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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 = alpha*A*B + beta*C`.
`void` | `dgemv(boolean transposeA, double alpha, DoubleMatrix2D A, DoubleMatrix1D x, double beta, DoubleMatrix1D y)` Generalized linear algebraic matrix-vector multiply; `y = alpha*A*x + beta*y`.
`void` | `dger(double alpha, DoubleMatrix1D x, DoubleMatrix1D y, DoubleMatrix2D A)` Performs a rank 1 update; `A = A + alpha*x*y'`.
`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 = c*x + s*y; y = c*y - s*x`.
`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 = alpha*A*x + beta*y`.
`void` | `dtrmv(boolean isUpperTriangular, boolean transposeA, boolean isUnitTriangular, DoubleMatrix2D A, DoubleMatrix1D x)` Triangular matrix-vector multiplication; `x = A*x` 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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