Mercurial > forge
comparison main/linear-algebra/funm.m @ 0:6b33357c7561 octave-forge
Initial revision
| author | pkienzle |
|---|---|
| date | Wed, 10 Oct 2001 19:54:49 +0000 |
| parents | |
| children | 2ac2777b30bc |
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| -1:000000000000 | 0:6b33357c7561 |
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| 1 ## Copyright (C) 2000 P.R. Nienhuis | |
| 2 ## | |
| 3 ## This program is free software; you can redistribute it and/or modify | |
| 4 ## it under the terms of the GNU General Public License as published by | |
| 5 ## the Free Software Foundation; either version 2, or (at your option) | |
| 6 ## any later version. | |
| 7 ## | |
| 8 ## This program is distributed in the hope that it will be useful, but | |
| 9 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 11 ## General Public License for more details. | |
| 12 ## | |
| 13 ## You should have received a copy of the GNU General Public License | |
| 14 ## along with this program; see the file COPYING. If not, write to the | |
| 15 ## Free Software Foundation, 59 Temple Place - Suite 330, Boston, MA | |
| 16 ## 02111-1307, USA. | |
| 17 | |
| 18 ## funm: Matrix equivalent of function 'name' | |
| 19 ## | |
| 20 ## Usage: B = funm(A, name) | |
| 21 ## where A = square non-singular matrix, provisionally | |
| 22 ## real-valued | |
| 23 ## B = square result matrix | |
| 24 ## name = string, name of function to apply to A. | |
| 25 ## args = any arguments to pass to function 'name' | |
| 26 ## The function must accept a vector and apply | |
| 27 ## element-wise to that vector. | |
| 28 ## | |
| 29 ## Example: To compute sqrtm(A), you could use funm(A, 'sqrt') | |
| 30 ## | |
| 31 ## Note that you should not use funm for 'sqrt', 'log' or 'exp'; instead | |
| 32 ## use sqrtm, logm and expm which are more robust. Similarly, | |
| 33 ## trigonometric and hyperbolic functions (cos, sin, tan, cot, sec, csc, | |
| 34 ## cosh, sinh, tanh, coth, sech, csch) are better handled by thfm(A, | |
| 35 ## name), which defines them in terms of the more robust expm. | |
| 36 | |
| 37 ## NOTE: the following comments are withheld until they can be verified | |
| 38 ## | |
| 39 ## If you have a network of coupled systems, where for the individual | |
| 40 ## systems a solution exists in terms of scalar variables, in many | |
| 41 ## cases the network might be solved using the same form of the | |
| 42 ## solution but with substituting the matrix equivalent of the function | |
| 43 ## applied to the scalar variables. | |
| 44 ## The approach is to do an eigen-analysis of the network to decouple | |
| 45 ## the systems, apply the scalar functions to the eigenvalues, | |
| 46 ## and then recombine the systems into a network. | |
| 47 | |
| 48 ## Author: P.R. Nienhuis, 106130.1515@compuserve.com | |
| 49 ## Additions by P. Kienzle, ......... | |
| 50 ## 2001-03-01 Paul Kienzle | |
| 51 ## * generate error for repeated eigenvalues | |
| 52 | |
| 53 function B = funm(A, name) | |
| 54 | |
| 55 if (nargin != 2 || !isstr(name) || isstr(A)) | |
| 56 usage ("B = funm (A, 'f' [, args])"); | |
| 57 endif | |
| 58 | |
| 59 [V, D] = eig (A); | |
| 60 D = diag (feval (name, diag(D))); | |
| 61 B = V * D * inv (V); | |
| 62 | |
| 63 endfunction |