resolution: Row and column resolution of a matrix.

In limSolve: Solving Linear Inverse Models

Description

Given an input matrix or its singular value decomposition,

calculates the resolution of the equations (rows) and of the unknowns (columns) of the matrix.

Usage

resolution (s, tol = sqrt(.Machine$double.eps))

Arguments

s	either a matrix or its singular value decomposition.
tol	tolerance for the singular values.

Value

a list containing:

row	resolution of the rows (equations).
col	resolution of the columns (variables).
nsolvable	number of solvable unknowns - the rank of the matrix.

Author(s)

Karline Soetaert <[e-mail]>

Dick van Oevelen<[e-mail]>

References

Menke, W., 1989. Geophysical Data Analysis: Discrete Inverse Theory. Revised edition. International Geophysics Series. Academic Press, London.

See Also

svd, the singluar value decomposition

Examples

resolution (matrix(nrow = 3, runif(9)))  #3rows,3columns
resolution (matrix(nrow = 3, runif(12))) #3rows,4columns
resolution (matrix(nrow = 3, runif(6)))  #3rows,2columns
resolution (cbind(c(1, 2, 3), c(2, 3, 4), c(3, 5, 7))) # r3=r1+r2,c3=c1+c2

Example output

$row
[1] 1 1 1

$col
[1] 1 1 1

$nsolvable
[1] 3

$row
[1] 1 1 1

$col
[1] 0.6999441 0.7307237 0.7768493 0.7924828

$nsolvable
[1] 3

$row
[1] 0.6369696 0.7246907 0.6383397

$col
[1] 1 1

$nsolvable
[1] 2

$row
[1] 0.8333333 0.3333333 0.8333333

$col
[1] 0.6666667 0.6666667 0.6666667

$nsolvable
[1] 2

limSolve documentation built on Nov. 12, 2019, 3 p.m.