bio_rtd.peak_shapes

Peak shapes based on mean residence time (rt_mean).

Notes

Functions are evaluated for given time vectors. Peaks are considered clipped if they do not fully fit on the time vector.

For un-clipped peak, the integral over the peak over time == 1.

For un-clipped peak, first momentum == rt_mean.

gaussian

bio_rtd.peak_shapes.gaussian(t, rt_mean, sigma, logger=None)[source]

Gaussian distribution.

p = exp(- ((t - rt_mean) / sigma) ** 2 / 2) / (sigma * sqrt(2 * pi))

Parameters

  • t (ndarray) – Time vector.

  • rt_mean (float) – Mean residence time (== first momentum of un-clipped peak)

  • sigma (float) – Standard deviation.

  • logger (Optional[RtdLogger]) – Logger for logging suspicious parameters or peak shapes.

Returns

p – Evaluated pdf for specified time vector (t).

Return type

ndarray

emg

bio_rtd.peak_shapes.emg(t, rt_mean, sigma, skew, logger=None)[source]

Exponentially modified Gaussian distribution.

Parameters

  • t – Time vector.

  • rt_mean – Mean residence time (== first momentum of un-clipped peak).

  • sigma – Standard deviation of Gaussian part.

  • skew – The rate of exponential part. Recommended: 1/40 < skew < 10.

  • logger (Optional[RtdLogger]) – Logger for logging suspicious parameters or peak shapes.

Returns

p – Evaluated pdf for specified time vector (t).

Return type

ndarray

skewed_normal

bio_rtd.peak_shapes.skewed_normal(t, rt_mean, sigma, skew, logger=None)[source]

Skewed normal distribution.

For skew == 0, the distribution becomes Gaussian distribution.

Parameters

  • t – Time vector.

  • rt_mean – Mean residence time (== first momentum of un-clipped peak).

  • sigma – Standard deviation of Gaussian part.

  • skew – Skewness of the peak. Recommended: -20 < skew < 20.

  • logger (Optional[RtdLogger]) – Logger for logging suspicious parameters or peak shapes.

Returns

p – Evaluated pdf for specified time vector (t).

Return type

ndarray

tanks_in_series

bio_rtd.peak_shapes.tanks_in_series(t, rt_mean, n_tanks, logger=None, allow_open_end=False)[source]

N tanks in series distribution.

rt_mean is for entire unit operation (all tanks together).

For n_tanks == 1, the distribution results in exponential decay.

Parameters

  • t (ndarray) – Time vector.

  • rt_mean (float) – Mean residence time (== first momentum of un-clipped peak).

  • n_tanks (int) – Number of tanks. Recommended: 1 <= n_tanks < 50

  • logger (Optional[RtdLogger]) – Logger for logging suspicious parameters or peak shapes.

Returns

p – Evaluated pdf for specified time vector (t).

Return type

ndarray