<p>snippet: varManager 2012.03.03</p>

2 3 decimal

&[DATE] &[TIME] - &[FILENAME]

check if #var is an array #var IsArray #var IsString 0 ≡ #e #var num2str eval : #e mat(findstr 1 + (2^0 > 21 line 0 if 11 line :

check if #var is a number #var IsScalar #var IsArray ¬ (#var IsString ¬ (& 11 line :

converts a system in a vector #system sys2mat #string #system eval num2str : #string sys(findstr stack 1 el 1 ≡ mat #string 4 substr concat str2num #system if 21 line :

converts a vector in a system #vector mat2sys #string #vector eval num2str : #string mat(findstr stack 1 el 1 ≡ #vector cols 1 ≡ sys #string 4 substr concat str2num #vector if #vector if 21 line :

returns rows and columns of an array
returns 1 if #var is a number
returns "text" if #var is a string #var size #var IsString ¬ #var num2str mat(findstr stack 1 el 1 ≡ #var rows #var cols 21 mat eval 1 if text if :

returns summation of M.D.A. elements #var sum.1 #size #var size : #size text ≡ 0 #size 1 ≡ #var #output 0 : #i 1 #size 1 el range #j 1 #size 2 el range #var #i #j el size 1 ≡ #output #output #var #i #j el + : #output #output #var #i #j el sum.1 + : if for for #output eval 31 line if if 21 line :

compare #var1 and #var2, using  a text #bool parameter (≡,<,>,≤,≥,≠)
works with numbers, strings, arrays and multi dimensional arrays #var1 #bool #var2 compare #bool #bool = ≡ (≡ #bool if : bools.allowed ≡ < > ≤ ≥ ≠ 16 mat transpose : bools.status 0 : n 1 bools.allowed length range #bool bools.allowed n el ≡ bools.status bools.status 1 + : 0 if for 41 line bools.status 1 ≡ #v1 #var1 : #v2 #var2 : #size1 #v1 size : #size2 #v2 size : #size1 text ≡ (#size2 text ≡ (| #bool ≡ ≡ #v1 #v2 ≡ #bool ≠ ≡ #v1 #v2 ≠ I can't determine if a string is larger or smaller than a number/matrix 021 line if if #size1 1 ≡ (#size2 1 ≡ (& #v1 num2str #bool #v2 num2str concat str2num #size1 1 ≡ (#size2 1 ≡ (| #size1 1 ≡ #v1 #v1 #size2 1 el #size2 2 el matrix + : #size1 #size2 : 21 line #v2 #v2 #size1 1 el #size1 2 el matrix + : #size2 #size1 : 21 line if 0 if #size1 #size2 ≡ #output 0 : #i 1 #size1 1 el range #j 1 #size1 2 el range #v1 #i #j el size 1 ≡ (#v2 #i #j el size 1 ≡ (& #output #i #j el #v1 #i #j el num2str #bool #v2 #i #j el num2str concat str2num : #output #i #j el #v1 #i #j el #bool #v2 #i #j el compare : if for for #output eval 31 line I can't compare matrix with different sizes 021 line if 21 line if if 51 line unallowed boolean: #bool concat if 21 line :

Bisection root-finding method.
reference function for Bisection() 1 f a b epsilon Bisection.ref i 0 : P1 a : P2 b : P1 f sign P2 f sign * 0 > wrong interval error epsilon IsArray ¬ ε 1 el epsilon : ε 2 el 10100 -^: 21 line ε epsilon : if maxIters 1 P2 P1 - ε 2 el / abs 2 log trunc + : i maxIters < P3 P1 P2 + 2 / : P3 f abs ε 1 el ≤ (P2 P1 - abs ε 2 el ≤ (| break 0 if P1 f sign P3 f sign * 0 > P1 P3 : P2 P3 : if i i 1 + : 41 line while 31 line if P3 i 11 mat 21 mat 51 line :

function used for testing (references: http://www.m-hikari.com/ams/ams-2010/ams-13-16-2010/gottliebAMS13-16-2010.pdf)

a f1 3 a sin * 2 - :

a f2 a e a^* 1 - :

a f3 11 a 11^* 1 - :

a f4 e a 2^7 a * + 30 -^1 - :

a f5 1 a / a sin - 1 + :

a f6 a 3^2 a * - 5 - :

a f7 1 a / 1 - :

a f0 a f1 a f2 21 sys :

x f2

Bound_P1 5 :

Bound_P2 20 - :

epsilon 105 -^:

ε.fx 105 -^:

Ε ε.fx ε.ΔB 21 sys :

ε.ΔB 1010 -^:

x f2 Bound_P1 Bound_P2 epsilon 1 Bisection 0.5671 2011 mat 21 mat

x f2 Bound_P1 Bound_P2 ε.fx ε.ΔB 21 mat 1 Bisection 0.5671 2011 mat 21 mat

x f2 Bound_P1 Bound_P2 ε.fx ε.ΔB 21 sys 1 Bisection 0.5671 2011 mat 21 mat

x f2 Bound_P1 Bound_P2 ε.fx ε.ΔB 12 mat 1 Bisection 0.5671 2011 mat 21 mat

x f2 Bound_P1 Bound_P2 Ε 1 Bisection 0.5671 2011 mat 21 mat

x# f2 1 epsilon 1001 Broyden 0.5671 1011 mat 21 mat

x f2 Bound_P1 Bound_P2 epsilon Bisection.ref 0.5671 2011 mat 21 mat

x f2 Bound_P1 Bound_P2 epsilon Bisection 0.5671

x f2 Bound_P1 Bound_P2 epsilon 102 -^21 mat Bisection.ref 0.5627 1211 mat 21 mat

x f2 Bound_P1 Bound_P2 epsilon 0 Bisection 0.5671

x f0

Bound_P1 0.1 :

Bound_P2 2.1 :

same bounds for all functions

x f0 Bound_P1 Bound_P2 epsilon 1 Bisection 0.7297 1511 mat 21 mat 0.5671 1711 mat 21 mat 21 mat

Bound_P1 01 - 21 sys :

Bound_P2 2.2 2.5 21 sys :

custom bounds

a f1 b f2 21 sys Bound_P1 Bound_P2 0.0001 0.0001 21 sys 1 Bisection 0.7297 1411 mat 21 mat 0.5671 1011 mat 21 mat 21 mat

a f1 b f2 21 sys Bound_P1 epsilon 1001 Broyden 0.7297 0.5671 21 sys 811 mat 21 mat

a f1 b f2 21 sys Bound_P1 Bound_P2 0.0001 0.0001 21 sys 1001 Secant #

unexpected type of arguments

a f1 b f2 21 sys Bound_P1 Bound_P2 0.0001 0.0001 21 sys 1001 Ridder 0.7297 1911 mat 21 mat 0.5671 211 mat 21 mat 21 mat

a f1 b f2 21 sys Bound_P1 Bound_P2 0.0001 0.0001 21 sys 1001 BDQRF 0.7297 311 mat 21 mat 0.5671 411 mat 21 mat 21 mat

a f1 b f2 21 sys Bound_P1 Bound_P2 0.0001 0.0001 21 sys 1001 Brent 0.907 211 mat 21 mat 0.75 111 mat 21 mat 21 mat

a a :

a f mapUnknowns a 11 mat