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/* $Id: nlm_linear_algebra.h,v 1.7 2005/12/19 15:38:01 gertz Exp $
* ===========================================================================
*
* PUBLIC DOMAIN NOTICE
* National Center for Biotechnology Information
*
* This software/database is a "United States Government Work" under the
* terms of the United States Copyright Act. It was written as part of
* the author's official duties as a United States Government employee and
* thus cannot be copyrighted. This software/database is freely available
* to the public for use. The National Library of Medicine and the U.S.
* Government have not placed any restriction on its use or reproduction.
*
* Although all reasonable efforts have been taken to ensure the accuracy
* and reliability of the software and data, the NLM and the U.S.
* Government do not and cannot warrant the performance or results that
* may be obtained by using this software or data. The NLM and the U.S.
* Government disclaim all warranties, express or implied, including
* warranties of performance, merchantability or fitness for any particular
* purpose.
*
* Please cite the author in any work or product based on this material.
*
* ===========================================================================*/
/**
* @file nlm_linear_algebra.h
* Declarations for several linear algebra routines
*
* @author E. Michael Gertz
*/
#ifndef __NLM_LINEAR_ALGEBRA__
#define __NLM_LINEAR_ALGEBRA__
#include <algo/blast/core/blast_export.h>
#include <algo/blast/core/ncbi_std.h>
#ifdef __cplusplus
extern "C" {
#endif
/**
* Create and return a new, dense matrix. Elements of the matrix A
* may be accessed as A[i][j]
*
* @param nrows the number of rows for the new matrix.
* @param ncols the number of columns for the new matrix.
*/
NCBI_XBLAST_EXPORT
double ** Nlm_DenseMatrixNew(int nrows, int ncols);
/**
* Create and return a new, dense, lower-triangular matrix. Elements
* of the matrix A may be accessed as A[i][j] for i <= j.
*
* @param n the dimension of the matrix.
*/
NCBI_XBLAST_EXPORT
double ** Nlm_LtriangMatrixNew(int n);
/**
* Free a matrix created by Nlm_DenseMatrixNew or
* Nlm_LtriangMatrixNew.
*
* @param mat the matrix to be freed
* @return always NULL
*/
NCBI_XBLAST_EXPORT
void Nlm_DenseMatrixFree(double *** mat);
/**
* Create and return a new Int4 matrix. Elements of the matrix A
* may be accessed as A[i][j]
*
* @param nrows the number of rows for the new matrix.
* @param ncols the number of columns for the new matrix.
*/
NCBI_XBLAST_EXPORT
Int4 ** Nlm_Int4MatrixNew(int nrows, int ncols);
/**
* Free a matrix created by Nlm_DenseMatrixNew or
* Nlm_LtriangMatrixNew.
*
* @param mat the matrix to be freed
* @return always NULL
*/
NCBI_XBLAST_EXPORT
void Nlm_Int4MatrixFree(Int4 *** mat);
/**
* Accessing only the lower triangular elements of the symmetric,
* positive definite matrix A, compute a lower triangular matrix L
* such that A = L L^T (Cholesky factorization.) Overwrite the lower
* triangle of A with L.
*
* This routine may be used with the Nlm_SolveLtriangPosDef routine to
* solve systems of equations.
*
* @param A the lower triangle of a symmetric, positive-definite
* matrix
* @param n the size of A
*/
NCBI_XBLAST_EXPORT
void Nlm_FactorLtriangPosDef(double ** A, int n);
/**
* Solve the linear system \f$ L L^T y = b \f$, where L is a non-singular
* lower triangular matrix, usually computed using
* the Nlm_FactorLtriangPosDef routine.
*
* @param x on entry, the right hand size of the linear system
* L L^T y = b; on exit the solution
* @param n the size of x
* @param L a non-singular lower triangular matrix
*/
NCBI_XBLAST_EXPORT
void Nlm_SolveLtriangPosDef(double x[], int n, double ** L);
/**
* Compute the Euclidean norm (2-norm) of a vector.
*
* This routine is based on the (freely available) BLAS routine dnrm2,
* which handles the scale of the elements of v in a stable fashion.
*
* @param v a vector
* @param n the length of v
*/
NCBI_XBLAST_EXPORT
double Nlm_EuclideanNorm(const double v[], int n);
/**
* Let y = y + alpha * x
*
* @param y a vector
* @param x another vector
* @param n the length of x and y
* @param alpha a scale factor
*/
NCBI_XBLAST_EXPORT
void Nlm_AddVectors(double y[], int n, double alpha,
const double x[]);
/**
* Given a nonnegative vector x and a nonnegative scalar max, returns
* the largest value in [0, max] for which x + alpha * step_x >= 0.
*
* @param x a vector with nonnegative elements
* @param step_x another vector
* @param n the size of x and step_x
* @param max a nonnegative scalar
*/
NCBI_XBLAST_EXPORT
double Nlm_StepBound(const double x[], int n,
const double step_x[], double max);
#ifdef __cplusplus
}
#endif
#endif
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