Linear algebra functions. More...

#include "lin_alg.h"
#include <stdexcept>
#include <cmath>
#include "arts.h"
#include "make_vector.h"
#include "array.h"
#include "logic.h"

Functions
void	ludcmp (MatrixView LU, ArrayOfIndex &indx, ConstMatrixView A)
	LU decomposition. More...

void	lubacksub (VectorView x, ConstMatrixView LU, ConstVectorView b, const ArrayOfIndex &indx)
	LU backsubstitution. More...

void	matrix_exp (MatrixView F, ConstMatrixView A, const Index &q)
	General exponential of a Matrix. More...

Numeric	norm_inf (ConstMatrixView A)
	Maximum absolute row sum norm. More...

void	id_mat (MatrixView I)
	Identity Matrix. More...

Numeric	det (ConstMatrixView A)

void	linreg (Vector &p, ConstVectorView x, ConstVectorView y)

Detailed Description

Linear algebra functions.

Author: Claudia Emde claud.nosp@m.ia.e.nosp@m.mde@d.nosp@m.lr.d.nosp@m.e

Date: Thu May 2 10:59:55 2002

This file contains mathematical tools to solve the vector radiative transfer equation.

Definition in file lin_alg.cc.

Function Documentation

◆ det()

Numeric det ( ConstMatrixView A )

Determinant of N by N matrix. Simple recursive method.

Parameters

A	In: Matrix of size NxN.

Author: Richard Larsson

Date: 2012-08-03

Definition at line 320 of file lin_alg.cc.

References det(), ConstMatrixView::ncols(), ConstMatrixView::nrows(), and temp.

Referenced by det().

◆ id_mat()

void id_mat ( MatrixView I )

Identity Matrix.

Parameters

I	Output: identity matrix

Definition at line 299 of file lin_alg.cc.

References ConstMatrixView::ncols(), and ConstMatrixView::nrows().

Referenced by fos(), get_ppath_trans(), get_ppath_trans2(), iyCloudRadar(), iyEmissionStandard(), iyTransmissionStandard(), matrix_exp(), MCGeneral(), MCIPA(), mcPathTraceGeneral(), mcPathTraceIPA(), and rte_step_doit().

◆ linreg()

void linreg	(	Vector &	p,
		ConstVectorView	x,
		ConstVectorView	y
	)

Determines coefficients for linear regression

Performs a least squares estimation of the model

y = p[0] + p[1] * x

Parameters

p	Out: Fitted coefficients.
x	In: x-value of data points
y	In: y-value of data points

Author: Patrick Eriksson

Date: 2013-01-25

Definition at line 371 of file lin_alg.cc.

References ConstVectorView::nelem(), and Vector::resize().

Referenced by pnd_fieldF07ML(), pnd_fieldF07TR(), and ppathFromRtePos2().

◆ lubacksub()

void lubacksub	(	VectorView	x,
		ConstMatrixView	LU,
		ConstVectorView	b,
		const ArrayOfIndex &	indx
	)

LU backsubstitution.

Solves a set of linear equations Ax=b. It is neccessairy to do a LU
decomposition using the function ludcp before using this function.

Parameters

x	Output: Solution vector of the equation system.
LU	Input: LU decomposition of the matrix (output of function ludcp).
b	Input: Right-hand-side vector of equation system.
indx	Input: Pivoting information (output of function ludcp).

Definition at line 142 of file lin_alg.cc.

References is_size(), and ConstMatrixView::nrows().

Referenced by matrix_exp(), rte_step_doit(), test_lusolve1D(), and test_lusolve4D().

◆ ludcmp()

void ludcmp	(	MatrixView	LU,
		ArrayOfIndex &	indx,
		ConstMatrixView	A
	)

LU decomposition.

This function performes a LU Decomposition of the matrix A. (Compare Numerical Recipies in C, pages 36-48.)

Parameters

LU	Output: returns L and U in one matrix
indx	Output: Vector that records the row permutation.
A	Input: Matrix for which the LU decomposition is performed

Definition at line 54 of file lin_alg.cc.

References abs, is_size(), ConstMatrixView::nrows(), and temp.

Referenced by matrix_exp(), rte_step_doit(), test_lusolve1D(), and test_lusolve4D().

◆ matrix_exp()

void matrix_exp	(	MatrixView	F,
		ConstMatrixView	A,
		const Index &	q
	)

General exponential of a Matrix.

The exponential of a matrix is computed using the Pade-Approximation. The method is decribed in: Golub, G. H. and C. F. Van Loan, Matrix Computation, p. 384, Johns Hopkins University Press, 1983.

The Pade-approximation is applied on all cases. If a faster option can be applied has to be checked before calling the function.

Parameters

F	Output: The matrix exponential of A (Has to be initialized before calling the function.
A	Input: arbitrary square matrix
q	Input: Parameter for the accuracy of the computation

Definition at line 194 of file lin_alg.cc.

References id_mat(), is_size(), joker, lubacksub(), ludcmp(), mult(), N, ConstMatrixView::ncols(), norm_inf(), and q.

Referenced by ext2trans(), test_matrix_exp1D(), test_matrix_exp3D(), and test_matrix_exp4D().