        l: port index on `B`
+
+    Returns:
+        new S-parameter matrix
+    """
+    if k > A.shape[-1] - 1 or l > B.shape[-1] - 1:
+        raise ValueError("port indices are out of range")
+
+    #C = scipy.sparse.block_diag((A, B), dtype=complex)
+    #return innerconnect_s(C, k, A.shape[0] + l)
+
+    nA = A.shape[-1]
+    nB = B.shape[-1]
+    nC = nA + nB - 2
+    assert numpy.array_equal(A.shape[:-2], B.shape[:-2])
+
+    ll = slice(l, l + 1)
+    kk = slice(k, k + 1)
+
+    denom = 1 - A[..., kk, kk] * B[..., ll, ll]
+    Anew = A + A[..., kk, :] * B[..., ll, ll] * A[..., :, kk] / denom
+    Bnew = A[..., kk, :] * B[..., :, ll] / denom
+    Anew = numpy.delete(Anew, (k,), 1)
+    Anew = numpy.delete(Anew, (k,), 2)
+    Bnew = numpy.delete(Bnew, (l,), 1)
+    Bnew = numpy.delete(Bnew, (l,), 2)
+
+    dtype = (A[0, 0] * B[0, 0]).dtype
+    C = numpy.zeros(tuple(A.shape[:-2]) + (nC, nC), dtype=dtype)
+    C[..., :nA - 1, :nA - 1] = Anew
+    C[..., nA - 1:, nA - 1:] = Bnew
+    return C
+
+
+def innerconnect_s(
+        S: NDArray[numpy.complex128],
+        k: int,
+        l: int,
+        ) -> NDArray[numpy.complex128]:
+    """
+    TODO
+    freq x ...  x n x n
+
+    Based on skrf implementation
+
+
+    Connect two ports of a single n-port network's s-matrix.
+    Specifically, connect port `k`  to port `l` on `S`. This results in
+    a (n-2)-port network.
+
+    Assumes same reference impedance for both `k` and `l`; may need to
+    connect an "impedance mismatch" thru element first!
+
+    Args:
+        S: S-parameter matrix of `S`, shape is fxnxn
+        k: port index on `S` (port indices start from 0)
+        l: port index on `S`
+
+    Returns:
+        new S-parameter matrix
+
+    Notes:
+        - Compton, R.C., "Perspectives in microwave circuit analysis",
+            doi:10.1109/MWSCAS.1989.101955
+        - Filipsson, G., "A New General Computer Algorithm for S-Matrix Calculation
+            of Interconnected Multiports",
+            doi:10.1109/EUMA.1981.332972
+    """
+    if k > S.shape[-1] - 1 or l > S.shape[-1] - 1:
+        raise ValueError("port indices are out of range")
+
+    ll = slice(l, l + 1)
+    kk = slice(k, k + 1)
+
+    mkl = 1 - S[..., kk, ll]
+    mlk = 1 - S[..., ll, kk]
+    C = S + (
+              S[..., kk, :] * S[..., :, l] * mlk
+            + S[..., ll, :] * S[..., :, k] * mkl
+            + S[..., kk, :] * S[..., l, l] * S[..., :, kk]
+            + S[..., ll, :] * S[..., k, k] * S[..., :, ll]
+        ) / (
+            mlk * mkl - S[..., kk, kk] * S[..., ll, ll]
+        )
+
+    # remove connected ports
+    C = numpy.delete(C, (k, l), 1)
+    C = numpy.delete(C, (k, l), 2)
+
+    return C
+
+
+def s2abcd(
+        S: NDArray[numpy.complex128],
+        z0: NDArray[numpy.complex128],
+        ) -> NDArray[numpy.complex128]:
+    assert numpy.array_equal(S.shape[:2] == (2, 2))
+    Z1, Z2 = z0
+    cross = S[0, 1] * S[1, 0]
+
+    T = numpy.empty_like(S, dtype=complex)
+    T[0, 0, :] = (Z1.conj() + S[0, 0] * Z1) * (1 - S[1, 1]) + cross * Z1    # A numerator
+    T[0, 1, :] = (Z1.conj() + S[0, 0] * Z1) * (Z1.conj() + S[1, 1] * Z2) - cross * Z1 * Z2  # B numerator
+    T[1, 0, :] = (1 - S[0, 0]) * (1 - S[1, 1]) - cross                      # C numerator
+    T[1, 1, :] = (1 - S[0, 0]) * (Z2.conj() + S[1, 1] * Z2) + cross * Z2    # D numerator
+    det = 2 * S[1, 0] * numpy.sqrt(Z1.real * Z2.real)
+    T /= det
+    return T
+
+
+def generalize_S(
+        S: NDArray[numpy.complex128],
+        r0: float,
+        z0: NDArray[numpy.complex128],
+        ) -> NDArray[numpy.complex128]:
+    g = (z0 - r0) / (z0 + r0)
+    D = numpy.diag((1 - g) / numpy.abs(1 - g.conj()) * numpy.sqrt(1 - numpy.abs(g * g.conj())))
+    G = numpy.diag(g)
+    U = numpy.eye(S.shape[-1]).reshape((S.ndim - 2) * (1,) + (S.shape[-2], S.shape[-1]))
+    S_gen = pinv(D.conj()) @ (S - G.conj()) @ pinv(U - G @ S) @ D
+    return S_gen
+
+
+def change_R0(
+        S: NDArray[numpy.complex128],
+        r1: float,
+        r2: float,
+        ) -> NDArray[numpy.complex128]:
+    g = (r2 - r1) / (r2 + r1)
+    U = numpy.eye(S.shape[-1]).reshape((S.ndim - 2) * (1,) + (S.shape[-2], S.shape[-1]))
+    G = U * g
+    S_r2 = (S - G) @ pinv(U - G @ S)
+    return S_r2
+
+# Zc = numpy.sqrt(B / C)
+# gamma = numpy.arccosh(A) / L_TL
+# n_eff = -1j * gamma * c_light / (2 * pi * f)
+# n_eff_grp = n_eff + f * diff(n_eff) / diff(f)
+# attenuation = (1 - S[0, 0] * S[0, 0].conj()) / (S[1, 0] * S[1, 0].conj())
+# R = numpy.real(gamma * Zc)
+# C = numpy.real(gamma / Zc)
+# L = numpy.imag(gamma * Zc) / (-1j * 2 * pi * f)
+# G = numpy.imag(gamma / Zc) / (-1j * 2 * pi * f)