{ "cells": [ { "cell_type": "markdown", "id": "396b2347", "metadata": {}, "source": [ "# Alternating direction algorithms for l1 problems in compressive sensing\n", "\n", "We provide a port of [YALL1 basic](http://yall1.blogs.rice.edu/) package. This is built on top of JAX and can be used to solve the following $\\ell_1$ minimization problems.\n", "\n", "The basis pursuit problem\n", "$$\n", "\\tag{BP}\n", "{\\min}_{x} \\| W x\\|_{w,1} \\; \\text{s.t.} \\, A x = b\n", "$$\n", "\n", "The L1/L2 minimization or basis pursuit denoising problem\n", "$$\n", "\\tag{L1/L2}\n", "{\\min}_{x} \\| W x\\|_{w,1} + \\frac{1}{2\\rho}\\| A x - b \\|_2^2 \n", "$$\n", "\n", "The L1 minimization problem with L2 constraints\n", "$$\n", "\\tag{L1/L2con}\n", "{\\min}_{x} \\| W x\\|_{w,1} \\; \\text{s.t.} \\, \\| A x - b \\|_2 \\leq \\delta\n", "$$\n", "\n", "We also support corresponding non-negative counter-parts.\n", "\n", "The nonnegative basis pursuit problem\n", "$$\n", "\\tag{BP+}\n", "{\\min}_{x} \\| W x\\|_{w,1} \\; \\text{s.t.} \\, A x = b \\, \\, \\text{and} \\, x \\succeq 0\n", "$$\n", "\n", "The nonnegative L1/L2 minimization or basis pursuit denoising problem\n", "$$\n", "\\tag{L1/L2+}\n", "{\\min}_{x} \\| W x\\|_{w,1} + \\frac{1}{2\\rho}\\| A x - b \\|_2^2 \\; \\text{s.t.} \\, x \\succeq 0\n", "$$\n", "\n", "The nonnegative L1 minimization problem with L2 constraints\n", "$$\n", "\\tag{L1/L2con+}\n", "{\\min}_{x} \\| W x\\|_{w,1} \\; \\text{s.t.} \\, \\| A x - b \\|_2 \\leq \\delta \\, \\, \\text{and} \\, x \\succeq 0\n", "$$\n", "\n", "\n", "In the above, $W$ is a sparsifying basis s.t. $Wx = \\alpha$ is a sparse representation of $x$ in $W$ given by \n", "$\\alpha = W^T x$. For simple examples, we can assume $W=I$ is the identity basis.\n", "\n", "The $\\| \\cdot \\|_{w,1}$ is the weighted L1 (semi-) norm defined as\n", "\n", "$$\n", "\\|x \\|_{w,1} = \\sum_{i=1}^n w_i |x_i| \n", "$$\n", "\n", "for a given non-negative weight vector $w$. In the simplest case, we assume $w=1$ reducing it to the famous $\\ell_1$ norm." ] }, { "cell_type": "markdown", "id": "ea3b67b4", "metadata": {}, "source": [ "Import relevant libraries" ] }, { "cell_type": "code", "execution_count": 1, "id": "31fba328", "metadata": {}, "outputs": [], "source": [ "from jax.config import config\n", "config.update(\"jax_enable_x64\", True)\n", "import jax\n", "import jax.numpy as jnp\n", "import numpy as np\n", "from jax import random\n", "from jax import jit, grad, vmap\n", "norm = jnp.linalg.norm" ] }, { "cell_type": "code", "execution_count": 2, "id": "8388b4ab", "metadata": {}, "outputs": [], "source": [ "import cr.sparse as crs\n", "import cr.sparse.dict as crdict\n", "import cr.sparse.data as crdata\n", "import cr.sparse.lop as lop\n", "from cr.sparse.cvx.adm import yall1" ] }, { "cell_type": "code", "execution_count": 3, "id": "db11fc41", "metadata": {}, "outputs": [], "source": [ "import matplotlib as mpl\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "id": "43487df4", "metadata": {}, "source": [ "Setup a problem with a random sensing matrix with orthonormal rows" ] }, { "cell_type": "code", "execution_count": 4, "id": "01e91bef", "metadata": {}, "outputs": [], "source": [ "N = 1000\n", "M = 300\n", "K = 50" ] }, { "cell_type": "code", "execution_count": 5, "id": "cd6e376c", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n" ] } ], "source": [ "key = random.PRNGKey(0)\n", "key1, key2, key3, key4 = random.split(key, 4)" ] }, { "cell_type": "code", "execution_count": 6, "id": "031fcbbd", "metadata": {}, "outputs": [], "source": [ "A = crdict.random_orthonormal_rows(key1, M, N)" ] }, { "cell_type": "code", "execution_count": 7, "id": "1598f000", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray(True, dtype=bool)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "crs.has_orthogonal_rows(A)" ] }, { "cell_type": "code", "execution_count": 8, "id": "6cf7860f", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.imshow(A, extent=[0, 2, 0, 1])\n", "plt.gray()\n", "plt.colorbar()\n", "plt.title(r'$A$');" ] }, { "cell_type": "code", "execution_count": 9, "id": "b7e7bed5", "metadata": {}, "outputs": [], "source": [ "x, omega = crdata.sparse_normal_representations(key2, N, K, 1)\n", "x = jnp.squeeze(x)" ] }, { "cell_type": "code", "execution_count": 10, "id": "7ffaa82a", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.stem(x, markerfmt='.');" ] }, { "cell_type": "code", "execution_count": 11, "id": "40263464", "metadata": {}, "outputs": [], "source": [ "# Convert A into a linear operator\n", "A = lop.matrix(A)" ] }, { "cell_type": "markdown", "id": "3a3e2478", "metadata": {}, "source": [ "## Standard sparse recovery problems for compressive sensing" ] }, { "cell_type": "markdown", "id": "605599aa", "metadata": {}, "source": [ "### Basis pursuit\n", "\n", "The simple form of basis pursuit problem is:\n", "\n", "$$\n", "{\\min}_{x} \\| x\\|_{1} \\; \\text{s.t.} \\, A x = b\n", "$$" ] }, { "cell_type": "code", "execution_count": 12, "id": "c766e6d2", "metadata": {}, "outputs": [], "source": [ "# Compute the measurements\n", "b0 = A.times(x)" ] }, { "cell_type": "code", "execution_count": 13, "id": "d3bf7d8f", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.stem(b0, markerfmt='.');" ] }, { "cell_type": "code", "execution_count": 14, "id": "2bf9d32b", "metadata": {}, "outputs": [], "source": [ "sol = yall1.solve(A, b0)" ] }, { "cell_type": "code", "execution_count": 15, "id": "fc597a44", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(30, 61, 32)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "int(sol.iterations), int(sol.n_times), int(sol.n_trans)" ] }, { "cell_type": "code", "execution_count": 16, "id": "5e586040", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray(0.01208655, dtype=float64)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "norm(sol.x-x)/norm(x)" ] }, { "cell_type": "code", "execution_count": 17, "id": "f8836b56", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.subplot(211)\n", "plt.title('original')\n", "plt.stem(x, markerfmt='.', linefmt='gray');\n", "plt.subplot(212)\n", "plt.stem(sol.x, markerfmt='.');\n", "plt.title('reconstruction');" ] }, { "cell_type": "code", "execution_count": 18, "id": "16270f3f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4.77 ms ± 47.5 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" ] } ], "source": [ "%timeit yall1.solve(A, b0).x.block_until_ready()" ] }, { "cell_type": "markdown", "id": "23974b52", "metadata": {}, "source": [ "### Basis pursuit denoising\n", "\n", "The simple form of L1-L2 unconstrained minimization or basis pursuit denoising is:\n", "$$\n", "{\\min}_{x} \\| x\\|_{1} + \\frac{1}{2\\rho}\\| A x - b \\|_2^2\n", "$$" ] }, { "cell_type": "code", "execution_count": 19, "id": "b1270d4c", "metadata": {}, "outputs": [], "source": [ "sigma = 0.01\n", "noise = sigma * random.normal(key3, (M,))" ] }, { "cell_type": "code", "execution_count": 20, "id": "c3065949", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray(27.34386008, dtype=float64)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "crs.snr(b0, noise)" ] }, { "cell_type": "code", "execution_count": 21, "id": "d2d58557", "metadata": {}, "outputs": [], "source": [ "b = b0 + noise" ] }, { "cell_type": "code", "execution_count": 22, "id": "8c90be7f", "metadata": {}, "outputs": [], "source": [ "sol = yall1.solve(A, b, rho=0.01)" ] }, { "cell_type": "code", "execution_count": 23, "id": "980e9825", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(28, 57, 30)" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "int(sol.iterations), int(sol.n_times), int(sol.n_trans)" ] }, { "cell_type": "code", "execution_count": 24, "id": "7bae3054", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray(0.05690205, dtype=float64)" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "norm(sol.x-x)/norm(x)" ] }, { "cell_type": "code", "execution_count": 25, "id": "a2e8af4a", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.subplot(211)\n", "plt.title('original')\n", "plt.stem(x, markerfmt='.', linefmt='gray');\n", "plt.subplot(212)\n", "plt.stem(sol.x, markerfmt='.');\n", "plt.title('reconstruction');" ] }, { "cell_type": "code", "execution_count": 26, "id": "6fd039c5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4.47 ms ± 49 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" ] } ], "source": [ "%timeit yall1.solve(A, b, rho=0.01).x.block_until_ready()" ] }, { "cell_type": "markdown", "id": "a2f52a39", "metadata": {}, "source": [ "### Basis pursuit with inequality constraints\n", "\n", "The simple form of L1 minimization with L2 constraints or basis pursuit with inequality constraints is:\n", "$$\n", "{\\min}_{x} \\| x\\|_{1} \\; \\text{s.t.} \\, \\| A x - b \\|_2 \\leq \\delta\n", "$$" ] }, { "cell_type": "code", "execution_count": 27, "id": "2b2e838d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.16467458902598495" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta = float(norm(noise))\n", "delta" ] }, { "cell_type": "code", "execution_count": 28, "id": "cd5079d3", "metadata": {}, "outputs": [], "source": [ "sol = yall1.solve(A, b, delta=delta)" ] }, { "cell_type": "code", "execution_count": 29, "id": "057dd93e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(26, 53, 28)" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "int(sol.iterations), int(sol.n_times), int(sol.n_trans)" ] }, { "cell_type": "code", "execution_count": 30, "id": "c1fd9105", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray(0.05584753, dtype=float64)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "norm(sol.x-x)/norm(x)" ] }, { "cell_type": "code", "execution_count": 31, "id": "ab383505", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.subplot(211)\n", "plt.title('original')\n", "plt.stem(x, markerfmt='.', linefmt='gray');\n", "plt.subplot(212)\n", "plt.stem(sol.x, markerfmt='.');\n", "plt.title('reconstruction');" ] }, { "cell_type": "code", "execution_count": 32, "id": "ae5cfd22", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4.65 ms ± 23.1 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" ] } ], "source": [ "%timeit yall1.solve(A, b, delta=delta).x.block_until_ready()" ] }, { "cell_type": "markdown", "id": "f34bb1f0", "metadata": {}, "source": [ "## Non-negative counterparts\n", "\n", "In this case, the signal $x$ with the sparse representation $\\alpha = W x$ has only non-negative entries. i.e. if an entry in $x$ is non-zero, it is positive. This is typical for images.\n", "\n", "Let us construct a sparse representation with non-negative entries." ] }, { "cell_type": "code", "execution_count": 33, "id": "884c67dc", "metadata": {}, "outputs": [], "source": [ "xp = jnp.abs(x)" ] }, { "cell_type": "code", "execution_count": 34, "id": "eba13f67", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.stem(xp, markerfmt='.');" ] }, { "cell_type": "markdown", "id": "688e4b8d", "metadata": {}, "source": [ "### Non-negative basis pursuit\n", "\n", "The simple form of basis pursuit for non-negative $x$ is:\n", "$$\n", "{\\min}_{x} \\| x\\|_{1} \\; \\text{s.t.} \\, A x = b \\, \\, \\text{and} \\, x \\succeq 0\n", "$$" ] }, { "cell_type": "code", "execution_count": 35, "id": "62e8a9c7", "metadata": {}, "outputs": [], "source": [ "b0p = A.times(xp)" ] }, { "cell_type": "code", "execution_count": 36, "id": "92248c67", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.stem(b0p, markerfmt='.');" ] }, { "cell_type": "code", "execution_count": 37, "id": "cd1267e9", "metadata": {}, "outputs": [], "source": [ "sol = yall1.solve(A, b0p, nonneg=True)" ] }, { "cell_type": "code", "execution_count": 38, "id": "e3dc6b07", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(36, 73, 38)" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "int(sol.iterations), int(sol.n_times), int(sol.n_trans)" ] }, { "cell_type": "code", "execution_count": 39, "id": "a3cde3ab", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray(0.01095682, dtype=float64)" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "norm(sol.x-xp)/norm(xp)" ] }, { "cell_type": "code", "execution_count": 40, "id": "4006db0d", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.subplot(211)\n", "plt.title('original')\n", "plt.stem(xp, markerfmt='.', linefmt='gray');\n", "plt.subplot(212)\n", "plt.stem(sol.x, markerfmt='.');\n", "plt.title('reconstruction');" ] }, { "cell_type": "code", "execution_count": 41, "id": "d9250905", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5.27 ms ± 72.9 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" ] } ], "source": [ "%timeit yall1.solve(A, b0p, nonneg=True).x.block_until_ready()" ] }, { "cell_type": "markdown", "id": "eca778f8", "metadata": {}, "source": [ "### Non-negative basis pursuit denoising\n", "\n", "The simple form of L1-L2 unconstrained minimization with non-negative $x$ is:\n", "$$\n", "{\\min}_{x} \\| x\\|_{1} + \\frac{1}{2\\rho}\\| A x - b \\|_2^2 \\; \\text{s.t.} \\, x \\succeq 0\n", "$$" ] }, { "cell_type": "code", "execution_count": 42, "id": "750c4934", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray(27.43652935, dtype=float64)" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "crs.snr(b0p, noise)" ] }, { "cell_type": "code", "execution_count": 43, "id": "9e8bbd6a", "metadata": {}, "outputs": [], "source": [ "bp = b0p + noise" ] }, { "cell_type": "code", "execution_count": 44, "id": "0246ec43", "metadata": {}, "outputs": [], "source": [ "sol = yall1.solve(A, bp, nonneg=True, rho=0.01)" ] }, { "cell_type": "code", "execution_count": 45, "id": "9739aa03", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(28, 57, 30)" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "int(sol.iterations), int(sol.n_times), int(sol.n_trans)" ] }, { "cell_type": "code", "execution_count": 46, "id": "11d9a1e8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray(0.04551954, dtype=float64)" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "norm(sol.x-xp)/norm(xp)" ] }, { "cell_type": "code", "execution_count": 47, "id": "06d3342b", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.subplot(211)\n", "plt.title('original')\n", "plt.stem(xp, markerfmt='.', linefmt='gray');\n", "plt.subplot(212)\n", "plt.stem(sol.x, markerfmt='.');\n", "plt.title('reconstruction');" ] }, { "cell_type": "code", "execution_count": 48, "id": "360e9861", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4.58 ms ± 85.4 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" ] } ], "source": [ "%timeit yall1.solve(A, bp, nonneg=True, rho=0.01).x.block_until_ready()" ] }, { "cell_type": "markdown", "id": "6e229a3b", "metadata": {}, "source": [ "### Non-negative basis pursuit with inequality constraints\n", "\n", "$$\n", "{\\min}_{x} \\| x\\|_{1} \\; \\text{s.t.} \\, \\| A x - b \\|_2 \\leq \\delta \\, \\, \\text{and} \\, x \\succeq 0\n", "$$" ] }, { "cell_type": "code", "execution_count": 49, "id": "9ef19b83", "metadata": {}, "outputs": [], "source": [ "sol = yall1.solve(A, bp, delta=delta)" ] }, { "cell_type": "code", "execution_count": 50, "id": "7eafaefb", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(24, 49, 26)" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "int(sol.iterations), int(sol.n_times), int(sol.n_trans)" ] }, { "cell_type": "code", "execution_count": 51, "id": "36e568ec", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray(0.05724303, dtype=float64)" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "norm(sol.x-xp)/norm(xp)" ] }, { "cell_type": "code", "execution_count": 52, "id": "a4e11f7a", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.subplot(211)\n", "plt.title('original')\n", "plt.stem(xp, markerfmt='.', linefmt='gray');\n", "plt.subplot(212)\n", "plt.stem(sol.x, markerfmt='.');\n", "plt.title('reconstruction');" ] }, { "cell_type": "code", "execution_count": 53, "id": "62c8f30f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4.35 ms ± 17 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" ] } ], "source": [ "%timeit yall1.solve(A, bp, delta=delta).x.block_until_ready()" ] }, { "cell_type": "code", "execution_count": null, "id": "6e0088e5", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.9.4" } }, "nbformat": 4, "nbformat_minor": 5 }