public class RowMatrix extends Object implements DistributedMatrix, Logging
| Constructor and Description |
|---|
RowMatrix(RDD<Vector> rows)
Alternative constructor leaving matrix dimensions to be determined automatically.
|
RowMatrix(RDD<Vector> rows,
long nRows,
int nCols) |
| Modifier and Type | Method and Description |
|---|---|
MultivariateStatisticalSummary |
computeColumnSummaryStatistics()
Computes column-wise summary statistics.
|
Matrix |
computeCovariance()
Computes the covariance matrix, treating each row as an observation.
|
Matrix |
computeGramianMatrix()
Computes the Gramian matrix
A^T A. |
Matrix |
computePrincipalComponents(int k)
Computes the top k principal components.
|
SingularValueDecomposition<RowMatrix,Matrix> |
computeSVD(int k,
boolean computeU,
double rCond)
Computes singular value decomposition of this matrix.
|
RowMatrix |
multiply(Matrix B)
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.
|
RDD<Vector> |
rows() |
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, waitinitialized, initializeIfNecessary, initializeLogging, initLock, isTraceEnabled, log_, log, logDebug, logDebug, logError, logError, logInfo, logInfo, logName, logTrace, logTrace, logWarning, logWarningpublic long numCols()
numCols in interface DistributedMatrixpublic long numRows()
numRows in interface DistributedMatrixpublic Matrix computeGramianMatrix()
A^T A.public SingularValueDecomposition<RowMatrix,Matrix> computeSVD(int k, boolean computeU, double rCond)
At most k largest non-zero 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. 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 1e-9. 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 eigen-decomposition is set to 1e-10.
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 ill-conditioned).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.public Matrix computeCovariance()
public Matrix computePrincipalComponents(int k)
k - number of top principal components.public MultivariateStatisticalSummary computeColumnSummaryStatistics()