wrstcse
wc_defaultsigma — Variable
Default value: 6
Defines how many sigmas of the gauss distribution that represents the tolerances of a parameter correspond to a tol[n] value of -1…1.
See also wc_005fmintypmax_005frss.
Example:
maxima
(%i1) load("wrstcse")$
(%i2) ratprint:false$
(%i3) vals: [
R_1= 1000.0*(1+tol[1]*.01),
R_2= 1000.0*(1+tol[2]*.01)
];
(%o3) [R_1 = 1000.0 (0.01 tol + 1),
1
R_2 = 1000.0 (0.01 tol + 1)]
2
(%i4) assume(U_In>0);
(%o4) [U_In > 0]
(%i5) divider:U_Out=U_In*R_1/(R_1+R_2);
R_1 U_In
(%o5) U_Out = ---------
R_2 + R_1
(%i6) wc_defaultsigma:1$
(%i7) lhs(divider)=wc_mintypmax_rss(subst(vals,rhs(divider)),6);
(%o7) U_Out = [min = 0.4787867965644036 U_In, typ = 0.5 U_In,
max = 0.5212132034355964 U_In, Fail = 0.0019731752898266564 ppm]
(%i8) wc_defaultsigma:3$
(%i9) lhs(divider)=wc_mintypmax_rss(subst(vals,rhs(divider)),6);
(%o9) U_Out = [min = 0.49292893218813455 U_In, typ = 0.5 U_In,
max = 0.5070710678118655 U_In, Fail = 0.0019731752898266564 ppm]
(%i10) wc_defaultsigma:6$
(%i11) lhs(divider)=wc_mintypmax_rss(subst(vals,rhs(divider)),6);
(%o11) U_Out = [min = 0.49646446609406725 U_In, typ = 0.5 U_In,
max = 0.5035355339059328 U_In, Fail = 0.0019731752898266564 ppm]
See also: wc_mintypmax_rss.
wc_defaultvaluespertol — Variable
Default value: 3
Defines how many samples per tol[n] the EWC method of
wc_systematic and wc_mintypmax shall use by default.
See also wc_systematic and wc_005fmintypmax.
Example:
maxima
(%i1) load("wrstcse")$
(%i2) ratprint:false$
(%i3) vals: [
R_1= 100.0*(1+tol[1]*.01),
R_2= 1000.0*(1+tol[2]*.01)
];
(%o3) [R_1 = 100.0 (0.01 tol + 1), R_2 = 1000.0 (0.01 tol + 1)]
1 2
(%i4) wc_defaultvaluespertol:2$
(%i5) wc_systematic(vals);
(%o5) [[R_1 = 99.0, R_2 = 990.0], [R_1 = 99.0, R_2 = 1010.0],
[R_1 = 101.0, R_2 = 990.0], [R_1 = 101.0, R_2 = 1010.0]]
(%i6) wc_defaultvaluespertol:3$
(%i7) wc_systematic(vals);
(%o7) [[R_1 = 99.0, R_2 = 990.0], [R_1 = 99.0, R_2 = 1000.0],
[R_1 = 99.0, R_2 = 1010.0], [R_1 = 100.0, R_2 = 990.0],
[R_1 = 100.0, R_2 = 1000.0], [R_1 = 100.0, R_2 = 1010.0],
[R_1 = 101.0, R_2 = 990.0], [R_1 = 101.0, R_2 = 1000.0],
[R_1 = 101.0, R_2 = 1010.0]]
(%i8) wc_defaultvaluespertol:5$
(%i9) wc_systematic(vals);
(%o9) [[R_1 = 99.0, R_2 = 990.0], [R_1 = 99.0, R_2 = 995.0],
[R_1 = 99.0, R_2 = 1000.0], [R_1 = 99.0,
R_2 = 1004.9999999999999], [R_1 = 99.0, R_2 = 1010.0],
[R_1 = 99.5, R_2 = 990.0], [R_1 = 99.5, R_2 = 995.0],
[R_1 = 99.5, R_2 = 1000.0], [R_1 = 99.5,
R_2 = 1004.9999999999999], [R_1 = 99.5, R_2 = 1010.0],
[R_1 = 100.0, R_2 = 990.0], [R_1 = 100.0, R_2 = 995.0],
[R_1 = 100.0, R_2 = 1000.0], [R_1 = 100.0,
R_2 = 1004.9999999999999], [R_1 = 100.0, R_2 = 1010.0],
[R_1 = 100.49999999999999, R_2 = 990.0],
[R_1 = 100.49999999999999, R_2 = 995.0],
[R_1 = 100.49999999999999, R_2 = 1000.0],
[R_1 = 100.49999999999999, R_2 = 1004.9999999999999],
[R_1 = 100.49999999999999, R_2 = 1010.0],
[R_1 = 101.0, R_2 = 990.0], [R_1 = 101.0, R_2 = 995.0],
[R_1 = 101.0, R_2 = 1000.0], [R_1 = 101.0,
R_2 = 1004.9999999999999], [R_1 = 101.0, R_2 = 1010.0]]
See also: wc_systematic, wc_mintypmax.
wc_ewc_simplify (expression, definitions…) — Function
Brute-forcing through all combinations of tol[n] in order to find the worst-case combination is O(m^n)-complete and therefore computationally intensive for high numbers of tol[n].
wc_ewc_simplify uses the sign of the derivatives of expression to combine
as many tol[n], as possible. The result is an expression that might run much
faster through wc_mintypmax and wc_systematic, but that, if the derivate
of expression doesn’t change sign in the tol[n] space, still yields the
same results for the brute-force approaches to worst-case analysis.
Note that changing the number of tol[n] will change the statistical distribution of the results over the tol[n] space and therefore will change the statistical distribution of the montecarlo method and the results of the root sum square functions.
See also wc_mintypmax and wc_005fmontecarlo.
definitions allows to temporarily asssign values to specific tol[n] during the optimizations (normally optimizagion is done with all tol[n] being zero) which has the side-effect of excempting these tol[n] from the optimization.
Example:
maxima
(%i1) load("wrstcse")$
(%i2) vals: [
R_1= 1000.0*(1+tol[1]*.01),
R_2= 2000.0*(1+tol[2]*.01)
];
(%o2) [R_1 = 1000.0 (0.01 tol + 1),
1
R_2 = 2000.0 (0.01 tol + 1)]
2
(%i3) ratprint:false;
(%o3) false
(%i4) assume(U_In>0);
(%o4) [U_In > 0]
(%i5) divider: U_Out=U_In*(R_1)/(R_1+R_2);
R_1 U_In
(%o5) U_Out = ---------
R_2 + R_1
(%i6) divider_vals:subst(vals,divider);
1000.0 (0.01 tol + 1) U_In
1
(%o6) U_Out = -----------------------------------------------
2000.0 (0.01 tol + 1) + 1000.0 (0.01 tol + 1)
2 1
(%i7) divider_vals_simplified:lhs(divider_vals)=wc_ewc_simplify(rhs(divider_vals));
1000.0 (1 - 0.01 tol ) U_In
2
(%o7) U_Out = -----------------------------------------------
2000.0 (0.01 tol + 1) + 1000.0 (1 - 0.01 tol )
2 2
(%i8) wc_systematic(rhs(divider_vals));
(%o8) [0.33333333333333337 U_In, 0.3311036789297659 U_In,
0.3289036544850498 U_In, 0.3355704697986577 U_In,
0.3333333333333333 U_In, 0.33112582781456956 U_In,
0.3377926421404682 U_In, 0.3355481727574751 U_In,
0.3333333333333333 U_In]
(%i9) wc_systematic(rhs(divider_vals_simplified));
(%o9) [0.3377926421404682 U_In, 0.3333333333333333 U_In,
0.3289036544850498 U_In]
(%i10) lhs(divider_vals)=wc_mintypmax(rhs(divider_vals));
(%o10) U_Out = [min = 0.3289036544850498 U_In,
typ = 0.3333333333333333 U_In, max = 0.3377926421404682 U_In]
(%i11) lhs(divider_vals_simplified)=wc_mintypmax(rhs(divider_vals_simplified));
(%o11) U_Out = [min = 0.3289036544850498 U_In,
typ = 0.3333333333333333 U_In, max = 0.3377926421404682 U_In]
Use case for adding definitions (tol[“E_Gain”] cannot be optimized without knowing the sign of tol[“U_In”]):
maxima
(%i1) load("wrstcse")$
(%i2) vals: [
U_In=1.2*tol["U_In"], /* The input voltage range */
n_Bits=16, /* The ADC's number of bits */
U_Ref=1.2*(1+.01*tol["U_Ref"]), /* The Adc's reference */
E_Gain=1+1.2e-6*tol["E_Gain"], /* Gain error */
E_Offset=1.5e-6 /* Offset error */
];
(%o2) [U_In = 1.2 tol , n_Bits = 16,
U_In
U_Ref = 1.2 (0.01 tol + 1), E_Gain = 1.2e-6 tol + 1,
U_Ref E_Gain
E_Offset = 1.5e-6]
(%i3) ratprint:false;
(%o3) false
(%i4) wc_inputvalueranges(vals);
[ U_In - 1.2 0 1.2 ]
[ ]
[ n_Bits 16 16 16 ]
[ ]
(%o4) [ U_Ref 1.188 1.2 1.212 ]
[ ]
[ E_Gain 0.9999988 1 1.0000012 ]
[ ]
[ E_Offset 1.5e-6 1.5e-6 1.5e-6 ]
(%i5) ndsadc:n_DSADC=((U_In*E_Gain+E_Offset)/U_Ref+.5)*(2^(n_Bits)-1);
n_Bits E_Gain U_In + E_Offset
(%o5) n_DSADC = (2 - 1) (---------------------- + 0.5)
U_Ref
(%i6) lhs(ndsadc)=wc_ewc_simplify(subst(vals,rhs(ndsadc)));
(%o6) n_DSADC = 65535 ((0.8333333333333334
(1.5e-6 - 1.2 (1.2e-6 tol + 1) tol ))
E_Gain U_Ref
/(0.01 tol + 1) + 0.5)
U_Ref
(%i7) lhs(ndsadc)=wc_ewc_simplify(subst(vals,rhs(ndsadc)),tol["U_In"]=1);
(%o7) n_DSADC = 65535 ((0.8333333333333334
(1.2 tol (1 - 1.2e-6 tol ) + 1.5e-6))
U_In U_Ref
/(0.01 tol + 1) + 0.5)
U_Ref
See also: wc_mintypmax, wc_montecarlo.
wc_inputvalueassumptions (expr) — Function
Often it is good practice to keep all numeric values with tolerances in a list and to introduce them into the equations only when needed.
wc_inputvalueassumptions in this case can inform the
assume database about the range each variable in that list will
be in.
See also wc_tolassumptions, wc_inputvalueranges and
assume.
Example:
maxima
(%i1) load("wrstcse");
(%o1) /home/gunter/src/maxima-code/share/contrib/wrstcse.mac
(%i2) vals:[
R_1=100*(1+1/100*tol["R1"])*(1+1/100*tol["Temp"]),
R_2=200*(1+1/100*tol["R2"])*(1+1/100*tol["Temp"])];
tol tol
R1 Temp
(%o2) [R_1 = 100 (----- + 1) (------- + 1),
100 100
tol tol
R2 Temp
R_2 = 200 (----- + 1) (------- + 1)]
100 100
(%i3) float(wc_inputvalueassumptions(%));
(%o3) [R_2 >= 196.02, R_2 <= 204.02, R_1 >= 98.01, R_1 <= 102.01]
(%i4) is(R_1>R_2);
(%o4) false
(%i5) is(R_1>90);
(%o5) true
(%i6) is(R_1>200);
(%o6) false
(%i7) is(R_1<200);
(%o7) true
(%i8) is(R_1>100);
(%o8) unknown
See also: wc_tolassumptions, wc_inputvalueranges, assume.
wc_inputvalueranges (expression, [show_tols]) — Function
Convenience function: Displays a list which parameter can vary between which values.
If show_tols is true then this function additionally displays
which tol[n] each variable is affected by.
See also wc_mintypmax2tol and wc_005finputvalueassumptions.
Example:
maxima
(%i1) fpprintprec:4;
(%o1) 4
(%i2) load("wrstcse")$
(%i3) vals: [
R_1= 1000.0*(1+tol["R_1"]*.01+tol["Temp"]*.001),
R_2= 2000.0*(1+tol["R_2"]*.01+tol["Temp"]*.001),
R_3= 2000.0*(1+tol["R_3"]*.01)
];
(%o3) [R_1 = 1000.0 (0.001 tol + 0.01 tol + 1),
Temp R_1
R_2 = 2.0e+3 (0.001 tol + 0.01 tol + 1),
Temp R_2
R_3 = 2.0e+3 (0.01 tol + 1)]
R_3
(%i4) wc_inputvalueranges(vals);
[ R_1 989.0 1000.0 1.011e+3 ]
[ ]
(%o4) [ R_2 1.978e+3 2.0e+3 2.022e+3 ]
[ ]
[ R_3 1.98e+3 2.0e+3 2.02e+3 ]
(%i5) wc_inputvalueranges(vals,true);
[ R_1 989.0 1000.0 1.011e+3 [tol , tol ] ]
[ Temp R_1 ]
[ ]
(%o5) [ R_2 1.978e+3 2.0e+3 2.022e+3 [tol , tol ] ]
[ Temp R_2 ]
[ ]
[ R_3 1.98e+3 2.0e+3 2.02e+3 [tol ] ]
[ R_3 ]
See also: wc_mintypmax2tol, wc_inputvalueassumptions.
wc_inputvalues_max (listofinputvalues) — Function
Sets all the input values contained in listofinputvalues to their maximum values and returns the result. Helpful for example when trying to determine the maximum result of complicated filters;
See also wc_005finputvalues_005fmin.
Example:
maxima
(%i1) fpprintprec:4;
(%o1) 4
(%i2) load("wrstcse")$
(%i3) vals: [
R_1= 1000.0*(1+tol["R_1"]*.01+tol["Temp"]*.001),
R_2= 2000.0*(1+tol["R_2"]*.01+tol["Temp"]*.001),
R_3= 2000.0*(1+tol["R_3"]*.01)
];
(%o3) [R_1 = 1000.0 (0.001 tol + 0.01 tol + 1),
Temp R_1
R_2 = 2.0e+3 (0.001 tol + 0.01 tol + 1),
Temp R_2
R_3 = 2.0e+3 (0.01 tol + 1)]
R_3
(%i4) wc_inputvalueranges(vals);
[ R_1 989.0 1000.0 1.011e+3 ]
[ ]
(%o4) [ R_2 1.978e+3 2.0e+3 2.022e+3 ]
[ ]
[ R_3 1.98e+3 2.0e+3 2.02e+3 ]
(%i5) vals_max:wc_inputvalues_max(vals);
(%o5) [R_1 = 1.011e+3, R_2 = 2.022e+3, R_3 = 2.02e+3]
(%i6) wc_inputvalueranges(vals_max);
[ R_1 1.011e+3 1.011e+3 1.011e+3 ]
[ ]
(%o6) [ R_2 2.022e+3 2.022e+3 2.022e+3 ]
[ ]
[ R_3 2.02e+3 2.02e+3 2.02e+3 ]
See also: wc_inputvalues_min.
wc_inputvalues_min (listofinputvalues) — Function
Sets all the input values contained in listofinputvalues to their minimum values and returns the result. Helpful for example when trying to determine the minimum result of complicated filters;
See also wc_005finputvalues_005fmin.
Example:
maxima
(%i1) load("wrstcse")$
(%i2) vals: [
R_1= 1000.0*(1+tol["R_1"]*.01+tol["Temp"]*.001),
R_2= 2000.0*(1+tol["R_2"]*.01+tol["Temp"]*.001),
R_3= 2000.0*(1+tol["R_3"]*.01)
];
(%o2) [R_1 = 1000.0 (0.001 tol + 0.01 tol + 1),
Temp R_1
R_2 = 2000.0 (0.001 tol + 0.01 tol + 1),
Temp R_2
R_3 = 2000.0 (0.01 tol + 1)]
R_3
(%i3) wc_inputvalueranges(vals);
[ R_1 989.0 1000.0 1010.9999999999999 ]
[ ]
(%o3) [ R_2 1978.0 2000.0 2021.9999999999998 ]
[ ]
[ R_3 1980.0 2000.0 2020.0 ]
(%i4) vals_min:wc_inputvalues_min(vals);
(%o4) [R_1 = 989.0, R_2 = 1978.0, R_3 = 1980.0]
(%i5) wc_inputvalueranges(vals_min);
[ R_1 989.0 989.0 989.0 ]
[ ]
(%o5) [ R_2 1978.0 1978.0 1978.0 ]
[ ]
[ R_3 1980.0 1980.0 1980.0 ]
See also: wc_inputvalues_min.
wc_max (expr, [num]) — Function
Outputs only the maximum value of expr). If num is present it tells maxima how many samples to try out of the range of each tolerance.
See also wc_max, wc_typicalvalues and wc_005fmintypmax.
Example:
maxima
(%i1) load("wrstcse");
(%o1) /home/gunter/src/maxima-code/share/contrib/wrstcse.mac
(%i2) vals:[
R_1=100*(1+1/100*tol["R1"])*(1+1/100*tol["Temp"]),
R_2=200*(1+1/100*tol["R2"])*(1+1/100*tol["Temp"])];
tol tol
R1 Temp
(%o2) [R_1 = 100 (----- + 1) (------- + 1),
100 100
tol tol
R2 Temp
R_2 = 200 (----- + 1) (------- + 1)]
100 100
(%i3) rtotal:R_Total=R_1+R_2;
(%o3) R_Total = R_2 + R_1
(%i4) wc_mintypmax(subst(vals,rhs(rtotal)));
29403 30603
(%o4) [min = -----, typ = 300, max = -----]
100 100
(%i5) wc_max(subst(vals,rhs(rtotal)));
30603
(%o5) -----
100
See also: wc_max, wc_typicalvalues, wc_mintypmax.
wc_min (expr, [num]) — Function
Outputs only the minimum value of expr). If num is present it tells maxima how many samples to try out of the range of each tolerance.
See also wc_max, wc_typicalvalues and wc_005fmintypmax.
Example:
maxima
(%i1) load("wrstcse");
(%o1) /home/gunter/src/maxima-code/share/contrib/wrstcse.mac
(%i2) vals:[
R_1=100*(1+1/100*tol["R1"])*(1+1/100*tol["Temp"]),
R_2=200*(1+1/100*tol["R2"])*(1+1/100*tol["Temp"])];
tol tol
R1 Temp
(%o2) [R_1 = 100 (----- + 1) (------- + 1),
100 100
tol tol
R2 Temp
R_2 = 200 (----- + 1) (------- + 1)]
100 100
(%i3) rtotal:R_Total=R_1+R_2;
(%o3) R_Total = R_2 + R_1
(%i4) wc_mintypmax(subst(vals,rhs(rtotal)));
29403 30603
(%o4) [min = -----, typ = 300, max = -----]
100 100
(%i5) wc_min(subst(vals,rhs(rtotal)));
29403
(%o5) -----
100
See also: wc_max, wc_typicalvalues, wc_mintypmax.
wc_mintypmax (expr, [n]) — Function
Prints the minimum, maximum and typical value of expr. If n is positive, n values for each parameter will be tried systematically. If n is negative, -n random values are used instead. If no n is given, wc_defaultvaluespertol is assumed.
See also wc_mintypmax_percent, wc_mintypmax_rss,
wc_mintypmax_num,
wc_min,
wc_max,
wc_ewc_simplify and wc_005fsystematic.
Example:
maxima
(%i1) load("wrstcse")$
(%i2) ratprint:false$
(%i3) vals: [
R_1= 1000.0*(1+tol[1]*.01),
R_2= 1000.0*(1+tol[2]*.01)
];
(%o3) [R_1 = 1000.0 (0.01 tol + 1),
1
R_2 = 1000.0 (0.01 tol + 1)]
2
(%i4) assume(U_In>0);
(%o4) [U_In > 0]
(%i5) divider:U_Out=U_In*R_1/(R_1+R_2);
R_1 U_In
(%o5) U_Out = ---------
R_2 + R_1
(%i6) lhs(divider)=wc_mintypmax(subst(vals,rhs(divider)));
(%o6) U_Out = [min = 0.495 U_In, typ = 0.5 U_In,
max = 0.505 U_In]
See also: wc_mintypmax_percent, wc_mintypmax_rss, wc_mintypmax_num, wc_min, wc_max, wc_ewc_simplify, wc_systematic.
wc_mintypmax2tol (tolname, minval, typval, maxval) — Function
Generates a parameter that uses the tolerance tolname and tolerates between the given values.
Example:
maxima
(%i1) load("wrstcse")$
(%i2) vals: [U_Diode=wc_mintypmax2tol(tol[1],.5,.75,.82),
R=wc_mintypmax2tol(tol[2],1,1.1,1.3),
U_In=wc_mintypmax2tol(tol[3],0,0,15)];
(%o2) [U_Diode = 0.034999999999999976 (|tol | + tol )
| 1| 1
+ 0.125 (tol - |tol |) + 0.75,
1 | 1|
R = 0.09999999999999998 (|tol | + tol )
| 2| 2
+ 0.050000000000000044 (tol - |tol |) + 1.1,
2 | 2|
15 (|tol | + tol )
| 3| 3
U_In = ------------------]
2
(%i3) wc_inputvalueranges(vals);
[ U_Diode 0.5 0.75 0.82 ]
[ ]
(%o3) [ R 1.0 1.1 1.3 ]
[ ]
[ U_In 0 0 15 ]
wc_mintypmax_num ((equation, var, range_min,) — Function
range_max, [n])
For each tolerance calculation in equation this tries to numerically find the value
of var that solves equation. Expects the value of var to be in the range
range_min…range_max. Additionally expects lhs(equation)-rhs(equation)
to change sign within that range.
See also wc_mintypmax,
Example:
maxima
(%i1) load("wrstcse")$
(%i2) ratprint:false$
(%i3) vals: [
f=(1+tol["f"]*.2),
A=(1+tol["A"]*.1)
]$
(%i4) wc_inputvalueranges(vals,true);
[ f 0.8 1 1.2 [tol ] ]
[ f ]
(%o4) [ ]
[ A 0.9 1 1.1 [tol ] ]
[ A ]
(%i5) assume(U_In>0);
(%o5) [U_In > 0]
(%i6) eq:cos(2*%pi*f*x)=A*x;
(%o6) cos(2 %pi f x) = A x
(%i7) x=wc_mintypmax_num(subst(vals,eq),x,0,.3);
(%o7) x = [min = 0.18165213379777342, typ = 0.21544061525279004,
max = 0.2646539803703126]
See also: wc_mintypmax.
wc_mintypmax_percent (expr, sigmas) — Function
Like wc_mintypmax, but outputs the tolerance range in percent.
See wc_005fmintypmax.
Example:
maxima
(%i1) load("wrstcse")$
(%i2) ratprint:false$
(%i3) wc_defaultsigma:6$
(%i4) vals: [
R_1= 1000.0*(1+tol[1]*.01),
R_2= 1000.0*(1+tol[2]*.01)
];
(%o4) [R_1 = 1000.0 (0.01 tol + 1),
1
R_2 = 1000.0 (0.01 tol + 1)]
2
(%i5) assume(U_In>0);
(%o5) [U_In > 0]
(%i6) divider:U_Out=U_In*R_1/(R_1+R_2);
R_1 U_In
(%o6) U_Out = ---------
R_2 + R_1
(%i7) lhs(divider)=wc_mintypmax(subst(vals,rhs(divider)));
(%o7) U_Out = [min = 0.495 U_In, typ = 0.5 U_In,
max = 0.505 U_In]
(%i8) lhs(divider)=wc_mintypmax_percent(subst(vals,rhs(divider)));
(%o8) U_Out = [min = - 1.0000000000000009 %, typ = 0.5 U_In,
max = 1.0000000000000009 %]
See also: wc_mintypmax.
wc_mintypmax_rss (expr, sigmas) — Function
Prints the minimum and maximum of expr, as well as how high the probability is that expr will lie out of that range based on a root sum square calculation and assuming all input ranges will be gauss-shaped.
wc_defaultsigma defines how many sigma of an input value’s tolerance distribution the range of tol[n]=[-1…1] corresponds to.
The RSS methods has a few advantages a brute-force worst-case calculation:
It is fast even witput wc_ewc_simplify. It prevents overengineering
resulting from assuming all tolerances to add up in a catastrophical way if
this only happens in a neglectible number of cases. But it will yield only
the correct results if the gaussian distribution of the input data is known.
Due to its nature this method doesn’t support tolerances that aren’t symmetrical. Therefore in that case the tolerances are extended in the direction that is less wide.
See also wc_defaultsigma wc_mintypmax_rss_percent, and
wc_005fmintypmax.
Example:
maxima
(%i1) load("wrstcse")$
(%i2) ratprint:false$
(%i3) wc_defaultsigma:6$
(%i4) vals: [
R_1= 1000.0*(1+tol[1]*.01),
R_2= 1000.0*(1+tol[2]*.01)
];
(%o4) [R_1 = 1000.0 (0.01 tol + 1),
1
R_2 = 1000.0 (0.01 tol + 1)]
2
(%i5) assume(U_In>0);
(%o5) [U_In > 0]
(%i6) divider:U_Out=U_In*R_1/(R_1+R_2);
R_1 U_In
(%o6) U_Out = ---------
R_2 + R_1
(%i7) lhs(divider)=wc_mintypmax_rss(subst(vals,rhs(divider)),6);
(%o7) U_Out = [min = 0.49646446609406725 U_In, typ = 0.5 U_In,
max = 0.5035355339059328 U_In, Fail = 0.0019731752898266564 ppm]
See also: wc_ewc_simplify, wc_defaultsigma, wc_mintypmax_rss_percent, wc_mintypmax.
wc_mintypmax_rss_percent (expr, sigmas) — Function
Like wc_mintypmax_rss, but outputs the tolerance range in percent.
See wc_005fmintypmax_005frss.
Example:
maxima
(%i1) load("wrstcse")$
(%i2) ratprint:false$
(%i3) wc_defaultsigma:6$
(%i4) vals: [
R_1= 1000.0*(1+tol[1]*.01),
R_2= 1000.0*(1+tol[2]*.01)
];
(%o4) [R_1 = 1000.0 (0.01 tol + 1),
1
R_2 = 1000.0 (0.01 tol + 1)]
2
(%i5) assume(U_In>0);
(%o5) [U_In > 0]
(%i6) divider:U_Out=U_In*R_1/(R_1+R_2);
R_1 U_In
(%o6) U_Out = ---------
R_2 + R_1
(%i7) lhs(divider)=wc_mintypmax_rss(subst(vals,rhs(divider)),6);
(%o7) U_Out = [min = 0.49646446609406725 U_In, typ = 0.5 U_In,
max = 0.5035355339059328 U_In, Fail = 0.0019731752898266564 ppm]
(%i8) lhs(divider)=float(wc_mintypmax_rss_percent(subst(vals,rhs(divider)),6));
(%o8) U_Out = [min = - 0.7071067811865506 %, typ = 0.5 U_In,
max = 0.7071067811865506 %, Fail = 0.0019731752898266564 ppm]
See also: wc_mintypmax_rss.
wc_montecarlo (expression, num) — Function
Introduces num random values per parameter into expression and returns a list of the result.
See also wc_005fsystematic.
Example:
maxima
(%i1) load("wrstcse")$
(%i2) vals: [
R_1= 1000.0*(1+tol[1]*.01),
R_2= 2000.0*(1+tol[2]*.01)
];
(%o2) [R_1 = 1000.0 (0.01 tol + 1),
1
R_2 = 2000.0 (0.01 tol + 1)]
2
(%i3) divider: U_Out=U_In*(R_1)/(R_1+R_2);
R_1 U_In
(%o3) U_Out = ---------
R_2 + R_1
(%i4) wc_montecarlo(subst(vals,rhs(divider)),10);
(%o4) [0.3301505377099377 U_In, 0.33276843198354916 U_In,
0.33406203454153227 U_In, 0.33434833585190965 U_In,
0.3341006856369802 U_In, 0.3359647531928058 U_In,
0.32911646313213117 U_In, 0.333158315034511 U_In,
0.3325173140803672 U_In, 0.3331108406798784 U_In]
See also: wc_systematic.
wc_systematic (expression, [num]) — Function
Systematically introduces num values per parameter into expression
and returns a list of the result. If no num is given, num defaults
to wc_defaultvaluespertol. Negative values for num make
wc_systematic use the monte carlo method with num samples,
instead.
If an equation uses the following values with tolerances:
vals:[R_1=100+tol[1],R_2=100+tol[2]];
num=2 will cause the following combinations of tolerances to be tested:
num=3 will cause the following combinations of tolerances to be tested:
num=-500 will cause the following combinations of tolerances to
be tested, instead:
See also wc_defaultvaluespertol, wc_mintypmax,
wc_defaultvaluespertol,
wc_ewc_simplify and wc_005fmontecarlo.
Example:
maxima
(%i1) load("wrstcse")$
(%i2) vals: [
R_1= 1000.0*(1+tol[1]*.01),
R_2= 2000.0*(1+tol[2]*.01)
];
(%o2) [R_1 = 1000.0 (0.01 tol + 1),
1
R_2 = 2000.0 (0.01 tol + 1)]
2
(%i3) divider: U_Out=U_In*(R_1)/(R_1+R_2);
R_1 U_In
(%o3) U_Out = ---------
R_2 + R_1
(%i4) wc_systematic(subst(vals,rhs(divider)));
(%o4) [0.33333333333333337 U_In, 0.3311036789297659 U_In,
0.3289036544850498 U_In, 0.3355704697986577 U_In,
0.3333333333333333 U_In, 0.33112582781456956 U_In,
0.3377926421404682 U_In, 0.3355481727574751 U_In,
0.3333333333333333 U_In]
See also: wc_defaultvaluespertol, wc_mintypmax, wc_ewc_simplify, wc_montecarlo.
wc_tolappend (list1, list2, …) — Function
Appends lists of parameters from independent sources making sure that tolerances of all elements in one list will stay independent from all elements in the others.
Works like append() in that it appends all values from all of its arguments to make one big list. But this command, if one list happens to contain a tol[n] with the same n as another list, changes one of these n to a new value that makes it independent from all tolerances from the other list.
See also append.
Example:
maxima
(%i1) load("wrstcse")$
(%i2) val_a: [
R_1= 1000.0*(1+tol[1]*.01),
R_2= 1000.0*(1+tol[2]*.01)
];
(%o2) [R_1 = 1000.0 (0.01 tol + 1),
1
R_2 = 1000.0 (0.01 tol + 1)]
2
(%i3) val_b: [
R_3= 1000.0*(1+tol[1]*.01),
R_4= 1000.0*(1+tol[4]*.01)
];
(%o3) [R_3 = 1000.0 (0.01 tol + 1),
1
R_4 = 1000.0 (0.01 tol + 1)]
4
(%i4) append(val_a,val_b);
(%o4) [R_1 = 1000.0 (0.01 tol + 1),
1
R_2 = 1000.0 (0.01 tol + 1), R_3 = 1000.0 (0.01 tol + 1),
2 1
R_4 = 1000.0 (0.01 tol + 1)]
4
(%i5) wc_tolappend(val_a,val_b);
used = 1
(%o5) [R_1 = 1000.0 (0.01 tol + 1),
1
R_2 = 1000.0 (0.01 tol + 1), R_3 = 1000.0 (0.01 tol + 1),
2 5
R_4 = 1000.0 (0.01 tol + 1)]
4
See also: append.
wc_tolassumptions (expr) — Function
Adds the range of the tol[n] contained in expr to the assume database.
See also wc_inputvalueassumptions, wc_inputvalueranges and assume.
Example:
maxima
(%i1) load("wrstcse");
(%o1) /home/gunter/src/maxima-code/share/contrib/wrstcse.mac
(%i2) vals:[
R_1=100*(1+1/100*tol["R1"])*(1+1/100*tol["Temp"]),
R_2=200*(1+1/100*tol["R2"])*(1+1/100*tol["Temp"])];
tol tol
R1 Temp
(%o2) [R_1 = 100 (----- + 1) (------- + 1),
100 100
tol tol
R2 Temp
R_2 = 200 (----- + 1) (------- + 1)]
100 100
(%i3) float(wc_tolassumptions(%));
(%o3) [tol >= - 1.0, tol <= 1.0, tol >= - 1.0,
R1 R1 Temp
tol <= 1.0, tol >= - 1.0, tol <= 1.0]
Temp R2 R2
(%i4) is(tol[R_1]>tol[R_2]);
(%o4) unknown
(%i5) is(tol[R_1]>1);
(%o5) unknown
(%i6) is(tol[R_1]<-1);
(%o6) unknown
(%i7) is(tol[R_1]<0);
(%o7) unknown
(%i8) is(tol[R_2]>2);
(%o8) unknown
See also: wc_inputvalueassumptions, wc_inputvalueranges, assume.
wc_typicalvalues (expression) — Function
Returns what happens if all tol[n] happen to be 0, which moves all parameter to the middle of their tolerance range.
Example:
maxima
(%i1) load("wrstcse")$
(%i2) vals: [
R_1= 1000.0*(1+tol[1]*.01),
R_2= 2000.0*(1+tol[2]*.01)
];
(%o2) [R_1 = 1000.0 (0.01 tol + 1),
1
R_2 = 2000.0 (0.01 tol + 1)]
2
(%i3) divider:U_Out=U_In*R_1/(R_1+R_2);
R_1 U_In
(%o3) U_Out = ---------
R_2 + R_1
(%i4) wc_typicalvalues(vals);
(%o4) [R_1 = 1000.0, R_2 = 2000.0]
(%i5) wc_typicalvalues(subst(vals,divider));
(%o5) U_Out = 0.3333333333333333 U_In