SmpBlas (Colt 1.2.0 - API Specification)

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cern.colt.matrix.linalg
Class SmpBlas

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

All Implemented Interfaces:: Blas

public class SmpBlas
extends 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
`static Blas`	`smpBlas` The public global parallel blas; initialized via `allocateBlas(int, cern.colt.matrix.linalg.Blas)`.

Method Summary
`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]\|,...).`.
`void`	`stats()` Prints various snapshot statistics to System.out; Simply delegates to `FJTaskRunnerGroup.stats()`.

Methods inherited from class java.lang.Object

equals, 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).

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,
Returns:: this (for convenience only).
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.

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).

stats

public void stats()

Prints various snapshot statistics to System.out; Simply delegates to FJTaskRunnerGroup.stats().

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cern.colt.matrix.linalg Class SmpBlas

Usage

Notes

smpBlas

allocateBlas

assign

assign

dasum

daxpy

daxpy

dcopy

dcopy

ddot

dgemm

dgemv

dger

dnrm2

drot

drotg

dscal

dscal

dswap

dswap

dsymv

dtrmv

idamax

stats

cern.colt.matrix.linalg
Class SmpBlas