{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"from pystencils.session import *"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Tutorial 01: Getting Started\n",
"\n",
"\n",
"## Overview\n",
"\n",
"\n",
"*pystencils* is a package that can speed up transformations on *numpy* arrays. All computations are carried out fully parallel on CPUs (single node with OpenMP, multiple nodes with MPI) or on GPUs.\n",
"\n",
"It is suited for applications that run the same operation on *numpy* arrays multiple times like for example:\n",
"- numerical simulations (finite difference, lattice Boltzmann)\n",
"- image processing\n",
"\n",
"As the name suggests, *pystencils* was developed for **stencil codes**, i.e. operations that update an element of a numpy array using only a local neighborhood. \n",
"\n",
"<img width=\"25%\" src='../../img/pystencils_stencil_four_points_with_arrows.svg'>\n",
"\n",
"It generates C code, compiles it behind the scenes, and lets you call the compiled C function as if it was a native Python function. \n",
"\n",
"But lets not dive too deep into the concepts of *pystencils* here, they are covered in detail in the following tutorials. Lets instead look at a simple example, that computes the average neighbor values of a *numpy* array.\n",
"\n",
"We create two rather large arrays for in- and output."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"input_arr = np.random.rand(1024, 1024)\n",
"output_arr = np.zeros_like(input_arr)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We first implement a version of this algorithm using pure numpy and benchmark it."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def numpy_kernel():\n",
" output_arr[1:-1, 1:-1] = input_arr[2:, 1:-1] + input_arr[:-2, 1:-1] + \\\n",
" input_arr[1:-1, 2:] + input_arr[1:-1, :-2]"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"7.13 ms ± 254 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
]
}
],
"source": [
"%%timeit \n",
"numpy_kernel()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now lets see how to run the same algorithm with *pystencils*."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$${{dst}_{(0,0)}} \\leftarrow \\frac{{{src}_{(-1,0)}}}{4} + \\frac{{{src}_{(0,-1)}}}{4} + \\frac{{{src}_{(0,1)}}}{4} + \\frac{{{src}_{(1,0)}}}{4}$$"
],
"text/plain": [
" src_W src_S src_N src_E\n",
"dst_C := ───── + ───── + ───── + ─────\n",
" 4 4 4 4 "
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"src, dst = ps.fields(src=input_arr, dst=output_arr)\n",
"\n",
"symbolic_description = ps.Assignment(dst[0,0], \n",
" (src[1, 0] + src[-1, 0] + src[0, 1] + src[0, -1]) / 4)\n",
"symbolic_description"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 216x216 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(3,3))\n",
"ps.visualize_stencil_expression(symbolic_description.rhs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we first have created a symbolic notation of the stencil itself. This representation is built on top of *sympy* and is explained in detail in the next section. \n",
"This description is then compiled and loaded as a Python function."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"kernel = ps.create_kernel(symbolic_description).compile()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This whole process might seem overly complicated. We have already spent more lines of code as for the *numpy* implementation and don't have anything running yet! However, this multi stage process of formulating the algorithm symbolically, and just in the end actually running it, is what makes *pystencils* faster and more flexible than other approaches.\n",
"\n",
"Now finally lets benchmark the *pystencils* kernel."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"def pystencils_kernel():\n",
" kernel(src=input_arr, dst=output_arr)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1.36 ms ± 51.5 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
]
}
],
"source": [
"%%timeit\n",
"pystencils_kernel()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This benchmark shows that *pystencils* is a lot faster than pure *numpy*, especially for large arrays. \n",
"If you are interested in performance details and comparison to other packages like Cython, have a look at [this page](demo_benchmark.ipynb).\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Short *sympy* introduction\n",
"\n",
"In this tutorial we continue with a short *sympy* introduction, since the symbolic kernel definition is built on top of this package. If you already know *sympy* you can skip this section. \n",
"You can also read the full [sympy documentation here](http://docs.sympy.org/latest/index.html)."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"import sympy as sp\n",
"sp.init_printing() # enable nice LaTeX output"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*sympy* is a package for symbolic calculation. So first we need some symbols:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"sympy.core.symbol.Symbol"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = sp.Symbol(\"x\")\n",
"y = sp.Symbol(\"y\")\n",
"type(x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The usual mathematical operations are defined for symbols:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$$x^{2} \\left(x + y + 5\\right) + x^{2}$$"
],
"text/plain": [
" 2 2\n",
"x ⋅(x + y + 5) + x "
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"expr = x**2 * ( y + x + 5) + x**2\n",
"expr"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can do all sorts of operations on these expressions: expand them, factor them, substitute variables:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$$x^{3} + x^{2} y + 6 x^{2}$$"
],
"text/plain": [
" 3 2 2\n",
"x + x ⋅y + 6⋅x "
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"expr.expand()"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$$x^{2} \\left(x + y + 6\\right)$$"
],
"text/plain": [
" 2 \n",
"x ⋅(x + y + 6)"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"expr.factor()"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$$x^{2} \\left(x + \\cos{\\left (x \\right )} + 5\\right) + x^{2}$$"
],
"text/plain": [
" 2 2\n",
"x ⋅(x + cos(x) + 5) + x "
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"expr.subs(y, sp.cos(x))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also built equations and solve them"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANAAAAAZBAMAAACybb07AAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsyme8Q6PJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAACxklEQVRIDa1VTWsTURQ9k04m6eTDoRHB3TSCu9JSCt3JbEQQ1OJCXAjRutFFsbhRF0pQF7qRoCiOHxDFhbhq0Z2I/gFpRFCKgnHpylRUUIT4Pu6dvEkzSaB5i7n3nnveOe9NXt4Aeiy98ijbcugr5QRjtS07aIH+Utkg/3NERv2lsgv2r1EZDZByN0ZkBPSXyvrKaN/wdpkggUtSCd0lhdsrCe0u+Kb3to65LpBLLcVVV8w0FDAedOEJ5ff2b2Bn7yZJmU33a1QdwTGZX4wAmTyOVbJwfQ3dmQ0Ah4ouHklponqW3kcHIH/v2arErhrtfkYzkmc1iR1bEEtRT4VUZFRst1sCsqvi0RkxAQXzjpQRbhM1xiOpjorIlNHErr27fYJTDbHO8tzhRV2TgDXl46CnIDaaP/tZ1Pyrs5EpRYo6SCPreOZytkZwbhnYgfP+dV2TgOM2Ma0RNlrFoQXgAk3jBZlSOB3K8VBRpJHjORtuQDOydeAEznhPdE0C+ws1vNQIGwG5KvBUg3wYYlLU0kHtCOMrEVgUy/RwX9ViRTfC8JbIvaKPHyI6YXj3WxjOqHZB3I1rMuvwLFNKkfihfiNs87mGNIISVRC/+4qX/6c5tCNx1TviblRGosE8U0rz6amN1t5EoHx1YNGOwDpSTc0ho2INBfHaj2qwY2RI4dQ1Oa4oijRyvWmkPJohD8OjVAuTuuaVPkdOvy/+wxYAeYC6DkNMihR1kEaV+mtEN6nTQPpvrmULPznY6BMqhNCO7AYuBcAHxYp4MSlq6SCNSuWJj6QCpKuwZienzsUFUFr8EmiIT92Bk+8E8CDOi0lRS4XCnj/zZi3ypCtonXhspEq7SijvnMphQvxS3a6njNUs/vxagaESXarEM1oD05wpxOzscs7n3IwJnwmTkpj3/PCly/Ji2zxebIaGR6IDOHhK4qe859T/bS2hHg5dmHoAAAAASUVORK5CYII=\n",
"text/latex": [
"$$x^{2} \\left(x + y + 5\\right) + x^{2} = 1$$"
],
"text/plain": [
" 2 2 \n",
"x ⋅(x + y + 5) + x = 1"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eq = sp.Eq(expr, 1)\n",
"eq"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$$\\left [ - x - 6 + \\frac{1}{x^{2}}\\right ]$$"
],
"text/plain": [
"⎡ 1 ⎤\n",
"⎢-x - 6 + ──⎥\n",
"⎢ 2⎥\n",
"⎣ x ⎦"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sp.solve(sp.Eq(expr, 1), y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A *sympy* expression is represented by an abstract syntax tree (AST), which can be inspected and modified."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAKoAAAAZBAMAAABTBqhqAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsyme8Q6PJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAACe0lEQVRIDa2Vv2sTYRjHv5deLtdcEo9WBLdrBLfSUgqut4ggqMVBHIRonRyKxUUdlCAuXeSwVDx1iOIgTi26ieg/II2LUhTM6mQq6iBCfH88z937Nj0Ummd4n1/f93N3712eANqWXocU7dnlKC8eS/aM0wAD5ce1HyOiGih/wf05KqqJqm6PiAoYKD9S1GP/z67EBVpCye6SkrjrBcod5bvhuw7mdxQ51SiZVbqqNh4r98/l2+AXcHB3GaFk8wzOSXdDLpk9ySIOqpGO7s3FgEcJbB2hhLD24PmG1N+WS2a2WpaZOisTpydXYZaOUaLeGAz6wrltseRmqVXZomKNpJZOoyYOHT0cUbskTtdpzp9e1DmpnekIJ0NVYuqRK59Fzq+FqTnKOV+55SdEDZaBA7gWrVhUr9rDjK4wdQOnFoDrtI2vnqO80NuuxtT2O8AFXA6f6pzUx+sJXukKU4GgDTzTRT5XA+VgfJ2a4njFDYR4qPJLaXonTVdFHDYifBfeS9P7X9N0VrXrYm5syijXWah9kZLJRVKhCNLzPaAV1v6oAn8DYsB5Ym4oqqGDgdp8q3eIVZ4AmJBTt1DqiYYwOoFGgrqYG2d1Mbs6MlQ1nEEppLZ8W49LfUzpnN/tCwT6sZlaFzeQDL0tA9XqvEE2Urwuyr+Dvivg0pj6CS2q0L26XdyMgQ9KlekM1GRz4iNtAcptOHNT01dtNSYXvwiGNP4GTlx8L7JHqpZRLRS1lCv6xW6RiKkqddtU5WeidMjZ02W/7o8lDv9ROLGxJZsupDNadhiYu7jlLwcRx6YvmISmRMe7Tu1yU/7oh+3lcKmgkn0OBX2jXPgPA/wF1cGLzQch/MoAAAAASUVORK5CYII=\n",
"text/latex": [
"$$x^{2} \\left(x + y + 5\\right) + x^{2}$$"
],
"text/plain": [
" 2 2\n",
"x ⋅(x + y + 5) + x "
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"expr"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
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"</g>\n",
"<!-- Pow(Symbol(x), Integer(2))_(0,)->Symbol(x)_(0, 0) -->\n",
"<g id=\"edge3\" class=\"edge\"><title>Pow(Symbol(x), Integer(2))_(0,)->Symbol(x)_(0, 0)</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M84.4297,-146.834C74.2501,-136.938 60.4761,-123.546 48.9694,-112.359\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"51.4055,-109.846 41.7957,-105.385 46.5259,-114.865 51.4055,-109.846\"/>\n",
"</g>\n",
"<!-- Integer(2)_(0, 1) -->\n",
"<g id=\"node4\" class=\"node\"><title>Integer(2)_(0, 1)</title>\n",
"<ellipse fill=\"none\" stroke=\"black\" cx=\"99\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"99\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">2</text>\n",
"</g>\n",
"<!-- Pow(Symbol(x), Integer(2))_(0,)->Integer(2)_(0, 1) -->\n",
"<g id=\"edge4\" class=\"edge\"><title>Pow(Symbol(x), Integer(2))_(0,)->Integer(2)_(0, 1)</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M99,-143.697C99,-135.983 99,-126.712 99,-118.112\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"102.5,-118.104 99,-108.104 95.5001,-118.104 102.5,-118.104\"/>\n",
"</g>\n",
"<!-- Pow(Symbol(x), Integer(2))_(1, 0) -->\n",
"<g id=\"node6\" class=\"node\"><title>Pow(Symbol(x), Integer(2))_(1, 0)</title>\n",
"<ellipse fill=\"none\" stroke=\"black\" cx=\"171\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"171\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">Pow</text>\n",
"</g>\n",
"<!-- Mul(Pow(Symbol(x), Integer(2)), Add(Integer(5), Symbol(x), Symbol(y)))_(1,)->Pow(Symbol(x), Integer(2))_(1, 0) -->\n",
"<g id=\"edge5\" class=\"edge\"><title>Mul(Pow(Symbol(x), Integer(2)), Add(Integer(5), Symbol(x), Symbol(y)))_(1,)->Pow(Symbol(x), Integer(2))_(1, 0)</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M171,-143.697C171,-135.983 171,-126.712 171,-118.112\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"174.5,-118.104 171,-108.104 167.5,-118.104 174.5,-118.104\"/>\n",
"</g>\n",
"<!-- Add(Integer(5), Symbol(x), Symbol(y))_(1, 1) -->\n",
"<g id=\"node9\" class=\"node\"><title>Add(Integer(5), Symbol(x), Symbol(y))_(1, 1)</title>\n",
"<ellipse fill=\"none\" stroke=\"black\" cx=\"279\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"279\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">Add</text>\n",
"</g>\n",
"<!-- Mul(Pow(Symbol(x), Integer(2)), Add(Integer(5), Symbol(x), Symbol(y)))_(1,)->Add(Integer(5), Symbol(x), Symbol(y))_(1, 1) -->\n",
"<g id=\"edge6\" class=\"edge\"><title>Mul(Pow(Symbol(x), Integer(2)), Add(Integer(5), Symbol(x), Symbol(y)))_(1,)->Add(Integer(5), Symbol(x), Symbol(y))_(1, 1)</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M189.812,-148.807C207.002,-137.665 232.618,-121.062 251.993,-108.504\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"253.916,-111.429 260.403,-103.053 250.108,-105.555 253.916,-111.429\"/>\n",
"</g>\n",
"<!-- Symbol(x)_(1, 0, 0) -->\n",
"<g id=\"node7\" class=\"node\"><title>Symbol(x)_(1, 0, 0)</title>\n",
"<ellipse fill=\"none\" stroke=\"black\" cx=\"99\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"99\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">x</text>\n",
"</g>\n",
"<!-- Pow(Symbol(x), Integer(2))_(1, 0)->Symbol(x)_(1, 0, 0) -->\n",
"<g id=\"edge7\" class=\"edge\"><title>Pow(Symbol(x), Integer(2))_(1, 0)->Symbol(x)_(1, 0, 0)</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M156.43,-74.8345C146.25,-64.9376 132.476,-51.5462 120.969,-40.3591\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"123.405,-37.8461 113.796,-33.3847 118.526,-42.865 123.405,-37.8461\"/>\n",
"</g>\n",
"<!-- Integer(2)_(1, 0, 1) -->\n",
"<g id=\"node8\" class=\"node\"><title>Integer(2)_(1, 0, 1)</title>\n",
"<ellipse fill=\"none\" stroke=\"black\" cx=\"171\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"171\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">2</text>\n",
"</g>\n",
"<!-- Pow(Symbol(x), Integer(2))_(1, 0)->Integer(2)_(1, 0, 1) -->\n",
"<g id=\"edge8\" class=\"edge\"><title>Pow(Symbol(x), Integer(2))_(1, 0)->Integer(2)_(1, 0, 1)</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M171,-71.6966C171,-63.9827 171,-54.7125 171,-46.1124\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"174.5,-46.1043 171,-36.1043 167.5,-46.1044 174.5,-46.1043\"/>\n",
"</g>\n",
"<!-- Integer(5)_(1, 1, 0) -->\n",
"<g id=\"node10\" class=\"node\"><title>Integer(5)_(1, 1, 0)</title>\n",
"<ellipse fill=\"none\" stroke=\"black\" cx=\"243\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"243\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">5</text>\n",
"</g>\n",
"<!-- Add(Integer(5), Symbol(x), Symbol(y))_(1, 1)->Integer(5)_(1, 1, 0) -->\n",
"<g id=\"edge9\" class=\"edge\"><title>Add(Integer(5), Symbol(x), Symbol(y))_(1, 1)->Integer(5)_(1, 1, 0)</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M270.65,-72.7646C266.288,-64.2831 260.853,-53.7144 255.959,-44.1974\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"258.99,-42.4395 251.304,-35.1473 252.765,-45.6409 258.99,-42.4395\"/>\n",
"</g>\n",
"<!-- Symbol(x)_(1, 1, 1) -->\n",
"<g id=\"node11\" class=\"node\"><title>Symbol(x)_(1, 1, 1)</title>\n",
"<ellipse fill=\"none\" stroke=\"black\" cx=\"315\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"315\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">x</text>\n",
"</g>\n",
"<!-- Add(Integer(5), Symbol(x), Symbol(y))_(1, 1)->Symbol(x)_(1, 1, 1) -->\n",
"<g id=\"edge10\" class=\"edge\"><title>Add(Integer(5), Symbol(x), Symbol(y))_(1, 1)->Symbol(x)_(1, 1, 1)</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M287.35,-72.7646C291.712,-64.2831 297.147,-53.7144 302.041,-44.1974\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"305.235,-45.6409 306.696,-35.1473 299.01,-42.4395 305.235,-45.6409\"/>\n",
"</g>\n",
"<!-- Symbol(y)_(1, 1, 2) -->\n",
"<g id=\"node12\" class=\"node\"><title>Symbol(y)_(1, 1, 2)</title>\n",
"<ellipse fill=\"none\" stroke=\"black\" cx=\"387\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"387\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">y</text>\n",
"</g>\n",
"<!-- Add(Integer(5), Symbol(x), Symbol(y))_(1, 1)->Symbol(y)_(1, 1, 2) -->\n",
"<g id=\"edge11\" class=\"edge\"><title>Add(Integer(5), Symbol(x), Symbol(y))_(1, 1)->Symbol(y)_(1, 1, 2)</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M297.812,-76.8069C315.002,-65.6653 340.618,-49.0622 359.993,-36.5043\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"361.916,-39.4294 368.403,-31.0533 358.108,-33.5553 361.916,-39.4294\"/>\n",
"</g>\n",
"</g>\n",
"</svg>\n"
],
"text/plain": [
"<graphviz.files.Source at 0x7f72368cf1d0>"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ps.to_dot(expr, graph_style={'size': \"9.5,12.5\"} )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Programatically the children node type is acessible as ``expr.func`` and its children as ``expr.args``.\n",
"With these members a tree can be traversed and modified."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"sympy.core.add.Add"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"expr.func"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$$\\left ( x^{2}, \\quad x^{2} \\left(x + y + 5\\right)\\right )$$"
],
"text/plain": [
"⎛ 2 2 ⎞\n",
"⎝x , x ⋅(x + y + 5)⎠"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"expr.args"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Using *pystencils* \n",
"\n",
"\n",
"### Fields\n",
"\n",
"*pystencils* is a module to generate code for stencil operations. \n",
"One has to specify an update rule for each element of an array, with optional dependencies to neighbors.\n",
"This is done use pure *sympy* with one addition: **Fields**.\n",
"\n",
"Fields represent a multidimensional array, where some dimensions are considered *spatial*, and some as *index* dimensions. Spatial coordinates are given relative (i.e. one can specify \"the current cell\" and \"the left neighbor\") whereas index dimensions are used to index multiple values per cell."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [],
"source": [
"my_field = ps.Field.create_generic('f', spatial_dimensions=2, index_shape=(3,))\n",
"# or equivalently:\n",
"my_field = ps.fields(\"f(3) : double[2D]\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Neighbors are labeled according to points on a compass where the first coordinate is west/east, second coordinate north/south and third coordinate top/bottom. "
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAACkAAAAdBAMAAADFpVh+AAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEJl2IquJVETdZu8yu83OyatpAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABHUlEQVQoFaWQPUvEQBCGnxjMFyEGQbirTOEPEIurFzsL8UARxCZcZ3eNhVpcGktBEBtBPPAnWNgGW1GvsfcneF1KJ7vJyRI7B3beeZ9ZhmHAxHujlrwcWbY1Z21h6f/o6paiO+FwMu5Sp+rRpf63bHNhbSTGu4bth30bR8e3mU20W9n8A7JXClW/nViXE8kemKsNBvhFjU/kHWCuFuX+kI2afkKcNxuHBXPWavoEy2VD10ueSRQ4FYTS1Jf4UNzhTiGYw86Cptwgo/FmcLWgSgYGM04T+X/ZUplbEX9x3xfy1lK9QzDksd6u7sjVdlM3k6FRLlYiTPXVXqeMRilLhYa4Y6NGEmNA9pDwlZZznSWZItLWybRIan5p66b8AFnOOMJB1gZeAAAAAElFTkSuQmCC\n",
"text/latex": [
"$${{f}_{(1,0)}^{1}}$$"
],
"text/plain": [
"f_E__1"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"field_access = my_field[1, 0](1)\n",
"field_access"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The result of indexing a field is an instance of ``Field.Access``. This class is a subclass of a *sympy* Symbol and thus can be used whereever normal symbols can be used. It is just like a normal symbol with some additional information attached to it."
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"isinstance(field_access, sp.Symbol)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Building our first stencil kernel\n",
"\n",
"Lets start by building a simple filter kernel. We create a field representing an image, then define a edge detection filter on the third pixel component which is blue for an RGB image."
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [],
"source": [
"img_field = ps.Field.create_generic('img', \n",
" spatial_dimensions=2, # 2D image \n",
" index_dimensions=1) # multiple values per pixel: e.g. RGB"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$$\\left(- {{img}_{(-1,-1)}^{2}} w_{1} - {{img}_{(-1,0)}^{2}} w_{2} - {{img}_{(-1,1)}^{2}} w_{1} + {{img}_{(1,-1)}^{2}} w_{1} + {{img}_{(1,0)}^{2}} w_{2} - {{img}_{(1,1)}^{2}} w_{1}\\right)^{2}$$"
],
"text/plain": [
" \n",
"(-img_SW__2⋅w₁ - img_W__2⋅w₂ - img_NW__2⋅w₁ + img_SE__2⋅w₁ + img_E__2⋅w₂ - img\n",
"\n",
" 2\n",
"_NE__2⋅w₁) "
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"w1, w2 = sp.symbols(\"w_1 w_2\")\n",
"color = 2\n",
"sobel_x = (-w2 * img_field[-1,0](color) - w1 * img_field[-1,-1](color) - w1 * img_field[-1, +1](color) \\\n",
" +w2 * img_field[+1,0](color) + w1 * img_field[+1,-1](color) - w1 * img_field[+1, +1](color))**2\n",
"sobel_x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have mixed some standard *sympy* symbols into this expression to possibly give the different directions different weights. The complete expression is still a valid *sympy* expression, so all features of *sympy* work on it. Lets for example now fix one weight by substituting it with a constant."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$$\\left(- 0.5 {{img}_{(-1,-1)}^{2}} - {{img}_{(-1,0)}^{2}} w_{2} - 0.5 {{img}_{(-1,1)}^{2}} + 0.5 {{img}_{(1,-1)}^{2}} + {{img}_{(1,0)}^{2}} w_{2} - 0.5 {{img}_{(1,1)}^{2}}\\right)^{2}$$"
],
"text/plain": [
" \n",
"(-0.5⋅img_SW__2 - img_W__2⋅w₂ - 0.5⋅img_NW__2 + 0.5⋅img_SE__2 + img_E__2⋅w₂ - \n",
"\n",
" 2\n",
"0.5⋅img_NE__2) "
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sobel_x = sobel_x.subs(w1, 0.5)\n",
"sobel_x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now lets built an executable kernel out of it, which writes the result to a second field. Assignments are created using *pystencils* `Assignment` class, that gets the left- and right hand side of the assignment."
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$${{dst}_{(0,0)}} \\leftarrow \\left(- 0.5 {{img}_{(-1,-1)}^{2}} - {{img}_{(-1,0)}^{2}} w_{2} - 0.5 {{img}_{(-1,1)}^{2}} + 0.5 {{img}_{(1,-1)}^{2}} + {{img}_{(1,0)}^{2}} w_{2} - 0.5 {{img}_{(1,1)}^{2}}\\right)^{2}$$"
],
"text/plain": [
" \n",
"dst_C := (-0.5⋅img_SW__2 - img_W__2⋅w₂ - 0.5⋅img_NW__2 + 0.5⋅img_SE__2 + img_E\n",
"\n",
" 2\n",
"__2⋅w₂ - 0.5⋅img_NE__2) "
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dst_field = ps.fields('dst: [2D]' )\n",
"update_rule = ps.Assignment(dst_field[0,0], sobel_x)\n",
"update_rule"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we can see *pystencils* in action which creates a kernel for us."
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [],
"source": [
"from pystencils import create_kernel\n",
"ast = create_kernel(update_rule, cpu_openmp=False)\n",
"compiled_kernel = ast.compile()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This compiled kernel is now just an ordinary Python function. \n",
"Now lets grab an image to apply this filter to:"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1152x432 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import requests\n",
"import imageio\n",
"from io import BytesIO\n",
"\n",
"response = requests.get(\"https://www.python.org/static/img/python-logo.png\")\n",
"img = imageio.imread(BytesIO(response.content)).astype(np.double)\n",
"img /= img.max()\n",
"plt.imshow(img);"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 1152x432 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"filtered_image = np.zeros_like(img[..., 0])\n",
"# here we call the compiled stencil function\n",
"compiled_kernel(img=img, dst=filtered_image, w_2=0.5)\n",
"plt.imshow(filtered_image, cmap='gray');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Digging into *pystencils*\n",
"\n",
"On our way we have created an ``ast``-object. We can inspect this, to see what *pystencils* actually does."
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
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"<!-- Title: %3 Pages: 1 -->\n",
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" viewBox=\"0.00 0.00 684.00 227.95\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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" <span class=\"p\">{</span>\n",
" <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">fd_dst_00</span> <span class=\"o\">=</span> <span class=\"n\">ctr_0</span><span class=\"o\">*</span><span class=\"n\">fstride_dst0</span> <span class=\"o\">+</span> <span class=\"n\">fd_dst</span><span class=\"p\">;</span>\n",
" <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"k\">const</span> <span class=\"n\">fd_img_22_01</span> <span class=\"o\">=</span> <span class=\"n\">ctr_0</span><span class=\"o\">*</span><span class=\"n\">fstride_img0</span> <span class=\"o\">+</span> <span class=\"n\">fd_img_22</span> <span class=\"o\">+</span> <span class=\"n\">fstride_img0</span><span class=\"p\">;</span>\n",
" <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"k\">const</span> <span class=\"n\">fd_img_22_0m1</span> <span class=\"o\">=</span> <span class=\"n\">ctr_0</span><span class=\"o\">*</span><span class=\"n\">fstride_img0</span> <span class=\"o\">+</span> <span class=\"n\">fd_img_22</span> <span class=\"o\">-</span> <span class=\"n\">fstride_img0</span><span class=\"p\">;</span>\n",
" <span class=\"k\">for</span> <span class=\"p\">(</span><span class=\"kt\">int</span> <span class=\"n\">ctr_1</span> <span class=\"o\">=</span> <span class=\"mi\">1</span><span class=\"p\">;</span> <span class=\"n\">ctr_1</span> <span class=\"o\"><</span> <span class=\"n\">fshape_dst1</span> <span class=\"o\">-</span> <span class=\"mi\">1</span><span class=\"p\">;</span> <span class=\"n\">ctr_1</span> <span class=\"o\">+=</span> <span class=\"mi\">1</span><span class=\"p\">)</span>\n",
" <span class=\"p\">{</span>\n",
" <span class=\"n\">fd_dst_00</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_dst1</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"p\">((</span><span class=\"n\">w_2</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_01</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">w_2</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_01</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span> <span class=\"o\">+</span> <span class=\"n\">fstride_img1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span> <span class=\"o\">+</span> <span class=\"n\">fstride_img1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span> <span class=\"o\">-</span> <span class=\"n\">fstride_img1</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_01</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span> <span class=\"o\">-</span> <span class=\"n\">fstride_img1</span><span class=\"p\">])</span><span class=\"o\">*</span><span class=\"p\">(</span><span class=\"n\">w_2</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_01</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">w_2</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_01</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span> <span class=\"o\">+</span> <span class=\"n\">fstride_img1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span> <span class=\"o\">+</span> <span class=\"n\">fstride_img1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span> <span class=\"o\">-</span> <span class=\"n\">fstride_img1</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_01</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span> <span class=\"o\">-</span> <span class=\"n\">fstride_img1</span><span class=\"p\">]));</span>\n",
" <span class=\"p\">}</span>\n",
" <span class=\"p\">}</span>\n",
"<span class=\"p\">}</span>\n",
"</pre></div>\n"
],
"text/plain": [
"FUNC_PREFIX void kernel(double * fd_dst, double * const fd_img, int64_t const * fshape_dst, int64_t const * fstride_dst, int64_t const * fstride_img, double w_2)\n",
"{\n",
" const int64_t fshape_dst0 = fshape_dst[0];\n",
" const int64_t fshape_dst1 = fshape_dst[1];\n",
" const int64_t fstride_dst0 = fstride_dst[0];\n",
" const int64_t fstride_img2 = fstride_img[2];\n",
" double * const fd_img_22 = fd_img + 2*fstride_img2;\n",
" const int64_t fstride_img0 = fstride_img[0];\n",
" const int64_t fstride_img1 = fstride_img[1];\n",
" const int64_t fstride_dst1 = fstride_dst[1];\n",
" for (int ctr_0 = 1; ctr_0 < fshape_dst0 - 1; ctr_0 += 1)\n",
" {\n",
" double * fd_dst_00 = ctr_0*fstride_dst0 + fd_dst;\n",
" double * const fd_img_22_01 = ctr_0*fstride_img0 + fd_img_22 + fstride_img0;\n",
" double * const fd_img_22_0m1 = ctr_0*fstride_img0 + fd_img_22 - fstride_img0;\n",
" for (int ctr_1 = 1; ctr_1 < fshape_dst1 - 1; ctr_1 += 1)\n",
" {\n",
" fd_dst_00[ctr_1*fstride_dst1] = ((w_2*fd_img_22_01[ctr_1*fstride_img1] - w_2*fd_img_22_0m1[ctr_1*fstride_img1] - 0.5*fd_img_22_01[ctr_1*fstride_img1 + fstride_img1] - 0.5*fd_img_22_0m1[ctr_1*fstride_img1 + fstride_img1] - 0.5*fd_img_22_0m1[ctr_1*fstride_img1 - fstride_img1] + 0.5*fd_img_22_01[ctr_1*fstride_img1 - fstride_img1])*(w_2*fd_img_22_01[ctr_1*fstride_img1] - w_2*fd_img_22_0m1[ctr_1*fstride_img1] - 0.5*fd_img_22_01[ctr_1*fstride_img1 + fstride_img1] - 0.5*fd_img_22_0m1[ctr_1*fstride_img1 + fstride_img1] - 0.5*fd_img_22_0m1[ctr_1*fstride_img1 - fstride_img1] + 0.5*fd_img_22_01[ctr_1*fstride_img1 - fstride_img1]));\n",
" }\n",
" }\n",
"}"
]
},
"execution_count": 33,
"metadata": {},
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}
],
"source": [
"ps.show_code(ast)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Behind the scenes this code is compiled into a shared library and made available as a Python function. Before compiling this function we can modify the AST object, for example to parallelize it with OpenMP."
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
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"<div class=\"highlight\"><pre><span></span><span class=\"n\">FUNC_PREFIX</span> <span class=\"kt\">void</span> <span class=\"nf\">kernel</span><span class=\"p\">(</span><span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">fd_dst</span><span class=\"p\">,</span> <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"k\">const</span> <span class=\"n\">fd_img</span><span class=\"p\">,</span> <span class=\"kt\">int64_t</span> <span class=\"k\">const</span> <span class=\"o\">*</span> <span class=\"n\">fshape_dst</span><span class=\"p\">,</span> <span class=\"kt\">int64_t</span> <span class=\"k\">const</span> <span class=\"o\">*</span> <span class=\"n\">fstride_dst</span><span class=\"p\">,</span> <span class=\"kt\">int64_t</span> <span class=\"k\">const</span> <span class=\"o\">*</span> <span class=\"n\">fstride_img</span><span class=\"p\">,</span> <span class=\"kt\">double</span> <span class=\"n\">w_2</span><span class=\"p\">)</span>\n",
"<span class=\"p\">{</span>\n",
" <span class=\"cp\">#pragma omp parallel num_threads(2)</span>\n",
" <span class=\"p\">{</span>\n",
" <span class=\"k\">const</span> <span class=\"kt\">int64_t</span> <span class=\"n\">fshape_dst0</span> <span class=\"o\">=</span> <span class=\"n\">fshape_dst</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">];</span>\n",
" <span class=\"k\">const</span> <span class=\"kt\">int64_t</span> <span class=\"n\">fshape_dst1</span> <span class=\"o\">=</span> <span class=\"n\">fshape_dst</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">];</span>\n",
" <span class=\"k\">const</span> <span class=\"kt\">int64_t</span> <span class=\"n\">fstride_dst0</span> <span class=\"o\">=</span> <span class=\"n\">fstride_dst</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">];</span>\n",
" <span class=\"k\">const</span> <span class=\"kt\">int64_t</span> <span class=\"n\">fstride_img2</span> <span class=\"o\">=</span> <span class=\"n\">fstride_img</span><span class=\"p\">[</span><span class=\"mi\">2</span><span class=\"p\">];</span>\n",
" <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"k\">const</span> <span class=\"n\">fd_img_22</span> <span class=\"o\">=</span> <span class=\"n\">fd_img</span> <span class=\"o\">+</span> <span class=\"mi\">2</span><span class=\"o\">*</span><span class=\"n\">fstride_img2</span><span class=\"p\">;</span>\n",
" <span class=\"k\">const</span> <span class=\"kt\">int64_t</span> <span class=\"n\">fstride_img0</span> <span class=\"o\">=</span> <span class=\"n\">fstride_img</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">];</span>\n",
" <span class=\"k\">const</span> <span class=\"kt\">int64_t</span> <span class=\"n\">fstride_img1</span> <span class=\"o\">=</span> <span class=\"n\">fstride_img</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">];</span>\n",
" <span class=\"k\">const</span> <span class=\"kt\">int64_t</span> <span class=\"n\">fstride_dst1</span> <span class=\"o\">=</span> <span class=\"n\">fstride_dst</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">];</span>\n",
" <span class=\"cp\">#pragma omp for schedule(static)</span>\n",
" <span class=\"k\">for</span> <span class=\"p\">(</span><span class=\"kt\">int</span> <span class=\"n\">ctr_0</span> <span class=\"o\">=</span> <span class=\"mi\">1</span><span class=\"p\">;</span> <span class=\"n\">ctr_0</span> <span class=\"o\"><</span> <span class=\"n\">fshape_dst0</span> <span class=\"o\">-</span> <span class=\"mi\">1</span><span class=\"p\">;</span> <span class=\"n\">ctr_0</span> <span class=\"o\">+=</span> <span class=\"mi\">1</span><span class=\"p\">)</span>\n",
" <span class=\"p\">{</span>\n",
" <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">fd_dst_00</span> <span class=\"o\">=</span> <span class=\"n\">ctr_0</span><span class=\"o\">*</span><span class=\"n\">fstride_dst0</span> <span class=\"o\">+</span> <span class=\"n\">fd_dst</span><span class=\"p\">;</span>\n",
" <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"k\">const</span> <span class=\"n\">fd_img_22_01</span> <span class=\"o\">=</span> <span class=\"n\">ctr_0</span><span class=\"o\">*</span><span class=\"n\">fstride_img0</span> <span class=\"o\">+</span> <span class=\"n\">fd_img_22</span> <span class=\"o\">+</span> <span class=\"n\">fstride_img0</span><span class=\"p\">;</span>\n",
" <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"k\">const</span> <span class=\"n\">fd_img_22_0m1</span> <span class=\"o\">=</span> <span class=\"n\">ctr_0</span><span class=\"o\">*</span><span class=\"n\">fstride_img0</span> <span class=\"o\">+</span> <span class=\"n\">fd_img_22</span> <span class=\"o\">-</span> <span class=\"n\">fstride_img0</span><span class=\"p\">;</span>\n",
" <span class=\"k\">for</span> <span class=\"p\">(</span><span class=\"kt\">int</span> <span class=\"n\">ctr_1</span> <span class=\"o\">=</span> <span class=\"mi\">1</span><span class=\"p\">;</span> <span class=\"n\">ctr_1</span> <span class=\"o\"><</span> <span class=\"n\">fshape_dst1</span> <span class=\"o\">-</span> <span class=\"mi\">1</span><span class=\"p\">;</span> <span class=\"n\">ctr_1</span> <span class=\"o\">+=</span> <span class=\"mi\">1</span><span class=\"p\">)</span>\n",
" <span class=\"p\">{</span>\n",
" <span class=\"n\">fd_dst_00</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_dst1</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"p\">((</span><span class=\"n\">w_2</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_01</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">w_2</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_01</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span> <span class=\"o\">+</span> <span class=\"n\">fstride_img1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span> <span class=\"o\">+</span> <span class=\"n\">fstride_img1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span> <span class=\"o\">-</span> <span class=\"n\">fstride_img1</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_01</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span> <span class=\"o\">-</span> <span class=\"n\">fstride_img1</span><span class=\"p\">])</span><span class=\"o\">*</span><span class=\"p\">(</span><span class=\"n\">w_2</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_01</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">w_2</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_01</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span> <span class=\"o\">+</span> <span class=\"n\">fstride_img1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span> <span class=\"o\">+</span> <span class=\"n\">fstride_img1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span> <span class=\"o\">-</span> <span class=\"n\">fstride_img1</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">fd_img_22_01</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"o\">*</span><span class=\"n\">fstride_img1</span> <span class=\"o\">-</span> <span class=\"n\">fstride_img1</span><span class=\"p\">]));</span>\n",
" <span class=\"p\">}</span>\n",
" <span class=\"p\">}</span>\n",
" <span class=\"p\">}</span>\n",
"<span class=\"p\">}</span>\n",
"</pre></div>\n"
],
"text/plain": [
"FUNC_PREFIX void kernel(double * fd_dst, double * const fd_img, int64_t const * fshape_dst, int64_t const * fstride_dst, int64_t const * fstride_img, double w_2)\n",
"{\n",
" #pragma omp parallel num_threads(2)\n",
" {\n",
" const int64_t fshape_dst0 = fshape_dst[0];\n",
" const int64_t fshape_dst1 = fshape_dst[1];\n",
" const int64_t fstride_dst0 = fstride_dst[0];\n",
" const int64_t fstride_img2 = fstride_img[2];\n",
" double * const fd_img_22 = fd_img + 2*fstride_img2;\n",
" const int64_t fstride_img0 = fstride_img[0];\n",
" const int64_t fstride_img1 = fstride_img[1];\n",
" const int64_t fstride_dst1 = fstride_dst[1];\n",
" #pragma omp for schedule(static)\n",
" for (int ctr_0 = 1; ctr_0 < fshape_dst0 - 1; ctr_0 += 1)\n",
" {\n",
" double * fd_dst_00 = ctr_0*fstride_dst0 + fd_dst;\n",
" double * const fd_img_22_01 = ctr_0*fstride_img0 + fd_img_22 + fstride_img0;\n",
" double * const fd_img_22_0m1 = ctr_0*fstride_img0 + fd_img_22 - fstride_img0;\n",
" for (int ctr_1 = 1; ctr_1 < fshape_dst1 - 1; ctr_1 += 1)\n",
" {\n",
" fd_dst_00[ctr_1*fstride_dst1] = ((w_2*fd_img_22_01[ctr_1*fstride_img1] - w_2*fd_img_22_0m1[ctr_1*fstride_img1] - 0.5*fd_img_22_01[ctr_1*fstride_img1 + fstride_img1] - 0.5*fd_img_22_0m1[ctr_1*fstride_img1 + fstride_img1] - 0.5*fd_img_22_0m1[ctr_1*fstride_img1 - fstride_img1] + 0.5*fd_img_22_01[ctr_1*fstride_img1 - fstride_img1])*(w_2*fd_img_22_01[ctr_1*fstride_img1] - w_2*fd_img_22_0m1[ctr_1*fstride_img1] - 0.5*fd_img_22_01[ctr_1*fstride_img1 + fstride_img1] - 0.5*fd_img_22_0m1[ctr_1*fstride_img1 + fstride_img1] - 0.5*fd_img_22_0m1[ctr_1*fstride_img1 - fstride_img1] + 0.5*fd_img_22_01[ctr_1*fstride_img1 - fstride_img1]));\n",
" }\n",
" }\n",
" }\n",
"}"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ast = ps.create_kernel(update_rule)\n",
"ps.cpu.add_openmp(ast, num_threads=2)\n",
"ps.show_code(ast)"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"False"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"loops = list(ast.atoms(ps.astnodes.LoopOverCoordinate))\n",
"l1 = loops[0]\n",
"l1.prefix_lines.append(\"#pragma someting\")\n",
"l1.is_outermost_loop"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Fixed array sizes\n",
"\n",
"Since we already know the arrays to which the kernel should be applied, we can \n",
"create *Field* objects with fixed size, based on a numpy array:"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
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"<div class=\"highlight\"><pre><span></span><span class=\"n\">FUNC_PREFIX</span> <span class=\"kt\">void</span> <span class=\"nf\">kernel</span><span class=\"p\">(</span><span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"k\">const</span> <span class=\"n\">fd_I</span><span class=\"p\">,</span> <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">fd_dst</span><span class=\"p\">)</span>\n",
"<span class=\"p\">{</span>\n",
" <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"k\">const</span> <span class=\"n\">fd_I_21</span> <span class=\"o\">=</span> <span class=\"n\">fd_I</span> <span class=\"o\">+</span> <span class=\"mi\">1</span><span class=\"p\">;</span>\n",
" <span class=\"k\">for</span> <span class=\"p\">(</span><span class=\"kt\">int</span> <span class=\"n\">ctr_0</span> <span class=\"o\">=</span> <span class=\"mi\">1</span><span class=\"p\">;</span> <span class=\"n\">ctr_0</span> <span class=\"o\"><</span> <span class=\"mi\">81</span><span class=\"p\">;</span> <span class=\"n\">ctr_0</span> <span class=\"o\">+=</span> <span class=\"mi\">1</span><span class=\"p\">)</span>\n",
" <span class=\"p\">{</span>\n",
" <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">fd_dst_00</span> <span class=\"o\">=</span> <span class=\"mi\">290</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">+</span> <span class=\"n\">fd_dst</span><span class=\"p\">;</span>\n",
" <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"k\">const</span> <span class=\"n\">fd_I_21_01</span> <span class=\"o\">=</span> <span class=\"mi\">1160</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">+</span> <span class=\"n\">fd_I_21</span> <span class=\"o\">+</span> <span class=\"mi\">1160</span><span class=\"p\">;</span>\n",
" <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"k\">const</span> <span class=\"n\">fd_I_21_0m1</span> <span class=\"o\">=</span> <span class=\"mi\">1160</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">+</span> <span class=\"n\">fd_I_21</span> <span class=\"o\">-</span> <span class=\"mi\">1160</span><span class=\"p\">;</span>\n",
" <span class=\"k\">for</span> <span class=\"p\">(</span><span class=\"kt\">int</span> <span class=\"n\">ctr_1</span> <span class=\"o\">=</span> <span class=\"mi\">1</span><span class=\"p\">;</span> <span class=\"n\">ctr_1</span> <span class=\"o\"><</span> <span class=\"mi\">289</span><span class=\"p\">;</span> <span class=\"n\">ctr_1</span> <span class=\"o\">+=</span> <span class=\"mi\">1</span><span class=\"p\">)</span>\n",
" <span class=\"p\">{</span>\n",
" <span class=\"n\">fd_dst_00</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"o\">-</span><span class=\"mi\">2</span><span class=\"o\">*</span><span class=\"n\">fd_I_21_0m1</span><span class=\"p\">[</span><span class=\"mi\">4</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"mi\">2</span><span class=\"o\">*</span><span class=\"n\">fd_I_21_01</span><span class=\"p\">[</span><span class=\"mi\">4</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">fd_I_21_01</span><span class=\"p\">[</span><span class=\"mi\">4</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">+</span> <span class=\"mi\">4</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">fd_I_21_01</span><span class=\"p\">[</span><span class=\"mi\">4</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">-</span> <span class=\"mi\">4</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">fd_I_21_0m1</span><span class=\"p\">[</span><span class=\"mi\">4</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">+</span> <span class=\"mi\">4</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">fd_I_21_0m1</span><span class=\"p\">[</span><span class=\"mi\">4</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">-</span> <span class=\"mi\">4</span><span class=\"p\">];</span>\n",
" <span class=\"p\">}</span>\n",
" <span class=\"p\">}</span>\n",
"<span class=\"p\">}</span>\n",
"</pre></div>\n"
],
"text/plain": [
"FUNC_PREFIX void kernel(double * const fd_I, double * fd_dst)\n",
"{\n",
" double * const fd_I_21 = fd_I + 1;\n",
" for (int ctr_0 = 1; ctr_0 < 81; ctr_0 += 1)\n",
" {\n",
" double * fd_dst_00 = 290*ctr_0 + fd_dst;\n",
" double * const fd_I_21_01 = 1160*ctr_0 + fd_I_21 + 1160;\n",
" double * const fd_I_21_0m1 = 1160*ctr_0 + fd_I_21 - 1160;\n",
" for (int ctr_1 = 1; ctr_1 < 289; ctr_1 += 1)\n",
" {\n",
" fd_dst_00[ctr_1] = -2*fd_I_21_0m1[4*ctr_1] + 2*fd_I_21_01[4*ctr_1] - fd_I_21_01[4*ctr_1 + 4] + fd_I_21_01[4*ctr_1 - 4] - fd_I_21_0m1[4*ctr_1 + 4] - fd_I_21_0m1[4*ctr_1 - 4];\n",
" }\n",
" }\n",
"}"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"img_field = ps.Field.create_from_numpy_array('I', img.astype(np.double), index_dimensions=1)\n",
"dst_field = ps.Field.create_from_numpy_array('dst', filtered_image, index_dimensions=0)\n",
"\n",
"sobel_x = -2 * img_field[-1,0](1) - img_field[-1,-1](1) - img_field[-1, +1](1) \\\n",
" +2 * img_field[+1,0](1) + img_field[+1,-1](1) - img_field[+1, +1](1)\n",
"update_rule = ps.Assignment(dst_field[0,0], sobel_x)\n",
"\n",
"ast = create_kernel([update_rule])\n",
"ps.show_code(ast)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Compare this code to the version above. In this code the loop bounds and array offsets are constants, which usually leads to faster kernels."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Running on GPU\n",
"\n",
"If you have a CUDA enabled graphics card and [pycuda](https://mathema.tician.de/software/pycuda/) installed, *pystencils* can run your kernel on the GPU as well. You can find more details about this in the GPU tutorial."
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [],
"source": [
"gpu_ast = create_kernel([update_rule], target='gpu', gpu_indexing=ps.gpucuda.indexing.BlockIndexing, \n",
" gpu_indexing_params={'blockSize': (8,8,4)})"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
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"<div class=\"highlight\"><pre><span></span><span class=\"n\">FUNC_PREFIX</span> <span class=\"kt\">void</span> <span class=\"nf\">kernel</span><span class=\"p\">(</span><span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"k\">const</span> <span class=\"n\">fd_I</span><span class=\"p\">,</span> <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">fd_dst</span><span class=\"p\">)</span>\n",
"<span class=\"p\">{</span>\n",
" <span class=\"k\">if</span> <span class=\"p\">(</span><span class=\"mi\">16</span><span class=\"o\">*</span><span class=\"n\">blockIdx</span><span class=\"p\">.</span><span class=\"n\">x</span> <span class=\"o\">+</span> <span class=\"n\">threadIdx</span><span class=\"p\">.</span><span class=\"n\">x</span> <span class=\"o\">+</span> <span class=\"mi\">1</span> <span class=\"o\"><</span> <span class=\"mi\">81</span> <span class=\"o\">&&</span> <span class=\"mi\">16</span><span class=\"o\">*</span><span class=\"n\">blockIdx</span><span class=\"p\">.</span><span class=\"n\">y</span> <span class=\"o\">+</span> <span class=\"n\">threadIdx</span><span class=\"p\">.</span><span class=\"n\">y</span> <span class=\"o\">+</span> <span class=\"mi\">1</span> <span class=\"o\"><</span> <span class=\"mi\">289</span><span class=\"p\">)</span>\n",
" <span class=\"p\">{</span>\n",
" <span class=\"k\">const</span> <span class=\"kt\">int64_t</span> <span class=\"n\">ctr_0</span> <span class=\"o\">=</span> <span class=\"mi\">16</span><span class=\"o\">*</span><span class=\"n\">blockIdx</span><span class=\"p\">.</span><span class=\"n\">x</span> <span class=\"o\">+</span> <span class=\"n\">threadIdx</span><span class=\"p\">.</span><span class=\"n\">x</span> <span class=\"o\">+</span> <span class=\"mi\">1</span><span class=\"p\">;</span>\n",
" <span class=\"k\">const</span> <span class=\"kt\">int64_t</span> <span class=\"n\">ctr_1</span> <span class=\"o\">=</span> <span class=\"mi\">16</span><span class=\"o\">*</span><span class=\"n\">blockIdx</span><span class=\"p\">.</span><span class=\"n\">y</span> <span class=\"o\">+</span> <span class=\"n\">threadIdx</span><span class=\"p\">.</span><span class=\"n\">y</span> <span class=\"o\">+</span> <span class=\"mi\">1</span><span class=\"p\">;</span>\n",
" <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">fd_dst_10</span> <span class=\"o\">=</span> <span class=\"n\">ctr_1</span> <span class=\"o\">+</span> <span class=\"n\">fd_dst</span><span class=\"p\">;</span>\n",
" <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"k\">const</span> <span class=\"n\">fd_I_11_21</span> <span class=\"o\">=</span> <span class=\"mi\">4</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">+</span> <span class=\"n\">fd_I</span> <span class=\"o\">+</span> <span class=\"mi\">5</span><span class=\"p\">;</span>\n",
" <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"k\">const</span> <span class=\"n\">fd_I_1m1_21</span> <span class=\"o\">=</span> <span class=\"mi\">4</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">+</span> <span class=\"n\">fd_I</span> <span class=\"o\">-</span> <span class=\"mi\">3</span><span class=\"p\">;</span>\n",
" <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"k\">const</span> <span class=\"n\">fd_I_10_21</span> <span class=\"o\">=</span> <span class=\"mi\">4</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">+</span> <span class=\"n\">fd_I</span> <span class=\"o\">+</span> <span class=\"mi\">1</span><span class=\"p\">;</span>\n",
" <span class=\"n\">fd_dst_10</span><span class=\"p\">[</span><span class=\"mi\">290</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"o\">-</span><span class=\"mi\">2</span><span class=\"o\">*</span><span class=\"n\">fd_I_10_21</span><span class=\"p\">[</span><span class=\"mi\">1160</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">-</span> <span class=\"mi\">1160</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"mi\">2</span><span class=\"o\">*</span><span class=\"n\">fd_I_10_21</span><span class=\"p\">[</span><span class=\"mi\">1160</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">+</span> <span class=\"mi\">1160</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">fd_I_11_21</span><span class=\"p\">[</span><span class=\"mi\">1160</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">+</span> <span class=\"mi\">1160</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">fd_I_11_21</span><span class=\"p\">[</span><span class=\"mi\">1160</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">-</span> <span class=\"mi\">1160</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">fd_I_1m1_21</span><span class=\"p\">[</span><span class=\"mi\">1160</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">+</span> <span class=\"mi\">1160</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">fd_I_1m1_21</span><span class=\"p\">[</span><span class=\"mi\">1160</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">-</span> <span class=\"mi\">1160</span><span class=\"p\">];</span>\n",
" <span class=\"p\">}</span> \n",
"<span class=\"p\">}</span>\n",
"</pre></div>\n"
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"FUNC_PREFIX void kernel(double * const fd_I, double * fd_dst)\n",
"{\n",
" if (16*blockIdx.x + threadIdx.x + 1 < 81 && 16*blockIdx.y + threadIdx.y + 1 < 289)\n",
" {\n",
" const int64_t ctr_0 = 16*blockIdx.x + threadIdx.x + 1;\n",
" const int64_t ctr_1 = 16*blockIdx.y + threadIdx.y + 1;\n",
" double * fd_dst_10 = ctr_1 + fd_dst;\n",
" double * const fd_I_11_21 = 4*ctr_1 + fd_I + 5;\n",
" double * const fd_I_1m1_21 = 4*ctr_1 + fd_I - 3;\n",
" double * const fd_I_10_21 = 4*ctr_1 + fd_I + 1;\n",
" fd_dst_10[290*ctr_0] = -2*fd_I_10_21[1160*ctr_0 - 1160] + 2*fd_I_10_21[1160*ctr_0 + 1160] - fd_I_11_21[1160*ctr_0 + 1160] - fd_I_11_21[1160*ctr_0 - 1160] + fd_I_1m1_21[1160*ctr_0 + 1160] - fd_I_1m1_21[1160*ctr_0 - 1160];\n",
" } \n",
"}"
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