Class RowMatrix
 All Implemented Interfaces:
Serializable
,org.apache.spark.internal.Logging
,DistributedMatrix
,scala.Serializable
param: rows rows stored as an RDD[Vector]
param: nRows number of rows. A nonpositive value means unknown, and then the number of rows will
be determined by the number of records in the RDD rows
.
param: nCols number of columns. A nonpositive value means unknown, and then the number of
columns will be determined by the size of the first row.
 See Also:

Nested Class Summary
Nested classes/interfaces inherited from interface org.apache.spark.internal.Logging
org.apache.spark.internal.Logging.SparkShellLoggingFilter

Constructor Summary

Method Summary
Modifier and TypeMethodDescriptionCompute all cosine similarities between columns of this matrix using the bruteforce approach of computing normalized dot products.columnSimilarities
(double threshold) Compute similarities between columns of this matrix using a sampling approach.Computes columnwise summary statistics.Computes the covariance matrix, treating each row as an observation.Computes the Gramian matrixA^T A
.computePrincipalComponents
(int k) Computes the top k principal components only.Computes the top k principal components and a vector of proportions of variance explained by each principal component.computeSVD
(int k, boolean computeU, double rCond) Computes singular value decomposition of this matrix.Multiply this matrix by a local matrix on the right.long
numCols()
Gets or computes the number of columns.long
numRows()
Gets or computes the number of rows.rows()
tallSkinnyQR
(boolean computeQ) Compute QR decomposition forRowMatrix
.Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
Methods inherited from interface org.apache.spark.internal.Logging
initializeForcefully, initializeLogIfNecessary, initializeLogIfNecessary, initializeLogIfNecessary$default$2, isTraceEnabled, log, logDebug, logDebug, logError, logError, logInfo, logInfo, logName, logTrace, logTrace, logWarning, logWarning, org$apache$spark$internal$Logging$$log_, org$apache$spark$internal$Logging$$log__$eq

Constructor Details

RowMatrix

RowMatrix
Alternative constructor leaving matrix dimensions to be determined automatically.


Method Details

rows

numCols
public long numCols()Gets or computes the number of columns. Specified by:
numCols
in interfaceDistributedMatrix

numRows
public long numRows()Gets or computes the number of rows. Specified by:
numRows
in interfaceDistributedMatrix

computeGramianMatrix
Computes the Gramian matrixA^T A
. Returns:
 (undocumented)
 Note:
 This cannot be computed on matrices with more than 65535 columns.

computeSVD
public SingularValueDecomposition<RowMatrix,Matrix> computeSVD(int k, boolean computeU, double rCond) Computes singular value decomposition of this matrix. Denote this matrix by A (m x n). This will compute matrices U, S, V such that A ~= U * S * V', where S contains the leading k singular values, U and V contain the corresponding singular vectors.At most k largest nonzero singular values and associated vectors are returned. If there are k such values, then the dimensions of the return will be:  U is a RowMatrix of size m x k that satisfies U' * U = eye(k),  s is a Vector of size k, holding the singular values in descending order,  V is a Matrix of size n x k that satisfies V' * V = eye(k).
We assume n is smaller than m, though this is not strictly required. The singular values and the right singular vectors are derived from the eigenvalues and the eigenvectors of the Gramian matrix A' * A. U, the matrix storing the right singular vectors, is computed via matrix multiplication as U = A * (V * S^1^), if requested by user. The actual method to use is determined automatically based on the cost:  If n is small (n < 100) or k is large compared with n (k > n / 2), we compute the Gramian matrix first and then compute its top eigenvalues and eigenvectors locally on the driver. This requires a single pass with O(n^2^) storage on each executor and on the driver, and O(n^2^ k) time on the driver.  Otherwise, we compute (A' * A) * v in a distributive way and send it to ARPACK's DSAUPD to compute (A' * A)'s top eigenvalues and eigenvectors on the driver node. This requires O(k) passes, O(n) storage on each executor, and O(n k) storage on the driver.
Several internal parameters are set to default values. The reciprocal condition number rCond is set to 1e9. All singular values smaller than rCond * sigma(0) are treated as zeros, where sigma(0) is the largest singular value. The maximum number of Arnoldi update iterations for ARPACK is set to 300 or k * 3, whichever is larger. The numerical tolerance for ARPACK's eigendecomposition is set to 1e10.
 Parameters:
k
 number of leading singular values to keep (0 < k <= n). It might return less than k if there are numerically zero singular values or there are not enough Ritz values converged before the maximum number of Arnoldi update iterations is reached (in case that matrix A is illconditioned).computeU
 whether to compute UrCond
 the reciprocal condition number. All singular values smaller than rCond * sigma(0) are treated as zero, where sigma(0) is the largest singular value. Returns:
 SingularValueDecomposition(U, s, V). U = null if computeU = false.
 Note:
 The conditions that decide which method to use internally and the default parameters are subject to change.

computeCovariance
Computes the covariance matrix, treating each row as an observation. Returns:
 a local dense matrix of size n x n
 Note:
 This cannot be computed on matrices with more than 65535 columns.

computePrincipalComponentsAndExplainedVariance
Computes the top k principal components and a vector of proportions of variance explained by each principal component. Rows correspond to observations and columns correspond to variables. The principal components are stored a local matrix of size nbyk. Each column corresponds for one principal component, and the columns are in descending order of component variance. The row data do not need to be "centered" first; it is not necessary for the mean of each column to be 0. But, if the number of columns are more than 65535, then the data need to be "centered". Parameters:
k
 number of top principal components. Returns:
 a matrix of size nbyk, whose columns are principal components, and a vector of values which indicate how much variance each principal component explains

computePrincipalComponents
Computes the top k principal components only. Parameters:
k
 number of top principal components. Returns:
 a matrix of size nbyk, whose columns are principal components
 See Also:

computeColumnSummaryStatistics
Computes columnwise summary statistics. Returns:
 (undocumented)

multiply
Multiply this matrix by a local matrix on the right. Parameters:
B
 a local matrix whose number of rows must match the number of columns of this matrix Returns:
 a
RowMatrix
representing the product, which preserves partitioning

columnSimilarities
Compute all cosine similarities between columns of this matrix using the bruteforce approach of computing normalized dot products. Returns:
 An n x n sparse uppertriangular matrix of cosine similarities between columns of this matrix.

columnSimilarities
Compute similarities between columns of this matrix using a sampling approach.The threshold parameter is a tradeoff knob between estimate quality and computational cost.
Setting a threshold of 0 guarantees deterministic correct results, but comes at exactly the same cost as the bruteforce approach. Setting the threshold to positive values incurs strictly less computational cost than the bruteforce approach, however the similarities computed will be estimates.
The sampling guarantees relativeerror 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 nonzero element of this matrix. Let B be the largest in magnitude nonzero element of this matrix. Let L be the maximum number of nonzeros 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 bruteforce approach, so for nonzero thresholds, the cost is always cheaper than the bruteforce approach.
 Parameters:
threshold
 Set to 0 for deterministic guaranteed correctness. Similarities above this threshold are estimated with the cost vs estimate quality tradeoff described above. Returns:
 An n x n sparse uppertriangular matrix of cosine similarities between columns of this matrix.

tallSkinnyQR
Compute QR decomposition forRowMatrix
. The implementation is designed to optimize the QR decomposition (factorization) for theRowMatrix
of a tall and skinny shape. Reference: Paul G. Constantine, David F. Gleich. "Tall and skinny QR factorizations in MapReduce architectures" (see here) Parameters:
computeQ
 whether to computeQ Returns:
 QRDecomposition(Q, R), Q = null if computeQ = false.
