#
# Licensed to the Apache Software Foundation (ASF) under one or more
# contributor license agreements. See the NOTICE file distributed with
# this work for additional information regarding copyright ownership.
# The ASF licenses this file to You under the Apache License, Version 2.0
# (the "License"); you may not use this file except in compliance with
# the License. You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
"""
Package for distributed linear algebra.
"""
import sys
if sys.version >= '3':
long = int
from py4j.java_gateway import JavaObject
from pyspark import RDD, since
from pyspark.mllib.common import callMLlibFunc, JavaModelWrapper
from pyspark.mllib.linalg import _convert_to_vector, Matrix, QRDecomposition
from pyspark.mllib.stat import MultivariateStatisticalSummary
from pyspark.storagelevel import StorageLevel
__all__ = ['DistributedMatrix', 'RowMatrix', 'IndexedRow',
'IndexedRowMatrix', 'MatrixEntry', 'CoordinateMatrix',
'BlockMatrix']
[docs]class DistributedMatrix(object):
"""
Represents a distributively stored matrix backed by one or
more RDDs.
"""
[docs] def numRows(self):
"""Get or compute the number of rows."""
raise NotImplementedError
[docs] def numCols(self):
"""Get or compute the number of cols."""
raise NotImplementedError
[docs]class RowMatrix(DistributedMatrix):
"""
Represents a row-oriented distributed Matrix with no meaningful
row indices.
:param rows: An RDD of vectors.
:param numRows: Number of rows in the matrix. A non-positive
value means unknown, at which point the number
of rows will be determined by the number of
records in the `rows` RDD.
:param numCols: Number of columns in the matrix. A non-positive
value means unknown, at which point the number
of columns will be determined by the size of
the first row.
"""
def __init__(self, rows, numRows=0, numCols=0):
"""
Note: This docstring is not shown publicly.
Create a wrapper over a Java RowMatrix.
Publicly, we require that `rows` be an RDD. However, for
internal usage, `rows` can also be a Java RowMatrix
object, in which case we can wrap it directly. This
assists in clean matrix conversions.
>>> rows = sc.parallelize([[1, 2, 3], [4, 5, 6]])
>>> mat = RowMatrix(rows)
>>> mat_diff = RowMatrix(rows)
>>> (mat_diff._java_matrix_wrapper._java_model ==
... mat._java_matrix_wrapper._java_model)
False
>>> mat_same = RowMatrix(mat._java_matrix_wrapper._java_model)
>>> (mat_same._java_matrix_wrapper._java_model ==
... mat._java_matrix_wrapper._java_model)
True
"""
if isinstance(rows, RDD):
rows = rows.map(_convert_to_vector)
java_matrix = callMLlibFunc("createRowMatrix", rows, long(numRows), int(numCols))
elif (isinstance(rows, JavaObject)
and rows.getClass().getSimpleName() == "RowMatrix"):
java_matrix = rows
else:
raise TypeError("rows should be an RDD of vectors, got %s" % type(rows))
self._java_matrix_wrapper = JavaModelWrapper(java_matrix)
@property
def rows(self):
"""
Rows of the RowMatrix stored as an RDD of vectors.
>>> mat = RowMatrix(sc.parallelize([[1, 2, 3], [4, 5, 6]]))
>>> rows = mat.rows
>>> rows.first()
DenseVector([1.0, 2.0, 3.0])
"""
return self._java_matrix_wrapper.call("rows")
[docs] def numRows(self):
"""
Get or compute the number of rows.
>>> rows = sc.parallelize([[1, 2, 3], [4, 5, 6],
... [7, 8, 9], [10, 11, 12]])
>>> mat = RowMatrix(rows)
>>> print(mat.numRows())
4
>>> mat = RowMatrix(rows, 7, 6)
>>> print(mat.numRows())
7
"""
return self._java_matrix_wrapper.call("numRows")
[docs] def numCols(self):
"""
Get or compute the number of cols.
>>> rows = sc.parallelize([[1, 2, 3], [4, 5, 6],
... [7, 8, 9], [10, 11, 12]])
>>> mat = RowMatrix(rows)
>>> print(mat.numCols())
3
>>> mat = RowMatrix(rows, 7, 6)
>>> print(mat.numCols())
6
"""
return self._java_matrix_wrapper.call("numCols")
[docs] @since('2.0.0')
def computeColumnSummaryStatistics(self):
"""
Computes column-wise summary statistics.
:return: :class:`MultivariateStatisticalSummary` object
containing column-wise summary statistics.
>>> rows = sc.parallelize([[1, 2, 3], [4, 5, 6]])
>>> mat = RowMatrix(rows)
>>> colStats = mat.computeColumnSummaryStatistics()
>>> colStats.mean()
array([ 2.5, 3.5, 4.5])
"""
java_col_stats = self._java_matrix_wrapper.call("computeColumnSummaryStatistics")
return MultivariateStatisticalSummary(java_col_stats)
[docs] @since('2.0.0')
def computeCovariance(self):
"""
Computes the covariance matrix, treating each row as an
observation.
.. note:: This cannot be computed on matrices with more than 65535 columns.
>>> rows = sc.parallelize([[1, 2], [2, 1]])
>>> mat = RowMatrix(rows)
>>> mat.computeCovariance()
DenseMatrix(2, 2, [0.5, -0.5, -0.5, 0.5], 0)
"""
return self._java_matrix_wrapper.call("computeCovariance")
[docs] @since('2.0.0')
def computeGramianMatrix(self):
"""
Computes the Gramian matrix `A^T A`.
.. note:: This cannot be computed on matrices with more than 65535 columns.
>>> rows = sc.parallelize([[1, 2, 3], [4, 5, 6]])
>>> mat = RowMatrix(rows)
>>> mat.computeGramianMatrix()
DenseMatrix(3, 3, [17.0, 22.0, 27.0, 22.0, 29.0, 36.0, 27.0, 36.0, 45.0], 0)
"""
return self._java_matrix_wrapper.call("computeGramianMatrix")
[docs] @since('2.0.0')
def columnSimilarities(self, threshold=0.0):
"""
Compute similarities between columns of this matrix.
The threshold parameter is a trade-off knob between estimate
quality and computational cost.
The default threshold setting of 0 guarantees deterministically
correct results, but uses the brute-force approach of computing
normalized dot products.
Setting the threshold to positive values uses a sampling
approach and incurs strictly less computational cost than the
brute-force approach. However the similarities computed will
be estimates.
The sampling guarantees relative-error correctness for those
pairs of columns that have similarity greater than the given
similarity threshold.
To describe the guarantee, we set some notation:
* Let A be the smallest in magnitude non-zero element of
this matrix.
* Let B be the largest in magnitude non-zero element of
this matrix.
* Let L be the maximum number of non-zeros per row.
For example, for {0,1} matrices: A=B=1.
Another example, for the Netflix matrix: A=1, B=5
For those column pairs that are above the threshold, the
computed similarity is correct to within 20% relative error
with probability at least 1 - (0.981)^10/B^
The shuffle size is bounded by the *smaller* of the following
two expressions:
* O(n log(n) L / (threshold * A))
* O(m L^2^)
The latter is the cost of the brute-force approach, so for
non-zero thresholds, the cost is always cheaper than the
brute-force approach.
:param: threshold: Set to 0 for deterministic guaranteed
correctness. Similarities above this
threshold are estimated with the cost vs
estimate quality trade-off described above.
:return: An n x n sparse upper-triangular CoordinateMatrix of
cosine similarities between columns of this matrix.
>>> rows = sc.parallelize([[1, 2], [1, 5]])
>>> mat = RowMatrix(rows)
>>> sims = mat.columnSimilarities()
>>> sims.entries.first().value
0.91914503...
"""
java_sims_mat = self._java_matrix_wrapper.call("columnSimilarities", float(threshold))
return CoordinateMatrix(java_sims_mat)
[docs] @since('2.0.0')
def tallSkinnyQR(self, computeQ=False):
"""
Compute the QR decomposition of this RowMatrix.
The implementation is designed to optimize the QR decomposition
(factorization) for the RowMatrix of a tall and skinny shape.
Reference:
Paul G. Constantine, David F. Gleich. "Tall and skinny QR
factorizations in MapReduce architectures"
([[http://dx.doi.org/10.1145/1996092.1996103]])
:param: computeQ: whether to computeQ
:return: QRDecomposition(Q: RowMatrix, R: Matrix), where
Q = None if computeQ = false.
>>> rows = sc.parallelize([[3, -6], [4, -8], [0, 1]])
>>> mat = RowMatrix(rows)
>>> decomp = mat.tallSkinnyQR(True)
>>> Q = decomp.Q
>>> R = decomp.R
>>> # Test with absolute values
>>> absQRows = Q.rows.map(lambda row: abs(row.toArray()).tolist())
>>> absQRows.collect()
[[0.6..., 0.0], [0.8..., 0.0], [0.0, 1.0]]
>>> # Test with absolute values
>>> abs(R.toArray()).tolist()
[[5.0, 10.0], [0.0, 1.0]]
"""
decomp = JavaModelWrapper(self._java_matrix_wrapper.call("tallSkinnyQR", computeQ))
if computeQ:
java_Q = decomp.call("Q")
Q = RowMatrix(java_Q)
else:
Q = None
R = decomp.call("R")
return QRDecomposition(Q, R)
[docs]class IndexedRow(object):
"""
Represents a row of an IndexedRowMatrix.
Just a wrapper over a (long, vector) tuple.
:param index: The index for the given row.
:param vector: The row in the matrix at the given index.
"""
def __init__(self, index, vector):
self.index = long(index)
self.vector = _convert_to_vector(vector)
def __repr__(self):
return "IndexedRow(%s, %s)" % (self.index, self.vector)
def _convert_to_indexed_row(row):
if isinstance(row, IndexedRow):
return row
elif isinstance(row, tuple) and len(row) == 2:
return IndexedRow(*row)
else:
raise TypeError("Cannot convert type %s into IndexedRow" % type(row))
[docs]class IndexedRowMatrix(DistributedMatrix):
"""
Represents a row-oriented distributed Matrix with indexed rows.
:param rows: An RDD of IndexedRows or (long, vector) tuples.
:param numRows: Number of rows in the matrix. A non-positive
value means unknown, at which point the number
of rows will be determined by the max row
index plus one.
:param numCols: Number of columns in the matrix. A non-positive
value means unknown, at which point the number
of columns will be determined by the size of
the first row.
"""
def __init__(self, rows, numRows=0, numCols=0):
"""
Note: This docstring is not shown publicly.
Create a wrapper over a Java IndexedRowMatrix.
Publicly, we require that `rows` be an RDD. However, for
internal usage, `rows` can also be a Java IndexedRowMatrix
object, in which case we can wrap it directly. This
assists in clean matrix conversions.
>>> rows = sc.parallelize([IndexedRow(0, [1, 2, 3]),
... IndexedRow(1, [4, 5, 6])])
>>> mat = IndexedRowMatrix(rows)
>>> mat_diff = IndexedRowMatrix(rows)
>>> (mat_diff._java_matrix_wrapper._java_model ==
... mat._java_matrix_wrapper._java_model)
False
>>> mat_same = IndexedRowMatrix(mat._java_matrix_wrapper._java_model)
>>> (mat_same._java_matrix_wrapper._java_model ==
... mat._java_matrix_wrapper._java_model)
True
"""
if isinstance(rows, RDD):
rows = rows.map(_convert_to_indexed_row)
# We use DataFrames for serialization of IndexedRows from
# Python, so first convert the RDD to a DataFrame on this
# side. This will convert each IndexedRow to a Row
# containing the 'index' and 'vector' values, which can
# both be easily serialized. We will convert back to
# IndexedRows on the Scala side.
java_matrix = callMLlibFunc("createIndexedRowMatrix", rows.toDF(),
long(numRows), int(numCols))
elif (isinstance(rows, JavaObject)
and rows.getClass().getSimpleName() == "IndexedRowMatrix"):
java_matrix = rows
else:
raise TypeError("rows should be an RDD of IndexedRows or (long, vector) tuples, "
"got %s" % type(rows))
self._java_matrix_wrapper = JavaModelWrapper(java_matrix)
@property
def rows(self):
"""
Rows of the IndexedRowMatrix stored as an RDD of IndexedRows.
>>> mat = IndexedRowMatrix(sc.parallelize([IndexedRow(0, [1, 2, 3]),
... IndexedRow(1, [4, 5, 6])]))
>>> rows = mat.rows
>>> rows.first()
IndexedRow(0, [1.0,2.0,3.0])
"""
# We use DataFrames for serialization of IndexedRows from
# Java, so we first convert the RDD of rows to a DataFrame
# on the Scala/Java side. Then we map each Row in the
# DataFrame back to an IndexedRow on this side.
rows_df = callMLlibFunc("getIndexedRows", self._java_matrix_wrapper._java_model)
rows = rows_df.rdd.map(lambda row: IndexedRow(row[0], row[1]))
return rows
[docs] def numRows(self):
"""
Get or compute the number of rows.
>>> rows = sc.parallelize([IndexedRow(0, [1, 2, 3]),
... IndexedRow(1, [4, 5, 6]),
... IndexedRow(2, [7, 8, 9]),
... IndexedRow(3, [10, 11, 12])])
>>> mat = IndexedRowMatrix(rows)
>>> print(mat.numRows())
4
>>> mat = IndexedRowMatrix(rows, 7, 6)
>>> print(mat.numRows())
7
"""
return self._java_matrix_wrapper.call("numRows")
[docs] def numCols(self):
"""
Get or compute the number of cols.
>>> rows = sc.parallelize([IndexedRow(0, [1, 2, 3]),
... IndexedRow(1, [4, 5, 6]),
... IndexedRow(2, [7, 8, 9]),
... IndexedRow(3, [10, 11, 12])])
>>> mat = IndexedRowMatrix(rows)
>>> print(mat.numCols())
3
>>> mat = IndexedRowMatrix(rows, 7, 6)
>>> print(mat.numCols())
6
"""
return self._java_matrix_wrapper.call("numCols")
[docs] def columnSimilarities(self):
"""
Compute all cosine similarities between columns.
>>> rows = sc.parallelize([IndexedRow(0, [1, 2, 3]),
... IndexedRow(6, [4, 5, 6])])
>>> mat = IndexedRowMatrix(rows)
>>> cs = mat.columnSimilarities()
>>> print(cs.numCols())
3
"""
java_coordinate_matrix = self._java_matrix_wrapper.call("columnSimilarities")
return CoordinateMatrix(java_coordinate_matrix)
[docs] @since('2.0.0')
def computeGramianMatrix(self):
"""
Computes the Gramian matrix `A^T A`.
.. note:: This cannot be computed on matrices with more than 65535 columns.
>>> rows = sc.parallelize([IndexedRow(0, [1, 2, 3]),
... IndexedRow(1, [4, 5, 6])])
>>> mat = IndexedRowMatrix(rows)
>>> mat.computeGramianMatrix()
DenseMatrix(3, 3, [17.0, 22.0, 27.0, 22.0, 29.0, 36.0, 27.0, 36.0, 45.0], 0)
"""
return self._java_matrix_wrapper.call("computeGramianMatrix")
[docs] def toRowMatrix(self):
"""
Convert this matrix to a RowMatrix.
>>> rows = sc.parallelize([IndexedRow(0, [1, 2, 3]),
... IndexedRow(6, [4, 5, 6])])
>>> mat = IndexedRowMatrix(rows).toRowMatrix()
>>> mat.rows.collect()
[DenseVector([1.0, 2.0, 3.0]), DenseVector([4.0, 5.0, 6.0])]
"""
java_row_matrix = self._java_matrix_wrapper.call("toRowMatrix")
return RowMatrix(java_row_matrix)
[docs] def toCoordinateMatrix(self):
"""
Convert this matrix to a CoordinateMatrix.
>>> rows = sc.parallelize([IndexedRow(0, [1, 0]),
... IndexedRow(6, [0, 5])])
>>> mat = IndexedRowMatrix(rows).toCoordinateMatrix()
>>> mat.entries.take(3)
[MatrixEntry(0, 0, 1.0), MatrixEntry(0, 1, 0.0), MatrixEntry(6, 0, 0.0)]
"""
java_coordinate_matrix = self._java_matrix_wrapper.call("toCoordinateMatrix")
return CoordinateMatrix(java_coordinate_matrix)
[docs] def toBlockMatrix(self, rowsPerBlock=1024, colsPerBlock=1024):
"""
Convert this matrix to a BlockMatrix.
:param rowsPerBlock: Number of rows that make up each block.
The blocks forming the final rows are not
required to have the given number of rows.
:param colsPerBlock: Number of columns that make up each block.
The blocks forming the final columns are not
required to have the given number of columns.
>>> rows = sc.parallelize([IndexedRow(0, [1, 2, 3]),
... IndexedRow(6, [4, 5, 6])])
>>> mat = IndexedRowMatrix(rows).toBlockMatrix()
>>> # This IndexedRowMatrix will have 7 effective rows, due to
>>> # the highest row index being 6, and the ensuing
>>> # BlockMatrix will have 7 rows as well.
>>> print(mat.numRows())
7
>>> print(mat.numCols())
3
"""
java_block_matrix = self._java_matrix_wrapper.call("toBlockMatrix",
rowsPerBlock,
colsPerBlock)
return BlockMatrix(java_block_matrix, rowsPerBlock, colsPerBlock)
[docs]class MatrixEntry(object):
"""
Represents an entry of a CoordinateMatrix.
Just a wrapper over a (long, long, float) tuple.
:param i: The row index of the matrix.
:param j: The column index of the matrix.
:param value: The (i, j)th entry of the matrix, as a float.
"""
def __init__(self, i, j, value):
self.i = long(i)
self.j = long(j)
self.value = float(value)
def __repr__(self):
return "MatrixEntry(%s, %s, %s)" % (self.i, self.j, self.value)
def _convert_to_matrix_entry(entry):
if isinstance(entry, MatrixEntry):
return entry
elif isinstance(entry, tuple) and len(entry) == 3:
return MatrixEntry(*entry)
else:
raise TypeError("Cannot convert type %s into MatrixEntry" % type(entry))
[docs]class CoordinateMatrix(DistributedMatrix):
"""
Represents a matrix in coordinate format.
:param entries: An RDD of MatrixEntry inputs or
(long, long, float) tuples.
:param numRows: Number of rows in the matrix. A non-positive
value means unknown, at which point the number
of rows will be determined by the max row
index plus one.
:param numCols: Number of columns in the matrix. A non-positive
value means unknown, at which point the number
of columns will be determined by the max row
index plus one.
"""
def __init__(self, entries, numRows=0, numCols=0):
"""
Note: This docstring is not shown publicly.
Create a wrapper over a Java CoordinateMatrix.
Publicly, we require that `rows` be an RDD. However, for
internal usage, `rows` can also be a Java CoordinateMatrix
object, in which case we can wrap it directly. This
assists in clean matrix conversions.
>>> entries = sc.parallelize([MatrixEntry(0, 0, 1.2),
... MatrixEntry(6, 4, 2.1)])
>>> mat = CoordinateMatrix(entries)
>>> mat_diff = CoordinateMatrix(entries)
>>> (mat_diff._java_matrix_wrapper._java_model ==
... mat._java_matrix_wrapper._java_model)
False
>>> mat_same = CoordinateMatrix(mat._java_matrix_wrapper._java_model)
>>> (mat_same._java_matrix_wrapper._java_model ==
... mat._java_matrix_wrapper._java_model)
True
"""
if isinstance(entries, RDD):
entries = entries.map(_convert_to_matrix_entry)
# We use DataFrames for serialization of MatrixEntry entries
# from Python, so first convert the RDD to a DataFrame on
# this side. This will convert each MatrixEntry to a Row
# containing the 'i', 'j', and 'value' values, which can
# each be easily serialized. We will convert back to
# MatrixEntry inputs on the Scala side.
java_matrix = callMLlibFunc("createCoordinateMatrix", entries.toDF(),
long(numRows), long(numCols))
elif (isinstance(entries, JavaObject)
and entries.getClass().getSimpleName() == "CoordinateMatrix"):
java_matrix = entries
else:
raise TypeError("entries should be an RDD of MatrixEntry entries or "
"(long, long, float) tuples, got %s" % type(entries))
self._java_matrix_wrapper = JavaModelWrapper(java_matrix)
@property
def entries(self):
"""
Entries of the CoordinateMatrix stored as an RDD of
MatrixEntries.
>>> mat = CoordinateMatrix(sc.parallelize([MatrixEntry(0, 0, 1.2),
... MatrixEntry(6, 4, 2.1)]))
>>> entries = mat.entries
>>> entries.first()
MatrixEntry(0, 0, 1.2)
"""
# We use DataFrames for serialization of MatrixEntry entries
# from Java, so we first convert the RDD of entries to a
# DataFrame on the Scala/Java side. Then we map each Row in
# the DataFrame back to a MatrixEntry on this side.
entries_df = callMLlibFunc("getMatrixEntries", self._java_matrix_wrapper._java_model)
entries = entries_df.rdd.map(lambda row: MatrixEntry(row[0], row[1], row[2]))
return entries
[docs] def numRows(self):
"""
Get or compute the number of rows.
>>> entries = sc.parallelize([MatrixEntry(0, 0, 1.2),
... MatrixEntry(1, 0, 2),
... MatrixEntry(2, 1, 3.7)])
>>> mat = CoordinateMatrix(entries)
>>> print(mat.numRows())
3
>>> mat = CoordinateMatrix(entries, 7, 6)
>>> print(mat.numRows())
7
"""
return self._java_matrix_wrapper.call("numRows")
[docs] def numCols(self):
"""
Get or compute the number of cols.
>>> entries = sc.parallelize([MatrixEntry(0, 0, 1.2),
... MatrixEntry(1, 0, 2),
... MatrixEntry(2, 1, 3.7)])
>>> mat = CoordinateMatrix(entries)
>>> print(mat.numCols())
2
>>> mat = CoordinateMatrix(entries, 7, 6)
>>> print(mat.numCols())
6
"""
return self._java_matrix_wrapper.call("numCols")
[docs] @since('2.0.0')
def transpose(self):
"""
Transpose this CoordinateMatrix.
>>> entries = sc.parallelize([MatrixEntry(0, 0, 1.2),
... MatrixEntry(1, 0, 2),
... MatrixEntry(2, 1, 3.7)])
>>> mat = CoordinateMatrix(entries)
>>> mat_transposed = mat.transpose()
>>> print(mat_transposed.numRows())
2
>>> print(mat_transposed.numCols())
3
"""
java_transposed_matrix = self._java_matrix_wrapper.call("transpose")
return CoordinateMatrix(java_transposed_matrix)
[docs] def toRowMatrix(self):
"""
Convert this matrix to a RowMatrix.
>>> entries = sc.parallelize([MatrixEntry(0, 0, 1.2),
... MatrixEntry(6, 4, 2.1)])
>>> mat = CoordinateMatrix(entries).toRowMatrix()
>>> # This CoordinateMatrix will have 7 effective rows, due to
>>> # the highest row index being 6, but the ensuing RowMatrix
>>> # will only have 2 rows since there are only entries on 2
>>> # unique rows.
>>> print(mat.numRows())
2
>>> # This CoordinateMatrix will have 5 columns, due to the
>>> # highest column index being 4, and the ensuing RowMatrix
>>> # will have 5 columns as well.
>>> print(mat.numCols())
5
"""
java_row_matrix = self._java_matrix_wrapper.call("toRowMatrix")
return RowMatrix(java_row_matrix)
[docs] def toIndexedRowMatrix(self):
"""
Convert this matrix to an IndexedRowMatrix.
>>> entries = sc.parallelize([MatrixEntry(0, 0, 1.2),
... MatrixEntry(6, 4, 2.1)])
>>> mat = CoordinateMatrix(entries).toIndexedRowMatrix()
>>> # This CoordinateMatrix will have 7 effective rows, due to
>>> # the highest row index being 6, and the ensuing
>>> # IndexedRowMatrix will have 7 rows as well.
>>> print(mat.numRows())
7
>>> # This CoordinateMatrix will have 5 columns, due to the
>>> # highest column index being 4, and the ensuing
>>> # IndexedRowMatrix will have 5 columns as well.
>>> print(mat.numCols())
5
"""
java_indexed_row_matrix = self._java_matrix_wrapper.call("toIndexedRowMatrix")
return IndexedRowMatrix(java_indexed_row_matrix)
[docs] def toBlockMatrix(self, rowsPerBlock=1024, colsPerBlock=1024):
"""
Convert this matrix to a BlockMatrix.
:param rowsPerBlock: Number of rows that make up each block.
The blocks forming the final rows are not
required to have the given number of rows.
:param colsPerBlock: Number of columns that make up each block.
The blocks forming the final columns are not
required to have the given number of columns.
>>> entries = sc.parallelize([MatrixEntry(0, 0, 1.2),
... MatrixEntry(6, 4, 2.1)])
>>> mat = CoordinateMatrix(entries).toBlockMatrix()
>>> # This CoordinateMatrix will have 7 effective rows, due to
>>> # the highest row index being 6, and the ensuing
>>> # BlockMatrix will have 7 rows as well.
>>> print(mat.numRows())
7
>>> # This CoordinateMatrix will have 5 columns, due to the
>>> # highest column index being 4, and the ensuing
>>> # BlockMatrix will have 5 columns as well.
>>> print(mat.numCols())
5
"""
java_block_matrix = self._java_matrix_wrapper.call("toBlockMatrix",
rowsPerBlock,
colsPerBlock)
return BlockMatrix(java_block_matrix, rowsPerBlock, colsPerBlock)
def _convert_to_matrix_block_tuple(block):
if (isinstance(block, tuple) and len(block) == 2
and isinstance(block[0], tuple) and len(block[0]) == 2
and isinstance(block[1], Matrix)):
blockRowIndex = int(block[0][0])
blockColIndex = int(block[0][1])
subMatrix = block[1]
return ((blockRowIndex, blockColIndex), subMatrix)
else:
raise TypeError("Cannot convert type %s into a sub-matrix block tuple" % type(block))
[docs]class BlockMatrix(DistributedMatrix):
"""
Represents a distributed matrix in blocks of local matrices.
:param blocks: An RDD of sub-matrix blocks
((blockRowIndex, blockColIndex), sub-matrix) that
form this distributed matrix. If multiple blocks
with the same index exist, the results for
operations like add and multiply will be
unpredictable.
:param rowsPerBlock: Number of rows that make up each block.
The blocks forming the final rows are not
required to have the given number of rows.
:param colsPerBlock: Number of columns that make up each block.
The blocks forming the final columns are not
required to have the given number of columns.
:param numRows: Number of rows of this matrix. If the supplied
value is less than or equal to zero, the number
of rows will be calculated when `numRows` is
invoked.
:param numCols: Number of columns of this matrix. If the supplied
value is less than or equal to zero, the number
of columns will be calculated when `numCols` is
invoked.
"""
def __init__(self, blocks, rowsPerBlock, colsPerBlock, numRows=0, numCols=0):
"""
Note: This docstring is not shown publicly.
Create a wrapper over a Java BlockMatrix.
Publicly, we require that `blocks` be an RDD. However, for
internal usage, `blocks` can also be a Java BlockMatrix
object, in which case we can wrap it directly. This
assists in clean matrix conversions.
>>> blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
... ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])
>>> mat = BlockMatrix(blocks, 3, 2)
>>> mat_diff = BlockMatrix(blocks, 3, 2)
>>> (mat_diff._java_matrix_wrapper._java_model ==
... mat._java_matrix_wrapper._java_model)
False
>>> mat_same = BlockMatrix(mat._java_matrix_wrapper._java_model, 3, 2)
>>> (mat_same._java_matrix_wrapper._java_model ==
... mat._java_matrix_wrapper._java_model)
True
"""
if isinstance(blocks, RDD):
blocks = blocks.map(_convert_to_matrix_block_tuple)
# We use DataFrames for serialization of sub-matrix blocks
# from Python, so first convert the RDD to a DataFrame on
# this side. This will convert each sub-matrix block
# tuple to a Row containing the 'blockRowIndex',
# 'blockColIndex', and 'subMatrix' values, which can
# each be easily serialized. We will convert back to
# ((blockRowIndex, blockColIndex), sub-matrix) tuples on
# the Scala side.
java_matrix = callMLlibFunc("createBlockMatrix", blocks.toDF(),
int(rowsPerBlock), int(colsPerBlock),
long(numRows), long(numCols))
elif (isinstance(blocks, JavaObject)
and blocks.getClass().getSimpleName() == "BlockMatrix"):
java_matrix = blocks
else:
raise TypeError("blocks should be an RDD of sub-matrix blocks as "
"((int, int), matrix) tuples, got %s" % type(blocks))
self._java_matrix_wrapper = JavaModelWrapper(java_matrix)
@property
def blocks(self):
"""
The RDD of sub-matrix blocks
((blockRowIndex, blockColIndex), sub-matrix) that form this
distributed matrix.
>>> mat = BlockMatrix(
... sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
... ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))]), 3, 2)
>>> blocks = mat.blocks
>>> blocks.first()
((0, 0), DenseMatrix(3, 2, [1.0, 2.0, 3.0, 4.0, 5.0, 6.0], 0))
"""
# We use DataFrames for serialization of sub-matrix blocks
# from Java, so we first convert the RDD of blocks to a
# DataFrame on the Scala/Java side. Then we map each Row in
# the DataFrame back to a sub-matrix block on this side.
blocks_df = callMLlibFunc("getMatrixBlocks", self._java_matrix_wrapper._java_model)
blocks = blocks_df.rdd.map(lambda row: ((row[0][0], row[0][1]), row[1]))
return blocks
@property
def rowsPerBlock(self):
"""
Number of rows that make up each block.
>>> blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
... ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])
>>> mat = BlockMatrix(blocks, 3, 2)
>>> mat.rowsPerBlock
3
"""
return self._java_matrix_wrapper.call("rowsPerBlock")
@property
def colsPerBlock(self):
"""
Number of columns that make up each block.
>>> blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
... ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])
>>> mat = BlockMatrix(blocks, 3, 2)
>>> mat.colsPerBlock
2
"""
return self._java_matrix_wrapper.call("colsPerBlock")
@property
def numRowBlocks(self):
"""
Number of rows of blocks in the BlockMatrix.
>>> blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
... ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])
>>> mat = BlockMatrix(blocks, 3, 2)
>>> mat.numRowBlocks
2
"""
return self._java_matrix_wrapper.call("numRowBlocks")
@property
def numColBlocks(self):
"""
Number of columns of blocks in the BlockMatrix.
>>> blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
... ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])
>>> mat = BlockMatrix(blocks, 3, 2)
>>> mat.numColBlocks
1
"""
return self._java_matrix_wrapper.call("numColBlocks")
[docs] def numRows(self):
"""
Get or compute the number of rows.
>>> blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
... ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])
>>> mat = BlockMatrix(blocks, 3, 2)
>>> print(mat.numRows())
6
>>> mat = BlockMatrix(blocks, 3, 2, 7, 6)
>>> print(mat.numRows())
7
"""
return self._java_matrix_wrapper.call("numRows")
[docs] def numCols(self):
"""
Get or compute the number of cols.
>>> blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
... ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])
>>> mat = BlockMatrix(blocks, 3, 2)
>>> print(mat.numCols())
2
>>> mat = BlockMatrix(blocks, 3, 2, 7, 6)
>>> print(mat.numCols())
6
"""
return self._java_matrix_wrapper.call("numCols")
[docs] @since('2.0.0')
def cache(self):
"""
Caches the underlying RDD.
"""
self._java_matrix_wrapper.call("cache")
return self
[docs] @since('2.0.0')
def persist(self, storageLevel):
"""
Persists the underlying RDD with the specified storage level.
"""
if not isinstance(storageLevel, StorageLevel):
raise TypeError("`storageLevel` should be a StorageLevel, got %s" % type(storageLevel))
javaStorageLevel = self._java_matrix_wrapper._sc._getJavaStorageLevel(storageLevel)
self._java_matrix_wrapper.call("persist", javaStorageLevel)
return self
[docs] @since('2.0.0')
def validate(self):
"""
Validates the block matrix info against the matrix data (`blocks`)
and throws an exception if any error is found.
"""
self._java_matrix_wrapper.call("validate")
[docs] def add(self, other):
"""
Adds two block matrices together. The matrices must have the
same size and matching `rowsPerBlock` and `colsPerBlock` values.
If one of the sub matrix blocks that are being added is a
SparseMatrix, the resulting sub matrix block will also be a
SparseMatrix, even if it is being added to a DenseMatrix. If
two dense sub matrix blocks are added, the output block will
also be a DenseMatrix.
>>> dm1 = Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])
>>> dm2 = Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12])
>>> sm = Matrices.sparse(3, 2, [0, 1, 3], [0, 1, 2], [7, 11, 12])
>>> blocks1 = sc.parallelize([((0, 0), dm1), ((1, 0), dm2)])
>>> blocks2 = sc.parallelize([((0, 0), dm1), ((1, 0), dm2)])
>>> blocks3 = sc.parallelize([((0, 0), sm), ((1, 0), dm2)])
>>> mat1 = BlockMatrix(blocks1, 3, 2)
>>> mat2 = BlockMatrix(blocks2, 3, 2)
>>> mat3 = BlockMatrix(blocks3, 3, 2)
>>> mat1.add(mat2).toLocalMatrix()
DenseMatrix(6, 2, [2.0, 4.0, 6.0, 14.0, 16.0, 18.0, 8.0, 10.0, 12.0, 20.0, 22.0, 24.0], 0)
>>> mat1.add(mat3).toLocalMatrix()
DenseMatrix(6, 2, [8.0, 2.0, 3.0, 14.0, 16.0, 18.0, 4.0, 16.0, 18.0, 20.0, 22.0, 24.0], 0)
"""
if not isinstance(other, BlockMatrix):
raise TypeError("Other should be a BlockMatrix, got %s" % type(other))
other_java_block_matrix = other._java_matrix_wrapper._java_model
java_block_matrix = self._java_matrix_wrapper.call("add", other_java_block_matrix)
return BlockMatrix(java_block_matrix, self.rowsPerBlock, self.colsPerBlock)
[docs] @since('2.0.0')
def subtract(self, other):
"""
Subtracts the given block matrix `other` from this block matrix:
`this - other`. The matrices must have the same size and
matching `rowsPerBlock` and `colsPerBlock` values. If one of
the sub matrix blocks that are being subtracted is a
SparseMatrix, the resulting sub matrix block will also be a
SparseMatrix, even if it is being subtracted from a DenseMatrix.
If two dense sub matrix blocks are subtracted, the output block
will also be a DenseMatrix.
>>> dm1 = Matrices.dense(3, 2, [3, 1, 5, 4, 6, 2])
>>> dm2 = Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12])
>>> sm = Matrices.sparse(3, 2, [0, 1, 3], [0, 1, 2], [1, 2, 3])
>>> blocks1 = sc.parallelize([((0, 0), dm1), ((1, 0), dm2)])
>>> blocks2 = sc.parallelize([((0, 0), dm2), ((1, 0), dm1)])
>>> blocks3 = sc.parallelize([((0, 0), sm), ((1, 0), dm2)])
>>> mat1 = BlockMatrix(blocks1, 3, 2)
>>> mat2 = BlockMatrix(blocks2, 3, 2)
>>> mat3 = BlockMatrix(blocks3, 3, 2)
>>> mat1.subtract(mat2).toLocalMatrix()
DenseMatrix(6, 2, [-4.0, -7.0, -4.0, 4.0, 7.0, 4.0, -6.0, -5.0, -10.0, 6.0, 5.0, 10.0], 0)
>>> mat2.subtract(mat3).toLocalMatrix()
DenseMatrix(6, 2, [6.0, 8.0, 9.0, -4.0, -7.0, -4.0, 10.0, 9.0, 9.0, -6.0, -5.0, -10.0], 0)
"""
if not isinstance(other, BlockMatrix):
raise TypeError("Other should be a BlockMatrix, got %s" % type(other))
other_java_block_matrix = other._java_matrix_wrapper._java_model
java_block_matrix = self._java_matrix_wrapper.call("subtract", other_java_block_matrix)
return BlockMatrix(java_block_matrix, self.rowsPerBlock, self.colsPerBlock)
[docs] def multiply(self, other):
"""
Left multiplies this BlockMatrix by `other`, another
BlockMatrix. The `colsPerBlock` of this matrix must equal the
`rowsPerBlock` of `other`. If `other` contains any SparseMatrix
blocks, they will have to be converted to DenseMatrix blocks.
The output BlockMatrix will only consist of DenseMatrix blocks.
This may cause some performance issues until support for
multiplying two sparse matrices is added.
>>> dm1 = Matrices.dense(2, 3, [1, 2, 3, 4, 5, 6])
>>> dm2 = Matrices.dense(2, 3, [7, 8, 9, 10, 11, 12])
>>> dm3 = Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])
>>> dm4 = Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12])
>>> sm = Matrices.sparse(3, 2, [0, 1, 3], [0, 1, 2], [7, 11, 12])
>>> blocks1 = sc.parallelize([((0, 0), dm1), ((0, 1), dm2)])
>>> blocks2 = sc.parallelize([((0, 0), dm3), ((1, 0), dm4)])
>>> blocks3 = sc.parallelize([((0, 0), sm), ((1, 0), dm4)])
>>> mat1 = BlockMatrix(blocks1, 2, 3)
>>> mat2 = BlockMatrix(blocks2, 3, 2)
>>> mat3 = BlockMatrix(blocks3, 3, 2)
>>> mat1.multiply(mat2).toLocalMatrix()
DenseMatrix(2, 2, [242.0, 272.0, 350.0, 398.0], 0)
>>> mat1.multiply(mat3).toLocalMatrix()
DenseMatrix(2, 2, [227.0, 258.0, 394.0, 450.0], 0)
"""
if not isinstance(other, BlockMatrix):
raise TypeError("Other should be a BlockMatrix, got %s" % type(other))
other_java_block_matrix = other._java_matrix_wrapper._java_model
java_block_matrix = self._java_matrix_wrapper.call("multiply", other_java_block_matrix)
return BlockMatrix(java_block_matrix, self.rowsPerBlock, self.colsPerBlock)
[docs] @since('2.0.0')
def transpose(self):
"""
Transpose this BlockMatrix. Returns a new BlockMatrix
instance sharing the same underlying data. Is a lazy operation.
>>> blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
... ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])
>>> mat = BlockMatrix(blocks, 3, 2)
>>> mat_transposed = mat.transpose()
>>> mat_transposed.toLocalMatrix()
DenseMatrix(2, 6, [1.0, 4.0, 2.0, 5.0, 3.0, 6.0, 7.0, 10.0, 8.0, 11.0, 9.0, 12.0], 0)
"""
java_transposed_matrix = self._java_matrix_wrapper.call("transpose")
return BlockMatrix(java_transposed_matrix, self.colsPerBlock, self.rowsPerBlock)
[docs] def toLocalMatrix(self):
"""
Collect the distributed matrix on the driver as a DenseMatrix.
>>> blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
... ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])
>>> mat = BlockMatrix(blocks, 3, 2).toLocalMatrix()
>>> # This BlockMatrix will have 6 effective rows, due to
>>> # having two sub-matrix blocks stacked, each with 3 rows.
>>> # The ensuing DenseMatrix will also have 6 rows.
>>> print(mat.numRows)
6
>>> # This BlockMatrix will have 2 effective columns, due to
>>> # having two sub-matrix blocks stacked, each with 2
>>> # columns. The ensuing DenseMatrix will also have 2 columns.
>>> print(mat.numCols)
2
"""
return self._java_matrix_wrapper.call("toLocalMatrix")
[docs] def toIndexedRowMatrix(self):
"""
Convert this matrix to an IndexedRowMatrix.
>>> blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
... ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])
>>> mat = BlockMatrix(blocks, 3, 2).toIndexedRowMatrix()
>>> # This BlockMatrix will have 6 effective rows, due to
>>> # having two sub-matrix blocks stacked, each with 3 rows.
>>> # The ensuing IndexedRowMatrix will also have 6 rows.
>>> print(mat.numRows())
6
>>> # This BlockMatrix will have 2 effective columns, due to
>>> # having two sub-matrix blocks stacked, each with 2 columns.
>>> # The ensuing IndexedRowMatrix will also have 2 columns.
>>> print(mat.numCols())
2
"""
java_indexed_row_matrix = self._java_matrix_wrapper.call("toIndexedRowMatrix")
return IndexedRowMatrix(java_indexed_row_matrix)
[docs] def toCoordinateMatrix(self):
"""
Convert this matrix to a CoordinateMatrix.
>>> blocks = sc.parallelize([((0, 0), Matrices.dense(1, 2, [1, 2])),
... ((1, 0), Matrices.dense(1, 2, [7, 8]))])
>>> mat = BlockMatrix(blocks, 1, 2).toCoordinateMatrix()
>>> mat.entries.take(3)
[MatrixEntry(0, 0, 1.0), MatrixEntry(0, 1, 2.0), MatrixEntry(1, 0, 7.0)]
"""
java_coordinate_matrix = self._java_matrix_wrapper.call("toCoordinateMatrix")
return CoordinateMatrix(java_coordinate_matrix)
def _test():
import doctest
from pyspark.sql import SparkSession
from pyspark.mllib.linalg import Matrices
import pyspark.mllib.linalg.distributed
globs = pyspark.mllib.linalg.distributed.__dict__.copy()
spark = SparkSession.builder\
.master("local[2]")\
.appName("mllib.linalg.distributed tests")\
.getOrCreate()
globs['sc'] = spark.sparkContext
globs['Matrices'] = Matrices
(failure_count, test_count) = doctest.testmod(globs=globs, optionflags=doctest.ELLIPSIS)
spark.stop()
if failure_count:
exit(-1)
if __name__ == "__main__":
_test()
