SmpBlas
cern.colt.matrix.linalg

Class SmpBlas

  • All Implemented Interfaces:
    Blas


    public class SmpBlasextends Objectimplements 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 thenumber 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.
    See Also:
    FJTaskRunnerGroup, FJTask
    • 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.
      • 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.
      • 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 andA 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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