{ "cells": [ { "cell_type": "markdown", "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "source": [ "# MatRepr\n", "\n", "Render sparse and dense matrices to HTML and Latex, with a Jupyter extension." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2023-09-12T03:27:08.569908Z", "start_time": "2023-09-12T03:27:08.562850Z" }, "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [], "source": [ "import scipy.sparse\n", "import numpy as np\n", "np.random.seed(123)\n", "\n", "# so matrepr can be imported from the source tree.\n", "import sys\n", "sys.path.insert(0, '..')\n", "\n", "from matrepr import mdisplay, mprint" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "source": [ "### Load MatRepr Jupyter extension" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2023-09-12T03:27:08.571818Z", "start_time": "2023-09-12T03:27:08.566180Z" }, "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [], "source": [ "%load_ext matrepr" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "source": [ "## SciPy sparse matrix" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2023-09-12T03:27:08.627283Z", "start_time": "2023-09-12T03:27:08.570110Z" }, "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "text/html": [ "
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6×6, 18 'float64' elements, coo
012345
00.6110.43370.43090.4264
10.31230.3230.0921
20.72240.50180.2937
30.4258
40.6240.9442
50.22830.36180.6310.89340.4937
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" ], "text/plain": [ "<6x6 sparse matrix of type ''\n", "\twith 18 stored elements in COOrdinate format>" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "scipy.sparse.random(6, 6, density=0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2D NumPy array" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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10×10, 100 'float64' elements, array
0123456789
00.120.320.410.870.250.480.990.520.610.12
10.830.600.550.340.300.420.680.880.510.67
20.590.620.670.840.080.760.240.190.570.10
30.890.630.720.020.590.560.160.150.700.32
40.690.550.390.930.840.360.040.300.400.70
51.000.360.760.590.690.150.400.240.340.51
60.670.110.130.320.660.850.550.850.380.32
70.350.170.830.340.550.580.520.000.990.91
80.210.290.520.900.980.260.560.810.390.73
90.160.600.870.980.080.430.200.450.550.09
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" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mat = np.random.random((10, 10))\n", "mdisplay(mat, floatfmt=\".2f\")" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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500×25, 12500 'float64' elements, array
0123456789101112131415161718192021222324
00.300.930.570.460.750.740.050.710.840.170.780.290.310.670.110.660.890.700.440.440.770.570.080.580.81
10.340.930.750.570.750.080.860.820.910.130.080.140.400.420.560.120.200.810.470.810.010.550.930.580.21
20.720.380.670.030.640.030.740.470.120.540.070.651.000.770.570.100.700.660.050.790.520.430.790.410.48
30.180.320.850.190.420.990.240.920.920.090.460.500.310.050.240.100.240.810.890.040.300.980.540.630.01
40.480.990.380.100.460.960.340.800.800.210.440.720.410.190.970.650.870.030.270.500.070.990.240.370.21
50.110.230.300.630.280.360.010.370.530.160.600.290.630.030.890.020.130.780.050.710.970.870.710.960.43
60.870.360.930.150.940.830.850.120.600.020.720.010.080.230.880.360.540.570.230.570.660.300.420.450.93
⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮
4930.210.030.820.020.410.690.870.630.340.320.190.330.090.990.750.720.190.150.660.590.770.930.560.680.63
4940.710.820.710.600.610.620.700.820.050.460.310.280.360.010.520.690.260.570.050.460.660.620.370.610.14
4950.620.210.610.300.660.290.670.240.090.410.960.800.210.790.100.180.160.990.960.570.560.430.910.090.36
4960.610.910.760.410.810.580.540.150.150.080.430.510.250.920.100.660.610.460.870.740.340.260.800.130.75
4970.210.260.870.690.470.020.150.310.370.460.070.100.070.150.950.120.140.150.730.330.720.440.040.670.11
4980.470.390.520.490.710.580.140.980.350.830.180.030.930.870.980.080.740.360.700.060.890.520.500.150.95
4990.030.320.400.760.430.120.920.490.230.230.290.330.230.570.230.480.410.540.050.340.920.850.700.360.52
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" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mat = np.random.random((500, 25))\n", "mdisplay(mat, floatfmt=\".2f\", max_rows=15, max_cols=25)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "source": [ "## 2D NumPy array with row and column labels" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2023-09-12T03:27:08.648723Z", "start_time": "2023-09-12T03:27:08.623744Z" }, "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "text/html": [ "
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BostonBuffaloChicagoClevelandDallasDenver
Boston--45798363918151991
Buffalo457--53619213871561
Chicago983536--3449311050
Cleveland639192344--12051369
Dallas181513879311205--801
Denver1991156110501369801--
\n", "
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cities = [\"Boston\", \"Buffalo\", \"Chicago\", \"Cleveland\", \"Dallas\", \"Denver\"]\n", "distances = np.array([\n", " [None, 457, 983, 639, 1815, 1991],\n", " [457, None, 536, 192, 1387, 1561],\n", " [983, 536, None, 344, 931, 1050],\n", " [639, 192, 344, None, 1205, 1369],\n", " [1815, 1387, 931, 1205, None, 801],\n", " [1991, 1561, 1050, 1369, 801, None],\n", "])\n", "\n", "mdisplay(distances, title=None, row_labels=cities, col_labels=cities, fill_value=\"--\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1D arrays and vectors" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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length=1000, 1000 'float64' elements, array
0123456993994995996997998999
0.17080.73650.41660.87640.9640.78090.1369⋯0.77040.16080.8160.0083670.28580.64230.8979
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" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "vec = np.random.random((1000,))\n", "mdisplay(vec)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.1708, 0.7365, 0.4166, 0.8764, 0.651, ..., 0.008367, 0.2858, 0.6423, 0.8979]\n" ] } ], "source": [ "mprint(vec, indices=False, title=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sparse N-dimensional Tensors\n", "\n", "Sparse multidimensional tensors are presented as a list of tuples." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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shape=(1000,10,10,10,10), 1234000 'float64' elements, coo, fill_value=0.0, read-only, 56.5MiB
01234val
0000010.8415
1000160.6691
2000210.6162
3000220.09681
4000470.4684
⋮⋮⋮⋮⋮⋮
123399599999670.9675
123399699999700.2194
123399799999770.188
123399899999850.03111
123399999999990.1041
\n", "
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import sparse\n", "tensor_4d = sparse.random((1000, 10, 10, 10, 10), density=0.1234)\n", "mdisplay(tensor_4d)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " 0 1 2 3 4 val\n", " 0 ( 0, 0, 0, 0, 1, 0.8415 )\n", " 1 ( 0, 0, 0, 1, 6, 0.6691 )\n", " 2 ( 0, 0, 0, 2, 1, 0.6162 )\n", " 3 ( 0, 0, 0, 2, 2, 0.09681)\n", " 4 ( 0, 0, 0, 4, 7, 0.4684 )\n", " ( :, :, :, :, :, : )\n", "1233995 (999, 9, 9, 6, 7, 0.9675 )\n", "1233996 (999, 9, 9, 7, 0, 0.2194 )\n", "1233997 (999, 9, 9, 7, 7, 0.188 )\n", "1233998 (999, 9, 9, 8, 5, 0.03111)\n", "1233999 (999, 9, 9, 9, 9, 0.1041 )\n" ] } ], "source": [ "mprint(tensor_4d)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Dense N-dimensional Numpy Arrays" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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shape=(3,3,3,3), 81 'float64' elements, array
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0.270.860.96
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0.410.470.98
0.810.250.24
0.620.130.24
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0.360.010.45
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0.470.130.87
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0.740.850.36
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0.260.870.67
0.540.380.86
0.530.090.30
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0.640.931.00
0.880.650.65
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0.530.220.78
0.250.440.88
0.500.490.87
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0.800.260.22
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0.750.800.65
1.000.220.78
0.820.110.03
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" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dense_4d = np.random.random((3, 3, 3, 3))\n", "mdisplay(dense_4d, floatfmt=\".2f\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Graph Adjacency Matrix with Edge and Vertex Weights" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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V1V2V3V4V5V6V7
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" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import graphblas as gb\n", "\n", "edges = gb.Matrix.from_coo(\n", " [3, 0, 3, 5, 6, 0, 6, 1, 6, 2, 4, 1],\n", " [0, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6],\n", " [3, 2, 3, 1, 5, 3, 7, 8, 3, 1, 7, 4],\n", " nrows=7, ncols=7\n", ")\n", "vertices = gb.Vector.from_coo([range(7)], [f\"V{i+1}\" for i in range(7)], size=7)\n", "\n", "mdisplay(edges, row_labels=vertices, col_labels=vertices, title=False)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "source": [ "## Nested matrices" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2023-09-12T03:27:08.649007Z", "start_time": "2023-09-12T03:27:08.624126Z" }, "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "text/html": [ "
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2×2, 4 elements, list
01
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0.510.92
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12
34
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0.32
0.56
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" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# You may mix types if the datastructure allows, as a Python list does\n", "mat = [\n", " [scipy.sparse.random(2, 2, density=0.8), [[1, 2], [3, 4]]],\n", " [np.array([[1, 2], [3, 4]]), scipy.sparse.random(2, 2, density=0.6)]\n", "]\n", "\n", "mdisplay(mat, floatfmt=\".2f\")" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "source": [ "## Large matrices" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "is_executing": true, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "text/html": [ "
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100000000×100000000, 100000000 'float64' elements, csr
012345699999993999999949999999599999996999999979999999899999999
01⋯
11⋯
21⋯
31⋯
41⋯
⋮⋮⋮⋮⋮⋮⋮⋱⋮⋮⋮⋮⋮⋮⋮
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99999999⋯1
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" ], "text/plain": [ "<100000000x100000000 sparse matrix of type ''\n", "\twith 100000000 stored elements in Compressed Sparse Row format>" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "scipy.sparse.eye(100_000_000, format=\"csr\")" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "ExecuteTime": { "start_time": "2023-09-12T03:27:08.624194Z" }, "collapsed": false, "is_executing": true, "jupyter": { "outputs_hidden": false } }, "outputs": [], "source": [ "r = scipy.sparse.random(10000, 10000, density=0.23456789, format=\"csr\")" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "is_executing": true, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "text/html": [ "
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10000×10000, 23456789 'float64' elements, csr
01234569993999499959996999799989999
00.52480.26460.038480.591⋯0.81660.89470.3634
10.62120.1660.7899⋯0.6492
20.6416⋯
3⋯0.71530.9322
4⋯0.1142
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99950.9442⋯0.29250.4961
99960.4630.37820.07874⋯0.6619
99970.28670.2823⋯0.31
99980.21220.4611⋯0.63780.2867
99990.23330.4093⋯
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" ], "text/plain": [ "<10000x10000 sparse matrix of type ''\n", "\twith 23456789 stored elements in Compressed Sparse Row format>" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "is_executing": true, "jupyter": { "outputs_hidden": false } }, "source": [ "## Duplicate entries\n", "\n", "Some sparse formats allow multiple values with the same indices." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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3×3, 6 'float64' elements, coo
012
01
12.1
2.2
23.1
3.2
3.3
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" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "row = [0, 1, 1, 2, 2, 2]\n", "col = [0, 1, 1, 2, 2, 2]\n", "val = [1, 2.1, 2.2, 3.1, 3.2, 3.3]\n", "dupes = scipy.sparse.coo_array((val, (row, col)), shape=(3, 3))\n", "\n", "mdisplay(dupes)" ] }, { "cell_type": "code", "execution_count": null, "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": "3.11.5" } }, "nbformat": 4, "nbformat_minor": 4 }