java.lang.Object
- cern.colt.matrix.linalg.SmpBlas

All Implemented Interfaces:

Blas
```
public class SmpBlas
extends java.lang.Object
implements Blas
```
Parallel implementation of the Basic Linear Algebra System for symmetric multi processing boxes. Currently only a few algorithms are parallelised; the others are fully functional, but run in sequential mode. Parallelised are:
- dgemm (matrix-matrix multiplication)
- dgemv (matrix-vector multiplication)
- assign(A,function) (generalized matrix scaling/transform): Strong speedup only for expensive functions like logarithm, sin, etc.
- assign(A,B,function) (generalized matrix scaling/transform): Strong speedup only for expensive functions like pow etc.
In all cases, no or only marginal speedup is seen for small problem sizes; they are detected and the sequential algorithm is used.
Usage
Call the static method allocateBlas(int, cern.colt.matrix.linalg.Blas) at the very beginning of your program, supplying the main parameter for SmpBlas, the number of available CPUs. The method sets the public global variable SmpBlas.smpBlas to a blas using a maximum of CPUs threads, each concurrently processing matrix blocks with the given sequential blas algorithms. Normally there is no need to call allocateBlas more than once. Then use SmpBlas.smpBlas.someRoutine(...) to run someRoutine in parallel. E.g.
int cpu_s = 4; SmpBlas.allocateBlas(cpu_s, SeqBlas.seqBlas); ... SmpBlas.smpBlas.dgemm(...) SmpBlas.smpBlas.dgemv(...)
Even if you don't call a blas routine yourself, it often makes sense to allocate a SmpBlas, because other matrix library routines sometimes call the blas. So if you're lucky, you get parallel performance for free.
Notes
- Unfortunately, there is no portable means of automatically detecting the number of CPUs on a JVM, so there is no good way to automate defaults.
- Only improves performance on boxes with > 1 CPUs and VMs with native threads.
- Currently only improves performance when working on dense matrix types. On sparse types, performance is likely to degrade (because of the implementation of sub-range views)!
- Implemented using Doug Lea's fast lightweight task framework (EDU.oswego.cs.dl.util.concurrent) built upon Java threads, and geared for parallel computation.
Version:

0.9, 16/04/2000

See Also:

FJTaskRunnerGroup, FJTask

Field Summary

Fields
Modifier and Type	Field	Description
`protected int`	`maxThreads`
`protected static int`	`NN_THRESHOLD`
`protected Blas`	`seqBlas`
`protected Smp`	`smp`
`static Blas`	`smpBlas`	The public global parallel blas; initialized via `allocateBlas(int, cern.colt.matrix.linalg.Blas)`.

Constructor Summary

Constructors
Modifier	Constructor	Description
`protected`	`SmpBlas(int maxThreads, Blas seqBlas)`	Constructs a blas using a maximum of `maxThreads threads; each executing the given sequential algos.`

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`static void`	`allocateBlas(int maxThreads, Blas seqBlas)`	Sets the public global variable `SmpBlas.smpBlas` to a blas using a maximum of `maxThreads` threads, each executing the given sequential algorithm; `maxThreads` is normally the number of CPUs.
`void`	`assign(DoubleMatrix2D A, DoubleFunction function)`	Assigns the result of a function to each cell; `x[row,col] = function(x[row,col])`.
`void`	`assign(DoubleMatrix2D A, DoubleMatrix2D B, DoubleDoubleFunction function)`	Assigns the result of a function to each cell; `x[row,col] = function(x[row,col],y[row,col])`.
`double`	`dasum(DoubleMatrix1D x)`	Returns the sum of absolute values; `\|x[0]\| + \|x[1]\| + ...`
`void`	`daxpy(double alpha, DoubleMatrix1D x, DoubleMatrix1D y)`	Combined vector scaling; `y = y + alpha*x`.
`void`	`daxpy(double alpha, DoubleMatrix2D A, DoubleMatrix2D B)`	Combined matrix scaling; `B = B + alpha*A`.
`void`	`dcopy(DoubleMatrix1D x, DoubleMatrix1D y)`	Vector assignment (copying); `y = x`.
`void`	`dcopy(DoubleMatrix2D A, DoubleMatrix2D B)`	Matrix assignment (copying); `B = A`.
`double`	`ddot(DoubleMatrix1D x, DoubleMatrix1D y)`	Returns the dot product of two vectors x and y, which is `Sum(x[i]*y[i])`.
`void`	`dgemm(boolean transposeA, boolean transposeB, double alpha, DoubleMatrix2D A, DoubleMatrix2D B, double beta, DoubleMatrix2D C)`	Generalized linear algebraic matrix-matrix multiply; `C = alphaAB + beta*C`.
`void`	`dgemv(boolean transposeA, double alpha, DoubleMatrix2D A, DoubleMatrix1D x, double beta, DoubleMatrix1D y)`	Generalized linear algebraic matrix-vector multiply; `y = alphaAx + beta*y`.
`void`	`dger(double alpha, DoubleMatrix1D x, DoubleMatrix1D y, DoubleMatrix2D A)`	Performs a rank 1 update; `A = A + alphaxy'`.
`double`	`dnrm2(DoubleMatrix1D x)`	Return the 2-norm; `sqrt(x[0]^2 + x[1]^2 + ...)`.
`void`	`drot(DoubleMatrix1D x, DoubleMatrix1D y, double c, double s)`	Applies a givens plane rotation to (x,y); `x = cx + sy; y = cy - sx`.
`void`	`drotg(double a, double b, double[] rotvec)`	Constructs a Givens plane rotation for `(a,b)`.
`void`	`dscal(double alpha, DoubleMatrix1D x)`	Vector scaling; `x = alpha*x`.
`void`	`dscal(double alpha, DoubleMatrix2D A)`	Matrix scaling; `A = alpha*A`.
`void`	`dswap(DoubleMatrix1D x, DoubleMatrix1D y)`	Swaps the elements of two vectors; `y <==> x`.
`void`	`dswap(DoubleMatrix2D A, DoubleMatrix2D B)`	Swaps the elements of two matrices; `B <==> A`.
`void`	`dsymv(boolean isUpperTriangular, double alpha, DoubleMatrix2D A, DoubleMatrix1D x, double beta, DoubleMatrix1D y)`	Symmetric matrix-vector multiplication; `y = alphaAx + beta*y`.
`void`	`dtrmv(boolean isUpperTriangular, boolean transposeA, boolean isUnitTriangular, DoubleMatrix2D A, DoubleMatrix1D x)`	Triangular matrix-vector multiplication; `x = Ax` or `x = A'x`.
`int`	`idamax(DoubleMatrix1D x)`	Returns the index of largest absolute value; `i such that \|x[i]\| == max(\|x[0]\|,\|x[1]\|,...).`.
`protected double[]`	`run(DoubleMatrix2D A, boolean collectResults, Matrix2DMatrix2DFunction fun)`
`protected double[]`	`run(DoubleMatrix2D A, DoubleMatrix2D B, boolean collectResults, Matrix2DMatrix2DFunction fun)`
`void`	`stats()`	Prints various snapshot statistics to System.out; Simply delegates to `FJTaskRunnerGroup.stats()`.
`private double`	`xsum(DoubleMatrix2D A)`

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - smpBlas
```
public static Blas smpBlas
```
    The public global parallel blas; initialized via allocateBlas(int, cern.colt.matrix.linalg.Blas). Do not modify this variable via other means (it is public).
  - seqBlas
```
protected Blas seqBlas
```
  - smp
```
protected Smp smp
```
  - maxThreads
```
protected int maxThreads
```
  - NN_THRESHOLD
```
protected static int NN_THRESHOLD
```
- Constructor Detail
  - SmpBlas
```
protected SmpBlas(int maxThreads,
                  Blas seqBlas)
```
    Constructs a blas using a maximum of maxThreads threads; each executing the given sequential algos.
Method Detail allocateBlas public static void allocateBlas(int maxThreads, Blas seqBlas) Sets the public global variable SmpBlas.smpBlas to a blas using a maximum of maxThreads threads, each executing the given sequential algorithm; maxThreads is normally the number of CPUs. Call this method at the very beginning of your program. Normally there is no need to call this method more than once. Parameters: maxThreads - the maximum number of threads (= CPUs) to be used seqBlas - the sequential blas algorithms to be used on concurrently processed matrix blocks. assign public void assign(DoubleMatrix2D A, DoubleFunction function) Description copied from interface: Blas Assigns the result of a function to each cell; x[row,col] = function(x[row,col]). Specified by: assign in interface Blas Parameters: A - the matrix to modify. function - a function object taking as argument the current cell's value. See Also: Functions assign public void assign(DoubleMatrix2D A, DoubleMatrix2D B, DoubleDoubleFunction function) Description copied from interface: Blas Assigns the result of a function to each cell; x[row,col] = function(x[row,col],y[row,col]). Specified by: assign in interface Blas Parameters: A - the matrix to modify. B - the secondary matrix to operate on. function - a function object taking as first argument the current cell's value of this, and as second argument the current cell's value of y, See Also: Functions dasum public double dasum(DoubleMatrix1D x) Description copied from interface: Blas Returns the sum of absolute values; |x[0]| + |x[1]| + ... . In fact equivalent to x.aggregate(cern.jet.math.Functions.plus, cern.jet.math.Functions.abs). Specified by: dasum in interface Blas Parameters: x - the first vector. daxpy public void daxpy(double alpha, DoubleMatrix1D x, DoubleMatrix1D y) Description copied from interface: Blas Combined vector scaling; y = y + alpha*x. In fact equivalent to y.assign(x,cern.jet.math.Functions.plusMult(alpha)). Specified by: daxpy in interface Blas Parameters: alpha - a scale factor. x - the first source vector. y - the second source vector, this is also the vector where results are stored. daxpy public void daxpy(double alpha, DoubleMatrix2D A, DoubleMatrix2D B) Description copied from interface: Blas Combined matrix scaling; B = B + alpha*A. In fact equivalent to B.assign(A,cern.jet.math.Functions.plusMult(alpha)). Specified by: daxpy in interface Blas Parameters: alpha - a scale factor. A - the first source matrix. B - the second source matrix, this is also the matrix where results are stored. dcopy public void dcopy(DoubleMatrix1D x, DoubleMatrix1D y) Description copied from interface: Blas Vector assignment (copying); y = x. In fact equivalent to y.assign(x). Specified by: dcopy in interface Blas Parameters: x - the source vector. y - the destination vector. dcopy public void dcopy(DoubleMatrix2D A, DoubleMatrix2D B) Description copied from interface: Blas Matrix assignment (copying); B = A. In fact equivalent to B.assign(A). Specified by: dcopy in interface Blas Parameters: A - the source matrix. B - the destination matrix. ddot public double ddot(DoubleMatrix1D x, DoubleMatrix1D y) Description copied from interface: Blas Returns the dot product of two vectors x and y, which is Sum(x[i]*y[i]). In fact equivalent to x.zDotProduct(y). Specified by: ddot in interface Blas Parameters: x - the first vector. y - the second vector. Returns: the sum of products. dgemm public void dgemm(boolean transposeA, boolean transposeB, double alpha, DoubleMatrix2D A, DoubleMatrix2D B, double beta, DoubleMatrix2D C) Description copied from interface: Blas Generalized linear algebraic matrix-matrix multiply; C = alpha*A*B + beta*C. In fact equivalent to A.zMult(B,C,alpha,beta,transposeA,transposeB). Note: Matrix shape conformance is checked after potential transpositions. Specified by: dgemm in interface Blas Parameters: transposeA - set this flag to indicate that the multiplication shall be performed on A'. transposeB - set this flag to indicate that the multiplication shall be performed on B'. alpha - a scale factor. A - the first source matrix. B - the second source matrix. beta - a scale factor. C - the third source matrix, this is also the matrix where results are stored. dgemv public void dgemv(boolean transposeA, double alpha, DoubleMatrix2D A, DoubleMatrix1D x, double beta, DoubleMatrix1D y) Description copied from interface: Blas Generalized linear algebraic matrix-vector multiply; y = alpha*A*x + beta*y. In fact equivalent to A.zMult(x,y,alpha,beta,transposeA). Note: Matrix shape conformance is checked after potential transpositions. Specified by: dgemv in interface Blas Parameters: transposeA - set this flag to indicate that the multiplication shall be performed on A'. alpha - a scale factor. A - the source matrix. x - the first source vector. beta - a scale factor. y - the second source vector, this is also the vector where results are stored. dger public void dger(double alpha, DoubleMatrix1D x, DoubleMatrix1D y, DoubleMatrix2D A) Description copied from interface: Blas Performs a rank 1 update; A = A + alpha*x*y'. Example: A = { {6,5}, {7,6} }, x = {1,2}, y = {3,4}, alpha = 1 --> A = { {9,9}, {13,14} } Specified by: dger in interface Blas Parameters: alpha - a scalar. x - an m element vector. y - an n element vector. A - an m by n matrix. dnrm2 public double dnrm2(DoubleMatrix1D x) Description copied from interface: Blas Return the 2-norm; sqrt(x[0]^2 + x[1]^2 + ...). In fact equivalent to Math.sqrt(Algebra.DEFAULT.norm2(x)). Specified by: dnrm2 in interface Blas Parameters: x - the vector. drot public void drot(DoubleMatrix1D x, DoubleMatrix1D y, double c, double s) Description copied from interface: Blas Applies a givens plane rotation to (x,y); x = c*x + s*y; y = c*y - s*x. Specified by: drot in interface Blas Parameters: x - the first vector. y - the second vector. c - the cosine of the angle of rotation. s - the sine of the angle of rotation. drotg public void drotg(double a, double b, double[] rotvec) Description copied from interface: Blas Constructs a Givens plane rotation for (a,b). Taken from the LINPACK translation from FORTRAN to Java, interface slightly modified. In the LINPACK listing DROTG is attributed to Jack Dongarra Specified by: drotg in interface Blas Parameters: a - rotational elimination parameter a. b - rotational elimination parameter b. rotvec - [] Must be at least of length 4. On output contains the values {a,b,c,s}. dscal public void dscal(double alpha, DoubleMatrix1D x) Description copied from interface: Blas Vector scaling; x = alpha*x. In fact equivalent to x.assign(cern.jet.math.Functions.mult(alpha)). Specified by: dscal in interface Blas Parameters: alpha - a scale factor. x - the first vector. dscal public void dscal(double alpha, DoubleMatrix2D A) Description copied from interface: Blas Matrix scaling; A = alpha*A. In fact equivalent to A.assign(cern.jet.math.Functions.mult(alpha)). Specified by: dscal in interface Blas Parameters: alpha - a scale factor. A - the matrix. dswap public void dswap(DoubleMatrix1D x, DoubleMatrix1D y) Description copied from interface: Blas Swaps the elements of two vectors; y <==> x. In fact equivalent to y.swap(x). Specified by: dswap in interface Blas Parameters: x - the first vector. y - the second vector. dswap public void dswap(DoubleMatrix2D A, DoubleMatrix2D B) Description copied from interface: Blas Swaps the elements of two matrices; B <==> A. Specified by: dswap in interface Blas dsymv public void dsymv(boolean isUpperTriangular, double alpha, DoubleMatrix2D A, DoubleMatrix1D x, double beta, DoubleMatrix1D y) Description copied from interface: Blas Symmetric matrix-vector multiplication; y = alpha*A*x + beta*y. Where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix. A can be in upper or lower triangular format. Specified by: dsymv in interface Blas Parameters: isUpperTriangular - is A upper triangular or lower triangular part to be used? alpha - scaling factor. A - the source matrix. x - the first source vector. beta - scaling factor. y - the second vector holding source and destination. dtrmv public void dtrmv(boolean isUpperTriangular, boolean transposeA, boolean isUnitTriangular, DoubleMatrix2D A, DoubleMatrix1D x) Description copied from interface: Blas Triangular matrix-vector multiplication; x = A*x or x = A'*x. Where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix. Specified by: dtrmv in interface Blas Parameters: isUpperTriangular - is A upper triangular or lower triangular? transposeA - set this flag to indicate that the multiplication shall be performed on A'. isUnitTriangular - true --> A is assumed to be unit triangular; false --> A is not assumed to be unit triangular A - the source matrix. x - the vector holding source and destination. idamax public int idamax(DoubleMatrix1D x) Description copied from interface: Blas Returns the index of largest absolute value; i such that |x[i]| == max(|x[0]|,|x[1]|,...).. Specified by: idamax in interface Blas Parameters: x - the vector to search through. Returns: the index of largest absolute value (-1 if x is empty). run protected double[] run(DoubleMatrix2D A, DoubleMatrix2D B, boolean collectResults, Matrix2DMatrix2DFunction fun) run protected double[] run(DoubleMatrix2D A, boolean collectResults, Matrix2DMatrix2DFunction fun) stats public void stats() Prints various snapshot statistics to System.out; Simply delegates to FJTaskRunnerGroup.stats(). xsum private double xsum(DoubleMatrix2D A)

Class SmpBlas

Usage

Notes

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

smpBlas

seqBlas

smp

maxThreads

NN_THRESHOLD

Constructor Detail

SmpBlas

Method Detail

allocateBlas

assign

assign

dasum

daxpy

daxpy

dcopy

dcopy

ddot

dgemm

dgemv

dger

dnrm2

drot

drotg

dscal

dscal

dswap

dswap

dsymv

dtrmv

idamax

run

run

stats

xsum