Issue with standard_complex_sweep finding solutions.

[Kgeorge1729]

I'm having some difficulty with the standard_complex_sweep method tracking solutions for a set of polynomials. The issue I'm having is that I'm trying to track the solutions for two system of polynomials simultaneously for a change in parameters. I can track the solutions for one of the polynomials. That is to say that I'm only looking for solutions within a certain range of values for which one polynomial produces a continuum in this range and the other does not despite the fact that I know that these solutions should be present.

The two polynomials I'm trying to solve are as follows:

Pressure polynomials:
1: Q14 - Q46 + Q54;
2: Q25 - Q54 - Q56;
3: Q46 + Q56 - Q63;
Flow polynomials:
1: 0.31684P4 + 3.07780911325921Q14 - 0.31684x;
2: Q46(3.46301518876535H46 + 1) - (0.7921 - 0.7921H46)(P4 - P6);
3: 0.31684P5 + 3.07780911325921Q25 + 0.31684x - 0.31684;
4: Q54*(3.46301518876535H45 + 1) - (0.7921 - 0.7921H45)(-P4 + P5);
5: Q56(3.46301518876535H56 + 1) - (0.7921 - 0.7921H56)(P5 - P6);
6: -P6(0.7921 - 0.7921H63) + Q63(3.46301518876535H63 + 1);
Ratio polynomials:
1: -Q14 + Q46r56;
2: Q25r14 - Q54;
3: -Q46 + Q63r63;
Haematocrit polynomials:
1: H45*(1 - r56) - H46 + 0.6r56;
2: -a45 + r14 - 0.04;
3: -a46 - r14 + 0.96;
4: -H45r14*(1.0a45 + a46) + 0.6a45;
5: H45r14 + H56(1 - r14) - 0.6;
6: H46r63 + H56(1 - r63) - H63;

Pressure polynomials:
1: Q14 - Q45 - Q46;
2: Q25 + Q45 - Q56;
3: Q46 + Q56 - Q63;
Flow polynomials:
1: 0.31684P4 + 3.07780911325921Q14 - 0.31684x;
2: Q45(3.46301518876535H45 + 1) - (0.7921 - 0.7921H45)(P4 - P5);
3: Q46(3.46301518876535H46 + 1) - (0.7921 - 0.7921H46)(P4 - P6);
4: 0.31684P5 + 3.07780911325921Q25 + 0.31684x - 0.31684;
5: Q56*(3.46301518876535H56 + 1) - (0.7921 - 0.7921H56)(P5 - P6);
6: -P6(0.7921 - 0.7921H63) + Q63(3.46301518876535H63 + 1);
Ratio polynomials:
1: Q14r14 - Q45;
2: -Q25 + Q56r56;
3: -Q46 + Q63r63;
Haematocrit polynomials:
1: -a45 + r14 - 0.04;
2: -a46 - r14 + 0.96;
3: -H45r14(1.0a45 + a46) + 0.6a45;
4: H45r14 + H46(1 - r14) - 0.6;
5: H45*(1 - r56) - H56 + 0.6r56;
6: H46r63 + H56*(1 - r63) - H63;

The x variable is the one that I'm performing a sweep for for the values between 0.4 to 0.6. The first polynomial system here is the one for which I can obtain values for. For instance when x = 0.505038, the solution to the first polynomial is:
P4: 0.37741144658028 P5: 0.372872011901421 P6: 0.249716541518299
H45:0.338836966697101 H46:0.623717837897984 H56:0.0136621865184432
H63: 0.6 Q14:0.0131383057549933 Q25:0.0125683531387659
Q45:0.00109383337967731 Q46:0.012044472375316 Q56:0.0136621865184432
Q63:0.0257066588937592 r14:0.083255284210568 r56:0.919937165387056
r63: 0.468535114776818 a45:0.043255284210568 a46:0.876744715789432

The complex sweep is able to find this solution but for the second polynomial the solution is:
P4: 0.374835183546721 P5: 0.375468918441703 P6: 0.249695898011577
H45:0.00334358031025163 H46:0.57876743256638 H56:0.624994164006294
H63: 0.6 Q14:0.0134035149182375 Q25:0.012301018863655
Q45:0.000494576360074708 Q46:0.0138980912783122 Q56:0.0118064425035803
Q63:0.0257045337818925 r14:0.0402061297162953 r56:0.964414080309971
r63: 0.540686378373557 a45:0.000206129716295259 a46:0.919793870283705

This solution doesn't appear when performing a complex sweep. One thing that does seem to constantly come up is that I keep getting the following error.

File "", line 1
NaN******
^
SyntaxError: invalid syntax

And one or more of the fields for the solution is filled with NaN********.

Are the sweep functions known to fail tracking some solutions some times or can my system not be solved in this way?

[janverschelde]

Thanks for reporting this issue. The sweep was designed to detect singular solutions and then to stop at the first encounter of a singular solutions. The real sweep could compute quadratic turning points well because of its arc-length parameter parametrization, which might not work well enough in a complex sweep. Without seeing the actual script that defines the homotopy, it is difficult for me to write more.

[Kgeorge1729]

Thank you for the advice. Unfortunately the script is integrated into a program so it will not make sense posting the whole thing but I'll try the real sweep to see if this works.