cern.colt.matrix.linalg
Class SeqBlas

java.lang.Object
  extended by cern.colt.matrix.linalg.SeqBlas
All Implemented Interfaces:
Blas

public class SeqBlas
extends java.lang.Object
implements Blas

Sequential implementation of the Basic Linear Algebra System.

Author:
wolfgang.hoschek@cern.ch

Field Summary
static Blas seqBlas
          Little trick to allow for "aliasing", that is, renaming this class.
 
Constructor Summary
protected SeqBlas()
          Makes this class non instantiable, but still let's others inherit from it.
 
Method Summary
 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]|,...)..
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

seqBlas

public static final Blas seqBlas
Little trick to allow for "aliasing", that is, renaming this class. Time and again writing code like

SeqBlas.blas.dgemm(...);

is a bit awkward. Using the aliasing you can instead write

Blas B = SeqBlas.blas;
B.dgemm(...);

Constructor Detail

SeqBlas

protected SeqBlas()
Makes this class non instantiable, but still let's others inherit from it.

Method Detail

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.

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).