@@ -18,8 +18,7 @@
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18 18
def threebody(t0=0.0, tmax=17.0652165601579625588917206249, y0=None):
19 19
    r"""Initial value problem (IVP) based on a three-body problem.
20 20
21 -
    Let the initial conditions be :math:`y = (y_1, y_2, \dot{y}_1, \dot{y}_2)^T`.
22 -
    This function implements the second-order three-body problem as a system of
21 +
    For the initial conditions :math:`y = (y_1, y_2, \dot{y}_1, \dot{y}_2)^T`, this function implements the second-order three-body problem as a system of
23 22
    first-order ODEs, which is defined as follows: [1]_
24 23
25 24
    .. math::
@@ -45,7 +44,7 @@
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45 44
    Parameters
46 45
    ----------
47 46
    t0
48 -
        Initial time. Default is ``0.0``.
47 +
        Initial time.
49 48
    tmax
50 49
        Final time. Default is ``17.0652165601579625588917206249`` which is the period of the solution.
51 50
    y0
@@ -54,8 +53,7 @@
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    Returns
55 54
    -------
56 55
    InitialValueProblem
57 -
        InitialValueProblem object describing a three-body problem IVP with the prescribed
58 -
        configuration.
56 +
        InitialValueProblem object describing a three-body problem IVP with the prescribed configuration.
59 57
60 58
    References
61 59
    ----------
@@ -65,7 +63,7 @@
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65 63
    """
66 64
67 65
    def rhs(t, y):
68 -
        mu = 0.012277471  # a constant (standardised moon mass)
66 +
        mu = 0.012277471  # a constant (standardized moon mass)
69 67
        mp = 1 - mu
70 68
        D1 = ((y[0] + mu) ** 2 + y[1] ** 2) ** (3 / 2)
71 69
        D2 = ((y[0] - mp) ** 2 + y[1] ** 2) ** (3 / 2)
@@ -80,11 +78,10 @@
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def vanderpol(t0=0.0, tmax=30, y0=None, params=1e1):
83 -
    r"""Initial value problem (IVP) based on the Van der Pol Oscillator, implemented in `jax`.
81 +
    r"""Initial value problem (IVP) based on the Van der Pol Oscillator.
84 82
85 83
    This function implements the second-order Van-der-Pol Oscillator as a system
86 -
    of first-order ODEs.
87 -
    The Van der Pol Oscillator is defined as
84 +
    of first-order ODEs. The Van der Pol Oscillator is defined as
88 85
89 86
    .. math::
90 87
@@ -107,10 +104,9 @@
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107 104
    tmax : float
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        Final time point. Rightmost point of the integration domain.
109 106
    y0 : np.ndarray,
110 -
        *(shape=(2, ))* -- Initial value of the problem.
107 +
        *(shape=(2, ))* -- Initial value of the problem. Defaults to ``[2.0, 0.0]``.
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    params : (float), optional
112 -
        Parameter :math:`\mu` for the Van der Pol Equations
113 -
        Default is :math:`\mu=0.1`.
109 +
        Parameter :math:`\mu` for the Van der Pol equations.
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    Returns
116 112
    -------
@@ -144,7 +140,7 @@
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def rigidbody(t0=0.0, tmax=20.0, y0=None, params=(-2.0, 1.25, -0.5)):
147 -
    r"""Initial value problem (IVP) for rigid body dynamics without external forces
143 +
    r"""Initial value problem (IVP) for rigid body dynamics without external forces.
148 144
149 145
    The rigid body dynamics without external forces is defined through
150 146
@@ -152,24 +148,24 @@
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152 148
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        f(t, y) =
154 150
        \begin{pmatrix}
155 -
            y_2 y_3 \\
156 -
            -y_1 y_3 \\
157 -
            -0.51 \cdot y_1 y_2
151 +
            a y_2 y_3 \\
152 +
            b y_1 y_3 \\
153 +
            c y_1 y_2
158 154
        \end{pmatrix}
159 155
160 -
    The ODE system has no parameters.
156 +
    for parameters :math:`(a, b, c)`.
161 157
    This implementation includes the Jacobian :math:`J_f` of :math:`f`.
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    Parameters
164 160
    ----------
165 161
    t0
166 -
        Initial time. Default is 0.0
162 +
        Initial time.
167 163
    tmax
168 -
        Final time. Default is 20.0
164 +
        Final time.
169 165
    y0
170 -
        *(shape=(3, ))* -- Initial value. Default is ``[1., 0., 0.9]``.
166 +
        *(shape=(3, ))* -- Initial value. Defaults to ``[1., 0., 0.9]``.
171 167
    params
172 -
        Parameter of the rigid body problem. Default is ``(-2.0, 1.25, -0.5)``.
168 +
        Parameters ``(a, b, c)`` of the rigid body problem.
173 169
174 170
    Returns
175 171
    -------
@@ -205,7 +201,7 @@
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        f(t, y) = a  y  \left( 1 - \frac{y}{b} \right)
207 203
208 -
    for some parameters :math:`(a, b)`.
204 +
    for parameters :math:`(a, b)`.
209 205
    Default is :math:`(a, b)=(3.0, 1.0)`. This implementation includes
210 206
    the Jacobian :math:`J_f` of :math:`f` as well as a closed form
211 207
    solution given by
@@ -219,14 +215,13 @@
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219 215
    Parameters
220 216
    ----------
221 217
    t0
222 -
        Initial time. Default is 0.0
218 +
        Initial time.
223 219
    tmax
224 -
        Final time. Default is 2.0
220 +
        Final time.
225 221
    y0
226 222
        *(shape=(1, ))* -- Initial value. Default is ``[0.1]``.
227 223
    params
228 -
        Parameters :math:`(a, b)` for the logistic IVP.
229 -
        Default is :math:`(a, b) = (3.0, 1.0)`.
224 +
        Parameters :math:`(a, b)` of the logistic IVP.
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231 226
    Returns
232 227
    -------
@@ -273,26 +268,25 @@
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273 268
            \frac{1}{d} (y_1 + b - c y_2)
274 269
        \end{pmatrix}
275 270
276 -
    for some parameters :math:`(a, b, c, d)`.
271 +
    for parameters :math:`(a, b, c, d)`.
277 272
    Default is :math:`(a, b)=(0.2, 0.2, 3.0)`.
278 273
    This implementation includes the Jacobian :math:`J_f` of :math:`f`.
279 274
280 275
    Parameters
281 276
    ----------
282 277
    t0
283 -
        Initial time. Default is 0.0
278 +
        Initial time.
284 279
    tmax
285 -
        Final time. Default is 20.0
280 +
        Final time.
286 281
    y0
287 -
        *(shape=(2, ))* -- Initial value. Default is ``[1., -1.]``.
282 +
        *(shape=(2, ))* -- Initial value. Defaults to ``[1., -1.]``.
288 283
    params
289 -
        Parameter of the FitzHugh-Nagumo model. Default is ``(0.2, 0.2, 3.0, 1.0)``.
284 +
        Parameters ``(a, b, c, d)`` of the FitzHugh-Nagumo model.
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291 286
    Returns
292 287
    -------
293 288
    InitialValueProblem
294 -
        InitialValueProblem object describing the FitzHugh-Nagumo model with the prescribed
295 -
        configuration.
289 +
        InitialValueProblem object describing the FitzHugh-Nagumo model with the prescribed configuration.
296 290
    """
297 291
    if y0 is None:
298 292
        y0 = np.array([1.0, -1.0])
@@ -323,26 +317,25 @@
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            -c y_2 + d y_1 y_2
324 318
        \end{pmatrix}
325 319
326 -
    for some parameters :math:`(a, b, c, d)`.
320 +
    for parameters :math:`(a, b, c, d)`.
327 321
    Default is :math:`(a, b)=(0.5, 0.05, 0.5, 0.05)`.
328 322
    This implementation includes the Jacobian :math:`J_f` of :math:`f`.
329 323
330 324
    Parameters
331 325
    ----------
332 326
    t0
333 -
        Initial time. Default is 0.0
327 +
        Initial time.
334 328
    tmax
335 -
        Final time. Default is 20.0
329 +
        Final time.
336 330
    y0
337 -
        *(shape=(2, ))* -- Initial value. Default is ``[1., -1.]``.
331 +
        *(shape=(2, ))* -- Initial value. Defaults to ``[20., 20.]``.
338 332
    params
339 -
        Parameter of the Lotka-Volterra model. Default is ``(0.2, 0.2, 3.0)``.
333 +
        Parameters ``(a, b, c, d)`` of the Lotka-Volterra model.
340 334
341 335
    Returns
342 336
    -------
343 337
    InitialValueProblem
344 -
        InitialValueProblem object describing the Lotka-Volterra system with the prescribed
345 -
        configuration.
338 +
        InitialValueProblem object describing the Lotka-Volterra system with the prescribed configuration.
346 339
    """
347 340
    if y0 is None:
348 341
        y0 = np.array([20.0, 20.0])
@@ -392,13 +385,13 @@
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392 385
    Parameters
393 386
    ----------
394 387
    t0
395 -
        Initial time. Default is 0.0
388 +
        Initial time.
396 389
    tmax
397 -
        Final time. Default is 200.0
390 +
        Final time.
398 391
    y0
399 -
        *(shape=(4, ))* -- Initial value. Default is ``[998, 1, 1, 0]``.
392 +
        *(shape=(4, ))* -- Initial value. Defaults to ``[998, 1, 1, 0]``.
400 393
    params
401 -
        Parameter of the SEIR model. Default is ``(0.3, 0.3, 0.1)``.
394 +
        Parameters :math:`(\alpha, \beta, \gamma)` of the SEIR model.
402 395
403 396
    Returns
404 397
    -------
@@ -458,13 +451,13 @@
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458 451
    Parameters
459 452
    ----------
460 453
    t0
461 -
        Initial time. Default is 0.0
454 +
        Initial time.
462 455
    tmax
463 -
        Final time. Default is 20.0
456 +
        Final time.
464 457
    y0
465 -
        *(shape=(3, ))* -- Initial value. Default is ``[0., 1., 1.05]``.
458 +
        *(shape=(3, ))* -- Initial value. Defaults to ``[0., 1., 1.05]``.
466 459
    params
467 -
        Parameter of the Lorenz63 model. Default is ``(10.0, 28.0, 8.0 / 3.0)``.
460 +
        Parameters ``(a, b, c)`` of the Lorenz63 model.
468 461
469 462
    Returns
470 463
    -------
@@ -502,9 +495,9 @@
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502 495
    Parameters
503 496
    ----------
504 497
    t0
505 -
        Initial time. Default is 0.0
498 +
        Initial time.
506 499
    tmax
507 -
        Final time. Default is 20.0
500 +
        Final time.
508 501
    y0
509 502
        *(shape=(N, ))* -- Initial value. Default is ``[1/F, ..., 1/F]``. `N` is the number of variables in the model.
510 503
    num_variables
Files Coverage
src/probnum 87.64%
Project Totals (163 files) 87.64%
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coverage:
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  precision: 2
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    project:
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      default:
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        target: auto
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        threshold: 1%
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    patch:
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      default:
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        target: 90%
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        threshold: 1%
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comment:
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  layout: "reach, diff, files"
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  behavior: default
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  require_changes: true
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