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reset_misuse_1_touchingnotcrossing.rst

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Misuse: Touching, not crossing

Description: Resets whose test_value coincides with a turning point of the test_variable risk missing detection of the reset point.

Note that:

  • all elements are in the same component;
  • the order values of resets are not shown; and
  • the units of variables are not shown.
component: TouchingNotCrossing
  ├─ math: x = sin(t*pi/2)
  ├─ variable: x
  └─ variable: y initially 0
      ├─ reset: rule 1
      │   ├─ when x == 1
      │   └─ then y = 1
      └─ reset: rule 2
          ├─ when x == -1
          └─ then y = 0

See CellML syntax

<variable name="t" units="dimensionless" />
<variable name="x" units="dimensionless" />
<variable name="y" units="dimensionless" initial_value="0" />

<math>
    <apply><eq/>
        <ci>x</ci>
        <apply><sin/>
            <apply><times/>
                <ci>t</ci>
                <apply><divide/>
                    <pi/>
                    <cn cellml:units="dimensionless">2</cn>
                </apply>
            </apply>
        </apply>
    </apply>
</math>

<!-- Reset rule 1: -->
<reset variable="y" test_variable="x">
    <test_value>
        <cn units="cellml:dimensionless">1</cn>
    </test_value>
    <reset_value>
        <cn units="cellml:dimensionless">1</cn>
    </reset_value>
</reset>

<!-- Reset rule 2: -->
<reset variable="y" test_variable="x">
    <test_value>
        <cn units="cellml:dimensionless">-1</cn>
    </test_value>
    <reset_value>
        <cn units="cellml:dimensionless">0</cn>
    </reset_value>
</reset>

A simulation with this model might proceed as follows:

t 0.0 0.1 ... 0.9 1.0 1.1 ... 2.9 3.0 3.3 ...
x 0 0.156 ... 0.988 1 0.988 ... -0.988 -1 0.988 ...
y 0 0 ... 0 0 → 1 1 ... 1 1 → 0 0 ...

However, it is easy for implementations to "miss" this type of reset in a simulation. For example, the following may occur in an implementation with adaptive step sizes that uses root finding to detect resets (i.e.: by searching for sign changes in x - 1):

t 0.0 0.4 ... 0.9 1.1 1.7 ...
x 0 0.588 ... 0.988 0.988 0.454 ...
y 0 0 ... 0 0 0 0
x - 1 -1 -0.412 ... -0.12 -0.12 -0.546 ...

This behaviour is expected to be common in implementations. For example, the popular adaptive solver CVODE has a root finding mechanism that can be used to implement reset rules, but its documentation explicitly states it is unlikely to find roots where the sign does not change. As a result, this type of reset rule is probably best avoided.

Suggestions

TODO ?