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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"

"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">

<head>

<title>systemml documentation</title>

var DOCUMENTATION_OPTIONS = {

URL_ROOT: './',

VERSION: '',

COLLAPSE_INDEX: false,

FILE_SUFFIX: '.html',

HAS_SOURCE: true

};

</script>

</head>

<h1>Welcome to systemml’s documentation!<a class="headerlink" href="#welcome-to-systemml-s-documentation" title="Permalink to this headline">¶</a></h1>

Contents:

<h2>systemml package<a class="headerlink" href="#systemml-package" title="Permalink to this headline">¶</a></h2>

<h3>Subpackages<a class="headerlink" href="#subpackages" title="Permalink to this headline">¶</a></h3>

<h4>systemml.mllearn package<a class="headerlink" href="#systemml-mllearn-package" title="Permalink to this headline">¶</a></h4>

<h5>Submodules<a class="headerlink" href="#submodules" title="Permalink to this headline">¶</a></h5>

</div>

<h5>systemml.mllearn.estimators module<a class="headerlink" href="#module-systemml.mllearn.estimators" title="Permalink to this headline">¶</a></h5>

class <code class="descclassname">systemml.mllearn.estimators.</code><code class="descname">LinearRegression</code>(sqlCtx, fit_intercept=True, max_iter=100, tol=1e-06, C=1.0, solver='newton-cg', transferUsingDF=False)<a class="reference internal" href="_modules/systemml/mllearn/estimators.html#LinearRegression">[source]</a><a class="headerlink" href="#systemml.mllearn.estimators.LinearRegression" title="Permalink to this definition">¶</a></dt>

<dd>Bases: <code class="xref py py-class docutils literal">systemml.mllearn.estimators.BaseSystemMLRegressor</code>

Performs linear regression to model the relationship between one numerical response variable and one or more explanatory (feature) variables.

<div class="highlight-default"><div class="highlight"><pre>>>> import numpy as np

>>> from sklearn import datasets

>>> from systemml.mllearn import LinearRegression

>>> from pyspark.sql import SQLContext

>>> # Load the diabetes dataset

>>> diabetes = datasets.load_diabetes()

>>> # Use only one feature

>>> diabetes_X = diabetes.data[:, np.newaxis, 2]

>>> # Split the data into training/testing sets

>>> diabetes_X_train = diabetes_X[:-20]

>>> diabetes_X_test = diabetes_X[-20:]

>>> # Split the targets into training/testing sets

>>> diabetes_y_train = diabetes.target[:-20]

>>> diabetes_y_test = diabetes.target[-20:]

>>> # Create linear regression object

>>> regr = LinearRegression(sqlCtx, solver='newton-cg')

>>> # Train the model using the training sets

>>> regr.fit(diabetes_X_train, diabetes_y_train)

>>> # The mean square error

>>> print("Residual sum of squares: %.2f" % np.mean((regr.predict(diabetes_X_test) - diabetes_y_test) ** 2))

</pre></div>

</div>

</dd></dl>

class <code class="descclassname">systemml.mllearn.estimators.</code><code class="descname">LogisticRegression</code>(sqlCtx, penalty='l2', fit_intercept=True, max_iter=100, max_inner_iter=0, tol=1e-06, C=1.0, solver='newton-cg', transferUsingDF=False)<a class="reference internal" href="_modules/systemml/mllearn/estimators.html#LogisticRegression">[source]</a><a class="headerlink" href="#systemml.mllearn.estimators.LogisticRegression" title="Permalink to this definition">¶</a></dt>

<dd>Bases: <code class="xref py py-class docutils literal">systemml.mllearn.estimators.BaseSystemMLClassifier</code>

Performs both binomial and multinomial logistic regression.

Scikit-learn way

<div class="highlight-default"><div class="highlight"><pre>>>> from sklearn import datasets, neighbors

>>> from systemml.mllearn import LogisticRegression

>>> from pyspark.sql import SQLContext

>>> sqlCtx = SQLContext(sc)

>>> digits = datasets.load_digits()

>>> X_digits = digits.data

>>> y_digits = digits.target + 1

>>> n_samples = len(X_digits)

>>> X_train = X_digits[:.9 * n_samples]

>>> y_train = y_digits[:.9 * n_samples]

>>> X_test = X_digits[.9 * n_samples:]

>>> y_test = y_digits[.9 * n_samples:]

>>> logistic = LogisticRegression(sqlCtx)

>>> print('LogisticRegression score: %f' % logistic.fit(X_train, y_train).score(X_test, y_test))

</pre></div>

</div>

MLPipeline way

<div class="highlight-default"><div class="highlight"><pre>>>> from pyspark.ml import Pipeline

>>> from systemml.mllearn import LogisticRegression

>>> from pyspark.ml.feature import HashingTF, Tokenizer

>>> from pyspark.sql import SQLContext

>>> sqlCtx = SQLContext(sc)

>>> training = sqlCtx.createDataFrame([

>>> (0L, "a b c d e spark", 1.0),

>>> (1L, "b d", 2.0),

>>> (2L, "spark f g h", 1.0),

>>> (3L, "hadoop mapreduce", 2.0),

>>> (4L, "b spark who", 1.0),

>>> (5L, "g d a y", 2.0),

>>> (6L, "spark fly", 1.0),

>>> (7L, "was mapreduce", 2.0),

>>> (8L, "e spark program", 1.0),

>>> (9L, "a e c l", 2.0),

>>> (10L, "spark compile", 1.0),

>>> (11L, "hadoop software", 2.0)

>>> ], ["id", "text", "label"])

>>> tokenizer = Tokenizer(inputCol="text", outputCol="words")

>>> hashingTF = HashingTF(inputCol="words", outputCol="features", numFeatures=20)

>>> lr = LogisticRegression(sqlCtx)

>>> pipeline = Pipeline(stages=[tokenizer, hashingTF, lr])

>>> model = pipeline.fit(training)

>>> test = sqlCtx.createDataFrame([

>>> (12L, "spark i j k"),

>>> (13L, "l m n"),

>>> (14L, "mapreduce spark"),

>>> (15L, "apache hadoop")], ["id", "text"])

>>> prediction = model.transform(test)

>>> prediction.show()

</pre></div>

</div>

</dd></dl>

class <code class="descclassname">systemml.mllearn.estimators.</code><code class="descname">SVM</code>(sqlCtx, fit_intercept=True, max_iter=100, tol=1e-06, C=1.0, is_multi_class=False, transferUsingDF=False)<a class="reference internal" href="_modules/systemml/mllearn/estimators.html#SVM">[source]</a><a class="headerlink" href="#systemml.mllearn.estimators.SVM" title="Permalink to this definition">¶</a></dt>

<dd>Bases: <code class="xref py py-class docutils literal">systemml.mllearn.estimators.BaseSystemMLClassifier</code>

Performs both binary-class and multiclass SVM (Support Vector Machines).

>>> from systemml.mllearn import SVM

>>> from pyspark.sql import SQLContext

>>> sqlCtx = SQLContext(sc)

>>> digits = datasets.load_digits()

>>> X_digits = digits.data

>>> y_digits = digits.target

>>> n_samples = len(X_digits)

>>> svm = SVM(sqlCtx, is_multi_class=True)

>>> print('LogisticRegression score: %f' % svm.fit(X_train, y_train).score(X_test, y_test))

</pre></div>

</div>

</dd></dl>

class <code class="descclassname">systemml.mllearn.estimators.</code><code class="descname">NaiveBayes</code>(sqlCtx, laplace=1.0, transferUsingDF=False)<a class="reference internal" href="_modules/systemml/mllearn/estimators.html#NaiveBayes">[source]</a><a class="headerlink" href="#systemml.mllearn.estimators.NaiveBayes" title="Permalink to this definition">¶</a></dt>

<dd>Bases: <code class="xref py py-class docutils literal">systemml.mllearn.estimators.BaseSystemMLClassifier</code>

Performs Naive Bayes.

<div class="highlight-default"><div class="highlight"><pre>>>> from sklearn.datasets import fetch_20newsgroups

>>> from sklearn.feature_extraction.text import TfidfVectorizer

>>> from systemml.mllearn import NaiveBayes

>>> from sklearn import metrics

>>> from pyspark.sql import SQLContext

>>> sqlCtx = SQLContext(sc)

>>> categories = ['alt.atheism', 'talk.religion.misc', 'comp.graphics', 'sci.space']

>>> newsgroups_train = fetch_20newsgroups(subset='train', categories=categories)

>>> newsgroups_test = fetch_20newsgroups(subset='test', categories=categories)

>>> vectorizer = TfidfVectorizer()

>>> # Both vectors and vectors_test are SciPy CSR matrix

>>> vectors = vectorizer.fit_transform(newsgroups_train.data)

>>> vectors_test = vectorizer.transform(newsgroups_test.data)

>>> nb = NaiveBayes(sqlCtx)

>>> nb.fit(vectors, newsgroups_train.target)

>>> pred = nb.predict(vectors_test)

>>> metrics.f1_score(newsgroups_test.target, pred, average='weighted')

</pre></div>

</div>

</dd></dl>

</div>

<h5>Module contents<a class="headerlink" href="#module-systemml.mllearn" title="Permalink to this headline">¶</a></h5>

<h6>SystemML Algorithms<a class="headerlink" href="#systemml-algorithms" title="Permalink to this headline">¶</a></h6>

</colgroup>

<tr class="row-odd"><th class="head" colspan="2">Classification Algorithms</th>

</tr>

</thead>

<tr class="row-even"><td>LogisticRegression</td>

<td>Performs binomial and multinomial logistic regression</td>

</tr>

<td>Performs both binary-class and multi-class SVM</td>

</tr>

<tr class="row-even"><td>NaiveBayes</td>

<td>Multinomial naive bayes classifier</td>

</tr>

</tbody>

</table>

</colgroup>

<tr class="row-odd"><th class="head" colspan="2">Regression Algorithms</th>

</tr>

</thead>

<tr class="row-even"><td>LinearRegression</td>

<td>Performs linear regression</td>

</tr>

</tbody>

</table>

class <code class="descclassname">systemml.mllearn.</code><code class="descname">LinearRegression</code>(sqlCtx, fit_intercept=True, max_iter=100, tol=1e-06, C=1.0, solver='newton-cg', transferUsingDF=False)<a class="reference internal" href="_modules/systemml/mllearn/estimators.html#LinearRegression">[source]</a><a class="headerlink" href="#systemml.mllearn.LinearRegression" title="Permalink to this definition">¶</a></dt>

<dd>Bases: <code class="xref py py-class docutils literal">systemml.mllearn.estimators.BaseSystemMLRegressor</code>

Performs linear regression to model the relationship between one numerical response variable and one or more explanatory (feature) variables.

>>> from sklearn import datasets

>>> from systemml.mllearn import LinearRegression

>>> from pyspark.sql import SQLContext

>>> # Load the diabetes dataset

>>> # Use only one feature

>>> # Split the data into training/testing sets

>>> # Split the targets into training/testing sets

>>> # Create linear regression object

>>> # Train the model using the training sets

>>> # The mean square error

</pre></div>

</div>

</dd></dl>

class <code class="descclassname">systemml.mllearn.</code><code class="descname">LogisticRegression</code>(sqlCtx, penalty='l2', fit_intercept=True, max_iter=100, max_inner_iter=0, tol=1e-06, C=1.0, solver='newton-cg', transferUsingDF=False)<a class="reference internal" href="_modules/systemml/mllearn/estimators.html#LogisticRegression">[source]</a><a class="headerlink" href="#systemml.mllearn.LogisticRegression" title="Permalink to this definition">¶</a></dt>

<dd>Bases: <code class="xref py py-class docutils literal">systemml.mllearn.estimators.BaseSystemMLClassifier</code>

Performs both binomial and multinomial logistic regression.

Scikit-learn way

>>> from systemml.mllearn import LogisticRegression

>>> from pyspark.sql import SQLContext

>>> sqlCtx = SQLContext(sc)

>>> digits = datasets.load_digits()

>>> X_digits = digits.data

>>> n_samples = len(X_digits)

</pre></div>

</div>

MLPipeline way

>>> from systemml.mllearn import LogisticRegression

>>> from pyspark.sql import SQLContext

>>> sqlCtx = SQLContext(sc)

>>> lr = LogisticRegression(sqlCtx)

>>> test = sqlCtx.createDataFrame([

>>> (12L, "spark i j k"),

>>> (13L, "l m n"),

>>> (14L, "mapreduce spark"),

>>> prediction.show()

</pre></div>

</div>

</dd></dl>

class <code class="descclassname">systemml.mllearn.</code><code class="descname">SVM</code>(sqlCtx, fit_intercept=True, max_iter=100, tol=1e-06, C=1.0, is_multi_class=False, transferUsingDF=False)<a class="reference internal" href="_modules/systemml/mllearn/estimators.html#SVM">[source]</a><a class="headerlink" href="#systemml.mllearn.SVM" title="Permalink to this definition">¶</a></dt>

<dd>Bases: <code class="xref py py-class docutils literal">systemml.mllearn.estimators.BaseSystemMLClassifier</code>

Performs both binary-class and multiclass SVM (Support Vector Machines).

>>> from systemml.mllearn import SVM

>>> from pyspark.sql import SQLContext

>>> sqlCtx = SQLContext(sc)

>>> digits = datasets.load_digits()

>>> X_digits = digits.data

>>> y_digits = digits.target

>>> n_samples = len(X_digits)

>>> print('LogisticRegression score: %f' % svm.fit(X_train, y_train).score(X_test, y_test))

</pre></div>

</div>

</dd></dl>

class <code class="descclassname">systemml.mllearn.</code><code class="descname">NaiveBayes</code>(sqlCtx, laplace=1.0, transferUsingDF=False)<a class="reference internal" href="_modules/systemml/mllearn/estimators.html#NaiveBayes">[source]</a><a class="headerlink" href="#systemml.mllearn.NaiveBayes" title="Permalink to this definition">¶</a></dt>

<dd>Bases: <code class="xref py py-class docutils literal">systemml.mllearn.estimators.BaseSystemMLClassifier</code>

Performs Naive Bayes.

>>> from sklearn.feature_extraction.text import TfidfVectorizer

>>> from systemml.mllearn import NaiveBayes

>>> from sklearn import metrics

>>> from pyspark.sql import SQLContext

>>> sqlCtx = SQLContext(sc)

>>> vectorizer = TfidfVectorizer()

>>> # Both vectors and vectors_test are SciPy CSR matrix

>>> nb = NaiveBayes(sqlCtx)

</pre></div>

</div>

</dd></dl>

</div>

<h4>systemml.random package<a class="headerlink" href="#systemml-random-package" title="Permalink to this headline">¶</a></h4>

<h5>Submodules<a class="headerlink" href="#submodules" title="Permalink to this headline">¶</a></h5>

</div>

<h5>systemml.random.sampling module<a class="headerlink" href="#module-systemml.random.sampling" title="Permalink to this headline">¶</a></h5>

<code class="descclassname">systemml.random.sampling.</code><code class="descname">normal</code>(loc=0.0, scale=1.0, size=(1, 1), sparsity=1.0)<a class="reference internal" href="_modules/systemml/random/sampling.html#normal">[source]</a><a class="headerlink" href="#systemml.random.sampling.normal" title="Permalink to this definition">¶</a></dt>

<dd>Draw random samples from a normal (Gaussian) distribution.

loc: Mean (“centre”) of the distribution.

scale: Standard deviation (spread or “width”) of the distribution.

size: Output shape (only tuple of length 2, i.e. (m, n), supported).

sparsity: Sparsity (between 0.0 and 1.0).

<div class="highlight-default"><div class="highlight"><pre>>>> import systemml as sml

>>> import numpy as np

>>> sml.setSparkContext(sc)

>>> from systemml import random

>>> m1 = sml.random.normal(loc=3, scale=2, size=(3,3))

>>> m1.toNumPy()

array([[ 3.48857226, 6.17261819, 2.51167259],

[ 3.60506708, -1.90266305, 3.97601633],

[ 3.62245706, 5.9430881 , 2.53070413]])

</pre></div>

</div>

</dd></dl>

<code class="descclassname">systemml.random.sampling.</code><code class="descname">uniform</code>(low=0.0, high=1.0, size=(1, 1), sparsity=1.0)<a class="reference internal" href="_modules/systemml/random/sampling.html#uniform">[source]</a><a class="headerlink" href="#systemml.random.sampling.uniform" title="Permalink to this definition">¶</a></dt>

<dd>Draw samples from a uniform distribution.

low: Lower boundary of the output interval.

high: Upper boundary of the output interval.

size: Output shape (only tuple of length 2, i.e. (m, n), supported).

sparsity: Sparsity (between 0.0 and 1.0).

>>> import numpy as np

>>> sml.setSparkContext(sc)

>>> from systemml import random

>>> m1.toNumPy()

array([[ 0.54511396, 0.11937437, 0.72975775],

[ 0.14135946, 0.01944448, 0.52544478],

[ 0.67582422, 0.87068849, 0.02766852]])

</pre></div>

</div>

</dd></dl>

<code class="descclassname">systemml.random.sampling.</code><code class="descname">poisson</code>(lam=1.0, size=(1, 1), sparsity=1.0)<a class="reference internal" href="_modules/systemml/random/sampling.html#poisson">[source]</a><a class="headerlink" href="#systemml.random.sampling.poisson" title="Permalink to this definition">¶</a></dt>

<dd>Draw samples from a Poisson distribution.

lam: Expectation of interval, should be > 0.

size: Output shape (only tuple of length 2, i.e. (m, n), supported).

sparsity: Sparsity (between 0.0 and 1.0).

>>> import numpy as np

>>> sml.setSparkContext(sc)

>>> from systemml import random

>>> m1 = sml.random.poisson(lam=1, size=(3,3))

>>> m1.toNumPy()

array([[ 1., 0., 2.],

[ 1., 0., 0.],

[ 0., 0., 0.]])

</pre></div>

</div>

</dd></dl>

</div>

<h5>Module contents<a class="headerlink" href="#module-systemml.random" title="Permalink to this headline">¶</a></h5>

<h6>Random Number Generation<a class="headerlink" href="#random-number-generation" title="Permalink to this headline">¶</a></h6>

</colgroup>

<tr class="row-odd"><th class="head" colspan="2">Univariate distributions</th>

</tr>

</thead>

<tr class="row-even"><td>normal</td>

<td>Normal / Gaussian distribution.</td>

</tr>

<tr class="row-odd"><td>poisson</td>

<td>Poisson distribution.</td>

</tr>

<tr class="row-even"><td>uniform</td>

<td>Uniform distribution.</td>

</tr>

</tbody>

</table>

<code class="descclassname">systemml.random.</code><code class="descname">normal</code>(loc=0.0, scale=1.0, size=(1, 1), sparsity=1.0)<a class="reference internal" href="_modules/systemml/random/sampling.html#normal">[source]</a><a class="headerlink" href="#systemml.random.normal" title="Permalink to this definition">¶</a></dt>

<dd>Draw random samples from a normal (Gaussian) distribution.

loc: Mean (“centre”) of the distribution.

scale: Standard deviation (spread or “width”) of the distribution.

size: Output shape (only tuple of length 2, i.e. (m, n), supported).

sparsity: Sparsity (between 0.0 and 1.0).

>>> import numpy as np

>>> sml.setSparkContext(sc)

>>> from systemml import random

>>> m1.toNumPy()

array([[ 3.48857226, 6.17261819, 2.51167259],

[ 3.60506708, -1.90266305, 3.97601633],

[ 3.62245706, 5.9430881 , 2.53070413]])

</pre></div>

</div>

</dd></dl>

<code class="descclassname">systemml.random.</code><code class="descname">uniform</code>(low=0.0, high=1.0, size=(1, 1), sparsity=1.0)<a class="reference internal" href="_modules/systemml/random/sampling.html#uniform">[source]</a><a class="headerlink" href="#systemml.random.uniform" title="Permalink to this definition">¶</a></dt>

<dd>Draw samples from a uniform distribution.

low: Lower boundary of the output interval.

high: Upper boundary of the output interval.

size: Output shape (only tuple of length 2, i.e. (m, n), supported).

sparsity: Sparsity (between 0.0 and 1.0).

>>> import numpy as np

>>> sml.setSparkContext(sc)

>>> from systemml import random

>>> m1.toNumPy()

array([[ 0.54511396, 0.11937437, 0.72975775],

[ 0.14135946, 0.01944448, 0.52544478],

[ 0.67582422, 0.87068849, 0.02766852]])

</pre></div>

</div>

</dd></dl>

<code class="descclassname">systemml.random.</code><code class="descname">poisson</code>(lam=1.0, size=(1, 1), sparsity=1.0)<a class="reference internal" href="_modules/systemml/random/sampling.html#poisson">[source]</a><a class="headerlink" href="#systemml.random.poisson" title="Permalink to this definition">¶</a></dt>

<dd>Draw samples from a Poisson distribution.

lam: Expectation of interval, should be > 0.

size: Output shape (only tuple of length 2, i.e. (m, n), supported).

sparsity: Sparsity (between 0.0 and 1.0).

>>> import numpy as np

>>> sml.setSparkContext(sc)

>>> from systemml import random

>>> m1 = sml.random.poisson(lam=1, size=(3,3))

>>> m1.toNumPy()

array([[ 1., 0., 2.],

[ 1., 0., 0.],

[ 0., 0., 0.]])

</pre></div>

</div>

</dd></dl>

</div>

<h3>Submodules<a class="headerlink" href="#submodules" title="Permalink to this headline">¶</a></h3>

</div>

<h3>systemml.converters module<a class="headerlink" href="#module-systemml.converters" title="Permalink to this headline">¶</a></h3>

<code class="descclassname">systemml.converters.</code><code class="descname">getNumCols</code>(numPyArr)<a class="reference internal" href="_modules/systemml/converters.html#getNumCols">[source]</a><a class="headerlink" href="#systemml.converters.getNumCols" title="Permalink to this definition">¶</a></dt>

<code class="descclassname">systemml.converters.</code><code class="descname">convertToMatrixBlock</code>(sc, src)<a class="reference internal" href="_modules/systemml/converters.html#convertToMatrixBlock">[source]</a><a class="headerlink" href="#systemml.converters.convertToMatrixBlock" title="Permalink to this definition">¶</a></dt>

<code class="descclassname">systemml.converters.</code><code class="descname">convertToNumPyArr</code>(sc, mb)<a class="reference internal" href="_modules/systemml/converters.html#convertToNumPyArr">[source]</a><a class="headerlink" href="#systemml.converters.convertToNumPyArr" title="Permalink to this definition">¶</a></dt>

<code class="descclassname">systemml.converters.</code><code class="descname">convertToPandasDF</code>(X)<a class="reference internal" href="_modules/systemml/converters.html#convertToPandasDF">[source]</a><a class="headerlink" href="#systemml.converters.convertToPandasDF" title="Permalink to this definition">¶</a></dt>

<code class="descclassname">systemml.converters.</code><code class="descname">convertToLabeledDF</code>(sqlCtx, X, y=None)<a class="reference internal" href="_modules/systemml/converters.html#convertToLabeledDF">[source]</a><a class="headerlink" href="#systemml.converters.convertToLabeledDF" title="Permalink to this definition">¶</a></dt>

</div>

<h3>systemml.defmatrix module<a class="headerlink" href="#module-systemml.defmatrix" title="Permalink to this headline">¶</a></h3>

<code class="descclassname">systemml.defmatrix.</code><code class="descname">setSparkContext</code>(sc)<a class="reference internal" href="_modules/systemml/defmatrix.html#setSparkContext">[source]</a><a class="headerlink" href="#systemml.defmatrix.setSparkContext" title="Permalink to this definition">¶</a></dt>

<dd>Before using the matrix, the user needs to invoke this function.

<dt>sc: SparkContext</dt>

<dd>SparkContext</dd>

</dl>

</dd></dl>

class <code class="descclassname">systemml.defmatrix.</code><code class="descname">matrix</code>(data, op=None)<a class="reference internal" href="_modules/systemml/defmatrix.html#matrix">[source]</a><a class="headerlink" href="#systemml.defmatrix.matrix" title="Permalink to this definition">¶</a></dt>

<dd>Bases: <code class="xref py py-class docutils literal">object</code>

matrix class is a python wrapper that implements basic matrix operators, matrix functions

as well as converters to common Python types (for example: Numpy arrays, PySpark DataFrame

and Pandas DataFrame).

The operators supported are:

<li>Arithmetic operators: +, -, , /, //, %, * as well as dot (i.e. matrix multiplication)</li>

<li>Indexing in the matrix</li>

<li>Relational/Boolean operators: <, <=, >, >=, ==, !=, &, |</li>

</ol>

In addition, following functions are supported for matrix:

<li>transpose</li>

<li>Aggregation functions: sum, mean, var, sd, max, min, argmin, argmax, cumsum</li>

<li>Global statistical built-In functions: exp, log, abs, sqrt, round, floor, ceil, sin, cos, tan, asin, acos, atan, sign, solve</li>

</ol>

Note: an evaluated matrix contains a data field computed by eval method as DataFrame or NumPy array.

<div class="highlight-default"><div class="highlight"><pre>>>> import SystemML as sml

>>> import numpy as np

>>> sml.setSparkContext(sc)

</pre></div>

</div>

Welcome to Apache SystemML!

<div class="highlight-default"><div class="highlight"><pre>>>> m1 = sml.matrix(np.ones((3,3)) + 2)

>>> m2 = sml.matrix(np.ones((3,3)) + 3)

>>> m2 = m1 * (m2 + m1)

>>> m4 = 1.0 - m2

>>> m4

# This matrix (mVar5) is backed by below given PyDML script (which is not yet evaluated). To fetch the data of this matrix, invoke toNumPy() or toDF() or toPandas() methods.

mVar1 = load(" ", format="csv")

mVar2 = load(" ", format="csv")

mVar3 = mVar2 + mVar1

mVar4 = mVar1 * mVar3

mVar5 = 1.0 - mVar4

save(mVar5, " ")

>>> m2.eval()

>>> m2

# This matrix (mVar4) is backed by NumPy array. To fetch the NumPy array, invoke toNumPy() method.

>>> m4

# This matrix (mVar5) is backed by below given PyDML script (which is not yet evaluated). To fetch the data of this matrix, invoke toNumPy() or toDF() or toPandas() methods.

mVar4 = load(" ", format="csv")

mVar5 = 1.0 - mVar4

save(mVar5, " ")

>>> m4.sum(axis=1).toNumPy()

array([[-60.],

[-60.],

[-60.]])

</pre></div>

</div>

Design Decisions:

<li>Until eval() method is invoked, we create an AST (not exposed to the user) that consist of unevaluated operations and data required by those operations.

As an anology, a spark user can treat eval() method similar to calling RDD.persist() followed by RDD.count().</li>

<li>The AST consist of two kinds of nodes: either of type matrix or of type DMLOp.

Both these classes expose _visit method, that helps in traversing the AST in DFS manner.</li>

<li>A matrix object can either be evaluated or not.

If evaluated, the attribute ‘data’ is set to one of the supported types (for example: NumPy array or DataFrame). In this case, the attribute ‘op’ is set to None.

If not evaluated, the attribute ‘op’ which refers to one of the intermediate node of AST and if of type DMLOp. In this case, the attribute ‘data’ is set to None.</li>

</ol>

<li>DMLOp has an attribute ‘inputs’ which contains list of matrix objects or DMLOp.

</li>

<li>To simplify the traversal, every matrix object is considered immutable and an matrix operations creates a new matrix object.

As an example:

<cite>m1 = sml.matrix(np.ones((3,3)))</cite> creates a matrix object backed by ‘data=(np.ones((3,3))’.

<cite>m1 = m1 * 2</cite> will create a new matrix object which is now backed by ‘op=DMLOp( ... )’ whose input is earlier created matrix object.

</li>

<li>Left indexing (implemented in __setitem__ method) is a special case, where Python expects the existing object to be mutated.

To ensure the above property, we make deep copy of existing object and point any references to the left-indexed matrix to the newly created object.

Then the left-indexed matrix is set to be backed by DMLOp consisting of following pydml:

left-indexed-matrix = new-deep-copied-matrix

left-indexed-matrix[index] = value

</li>

<li>Please use m.printAST() and/or type <cite>m</cite> for debugging. Here is a sample session:

<div class="highlight-default"><div class="highlight"><pre>>>> npm = np.ones((3,3))

>>> m1 = sml.matrix(npm + 3)

>>> m3 = m1 + m2

>>> m3

mVar2 = load(" ", format="csv")

mVar1 = load(" ", format="csv")

mVar3 = mVar1 + mVar2

save(mVar3, " ")

>>> m3.printAST()

- [mVar3] (op).

- [mVar1] (data).

- [mVar2] (data).

</pre></div>

</div>

</li>

</ol>

<code class="descname">argmax</code>(axis=None)<a class="reference internal" href="_modules/systemml/defmatrix.html#matrix.argmax">[source]</a><a class="headerlink" href="#systemml.defmatrix.matrix.argmax" title="Permalink to this definition">¶</a></dt>

<dd>Returns the indices of the maximum values along an axis.

axis : int, optional (only axis=1, i.e. rowIndexMax is supported in this version)

</dd></dl>

<code class="descname">argmin</code>(axis=None)<a class="reference internal" href="_modules/systemml/defmatrix.html#matrix.argmin">[source]</a><a class="headerlink" href="#systemml.defmatrix.matrix.argmin" title="Permalink to this definition">¶</a></dt>

<dd>Returns the indices of the minimum values along an axis.

axis : int, optional (only axis=1, i.e. rowIndexMax is supported in this version)

</dd></dl>

<code class="descname">cumsum</code>(axis=None)<a class="reference internal" href="_modules/systemml/defmatrix.html#matrix.cumsum">[source]</a><a class="headerlink" href="#systemml.defmatrix.matrix.cumsum" title="Permalink to this definition">¶</a></dt>

<dd>Returns the indices of the maximum values along an axis.

axis : int, optional (only axis=0, i.e. cumsum along the rows is supported in this version)

</dd></dl>

<code class="descname">dot</code>(other)<a class="reference internal" href="_modules/systemml/defmatrix.html#matrix.dot">[source]</a><a class="headerlink" href="#systemml.defmatrix.matrix.dot" title="Permalink to this definition">¶</a></dt>

<dd>Numpy way of performing matrix multiplication

</dd></dl>

<code class="descname">eval</code>(outputDF=False)<a class="reference internal" href="_modules/systemml/defmatrix.html#matrix.eval">[source]</a><a class="headerlink" href="#systemml.defmatrix.matrix.eval" title="Permalink to this definition">¶</a></dt>

<dd>This is a convenience function that calls the global eval method

</dd></dl>

<code class="descname">max</code>(axis=None)<a class="reference internal" href="_modules/systemml/defmatrix.html#matrix.max">[source]</a><a class="headerlink" href="#systemml.defmatrix.matrix.max" title="Permalink to this definition">¶</a></dt>

<dd>Compute the maximum value along the specified axis

axis : int, optional

</dd></dl>

<code class="descname">mean</code>(axis=None)<a class="reference internal" href="_modules/systemml/defmatrix.html#matrix.mean">[source]</a><a class="headerlink" href="#systemml.defmatrix.matrix.mean" title="Permalink to this definition">¶</a></dt>

<dd>Compute the arithmetic mean along the specified axis

axis : int, optional

</dd></dl>

<code class="descname">min</code>(axis=None)<a class="reference internal" href="_modules/systemml/defmatrix.html#matrix.min">[source]</a><a class="headerlink" href="#systemml.defmatrix.matrix.min" title="Permalink to this definition">¶</a></dt>

<dd>Compute the minimum value along the specified axis

axis : int, optional

</dd></dl>

<code class="descname">printAST</code>(numSpaces=0)<a class="reference internal" href="_modules/systemml/defmatrix.html#matrix.printAST">[source]</a><a class="headerlink" href="#systemml.defmatrix.matrix.printAST" title="Permalink to this definition">¶</a></dt>

<dd>Please use m.printAST() and/or type <cite>m</cite> for debugging. Here is a sample session:

>>> m3 = m1 + m2

>>> m3

mVar2 = load(" ", format="csv")

mVar1 = load(" ", format="csv")

mVar3 = mVar1 + mVar2

save(mVar3, " ")

>>> m3.printAST()

- [mVar3] (op).

- [mVar1] (data).

- [mVar2] (data).

</pre></div>

</div>

</dd></dl>

<code class="descname">script</code> = None<a class="headerlink" href="#systemml.defmatrix.matrix.script" title="Permalink to this definition">¶</a></dt>

<code class="descname">sd</code>(axis=None)<a class="reference internal" href="_modules/systemml/defmatrix.html#matrix.sd">[source]</a><a class="headerlink" href="#systemml.defmatrix.matrix.sd" title="Permalink to this definition">¶</a></dt>

<dd>Compute the standard deviation along the specified axis

axis : int, optional

</dd></dl>

<code class="descname">sum</code>(axis=None)<a class="reference internal" href="_modules/systemml/defmatrix.html#matrix.sum">[source]</a><a class="headerlink" href="#systemml.defmatrix.matrix.sum" title="Permalink to this definition">¶</a></dt>

<dd>Compute the sum along the specified axis

axis : int, optional

</dd></dl>

<code class="descname">systemmlVarID</code> = 0<a class="headerlink" href="#systemml.defmatrix.matrix.systemmlVarID" title="Permalink to this definition">¶</a></dt>

<code class="descname">toDF</code>()<a class="reference internal" href="_modules/systemml/defmatrix.html#matrix.toDF">[source]</a><a class="headerlink" href="#systemml.defmatrix.matrix.toDF" title="Permalink to this definition">¶</a></dt>

<dd>This is a convenience function that calls the global eval method and then converts the matrix object into DataFrame.

</dd></dl>

<code class="descname">toNumPy</code>()<a class="reference internal" href="_modules/systemml/defmatrix.html#matrix.toNumPy">[source]</a><a class="headerlink" href="#systemml.defmatrix.matrix.toNumPy" title="Permalink to this definition">¶</a></dt>

<dd>This is a convenience function that calls the global eval method and then converts the matrix object into NumPy array.

</dd></dl>

<code class="descname">toPandas</code>()<a class="reference internal" href="_modules/systemml/defmatrix.html#matrix.toPandas">[source]</a><a class="headerlink" href="#systemml.defmatrix.matrix.toPandas" title="Permalink to this definition">¶</a></dt>

<dd>This is a convenience function that calls the global eval method and then converts the matrix object into Pandas DataFrame.

</dd></dl>

<code class="descname">trace</code>()<a class="reference internal" href="_modules/systemml/defmatrix.html#matrix.trace">[source]</a><a class="headerlink" href="#systemml.defmatrix.matrix.trace" title="Permalink to this definition">¶</a></dt>

<dd>Return the sum of the cells of the main diagonal square matrix

</dd></dl>

<code class="descname">transpose</code>()<a class="reference internal" href="_modules/systemml/defmatrix.html#matrix.transpose">[source]</a><a class="headerlink" href="#systemml.defmatrix.matrix.transpose" title="Permalink to this definition">¶</a></dt>

<dd>Transposes the matrix.

</dd></dl>

<code class="descname">var</code>(axis=None)<a class="reference internal" href="_modules/systemml/defmatrix.html#matrix.var">[source]</a><a class="headerlink" href="#systemml.defmatrix.matrix.var" title="Permalink to this definition">¶</a></dt>

<dd>Compute the variance along the specified axis

axis : int, optional

</dd></dl>

<code class="descname">visited</code> = []<a class="headerlink" href="#systemml.defmatrix.matrix.visited" title="Permalink to this definition">¶</a></dt>

</dd></dl>

<code class="descclassname">systemml.defmatrix.</code><code class="descname">eval</code>(outputs, outputDF=False, execute=True)<a class="reference internal" href="_modules/systemml/defmatrix.html#eval">[source]</a><a class="headerlink" href="#systemml.defmatrix.eval" title="Permalink to this definition">¶</a></dt>

<dd>Executes the unevaluated DML script and computes the matrices specified by outputs.

outputs: list of matrices or a matrix object

outputDF: back the data of matrix as PySpark DataFrame

</dd></dl>

<code class="descclassname">systemml.defmatrix.</code><code class="descname">solve</code>(A, b)<a class="reference internal" href="_modules/systemml/defmatrix.html#solve">[source]</a><a class="headerlink" href="#systemml.defmatrix.solve" title="Permalink to this definition">¶</a></dt>

<dd>Computes the least squares solution for system of linear equations A %*% x = b

>>> from sklearn import datasets

>>> import SystemML as sml

>>> from pyspark.sql import SQLContext

>>> X_train = diabetes_X[:-20]

>>> X_test = diabetes_X[-20:]

>>> y_train = diabetes.target[:-20]

>>> y_test = diabetes.target[-20:]

>>> sml.setSparkContext(sc)

>>> X = sml.matrix(X_train)

>>> y = sml.matrix(y_train)

>>> A = X.transpose().dot(X)

>>> b = X.transpose().dot(y)

>>> beta = sml.solve(A, b).toNumPy()

>>> y_predicted = X_test.dot(beta)

>>> print('Residual sum of squares: %.2f' % np.mean((y_predicted - y_test) ** 2))

Residual sum of squares: 25282.12

</pre></div>

</div>

</dd></dl>

class <code class="descclassname">systemml.defmatrix.</code><code class="descname">DMLOp</code>(inputs, dml=None)<a class="reference internal" href="_modules/systemml/defmatrix.html#DMLOp">[source]</a><a class="headerlink" href="#systemml.defmatrix.DMLOp" title="Permalink to this definition">¶</a></dt>

<dd>Bases: <code class="xref py py-class docutils literal">object</code>

Represents an intermediate node of Abstract syntax tree created to generate the PyDML script

<code class="descname">printAST</code>(numSpaces)<a class="reference internal" href="_modules/systemml/defmatrix.html#DMLOp.printAST">[source]</a><a class="headerlink" href="#systemml.defmatrix.DMLOp.printAST" title="Permalink to this definition">¶</a></dt>

</dd></dl>

<code class="descclassname">systemml.defmatrix.</code><code class="descname">exp</code>(X)<a class="reference internal" href="_modules/systemml/defmatrix.html#exp">[source]</a><a class="headerlink" href="#systemml.defmatrix.exp" title="Permalink to this definition">¶</a></dt>

<code class="descclassname">systemml.defmatrix.</code><code class="descname">log</code>(X, y=None)<a class="reference internal" href="_modules/systemml/defmatrix.html#log">[source]</a><a class="headerlink" href="#systemml.defmatrix.log" title="Permalink to this definition">¶</a></dt>

<code class="descclassname">systemml.defmatrix.</code><code class="descname">abs</code>(X)<a class="reference internal" href="_modules/systemml/defmatrix.html#abs">[source]</a><a class="headerlink" href="#systemml.defmatrix.abs" title="Permalink to this definition">¶</a></dt>

<code class="descclassname">systemml.defmatrix.</code><code class="descname">sqrt</code>(X)<a class="reference internal" href="_modules/systemml/defmatrix.html#sqrt">[source]</a><a class="headerlink" href="#systemml.defmatrix.sqrt" title="Permalink to this definition">¶</a></dt>

<code class="descclassname">systemml.defmatrix.</code><code class="descname">round</code>(X)<a class="reference internal" href="_modules/systemml/defmatrix.html#round">[source]</a><a class="headerlink" href="#systemml.defmatrix.round" title="Permalink to this definition">¶</a></dt>

<code class="descclassname">systemml.defmatrix.</code><code class="descname">floor</code>(X)<a class="reference internal" href="_modules/systemml/defmatrix.html#floor">[source]</a><a class="headerlink" href="#systemml.defmatrix.floor" title="Permalink to this definition">¶</a></dt>

<code class="descclassname">systemml.defmatrix.</code><code class="descname">ceil</code>(X)<a class="reference internal" href="_modules/systemml/defmatrix.html#ceil">[source]</a><a class="headerlink" href="#systemml.defmatrix.ceil" title="Permalink to this definition">¶</a></dt>

<code class="descclassname">systemml.defmatrix.</code><code class="descname">sin</code>(X)<a class="reference internal" href="_modules/systemml/defmatrix.html#sin">[source]</a><a class="headerlink" href="#systemml.defmatrix.sin" title="Permalink to this definition">¶</a></dt>

<code class="descclassname">systemml.defmatrix.</code><code class="descname">cos</code>(X)<a class="reference internal" href="_modules/systemml/defmatrix.html#cos">[source]</a><a class="headerlink" href="#systemml.defmatrix.cos" title="Permalink to this definition">¶</a></dt>

<code class="descclassname">systemml.defmatrix.</code><code class="descname">tan</code>(X)<a class="reference internal" href="_modules/systemml/defmatrix.html#tan">[source]</a><a class="headerlink" href="#systemml.defmatrix.tan" title="Permalink to this definition">¶</a></dt>

<code class="descclassname">systemml.defmatrix.</code><code class="descname">asin</code>(X)<a class="reference internal" href="_modules/systemml/defmatrix.html#asin">[source]</a><a class="headerlink" href="#systemml.defmatrix.asin" title="Permalink to this definition">¶</a></dt>

<code class="descclassname">systemml.defmatrix.</code><code class="descname">acos</code>(X)<a class="reference internal" href="_modules/systemml/defmatrix.html#acos">[source]</a><a class="headerlink" href="#systemml.defmatrix.acos" title="Permalink to this definition">¶</a></dt>

<code class="descclassname">systemml.defmatrix.</code><code class="descname">atan</code>(X)<a class="reference internal" href="_modules/systemml/defmatrix.html#atan">[source]</a><a class="headerlink" href="#systemml.defmatrix.atan" title="Permalink to this definition">¶</a></dt>

<code class="descclassname">systemml.defmatrix.</code><code class="descname">sign</code>(X)<a class="reference internal" href="_modules/systemml/defmatrix.html#sign">[source]</a><a class="headerlink" href="#systemml.defmatrix.sign" title="Permalink to this definition">¶</a></dt>

</div>

<h3>systemml.mlcontext module<a class="headerlink" href="#systemml-mlcontext-module" title="Permalink to this headline">¶</a></h3>

class <code class="descclassname">systemml.mlcontext.</code><code class="descname">MLResults</code>(results, sc)<a class="reference internal" href="_modules/systemml/mlcontext.html#MLResults">[source]</a><a class="headerlink" href="#systemml.mlcontext.MLResults" title="Permalink to this definition">¶</a></dt>

<dd>Bases: <code class="xref py py-class docutils literal">object</code>

Wrapper around a Java ML Results object.

<dt>results: JavaObject</dt>

<dd>A Java MLResults object as returned by calling <cite>ml.execute()</cite>.</dd>

<dt>sc: SparkContext</dt>

<dd>SparkContext</dd>

</dl>

<code class="descname">get</code>(*outputs)<a class="reference internal" href="_modules/systemml/mlcontext.html#MLResults.get">[source]</a><a class="headerlink" href="#systemml.mlcontext.MLResults.get" title="Permalink to this definition">¶</a></dt>

<dt>outputs: string, list of strings</dt>

<dd>Output variables as defined inside the DML script.</dd>

</dl>

</dd></dl>

class <code class="descclassname">systemml.mlcontext.</code><code class="descname">MLContext</code>(sc)<a class="reference internal" href="_modules/systemml/mlcontext.html#MLContext">[source]</a><a class="headerlink" href="#systemml.mlcontext.MLContext" title="Permalink to this definition">¶</a></dt>

<dd>Bases: <code class="xref py py-class docutils literal">object</code>

Wrapper around the new SystemML MLContext.

<dt>sc: SparkContext</dt>

<dd>SparkContext</dd>

</dl>

<code class="descname">execute</code>(script)<a class="reference internal" href="_modules/systemml/mlcontext.html#MLContext.execute">[source]</a><a class="headerlink" href="#systemml.mlcontext.MLContext.execute" title="Permalink to this definition">¶</a></dt>

<dd>Execute a DML / PyDML script.

<dt>script: Script instance</dt>

<dd>Script instance defined with the appropriate input and output variables.</dd>

</dl>

<dt>ml_results: MLResults</dt>

<dd>MLResults instance.</dd>

</dl>

</dd></dl>

<code class="descname">setExplain</code>(explain)<a class="reference internal" href="_modules/systemml/mlcontext.html#MLContext.setExplain">[source]</a><a class="headerlink" href="#systemml.mlcontext.MLContext.setExplain" title="Permalink to this definition">¶</a></dt>

<dd>Explanation about the program. Mainly intended for developers.

explain: boolean

</dd></dl>

<code class="descname">setExplainLevel</code>(explainLevel)<a class="reference internal" href="_modules/systemml/mlcontext.html#MLContext.setExplainLevel">[source]</a><a class="headerlink" href="#systemml.mlcontext.MLContext.setExplainLevel" title="Permalink to this definition">¶</a></dt>

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