From 859b256f6fc99829753ad41cbef8c7c12fb178db Mon Sep 17 00:00:00 2001
From: Anton Khirnov <anton@khirnov.net>
Date: Mon, 18 Oct 2021 12:12:45 +0200
Subject: critical: add naive echo finder

---
 critical.py | 92 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 92 insertions(+)
 create mode 100644 critical.py

diff --git a/critical.py b/critical.py
new file mode 100644
index 0000000..062f12c
--- /dev/null
+++ b/critical.py
@@ -0,0 +1,92 @@
+import numpy as np
+from scipy.integrate import cumulative_trapezoid
+
+from . import interp
+
+class _Echo:
+    z        = None
+    t_min    = None
+    tau_min  = None
+    zeta_min = None
+
+    t    = None
+    tau  = None
+    zeta = None
+
+    t_interp    = None
+    tau_interp  = None
+    zeta_interp = None
+
+    def __init__(self, el, z, t, zeta1d, alpha1d, idx_pos_prev, idx_pos_next):
+        dt = t[1] - t[0]
+        interp_stencil = 4
+
+        self.z = z
+
+        # interpolate ζ between two neighboring positive values
+        # to find the true minimum
+        t_interp    = np.linspace(t[idx_pos_prev], t[idx_pos_next], 1024)
+        zeta_interp = interp.interp1d(t[0], dt, zeta1d, t_interp, interp_stencil)
+
+        idx_min         = np.argmin(zeta_interp)
+        self.t_min      = t_interp[idx_min]
+        self.zeta_min   = zeta_interp[idx_min]
+
+        # integrate the proper time along the z=const wordline corresponding to
+        # the minimum of ζ
+        tau  = cumulative_trapezoid(alpha1d, t, initial = 0.0)
+        self.tau_min = interp.interp1d(t[0], dt, tau, np.array([self.t_min]), interp_stencil)
+
+        self.t    = t
+        self.tau  = tau
+        self.zeta = zeta1d
+
+        self.t_interp       = np.linspace(t[0] + 16 * dt, t[-1] - 16 * dt, 4096)
+        self.tau_interp     = interp.interp1d(t[0], dt, tau, self.t_interp, interp_stencil)
+        self.zeta_interp    = interp.interp1d(t[0], dt, zeta1d, self.t_interp, interp_stencil)
+
+    def __repr__(self):
+        return 'Echo(t=%g,z=%g,minζ=%g)' % (self.t_min, self.z, self.zeta_min)
+
+class EchoLoc:
+
+    t    = None
+    z    = None
+    zeta = None
+
+    echoes = None
+
+    def __init__(self, t, z, zeta, alpha):
+        self.t    = t
+        self.z    = z
+        self.zeta = zeta
+
+        remainder = zeta
+        echoes    = []
+        while remainder.shape[0] > 0:
+            # find the global minimum in the remaining part of the data
+            idx_min = np.unravel_index(np.argmin(remainder), remainder.shape)
+
+            # out of negative minima, finish
+            if remainder[idx_min] >= 0.0:
+                break
+
+            # find the index where zeta along this z=const. line becomes positive again
+            idx_pos = np.argwhere(remainder[:idx_min[0], idx_min[1]] >= 0.0)
+            if idx_pos.shape[0] == 0:
+                break
+
+            # find the index where zeta becomes positive _after_ the minimum
+            # if there is no such index, skip this as a false positive
+            idx_pos_next = np.argwhere(remainder[idx_min[0]:, idx_min[1]] >= 0.0)
+            if idx_pos_next.shape[0] > 0:
+                echoes.append(_Echo(self, z[idx_min[1]], t[:remainder.shape[0]],
+                                    remainder[:, idx_min[1]], alpha[:remainder.shape[0], idx_min[1]],
+                                    idx_pos[-1, 0], idx_min[0] + idx_pos_next[0, 0]))
+
+            remainder = remainder[:idx_pos[-1, 0]]
+
+        self.echoes = echoes
+
+    def __repr__(self):
+        return '%d echoes: t=[%s]' % (len(self.echoes), ','.join((str(e.t_min) for e in self.echoes)))
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