cern.colt.matrix.linalg

Class SeqBlas

java.lang.Object

cern.colt.matrix.linalg.SeqBlas

All Implemented Interfaces:

Blas

public class SeqBlas
extends Object
implements Blas

Sequential implementation of the Basic Linear Algebra System.

Version:

0.9, 16/04/2000

Author:

wolfgang.hoschek@cern.ch

Field Summary

Fields

Modifier and Type	Field and Description
static Blas	seqBlas Little trick to allow for "aliasing", that is, renaming this class.

Constructor Summary

Constructors

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

Method Summary

Methods

Modifier and Type	Method and Description
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).