From edd87d5ff1343e02e43ad2fe5633320f0f0a409f Mon Sep 17 00:00:00 2001
From: Philipp Frank <philipp@mpa-garching.mpg.de>
Date: Mon, 7 Nov 2022 09:02:06 -0500
Subject: [PATCH] gp examples
---
gaussian_processes.py | 59 +++++++++++++++++++++++++++++++++++++++++++
1 file changed, 59 insertions(+)
create mode 100644 gaussian_processes.py
diff --git a/gaussian_processes.py b/gaussian_processes.py
new file mode 100644
index 0000000..998ee07
--- /dev/null
+++ b/gaussian_processes.py
@@ -0,0 +1,59 @@
+import nifty8 as ift
+
+position_space = ift.RGSpace((128,128))
+harmonic_space = position_space.get_default_codomain()
+HT = ift.HarmonicTransformOperator(harmonic_space)
+print(HT)
+print(HT.domain, HT.target)
+
+power_space = ift.PowerSpace(harmonic_space)
+power_spectrum = (lambda k: 1./(10.+ k**4))
+power_spectrum = ift.PS_field(power_space, power_spectrum)
+
+pl = ift.Plot()
+pl.add(power_spectrum)
+pl.output()
+
+PD = ift.PowerDistributor(harmonic_space)
+spectrum = PD(power_spectrum)
+
+xi = ift.FieldAdapter(harmonic_space, 'inp')
+
+# s = HT(sqrt(power_spectrum) * xi)
+s = HT @ ift.DiagonalOperator(spectrum.sqrt()) @ xi
+# s = s.exp()
+print(s)
+print(s.domain, s.target)
+
+pl = ift.Plot()
+for _ in range(6):
+ pl.add(s(ift.from_random(s.domain)))
+pl.output()
+
+args = {
+ 'offset_mean': 0,
+ 'offset_std': (1e-3, 1e-6),
+
+ # Amplitude of field fluctuations
+ 'fluctuations': (1., 0.8), # 1.0, 1e-2
+
+ # Exponent of power law power spectrum component
+ 'loglogavgslope': (-3., 1), # -6.0, 1
+
+ # Amplitude of integrated Wiener process power spectrum component
+ 'flexibility': (2, 1.), # 1.0, 0.5
+
+ # How ragged the integrated Wiener process component is
+ 'asperity': (0.2, 0.1) # 0.1, 0.5
+}
+correlated_field = ift.SimpleCorrelatedField(position_space, **args)
+power_spectrum = correlated_field.power_spectrum
+
+pl = ift.Plot()
+pl.add([power_spectrum(ift.from_random(power_spectrum.domain)) for _ in range(10)])
+pl.output()
+
+pl = ift.Plot()
+for _ in range(6):
+ pl.add(correlated_field(ift.from_random(correlated_field.domain)))
+pl.output()
\ No newline at end of file
--
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