{ "cells": [ { "cell_type": "markdown", "id": "184fff06-9cd1-4b25-b2e2-f2bd14bd2a0e", "metadata": {}, "source": [ "# Overview of functions from cross interactions from Laplace" ] }, { "cell_type": "markdown", "id": "28f7928a-ebc5-4e3e-96dc-99c1fd6ed556", "metadata": {}, "source": [ "Overview of python functions from `biosspheres.laplace.crossinteractions`." ] }, { "cell_type": "code", "execution_count": 1, "id": "ee48373a-a0ff-4707-a951-c833c1caaf99", "metadata": {}, "outputs": [], "source": [ "import biosspheres.laplace.crossinteractions as cross" ] }, { "cell_type": "code", "execution_count": 2, "id": "c9063d2a-4a56-4676-a70c-9ebd171e02db", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib.colors as colors\n", "import biosspheres.quadratures.sphere as quadratures\n", "import biosspheres.utils.auxindexes as auxindexes" ] }, { "cell_type": "markdown", "id": "cc2dab6c-8ed7-4900-b05a-48a11e8613e9", "metadata": {}, "source": [ "## Preliminaries" ] }, { "cell_type": "markdown", "id": "430aad52-1ea2-48ad-8184-e3f2dbd10259", "metadata": {}, "source": [ "### Geometry\n" ] }, { "cell_type": "markdown", "id": "07c1877b-db71-4468-8b5d-82ff26270145", "metadata": {}, "source": [ "All the python functions assume the following geometry:" ] }, { "cell_type": "markdown", "id": "7a5530c9-2188-4868-9b64-150ff585dbd3", "metadata": {}, "source": [ "$N$ disjoint spheres in $\\mathbb{R}^3$:\n", "- Position vectors of the sphere centers: $\\mathbf{p_j} \\in \\mathbb{R}^3$, with $j \\in \\{1,...,N\\}$. \n", "- Radii: $\\tilde{r}_j\\in \\mathbb{R}^+$, with $j \\in \\{1,...,N\\}$.\n", "- Interior of sphere $j$: $\\Omega_j:=\\{ \\mathbf{x} \\in \\mathbb{R}^3:||\\mathbf{x}-\\mathbf{p_j}||_2<\\tilde{r}_j \\}$.\n", "- Boundary of sphere $j$: $\\Gamma_j:=\\partial \\Omega_j$.\n", "- Exterior medium, $\\Omega_0$: defined as $\\mathbb{R}^3$ without the spheres and their boundaries." ] }, { "cell_type": "markdown", "id": "6ef35104-4fc1-4464-b9f5-e10bb8070f60", "metadata": {}, "source": [ "\n", "### Free space fundamental solution for the Laplace equation" ] }, { "cell_type": "markdown", "id": "69cd17fe-1a9b-4043-8b9d-46340c9bbf72", "metadata": {}, "source": [ "The free space fundamental solution of the Laplace equation, which satisfies the radiation condition is:\n", "$$g\\left(\\mathbf{r},\\mathbf{r'}\\right):= \\frac{1}{4\\pi ||\\mathbf{r}-\\mathbf{r}'||_2}, \\quad \\text{with }\\mathbf{r}\\not = \\mathbf{r'}, \\quad \\text{and }-\\Delta g \\left(\\mathbf{r},\\mathbf{r'}\\right)=\\delta \\left(\\mathbf{r}-\\mathbf{r'}\\right).$$" ] }, { "cell_type": "markdown", "id": "c1ca7f67-f5d9-4355-8908-efa0b7fcd590", "metadata": {}, "source": [ "This is the kernel of the operators which numerical approximations are python functions from this module." ] }, { "cell_type": "markdown", "id": "dedef543-9026-4807-ac60-3e45e9845265", "metadata": {}, "source": [ "### Layer operators" ] }, { "cell_type": "markdown", "id": "4af0bee6-4251-400a-a73d-3c4f6637f40f", "metadata": {}, "source": [ "Single and double layer operators defined for smooth densities:\n", "$$DL_{0j} \\left(\\psi\\right)\\left(\\mathbf{r}\\right):=\\int_{\\Gamma_j} \\psi\\left(\\mathbf{r}'\\right) \\nabla g\\left(\\mathbf{r},\\mathbf{r'}\\right) \\cdot \\widehat{\\mathbf{n}}_{0j} \\ dS',$$\n", "$$SL_{0j} \\left(\\psi\\right)\\left(\\mathbf{r}\\right):=\\int_{\\Gamma_j} {\\psi\\left(\\mathbf{r}'\\right) g\\left(\\mathbf{r},\\mathbf{r'}\\right) dS'},$$\n", "$$DL_j \\left(\\psi\\right)\\left(\\mathbf{r}\\right):=\\int_{\\Gamma_j} {\\psi\\left(\\mathbf{r}'\\right) \\nabla g\\left(\\mathbf{r},\\mathbf{r'}\\right) \\cdot \\widehat{\\mathbf{n}}_{j} \\ dS'},$$\n", "$$SL_j \\left(\\psi\\right)\\left(\\mathbf{r}\\right):=\\int_{\\Gamma_j} {\\psi\\left(\\mathbf{r}' \\right) g\\left(\\mathbf{r},\\mathbf{r'}\\right) dS'}$$\n", "\n", "with the gradient being taken with respect to $\\mathbf{r}'$, $\\widehat{\\mathbf{n}}_j$ being the exterior normal vector of $\\Omega_j$, and $\\widehat{\\mathbf{n}}_j=-\\widehat{\\mathbf{n}}_{0j}$.\n", "\n", "These operators are linear and continuous in the following Sobolev spaces:\n", "$$DL_{0j}: H^{\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^1_{loc} \\left(\\mathbb{R}^3 \\setminus \\cup_{j=1}^{N}\\Gamma_j\\right),$$\n", "$$SL_{0j}: H^{-\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^1_{loc} \\left(\\mathbb{R}^3 \\setminus \\cup_{j=1}^{N}\\Gamma_j\\right) , $$\n", "$$DL_{j}: H^{\\frac{1}{2}}(\\Gamma_j)\\rightarrow H^1_{loc} \\left(\\mathbb{R}^3 \\setminus \\cup_{j=1}^{N}\\Gamma_j\\right),$$\n", "$$SL_{j}: H^{-\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^1_{loc}\\left(\\mathbb{R}^3 \\setminus \\cup_{j=1}^{N}\\Gamma_j\\right).$$" ] }, { "cell_type": "markdown", "id": "31426757-7914-4bd6-a6a1-f665f5752869", "metadata": {}, "source": [ "### Boundary integral operators" ] }, { "cell_type": "markdown", "id": "5dff58d6-88ab-482f-a1a0-e9bad6e83966", "metadata": {}, "source": [ "For $u\\in C^\\infty(\\overline\\Omega)$, Dirichlet and Neumann traces operators are defined as \n", "$$\\gamma_d u := u|_{\\Gamma},\\qquad \\gamma_n u := \\nabla u|_{\\Gamma} \\cdot \\widehat{n},$$\n", "where $\\widehat{n}$ is the exterior unit normal.\n", "\n", "By density arguments, the definition of Dirichlet and Neumann traces operator can be extended to $u_j \\in H^1_{loc}(\\Omega_j)$, with $j \\{0, ..., N \\}$. We extend the notation as follows\n", "\n", "$$\\gamma_d^{0j} u_0 := u_0|_{\\Gamma_j},$$\n", "$$\\gamma_d^{j} u_j := u_j|_{\\Gamma_j},$$\n", "$$\\gamma_n^{0j} u_0 := \\nabla u_0|_{\\Gamma_j} \\cdot \\widehat{n}_{0j},$$\n", "$$\\gamma_n^{j} u_j := \\nabla u_j|_{\\Gamma_j}\\cdot \\widehat{n}_{j},$$\n", "where $\\widehat{n}_{j}$ is the exterior normal of $\\Omega_j$, with $j\\in \\{ 1, ..., N\\}$ and $\\widehat{n}_{0j}=-\\widehat{n}_{j}$.\n", "\n", "Now, we recall the definition of the boundary integral operators:\n", "$$\\begin{aligned}\n", "\tV_{i,j}^0 &:= \\frac{1}{2} \\left( \\gamma_d^{i} SL_{0j} + \\gamma_d^{0i} SL_{0j} \\right) ,\n", "\t& V_{j}&:= \\frac{1}{2} \\left( \\gamma_d^{0j} SL_{j} + \\gamma_d^{j} SL_{j} \\right) ,\\\\\n", "\tK_{i,j}^0&:= \\frac{1}{2} \\left(\\gamma_d^{i} DL_{0j} + \\gamma_d^{0i} DL_{0j} \\right) ,\n", "\t&K_{j}&:= \\frac{1}{2} \\left(\\gamma_d^{0j} DL_{j} + \\gamma_d^{j} DL_{j} \\right),\\\\\n", "\tK^{*0}_{i,j}&:= \\frac{1}{2} \\left( - \\gamma_n ^{i} SL_{0j} + \\gamma_n ^{0i} SL_{0j} \\right),\n", "\t & K^{*}_{j} &:= \\frac{1}{2} \\left( -\\gamma_n ^{0j} SL_{j} + \\gamma_n ^{j} SL_{j} \\right), \\\\\n", "\tW_{i,j}^0 &:= -\\frac{1}{2} \\left( - \\gamma_n^{i} DL_{0j} + \\gamma_n^{0i} DL_{0j} \\right) ,\n", "\t& W_{j} &:=- \\frac{1}{2} \\left( -\\gamma_n^{0j} DL_{j} + \\gamma_n^{j} DL_{j} \\right).\n", "\\end{aligned}$$\n", "\n", "These operators are linear and continuous in the following Sobolev spaces: \n", "$$\\begin{aligned}\n", "\tV_{{i},j}^0 &: H^{-\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^{\\frac{1}{2}}(\\Gamma_i),\n", "\t&V_{j}&: H^{-\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^{\\frac{1}{2}}(\\Gamma_j),\\\\\n", "\tW_{{i},j}^0&: H^{\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^{-\\frac{1}{2}}(\\Gamma_i),\n", "\t&W_{j}&: H^{\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^{-\\frac{1}{2}}(\\Gamma_j) ,\\\\\n", "\tK_{{i},j}^0&: H^{\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^{\\frac{1}{2}}(\\Gamma_i),\n", "\t&K_{j}&: H^{\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^{\\frac{1}{2}}(\\Gamma_j) ,\\\\\n", "\tK^{*0}_{{i},j}&: H^{-\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^{-\\frac{1}{2}}(\\Gamma_i),\n", "\t&K^*_{j}&: H^{-\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^{-\\frac{1}{2}}(\\Gamma_j).\n", "\\end{aligned}$$\n", "\n", "Since the domains are smooth, the jump relations for the potentials across a closed boundary yield\n", "$$\\begin{aligned}\n", "\tV_{{i},j}^0 &= \\gamma_d^{0{i}} SL_{0j},\n", "\t& V_{j}&= \\gamma_d^{j} SL_{j},\\\\\n", "\tW_{{i},j}^0 &=- \\gamma_n^{0{i}} DL_{0j},\n", "\t& W_{j} &=- \\gamma_n^{j} DL_{j}, \\\\\n", "\t K_{{i},j}^0&= \\gamma_d^{0{i}} DL_{0j}, {i} \\not=j,\n", "\t & K^{*0}_{{i},j} &= \\gamma_n ^{0{i}} SL_{0j}, {i} \\not=j,\n", "\\end{aligned}$$\n", "and\n", "$$\\begin{aligned}\n", "\tK_{j,j}^0(\\psi) &= \\frac{1}{2}\\psi +\\gamma_d^{0j} {DL_{0j}(\\psi)} ,\n", "\t&K_{j}(\\psi) &= \\frac{1}{2} \\psi +\\gamma_d^{j} {DL_{j}(\\psi)} ,\\\\\n", "\t K^{*0}_{j,j}(\\psi) &= -\\frac{1}{2} \\psi + \\gamma_n^{0j} {SL_{0j}(\\psi)},\n", "\t&K^*_{j}(\\psi) &= -\\frac{1}{2} \\psi + \\gamma_n^j {SL_{j}(\\psi)}.\n", "\\end{aligned}$$" ] }, { "cell_type": "markdown", "id": "0a560354-52b4-4a47-a63c-2a23071ba8a7", "metadata": {}, "source": [ "### Spherical coordinate system" ] }, { "cell_type": "markdown", "id": "fefe1932-8b7f-4711-846d-1d278a77e934", "metadata": {}, "source": [ "A vector is written as $\\mathbf{r}=\\left(r,\\varphi,\\theta\\right)^t$, with $r \\in [0,\\infty)$, $\\varphi \\in [0,2\\pi)$ and $\\theta \\in [0,\\pi]$, which in Cartesian coordinates is equivalent to $\\mathbf{r}=r\\left(\\sin \\theta \\cos \\varphi,\\sin \\theta \\sin \\varphi,\\cos \\theta\\right)^t$. The unitary vectors of the spherical coordinate system can be written in Cartesian coordinates as\n", "$$\\begin{aligned}\n", " &\\widehat{\\mathbf{e}}_r= (\\sin \\theta \\cos \\varphi , \\sin \\theta \\sin \\varphi , \\cos \\theta )^t, \\\\\n", " &\\widehat{\\mathbf{e}}_\\theta=(\\cos \\theta \\cos \\varphi , \\cos \\theta \\sin \\varphi , -\\sin \\theta )^t, \\\\\n", " &\\widehat{\\mathbf{e}}_{\\varphi}=(-\\sin \\varphi , \\cos \\varphi , 0 )^t.\n", "\\end{aligned}$$\n", "\n", "Also, the gradient operator in spherical coordinates:\n", "$$\\begin{aligned}\n", " \\nabla f&=\\frac{\\partial f}{\\partial r} \\widehat{\\mathbf{e}}_r+\\frac{1}{r} \\frac{\\partial f}{\\partial \\theta} \\widehat{\\mathbf{e}}_\\theta+\\frac{1}{r \\sin \\theta} \\frac{\\partial f}{\\partial \\varphi} \\widehat{\\mathbf{e}}_{\\varphi}\n", "\\end{aligned}$$" ] }, { "cell_type": "markdown", "id": "d951592b-08dc-43d7-ba80-f9c15459959b", "metadata": {}, "source": [ "### Associated Legendre functions" ] }, { "cell_type": "markdown", "id": "3889b52b-0006-46fe-aec0-8bc120494b71", "metadata": {}, "source": [ "$P_l^m$ are the associated Legendre functions of degree $l$ and order $m$ defined as:\n", "$$P_{l}^m\\left(x\\right) := (-1)^m \\left( 1- x^2\\right)^{\\frac{m}{2}} \\frac{d^m}{dx^m}P_l(x), \\quad P_{l}\\left(x\\right) := \\frac{1}{2^ll!}\\frac{d^l}{dx^l}(x^2-1)^l.$$\n", "\n", "Here, the term $(-1)^m$ is the Condon-Shortley phase factor." ] }, { "cell_type": "markdown", "id": "84fbc971-bff1-4790-a9d5-cdc6fdd77e40", "metadata": {}, "source": [ "### Real spherical harmonics" ] }, { "cell_type": "markdown", "id": "162f1fb2-8a4c-4a5f-8cf7-6c0929687790", "metadata": {}, "source": [ "Real spherical harmonics of degree $l$ and order $m$ are defined using spherical coordinates:\n", "$$\\begin{aligned}\n", "\t\t Y_{l,m}\\left(\\theta,\\varphi\\right) &:= \\sqrt{ (2-\\delta_{m,0}) \\frac{\\left(2l+1\\right)\\left(l-m\\right)!}{4 \\pi \\left(l+m\\right)!}} P_l^{m} \\left(\\cos\\theta\\right) \\cos m \\varphi ,\\\\\n", "\t\tY_{l,-m}\\left(\\theta,\\varphi\\right) &:= \\sqrt{ (2-\\delta_{m,0})\\frac{\\left(2l+1\\right)\\left(l-m\\right)!}{4 \\pi \\left(l+m\\right)!}} P_l^{m} \\left(\\cos\\theta\\right) \\sin m \\varphi ,\n", "\\end{aligned}$$\n", "with $l\\in \\mathbb{N}_0$, $m\\in \\mathbb{Z}$ such that $0\\leq m\\leq l$. If $m=0$, then $\\delta_{m,0}=1$, and it is zero otherwise." ] }, { "cell_type": "markdown", "id": "04743e8f-9eca-4b5e-bf35-676f139ea098", "metadata": {}, "source": [ "### Orthonormality of spherical harmonics" ] }, { "cell_type": "markdown", "id": "5f0bdc99-0614-48b3-834e-773aa0d6d2f2", "metadata": {}, "source": [ "Spherical harmonics are dense in $C(\\mathbb{S}^2)$, with $\\mathbb{S}^2$ the surface of the unit sphere, and form a complete orthonormal system in $L^2(\\mathbb{S}^2)$ with respect to the internal product defined by:\n", "$$\\left( \\psi , \\xi \\right)_{L^2(\\mathbb{S}^2)} = \\int_{0}^{2\\pi}\\int_{0}^{\\pi} \\psi\\left(\\theta,\\varphi\\right) \\xi\\left(\\theta,\\varphi\\right) \\sin\\left(\\theta\\right) d\\theta d\\varphi.$$\n", "\n", "They also are orthogonal in $H^1(\\mathbb{S}^2)$." ] }, { "cell_type": "markdown", "id": "ca5e406a-f8f1-4408-8ebd-e54ac358dcb5", "metadata": {}, "source": [ "### Reference systems" ] }, { "cell_type": "markdown", "id": "c20887a9-2d26-47a3-ac8b-53dcd1759b9e", "metadata": {}, "source": [ "Let be $j\\in \\{1,...,N\\}$. We define the reference system $j$ as the one centered at $\\mathbf{p_j}$ with the same orientation that the reference system centered in the origin. Furthermore, we denote by $Y_{l,m,j}$ the spherical harmonic $Y_{l,m}$ centered in the origin of the reference system $j$. Thus, if $\\left( r_j, \\varphi_j, \\theta_j \\right)$ are the vector spherical coordinates of $\\mathbf{r_j}$ in the reference system $j$, we have that $Y_{l,m,j}\\left(\\mathbf{r}_j\\right)=Y_{l,m}\\left(\\theta_j, \\varphi_j\\right)$." ] }, { "cell_type": "markdown", "id": "6a688f45-ad62-465f-9237-8f8fb71f7140", "metadata": {}, "source": [ "### Some expansions in spherical harmonics" ] }, { "cell_type": "markdown", "id": "38e033ab-5097-4933-8554-eae0ea82f8fe", "metadata": {}, "source": [ "#### Expansion of the fundamental solution" ] }, { "cell_type": "markdown", "id": "6fdb37f5-d913-4f6e-b7f3-0b499232990f", "metadata": {}, "source": [ "Let $\\mathbf{r}$, $\\mathbf{r}'$ be vectors, whose spherical coordinates in the reference system $j$ are $\\left(r_j,\\theta_j, \\varphi_j \\right)$ and $\\left(r_j',\\theta_j', \\varphi_j' \\right)$, respectively. For $r_j>r_j'$ we have\n", "$$g\\left(\\mathbf{r}, \\mathbf{r}'\\right) = \\sum_{l=0}^{\\infty} \\frac{1}{2l+1} \\frac{r_j^{'l}}{r_j^{l+1}}\\sum_{m=-l}^l Y_{l,m,j}\\left(\\mathbf{r}\\right) Y_{l,m,j}\\left(\\mathbf{r}'\\right).$$\n", "This series and its term by term first derivatives with respect to $r_j$ or $r_j'$ are absolutely and uniformly convergent on compact subsets with $r_j>r_j'$." ] }, { "cell_type": "markdown", "id": "40c3dcb2-e35d-42f9-a813-a0c5f171ee51", "metadata": {}, "source": [ "#### Results for layer potentials" ] }, { "cell_type": "markdown", "id": "2dc5fcc3-4ed9-40b5-ab0c-c6529241f978", "metadata": {}, "source": [ "Let be $j\\in \\{1,\\ldots,N\\}$, and $\\tilde{r}_j$ the radius of $\\Omega_j$.\n", "- Let $\\mathbf{r} \\in \\Omega_0$ and $\\mathbf{r}=(r,\\theta,\\varphi )$ be expressed in the $j$th spherical coordinate system, then\n", "$$\\begin{aligned}\n", " DL_{0j} ( Y_{l,m,j}) (\\mathbf{r}) &= -\\frac{l}{2l+1} \\left( \\frac{\\tilde{r}_j}{r} \\right)^{l+1} Y_{l,m}(\\theta, \\varphi ),\\\\\n", " SL_{0j} ( Y_{l,m,j}) (\\mathbf{r}) &= \\frac{\\tilde{r}_j}{2l+1} \\left( \\frac{\\tilde{r}_j}{r} \\right)^{l+1} Y_{l,m}(\\theta, \\varphi ).\n", "\\end{aligned}$$\n", "- Let $\\mathbf{r} \\in \\Omega_j$ and $\\mathbf{r}=(r,\\theta,\\varphi )$ expressed in the $j$th spherical coordinate system, then\n", "$$\\begin{aligned}\n", " DL_{j} ( Y_{l,m,j}) (\\mathbf{r}) &= -\\frac{l+1}{2l+1} \\left( \\frac{r}{\\tilde{r}_j} \\right)^{l} Y_{l,m}(\\theta, \\varphi ),\\\\\n", " SL_{j} ( Y_{l,m,j}) (\\mathbf{r}) &= \\frac{\\tilde{r}_j}{2l+1} \\left( \\frac{r}{\\tilde{r}_j} \\right)^{l} Y_{l,m}(\\theta, \\varphi ).\n", "\\end{aligned}$$" ] }, { "cell_type": "markdown", "id": "586bb1ca-5979-48a7-b9dd-38caf0510d7f", "metadata": {}, "source": [ "#### Results for operators of Cross-interactions" ] }, { "cell_type": "markdown", "id": "728293a6-c2c1-41e3-a107-29276dd5a607", "metadata": {}, "source": [ "The following holds\n", "$$\\begin{aligned}\n", "\\left( V_{i,j}^0\\left( Y_{l,m,j} \\right) ; Y_{p,q,i} \\right)_{L^2(\\Gamma_i)} &= \\left( V_{j,i}^0\\left( Y_{p,q,i} \\right) ; Y_{l,m,j} \\right)_{L^2(\\Gamma_j)},\\\\\n", "\\left( K_{i,j}^0\\left( Y_{l,m,j} \\right) ; Y_{p,q,i} \\right)_{L^2(\\Gamma_i)} &= - \\frac{l}{\\tilde{r}_j} \\left( V_{i,j}^0\\left( Y_{l,m,j} \\right) ; Y_{p,q,i} \\right)_{L^2(\\Gamma_i)}, \\\\\n", "\\left( K_{j,i}^{*0}\\left( Y_{p,q,i} \\right) ; Y_{l,m,j} \\right)_{L^2(\\Gamma_j)} &= \\left( K_{i,j}^0\\left( Y_{l,m,j} \\right) ; Y_{p,q,i} \\right)_{L^2(\\Gamma_i)}, \\\\\n", "\\left( W_{i,j}^0\\left( Y_{l,m,j} \\right) ; Y_{p,q,i} \\right)_{L^2(\\Gamma_i)} &= \\frac{l}{\\tilde{r}_j} \\left( K_{i,j}^{*0}\\left( Y_{l,m,j} \\right) ; Y_{p,q,i} \\right)_{L^2(\\Gamma_i)} .\n", "\\end{aligned}$$\n", "It can be deduced that the integrals of all the cross-interactions of a couple of spheres $i$ and $j$ can be derived having the results of the expression $\\left( V_{i,j}^0\\left( Y_{l,m,j} \\right) ; Y_{p,q,i} \\right)_{L^2(\\Gamma_i)}$ for all of the $l$, $m$, $p$ and $q$ needed, which avoids the need of computing numerically the other integral expressions." ] }, { "cell_type": "markdown", "id": "7390b679-409c-439e-9ea9-c7be180684c0", "metadata": {}, "source": [ "## Comments on the numerical algorithms implemented" ] }, { "cell_type": "markdown", "id": "f06301c0-ba78-449e-8b68-814f2f0474b8", "metadata": {}, "source": [ "Cross-interaction operators, e.g.~$V_{i,j}^0$ for $i \\not = j$, are non-singular, but are non diagonalizable. The double and single layer operators analytic expressions are used in the numerical computation of the boundary integral operators: \n", "$$\\begin{aligned}\n", "\t\\left( V_{i,j}^0\\left( Y_{l,m,j} \\right) ; Y_{p,q,i} \\right)_{L^2(\\Gamma_i)} &= \\int_{\\Gamma_i} SL_{0j}(Y_{l,m,j}) Y_{p,q,i} \\ d \\Gamma_i ,\\\\\n", "\t\\left( K_{i,j}^0\\left( Y_{l,m,j} \\right) ; Y_{p,q,i} \\right)_{L^2(\\Gamma_i)} &= \\int_{\\Gamma_i} DL_{0j}(Y_{l,m,j}) Y_{p,q,i} \\ d \\Gamma_i,\\\\\n", "\t\\left( K^{*0}_{i,j}\\left( Y_{l,m,j} \\right) ; Y_{p,q,i} \\right)_{L^2(\\Gamma_i)} &= \\int_{\\Gamma_i} \\widehat{\\mathbf{n}}_{0i} \\cdot\\nabla SL_{0j}(Y_{l,m,j}) Y_{p,q,i} \\ d \\Gamma_i,\\\\\n", "\t\\left( W_{i,j}^0\\left( Y_{l,m,j} \\right) ; Y_{p,q,i} \\right)_{L^2(\\Gamma_i)} &= - \\int_{\\Gamma_i} \\widehat{\\mathbf{n}}_{0i}\\cdot \\nabla DL_{0j}(Y_{l,m,j}) Y_{p,q,i} \\ d \\Gamma_i .\n", "\\end{aligned}$$\n", "\n", "Approximations of this integrals are provided via Gauss-Legendre quadratures. Specifically, along $\\theta$, we use the change of variable $u=cos(\\theta)$. Then, variable functions are sampled at the zeros of the Legendre Polynomial of degree $L_c+1$, whereas the trapezoidal rule is applied to equally spaced nodes in $\\varphi$, with $2L_c+1$ points. If the function being integrated has a spherical harmonic expansion with coefficients equal to zero for degrees higher than $L_c$, then the quadrature yields the exact result, assuming that there are not other sources of error. Moreover, the integral in the variable $\\varphi$ can be computed using the Fast Fourier Transform." ] }, { "cell_type": "markdown", "id": "62f68ab0-1be7-4b7c-8d28-8ee59c2db420", "metadata": {}, "source": [ "## `v_0_sj_semi_analytic_v1d`" ] }, { "cell_type": "markdown", "id": "6ba8a5fa-3347-46a2-9aa2-e9de9dba2755", "metadata": {}, "source": [ "This function returns a numpy array of two dimensions, which we will call `data_v`. The entries of the array are\n", "$$data_v[p(2p + 1) + q, l(2l + 1) + m] = ( V_{s,j}^0 Y_{l,m,j} , Y_{p,q,s} )_{L^2(\\mathcal{S}_s)}.$$\n", "with Laplace kernel." ] }, { "cell_type": "markdown", "id": "ccc1052c-8240-40f9-b8b0-17c1eb1bd14d", "metadata": {}, "source": [ "The `1d` on the name of the routine indicates the type of input it needs. See the following sections for details." ] }, { "cell_type": "markdown", "id": "de38b791-c238-49f3-bfd2-8d836da0018c", "metadata": {}, "source": [ "### Docstring" ] }, { "cell_type": "code", "execution_count": 3, "id": "b1b4456b-70c1-4e1b-8f7f-c8d74afebd18", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Returns a numpy array that represents a numerical approximation of\n", " the matrix formed by the boundary integral operator V_{s,j}^0 with\n", " Laplace kernel evaluated and tested with real spherical harmonics.\n", " In this routine the quadrature points NEED to be ordered in an array\n", " of one dimension.\n", " It is a SLOW routine, because it does not have performance\n", " improvements for the real spherical harmonic transform algorithm.\n", "\n", " Notes\n", " -----\n", " data_v[p(2p + 1) + q, l(2l + 1) + m] =\n", " ( V_{s,j}^0 Y_{l,m,j} ; Y_{p,q,s} )_{L^2(S_s)}\n", " Y_{l,m,j} : spherical harmonic degree l, order m, in the coordinate\n", " system j.\n", " S_s : surface of the sphere s.\n", "\n", " The expression V_{s,j}^0 Y_{l,m,j} is analytic. A quadrature scheme\n", " is used to compute the surface integral corresponding to the inner\n", " product.\n", "\n", " Parameters\n", " ----------\n", " big_l : int\n", " >= 0, max degree of spherical harmonics used.\n", " r_j : float\n", " > 0, radius of the sphere j.\n", " r_s : float\n", " > 0, radius of the sphere s.\n", " r_coord : np.ndarray\n", " Array of floats with the spherical coordinate r of the\n", " quadrature points in the coordinate system s. Length equals to\n", " final_length. Can come from the\n", " function from_sphere_s_cartesian_to_j_spherical_1d of the module\n", " biosspheres.quadratures.spheres.\n", " phi_coord : np.ndarray\n", " Array of floats with the phi coordinate r of the quadrature\n", " points in the coordinate system s. Length equals to\n", " final_length. Can come from the function\n", " from_sphere_s_cartesian_to_j_spherical_1d of the module\n", " biosspheres.quadratures.spheres.\n", " cos_theta_coord : np.ndarray\n", " Array of floats with the cosine of the spherical coordinate\n", " theta of the quadrature points in the coordinate system s.\n", " Lengths equal to final_length. Can come from the function\n", " from_sphere_s_cartesian_to_j_spherical_1d of the module\n", " biosspheres.quadratures.spheres.\n", " final_length : int\n", " How many points for the surface integral.\n", " Can come from the function spherical_harmonic_transform_1d of\n", " the module biosspheres.quadratures.spheres.\n", " transform : np.ndarray\n", " of floats, for doing the real spherical harmonic transform.\n", " Can come from the function real_spherical_harmonic_transform_1d\n", " of the module biosspheres.quadratures.spheres.\n", "\n", " Returns\n", " -------\n", " data_v : numpy array\n", " of floats. Shape ((big_l+1)**2, (big_l+1)**2).\n", " See notes for the indexes ordering.\n", "\n", " See Also\n", " --------\n", " v_0_sj_semi_analytic_v2d\n", "\n", " \n" ] } ], "source": [ "print(cross.v_0_sj_semi_analytic_v1d.__doc__)" ] }, { "cell_type": "markdown", "id": "e1c3269a-5bc1-469f-8426-3b17def9b180", "metadata": {}, "source": [ "### Example" ] }, { "cell_type": "markdown", "id": "bdbcef7b-3a67-47eb-ad3f-8ae5a8014f60", "metadata": {}, "source": [ "Definition of the parameters:" ] }, { "cell_type": "markdown", "id": "11a875ef-dc69-422e-9ad5-d23822e27597", "metadata": {}, "source": [ "Radii:" ] }, { "cell_type": "code", "execution_count": 4, "id": "2b7118a2-a011-4506-a53d-f2977b56ad56", "metadata": {}, "outputs": [], "source": [ "radio_1 = 3.\n", "radio_2 = 2.\n", "rs = np.asarray([radio_1, radio_2])" ] }, { "cell_type": "markdown", "id": "7653c89d-bf75-4fea-8382-a0af6ddc9d3d", "metadata": {}, "source": [ "Center positions of the spheres:" ] }, { "cell_type": "code", "execution_count": 5, "id": "3f98d4fa-e647-4603-ab5b-4d8ae2de3589", "metadata": {}, "outputs": [], "source": [ "p_1 = np.asarray([2., 3., 4.])\n", "p_2 = -p_1" ] }, { "cell_type": "markdown", "id": "2d8c0889-9c13-465a-8d42-e3df1bf315ca", "metadata": {}, "source": [ "Maximum degree of spherical harmonics used, and parameter for the quadrature rule:" ] }, { "cell_type": "code", "execution_count": 6, "id": "95233fb1-50c1-48b6-9538-c43c8a0ab485", "metadata": {}, "outputs": [], "source": [ "big_l = 18\n", "big_l_c = 25" ] }, { "cell_type": "markdown", "id": "0f53094f-86a6-4722-bb1f-be8ad6141d9e", "metadata": {}, "source": [ "Auxiliary parameters that use the ones previously defined, which are related to the implemented quadrature, this differs from the routines without the `1d` in its name:" ] }, { "cell_type": "code", "execution_count": 7, "id": "d6363545-171e-4c82-9b70-17657deaf066", "metadata": {}, "outputs": [], "source": [ "final_length, pre_vector_t, transform = quadratures.real_spherical_harmonic_transform_1d(big_l, big_l_c)" ] }, { "cell_type": "code", "execution_count": 8, "id": "ce117336-a33c-4b2b-a288-4baef5e1a723", "metadata": {}, "outputs": [], "source": [ "r_coord_1tf, phi_coord_1tf, cos_theta_coord_1tf = quadratures.from_sphere_s_cartesian_to_j_spherical_1d(\n", " radio_2, p_1, p_2, final_length, pre_vector_t)\n", "r_coord_2tf, phi_coord_2tf, cos_theta_coord_2tf = quadratures.from_sphere_s_cartesian_to_j_spherical_1d(\n", " radio_1, p_2, p_1, final_length, pre_vector_t)" ] }, { "cell_type": "markdown", "id": "f34a13c5-2175-45d8-bb38-0a9ac1ce09db", "metadata": {}, "source": [ "Now, we can obtain the arrays for the $V_{2,1}^0$ and $V_{1,2}^0$ operators (notice how their inputs are different depending on the subindexes):" ] }, { "cell_type": "code", "execution_count": 9, "id": "b21e5c49-3229-43e3-a556-ef3531762819", "metadata": {}, "outputs": [], "source": [ "data_v21 = cross.v_0_sj_semi_analytic_v1d(\n", " big_l, radio_1, radio_2, r_coord_1tf, phi_coord_1tf,\n", " cos_theta_coord_1tf, final_length, transform)\n", "data_v12 = cross.v_0_sj_semi_analytic_v1d(\n", " big_l, radio_2, radio_1, r_coord_2tf, phi_coord_2tf,\n", " cos_theta_coord_2tf, final_length, transform)" ] }, { "cell_type": "markdown", "id": "4c89a0b9-fc41-4e36-91ee-1390a8a5ad6b", "metadata": {}, "source": [ "One of the properties of the cross-interactions given in the preliminaries results in `data_v21 = data_v12`$^t$. As this a numerical approximation, we will not have the equality." ] }, { "cell_type": "markdown", "id": "07344166", "metadata": {}, "source": [ "The absolute error obtained is good:" ] }, { "cell_type": "code", "execution_count": 10, "id": "97cf83ea", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(dpi=75., layout='constrained')\n", "im = np.abs(data_v12 - data_v21.T)\n", "plt.imshow(im)\n", "plt.colorbar()\n", "plt.title('Absolute error between data_v21 and data_v12$^t$.')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "55711a69", "metadata": {}, "source": [ "However, the relative error of each entry is not good for all values, specially when the entries are near to zero:" ] }, { "cell_type": "code", "execution_count": 11, "id": "2166a892-67ba-4d71-a344-3a71c1a6e3f2", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\there\\AppData\\Local\\Temp\\ipykernel_8924\\2109776671.py:3: RuntimeWarning: divide by zero encountered in log\n", " plt.imshow(np.log(im), cmap='RdBu', norm=colors.CenteredNorm(vcenter=-10))\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(dpi=75., layout='constrained')\n", "im = np.abs(data_v12 - data_v21.T) / np.abs(data_v12)\n", "plt.imshow(np.log(im), cmap='RdBu', norm=colors.CenteredNorm(vcenter=-10))\n", "plt.colorbar()\n", "plt.title('Logarithm of the relative error between data_v21 and data_v12$^t$.')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "7aa9f0ad", "metadata": {}, "source": [ "The checking of this property could be useful, specially when the relative error increases for some entries when using higher degrees of spherical harmonics." ] }, { "cell_type": "markdown", "id": "a4c475be-9802-4a78-b1a8-318b94e64193", "metadata": {}, "source": [ "## `v_0_sj_semi_analytic_v2d`" ] }, { "cell_type": "markdown", "id": "2eeb41c0-faac-47ad-b902-c1cb05439d4c", "metadata": {}, "source": [ "This function returns a numpy array of two dimensions, which we will call `data_v`. The entries of the array are\n", "$$data_v[p(2p + 1) + q, l(2l + 1) + m] = ( V_{s,j}^0 Y_{l,m,j} , Y_{p,q,s} )_{L^2(\\mathcal{S}_s)}.$$" ] }, { "cell_type": "markdown", "id": "4db11142-c16e-4d15-8ffd-da26c38966c7", "metadata": {}, "source": [ "It is the same than `v_0_sj_semi_analytic_v1d`, but with different inputs. For bigger computations this one is faster." ] }, { "cell_type": "markdown", "id": "bb35d0a1-5004-4f57-a5ca-0fd12954ff25", "metadata": {}, "source": [ "See the following section for details." ] }, { "cell_type": "markdown", "id": "0b49906d-fd77-45c9-8e1a-f964908c4e32", "metadata": {}, "source": [ "### Docstring" ] }, { "cell_type": "code", "execution_count": 12, "id": "6295686e-6bd9-40e8-b972-f18ed0441fb1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Returns a numpy array that represents a numerical approximation of\n", " the matrix formed by the boundary integral operator V_{s,j}^0 with\n", " Laplace kernel evaluated and tested with real spherical harmonics.\n", " In this routine the quadrature points NEED to be ordered in an array\n", " of two dimensions, given by the function\n", " from_sphere_s_cartesian_to_j_spherical_2d of the module\n", " biosspheres.quadratures.spheres.\n", "\n", " Notes\n", " -----\n", " data_v[p(2p + 1) + q, l(2l + 1) + m] =\n", " ( V_{s,j}^0 Y_{l,m,j} ; Y_{p,q,s} )_{L^2(S_s)}.\n", " Y_{l,m,j} : spherical harmonic degree l, order m, in the coordinate\n", " system j.\n", " S_s : surface of the sphere s.\n", "\n", " The expression V_{s,j}^0 Y_{l,m,j} is analytic. A quadrature scheme\n", " is used to compute the surface integral corresponding to the inner\n", " product.\n", "\n", " It uses functions from the package pyshtools to compute the\n", " spherical harmonic transforms. These functions have performance\n", " improvements.\n", "\n", " Parameters\n", " ----------\n", " big_l : int\n", " >= 0, max degree of spherical harmonics used.\n", " r_j : float\n", " > 0, radius of the sphere j.\n", " r_s : float\n", " > 0, radius of the sphere s.\n", " r_coord : np.ndarray\n", " Two dimensional array of floats with the spherical coordinate r\n", " of the quadrature points in the coordinate system s.\n", " Shape equals to (quantity_theta_points, quantity_phi_points).\n", " Comes from the function\n", " from_sphere_s_cartesian_to_j_spherical_2d of the module\n", " biosspheres.quadratures.spheres.\n", " phi_coord : np.ndarray\n", " Two dimensional array of floats with the phi coordinate r of the\n", " quadrature points in the coordinate system s. Shape equals to\n", " (quantity_theta_points, quantity_phi_points).\n", " Comes from the function\n", " from_sphere_s_cartesian_to_j_spherical_2d of the module\n", " biosspheres.quadratures.spheres.\n", " cos_theta_coord : np.ndarray\n", " Two dimensional array of floats with the cosine of the spherical\n", " coordinate theta of the quadrature points in the coordinate\n", " system s. Shape equals to\n", " (quantity_theta_points, quantity_phi_points). Comes from the\n", " function from_sphere_s_cartesian_to_j_spherical_2d of\n", " the module biosspheres.quadratures.spheres.\n", " weights : np.ndarray\n", " of floats. Weights for the integral quadrature in the theta\n", " variable. Comes from the function\n", " gauss_legendre_trapezoidal_shtools_2d\n", " from the module biosspheres.quadratures.spheres.\n", " zeros : np.ndarray\n", " of floats. Zeros of the integral quadrature in the theta\n", " variable. Comes from the function\n", " gauss_legendre_trapezoidal_shtools_2d\n", " from the module biosspheres.quadratures.spheres.\n", " quantity_theta_points : int\n", " how many points for the integral in theta.\n", " Can come from the function\n", " gauss_legendre_trapezoidal_shtools_2d\n", " from the module biosspheres.quadratures.spheres.\n", " quantity_phi_points : int\n", " how many points for the integral in phi.\n", " Comes from the function\n", " gauss_legendre_trapezoidal_shtools_2d\n", " from the module biosspheres.quadratures.spheres.\n", " pesykus : np.ndarray\n", " dtype int, shape ((big_l+1) * big_l // 2, 2).\n", " Used for the vectorization of some computations.\n", " Comes from the function\n", " biosspheres.miscella.auxindexes.pes_y_kus(big_l)\n", " p2_plus_p_plus_q : np.ndarray\n", " dtype int, length (big_l+1) * big_l // 2.\n", " Used for the vectorization of some computations.\n", " Comes from the function\n", " biosspheres.miscella.auxindexes.pes_y_kus(big_l)\n", " p2_plus_p_minus_q : np.ndarray\n", " dtype int, length (big_l+1) * big_l // 2.\n", " Used for the vectorization of some computations.\n", " Comes from the function\n", " biosspheres.miscella.auxindexes.pes_y_kus(big_l)\n", "\n", " Returns\n", " -------\n", " data_v : numpy array\n", " of floats. Shape ((big_l+1)**2, (big_l+1)**2).\n", " See notes for the indexes ordering.\n", "\n", " See Also\n", " --------\n", " v_0_sj_semi_analytic_v1d\n", "\n", " \n" ] } ], "source": [ "print(cross.v_0_sj_semi_analytic_v2d.__doc__)" ] }, { "cell_type": "markdown", "id": "4ef4880a-5980-4706-987d-82c926289d1e", "metadata": {}, "source": [ "### Example" ] }, { "cell_type": "markdown", "id": "53d831f3-c596-40ea-b27d-36e063b92652", "metadata": {}, "source": [ "Definition of parameters:" ] }, { "cell_type": "markdown", "id": "be85e039-15a7-4775-8e23-c09c7ad032fe", "metadata": {}, "source": [ "Radii:" ] }, { "cell_type": "code", "execution_count": 13, "id": "5d0c17c4-1bc0-42df-9d3f-5b768ca8d14d", "metadata": {}, "outputs": [], "source": [ "radio_1 = 3.\n", "radio_2 = 2." ] }, { "cell_type": "markdown", "id": "b7d4c442-5314-4ae8-ac7f-1e3485eb0429", "metadata": {}, "source": [ "Center positions of the spheres:" ] }, { "cell_type": "code", "execution_count": 14, "id": "01b93db1-c3c5-40ee-b5ec-dd943558f8be", "metadata": {}, "outputs": [], "source": [ "p_1 = np.asarray([2., 3., 4.])\n", "p_2 = -p_1" ] }, { "cell_type": "markdown", "id": "bb13d1d6-6a54-4e71-a829-39db759b18eb", "metadata": {}, "source": [ "Maximum degree of spherical harmonics used, and parameter for the quadrature rule:" ] }, { "cell_type": "code", "execution_count": 15, "id": "ed5a8532-1376-4576-a5ce-26c196dc8bed", "metadata": {}, "outputs": [], "source": [ "big_l = 10\n", "big_l_c = 25" ] }, { "cell_type": "markdown", "id": "069ad0bc-13b6-4d1d-a7e2-a23309825ba4", "metadata": {}, "source": [ "Auxiliary parameters that use the ones previously defined, which are related to the implemented quadrature. This differs from the routines without the `2d` in its name:" ] }, { "cell_type": "code", "execution_count": 16, "id": "1576868a-4e2a-49cb-801a-b103d9ccef63", "metadata": {}, "outputs": [], "source": [ "quantity_theta_points, quantity_phi_points, weights, pre_vector_t_2d = \\\n", " quadratures.gauss_legendre_trapezoidal_2d(big_l_c)\n", "r_coord_1tf_2d, phi_coord_1tf_2d, cos_theta_coord_1tf_2d = (\n", " quadratures.from_sphere_s_cartesian_to_j_spherical_2d(\n", " radio_2, p_1, p_2, quantity_theta_points, quantity_phi_points,\n", " pre_vector_t_2d))\n", "pesykus, p2_plus_p_plus_q, p2_plus_p_minus_q = auxindexes.pes_y_kus(big_l)" ] }, { "cell_type": "markdown", "id": "17e9c6a1-45e5-4e04-9e19-9cdd5d203d63", "metadata": {}, "source": [ "Now, we can obtain the array for the $V_{2,1}^0$ operator:" ] }, { "cell_type": "code", "execution_count": 17, "id": "ccc3a793-6ac4-4d03-bb4a-2144e4cd0378", "metadata": {}, "outputs": [], "source": [ "data_v21_2d = cross.v_0_sj_semi_analytic_v2d(\n", " big_l, radio_1, radio_2, r_coord_1tf_2d, phi_coord_1tf_2d,\n", " cos_theta_coord_1tf_2d, weights, pre_vector_t_2d[2, :, 0],\n", " quantity_theta_points, quantity_phi_points, pesykus, p2_plus_p_plus_q,\n", " p2_plus_p_minus_q)" ] }, { "cell_type": "markdown", "id": "7a2ac1ea-cb46-4306-9a78-aedc6a356e2c", "metadata": {}, "source": [ "We can compare the result with the one given by `v_0_sj_semi_analytic_v1d`:" ] }, { "cell_type": "code", "execution_count": 18, "id": "8dfdfea3-647d-40aa-89d7-8d1dc9026c3d", "metadata": {}, "outputs": [], "source": [ "final_length, pre_vector_t, transform = \\\n", " quadratures.real_spherical_harmonic_transform_1d(big_l, big_l_c)\n", "r_coord_1tf, phi_coord_1tf, cos_theta_coord_1tf = (\n", " quadratures.from_sphere_s_cartesian_to_j_spherical_1d(\n", " radio_2, p_1, p_2, final_length, pre_vector_t))\n", "data_v21 = cross.v_0_sj_semi_analytic_v1d(\n", " big_l, radio_1, radio_2, r_coord_1tf, phi_coord_1tf,\n", " cos_theta_coord_1tf, final_length, transform)" ] }, { "cell_type": "markdown", "id": "76a62b04", "metadata": {}, "source": [ "Relative error:" ] }, { "cell_type": "code", "execution_count": 19, "id": "506acdbe-fa89-44bf-becd-17c86878829d", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\there\\AppData\\Local\\Temp\\ipykernel_8924\\761239704.py:3: RuntimeWarning: divide by zero encountered in log\n", " plt.imshow(np.log(im), cmap='RdBu', norm=colors.CenteredNorm(vcenter=-10))\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(dpi=75., layout='constrained')\n", "im = np.abs(data_v21_2d - data_v21) / np.abs(data_v21)\n", "plt.imshow(np.log(im), cmap='RdBu', norm=colors.CenteredNorm(vcenter=-10))\n", "plt.colorbar(shrink=0.9)\n", "plt.title('Logarithm of the relative error between data_v21 from 1d and 2d routines')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "f3f9c825-f907-4bc4-b5ac-6ccfb7c38107", "metadata": {}, "source": [ "## `v_0_js_from_v_0_sj`" ] }, { "cell_type": "markdown", "id": "7ecb2ed8-ef3f-485c-9db6-bde964a4745c", "metadata": {}, "source": [ "This function returns a numpy array of two dimensions, which we will call `data_vjs`. The entries of the array are\n", "$$data_vjs[p(2p+1) + q, l(2l+1) + m] = ( V_{j,s}^0 Y_{l,m,s} ; Y_{p,q,j} )_{L^2(\\mathcal{S}_s)}.$$" ] }, { "cell_type": "markdown", "id": "515e67fe-a3fc-45a6-b843-b124a10880cc", "metadata": {}, "source": [ "For obtaining the array corresponding to the operator $V^0_{j,s}$ the input needed is the array corresponding to the operator $V^0_{s,j}$. This functions uses the property of the arrays `data_v21 = data_v12`$^t$, showed in the example of `v_0_sj_semi_analytic_v1d`." ] }, { "cell_type": "markdown", "id": "e7965f44-22ab-4c75-bf0e-3379e2bd4457", "metadata": {}, "source": [ "### Docstring" ] }, { "cell_type": "code", "execution_count": 20, "id": "63fa9845-556a-4686-885a-272719116a36", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Returns a numpy array that represents a numerical approximation of\n", " the matrix formed by the boundary integral operator V_{j,s}^0 with\n", " Laplace kernel evaluated and tested with real spherical harmonics.\n", " This routine needs the numpy array corresponding to V_{s,j}^0\n", " (notice the change of the order of the indexes indicating the\n", " spheres).\n", "\n", " Notes\n", " -----\n", " data_v_js[p*(2p+1) + q, l*(2l+1) + m] =\n", " ( V_{j,s}^0 Y_{l,m,s} ; Y_{p,q,j} )_{L^2(S_j)}.\n", " Y_{l,m,s} : spherical harmonic degree l, order m, in the coordinate\n", " system s.\n", " S_j : surface of the sphere j.\n", "\n", " This computation uses the following result for this specific case:\n", " ( V_{j,s}^0 Y_{l,m,s} ; Y_{p,q,j} )_{L^2(S_j)}.\n", " = ( V_{s,j}^0 Y_{p,q,j} ; Y_{l,m,s} )_{L^2(S_s)}\n", "\n", " Parameters\n", " ----------\n", " data_v_sj: np.ndarray\n", " of floats. Represents a numerical approximation of the matrix\n", " formed by the boundary integral operator V_{s,j}^0 with Laplace\n", " kernel evaluated and tested with spherical harmonics.\n", "\n", " Returns\n", " -------\n", " data_v_js: np.ndarray\n", " of floats. Same shape than data_v_sj.\n", " See notes for the indexes ordering.\n", "\n", " See Also\n", " --------\n", " v_0_sj_semi_analytic_v1d\n", " v_0_sj_semi_analytic_v2d\n", "\n", " \n" ] } ], "source": [ "print(cross.v_0_js_from_v_0_sj.__doc__)" ] }, { "cell_type": "markdown", "id": "34b7a355-90e7-4dfb-8fa5-02606f682f69", "metadata": {}, "source": [ "### Example" ] }, { "cell_type": "markdown", "id": "44e36bc4-6d66-4fd2-9624-4e10fccfe2c8", "metadata": {}, "source": [ "Definition of the parameters:" ] }, { "cell_type": "markdown", "id": "5dd779fb-b255-49a5-a61f-7c6359f701e6", "metadata": {}, "source": [ "Radii:" ] }, { "cell_type": "code", "execution_count": 21, "id": "9aabb48d-0de4-4ed6-ba21-2e9ad9b7a889", "metadata": {}, "outputs": [], "source": [ "radio_1 = 3.\n", "radio_2 = 2." ] }, { "cell_type": "markdown", "id": "ef666a5c-70dd-48e7-9778-db34335c4c9b", "metadata": {}, "source": [ "Center positions of the spheres:" ] }, { "cell_type": "code", "execution_count": 22, "id": "fabaf1b9-4d5b-42d9-a328-8bc17654d39a", "metadata": {}, "outputs": [], "source": [ "p_1 = np.asarray([2., 3., 4.])\n", "p_2 = -p_1" ] }, { "cell_type": "markdown", "id": "591149d4-ebb2-4952-8040-51bf1be8b63b", "metadata": {}, "source": [ "Maximum degree of spherical harmonics used, and parameter for the quadrature rules:" ] }, { "cell_type": "code", "execution_count": 23, "id": "1f6ddc25-5d3a-416a-b505-0b8b91e73675", "metadata": {}, "outputs": [], "source": [ "big_l = 3\n", "big_l_c = 25" ] }, { "cell_type": "markdown", "id": "7e630de7-0f7f-4859-b874-0532bf9f9eb5", "metadata": {}, "source": [ "We use one of the previous routines to compute the array `data_v12_2d`:" ] }, { "cell_type": "code", "execution_count": 24, "id": "d2651cec-5963-4a17-a179-143ff2c51d3a", "metadata": {}, "outputs": [], "source": [ "quantity_theta_points, quantity_phi_points, weights, pre_vector_t_2d = quadratures.gauss_legendre_trapezoidal_2d(big_l_c)\n", "r_coord_2tf_2d, phi_coord_2tf_2d, cos_theta_coord_2tf_2d = \\\n", " (quadratures.from_sphere_s_cartesian_to_j_spherical_2d(\n", " radio_1, p_2, p_1, quantity_theta_points, quantity_phi_points,\n", " pre_vector_t_2d))\n", "pesykus, p2_plus_p_plus_q, p2_plus_p_minus_q = auxindexes.pes_y_kus(big_l)\n", "data_v12_2d = cross.v_0_sj_semi_analytic_v2d(\n", " big_l, radio_2, radio_1, r_coord_2tf_2d, phi_coord_2tf_2d,\n", " cos_theta_coord_2tf_2d, weights, pre_vector_t_2d[2, :, 0],\n", " quantity_theta_points, quantity_phi_points, pesykus, p2_plus_p_plus_q,\n", " p2_plus_p_minus_q)" ] }, { "cell_type": "markdown", "id": "545093ec-e715-453a-804d-c9514d547708", "metadata": {}, "source": [ "And we use that as input to compute the array `data_v21`:" ] }, { "cell_type": "code", "execution_count": 25, "id": "2350774f-e7ca-4fb6-bbd0-2dd59abc2b9b", "metadata": {}, "outputs": [], "source": [ "data_v21 = cross.v_0_js_from_v_0_sj(data_v12_2d)" ] }, { "cell_type": "markdown", "id": "37ff015a-14a3-4560-9326-557992fb5d86", "metadata": {}, "source": [ "We can compare the given result with the version computed by one of the previous routines:" ] }, { "cell_type": "code", "execution_count": 26, "id": "6e1a1002-5716-43e1-8d79-b0ba045d3c84", "metadata": {}, "outputs": [], "source": [ "r_coord_1tf_2d, phi_coord_1tf_2d, cos_theta_coord_1tf_2d = (\n", " quadratures.from_sphere_s_cartesian_to_j_spherical_2d(\n", " radio_2, p_1, p_2, quantity_theta_points, quantity_phi_points,\n", " pre_vector_t_2d))\n", "data_v21_2d = cross.v_0_sj_semi_analytic_v2d(\n", " big_l, radio_1, radio_2, r_coord_1tf_2d, phi_coord_1tf_2d,\n", " cos_theta_coord_1tf_2d, weights, pre_vector_t_2d[2, :, 0],\n", " quantity_theta_points, quantity_phi_points, pesykus, p2_plus_p_plus_q,\n", " p2_plus_p_minus_q)" ] }, { "cell_type": "code", "execution_count": 27, "id": "6a561bfd-dbb7-4206-b9f7-d531384d9a92", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(dpi=75., layout='constrained')\n", "im = np.abs(data_v21_2d - data_v21) / np.abs(data_v21)\n", "plt.imshow(im, cmap='RdBu')\n", "plt.colorbar(shrink = 0.9)\n", "plt.title('Relative error between `data_v21` with direct and indirect '\n", " 'routines')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "89485a4f-7d9d-4198-ac2d-9e9d42482314", "metadata": {}, "source": [ "## `k_0_sj_semi_analytic_v1d`" ] }, { "cell_type": "markdown", "id": "9d45096f-8138-495f-8696-c653a9413ada", "metadata": {}, "source": [ "This function returns a numpy array of two dimensions, which we will call `data_k`. The entries of the array are\n", "$$data_k[p(2p + 1) + q, l(2l + 1) + m] = ( K_{s,j}^0 Y_{l,m,j} , Y_{p,q,s} )_{L^2(\\mathcal{S}_s)}.$$" ] }, { "cell_type": "markdown", "id": "dbaa4a0a-6700-4441-9cec-50fb2b02ec5b", "metadata": {}, "source": [ "The `1d` on the name of the routine references the type of input it needs. See the following sections for details." ] }, { "cell_type": "markdown", "id": "ce2621d3-0d10-44ec-b8f9-56f96ce91118", "metadata": {}, "source": [ "### Docstring" ] }, { "cell_type": "code", "execution_count": 28, "id": "906df3ab-e184-495a-a461-d6b3584442ac", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Returns a numpy array that represents a numerical approximation of\n", " the matrix formed by the boundary integral operator K_{s,j}^0 with\n", " Laplace kernel evaluated and tested with real spherical harmonics.\n", " In this routine the quadrature points NEED to be ordered in an array\n", " of one dimension.\n", " It is a SLOW routine, because it does not use any symmetry or\n", " properties of the spherical harmonics.\n", "\n", " Notes\n", " -----\n", " data_k[p*(2p+1) + q, l*(2l+1) + m] =\n", " ( K_{s,j}^0 Y_{l,m,j} ; Y_{p,q,s} )_{L^2(S_s)}.\n", " Y_{l,m,j} : spherical harmonic degree l, order m, in the coordinate\n", " system j.\n", " S_s : surface of the sphere s.\n", "\n", " The expression K_{s,j}^0 Y_l,m,j can be obtained analytically. A\n", " quadrature scheme is used to compute the surface integral\n", " corresponding to the inner product.\n", "\n", " Parameters\n", " ----------\n", " big_l : int\n", " >= 0, max degree.\n", " r_j : float\n", " > 0, radius of the sphere j.\n", " r_s : float\n", " > 0, radius of the sphere s.\n", " r_coord : np.ndarray\n", " Array of floats with the spherical coordinate r of the\n", " quadrature points in the coordinate system s. Length equals to\n", " final_length. Can come from the function\n", " from_sphere_s_cartesian_to_j_spherical_1d of the module\n", " biosspheres.quadratures.spheres.\n", " phi_coord : np.ndarray\n", " Array of floats with the phi coordinate r of the quadrature\n", " points in the coordinate system s. Length equals to\n", " final_length. Can come from the function\n", " from_sphere_s_cartesian_to_j_spherical_1d of the module\n", " biosspheres.quadratures.spheres.\n", " cos_theta_coord : np.ndarray\n", " Array of floats with the cosine of the spherical coordinate\n", " theta of the quadrature points in the coordinate system s.\n", " Lengths equal to final_length. Can come from the function\n", " from_sphere_s_cartesian_to_j_spherical_1d of the module\n", " biosspheres.quadratures.spheres.\n", " final_length : int\n", " How many points for the surface integral.\n", " Can come from the function spherical_harmonic_transform_1d of\n", " the module biosspheres.quadratures.spheres.\n", " transform : np.ndarray\n", " of floats, for doing the real spherical harmonic transform.\n", " Can come from the function real_spherical_harmonic_transform_1d\n", " of the module biosspheres.quadratures.spheres.\n", "\n", " Returns\n", " -------\n", " data_k : numpy array\n", " of floats. Shape ((big_l+1)**2, (big_l+1)**2).\n", " See notes for the indexes ordering.\n", "\n", " See Also\n", " --------\n", " k_0_sj_semi_analytic_v2d\n", " k_0_sj_from_v_0_sj\n", "\n", " \n" ] } ], "source": [ "print(cross.k_0_sj_semi_analytic_v1d.__doc__)" ] }, { "cell_type": "markdown", "id": "e6e826b8-e90a-4f47-96a0-87677b24d488", "metadata": {}, "source": [ "### Example" ] }, { "cell_type": "markdown", "id": "e8af51b8-6203-46cf-b832-c3ade1be3a73", "metadata": {}, "source": [ "Definition of the parameters:" ] }, { "cell_type": "markdown", "id": "f66fc3fe-1a4d-4246-957e-a4c8e69e79d9", "metadata": {}, "source": [ "Radii:" ] }, { "cell_type": "code", "execution_count": 29, "id": "0e4df474-f617-48e8-b842-ee171d68fbff", "metadata": {}, "outputs": [], "source": [ "radio_1 = 1.2\n", "radio_2 = 3." ] }, { "cell_type": "markdown", "id": "631477b7-9eb8-4dad-9012-05b4a8460a6c", "metadata": {}, "source": [ "Positions of the center of the spheres:" ] }, { "cell_type": "code", "execution_count": 30, "id": "990950bb-c40b-41e8-bedc-316875d52f68", "metadata": {}, "outputs": [], "source": [ "p_1 = np.asarray([2., 3., 4.])\n", "p_2 = -p_1" ] }, { "cell_type": "markdown", "id": "68c74a8e-80a4-490c-b991-4eb5e840cbb1", "metadata": {}, "source": [ "Maximum degree of spherical harmonics used, and parameter for the quadrature rule:" ] }, { "cell_type": "code", "execution_count": 31, "id": "edeff685-e4ac-4bf8-a7ef-070ae8998aec", "metadata": {}, "outputs": [], "source": [ "big_l = 2\n", "big_l_c = 25" ] }, { "cell_type": "markdown", "id": "8203de80-3f88-4a15-8e67-bc38b5b529e5", "metadata": {}, "source": [ "Auxiliary parameters that use the ones previously defined, which are related to the implemented quadrature, this differs from the routines without the `1d` in its name:" ] }, { "cell_type": "code", "execution_count": 32, "id": "6b35251b-982f-49da-a4bc-998ee99f917f", "metadata": {}, "outputs": [], "source": [ "final_length, pre_vector_t, transform = \\\n", " quadratures.real_spherical_harmonic_transform_1d(big_l, big_l_c)" ] }, { "cell_type": "code", "execution_count": 33, "id": "87a9fce1-dba0-4bf1-8563-6a643308fb4b", "metadata": {}, "outputs": [], "source": [ "r_coord_1tf, phi_coord_1tf, cos_theta_coord_1tf = (\n", " quadratures.from_sphere_s_cartesian_to_j_spherical_1d(\n", " radio_2, p_1, p_2, final_length, pre_vector_t))" ] }, { "cell_type": "markdown", "id": "45ba6a30-829d-438b-bdd5-5aabe0e7427d", "metadata": {}, "source": [ "We compute the array `data_k21`:" ] }, { "cell_type": "code", "execution_count": 34, "id": "5b933d3a-bbaa-4242-b6ab-7d4675494519", "metadata": {}, "outputs": [], "source": [ "data_k21 = cross.k_0_sj_semi_analytic_v1d(\n", " big_l, radio_1, radio_2, r_coord_1tf, phi_coord_1tf,\n", " cos_theta_coord_1tf, final_length, transform)" ] }, { "cell_type": "markdown", "id": "21d926b7-a4bf-4ad0-9474-4dbee860ba32", "metadata": {}, "source": [ "To check its relationship with the $V^0_{2,1}$ operator, showed in the preliminaries:" ] }, { "cell_type": "code", "execution_count": 35, "id": "9cc1c141-74da-4914-8a5c-53a43cb592bd", "metadata": {}, "outputs": [], "source": [ "data_v21 = cross.v_0_sj_semi_analytic_v1d(\n", " big_l, radio_1, radio_2, r_coord_1tf, phi_coord_1tf,\n", " cos_theta_coord_1tf, final_length, transform)" ] }, { "cell_type": "code", "execution_count": 36, "id": "b735721c-ea8c-4469-8b15-9704c38537b1", "metadata": {}, "outputs": [], "source": [ "eles = np.arange(0, big_l + 1)\n", "el_diagonal_array = np.diag(np.repeat(eles / -radio_1, 2 * eles + 1))" ] }, { "cell_type": "code", "execution_count": 37, "id": "5e3fca83-5c5c-4171-99d0-d1e23811b881", "metadata": {}, "outputs": [], "source": [ "aux = data_v21 @ el_diagonal_array" ] }, { "cell_type": "code", "execution_count": 38, "id": "b808eb44-1231-4809-b48f-a59903be017f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(dpi=75., layout='constrained')\n", "im = np.abs(data_k21 - aux)\n", "plt.imshow(im, cmap='RdBu')\n", "plt.colorbar(shrink=0.9)\n", "plt.title('Absolute error between data_k21 and'\n", " ' a linear transformation of data_v21.')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "253760cb-faaf-4d7c-b6ca-992c192a5d09", "metadata": {}, "source": [ "## `k_0_sj_semi_analytic_v2d`" ] }, { "cell_type": "markdown", "id": "49c3a377-8277-49c8-9832-a265279bc74d", "metadata": {}, "source": [ "This function returns a numpy array of two dimensions, which we will call `data_k`. The entries of the array are\n", "$$data_k[p(2p + 1) + q, l(2l + 1) + m] = ( K_{s,j}^0 Y_{l,m,j} , Y_{p,q,s} )_{L^2(\\mathcal{S}_s)}.$$" ] }, { "cell_type": "markdown", "id": "219d2eac-8e41-47ec-942d-a3555f11bc71", "metadata": {}, "source": [ "It is the same than `k_0_sj_semi_analytic_v1d`, but with different inputs. For bigger computations this one is faster." ] }, { "cell_type": "markdown", "id": "8ca1eca2-f78d-48d8-a2d4-da7b789f6dc1", "metadata": {}, "source": [ "### Docstring" ] }, { "cell_type": "code", "execution_count": 39, "id": "768f1668-87e9-403a-8f35-8432c6affe57", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Returns a numpy array that represents a numerical approximation of\n", " the matrix formed by the boundary integral operator K_{s,j}^0 with\n", " Laplace kernel evaluated and tested with real spherical harmonics.\n", " In this routine the quadrature points NEED to be ordered in an array\n", " of two dimensions, given by the function\n", " from_sphere_s_cartesian_to_j_spherical_2d of the module\n", " biosspheres.quadratures.spheres.\n", "\n", " Notes\n", " -----\n", " data_k[p(2p + 1) + q, l(2l + 1) + m] =\n", " ( K_{s,j}^0 Y_{l,m,j} ; Y_{p,q,s} )_{L^2(S_s)}.\n", " Y_{l,m,j} : spherical harmonic degree l, order m, in the coordinate\n", " system j.\n", " S_s : surface of the sphere s.\n", "\n", " The expression K_{s,j}^0 Y_l,m,j can be obtained analytically.\n", " A quadrature scheme is used to compute the other surface integral.\n", " It uses functions from the package pyshtools to compute the\n", " spherical harmonic transforms.\n", "\n", " Parameters\n", " ----------\n", " big_l : int\n", " >= 0, max degree of spherical harmonics used.\n", " r_j : float\n", " > 0, radius of the sphere j.\n", " r_s : float\n", " > 0, radius of the sphere s.\n", " r_coord : np.ndarray\n", " Two dimensional array of floats with the spherical coordinate r\n", " of the quadrature points in the coordinate system s.\n", " Shape equals to (quantity_theta_points, quantity_phi_points).\n", " Comes from the function\n", " from_sphere_s_cartesian_to_j_spherical_2d of the module\n", " biosspheres.quadratures.spheres.\n", " phi_coord : np.ndarray\n", " Two dimensional array of floats with the phi coordinate r of the\n", " quadrature points in the coordinate system s. Shape equals to\n", " (quantity_theta_points, quantity_phi_points).\n", " Comes from the function\n", " from_sphere_s_cartesian_to_j_spherical_2d of the module\n", " biosspheres.quadratures.spheres.\n", " cos_theta_coord : np.ndarray\n", " Two dimensional array of floats with the cosine of the spherical\n", " coordinate theta of the quadrature points in the coordinate\n", " system s. Shape equals to\n", " (quantity_theta_points, quantity_phi_points). Comes from the\n", " function from_sphere_s_cartesian_to_j_spherical_2d of\n", " the module biosspheres.quadratures.spheres.\n", " weights : np.ndarray\n", " of floats. Weights for the integral quadrature in the theta\n", " variable. Comes from the function\n", " gauss_legendre_trapezoidal_shtools_2d\n", " from the module biosspheres.quadratures.spheres.\n", " zeros : np.ndarray\n", " of floats. Zeros of the integral quadrature in the theta\n", " variable. Comes from the function\n", " gauss_legendre_trapezoidal_shtools_2d\n", " from the module biosspheres.quadratures.spheres.\n", " quantity_theta_points : int\n", " how many points for the integral in theta.\n", " Can come from the function\n", " gauss_legendre_trapezoidal_shtools_2d\n", " from the module biosspheres.quadratures.spheres.\n", " quantity_phi_points : int\n", " how many points for the integral in phi.\n", " Can come fron the function\n", " gauss_legendre_trapezoidal_shtools_2d\n", " from the module biosspheres.quadratures.spheres.\n", " pesykus : np.ndarray\n", " dtype int, shape ((big_l+1) * big_l // 2, 2).\n", " Used for the vectorization of some computations.\n", " Comes from the function\n", " biosspheres.miscella.auxindexes.pes_y_kus(big_l)\n", " p2_plus_p_plus_q : np.ndarray\n", " dtype int, length (big_l+1) * big_l // 2.\n", " Used for the vectorization of some computations.\n", " Comes from the function\n", " biosspheres.miscella.auxindexes.pes_y_kus(big_l)\n", " p2_plus_p_minus_q : np.ndarray\n", " dtype int, length (big_l+1) * big_l // 2.\n", " Used for the vectorization of some computations.\n", " Comes from the function\n", " biosspheres.miscella.auxindexes.pes_y_kus(big_l)\n", "\n", " Returns\n", " -------\n", " data_k : numpy array\n", " of floats. Shape ((big_l+1)**2, (big_l+1)**2).\n", " See notes for the indexes ordering.\n", "\n", " See Also\n", " --------\n", " k_0_sj_semi_analytic_v1d\n", " k_0_sj_from_v_0_sj\n", "\n", " \n" ] } ], "source": [ "print(cross.k_0_sj_semi_analytic_v2d.__doc__)" ] }, { "cell_type": "markdown", "id": "99ecfee3-889c-45f0-8e7d-2db861fed7ec", "metadata": {}, "source": [ "### Example" ] }, { "cell_type": "markdown", "id": "77f87573-ae01-476c-b0fb-b3c51d60f8f9", "metadata": {}, "source": [ "Definition of parameters:" ] }, { "cell_type": "markdown", "id": "bb87c965-66bf-42c6-bb83-103f59fd37d5", "metadata": {}, "source": [ "Radii:" ] }, { "cell_type": "code", "execution_count": 40, "id": "50996cf5-a196-43bd-a5e5-1c76688c49ea", "metadata": {}, "outputs": [], "source": [ "radio_1 = 3.\n", "radio_2 = 2." ] }, { "cell_type": "markdown", "id": "79f6e016-9028-4d39-8ca8-a821164e4734", "metadata": {}, "source": [ "Position of the center of the spheres:" ] }, { "cell_type": "code", "execution_count": 41, "id": "afc4b913-f85f-4961-8e2d-d14552be478e", "metadata": {}, "outputs": [], "source": [ "p_1 = np.asarray([2., 3., 4.])\n", "p_2 = -p_1" ] }, { "cell_type": "markdown", "id": "a9970dfe-35f9-41e0-b94f-6278864d2d3d", "metadata": {}, "source": [ "Maximum degree of spherical harmonics used, and parameter for the quadrature rule:" ] }, { "cell_type": "code", "execution_count": 42, "id": "096f88bf-087b-4b6c-8580-b2404f3a12a1", "metadata": {}, "outputs": [], "source": [ "big_l = 3\n", "big_l_c = 25" ] }, { "cell_type": "markdown", "id": "b9390883-1411-4941-9f21-70c5b84afb8c", "metadata": {}, "source": [ "Auxiliary parameters that use the ones previously defined, which are related to the implemented quadrature. This differs from the routines without the `2d` in its name:" ] }, { "cell_type": "code", "execution_count": 43, "id": "1896e7d6-f949-4f32-bd73-1f142913a996", "metadata": {}, "outputs": [], "source": [ "quantity_theta_points, quantity_phi_points, weights, pre_vector_t_2d = \\\n", " quadratures.gauss_legendre_trapezoidal_2d(big_l_c)\n", "r_coord_1tf_2d, phi_coord_1tf_2d, cos_theta_coord_1tf_2d = \\\n", " (quadratures.from_sphere_s_cartesian_to_j_spherical_2d(\n", " radio_2, p_1, p_2, quantity_theta_points, quantity_phi_points,\n", " pre_vector_t_2d))\n", "pesykus, p2_plus_p_plus_q, p2_plus_p_minus_q = auxindexes.pes_y_kus(big_l)" ] }, { "cell_type": "markdown", "id": "19a30ff6-e9b9-4702-8aca-7f58cfcbca4f", "metadata": {}, "source": [ "We obtain the array data_k21:" ] }, { "cell_type": "code", "execution_count": 44, "id": "e486e227-b4b6-4e1d-a5ad-69ba951b5f65", "metadata": {}, "outputs": [], "source": [ "data_k21_2d = cross.k_0_sj_semi_analytic_v2d(\n", " big_l, radio_1, radio_2, r_coord_1tf_2d, phi_coord_1tf_2d,\n", " cos_theta_coord_1tf_2d, weights, pre_vector_t_2d[2, :, 0],\n", " quantity_theta_points, quantity_phi_points, pesykus, p2_plus_p_plus_q,\n", " p2_plus_p_minus_q)" ] }, { "cell_type": "markdown", "id": "8ac390c0-bd19-47f7-b897-3e815cd2c083", "metadata": {}, "source": [ "The result can be compared to the one computed by the previous routine:" ] }, { "cell_type": "code", "execution_count": 45, "id": "16c231ba-1831-447f-bc92-dd5d8b5688c9", "metadata": {}, "outputs": [], "source": [ "final_length, pre_vector_t, transform = quadratures.real_spherical_harmonic_transform_1d(big_l, big_l_c)\n", "r_coord_1tf, phi_coord_1tf, cos_theta_coord_1tf = (\n", " quadratures.\n", " from_sphere_s_cartesian_to_j_spherical_1d(\n", " radio_2, p_1, p_2, final_length, pre_vector_t))\n", "data_k21 = cross.k_0_sj_semi_analytic_v1d(\n", " big_l, radio_1, radio_2, r_coord_1tf, phi_coord_1tf,\n", " cos_theta_coord_1tf, final_length, transform)" ] }, { "cell_type": "code", "execution_count": 46, "id": "665e8845-0e6b-4d81-af9b-ace5bf799ad7", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(dpi=75., layout='constrained')\n", "im = np.abs(data_k21_2d - data_k21)\n", "plt.imshow(im, cmap='RdBu')\n", "plt.colorbar()\n", "plt.title('Absolute error between $K_{2,1}^0$ with 1d and 2d routines')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "02838bb1-5c82-4424-bc3c-482d3490b529", "metadata": {}, "source": [ "## `k_0_sj_from_v_0_sj`" ] }, { "cell_type": "markdown", "id": "d38d2598-cdf4-4dbd-8038-8fec8cd3b4f3", "metadata": {}, "source": [ "This functions uses the relationship between the operators $K^0_{s,j}$ and $V^0_{s,j}$ to compute `data_k` from `data_v`. See docstring for details." ] }, { "cell_type": "markdown", "id": "3c5163ab-471b-409d-ad26-a79320f57e23", "metadata": {}, "source": [ "### Docstring" ] }, { "cell_type": "code", "execution_count": 47, "id": "4aa1810f-4822-4199-a78d-f3b953f273f6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Returns a numpy array that represents a numerical approximation of\n", " the matrix formed by the boundary integral operator K_{s,j}^0 with\n", " Laplace kernel evaluated and tested with real spherical harmonics.\n", " This routine needs the numpy array corresponding to the testing of\n", " V_{s,j}^0.\n", "\n", " Notes\n", " -----\n", " data_k[p*(2p+1) + q, l*(2l+1) + m] =\n", " ( K_{s,j}^0 Y_{l,m,j} ; Y_{p,q,s} )_{L^2(S_s)}.\n", " Y_{l,m,j} : spherical harmonic degree l, order m, in the coordinate\n", " system j.\n", " S_s : surface of the sphere s.\n", "\n", " This computation uses the following result for this specific case:\n", " K_{s,j}^0 Y_{l,m} = - l / r_j V_{s,j}^0 Y_{l,m}.\n", "\n", " Parameters\n", " ----------\n", " data_v : np.ndarray\n", " that represents a numerical approximation of the matrix formed\n", " by the boundary integral operator V_{s,j}^0 with Laplace kernel\n", " evaluated and tested with spherical harmonics.\n", " r_j : float\n", " > 0, radius of the sphere j.\n", " el_diagonal : scipy.sparse.dia_array\n", " comes from biosspheres.miscella.auxindexes.diagonal_l_sparse\n", "\n", " Returns\n", " -------\n", " data_k : np.ndarray\n", " Same shape than data_v. See notes for the indexes ordering.\n", "\n", " See Also\n", " --------\n", " k_0_sj_semi_analytic_v1d\n", " k_0_sj_semi_analytic_v2d\n", "\n", " \n" ] } ], "source": [ "print(cross.k_0_sj_from_v_0_sj.__doc__)" ] }, { "cell_type": "markdown", "id": "bf3ac077-87d6-4ac2-a957-cf1bae822c52", "metadata": {}, "source": [ "### Example" ] }, { "cell_type": "markdown", "id": "55d90ad7-7040-4944-bbd5-c733c73560e1", "metadata": {}, "source": [ "Definition of the parameters:" ] }, { "cell_type": "markdown", "id": "7e05fff4-8ca9-459e-a494-c9c65b2867cd", "metadata": {}, "source": [ "Radii:" ] }, { "cell_type": "code", "execution_count": 48, "id": "4f13177e-c8ce-4ea7-b6ac-cdace6a8342e", "metadata": {}, "outputs": [], "source": [ "radio_1 = 1.3\n", "radio_2 = 1.7" ] }, { "cell_type": "markdown", "id": "21286314-074b-4890-b6db-8741a41ac5f8", "metadata": {}, "source": [ "Positions of the center of the spheres:" ] }, { "cell_type": "code", "execution_count": 49, "id": "f3d436df-33b2-4351-b177-654bf13d70b8", "metadata": {}, "outputs": [], "source": [ "p_1 = np.asarray([2., 3., 4.])\n", "p_2 = -p_1" ] }, { "cell_type": "markdown", "id": "c4b9955a-a384-4a8a-b060-4447dd7461d6", "metadata": {}, "source": [ "Maximum degree of spherical harmonics used, and parameter for the quadrature rules:" ] }, { "cell_type": "code", "execution_count": 50, "id": "63fd4166-1835-4b90-b81c-a0190b774fe2", "metadata": {}, "outputs": [], "source": [ "big_l = 3\n", "big_l_c = 25" ] }, { "cell_type": "markdown", "id": "b07bc021-d663-41f7-90dc-2c17d2afdf69", "metadata": {}, "source": [ "We use one of the previous routine to calculate `data_21_2d`, which will be the input for computing `data_k21`" ] }, { "cell_type": "code", "execution_count": 51, "id": "a390eb64-efb0-43fc-9b48-8b9412e196d7", "metadata": {}, "outputs": [], "source": [ "quantity_theta_points, quantity_phi_points, weights, pre_vector_t_2d = \\\n", " quadratures.gauss_legendre_trapezoidal_2d(big_l_c)\n", "r_coord_1tf_2d, phi_coord_1tf_2d, cos_theta_coord_1tf_2d = (\n", " quadratures.from_sphere_s_cartesian_to_j_spherical_2d(\n", " radio_2, p_1, p_2, quantity_theta_points, quantity_phi_points,\n", " pre_vector_t_2d))\n", "pesykus, p2_plus_p_plus_q, p2_plus_p_minus_q = auxindexes.pes_y_kus(big_l)\n", "data_v21_2d = cross.v_0_sj_semi_analytic_v2d(\n", " big_l, radio_1, radio_2, r_coord_1tf_2d, phi_coord_1tf_2d,\n", " cos_theta_coord_1tf_2d, weights, pre_vector_t_2d[2, :, 0],\n", " quantity_theta_points, quantity_phi_points, pesykus, p2_plus_p_plus_q,\n", " p2_plus_p_minus_q)" ] }, { "cell_type": "code", "execution_count": 52, "id": "1729c1de-dd33-4570-8197-b85f4c1731ed", "metadata": {}, "outputs": [], "source": [ "el_diagonal = auxindexes.diagonal_l_sparse(big_l)\n", "data_k21 = cross.k_0_sj_from_v_0_sj(\n", " data_v21_2d, radio_1, el_diagonal)" ] }, { "cell_type": "markdown", "id": "4a513c07-d5e8-4f4d-9500-084b2c30c88f", "metadata": {}, "source": [ "To compare" ] }, { "cell_type": "code", "execution_count": 53, "id": "c085c3cc-f14e-49b4-8af2-17b5244cd4b0", "metadata": {}, "outputs": [], "source": [ "data_k21_2d = cross.k_0_sj_semi_analytic_v2d(\n", " big_l, radio_1, radio_2, r_coord_1tf_2d, phi_coord_1tf_2d,\n", " cos_theta_coord_1tf_2d, weights, pre_vector_t_2d[2, :, 0],\n", " quantity_theta_points, quantity_phi_points, pesykus, p2_plus_p_plus_q,\n", " p2_plus_p_minus_q)" ] }, { "cell_type": "code", "execution_count": 54, "id": "ef938b32-0d8d-41f2-a555-1d60645e4acc", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(dpi=75., layout='constrained')\n", "im = np.abs(data_k21_2d - data_k21)\n", "plt.imshow(im, cmap='RdBu')\n", "plt.colorbar(shrink=0.9)\n", "plt.title('Absolute error between $K_{2,1}^0$ with direct and indirect '\n", " 'routines')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "224719ec-11d0-4725-b929-732bef3582e4", "metadata": {}, "source": [ "## `ka_0_sj_semi_analytic_recurrence_v1d`" ] }, { "cell_type": "markdown", "id": "b0c3c55c-b70a-432f-9548-490708c5e418", "metadata": {}, "source": [ "The `1d` on the name of the routine references the type of input it needs. See the following sections for details." ] }, { "cell_type": "markdown", "id": "697eb01a-f0b9-41af-a511-d9d1d08eab6d", "metadata": {}, "source": [ "### Docstring" ] }, { "cell_type": "code", "execution_count": 55, "id": "a19b43cf-0e83-4c83-90b0-492dec6a8f78", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Returns a numpy array that represents a numerical approximation of\n", " the matrix formed by the boundary integral operator K_{s,j}^{*0}\n", " with Laplace kernel evaluated and tested with real spherical\n", " harmonics.\n", " In this routine the quadrature points NEED to be ordered in an array\n", " of one dimension.\n", " It is a SLOW routine, because it does not use any symmetry or\n", " properties of the spherical harmonics.\n", "\n", " Notes\n", " -----\n", " data_ka[p*(2p+1) + q, l*(2l+1) + m] =\n", " ( K_{s,j}^{*0} Y_{l,m,j} ; Y_{p,q,s} )_{L^2(S_s)}.\n", " Y_{l,m,j} : spherical harmonic degree l, order m, in the coordinate\n", " system j.\n", " S_s : surface of the sphere s.\n", "\n", " The expression K_{s,j}^{*0} Y_l,m,j can be obtained analytically.\n", " A quadrature scheme is used to compute the other surface integral\n", " corresponding to the inner product.\n", " For computing the derivative in theta a recurrence formula for\n", " Legendre Functions is used.\n", "\n", " In this routine the quadrature points NEED to be ordered in an array\n", " of one dimension.\n", "\n", " Parameters\n", " ----------\n", " big_l : int\n", " >= 0, max degree.\n", " r_j : float\n", " > 0, radius of the sphere j.\n", " r_s : float\n", " > 0, radius of the sphere s.\n", " r_coord : np.ndarray\n", " One dimensional array of floats with the spherical coordinate r\n", " of the quadrature points in the coordinate system s. Length\n", " equals to final_length. Can come from\n", " biosspheres.quadratures.spheres.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_1d\n", " phi_coord : np.ndarray\n", " One dimensional array of floats with the phi coordinate r of the\n", " quadrature points in the coordinate system s. Length equals to\n", " final_length. Can come from biosspheres.quadratures.spheres.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_1d\n", " cos_theta_coord : np.ndarray\n", " One dimensional array of floats with the cosine of the spherical\n", " coordinate theta of the quadrature points in the coordinate\n", " system s. Lenght equals to final_length.\n", " Can come from biosspheres.quadratures.spheres.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_1d\n", " er_times_n : np.ndarray\n", " One dimensional array of floats with the dot product of the\n", " canonical vector of the spherical coordinate r in the points\n", " in the coordinate system s and the normal of a sphere.\n", " Length final_length. Can come from\n", " biosspheres.quadratures.spheres.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_1d\n", " etheta_times_n : np.ndarray\n", " One dimensional array of floats with the dot product of the\n", " canonical vector of the spherical coordinate theta in the points\n", " in the coordinate system s and the normal of a sphere.\n", " Length final_length. Can come from\n", " biosspheres.quadratures.spheres.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_1d\n", " ephi_times_n : np.ndarray\n", " One dimensional array of floats with the dot product of the\n", " canonical vector of the spherical coordinate phi in the points\n", " in the coordinate system s and the normal of a sphere.\n", " Length final_length. Can come from\n", " biosspheres.quadratures.spheres.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_1d\n", " final_length : int\n", " how many points for the surface integral,\n", " (big_l_c + 1) * (2 * big_l_c + 1).\n", " transform : np.ndarray\n", " of floats, for doing the real spherical harmonic\n", " transform. Shape ((big_l+1)**2, final_length)\n", "\n", " Returns\n", " -------\n", " data_ka : numpy array\n", " Shape ((big_l+1)**2, (big_l+1)**2). See notes for the indexes\n", " ordering.\n", "\n", " See Also\n", " --------\n", " ka_0_sj_semi_analytic_recurrence_v2d\n", " ka_0_sj_from_v_sj\n", " ka_0_sj_from_k_js\n", "\n", " \n" ] } ], "source": [ "print(cross.ka_0_sj_semi_analytic_recurrence_v1d.__doc__)" ] }, { "cell_type": "markdown", "id": "b8ddb4b2-0b9c-40e5-ba36-84f8d5dfeded", "metadata": {}, "source": [ "### Example" ] }, { "cell_type": "markdown", "id": "e41f4a83", "metadata": {}, "source": [ "Definition of the parameters:" ] }, { "cell_type": "markdown", "id": "b33081a1", "metadata": {}, "source": [ "Radii:" ] }, { "cell_type": "code", "execution_count": 56, "id": "d34a7542-72f9-44ac-b445-c6407cb4264c", "metadata": {}, "outputs": [], "source": [ "radio_1 = 3.\n", "radio_2 = 2." ] }, { "cell_type": "markdown", "id": "a03b2a0f", "metadata": {}, "source": [ "Positions of the center of the spheres:" ] }, { "cell_type": "code", "execution_count": 57, "id": "309f6eb6", "metadata": {}, "outputs": [], "source": [ "p_1 = np.asarray([2., 3., 4.])\n", "p_2 = -p_1" ] }, { "cell_type": "markdown", "id": "20672ea3", "metadata": {}, "source": [ "Maximum degree of spherical harmonics used, and parameter for the quadrature rule:" ] }, { "cell_type": "code", "execution_count": 58, "id": "ca0fab39", "metadata": {}, "outputs": [], "source": [ "big_l = 5\n", "big_l_c = 25" ] }, { "cell_type": "markdown", "id": "59c5207d", "metadata": {}, "source": [ "Auxiliary parameters that use the ones previously defined, which are related to the implemented quadrature, this differs from the routines without the `1d` in its name:" ] }, { "cell_type": "code", "execution_count": 59, "id": "ceebd7ac-37e6-4ac6-a5cf-49f04fbecd46", "metadata": {}, "outputs": [], "source": [ "final_length, pre_vector_t, transform = \\\n", " quadratures.real_spherical_harmonic_transform_1d(big_l, big_l_c)\n", "(r_coord_1tf, phi_coord_1tf, cos_theta_coord_1tf,\n", " er_1tf, eth_1tf, ephi_1tf) = (\n", " quadratures.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_1d(\n", " radio_2, p_1, p_2, final_length, pre_vector_t))" ] }, { "cell_type": "markdown", "id": "a4687fc3", "metadata": {}, "source": [ "Calling of the function:" ] }, { "cell_type": "code", "execution_count": 60, "id": "fb03bb38-8205-4208-a373-7580d069eaef", "metadata": {}, "outputs": [], "source": [ "data_ka21 = cross.ka_0_sj_semi_analytic_recurrence_v1d(\n", " big_l, radio_1, radio_2, r_coord_1tf, phi_coord_1tf,\n", " cos_theta_coord_1tf, er_1tf, eth_1tf, ephi_1tf, final_length,\n", " transform)" ] }, { "cell_type": "markdown", "id": "a7a37b9c-70e8-45f8-80c4-b4f67dcafa37", "metadata": {}, "source": [ "## `ka_0_sj_semi_analytic_recurrence_v2d`" ] }, { "cell_type": "markdown", "id": "bd1bfd9b-1a23-48bb-ac1b-2c9a81ecb494", "metadata": {}, "source": [ "### Docstring" ] }, { "cell_type": "code", "execution_count": 61, "id": "0de4bca2-028d-4344-b53f-adf899599874", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Returns a numpy array that represents a numerical approximation of\n", " the matrix formed by the boundary integral operator K_{s,j}^{*0}\n", " with Laplace kernel evaluated and tested with real spherical\n", " harmonics.\n", " In this routine the quadrature points NEED to be ordered in an array\n", " of two dimensions, given by the function\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_2d of\n", " the module biosspheres.quadratures.spheres.\n", "\n", " Notes\n", " -----\n", " data_ka[p*(2p+1) + q, l*(2l+1) + m] =\n", " ( K_{s,j}^{*0} Y_{l,m,j} ; Y_{p,q,s} )_{L^2(S_s)}.\n", " Y_{l,m,j} : spherical harmonic degree l, order m, in the coordinate\n", " system j.\n", " S_s : surface of the sphere s.\n", "\n", " The expression K_{s,j}^{*0} Y_l,m,j can be obtained analytically.\n", " A quadrature scheme is used to compute the other surface integral\n", " corresponding to the inner product.\n", " For computing the derivative in theta a recurrence formula for\n", " Legendre Functions is used.\n", "\n", " In this routine the quadrature points NEED to be ordered in an array\n", " of two dimensions, given by the function\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_2d of\n", " the module biosspheres.quadratures.spheres.\n", " It uses functions from the package pyshtools to compute the\n", " spherical harmonic transforms.\n", "\n", " Parameters\n", " ----------\n", " big_l : int\n", " >= 0, max degree.\n", " r_j : float\n", " > 0, radius of the sphere j.\n", " r_s : float\n", " > 0, radius of the sphere s.\n", " r_coord : np.ndarray\n", " Two dimensional array of floats with the spherical coordinate r\n", " of the quadrature points in the coordinate system s. Shape\n", " equals to (quantity_theta_points, quantity_phi_points).\n", " Comes from biosspheres.quadratures.spheres.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_2d\n", " phi_coord : np.ndarray\n", " Two dimensional array of floats with the phi coordinate r of the\n", " quadrature points in the coordinate system s. Shape equals to\n", " (quantity_theta_points, quantity_phi_points).\n", " Comes from biosspheres.quadratures.spheres.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_2d\n", " cos_theta_coord : np.ndarray\n", " Two dimensional array of floats with the cosine of the spherical\n", " coordinate theta of the quadrature points in the coordinate\n", " system s. Shape equals to\n", " (quantity_theta_points, quantity_phi_points).\n", " Comes from biosspheres.quadratures.spheres.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_2d\n", " er_times_n : np.ndarray\n", " Two dimensional array of floats with the dot product of the\n", " canonical vector of the spherical coordinate r in the points\n", " in the coordinate system s and the normal of a sphere. Shape\n", " equals to (quantity_theta_points, quantity_phi_points). Comes\n", " from biosspheres.quadratures.spheres.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_2d\n", " etheta_times_n : np.ndarray\n", " Two dimensional array of floats with the dot product of the\n", " canonical vector of the spherical coordinate theta in the points\n", " in the coordinate system s and the normal of a sphere. Shape\n", " equals to (quantity_theta_points, quantity_phi_points). Comes\n", " from biosspheres.quadratures.spheres.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_2d\n", " ephi_times_n : np.ndarray\n", " Two dimensional array of floats with the dot product of the\n", " canonical vector of the spherical coordinate phi in the points\n", " in the coordinate system s and the normal of a sphere. Shape\n", " equals to (quantity_theta_points, quantity_phi_points). Comes\n", " from biosspheres.quadratures.spheres.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_2d\n", " weights : np.ndarray\n", " of floats. Weights for the integral quadrature in the theta\n", " variable. Comes from the function\n", " gauss_legendre_trapezoidal_shtools_2d\n", " from the module biosspheres.quadratures.spheres.\n", " zeros : np.ndarray\n", " of floats. Zeros of the integral quadrature in the theta\n", " variable. Comes from the function\n", " gauss_legendre_trapezoidal_shtools_2d\n", " from the module biosspheres.quadratures.spheres.\n", " quantity_theta_points : int\n", " how many points for the integral in theta.\n", " Can come from the function\n", " gauss_legendre_trapezoidal_shtools_2d\n", " from the module biosspheres.quadratures.spheres.\n", " quantity_phi_points : int\n", " how many points for the integral in phi.\n", " Comes from the function\n", " gauss_legendre_trapezoidal_shtools_2d\n", " from the module biosspheres.quadratures.spheres.\n", " pesykus : np.ndarray\n", " dtype int, shape ((big_l+1) * big_l // 2, 2).\n", " Used for the vectorization of some computations.\n", " Comes from the function\n", " biosspheres.miscella.auxindexes.pes_y_kus(big_l)\n", " p2_plus_p_plus_q : np.ndarray\n", " dtype int, length (big_l+1) * big_l // 2.\n", " Used for the vectorization of some computations.\n", " Comes from the function\n", " biosspheres.miscella.auxindexes.pes_y_kus(big_l)\n", " p2_plus_p_minus_q : np.ndarray\n", " dtype int, length (big_l+1) * big_l // 2.\n", " Used for the vectorization of some computations.\n", " Comes from the function\n", " biosspheres.miscella.auxindexes.pes_y_kus(big_l)\n", "\n", " Returns\n", " -------\n", " data_ka : numpy array\n", " Shape ((big_l+1)**2, (big_l+1)**2). See notes for the indexes\n", " ordering.\n", "\n", " See Also\n", " --------\n", " ka_0_sj_semi_analytic_recurrence_v1d\n", " ka_0_sj_from_v_sj\n", " ka_0_sj_from_k_js\n", "\n", " \n" ] } ], "source": [ "print(cross.ka_0_sj_semi_analytic_recurrence_v2d.__doc__)" ] }, { "cell_type": "markdown", "id": "936a3f95-fffa-46f3-bef8-455d97507e56", "metadata": {}, "source": [ "### Example" ] }, { "cell_type": "markdown", "id": "d1dcd835", "metadata": {}, "source": [ "Definition of the parameters:" ] }, { "cell_type": "markdown", "id": "cef1e9a4", "metadata": {}, "source": [ "Radii:" ] }, { "cell_type": "code", "execution_count": 62, "id": "c041f142-846b-4d05-b288-a3cbeaebd8de", "metadata": {}, "outputs": [], "source": [ "radio_1 = 3.\n", "radio_2 = 2." ] }, { "cell_type": "markdown", "id": "cae4dd63", "metadata": {}, "source": [ "Positions of the center of the spheres:" ] }, { "cell_type": "code", "execution_count": 63, "id": "27b13673", "metadata": {}, "outputs": [], "source": [ "p_1 = np.asarray([2., 3., 4.])\n", "p_2 = -p_1" ] }, { "cell_type": "markdown", "id": "73aa4a4a", "metadata": {}, "source": [ "Maximum degree of spherical harmonics used, and parameter for the quadrature rule:" ] }, { "cell_type": "code", "execution_count": 64, "id": "e0e6f7a6", "metadata": {}, "outputs": [], "source": [ "big_l = 5\n", "big_l_c = 25" ] }, { "cell_type": "markdown", "id": "879541c3", "metadata": {}, "source": [ "Auxiliary parameters that use the ones previously defined, which are related to the implemented quadrature. This differs from the routines without the `2d` in its name:" ] }, { "cell_type": "code", "execution_count": 65, "id": "e5f3ed88-edb2-47ac-aff3-a8082120d83b", "metadata": {}, "outputs": [], "source": [ "quantity_theta_points, quantity_phi_points, weights, pre_vector_t_2d = \\\n", " quadratures.gauss_legendre_trapezoidal_2d(big_l_c)\n", "(r_coord_1tf_2d, phi_coord_1tf_2d, cos_theta_coord_1tf_2d,\n", " er_1tf_2d, eth_1tf_2d, ephi_1tf_2d) = (\n", " quadratures.from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_2d(\n", " radio_2, p_1, p_2, quantity_theta_points, quantity_phi_points,\n", " pre_vector_t_2d))\n", "pesykus, p2_plus_p_plus_q, p2_plus_p_minus_q = auxindexes.pes_y_kus(big_l)" ] }, { "cell_type": "markdown", "id": "0464bc52", "metadata": {}, "source": [ "Calling of the function:" ] }, { "cell_type": "code", "execution_count": 66, "id": "bcd38b26-55f9-49cb-a684-d64393b54b8c", "metadata": {}, "outputs": [], "source": [ "data_ka21_2d = cross.ka_0_sj_semi_analytic_recurrence_v2d(\n", " big_l, radio_1, radio_2, r_coord_1tf_2d, phi_coord_1tf_2d,\n", " cos_theta_coord_1tf_2d, er_1tf_2d, eth_1tf_2d, ephi_1tf_2d, weights,\n", " pre_vector_t_2d[2, :, 0], quantity_theta_points, quantity_phi_points,\n", " pesykus, p2_plus_p_plus_q, p2_plus_p_minus_q)" ] }, { "cell_type": "markdown", "id": "c40e5f3a-a22e-456b-b548-f60a38b61f07", "metadata": {}, "source": [ "If we compare with the previous routine:" ] }, { "cell_type": "code", "execution_count": 67, "id": "c5f41714-bada-4218-8df7-b77ea9c19e26", "metadata": {}, "outputs": [], "source": [ "final_length, pre_vector_t, transform = \\\n", " quadratures.real_spherical_harmonic_transform_1d(big_l, big_l_c)\n", "(r_coord_1tf, phi_coord_1tf, cos_theta_coord_1tf,\n", " er_1tf, eth_1tf, ephi_1tf) = (\n", " quadratures.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_1d(\n", " radio_2, p_1, p_2, final_length, pre_vector_t))\n", "data_ka21 = cross.ka_0_sj_semi_analytic_recurrence_v1d(\n", " big_l, radio_1, radio_2, r_coord_1tf, phi_coord_1tf,\n", " cos_theta_coord_1tf, er_1tf, eth_1tf, ephi_1tf, final_length,\n", " transform)" ] }, { "cell_type": "code", "execution_count": 68, "id": "e4f66594-be6d-49af-b57c-05f0e5dfec49", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(dpi=75., layout='constrained')\n", "im = np.abs(data_ka21_2d - data_ka21)\n", "plt.imshow(im, cmap='RdBu')\n", "plt.colorbar()\n", "plt.title('Absolute error between $K_{2,1}^{*0}$ with 1d and 2d routines')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "2dad2e48-8b59-4c53-a08f-3d5ebee467e9", "metadata": {}, "source": [ "## `ka_0_sj_from_k_js`" ] }, { "cell_type": "markdown", "id": "eba65e1d-2dcd-40d1-a85e-de185adc3cf6", "metadata": {}, "source": [ "### Docstring" ] }, { "cell_type": "code", "execution_count": 69, "id": "6d1937e5-e3d7-4a5f-a4ab-86c705b9b7f1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Returns a numpy array that represents a numerical approximation of\n", " the matrix formed by the boundary integral operator K_{s,j}^{*0}\n", " with Laplace kernel evaluated and tested with real spherical\n", " harmonics.\n", " This routine needs the numpy array corresponding to K_{j,s}^0\n", " (notice the change of the order of the indexes indicating the\n", " spheres).\n", "\n", " Notes\n", " -----\n", " data_ka_sj[p*(2p+1) + q, l*(2l+1) + m] =\n", " ( K_{s,j}^{*0} Y_{l,m,j} ; Y_{p,q,s} )_{L^2(S_s)}.\n", " Y_{l,m,j} : spherical harmonic degree l, order m, in the coordinate\n", " system j.\n", " S_s : surface of the sphere s.\n", "\n", " This computation uses the following result for this specific case:\n", " ( K_{s,j}^{*0} Y_{l,m,j} ; Y_{p,q,s} )_{L^2(S_s)}\n", " = ( K_{j,s}^0 Y_p,q,s ; Y_l,m,j )_{L^2(S_j)}.\n", "\n", " Parameters\n", " ----------\n", " data_kjs : numpy array.\n", " represents a numerical approximation of the matrix formed by the\n", " boundary integral operator V_{s,j}^0 with Laplace kernel\n", " evaluated and tested with spherical harmonics.\n", "\n", " Returns\n", " -------\n", " data_ka_sj : numpy array.\n", " Same shape than data_kjs. See notes for the indexes ordering.\n", "\n", " See Also\n", " --------\n", " ka_0_sj_semi_analytic_recurrence_v1d\n", " ka_0_sj_semi_analytic_recurrence_v2d\n", " ka_0_sj_from_v_sj\n", "\n", " \n" ] } ], "source": [ "print(cross.ka_0_sj_from_k_js.__doc__)" ] }, { "cell_type": "markdown", "id": "1cdd2b33-fde9-444f-b353-3dcaa184ec9c", "metadata": {}, "source": [ "### Example" ] }, { "cell_type": "markdown", "id": "1a03004f", "metadata": {}, "source": [ "Definition of parameters:" ] }, { "cell_type": "markdown", "id": "f103fdb5", "metadata": {}, "source": [ "Radii:" ] }, { "cell_type": "code", "execution_count": 70, "id": "df1f31c7-464b-4489-8197-1219fbf33b78", "metadata": {}, "outputs": [], "source": [ "radio_1 = 3.\n", "radio_2 = 2." ] }, { "cell_type": "markdown", "id": "dac5b1e0", "metadata": {}, "source": [ "Position of the center of the spheres:" ] }, { "cell_type": "code", "execution_count": 71, "id": "c0440afb", "metadata": {}, "outputs": [], "source": [ "p_1 = np.asarray([2., 3., 4.])\n", "p_2 = -p_1" ] }, { "cell_type": "markdown", "id": "0f3a5e94", "metadata": {}, "source": [ "Maximum degree of spherical harmonics used, and parameter for the quadrature rule:" ] }, { "cell_type": "code", "execution_count": 72, "id": "cf2e9aad", "metadata": {}, "outputs": [], "source": [ "big_l = 3\n", "big_l_c = 25" ] }, { "cell_type": "markdown", "id": "34f9d96f", "metadata": {}, "source": [ "Auxiliary parameters that use the ones previously defined, which are related to the implemented quadrature. This differs from the routines without the `2d` in its name:" ] }, { "cell_type": "code", "execution_count": 73, "id": "31e62556-a2fa-4b4b-b744-9b54ee987b44", "metadata": {}, "outputs": [], "source": [ "quantity_theta_points, quantity_phi_points, weights, pre_vector_t_2d = \\\n", " quadratures.gauss_legendre_trapezoidal_2d(big_l_c)\n", "r_coord_2tf_2d, phi_coord_2tf_2d, cos_theta_coord_2tf_2d = \\\n", " (quadratures.from_sphere_s_cartesian_to_j_spherical_2d(\n", " radio_1, p_2, p_1, quantity_theta_points, quantity_phi_points,\n", " pre_vector_t_2d))\n", "pesykus, p2_plus_p_plus_q, p2_plus_p_minus_q = auxindexes.pes_y_kus(big_l)" ] }, { "cell_type": "code", "execution_count": 74, "id": "3f33f4ff-dff1-4a67-9718-0c3fc5940d03", "metadata": {}, "outputs": [], "source": [ "data_k12_2d = cross.k_0_sj_semi_analytic_v2d(\n", " big_l, radio_2, radio_1, r_coord_2tf_2d, phi_coord_2tf_2d,\n", " cos_theta_coord_2tf_2d, weights, pre_vector_t_2d[2, :, 0],\n", " quantity_theta_points, quantity_phi_points, pesykus, p2_plus_p_plus_q,\n", " p2_plus_p_minus_q)" ] }, { "cell_type": "markdown", "id": "f7765eb9", "metadata": {}, "source": [ "Calling of the function:" ] }, { "cell_type": "code", "execution_count": 75, "id": "c168697d-303e-4035-92da-028c5353a8be", "metadata": {}, "outputs": [], "source": [ "data_ka21 = cross.ka_0_sj_from_k_js(data_k12_2d)" ] }, { "cell_type": "markdown", "id": "0cb534b0-ae40-4e84-af13-0eec3a2988fc", "metadata": {}, "source": [ "To compare" ] }, { "cell_type": "code", "execution_count": 76, "id": "f60dfea8-eb60-46e8-9011-8a383a791a1c", "metadata": {}, "outputs": [], "source": [ "(r_coord_1tf_2d, phi_coord_1tf_2d, cos_theta_coord_1tf_2d,\n", " er_1tf_2d, eth_1tf_2d, ephi_1tf_2d) = (\n", " quadratures.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_2d(\n", " radio_2, p_1, p_2, quantity_theta_points, quantity_phi_points,\n", " pre_vector_t_2d))\n", "data_ka21_2d = cross.ka_0_sj_semi_analytic_recurrence_v2d(\n", " big_l, radio_1, radio_2, r_coord_1tf_2d, phi_coord_1tf_2d,\n", " cos_theta_coord_1tf_2d, er_1tf_2d, eth_1tf_2d, ephi_1tf_2d, weights,\n", " pre_vector_t_2d[2, :, 0], quantity_theta_points, quantity_phi_points,\n", " pesykus, p2_plus_p_plus_q, p2_plus_p_minus_q)" ] }, { "cell_type": "code", "execution_count": 77, "id": "4a512c7f-c467-4069-9e57-fa2aeb693d26", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Absolute error between $K_{2,1}^{*0}$ from $K_{2,1}^{0}$')" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(dpi=75., layout='constrained')\n", "im = np.abs(data_ka21_2d - data_ka21)\n", "plt.imshow(im, cmap='RdBu')\n", "plt.colorbar()\n", "plt.title('Absolute error between $K_{2,1}^{*0}$ from $K_{2,1}^{0}$')" ] }, { "cell_type": "markdown", "id": "57a5ca83-d1c1-4d28-8e8c-5fb6cf0d7849", "metadata": {}, "source": [ "## `ka_0_sj_from_v_sj`" ] }, { "cell_type": "markdown", "id": "4aacff88-3c32-49ca-bcdf-b5e6a3de7960", "metadata": {}, "source": [ "### Docstring" ] }, { "cell_type": "code", "execution_count": 78, "id": "a35d5138-e52e-4cd4-bd2a-8a9d0dcfdf09", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Returns a numpy array that represents a numerical approximation of\n", " the matrix formed by the boundary integral operator K_{s,j}^{*0} with\n", " Laplace kernel evaluated and tested with real spherical harmonics.\n", " This routine needs the numpy array corresponding to V_{s,j}^0.\n", "\n", " Notes\n", " -----\n", " data_ka[p*(2p+1) + q, l*(2l+1) + m] =\n", " ( K_{s,j}^{*0} Y_{l,m,j} ; Y_{p,q,s} )_{L^2(S_s)}.\n", " Y_{l,m,j} : spherical harmonic degree l, order m, in the coordinate\n", " system j.\n", " S_s : surface of the sphere s.\n", "\n", " This computation uses the following result for this specific case:\n", " ( K_{s,j}^{*0} Y_{l,m,j} ; Y_{p,q,s} )_{L^2(S_s)}\n", " = -\frac{p}{r_j} ( V_{s,j}^0 Y_{l,m,j} ; Y_{p,q,s} )_{L^2(S_s)}\n", "\n", " Parameters\n", " ----------\n", " data_v_sj : np.ndarray\n", " represents a numerical approximation of the matrix formed by the\n", " boundary integral operator V_{s,j}^0 with Laplace kernel evaluated and\n", " tested with spherical harmonics.\n", " r_s : float\n", " > 0, radius of the sphere s.\n", " el_diagonal : scipy.sparse.dia_array\n", " that comes from biosspheres.miscella.auxindexes.diagonal_l_sparse\n", "\n", " Returns\n", " -------\n", " data_ka : numpy array.\n", " Same shape than data_v_sj. See notes for the indexes ordering.\n", "\n", " See Also\n", " --------\n", " ka_0_sj_semi_analytic_recurrence_v1d\n", " ka_0_sj_semi_analytic_recurrence_v2d\n", " ka_0_sj_from_k_js\n", "\n", " \n" ] } ], "source": [ "print(cross.ka_0_sj_from_v_sj.__doc__)" ] }, { "cell_type": "markdown", "id": "5402bf9d-c23a-4e15-9d33-8c7222657cf0", "metadata": {}, "source": [ "### Example" ] }, { "cell_type": "markdown", "id": "3aa8de73", "metadata": {}, "source": [ "Definition of parameters:" ] }, { "cell_type": "markdown", "id": "fa6526f7", "metadata": {}, "source": [ "Radii:" ] }, { "cell_type": "code", "execution_count": 79, "id": "74cdf9fa-5378-4972-bdd3-92536fbecf91", "metadata": {}, "outputs": [], "source": [ "radio_1 = 3.\n", "radio_2 = 2." ] }, { "cell_type": "markdown", "id": "991fec5e", "metadata": {}, "source": [ "Position of the center of the spheres:" ] }, { "cell_type": "code", "execution_count": 80, "id": "8b3f0311", "metadata": {}, "outputs": [], "source": [ "p_1 = np.asarray([2., 3., 4.])\n", "p_2 = -p_1" ] }, { "cell_type": "markdown", "id": "f5e3a9d0", "metadata": {}, "source": [ "Maximum degree of spherical harmonics used, and parameter for the quadrature rule:" ] }, { "cell_type": "code", "execution_count": 81, "id": "ea221fcd", "metadata": {}, "outputs": [], "source": [ "big_l = 3\n", "big_l_c = 25" ] }, { "cell_type": "markdown", "id": "edebb58b", "metadata": {}, "source": [ "Auxiliary parameters that use the ones previously defined, which are related to the implemented quadrature. This differs from the routines without the `2d` in its name:" ] }, { "cell_type": "code", "execution_count": 82, "id": "e2935138-2a70-4d16-8000-2f3a6ed7e55c", "metadata": {}, "outputs": [], "source": [ "quantity_theta_points, quantity_phi_points, weights, pre_vector_t_2d = \\\n", " quadratures.gauss_legendre_trapezoidal_2d(big_l_c)\n", "r_coord_1tf_2d, phi_coord_1tf_2d, cos_theta_coord_1tf_2d = \\\n", " (quadratures.from_sphere_s_cartesian_to_j_spherical_2d(\n", " radio_2, p_1, p_2, quantity_theta_points, quantity_phi_points,\n", " pre_vector_t_2d))\n", "pesykus, p2_plus_p_plus_q, p2_plus_p_minus_q = auxindexes.pes_y_kus(big_l)\n", "data_v21_2d = cross.v_0_sj_semi_analytic_v2d(\n", " big_l, radio_1, radio_2, r_coord_1tf_2d, phi_coord_1tf_2d,\n", " cos_theta_coord_1tf_2d, weights, pre_vector_t_2d[2, :, 0],\n", " quantity_theta_points, quantity_phi_points, pesykus, p2_plus_p_plus_q,\n", " p2_plus_p_minus_q)" ] }, { "cell_type": "code", "execution_count": 83, "id": "eaefeedf-975d-4c7e-a83d-9c76b3b83150", "metadata": {}, "outputs": [], "source": [ "el_diagonal = auxindexes.diagonal_l_sparse(big_l)" ] }, { "cell_type": "markdown", "id": "5c9c285e", "metadata": {}, "source": [ "Calling of the function:" ] }, { "cell_type": "code", "execution_count": 84, "id": "54bfeeec-dcac-498c-a57f-3f31ae7fca15", "metadata": {}, "outputs": [], "source": [ "data_ka21 = cross.ka_0_sj_from_v_sj(data_v21_2d, radio_2, el_diagonal)" ] }, { "cell_type": "markdown", "id": "2c4300ee-6692-4df7-b842-23d00c86910e", "metadata": {}, "source": [ "To compare" ] }, { "cell_type": "code", "execution_count": 85, "id": "ecac3f70-4c88-427a-b0bd-47369024f31b", "metadata": {}, "outputs": [], "source": [ "(r_coord_1tf_2d, phi_coord_1tf_2d, cos_theta_coord_1tf_2d,\n", " er_1tf_2d, eth_1tf_2d, ephi_1tf_2d) = (\n", " quadratures.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_2d(\n", " radio_2, p_1, p_2, quantity_theta_points, quantity_phi_points,\n", " pre_vector_t_2d))\n", "data_ka21_2d = cross.ka_0_sj_semi_analytic_recurrence_v2d(\n", " big_l, radio_1, radio_2, r_coord_1tf_2d, phi_coord_1tf_2d,\n", " cos_theta_coord_1tf_2d, er_1tf_2d, eth_1tf_2d, ephi_1tf_2d, weights,\n", " pre_vector_t_2d[2, :, 0], quantity_theta_points, quantity_phi_points,\n", " pesykus, p2_plus_p_plus_q, p2_plus_p_minus_q)" ] }, { "cell_type": "code", "execution_count": 86, "id": "85c436ae-793c-43c6-b8ae-d497dc7ea544", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(dpi=75., layout='constrained')\n", "im = np.abs(data_ka21_2d - data_ka21)\n", "plt.imshow(im, cmap='RdBu')\n", "plt.colorbar()\n", "plt.title('Absolute error between $K_{2,1}^{*0}$ from $V_{2,1}^{0}$')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "869cf292-5ea7-4e94-8f4c-9416394550a8", "metadata": {}, "source": [ "## `w_0_sj_from_v_sj`" ] }, { "cell_type": "markdown", "id": "3a87bdcf-654c-4891-b1fc-a9ae35417ce8", "metadata": {}, "source": [ "### Docstring" ] }, { "cell_type": "code", "execution_count": 87, "id": "9b805491-121b-4d18-89df-ec03950530a2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Returns a numpy array that represents a numerical approximation of\n", " the matrix formed by the boundary integral operator W_{s,j}^0 with\n", " Laplace kernel evaluated and tested with real spherical harmonics.\n", " This routine needs the numpy array corresponding to V_{s,j}^0.\n", "\n", " Notes\n", " -----\n", " data_w[p*(2p+1) + q, l*(2l+1) + m] =\n", " ( W_{s,j}^0 Y_{l,m,j} ; Y_{p,q,s} )_{L^2(S_s)}.\n", " Y_{l,m,j} : spherical harmonic degree l, order m, in the coordinate\n", " system j.\n", " S_s : surface of the sphere s.\n", "\n", " This computation uses the following result for this specific case:\n", " ( W_{s,j}^0 Y_{l,m,j} ; Y_{p,q,s} )_{L^2(S_s)}\n", " = -\frac{l p}{r_j r_s}\n", " * ( V_{s,j}^0 Y_{l,m,j} ; Y_{p,q,s} )_{L^2(S_s)}\n", "\n", " Parameters\n", " ----------\n", " data_v_sj : np.ndarray\n", " represents a numerical approximation of the matrix formed by the\n", " boundary integral operator V_{s,j}^0 with Laplace kernel\n", " evaluated and\n", " tested with spherical harmonics.\n", " r_j : float\n", " > 0, radius of the sphere j.\n", " r_s : float\n", " > 0, radius of the sphere s.\n", " el_diagonal : scipy.sparse.dia_array\n", " that comes from\n", " biosspheres.miscella.auxindexes.diagonal_l_sparse\n", "\n", " Returns\n", " -------\n", " data_w : numpy array.\n", " Same shape than data_v_js. See notes for the indexes ordering.\n", "\n", " \n" ] } ], "source": [ "print(cross.w_0_sj_from_v_sj.__doc__)" ] }, { "cell_type": "markdown", "id": "87fc3728-8602-4ae2-a84e-5c2d6dc3a59e", "metadata": {}, "source": [ "### Example" ] }, { "cell_type": "markdown", "id": "7d6f00f6", "metadata": {}, "source": [ "Definition of parameters:" ] }, { "cell_type": "markdown", "id": "33e45e50", "metadata": {}, "source": [ "Radii:" ] }, { "cell_type": "code", "execution_count": 88, "id": "2d72469e-964f-487f-a9d6-bc93c8462a7d", "metadata": {}, "outputs": [], "source": [ "radio_1 = 3.\n", "radio_2 = 2." ] }, { "cell_type": "markdown", "id": "11a97219", "metadata": {}, "source": [ "Position of the center of the spheres:" ] }, { "cell_type": "code", "execution_count": 89, "id": "f26d6688", "metadata": {}, "outputs": [], "source": [ "p_1 = np.asarray([2., 3., 4.])\n", "p_2 = -p_1" ] }, { "cell_type": "markdown", "id": "0f64a8fa", "metadata": {}, "source": [ "Maximum degree of spherical harmonics used, and parameter for the quadrature rule:" ] }, { "cell_type": "code", "execution_count": 90, "id": "edddf158", "metadata": {}, "outputs": [], "source": [ "big_l = 3\n", "big_l_c = 25" ] }, { "cell_type": "markdown", "id": "96b8a2c2", "metadata": {}, "source": [ "Auxiliary parameters that use the ones previously defined, which are related to the implemented quadrature. This differs from the routines without the `1d` in its name:" ] }, { "cell_type": "code", "execution_count": 91, "id": "1535bc3a-9d3e-44ae-abb8-d44bfbaa516c", "metadata": {}, "outputs": [], "source": [ "final_length, pre_vector_t, transform = \\\n", " quadratures.real_spherical_harmonic_transform_1d(big_l, big_l_c)\n", "(r_coord_1tf, phi_coord_1tf, cos_theta_coord_1tf, er_times_n_1tf,\n", " etheta_times_n_1tf, ephi_times_n_1tf) = (\n", " quadratures.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_1d(\n", " radio_2, p_1, p_2, final_length, pre_vector_t))" ] }, { "cell_type": "code", "execution_count": 92, "id": "b5046170-f025-4edf-bc61-f0e8437cdb2a", "metadata": {}, "outputs": [], "source": [ "data_v21 = cross.v_0_sj_semi_analytic_v1d(\n", " big_l, radio_1, radio_2, r_coord_1tf, phi_coord_1tf,\n", " cos_theta_coord_1tf, final_length, transform)" ] }, { "cell_type": "code", "execution_count": 93, "id": "009c878e-6877-4941-ab9a-047dc21142fd", "metadata": {}, "outputs": [], "source": [ "el_diagonal = auxindexes.diagonal_l_sparse(big_l)" ] }, { "cell_type": "markdown", "id": "39a69e95", "metadata": {}, "source": [ "Calling of the function:" ] }, { "cell_type": "code", "execution_count": 94, "id": "b7046362-eec2-4546-b61b-3af09b9d4380", "metadata": {}, "outputs": [], "source": [ "data_w21 = cross.w_0_sj_from_v_sj(data_v21, radio_1, radio_2, el_diagonal)" ] }, { "cell_type": "markdown", "id": "481901d7-babf-4084-867b-9cb7bfc7058f", "metadata": {}, "source": [ "We check if `data_w21 = data_w_12`:" ] }, { "cell_type": "code", "execution_count": 95, "id": "ac045308-880f-4918-b16e-5bbe22354a5b", "metadata": {}, "outputs": [], "source": [ "(r_coord_2tf, phi_coord_2tf, cos_theta_coord_2tf, er_times_n_2tf,\n", " etheta_times_n_2tf, ephi_times_n_2tf) = (\n", " quadratures.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_1d(\n", " radio_1, p_2, p_1, final_length, pre_vector_t))" ] }, { "cell_type": "code", "execution_count": 96, "id": "868147a0-c28e-43c4-b58e-e96af748f12b", "metadata": {}, "outputs": [], "source": [ "data_v12 = cross.v_0_sj_semi_analytic_v1d(\n", " big_l, radio_2, radio_1, r_coord_2tf, phi_coord_2tf,\n", " cos_theta_coord_2tf, final_length, transform)" ] }, { "cell_type": "code", "execution_count": 97, "id": "e336f946-60b7-4c96-aa4b-e5a326fad935", "metadata": {}, "outputs": [], "source": [ "data_w12 = cross.w_0_sj_from_v_sj(data_v12, radio_2, radio_1, el_diagonal)" ] }, { "cell_type": "code", "execution_count": 98, "id": "4b471e24-2f03-4065-bd41-1545da8db3f4", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(dpi=75., layout='constrained')\n", "im = np.abs(data_w12 - np.transpose(data_w21))\n", "plt.imshow(im, cmap='RdBu')\n", "plt.colorbar()\n", "plt.title('Relative error between $W_{1,2}^0$ and $W_{2,1}^{0t}$.')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c3a0a291-7fa6-4654-ab46-b1c38cc25a0a", "metadata": {}, "source": [ "## `a_0_sj_and_js_v1d`" ] }, { "cell_type": "markdown", "id": "47d117ae-98b7-46c6-89ae-fd82a2ab4692", "metadata": {}, "source": [ "The `1d` on the name of the routines references the type of input it needs. See the following sections for details." ] }, { "cell_type": "markdown", "id": "1a7f2eab-01b2-47ea-99ba-204453693ffc", "metadata": {}, "source": [ "### Docstring" ] }, { "cell_type": "code", "execution_count": 99, "id": "7607f71d-ad88-4406-a446-05a8a4d2d77f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Returns two numpy arrays that represents a numerical approximation\n", " of two matrices formed by the following boundary integral operators:\n", " a_sj = [-K_{s,j}^0 , V_{s,j}^0 ]\n", " [ W_{s,j}^0 , K_{s,j}^{*0}]\n", " a_js = [-K_{j,s}^0 , V_{j,s}^0 ]\n", " [ W_{j,s}^0 , K_{j,s}^{*0}]\n", " with Laplace kernel evaluated and tested with real spherical\n", " harmonics.\n", " In this routine the quadrature points NEED to be ordered in an array\n", " of one dimension.\n", " It is a SLOW routine, because it does not use any symmetry or\n", " properties of the spherical harmonics.\n", "\n", " Notes\n", " -----\n", " The only operator computed directly with the numerical quadrature is\n", " V_{s,j}^0, which follows the same steps as v_0_sj_semi_analytic_v1d.\n", " The others are computed with the same properties used in:\n", " v_0_js_from_v_0_sj\n", " k_0_sj_from_v_0_sj\n", " ka_0_sj_from_v_sj\n", " w_0_sj_from_v_sj\n", "\n", " Parameters\n", " ----------\n", " big_l : int\n", " >= 0, max degree.\n", " r_j : float\n", " > 0, radius of the sphere j.\n", " r_s : float\n", " > 0, radius of the sphere s.\n", " r_coord : np.ndarray\n", " Array of floats with the spherical coordinate r of the\n", " quadrature points in the coordinate system s. Length equals to\n", " final_length. Can come from the\n", " function from_sphere_s_cartesian_to_j_spherical_1d of the module\n", " biosspheres.quadratures.spheres.\n", " phi_coord : np.ndarray\n", " Array of floats with the phi coordinate r of the quadrature\n", " points in the coordinate system s. Length equals to\n", " final_length. Can come from the function\n", " from_sphere_s_cartesian_to_j_spherical_1d of the module\n", " biosspheres.quadratures.spheres.\n", " cos_theta_coord : np.ndarray\n", " Array of floats with the cosine of the spherical coordinate\n", " theta of the quadrature points in the coordinate system s.\n", " Lengths equal to final_length. Can come from the function\n", " from_sphere_s_cartesian_to_j_spherical_1d of the module\n", " biosspheres.quadratures.spheres.\n", " final_length : int\n", " How many points for the surface integral.\n", " Can come from the function spherical_harmonic_transform_1d of\n", " the module biosspheres.quadratures.spheres.\n", " transform : np.ndarray\n", " of floats, for doing the real spherical harmonic transform.\n", " Can come from the function real_spherical_harmonic_transform_1d\n", " of the module biosspheres.quadratures.spheres.\n", " diagonal : np.ndarray\n", " from diagonal_l_dense\n", "\n", " Returns\n", " -------\n", " a_sj : numpy array\n", " Shape (2 * (big_l+1)**2, 2 * (big_l+1)**2).\n", " a_js : numpy array\n", " Shape (2 * (big_l+1)**2, 2 * (big_l+1)**2).\n", "\n", " See Also\n", " --------\n", " a_0_sj_and_js_v2d\n", " v_0_sj_semi_analytic_v1d\n", " v_0_js_from_v_0_sj\n", " k_0_sj_from_v_0_sj\n", " ka_0_sj_from_v_sj\n", " w_0_sj_from_v_sj\n", "\n", " \n" ] } ], "source": [ "print(cross.a_0_sj_and_js_v1d.__doc__)" ] }, { "cell_type": "markdown", "id": "ce1af6f9-5a58-4ad5-9dbc-4054450ef4cc", "metadata": {}, "source": [ "### Example" ] }, { "cell_type": "code", "execution_count": 100, "id": "ce147d63-ba0e-4fbc-9fbe-49de5e1b3465", "metadata": {}, "outputs": [], "source": [ "radio_1 = 3.\n", "radio_2 = 2.\n", "\n", "p_1 = np.asarray([2., 3., 4.])\n", "p_2 = -p_1\n", "\n", "big_l = 3\n", "big_l_c = 50" ] }, { "cell_type": "code", "execution_count": 101, "id": "5c4ea62f-0590-4b0e-9f08-85750281a2a6", "metadata": {}, "outputs": [], "source": [ "final_length, pre_vector_t, transform = quadratures.real_spherical_harmonic_transform_1d(big_l, big_l_c)\n", "r_coord_1tf, phi_coord_1tf, cos_theta_coord_1tf = (\n", " quadratures.\n", " from_sphere_s_cartesian_to_j_spherical_1d(\n", " radio_2, p_1, p_2, final_length, pre_vector_t))" ] }, { "cell_type": "code", "execution_count": 102, "id": "79f6b6a7-1aef-4d74-87fa-b2d34b7c8f97", "metadata": {}, "outputs": [], "source": [ "diagonal = auxindexes.diagonal_l_dense(big_l)" ] }, { "cell_type": "code", "execution_count": 103, "id": "195e7183-21d1-4aea-8400-2caefc51f4a7", "metadata": {}, "outputs": [], "source": [ "a_21, a_12 = cross.a_0_sj_and_js_v1d(\n", " big_l, radio_1, radio_2, r_coord_1tf, phi_coord_1tf,\n", " cos_theta_coord_1tf, final_length, transform, diagonal)" ] }, { "cell_type": "markdown", "id": "ee4cfb3a-80ae-464c-8a07-7e9c84d978eb", "metadata": {}, "source": [ "To compare" ] }, { "cell_type": "code", "execution_count": 104, "id": "3c099f12-7a6a-425e-9856-bc89e792f086", "metadata": {}, "outputs": [], "source": [ "data_v21 = cross.v_0_sj_semi_analytic_v1d(\n", " big_l, radio_1, radio_2, r_coord_1tf, phi_coord_1tf,\n", " cos_theta_coord_1tf, final_length, transform)\n", "data_k21 = cross.k_0_sj_semi_analytic_v1d(\n", " big_l, radio_1, radio_2, r_coord_1tf, phi_coord_1tf,\n", " cos_theta_coord_1tf, final_length, transform)\n", "el_diagonal = auxindexes.diagonal_l_sparse(big_l)\n", "data_ka21 = cross.ka_0_sj_from_v_sj(data_v21, radio_2, el_diagonal)\n", "data_w21 = cross.w_0_sj_from_v_sj(data_v21, radio_1, radio_2, el_diagonal)" ] }, { "cell_type": "code", "execution_count": 105, "id": "61ee709f-00b9-4fc5-aaf1-b3d3a2f0d990", "metadata": {}, "outputs": [], "source": [ "a_21_prev = np.concatenate((\n", " np.concatenate((-data_k21, data_v21), axis=1),\n", " np.concatenate((data_w21, data_ka21), axis=1)),\n", " axis=0)" ] }, { "cell_type": "code", "execution_count": 106, "id": "ca162c92-7edd-4a8f-9eab-79c1ea1585e1", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "aux = np.abs(a_21 - a_21_prev)\n", "plt.figure()\n", "plt.imshow(aux, cmap='RdBu',\n", " norm=colors.SymLogNorm(linthresh=10**(-8)))\n", "plt.colorbar()\n", "plt.title('Checking routine A_sj.')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "b026b554-7129-4d52-b625-541486951a55", "metadata": {}, "source": [ "## `a_0_sj_and_js_v2d`" ] }, { "cell_type": "markdown", "id": "cd95747a-79aa-4270-92ea-c4afe1af389f", "metadata": {}, "source": [ "### Docstring" ] }, { "cell_type": "code", "execution_count": 107, "id": "ff698911-a24d-4257-9dbe-207c32d6db09", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Returns two numpy arrays that represents a numerical approximation\n", " of two matrices formed by the following boundary integral operators:\n", " a_sj = [-K_{s,j}^0 , V_{s,j}^0 ]\n", " [ W_{s,j}^0 , K_{s,j}^{*0}]\n", " a_js = [-K_{j,s}^0 , V_{j,s}^0 ]\n", " [ W_{j,s}^0 , K_{j,s}^{*0}]\n", " with Laplace kernel evaluated and tested with real spherical\n", " harmonics.\n", " In this routine the quadrature points NEED to be ordered in an array\n", " of two dimensions, given by the function\n", " from_sphere_s_cartesian_to_j_spherical_2d\n", " of the module biosspheres.quadratures.spheres.\n", "\n", " Notes\n", " -----\n", " The only operator computed directly with the numerical quadrature is\n", " V_{s,j}^0, which follows the same steps as v_0_sj_semi_analytic_v2d.\n", " The others are computed with the same properties used in:\n", " v_0_js_from_v_0_sj\n", " k_0_sj_from_v_0_sj\n", " ka_0_sj_from_v_sj\n", " w_0_sj_from_v_sj\n", "\n", " Parameters\n", " ----------\n", " big_l : int\n", " >= 0, max degree of spherical harmonics used.\n", " r_j : float\n", " > 0, radius of the sphere j.\n", " r_s : float\n", " > 0, radius of the sphere s.\n", " r_coord : np.ndarray\n", " Two dimensional array of floats with the spherical coordinate r\n", " of the quadrature points in the coordinate system s. Shape\n", " equals to (quantity_theta_points, quantity_phi_points).\n", " Comes from biosspheres.quadratures.spheres.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_2d\n", " phi_coord : np.ndarray\n", " Two dimensional array of floats with the phi coordinate r of the\n", " quadrature points in the coordinate system s. Shape equals to\n", " (quantity_theta_points, quantity_phi_points).\n", " Comes from biosspheres.quadratures.spheres.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_2d\n", " cos_theta_coord : np.ndarray\n", " Two dimensional array of floats with the cosine of the spherical\n", " coordinate theta of the quadrature points in the coordinate\n", " system s. Shape equals to\n", " (quantity_theta_points, quantity_phi_points).\n", " Comes from biosspheres.quadratures.spheres.\n", " from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_2d\n", " weights : np.ndarray\n", " of floats. Weights for the integral quadrature in the theta\n", " variable. Comes from the function\n", " gauss_legendre_trapezoidal_shtools_2d\n", " from the module biosspheres.quadratures.spheres.\n", " zeros : np.ndarray\n", " of floats. Zeros of the integral quadrature in the theta\n", " variable. Comes from the function\n", " gauss_legendre_trapezoidal_shtools_2d\n", " from the module biosspheres.quadratures.spheres.\n", " quantity_theta_points : int\n", " how many points for the integral in theta.\n", " Can come from the function\n", " gauss_legendre_trapezoidal_shtools_2d\n", " from the module biosspheres.quadratures.spheres.\n", " quantity_phi_points : int\n", " how many points for the integral in phi.\n", " Comes from the function\n", " gauss_legendre_trapezoidal_shtools_2d\n", " from the module biosspheres.quadratures.spheres.\n", " pesykus : np.ndarray\n", " dtype int, shape ((big_l+1) * big_l // 2, 2).\n", " Used for the vectorization of some computations.\n", " Comes from the function\n", " biosspheres.miscella.auxindexes.pes_y_kus(big_l)\n", " p2_plus_p_plus_q : np.ndarray\n", " dtype int, length (big_l+1) * big_l // 2.\n", " Used for the vectorization of some computations.\n", " Comes from the function\n", " biosspheres.miscella.auxindexes.pes_y_kus(big_l)\n", " p2_plus_p_minus_q : np.ndarray\n", " dtype int, length (big_l+1) * big_l // 2.\n", " Used for the vectorization of some computations.\n", " Comes from the function\n", " biosspheres.miscella.auxindexes.pes_y_kus(big_l)\n", " diagonal : np.ndarray\n", " from diagonal_l_dense\n", "\n", " Returns\n", " -------\n", " a_sj : numpy array\n", " Shape (2 * (big_l+1)**2, 2 * (big_l+1)**2).\n", " a_js : numpy array\n", " Shape (2 * (big_l+1)**2, 2 * (big_l+1)**2).\n", "\n", " See Also\n", " --------\n", " a_0_sj_and_js_v1d\n", " v_0_sj_semi_analytic_v2d\n", " v_0_js_from_v_0_sj\n", " k_0_sj_from_v_0_sj\n", " ka_0_sj_from_v_sj\n", " w_0_sj_from_v_sj\n", "\n", " \n" ] } ], "source": [ "print(cross.a_0_sj_and_js_v2d.__doc__)" ] }, { "cell_type": "markdown", "id": "3be3fd2c-fb84-45a2-bd0d-db22c18b161e", "metadata": {}, "source": [ "### Example" ] }, { "cell_type": "code", "execution_count": 108, "id": "5d708882-c3e3-410c-b498-1a85a855a3ba", "metadata": {}, "outputs": [], "source": [ "radio_1 = 3.\n", "radio_2 = 2.\n", "\n", "p_1 = np.asarray([2., 3., 4.])\n", "p_2 = -p_1\n", "\n", "big_l = 3\n", "big_l_c = 50" ] }, { "cell_type": "code", "execution_count": 109, "id": "a1c3813a-3ada-4708-b653-3837261d94af", "metadata": {}, "outputs": [], "source": [ "quantity_theta_points, quantity_phi_points, weights, pre_vector_t_2d = \\\n", " quadratures.gauss_legendre_trapezoidal_2d(big_l_c)\n", "r_coord_1tf_2d, phi_coord_1tf_2d, cos_theta_coord_1tf_2d = \\\n", " (quadratures.\n", " from_sphere_s_cartesian_to_j_spherical_2d(\n", " radio_2, p_1, p_2, quantity_theta_points, quantity_phi_points,\n", " pre_vector_t_2d))\n", "pesykus, p2_plus_p_plus_q, p2_plus_p_minus_q = auxindexes.pes_y_kus(big_l)" ] }, { "cell_type": "code", "execution_count": 110, "id": "d60852dd-3e1b-47dc-8c15-e0f8a5bd3563", "metadata": {}, "outputs": [], "source": [ "diagonal = auxindexes.diagonal_l_dense(big_l)" ] }, { "cell_type": "code", "execution_count": 111, "id": "b3de7a7a-31f1-4692-8753-1e98d9263808", "metadata": {}, "outputs": [], "source": [ "a_21_2d, a_12_2d = cross.a_0_sj_and_js_v2d(\n", " big_l, radio_1, radio_2, r_coord_1tf_2d, phi_coord_1tf_2d,\n", " cos_theta_coord_1tf_2d, weights, pre_vector_t_2d[2, :, 0],\n", " quantity_theta_points, quantity_phi_points, pesykus, p2_plus_p_plus_q,\n", " p2_plus_p_minus_q, diagonal)" ] }, { "cell_type": "markdown", "id": "8d21f4b1-6d22-429d-aa54-6886710a8f11", "metadata": {}, "source": [ "To compare" ] }, { "cell_type": "code", "execution_count": 112, "id": "9f2b49a4-1880-403e-99d1-f5a943dabf1f", "metadata": {}, "outputs": [], "source": [ "final_length, pre_vector_t, transform = \\\n", " quadratures.real_spherical_harmonic_transform_1d(big_l, big_l_c)\n", "r_coord_1tf, phi_coord_1tf, cos_theta_coord_1tf = (\n", " quadratures.\n", " from_sphere_s_cartesian_to_j_spherical_1d(\n", " radio_2, p_1, p_2, final_length, pre_vector_t))" ] }, { "cell_type": "code", "execution_count": 113, "id": "93b1c9b6-c866-4f1a-9f5b-e94ca836388f", "metadata": {}, "outputs": [], "source": [ "a_21, a_12 = cross.a_0_sj_and_js_v1d(\n", " big_l, radio_1, radio_2, r_coord_1tf, phi_coord_1tf,\n", " cos_theta_coord_1tf, final_length, transform, diagonal)" ] }, { "cell_type": "code", "execution_count": 114, "id": "8324a850-6277-4020-a42b-f29e74327ac9", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "aux = np.abs(a_21 - a_21_2d)\n", "plt.figure()\n", "plt.imshow(aux, cmap='RdBu',\n", " norm=colors.SymLogNorm(linthresh=10**(-8)))\n", "plt.colorbar()\n", "plt.title('Checking routine A_sj.')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 115, "id": "6336de1c-459a-4bb8-8641-1016753cc7c1", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "aux = np.abs(a_12 - a_12_2d)\n", "plt.figure()\n", "plt.imshow(aux, cmap='RdBu',\n", " norm=colors.SymLogNorm(linthresh=10**(-8)))\n", "plt.colorbar()\n", "plt.title('Checking routine A_sj.')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "6d589c42-d1f1-4d23-9244-6ea1d91885b6", "metadata": {}, "source": [ "## `all_cross_interactions_n_spheres_v1d`" ] }, { "cell_type": "markdown", "id": "4f9efd3b-77a8-4753-8dea-336b8c5c527f", "metadata": {}, "source": [ "The `1d` on the name of the routine references the type of input it needs. See the following sections for details." ] }, { "cell_type": "markdown", "id": "a78186e3-15b5-40fb-abd2-2e8eda642978", "metadata": {}, "source": [ "### Docstring" ] }, { "cell_type": "code", "execution_count": 116, "id": "3e978398-96f9-4479-869a-1f1e1c7b6fe6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Returns an array with all the cross interactions for the given n\n", " spheres.\n", " It is a SLOW routine.\n", "\n", " Notes\n", " -----\n", " Uses the following:\n", " quadratures.real_spherical_harmonic_transform_1d(big_l, big_l_c)\n", " auxindexes.diagonal_l_dense(big_l)\n", " quadratures.from_sphere_s_cartesian_to_j_spherical_1d\n", " a_0_sj_and_js_v1d\n", "\n", " Parameters\n", " ----------\n", " n : int\n", " >= 2. Number of spheres.\n", " big_l : int\n", " >= 0, max degree.\n", " big_l_c : int\n", " >= 0. It's the parameter used to compute the points of the\n", " quadrature.\n", " radii : np.ndarray\n", " Array with the radii of the spheres.\n", " center_positions :\n", " List or arrays with the center position of the spheres\n", "\n", " Returns\n", " -------\n", " almost_big_a_0 : np.ndarray\n", " Shape ( 2 * n * (big_l + 1) ** 2, 2 * n * (big_l + 1) ** 2).\n", "\n", " See Also\n", " --------\n", " all_cross_interactions_n_spheres_v2d\n", "\n", " \n" ] } ], "source": [ "print(cross.all_cross_interactions_n_spheres_v1d.__doc__)" ] }, { "cell_type": "markdown", "id": "b5ab990e-d77b-4c04-9407-08dc29e5b937", "metadata": {}, "source": [ "### Example" ] }, { "cell_type": "code", "execution_count": 117, "id": "5d6094f4-b392-4bea-83ff-fe2847bb9360", "metadata": {}, "outputs": [], "source": [ "radio_1 = 3.\n", "radio_2 = 2.\n", "rs = np.asarray([radio_1, radio_2])\n", "\n", "p_1 = np.asarray([2., 3., 4.])\n", "p_2 = -p_1\n", "\n", "big_l = 3\n", "big_l_c = 50\n", "\n", "n = 2\n", "p = [p_1, p_2]" ] }, { "cell_type": "code", "execution_count": 118, "id": "75de898f-a46a-4623-bcdb-4264f1496c5e", "metadata": {}, "outputs": [], "source": [ "cross_1 = cross.all_cross_interactions_n_spheres_v1d(\n", " n, big_l, big_l_c, rs, p)" ] }, { "cell_type": "markdown", "id": "c3cfb4e0-2e47-4bc2-83bb-df2f501878c2", "metadata": {}, "source": [ "## `all_cross_interactions_n_spheres_v2d`" ] }, { "cell_type": "markdown", "id": "17a0e9f1-650d-4f2f-91f9-b3280a56412c", "metadata": {}, "source": [ "### Docstring" ] }, { "cell_type": "code", "execution_count": 119, "id": "af03959b-5a96-45b9-a72f-cd4118c323c0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Returns an array with all the cross interactions for the given n\n", " spheres.\n", "\n", " Notes\n", " -----\n", " Uses the following:\n", " auxindexes.pes_y_kus\n", " quadratures.quadrature_points_sphere_shtools_version_2d\n", " auxindexes.diagonal_l_dense\n", " quadratures.from_sphere_s_cartesian_to_j_spherical_2d\n", " a_0_sj_and_js_v2d\n", "\n", " Parameters\n", " ----------\n", " n : int\n", " >= 2. Number of spheres.\n", " big_l : int\n", " >= 0, max degree.\n", " big_l_c : int\n", " >= 0. It's the parameter used to compute the points of the\n", " quadrature.\n", " radii : np.ndarray\n", " Array with the radii of the spheres.\n", " center_positions : array_like\n", " List or array with the center position of the spheres\n", "\n", " Returns\n", " -------\n", " almost_big_a_0 : np.ndarray\n", " Shape ( 2 * n * (big_l + 1) ** 2, 2 * n * (big_l + 1) ** 2).\n", "\n", " See Also\n", " --------\n", " all_cross_interactions_n_spheres_v1d\n", "\n", " \n" ] } ], "source": [ "print(cross.all_cross_interactions_n_spheres_v2d.__doc__)" ] }, { "cell_type": "markdown", "id": "d62cd9bb-8210-4271-9ebd-ad86597707fc", "metadata": {}, "source": [ "### Example " ] }, { "cell_type": "code", "execution_count": 120, "id": "711af0f9-d5b2-4b86-91dc-f80783698676", "metadata": {}, "outputs": [], "source": [ "radio_1 = 3.\n", "radio_2 = 2.\n", "rs = np.asarray([radio_1, radio_2])\n", "\n", "p_1 = np.asarray([2., 3., 4.])\n", "p_2 = -p_1\n", "\n", "big_l = 3\n", "big_l_c = 50\n", "\n", "n = 2\n", "p = [p_1, p_2]" ] }, { "cell_type": "code", "execution_count": 121, "id": "11150a78-159e-4557-b0d1-a5155c933549", "metadata": {}, "outputs": [], "source": [ "cross_2 = cross.all_cross_interactions_n_spheres_v2d(\n", " n, big_l, big_l_c, rs, p)" ] }, { "cell_type": "markdown", "id": "b97895d6-6549-4932-a848-f38e101c131e", "metadata": {}, "source": [ "To compare" ] }, { "cell_type": "code", "execution_count": 122, "id": "06547779-fc92-432b-ae84-ca2198138e3e", "metadata": {}, "outputs": [], "source": [ "cross_1 = cross.all_cross_interactions_n_spheres_v1d(\n", " n, big_l, big_l_c, rs, p)" ] }, { "cell_type": "code", "execution_count": 123, "id": "d113de2c-8850-4f30-9c33-2be57e01d0ac", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.575151838646758e-15\n" ] } ], "source": [ "print(np.linalg.norm(cross_2 - cross_1))" ] }, { "cell_type": "code", "execution_count": null, "id": "a74dd5de-dd67-44c3-9bf3-719287008dc3", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.18" } }, "nbformat": 4, "nbformat_minor": 5 }