### tweak docs

parent a4c2996b
Pipeline #24371 passed with stage
in 6 minutes and 18 seconds
 ... ... @@ -82,11 +82,11 @@ "\n", "- One-dimensional signal with power spectrum: $$P(k) = P_0\\,\\left(1+\\left(\\frac{k}{k_0}\\right)^2\\right)^{-\\gamma /2},$$\n", "with $P_0 = 0.2, k_0 = 5, \\gamma = 4$. Recall: $P(k)$ defines an isotropic and homogeneous $S$.\n", "- $N = 0.5 \\cdot \\text{id}$.\n", "- Number data points $N_{pix} = 512$.\n", "- $N = 0.05 \\cdot \\text{id}$.\n", "- Number of data points $N_{pix} = 512$.\n", "- reconstruction in harmonic space.\n", "- Response operator:\n", "$$R_x=\\begin{pmatrix} \\delta(x-0)\\\\\\delta(x-1)\\\\\\ldots\\\\ \\delta(x-511) \\end{pmatrix}.$$\n", "However, the signal space is also discrete on the computer and $R = \\text{id}$." "$$R = FFT(\\text{harmonic} \\rightarrow \\text{position})$$\n" ] }, { ... ... @@ -167,7 +167,7 @@ "outputs": [], "source": [ "def PropagatorOperator(R, N, Sh):\n", " IC = ift.GradientNormController(name=\"inverter\", iteration_limit=50000,\n", " IC = ift.GradientNormController(iteration_limit=50000,\n", " tol_abs_gradnorm=0.1)\n", " inverter = ift.ConjugateGradient(controller=IC)\n", " D = (R.adjoint*N.inverse*R + Sh.inverse).inverse\n", ... ... @@ -186,9 +186,10 @@ "### Conjugate Gradient Preconditioning\n", "\n", "- $D$ is defined via:\n", "$$D^{-1} = \\mathcal F^\\dagger S_h^{-1}\\mathcal F + R^\\dagger N^{-1} R.$$\n", "$$D^{-1} = \\mathcal S_h^{-1} + R^\\dagger N^{-1} R.$$\n", "In the end, we want to apply $D$ to $j$, i.e. we need the inverse action of $D^{-1}$. This is done numerically (algorithm: *Conjugate Gradient*). \n", "\n", "" ] }, { ... ...
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!