cern.colt.matrix.linalg
Interface Blas

All Known Implementing Classes:
SeqBlas

public interface Blas

Subset of the BLAS (Basic Linear Algebra System); High quality "building block" routines for performing basic vector and matrix operations. Because the BLAS are efficient, portable, and widely available, they're commonly used in the development of high quality linear algebra software.

Mostly for compatibility with legacy notations. Most operations actually just delegate to the appropriate methods directly defined on matrices and vectors.

This class implements the BLAS functions for operations on matrices from the matrix package. It follows the spirit of the Draft Proposal for Java BLAS Interface, by Roldan Pozo of the National Institute of Standards and Technology. Interface definitions are also identical to the Ninja interface. Because the matrix package supports sections, the interface is actually simpler.

Currently, the following operations are supported:

  1. BLAS Level 1: Vector-Vector operations
  2. 2.BLAS Level 2: Matrix-Vector operations
  3. 3.BLAS Level 3: Matrix-Matrix operations

Author:
wolfgang.hoschek@cern.ch

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 x, DoubleMatrix2D y, 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 x, DoubleMatrix2D y)
          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]|,...)..
 

Method Detail

assign

void assign(DoubleMatrix2D A,
            DoubleFunction function)
Assigns the result of a function to each cell; x[row,col] = function(x[row,col]).

Parameters:
A - the matrix to modify.
function - a function object taking as argument the current cell's value.
See Also:
Functions

assign

void assign(DoubleMatrix2D x,
            DoubleMatrix2D y,
            DoubleDoubleFunction function)
Assigns the result of a function to each cell; x[row,col] = function(x[row,col],y[row,col]).

Parameters:
x - the matrix to modify.
y - 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,
Throws:
java.lang.IllegalArgumentException - if x.columns() != y.columns() || x.rows() != y.rows()
See Also:
Functions

dasum

double dasum(DoubleMatrix1D x)
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).

Parameters:
x - the first vector.

daxpy

void daxpy(double alpha,
           DoubleMatrix1D x,
           DoubleMatrix1D y)
Combined vector scaling; y = y + alpha*x. In fact equivalent to y.assign(x,cern.jet.math.Functions.plusMult(alpha)).

Parameters:
alpha - a scale factor.
x - the first source vector.
y - the second source vector, this is also the vector where results are stored.
Throws:
java.lang.IllegalArgumentException - x.size() != y.size()..

daxpy

void daxpy(double alpha,
           DoubleMatrix2D A,
           DoubleMatrix2D B)
Combined matrix scaling; B = B + alpha*A. In fact equivalent to B.assign(A,cern.jet.math.Functions.plusMult(alpha)).

Parameters:
alpha - a scale factor.
A - the first source matrix.
B - the second source matrix, this is also the matrix where results are stored.
Throws:
java.lang.IllegalArgumentException - if A.columns() != B.columns() || A.rows() != B.rows().

dcopy

void dcopy(DoubleMatrix1D x,
           DoubleMatrix1D y)
Vector assignment (copying); y = x. In fact equivalent to y.assign(x).

Parameters:
x - the source vector.
y - the destination vector.
Throws:
java.lang.IllegalArgumentException - x.size() != y.size().

dcopy

void dcopy(DoubleMatrix2D A,
           DoubleMatrix2D B)
Matrix assignment (copying); B = A. In fact equivalent to B.assign(A).

Parameters:
A - the source matrix.
B - the destination matrix.
Throws:
java.lang.IllegalArgumentException - if A.columns() != B.columns() || A.rows() != B.rows().

ddot

double ddot(DoubleMatrix1D x,
            DoubleMatrix1D y)
Returns the dot product of two vectors x and y, which is Sum(x[i]*y[i]). In fact equivalent to x.zDotProduct(y).

Parameters:
x - the first vector.
y - the second vector.
Returns:
the sum of products.
Throws:
java.lang.IllegalArgumentException - if x.size() != y.size().

dgemm

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. In fact equivalent to A.zMult(B,C,alpha,beta,transposeA,transposeB). Note: Matrix shape conformance is checked after potential transpositions.

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.
Throws:
java.lang.IllegalArgumentException - if B.rows() != A.columns().
java.lang.IllegalArgumentException - if C.rows() != A.rows() || C.columns() != B.columns().
java.lang.IllegalArgumentException - if A == C || B == C.

dgemv

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. In fact equivalent to A.zMult(x,y,alpha,beta,transposeA). Note: Matrix shape conformance is checked after potential transpositions.

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.
Throws:
java.lang.IllegalArgumentException - A.columns() != x.size() || A.rows() != y.size())..

dger

void dger(double alpha,
          DoubleMatrix1D x,
          DoubleMatrix1D y,
          DoubleMatrix2D A)
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} }

Parameters:
alpha - a scalar.
x - an m element vector.
y - an n element vector.
A - an m by n matrix.

dnrm2

double dnrm2(DoubleMatrix1D x)
Return the 2-norm; sqrt(x[0]^2 + x[1]^2 + ...). In fact equivalent to Math.sqrt(Algebra.DEFAULT.norm2(x)).

Parameters:
x - the vector.

drot

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.

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

void drotg(double a,
           double b,
           double[] rotvec)
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

Parameters:
a - rotational elimination parameter a.
b - rotational elimination parameter b.
rotvec[] - Must be at least of length 4. On output contains the values {a,b,c,s}.

dscal

void dscal(double alpha,
           DoubleMatrix1D x)
Vector scaling; x = alpha*x. In fact equivalent to x.assign(cern.jet.math.Functions.mult(alpha)).

Parameters:
alpha - a scale factor.
x - the first vector.

dscal

void dscal(double alpha,
           DoubleMatrix2D A)
Matrix scaling; A = alpha*A. In fact equivalent to A.assign(cern.jet.math.Functions.mult(alpha)).

Parameters:
alpha - a scale factor.
A - the matrix.

dswap

void dswap(DoubleMatrix1D x,
           DoubleMatrix1D y)
Swaps the elements of two vectors; y <==> x. In fact equivalent to y.swap(x).

Parameters:
x - the first vector.
y - the second vector.
Throws:
java.lang.IllegalArgumentException - x.size() != y.size().

dswap

void dswap(DoubleMatrix2D x,
           DoubleMatrix2D y)
Swaps the elements of two matrices; B <==> A.

Parameters:
A - the first matrix.
B - the second matrix.
Throws:
java.lang.IllegalArgumentException - if A.columns() != B.columns() || A.rows() != B.rows().

dsymv

void dsymv(boolean isUpperTriangular,
           double alpha,
           DoubleMatrix2D A,
           DoubleMatrix1D x,
           double beta,
           DoubleMatrix1D y)
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.

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

void dtrmv(boolean isUpperTriangular,
           boolean transposeA,
           boolean isUnitTriangular,
           DoubleMatrix2D A,
           DoubleMatrix1D x)
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.

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

int idamax(DoubleMatrix1D x)
Returns the index of largest absolute value; i such that |x[i]| == max(|x[0]|,|x[1]|,...)..

Parameters:
x - the vector to search through.
Returns:
the index of largest absolute value (-1 if x is empty).