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| <div class="title">Matrix Operations<div class="ingroups"><a class="el" href="group__grp__datatrans.html">Data Types and Transforms</a> » <a class="el" href="group__grp__arraysmatrix.html">Arrays and Matrices</a></div></div> </div> |
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| <div class="contents"> |
| <div class="toc"><b>Contents</b> </p><ul> |
| <li class="level1"> |
| <a href="#description">Description</a> </li> |
| <li class="level1"> |
| <a href="#operations">Matrix Operations</a> </li> |
| <li class="level1"> |
| <a href="#glossary">Glossary of arguments</a> </li> |
| <li class="level1"> |
| <a href="#examples">Examples</a> </li> |
| <li class="level1"> |
| <a href="#related">Related Topics</a> </li> |
| </ul> |
| </div><p><a class="anchor" id="description"></a>This module provides a set of basic matrix operations for matrices that are too big to fit in memory. We provide two storage formats for a matrix:</p> |
| <ul> |
| <li>Dense: The matrix is represented as a distributed collection of 1-D arrays. An example 3x10 matrix would be the below table: <pre> |
| row_id | row_vec |
| --------+------------------------- |
| 1 | {9,6,5,8,5,6,6,3,10,8} |
| 2 | {8,2,2,6,6,10,2,1,9,9} |
| 3 | {3,9,9,9,8,6,3,9,5,6} |
| </pre></li> |
| </ul> |
| <p>A '<em>row</em>' column (called as <em>row_id</em> above) provides the row number of each row and a '<em>val</em>' column (called as <em>row_vec</em> above) provides each row as an array. <b>The <em>row</em> column should contain a series of integers from 1 to <em>N</em> with no duplicates, where <em>N</em> is the row dimensionality</b>.</p> |
| <ul> |
| <li>Sparse: The matrix is represented using the row and column indices for each non-zero entry of the matrix. This representation is useful for sparse matrices, containing multiple zero elements. Given below is an example of a sparse 4x7 matrix with just 6 out of 28 entries being non-zero. The dimensionality of the matrix is inferred using the max value in <em>row</em> and <em>col</em> columns. Note the last entry is included (even though it is 0) to provide the dimensionality of the matrix (indicating that the 4th row and 7th column contain all zeros). <pre> |
| row_id | col_id | value |
| --------+--------+------- |
| 1 | 1 | 9 |
| 1 | 5 | 6 |
| 1 | 6 | 6 |
| 2 | 1 | 8 |
| 3 | 1 | 3 |
| 3 | 2 | 9 |
| 4 | 7 | 0 |
| (6 rows) |
| </pre></li> |
| </ul> |
| <p><b>For sparse matrices, the <em>row</em> and <em>col</em> columns together should not contain a duplicate entry and the <em>val</em> column should be of scalar (non-array) data type</b>. <br /> |
| For comparison, the dense representation of this matrix is shown below. Note the dimensionality of the dense matrix is 4 x 7 since the max value of <em>row</em> and <em>col</em> is 4 and 7 respectively, leading to all zeros in the last row and last column.   </p><pre> |
| row_id | row_vec |
| --------+------------------------- |
| 1 | {9,0,0,0,6,6,0} |
| 2 | {8,0,0,0,0,0,0} |
| 3 | {3,9,0,0,0,0,0} |
| 4 | {0,0,0,0,0,0,0} |
| </pre><dl class="section note"><dt>Note</dt><dd>The functions below support several numeric types (unless otherwise noted) including SMALLINT, INTEGER, BIGINT, DOUBLE PRECISION (FLOAT8), NUMERIC (internally casted into FLOAT8, loss of precision can happen).</dd></dl> |
| <p><a class="anchor" id="operations"></a></p><dl class="section user"><dt>Matrix Operations</dt><dd></dd></dl> |
| <p>Given below are the supported matrix operations. The meaning of the arguments and other terms are common to all functions and provided at the end of the list as a glossary.</p> |
| <ul> |
| <li><b>Representation</b> <pre class="syntax"> |
| -- Convert to sparse representation |
|   <b>matrix_sparsify</b>( matrix_in, in_args, matrix_out, out_args) |
|   |
| -- Convert to dense representation |
|   <b>matrix_densify</b>( matrix_in, in_args, matrix_out, out_args) |
| </pre></li> |
| <li><b>Mathematical operations</b> <pre class="syntax"> |
| -- Matrix transposition |
|   <b>matrix_trans</b>( matrix_in, in_args, matrix_out, out_args) |
|   |
| -- Matrix addition |
|   <b>matrix_add</b>( matrix_a, a_args, matrix_b, b_args, matrix_out, out_args) |
|   |
| -- Matrix subtraction |
|   <b>matrix_sub</b>( matrix_a, a_args, matrix_b, b_args, matrix_out, out_args) |
|   |
| -- Matrix multiplication |
|   <b>matrix_mult</b>( matrix_a, a_args, matrix_b, b_args, matrix_out, out_args) |
|   |
| -- Element-wise matrix multiplication |
|   <b>matrix_elem_mult</b>( matrix_a, a_args, matrix_b, b_args, matrix_out, out_args) |
|   |
| -- Multiply matrix with scalar. |
|   <b>matrix_scalar_mult</b>( matrix_in, in_args, scalar, matrix_out, out_args) |
|   |
| -- Multiply matrix with vector. |
|   <b>matrix_vec_mult</b>( matrix_in, in_args, vector) |
| </pre></li> |
| <li><b>Extraction/visitor methods</b> <pre class="syntax"> |
| -- Extract row from matrix given row index |
|   <b>matrix_extract_row</b>( matrix_in, in_args, index) |
|   |
| -- Extract column from matrix given column index |
|   <b>matrix_extract_col</b>( matrix_in, in_args, index) |
| </pre></li> |
| <li><b>Reduction operations (aggregate across specific dimension)</b> <pre class="syntax"> |
| -- Get max value along dim. Also returns corresponding index if <em>fetch_index</em> = True |
|   <b>matrix_max</b>( matrix_in, in_args, dim, matrix_out, fetch_index) |
|   |
| -- Get min value along dim. Also returns corresponding index if <em>fetch_index</em> = True |
|   <b>matrix_min</b>( matrix_in, in_args, dim, matrix_out, fetch_index) |
|   |
| -- Get sum value along dimension from matrix. |
|   <b>matrix_sum</b>( matrix_in, in_args, dim) |
|   |
| -- Get mean value along dimension from matrix. |
|   <b>matrix_mean</b>( matrix_in, in_args, dim) |
| </pre></li> |
| </ul> |
| <p><a class="anchor" id="glossary"></a><b>Glossary</b> </p> |
| <p>The table below provides a glossary of the terms used in the matrix operations.</p> |
| <dl class="arglist"> |
| <dt>matrix_in, matrix_a, matrix_b </dt> |
| <dd><p class="startdd">TEXT. Name of the table containing the input matrix.</p><ul> |
| <li>For functions accepting one matrix, <em>matrix_in</em> denotes the input matrix.</li> |
| <li>For functions accepting two matrices, <em>matrix_a</em> denotes the first matrix and <em>matrix_b</em> denotes the second matrix. These two matrices can <b>independently</b> be in either dense or sparse format. </li> |
| </ul> |
| <p class="enddd"></p> |
| </dd> |
| <dt>in_args, a_args, b_args </dt> |
| <dd><p class="startdd">TEXT. A comma-delimited string containing multiple named arguments of the form "name=value". This argument is used as a container for multiple parameters related to a single matrix.</p> |
| <p>The following parameters are supported for this string argument: </p><table class="output"> |
| <tr> |
| <th>row </th><td>(Default: 'row_num') Name of the column containing row index of the matrix. </td></tr> |
| <tr> |
| <th>col </th><td>(Default: 'col_num') Name of the column containing column index of the matrix. </td></tr> |
| <tr> |
| <th>val </th><td>(Default: 'val') Name of the column containing the entries of the matrix. </td></tr> |
| <tr> |
| <th>trans </th><td>(Default: False) Boolean flag to indicate if the matrix should be transposed before the operation. This is currently functional only for <em>matrix_mult</em>. </td></tr> |
| </table> |
| <p>For example, the string argument with default values will be 'row=row_num, col=col_num, val=val, trans=False'. Alternatively, the string argument can be set to <em>NULL</em> or be blank ('') if default values are to be used. </p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>matrix_out </dt> |
| <dd><p class="startdd">TEXT. Name of the table to store the result matrix. </p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>out_args </dt> |
| <dd><p class="startdd">TEXT. A comma-delimited string containing named arguments of the form "name=value". This is an <b>optional parameter</b> and the default value is set as follows:</p><ul> |
| <li>For functions with one input matrix, default = <em>in_args</em></li> |
| <li>For functions with two input matrices, default = <em>a_args</em>.</li> |
| </ul> |
| <p>The following parameters are supported for this string argument: </p><table class="output"> |
| <tr> |
| <th>row </th><td>Name of the column containing row index of the matrix. </td></tr> |
| <tr> |
| <th>col </th><td>Name of the column containing column index of the matrix. </td></tr> |
| <tr> |
| <th>val </th><td>Name of the column containing the entries of the matrix. </td></tr> |
| </table> |
| <p class="enddd"></p> |
| </dd> |
| <dt>index </dt> |
| <dd><p class="startdd">INTEGER. An integer representing a row or column index of the matrix. Should be a number from 1 to <em>N</em>, where <em>N</em> is the maximum size of the dimension.</p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>dim </dt> |
| <dd><p class="startdd">INTEGER. Should either be 1 or 2. This value indicates the dimension to operate along for the reduction/aggregation operations. <b>The value of <em>dim</em> should be interpreted as the dimension to be flattened i.e. whose length reduces to 1 in the result.</b> <br /> |
| For <em>dim=1</em>, a reduction function on an <em>NxM</em> matrix operates on successive elements in each column and returns a single vector with <em>M</em> elements (i.e. matrix with just 1 row and <em>M</em> columns). <br /> |
| For <em>dim=2</em>, a single vector is returned with <em>N</em> elements (i.e. matrix with just 1 column and <em>N</em> rows). </p> |
| <p class="enddd"></p> |
| </dd> |
| </dl> |
| <p><a class="anchor" id="examples"></a></p><dl class="section user"><dt>Examples</dt><dd></dd></dl> |
| <ul> |
| <li>Create some random data tables in dense format. <pre class="syntax"> |
| CREATE TABLE "mat_A" ( |
| row_id integer, |
| row_vec integer[] |
| ); |
| INSERT INTO "mat_A" (row_id, row_vec) VALUES (1, '{9,6,5,8,5,6,6,3,10,8}'); |
| INSERT INTO "mat_A" (row_id, row_vec) VALUES (2, '{8,2,2,6,6,10,2,1,9,9}'); |
| INSERT INTO "mat_A" (row_id, row_vec) VALUES (3, '{3,9,9,9,8,6,3,9,5,6}'); |
| INSERT INTO "mat_A" (row_id, row_vec) VALUES (4, '{6,4,2,2,2,7,8,8,0,7}'); |
| INSERT INTO "mat_A" (row_id, row_vec) VALUES (5, '{6,8,9,9,4,6,9,5,7,7}'); |
| INSERT INTO "mat_A" (row_id, row_vec) VALUES (6, '{4,10,7,3,9,5,9,2,3,4}'); |
| INSERT INTO "mat_A" (row_id, row_vec) VALUES (7, '{8,10,7,10,1,9,7,9,8,7}'); |
| INSERT INTO "mat_A" (row_id, row_vec) VALUES (8, '{7,4,5,6,2,8,1,1,4,8}'); |
| INSERT INTO "mat_A" (row_id, row_vec) VALUES (9, '{8,8,8,5,2,6,9,1,8,3}'); |
| INSERT INTO "mat_A" (row_id, row_vec) VALUES (10, '{4,6,3,2,6,4,1,2,3,8}'); |
| |
| CREATE TABLE "mat_B" ( |
| row_id integer, |
| vector integer[] |
| ); |
| INSERT INTO "mat_B" (row_id, vector) VALUES (1, '{9,10,2,4,6,5,3,7,5,6}'); |
| INSERT INTO "mat_B" (row_id, vector) VALUES (2, '{5,3,5,2,8,6,9,7,7,6}'); |
| INSERT INTO "mat_B" (row_id, vector) VALUES (3, '{0,1,2,3,2,7,7,3,10,1}'); |
| INSERT INTO "mat_B" (row_id, vector) VALUES (4, '{2,9,0,4,3,6,8,6,3,4}'); |
| INSERT INTO "mat_B" (row_id, vector) VALUES (5, '{3,8,7,7,0,5,3,9,2,10}'); |
| INSERT INTO "mat_B" (row_id, vector) VALUES (6, '{5,3,1,7,6,3,5,3,6,4}'); |
| INSERT INTO "mat_B" (row_id, vector) VALUES (7, '{4,8,4,4,2,7,10,0,3,3}'); |
| INSERT INTO "mat_B" (row_id, vector) VALUES (8, '{4,6,0,1,3,1,6,6,9,8}'); |
| INSERT INTO "mat_B" (row_id, vector) VALUES (9, '{6,5,1,7,2,7,10,6,0,6}'); |
| INSERT INTO "mat_B" (row_id, vector) VALUES (10, '{1,4,4,4,8,5,2,8,5,5}'); |
| </pre></li> |
| <li>Transpose a matrix <pre class="syntax"> |
| SELECT madlib.matrix_trans('"mat_B"', 'row=row_id, val=vector', |
| 'mat_r'); |
| SELECT * FROM mat_r ORDER BY row_id; |
| </pre> <pre class="result"> |
| -- Note the result matrix has inherited 'vector' as the name of value column |
| row_id | vector |
| --------+------------------------- |
| 1 | {9,5,0,2,3,5,4,4,6,1} |
| 2 | {10,3,1,9,8,3,8,6,5,4} |
| 3 | {2,5,2,0,7,1,4,0,1,4} |
| 4 | {4,2,3,4,7,7,4,1,7,4} |
| 5 | {6,8,2,3,0,6,2,3,2,8} |
| 6 | {5,6,7,6,5,3,7,1,7,5} |
| 7 | {3,9,7,8,3,5,10,6,10,2} |
| 8 | {7,7,3,6,9,3,0,6,6,8} |
| 9 | {5,7,10,3,2,6,3,9,0,5} |
| 10 | {6,6,1,4,10,4,3,8,6,5} |
| (10 rows) |
| </pre></li> |
| <li>Add the two matrices <pre class="syntax"> |
| SELECT madlib.matrix_add('"mat_A"', 'row=row_id, val=row_vec', |
| '"mat_B"', 'row=row_id, val=vector', |
| 'mat_r', 'val=vector'); |
| SELECT * FROM mat_r ORDER BY row_id; |
| </pre> <pre class="result"> |
| row_id | vector |
| --------+------------------------------- |
| 1 | {18,16,7,12,11,11,9,10,15,14} |
| 2 | {13,5,7,8,14,16,11,8,16,15} |
| 3 | {3,10,11,12,10,13,10,12,15,7} |
| 4 | {8,13,2,6,5,13,16,14,3,11} |
| 5 | {9,16,16,16,4,11,12,14,9,17} |
| 6 | {9,13,8,10,15,8,14,5,9,8} |
| 7 | {12,18,11,14,3,16,17,9,11,10} |
| 8 | {11,10,5,7,5,9,7,7,13,16} |
| 9 | {14,13,9,12,4,13,19,7,8,9} |
| 10 | {5,10,7,6,14,9,3,10,8,13} |
| (10 rows) |
| </pre></li> |
| <li>Multiply the two matrices <pre class="syntax"> |
| DROP TABLE IF EXISTS mat_r; |
| SELECT madlib.matrix_mult('"mat_A"', 'row=row_id, val=row_vec', |
| '"mat_B"', 'row=row_id, val=vector, trans=true', |
| 'mat_r'); |
| SELECT * FROM mat_r ORDER BY row_id; |
| </pre> <pre class="result"> |
| row_id | row_vec |
| --------+------------------------------------------- |
| 1 | {380,373,251,283,341,303,302,309,323,281} |
| 2 | {318,318,222,221,269,259,236,249,264,248} |
| 3 | {382,366,216,300,397,276,277,270,313,338} |
| 4 | {275,284,154,244,279,183,226,215,295,204} |
| 5 | {381,392,258,319,394,298,342,302,360,300} |
| 6 | {321,333,189,276,278,232,300,236,281,250} |
| 7 | {443,411,282,365,456,318,360,338,406,330} |
| 8 | {267,240,150,186,270,194,210,184,233,193} |
| 9 | {322,328,234,264,291,245,317,253,291,219} |
| 10 | {246,221,109,173,222,164,167,185,181,189} |
| (10 rows) |
| </pre></li> |
| <li>Extract row and column from matrix given index <pre class="syntax"> |
| SELECT madlib.matrix_extract_row('"mat_A"', 'row=row_id, val=row_vec', 2) as row, |
| madlib.matrix_extract_col('"mat_A"', 'row=row_id, val=row_vec', 3) as col; |
| </pre> <pre class="result"> |
| row | col |
| ------------------------+----------------------- |
| {8,2,2,6,6,10,2,1,9,9} | {5,2,9,2,9,7,7,5,8,3} |
| (1 rows) |
| </pre></li> |
| <li>Get min and max values along a specific dimension as well as corresponding indicies. Note that <em>dim=2</em> implies that the min and max is computed on each row returning a column vector i.e. the column (dim=2) is flattened. <pre class="syntax"> |
| SELECT madlib.matrix_max('"mat_A"', 'row=row_id, val=row_vec', 2, 'mat_max_r', true), |
| madlib.matrix_min('"mat_A"', 'row=row_id, val=row_vec', 2, 'mat_min_r', true); |
| SELECT * from mat_max_r; |
| SELECT * from mat_min_r; |
| </pre> <pre class="result"> |
| index | max |
| -----------------------+--------------------------- |
| {8,5,1,6,2,1,1,5,6,9} | {10,10,9,8,9,10,10,8,9,8} |
| (1 rows) |
|   |
| index | min |
| -----------------------+----------------------- |
| {7,7,0,8,4,7,4,6,7,6} | {3,1,3,0,4,2,1,1,1,1} |
| (1 rows) |
| </pre></li> |
| <li>Element-wise multiplication between two matrices <pre class="syntax"> |
| SELECT madlib.matrix_elem_mult('"mat_A"', 'row=row_id, val=row_vec', |
| '"mat_B"', 'val=vector', |
| 'mat_r', 'val=vector'); |
| SELECT * FROM mat_r ORDER BY row_id; |
| </pre> <pre class="result"> |
| row_id | vector |
| --------+--------------------------------- |
| 1 | {81,60,10,32,30,30,18,21,50,48} |
| 2 | {40,6,10,12,48,60,18,7,63,54} |
| 3 | {0,9,18,27,16,42,21,27,50,6} |
| 4 | {12,36,0,8,6,42,64,48,0,28} |
| 5 | {18,64,63,63,0,30,27,45,14,70} |
| 6 | {20,30,7,21,54,15,45,6,18,16} |
| 7 | {32,80,28,40,2,63,70,0,24,21} |
| 8 | {28,24,0,6,6,8,6,6,36,64} |
| 9 | {48,40,8,35,4,42,90,6,0,18} |
| 10 | {4,24,12,8,48,20,2,16,15,40} |
| </pre></li> |
| <li>Get sum values along dimension. Sum is computed for each row (i.e. column is flattened since dim=2) <pre class="syntax"> |
| SELECT madlib.matrix_sum('"mat_A"', 'row=row_id, val=row_vec', 2); |
| </pre> <pre class="result"> |
| matrix_sum |
| --------------------------------- |
| {66,55,67,46,70,56,76,46,58,39} |
| (1 rows) |
| </pre></li> |
| <li>Multiply matrix with a scalar <pre class="syntax"> |
| DROP TABLE IF EXISTS mat_r; |
| SELECT madlib.matrix_scalar_mult('"mat_A"', 'row=row_id, val=row_vec', 3, 'mat_r'); |
| SELECT * FROM mat_r ORDER BY row_id; |
| </pre> <pre class="result"> |
| row_id | row_vec |
| --------+--------------------------------- |
| 0 | {27,18,15,24,15,18,18,9,30,24} |
| 1 | {24,6,6,18,18,30,6,3,27,27} |
| 2 | {9,27,27,27,24,18,9,27,15,18} |
| 3 | {18,12,6,6,6,21,24,24,0,21} |
| 4 | {18,24,27,27,12,18,27,15,21,21} |
| 5 | {12,30,21,9,27,15,27,6,9,12} |
| 6 | {24,30,21,30,3,27,21,27,24,21} |
| 7 | {21,12,15,18,6,24,3,3,12,24} |
| 8 | {24,24,24,15,6,18,27,3,24,9} |
| 9 | {12,18,9,6,18,12,3,6,9,24} |
| (10 rows) |
| </pre></li> |
| <li>Multiply matrix with a vector <pre class="syntax"> |
| SELECT madlib.matrix_vec_mult('"mat_A"', 'row=row_id, val=row_vec', |
| array[1,2,3,4,5,6,7,8,9,10]); |
| </pre> <pre class="result"> |
| matrix_vec_mult |
| ------------------------------------------- |
| {365,325,358,270,377,278,411,243,287,217} |
| (10 rows) |
| </pre></li> |
| <li><b>Examples with sparse representation</b>. The function calls are the same as before. <pre class="syntax"> |
| SELECT madlib.matrix_sparsify('"mat_B"', 'row=row_id, val=vector', |
| '"mat_B_sparse"', 'col=col_id, val=val'); |
| </pre></li> |
| <li>Create a matrix in sparse format. <pre class="syntax"> |
| CREATE TABLE "mat_A_sparse" ( |
| "rowNum" integer, |
| col_num integer, |
| entry integer |
| ); |
| INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (1, 1, 9); |
| INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (1, 2, 6); |
| INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (1, 7, 3); |
| INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (1, 8, 10); |
| INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (1, 9, 8); |
| INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (2, 1, 8); |
| INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (2, 2, 2); |
| INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (2, 3, 6); |
| INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (3, 5, 6); |
| INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (3, 6, 3); |
| INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (7, 1, 7); |
| INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (8, 2, 8); |
| INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (8, 3, 5); |
| INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (9, 1, 6); |
| INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (9, 2, 3); |
| INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (10, 10, 0); |
| </pre></li> |
| <li>Transpose a matrix in sparse format <pre class="syntax"> |
| -- Note the double quotes for '"rowNum"' required per PostgreSQL rules |
| SELECT madlib.matrix_trans('"mat_A_sparse"', 'row="rowNum", val=entry', |
| 'matrix_r_sparse'); |
| SELECT "rowNum", col_num, entry FROM matrix_r_sparse ORDER BY col_num; |
| </pre> <pre class="result"> |
| rowNum | col_num | entry |
| --------+---------+------- |
| 1 | 1 | 9 |
| 2 | 1 | 6 |
| 7 | 1 | 3 |
| 8 | 1 | 10 |
| 9 | 1 | 8 |
| 1 | 2 | 8 |
| 2 | 2 | 2 |
| 3 | 2 | 6 |
| 5 | 3 | 6 |
| 6 | 3 | 3 |
| 1 | 7 | 7 |
| 2 | 8 | 8 |
| 3 | 8 | 5 |
| 1 | 9 | 6 |
| 2 | 9 | 3 |
| 10 | 10 | 0 |
| (16 rows) |
| </pre></li> |
| <li>Add two sparse matrices <pre class="syntax"> |
| SELECT madlib.matrix_add('"mat_A_sparse"', 'row="rowNum", val=entry', |
| '"mat_B_sparse"', 'row=row_id, col=col_id, val=val', |
| 'matrix_r_sparse', 'col=col_out'); |
| SELECT madlib.matrix_densify('matrix_r_sparse', 'row="rowNum", col=col_out, val=entry', |
| 'matrix_r'); |
| SELECT * FROM matrix_r ORDER BY "rowNum"; |
| </pre> <pre class="result"> |
| rowNum | entry |
| --------+--------------------------- |
| 1 | {18,16,2,4,6,5,6,17,13,6} |
| 2 | {13,5,11,2,8,6,9,7,7,6} |
| 3 | {0,1,2,3,8,10,7,3,10,1} |
| 4 | {2,9,0,4,3,6,8,6,3,4} |
| 5 | {3,8,7,7,0,5,3,9,2,10} |
| 6 | {5,3,1,7,6,3,5,3,6,4} |
| 7 | {11,8,4,4,2,7,10,0,3,3} |
| 8 | {4,14,5,1,3,1,6,6,9,8} |
| 9 | {12,8,1,7,2,7,10,6,0,6} |
| 10 | {1,4,4,4,8,5,2,8,5,5} |
| (10 rows) |
| </pre></li> |
| <li>Multiply two sparse matrices <pre class="syntax"> |
| SELECT madlib.matrix_mult('"mat_A_sparse"', 'row="rowNum", col=col_num, val=entry', |
| '"mat_B_sparse"', 'row=row_id, col=col_id, val=val, trans=true', |
| 'matrix_r'); |
| SELECT * FROM matrix_r ORDER BY "rowNum"; |
| </pre> <pre class="result"> |
| rowNum | entry |
| --------+------------------------------------------- |
| 1 | {260,216,137,180,190,156,138,222,174,159} |
| 2 | {104,76,14,34,82,52,72,44,64,40} |
| 3 | {51,66,33,36,15,45,33,21,33,63} |
| 4 | {0,0,0,0,0,0,0,0,0,0} |
| 5 | {0,0,0,0,0,0,0,0,0,0} |
| 6 | {0,0,0,0,0,0,0,0,0,0} |
| 7 | {63,35,0,14,21,35,28,28,42,7} |
| 8 | {90,49,18,72,99,29,84,48,45,52} |
| 9 | {84,39,3,39,42,39,48,42,51,18} |
| 10 | {0,0,0,0,0,0,0,0,0,0} |
| (10 rows) |
| </pre></li> |
| </ul> |
| <p><a class="anchor" id="related"></a></p><dl class="section user"><dt>Related Topics</dt><dd></dd></dl> |
| <p>File <a class="el" href="array__ops_8sql__in.html" title="implementation of array operations in SQL ">array_ops.sql_in</a> documenting the array operations <a class="el" href="group__grp__array.html">Array Operations</a></p> |
| <p>File <a class="el" href="matrix__ops_8sql__in.html" title="Implementation of matrix operations in SQL. ">matrix_ops.sql_in</a> for list of functions and usage. </p> |
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