ihmt 0.9.4

Inhomogeneous magnetization transfer simulator for magnetic resonance research.

ihMT

License: GNU General Public License v3 or later (GPLv3+)

Table of contents

• Setup
  • Install
    • For developers
    • For users
    • Optional
  • Imports
  • Overview
    • Meta
      • Signal
      • CompositeDictionary
      • Duration
      • Frequency
      • AngularFrequency
      • Angle
    • Pulse
    • Sequence
    • System
      • Lineshapes
    • Simulator
    • Corrector
      • InterpolantDictionary
    • Trajector - WIP
• Applications
  • Simulating a single experiment
    • Using the ihmt.simulator.Simulator class
    • Using the ihmt.run.SingleRun function
      • Hand parametrized
      • Using a configuration object
      • From the command line
    • Example: Computing derivative maps: MT(s/d)R, ihMT, ihMTR, BP, BPR
      • Manual Computation
      • Using ihmt.meta.CompositeSignal
    • Example: Computing steady-state signals at every readout
      • Manual computation
      • Using ihmt.trajector.Trajector
        • Timing difference using stable=True
        • Value difference using stable=True
    • Example: Point Spread Function (PSF) - WIP
  • Simulating many experiments
    • Using the ihmt.run.GridRuns function
    • Example: Computing derivative maps: MT(s/d)R, ihMT, ihMTR, BP, BPR
    • Example: $\mathrm{B}_1^+$ correction
      • Manual computation
      • Using ihmt.corrector.Corrector
  • Visualization
    • Example: $\mathrm{B}_1^+$ correction
      • 1-Dim $\mathrm{B}_1^+$ correction
      • N-Dim $\mathrm{B}_1^+$ correction
      • Real-world data
    • Example: Steady-state signal with respect to readout
    • Exmple: PSF - WIP
  • Advanced
    • Sensivity analysis - WIP
      • Using fixed parameter vectors
      • Using distribution sampling
• Additional Information
  • Configuration files
    • Default configurations
      • 3 Teslas
      • 7 Teslas
    • Custom configurations
      • In a live environment
      • Stored on file
  • Loggers
  • The ihmt.meta.CompositeDictionary class
  • Optimizing ihmt.run.GridRuns runtime
  • Test suite
  • Contributing new features - WIP
    • Adding new modules
    • Modifying existing modules
• Notes
• To do

Setup

Install

For developers

• NumPy
• SciPy
• PyYAML
• Coverage

pip install numpy scipy pyyaml coverage
# or
conda install numpy scipy pyyaml coverage

Install ihmt in edit mode:

cd ihmt
pip install -e .

For users

• NumPy
• SciPy
• PyYAML

pip install numpy scipy pyyaml
# or
conda install numpy scipy pyyaml

Install ihmt in normal mode:

cd ihmt
pip install .

Optional

• Matplotlib
• Jupyter

pip install matplotlib jupyter
# or
conda install matplotlib jupyter

Imports

try:  # Basic import example
    from ihmt import (
        Tukey,
        Sequence,
        System,
        Simulator,
        Corrector,
        Trajector,
        Signal,               # Enum (flag)
        CompositeDictionary,  # Utility
        SingleRun,            # Utility
        GridRuns,             # Utility
        Duration,             # Utility
        Frequency,            # Utility
        AngularFrequency,     # Utility
        Angle,                # Utility
    )
    from ihmt.config import default

except ImportError as e:  # If the ihmt package is not installed
    %pip install -e .
    from os import _exit
    _exit(00)

# Additional imports for Applications & later sections
import matplotlib.pyplot as plt
import numpy as np
import scipy as sp
import yaml as ya
from copy import deepcopy

Overview

The ihmt package aims to provide an interface for simulation and manipulation of (ih)MT signal for varying configurations of MT-preparation pulses, sequences, and biophysical systems. To provide ample space for new features, the package separates each part of the process into different modules:

• MT-preparation pulse classes (e.g., Tukey) are declared in the ihmt.pulse module,
• the sequence-specifying class Sequence is defined in the ihmt.sequence module,
• the biophysical system class System is in the ihmt.system module,
• the simulator class Simulator is in the ihmt.simulator module,
• the signal correction class Corrector is defined in the ihmt.corrector module,
• the signal encoding class Trajector is defined in the ihmt.trajector module,
• some utility features such as the Signal, Angle, and Frequency classes are defined in the ihmt.meta module,
• and some utility functions to simplify obtaining results from command line (SingleRun) and from batched experiments (GridRuns) are defined in the ihmt.run module.

To enhance the user experience, important classes can be directly imported from the ihmt namespace. E.g., one can import the Tukey class using from ihmt.pulse import Tukey, or they can import it using from ihmt import Tukey directly.

Below is an object-by-object Initialization example of the various classes of the package, with further information on their interplay. The next section shows various example Applications of this package, like $\mathrm{B}_1^+$ correction, sensitivity analysis, and visualization. The third and final section contains Additional Information, such as defining configuration files for automated analyses and using loggers to manage the package output streams.

Meta

Signal

meta.Signal is an enumerator of the various signals that are defined within the package. This flag enumerator is used in various location to homogeneize requesting specific signals without risks of case-sensitive or misspelling errors. The following signals are currently implemented in this package:

• Native signals

  • MT0: [ $MT_0$ ], blablabla. unit: a.u.

  • MTs_Positive: [ $MT{_\mathrm{s}^+}$ ], blablabla. unit: a.u.

  • MTs_Negative: [ $MT{_\mathrm{s}^-}$ ], blablabla. unit: a.u.

  • MTd_CM: [ $MT{_\mathrm{d}^\mathrm{CM}}$ ], blablabla. unit: a.u.

  • MTd_ALT: [ $MT{_\mathrm{d}^\mathrm{ALT}}$ ], blablabla. unit: a.u.

• Composite signals

  • MTs: [ $MT{_\mathrm{s}}$ ], blablabla. unit: a.u.

    • $MT{\mathrm{s}} = \frac{1}{2} (MT{\mathrm{s}^+} + MT{_\mathrm{s}^-})$

  • ihMT_CM: [ $ihMT{^\mathrm{CM}}$ ], blablabla. unit: a.u.

    • $ihMT{^\mathrm{CM}} = 2 \times (MT{\mathrm{s}} - MT{\mathrm{d}^\mathrm{CM}})$

  • ihMT_ALT: [ $ihMT{^\mathrm{ALT}}$ ], blablabla. unit: a.u.

    • $ihMT{^\mathrm{ALT}} = 2 \times (MT{\mathrm{s}} - MT{\mathrm{d}^\mathrm{ALT}})$

  • BP: [ $BP$ ], blablabla. unit: a.u.

    • $BP = 2 \times (MT{\mathrm{d}^\mathrm{ALT}} - MT{\mathrm{d}^\mathrm{CM}})$

  • MTsR_Positive: [ $MTR{_\mathrm{s}^+}$ ], blablabla. unit: % of MT0

    • $MTR{\mathrm{s}^+} = 100 \times (1 - MT{\mathrm{s}^+} / MT_0)$

  • MTsR_Negative: [ $MTR{_\mathrm{s}^-}$ ], blablabla. unit: % of MT0

    • $MTR{\mathrm{s}^-} = 100 \times (1 - MT{\mathrm{s}^-} / MT_0)$

  • MTsR: [ $MTR{_\mathrm{s}}$ ], blablabla. unit: % of MT0

    • $MTR{\mathrm{s}} = 100 \times (1 - MT{\mathrm{s}} / MT_0)$

  • MTdR_CM: [ $MTR{_\mathrm{d}^\mathrm{CM}}$ ], blablabla. unit: % of MT0

    • $MTR{\mathrm{d}^\mathrm{CM}} = 100 \times (1 - MT{\mathrm{d}^\mathrm{CM}} / MT_0)$

  • MTdR_ALT: [ $MTR{_\mathrm{d}^\mathrm{ALT}}$ ], blablabla. unit: % of MT0

    • $MTR{\mathrm{d}^\mathrm{ALT}} = 100 \times (1 - MT{\mathrm{d}^\mathrm{ALT}} / MT_0)$

  • ihMTR_CM: [ $ihMTR{^\mathrm{CM}}$ ], blablabla. unit: % of MT0

    • $ihMTR{^\mathrm{CM}} = 100 \times ihMT{^\mathrm{CM}} / MT_0$

  • ihMTR_ALT: [ $ihMTR{^\mathrm{ALT}}$ ], blablabla. unit: % of MT0

    • $ihMTR{^\mathrm{ALT}} = 100 \times ihMT{^\mathrm{ALT}} / MT_0$

  • BPR: [ $BPR$ ], blablabla. unit: % of MT0

    • $BPR = 100 \times BP / MT_0$

print("Possible `Signal.flag` flags:")
print(*[value for value in Signal.values()], sep='\n')

Possible `Signal.flag` flags:
Signal.MT0
Signal.MTs_Positive
Signal.MTs_Negative
Signal.MTd_CM
Signal.MTd_ALT
Signal.MTs
Signal.ihMT_CM
Signal.ihMT_ALT
Signal.BP
Signal.MTsR_Positive
Signal.MTsR_Negative
Signal.MTsR
Signal.MTdR_CM
Signal.MTdR_ALT
Signal.ihMTR_CM
Signal.ihMTR_ALT
Signal.BPR
Signal.ALL

CompositeDictionary

meta.CompositeDictionary subclasses the standard python dictionary (dict). It is used to homogeneize & simplify requesting & computing signals. Any signal can be requested from a CompositeDictionary object by using the appropriate Signal flag. If a signal does not yet exist in the CompositeDictionary object, the object will try to auto-compute it if possible, otherwise, it will return the standard KeyError. The lazy evaluation of composite signals allows for great savings of RAM space and CPU time. Nevertheless, if all possible composite signals are necessary at once, Signal.ALL can be used to compute them all and return the filled CompositeDictionary object.

data = CompositeDictionary({
    Signal.MTd_CM      : [1],
    Signal.MTd_ALT     : [2],
    Signal.MTs_Negative: [3],
    Signal.MTs_Positive: [4],
    Signal.MT0         : [5],
})
print('Initial content of `data` (type: `CompositeDictionary`)')
[print(f'{str(key).replace('Signal.', '').rjust(13)}: {val}') for key, val in data.items()]

data[Signal.ALL]
print()

print('Post calling `data[Signal.ALL]`')
[print(f'{str(key).replace('Signal.', '').rjust(13)}: {val}') for key, val in data.items()]

print(end='')

Initial content of `data` (type: `CompositeDictionary`)
       MTd_CM: [1]
      MTd_ALT: [2]
 MTs_Negative: [3]
 MTs_Positive: [4]
          MT0: [5]

Post calling `data[Signal.ALL]`
       MTd_CM: [1]
      MTd_ALT: [2]
 MTs_Negative: [3]
 MTs_Positive: [4]
          MT0: [5]
          MTs: [3.5]
      ihMT_CM: [5.]
     ihMT_ALT: [3.]
           BP: [2]
MTsR_Positive: [20.]
MTsR_Negative: [40.]
         MTsR: [30.]
      MTdR_CM: [80.]
     MTdR_ALT: [60.]
     ihMTR_CM: [100.]
    ihMTR_ALT: [60.]
          BPR: [40.]

Duration

meta.Duration subclasses the standard python float. It is an optional class meant to remove potential doubt when submitting and manipulating time quantities around and within this package.

print('a =', a := Duration.from_seconds(1.5, 'Example'))
print('b =', b := Duration.from_milli(1, 'Example milli'))
print('c =', c := Duration.from_micro(1, 'Example micro'))

print()

print('repr(a) =', repr(a))
print('repr(b) =', repr(b))
print('repr(c) =', repr(c))

print()

print('a.label =', a.label)
print('b.label =', b.label)
print('c.label =', c.label)

print()

print("Arithmetic")
print('b + c =', b + c)
print('b * c =', b * c)
print('2 * (1 + a) =', 2 * (1 + a))

print()

print("Comparison")
print("Duration(5) == Duration.from_seconds(5, 'label') ?", Duration(5) == Duration.from_seconds(5, 'label'))
print("Duration(3) == Duration.from_milli(3) ?", Duration(3) == Duration.from_milli(3))
print("Duration(.003) == Duration.from_milli(3) ?", Duration(.003) == Duration.from_milli(3))

a = 1.5 s
b = 0.001 s
c = 1e-06 s

repr(a) = Duration(value=1.5, unit=s, label='Example')
repr(b) = Duration(value=0.001, unit=s, label='Example milli')
repr(c) = Duration(value=1e-06, unit=s, label='Example micro')

a.label = Example
b.label = Example milli
c.label = Example micro

Arithmetic
b + c = 0.001001
b * c = 1e-09
2 * (1 + a) = 5.0

Comparison
Duration(5) == Duration.from_seconds(5, 'label') ? True
Duration(3) == Duration.from_milli(3) ? False
Duration(.003) == Duration.from_milli(3) ? True

Frequency

meta.Frequency subclasses the standard python float. It is an optional class meant to remove potential doubt when submitting and manipulating rate quantities around and within this package.

print('a =', a := Frequency.from_hertz(1.5, 'Example'))
print('b =', b := Frequency.from_milli(1, 'Example milli'))
print('c =', c := Frequency.from_micro(1, 'Example micro'))

print()

print('repr(a) =', repr(a))
print('repr(b) =', repr(b))
print('repr(c) =', repr(c))

print()

print('a.label =', a.label)
print('b.label =', b.label)
print('c.label =', c.label)

print()

print("Arithmetic")
print('b + c =', b + c)
print('b * c =', b * c)
print('2 * (1 + a) =', 2 * (1 + a))

print()

print("Comparison")
print("Frequency(5) == Frequency.from_hertz(5, 'label') ?", Frequency(5) == Frequency.from_hertz(5, 'label'))
print("Frequency(3) == Frequency.from_milli(3) ?", Frequency(3) == Frequency.from_milli(3))
print("Frequency(.003) == Frequency.from_milli(3) ?", Frequency(.003) == Frequency.from_milli(3))

a = 1.5 Hz
b = 0.001 Hz
c = 1e-06 Hz

repr(a) = Frequency(value=1.5, unit=Hz, label='Example')
repr(b) = Frequency(value=0.001, unit=Hz, label='Example milli')
repr(c) = Frequency(value=1e-06, unit=Hz, label='Example micro')

a.label = Example
b.label = Example milli
c.label = Example micro

Arithmetic
b + c = 0.001001
b * c = 1e-09
2 * (1 + a) = 5.0

Comparison
Frequency(5) == Frequency.from_hertz(5, 'label') ? True
Frequency(3) == Frequency.from_milli(3) ? False
Frequency(.003) == Frequency.from_milli(3) ? True

AngularFrequency

meta.AngularFrequency subclasses the standard python float. It is an optional class meant to remove potential doubt when submitting and manipulating angular frequency quantities around and within this package.

print('a =', a := AngularFrequency.from_radHertz(1.5, 'Example'))
print('b =', b := AngularFrequency.from_milli(1, 'Example milli'))
print('c =', c := AngularFrequency.from_micro(1, 'Example micro'))

print()

print('repr(a) =', repr(a))
print('repr(b) =', repr(b))
print('repr(c) =', repr(c))

print()

print('a.label =', a.label)
print('b.label =', b.label)
print('c.label =', c.label)

print()

print("Arithmetic")
print('b + c =', b + c)
print('b * c =', b * c)
print('2 * (1 + a) =', 2 * (1 + a))

print()

print("Comparison")
print("AngularFrequency(5) == AngularFrequency.from_radHertz(5, 'label') ?", AngularFrequency(5) == AngularFrequency.from_radHertz(5, 'label'))
print("AngularFrequency(3) == AngularFrequency.from_milli(3) ?", AngularFrequency(3) == AngularFrequency.from_milli(3))
print("AngularFrequency(.003) == AngularFrequency.from_milli(3) ?", AngularFrequency(.003) == AngularFrequency.from_milli(3))

a = 1.5 rad • Hz
b = 0.001 rad • Hz
c = 1e-06 rad • Hz

repr(a) = AngularFrequency(value=1.5, unit=rad • Hz, label='Example')
repr(b) = AngularFrequency(value=0.001, unit=rad • Hz, label='Example milli')
repr(c) = AngularFrequency(value=1e-06, unit=rad • Hz, label='Example micro')

a.label = Example
b.label = Example milli
c.label = Example micro

Arithmetic
b + c = 0.001001
b * c = 1e-09
2 * (1 + a) = 5.0

Comparison
AngularFrequency(5) == AngularFrequency.from_radHertz(5, 'label') ? True
AngularFrequency(3) == AngularFrequency.from_milli(3) ? False
AngularFrequency(.003) == AngularFrequency.from_milli(3) ? True

Angle

meta.Angle subclasses the standard python float. It is an optional class meant to remove potential doubt when submitting and manipulating angular quantities around and within this package.

print('a =', a := Angle.from_radians(np.pi / 4, 'Example'))
print("a' =", a := Angle.from_degrees(45, 'Example'))
print('b =', b := Angle.from_milli(1, 'Example milli'))
print('c =', c := Angle.from_micro(1, 'Example micro'))

print()

print('repr(a) =', repr(a))
print('repr(b) =', repr(b))
print('repr(c) =', repr(c))

print()

print('a.label =', a.label)
print('b.label =', b.label)
print('c.label =', c.label)

print()

print("Value explicitely in radians")
print('a.rad =', a.rad)
print('b.rad =', b.rad)
print('c.rad =', c.rad)

print()

print("Value explicitely in degrees")
print('a.deg =', a.deg)
print('b.deg =', b.deg)
print('c.deg =', c.deg)

print()

print("Arithmetic")
print('b + c =', b + c)
print('b * c =', b * c)
print('2 * (1 + a) =', 2 * (1 + a))

print()

print("Trigonometry")
print('cos(a) =', a.cos)
print('sin(a) =', a.sin)
print('tan(a) =', a.tan)
print('1/cos(a) =', a.sec)
print('1/sin(a) =', a.csc)
print('1/tan(a) =', a.cot)

print()

print("Comparison")
print("Angle(5) == Angle.from_degrees(5, 'label') ?", Angle(5) == Angle.from_degrees(5, 'label'))
print("Angle(3) == Angle.from_milli(3) ?", Angle(3) == Angle.from_milli(3))
print("Angle(.003) == Angle.from_milli(3) ?", Angle(.003) == Angle.from_milli(3))

a = 45.0 °
a' = 45.0 °
b = 0.001 °
c = 1e-06 °

repr(a) = Angle(value=45.0, unit=°, label='Example')
repr(b) = Angle(value=0.001, unit=°, label='Example milli')
repr(c) = Angle(value=1e-06, unit=°, label='Example micro')

a.label = Example
b.label = Example milli
c.label = Example micro

Value explicitely in radians
a.rad = 0.7853981633974483
b.rad = 1.7453292519943296e-05
c.rad = 1.7453292519943295e-08

Value explicitely in degrees
a.deg = 45.0
b.deg = 0.001
c.deg = 1e-06

Arithmetic
b + c = 0.001001
b * c = 1e-09
2 * (1 + a) = 92.0

Trigonometry
cos(a) = 0.707106781186548
sin(a) = 0.707106781186548
tan(a) = 1.0
1/cos(a) = 1.414213562373094
1/sin(a) = 1.414213562373094
1/tan(a) = 1.0

Comparison
Angle(5) == Angle.from_degrees(5, 'label') ? True
Angle(3) == Angle.from_milli(3) ? False
Angle(.003) == Angle.from_milli(3) ? True

Pulse

Pulse objects define the off-resonance saturation pulses used during MT preparation. Currently, a single pulse class is available (Tukey).

Class Tukey, subclass of meta._Event & pulse._Pulse: Tukey-shaped MT pulse

• Input parameters, e.g., tukeyObject = Tukey(**inputs)

  • float duration: [ $pw$ ], pulse duration. unit: s

  • float shape: [ $r$ ], tukey shape factor. unit: ∅

  • float flipAngle: [ $FA_\mathrm{sat}$ ], MT-preparation pulse flip angle. unit: °

  • float offset: [ $\Delta f$ ], offset frequency from the gyromagnetic factor. unit: Hz

• Accessible methods, e.g., tukeyObject.method(*args, **kwargs)

  • copy:

    • inputs:

    • outputs:

      • Tukey newObj: fully independent copy of the current Tukey object

  • value: $\mathbb{R} \to \mathbb{R}$

    • inputs:

      • float t: [ $t$ ], time at which to sample the pulse shape. unit: s

    • outputs:

      • float value: [ $w(t)$ ], normalized amplitude of the pulse shape at time $t$. unit: ∅

• Accessible attributes, e.g., tukeyObject.attribute

  • Each input parameter

  • float gyromagneticFactor: [ $\gamma$ ], gyromagnetic factor. unit: rad•Hz/T

    • default value: 267513000 rad•Hz/T

  • float amplitudeIntegral: [ $AI$ ], the normalized integral of the amplitude of the pulse shape. unit: ∅

    • $AI = \frac{1}{pw} \int_0^{pw} w(t) dt = 1 - r/2$

  • float powerIntegral: [ $PI$ ], the normalized integral of the squared amplitude of the pulse shape. unit: ∅

    • $PI = \frac{1}{pw} \int_0^{pw} [w(t)]^2 dt = 1 - 5r/8$

  • float b1peak: [ $B_1^\mathrm{peak}$ ], peak pulse amplitude. unit: T

    • $B_1^\mathrm{peak} = (\pi/180) \times FA_\mathrm{sat} \times (\gamma \times AI \times pw)^{-1}$

  • float b1: [ $B_1$ ], average pulse amplitude. unit: T

    • $B_1 = AI \times B_1^{peak}$

  • float b1RMS: [ $B_1^\mathrm{rms}$ ], pulse root mean squared amplitude. unit: T

    • $B_1^\mathrm{rms} = \sqrt{PI} \times B_1^{peak}$

  • float omegaRMS: [ $\omega^\mathrm{rms}$ ], pulse $B_1^\mathrm{rms}$ as angular frequency. unit: rad•Hz

    • $\omega^\mathrm{rms} = \gamma B_1^\mathrm{rms}$

pulse = Tukey(
    shape     = .3,
    duration  = Duration.from_milli(1),   # in s
    flipAngle = Angle.from_degrees(299),  # in degree
    offset    = Frequency.from_kilo(7),   # in Hz
)

Sequence

Sequence objects define the mri sequence plan.

Class Sequence, subclass of meta._Event:

• Input parameters, e.g., sequenceObject = Sequence(**inputs)

  • Signal signal: [ $S$ ], logical flag specifying intended signal processing. unit: a.u. or %

  • Pulse pulse: off-resonance saturation pulse to use during MT preparation.

  • int N_pulsePerOffset: [ $N_\mathrm{switch}$ ], number of consecutive pulses with the same offset within a single burst. unit: ∅

  • int N_pulse: [ $N_\mathrm{pulse}$ ], total number of pulses within a single burst. unit: ∅

  • int N_burst: [ $N_\mathrm{burst}$ ], number of bursts within a preparation module. unit: ∅

  • int N_adc: [ $N_\mathrm{ADC}$ ], total number of adc events within a readout module. unit: ∅

  • int N_dummyADC: [ $N^\mathrm{dummy}_\mathrm{ADC}$ ], number of dummy ADC events within a readout module. unit: ∅

  • float dt_interPulse: [ $dt$ ], delay separating 2 pulses within a burst. unit: s

  • float TR_burst: [ $TR_\mathrm{burst}$ ], delay separating 2 bursts within a preparation module. unit: s

  • float dt_lastBurst: [ $dt^\mathrm{last}_\mathrm{burst}$ ], delay separating the beginning of the last burst and the beginning of the readout module. unit: s

  • float es: [ $ES$ ], delay between 2 adc events, "echo spacing". unit: s

  • float tr: [ $TR$ ], delay between 2 preparation modules. unit: s

  • float readout_flipAngle: [ $FA_\mathrm{read}$ ], readout pulse flip angle. unit: °

• Accessible methods, e.g., sequenceObject.method(*args, **kwargs)

  • copy:

    • inputs:

    • outputs:

      • Sequence newObj: fully independent copy of the current Sequence object

• Accessible attributes, e.g., sequenceObject.attribute

  • Each input parameter

  • float duration_preparation: [ $dt_\mathrm{prep}$ ], duration of the preparation module. unit: s

    • $dt_\mathrm{prep} = (N_\mathrm{burst} - 1) \times TR_\mathrm{burst} + N_\mathrm{pulse} \times dt + dt^\mathrm{last}_\mathrm{burst}$

  • float duration_readout: [ $dt_\mathrm{read}$ ], duration of the readout module. unit: s

    • $dt_\mathrm{read} = N_\mathrm{ADC} \times ES$

  • float duration_recovery: [ $dt_\mathrm{recov}$ ], duration of the recovery module. unit: s

    • $dt_\mathrm{recov} = TR - dt_\mathrm{prep} - dt_\mathrm{read}$

sequence = Sequence(
    signal            = Signal.ALL,
    pulse             = pulse,
    N_pulsePerOffset  = 1,
    N_pulse           = 6,
    N_burst           = 10,
    N_adc             = 96,
    N_dummyADC        = 0,
    dt_interPulse     = Duration.from_milli(1.5),   # in s
    TR_burst          = Duration.from_milli(100),   # in s
    dt_lastBurst      = Duration.from_milli(9),     # in s
    es                = Duration.from_milli(6),     # in s
    tr                = Duration.from_seconds(20),  # in s
    readout_flipAngle = Angle.from_degrees(6),      # in degrees
)

System

System objects define the biophysical model used to simulate the mri signal generated by sequences. Current implementation allows for N_poolFree Zeeman free pools and N_poolBound (Zeeman + Dipolar) bound pools. Current implementation fixes the free pool absorption lineshape to a Lorentzian distribution (Cauchy), and the bound pool absorption lineshape to a smoothed SuperLorentzian distribution (see Pampel 2015, on orientation dependence of MT signal). A future update will leave the choice of absorption lineshape free.

Class System, subclass of meta._Event:

• Input parameters, e.g., systemObject = System(**inputs)

  • Pulse pulse: off-resonance saturation pulse to use during MT preparation.

  • float or NDArray[float] poolFree_M0: [ $M_0^\mathrm{A}$ ], free pool initial magnetizations. unit: T

  • float or NDArray[float] poolFree_T1: [ $T_1^\mathrm{A}$ ], free pool Zeeman compartment longitudinal relaxation times. unit: s

  • float or NDArray[float] poolFree_T2: [ $T_2^\mathrm{A}$ ], free pool Zeeman compartment transverse relaxation times. unit: s

  • float or NDArray[float] poolFreeBound_exchangeRate: [ $R_\mathrm{AB}$ ], exchange rate between free and bound pools' Zeeman compartments. unit: Hz

  • float or NDArray[float] poolBound_M0: [ $M_0^\mathrm{B}$ ], bound pool initial magnetizations. unit: T

  • float or NDArray[float] poolBound_T1: [ $T_1^\mathrm{B}$ ], bound pool Zeeman compartment longitudinal relaxation times. unit: s

  • float or NDArray[float] poolBound_T2: [ $T_2^\mathrm{B}$ ], bound pool Zeeman compartment transverse relaxation times. unit: s

  • float or NDArray[float] poolBound_T1D: [ $T_{1\mathrm{D}}^\mathrm{B}$ ], bound pool dipolar compartment dipolar relaxation times. unit: s

  • float or NDArray[float] poolBound_lineshapeAsymmetry: [ $\delta f^\mathrm{B}$ ], bound pool lineshape frequency offsets w.r.t. water resonance. unit: Hz

• Accessible methods, e.g., systemObject.method(*args, **kwargs)

  • copy:

    • inputs:

    • outputs:

      • System newObj: fully independent copy of the current System object

  • Lorentzian: $\mathbb{R}^{(n+1)} \to \mathbb{R}^n = \mathbf{\vec{T}_2} / ( 1 + (2\pi \mathbf{\vec{T}_2} \Delta f)^2)$

    • inputs:

      • NDArray[float] T2: [ $\mathbf{\vec{T}_2}$ ], transverse relaxation time of the pools modeled by the given lineshape. unit: s

      • float offset: [ $\Delta f_\mathrm{eff}$ ], effective frequency offset of the pool modeled by the given lineshape. unit: Hz

        • $\Delta f_\mathrm{eff} = \Delta f_\mathrm{pulse} - \delta f^\mathrm{B}$

    • outputs:

      • NDArray[float] value: [ $\mathbf{\vec{g}}(\mathbf{\vec{T}2}, \Delta f\mathrm{eff})$ ], lineshape value for each element of $\mathbf{\vec{T}_2}$. unit: s / rad^2

  • Gaussian: (see: Lorentzian) $\mathbb{R}^{(n+1)} \to \mathbb{R}^n = \sqrt{2 \pi} \times \mathbf{\vec{T}_2} \exp( -(2\pi \mathbf{\vec{T}_2} \Delta f)^2 / 2)$

  • SuperLorentzian: (see: Lorentzian) $\mathbb{R}^{(n+1)} \to \mathbb{R}^n$

  • PampelSuperLorentzian: (see: Lorentzian) $\mathbb{R}^{(n+1)} \to \mathbb{R}^n$

  • Cylindrical: (see: Lorentzian) $\mathbb{R}^{(n+1)} \to \mathbb{R}^n$

  • DispersedCylindrical: (see: Lorentzian) $\mathbb{R}^{(n+1)} \to \mathbb{R}^n$

• Accessible attributes, e.g., systemObject.attribute

  • Each input parameter

  • int N_poolFree: [ $N_\mathrm{pools}$ ], number of free pools within the system. unit: ∅

  • int N_poolBound: [ $N_\mathrm{pools}$ ], number of bound pools within the system. unit: ∅

  • int N_pools: [ $N_\mathrm{pools}$ ], number of pools within the system. unit: ∅

  • NDArray[float] poolBound_omegaLocalField: [ $\omega_\mathrm{loc}$ ], square root of the 2nd moment of the bound pool absorption lineshape, interpreted as the local dipolar field amplitude as an angular frequency. unit: rad•Hz

    • $\omega_\mathrm{loc}(T_2) = \sqrt{\int_{-\infty}^{\infty} \nu^2 g(T_2, \nu) d\nu}$, in particular:

      • Gaussian: $\omega_\mathrm{loc}(T_2) = (T_2^\mathrm{B})^{-1}$

      • Lorentz: $\omega_\mathrm{loc}(T_2) = \mathrm{undefined}$

      • SuperLorentz: $\omega_\mathrm{loc}(T_2) = (\sqrt{15} T_2^\mathrm{B})^{-1}$

  • NDArray[float] poolFree_Rrf: [ $\mathbf{\hat{R}_\mathrm{RF}^\mathrm{A}}$ ], exchange matrix of the system containing the elements specifying the Zeeman-Zeeman interactions. unit: Hz

    • $\mathbf{\hat{R}\mathrm{RF}^\mathrm{A}} = -\frac{1}{2} (\omega^\mathrm{rms}\mathrm{pulse})^2 g_\mathrm{Lorentz}(T_2^\mathrm{A}, \Delta f) \begin{bmatrix} 1 & \\ & \mathbf{\hat{0}_2} \end{bmatrix}$

  • NDArray[float] poolBound_Rrf_singleSat_Positive: [ $\mathbf{\hat{R}_\mathrm{RF}^{\mathrm{B},+}}$ ], exchange matrix of the system containing the elements specifying the Zeeman-Dipolar interactions for a single-sided positive off-resonance RF saturation. unit: Hz

    • $\mathbf{\hat{R}\mathrm{RF}^{\mathrm{B},+}} = -\frac{1}{2}(\omega\mathrm{pulse}^\mathrm{rms})^2 g_\mathrm{SuperLorentz}(T_2^\mathrm{B}, +|\Delta f| - \delta f^\mathrm{B}) \begin{bmatrix}\mathbf{\hat{0}1} & & \\ & 1 & -2\pi|\Delta f| \\ & -2\pi|\Delta f| / (\omega\mathrm{loc})^2 & (2\pi|\Delta f| / \omega_\mathrm{loc})^2 \end{bmatrix}$

  • NDArray[float] poolBound_Rrf_singleSat_Negative: [ $\mathbf{\hat{R}_\mathrm{RF}^{\mathrm{B},-}}$ ], exchange matrix of the system containing the elements specifying the Zeeman-Dipolar interactions for a single-sided negative off-resonance RF saturation. unit: Hz

    • $\mathbf{\hat{R}\mathrm{RF}^{\mathrm{B},-}} = -\frac{1}{2}(\omega\mathrm{pulse}^\mathrm{rms})^2 g_\mathrm{SuperLorentz}(T_2^\mathrm{B}, -|\Delta f| - \delta f^\mathrm{B}) \begin{bmatrix} \mathbf{\hat{0}1} & & \\ & 1 & 2\pi|\Delta f| \\ & 2\pi|\Delta f| / (\omega\mathrm{loc})^2 & (2\pi|\Delta f| / \omega_\mathrm{loc})^2 \end{bmatrix}$

  • NDArray[float] poolBound_Rrf_dualSat: [ $\mathbf{\hat{R}_\mathrm{RF}^{\mathrm{B},\pm}}$ ], exchange matrix of the system containing the elements specifying the Zeeman-Dipolar interactions for a dual-sided off-resonance RF saturation. unit: Hz

    • $\mathbf{\hat{R}\mathrm{RF}^{\mathrm{B},\pm}} = \frac{1}{2} \left( R\mathrm{RF}^{\mathrm{B},+} + R_\mathrm{RF}^{\mathrm{B},-} \right)$

  • NDArray[float] relaxation: [ $\mathbf{\hat{R}}_\mathrm{relax}$ ], relaxation and exchanges matrix of the system when not under RF saturation. unit: T

    • $\mathbf{\hat{R}}_\mathrm{relax} = blablabla$

  • NDArray[float] magnetization_recovery: [ $\mathbf{\vec{V}}_\mathrm{equil}$ ], vector of relaxation rates toward thermodynamic equilibrium under no RF saturation. unit: T•Hz

    • $\mathbf{\vec{V}}_\mathrm{equil} = \begin{bmatrix} \mathbf{\vec{M}_0^{A}} / \mathbf{\vec{T}_1^{A}} \\ \mathbf{\vec{M}_0^{B}} / \mathbf{\vec{T}_1^{B}} \\ \mathbf{\vec{0}} \end{bmatrix}$

system = System(
    pulse                        = pulse,
    poolFree_M0                  = 1,
    poolFree_T1                  = Duration.from_milli(1000),     # in s
    poolFree_T2                  = Duration.from_milli(100),      # in s
    poolFreeBound_exchangeRate   = Frequency.from_hertz(20),      # in s^-1
    poolBound_M0                 = 0.1,
    poolBound_T1                 = Duration.from_milli(1000),     # in s 
    poolBound_T1D                = Duration.from_milli(10),       # in s
    poolBound_T2                 = Duration.from_micro(10),       # in s
    poolBound_lineshapeAsymmetry = Frequency.from_hertz(-593.83)  # in s^-1
)

# system = System(
#     pulse                        = pulse,
#     poolFree_M0                  = [1, .8],
#     poolFree_T1                  = [2,  1],                 # in s
#     poolFree_T2                  = [100e-2, 100e-2],        # in s
#     poolFreeBound_exchangeRate   = [[20, 20], [10, 10]],    # in s^-1
#     poolBound_M0                 = [0.06, 0.04],
#     poolBound_T1                 = [1000, 1000],            # in s 
#     poolBound_T1D                = [20, 1],                 # in s
#     poolBound_T2                 = [10e-6, 10e-6],          # in s
#     poolBound_lineshapeAsymmetry = [-593.83, 593.83],       # in s^-1
# )

# print(sp.integrate.quad_vec(lambda x: system.Lorentzian(system.poolFree_T2, x), -np.inf, np.inf))
# print('Gaussian Integrated =', sp.integrate.quad_vec(lambda x: system.Gaussian(system.poolFree_T2, x), -np.inf, np.inf))

Lineshapes

print("Lineshapes")
print('Lorentzian Integrated =', np.round(sp.integrate.quad(lambda x: system.Lorentzian(system.poolFree_T2, x)[0], -np.inf, np.inf)[0], 6))
print('Gaussian Integrated =', np.round(sp.integrate.quad(lambda x: system.Gaussian(system.poolFree_T2, x)[0], -np.inf, np.inf)[0], 6))
print('SuperLorentzian Integrated =', np.round(sp.integrate.quad(lambda x: system.SuperLorentzian(system.poolBound_T2, x)[0], -np.inf, np.inf, limit=100)[0], 6))
print('PampelSuperLorentzian Integrated =', np.round(sp.integrate.quad(lambda x: system.PampelSuperLorentzian(system.poolBound_T2, x)[0], -np.inf, np.inf, limit=100)[0], 6))

# Needs to be defined for Cylindrical lineshape but not currently implemented in initializer
# system.axonal_angle = 15
# print('Cylindrical Integrated =', np.round(sp.integrate.quad(lambda x: system.Cylindrical(system.poolBound_T2, x)[0], -np.inf, np.inf, limit=100)[0], 6))

Lineshapes
Lorentzian Integrated = 1.0
Gaussian Integrated = 1.0
SuperLorentzian Integrated = 1.0
PampelSuperLorentzian Integrated = 1.0

Simulator

Simulator objects groups and links the various objects needed to start one or many simulations, ensuring compatibility between RF pulse, system, and sequence. Additionally, it gives access to the various solver methods to compute the requested signal values.

Class Simulator, subclass of meta._Event:

• Input parameters, e.g., simulatorObject = Simulator(**inputs)

  • System system: biophysical model.

  • Sequence sequence: mri sequence plan.

  • slice output_vectorSlice: subsection of the magnetization vector to output for each signal computation.

    • slice(None) == [:]: outputs all elements (compartments) of the magnetization vector.
    • slice(1) == [:1]: outputs up to the 1st element (compartment) included of the magnetization vector, i.e., only the free pool Zeeman compartment.
    • slice(1, None, 1) == array[1::1]: outputs from the 2nd up to the last element (compartment) included of the magnetization vector, i.e., each compartment of the (possibly multiple) bound pools.
    • slice(1, None, 2) == array[1::2]: outputs every other element (compartment) from the 2nd up to the last element included of the magnetization vector, i.e., each Zeeman compartment of the (possibly multiple) bound pools.
    • slice(start, stop, step) == [start:stop:step]: general slice constructor. start is included in the range but stop is not.

  • bool export_readMatrix: [ $\mathbf{\hat{A}_\mathrm{read}}$ ] Whether or not to export the readout evolution matrix, for use in computing the signal at each readout event. Note: the output matrix dimension has 1 additional column/row due the SteadyState solver requiring that additional degree of freedom for normalizing eigenvectors.

    • $\mathbf{\hat{A}\mathrm{read}} = \exp(\mathbf{\hat{a}\mathrm{relax}} \times ES) \exp(\begin{bmatrix}\cos{[(\pi / 180) \times FA_\mathrm{read}]} & \\ & \mathbf{\hat{\mathbb{1}}_{2+1}} \end{bmatrix})$

• Accessible methods, e.g., simulatorObject.method(*args, **kwargs)

  • copy:

    • inputs:

    • outputs:

      • Simulator newObj: fully independent copy of the current Simulator object

  • SteadyState:

    • inputs:

    • outputs:

      • dict[str, NDArray[float]] signals: dictionary containing the different computed signal magnetization vectors. Available keys depend on sequence.signal flag.
        • Keys: {MT0, MTs_Positive, MTs_Negative, MTd_CM, MTd_ALT}

• Accessible attributes, e.g., simulatorObject.attribute

  • Each input parameter

  • Pulse pulse: off-resonance saturation pulse to use during MT preparation.

simulator = Simulator(
    system             = system,
    sequence           = sequence,
    output_vectorSlice = slice(1),
    export_readMatrix  = True,
)

Corrector

Corrector objects define the biophysical system used to simulate the mri signal generated by sequences.

Class Corrector, subclass of meta._Event:

• Input parameters, e.g., correctorObject = Corrector(**inputs)

  • Simulator simulator: simulator object

  • dict[str, NDArray[int64 | float64]] ranges: dictionary of parameters and associated range of values to build the corrector interpolants with

• Accessible methods, e.g., correctorObject.method(*args, **kwargs)

  • static Simple: alternative constructor which defines a 1D correction interpolant parametrized by the nominal MT-preparation RF pulse's flip angle (related to $B_1^+$ map)

    • inputs:

      • Simulator simulator: simulator object

    • outputs:

      • Corrector newObj: fully independent copy of the current Corrector object

  • copy:

    • inputs:

    • outputs:

      • Corrector newObj: fully independent copy of the current Corrector object

  • apply: helper method managing the signal simulation, creation of interpolants and correctors, and correction of signal maps

    • inputs:

      • dict[str, NDArray[int64 | float64]] parameter_maps: value map for each parameter specified in ranges during creation of the Corrector object

      • dict[Signal, NDArray[int64 | float64]] data_maps: value map for each signal desired to be $B_1^+$ corrected

    • outputs:

      • CompositeDictionary[Signal, NDArray[int64 | float64]] corrected_maps: corrected value map for each signal

• Accessible attributes, e.g., correctorObject.attribute

  • Each input parameter

  • dict[str, NDArray[int64 | float64]] mesh: N-dimensional sparse arrays for each interpolation parameter matching the shape of the interpolation range matrix

  • CompositeDictionary[str, NDArray[int64 | float64]] simulated: N-dimensional sparse arrays for requested each simulated and composite signal matching the shape of the interpolation range matrix

  • CompositeDictionary[str, float] nominals: requested simulated and composite signal value for nominal parameters, used for establishing baseline values and dimensionalizing corrected results

  • InterpolantDictionary[str, PchipInterpolator | RegularGridInterpolator] interpolants: interpolator objects for each requested simulated and composite signal

# 1D Corrector using `Corrector.Simple` for a typical B1+ correction
corrector = Corrector.Simple(simulator=simulator)

# # 2D Corrector
# corrector = Corrector(
#     simulator=simulator,
#     ranges={
#         'flipAngle': simulator.pulse.flipAngle * np.linspace(.1, 1.5, 141),
#         'poolFree_T1': simulator.system.poolFree_T1 * np.linspace(.1, 2., 191),
#     }
# )

InterpolantDictionary

corrector.InterpolantDictionary subclasses the standard python float. It is used to homogeneize & simplify requesting & computing interpolators. Any interpolator can be requested from a InterpolantDictionary object by using the appropriate Signal flag. If a signal does not yet exist in the InterpolantDictionary object, the object will try to auto-compute it if possible, otherwise, it will return the standard KeyError. The lazy evaluation of interpolators allows for great savings of RAM space and CPU time. Nevertheless, if all possible interpolators are necessary at once, Signal.ALL can be used to compute them all and return the filled InterpolantDictionary object.

interpolants = corrector.interpolants

print('Initial interpolants dictionary:', interpolants)

interpolants[Signal.ALL]

print('Post calling `corrector.interpolants[Signal.ALL]`')
[print(f'{str(key).replace('Signal.', '').rjust(13)}: {val}') for key, val in interpolants.items()]

print(end='')

Initial interpolants dictionary: {}
Post calling `corrector.interpolants[Signal.ALL]`
          MT0: <scipy.interpolate._cubic.PchipInterpolator object at 0x7fe1cb33e160>
 MTs_Positive: <scipy.interpolate._cubic.PchipInterpolator object at 0x7fe1cb33e2d0>
 MTs_Negative: <scipy.interpolate._cubic.PchipInterpolator object at 0x7fe1cb200cb0>
       MTd_CM: <scipy.interpolate._cubic.PchipInterpolator object at 0x7fe1cb200e10>
      MTd_ALT: <scipy.interpolate._cubic.PchipInterpolator object at 0x7fe1cb163b60>
          MTs: <scipy.interpolate._cubic.PchipInterpolator object at 0x7fe1cb163cb0>
      ihMT_CM: <scipy.interpolate._cubic.PchipInterpolator object at 0x7fe1cb1bbed0>
     ihMT_ALT: <scipy.interpolate._cubic.PchipInterpolator object at 0x7fe1cb2055b0>
           BP: <scipy.interpolate._cubic.PchipInterpolator object at 0x7fe1cb2056e0>
MTsR_Positive: <scipy.interpolate._cubic.PchipInterpolator object at 0x7fe1cb059370>
MTsR_Negative: <scipy.interpolate._cubic.PchipInterpolator object at 0x7fe1cb058b90>
         MTsR: <scipy.interpolate._cubic.PchipInterpolator object at 0x7fe1cb1bf240>
      MTdR_CM: <scipy.interpolate._cubic.PchipInterpolator object at 0x7fe1cb1be9c0>
     MTdR_ALT: <scipy.interpolate._cubic.PchipInterpolator object at 0x7fe1cb094850>
     ihMTR_CM: <scipy.interpolate._cubic.PchipInterpolator object at 0x7fe1cb2286e0>
    ihMTR_ALT: <scipy.interpolate._cubic.PchipInterpolator object at 0x7fe1cb228500>
          BPR: <scipy.interpolate._cubic.PchipInterpolator object at 0x7fe1cb19baf0>

Trajector - WIP

Trajector objects define the biophysical system used to simulate the mri signal generated by sequences.

Class Trajector, subclass of meta._Event:

• Input parameters, e.g., trajectorObject = Trajector(**inputs)

  • int N_readoutDirection: blablabla

  • tuple[int, int] N_inPlaneDirection: blablabla

  • tuple[tuple[int, int, int]] trajectory: blablabla

  • Simulator simulator: blablabla

• Accessible methods, e.g., trajectorObject.method(*args, **kwargs)

  • static CartesianSpiral_CentricOut:

    • inputs:

      • Simulator simulator: blablabla

    • outputs:

      • Trajector trajectorObject: blablabla

  • static CentricOut_Linear: (see CartesianSpiral_CentricOut)

  • static Linear_Linear: (see CartesianSpiral_CentricOut)

  • static readouts:

    • inputs:

      • Simulator simulator: blablabla

      • bool stable: blablabla

        • default value: True

    • outputs:

      • CompositeDictionary[str, NDArray[float64]] readoutVector: blablabla

  • copy:

    • inputs:

    • outputs:

      • Trajector newObj: fully independent copy of the current Trajector object

  • PointSpreadFunction:

    • inputs:

    • outputs:

      • NDArray[float64] value:

  • VectorialPointSpreadFunction: (see PointSpreadFunction)

  • LineSpreadFunction: (see PointSpreadFunction)

  • EdgeSpreadFunction: (see PointSpreadFunction)

  • VectorialOpticalTransferFunction: (see PointSpreadFunction)

  • OpticalTransferFunction: (see PointSpreadFunction)

  • ModulationTransferFunction: (see PointSpreadFunction)

  • PhaseTransferFunction: (see PointSpreadFunction)

• Accessible attributes, e.g., trajectorObject.attribute

  • Each input parameter

try:
    trajector = Trajector.CentricOut_Linear(simulator=simulator)
except NotImplementedError as e:
    print('`Trajector` module not yet implemented.')

`Trajector` module not yet implemented.

Applications

Simulating a single experiment

Using the ihmt.simulator.Simulator class

simulator.SteadyState()

{'MT0': array([1.]),
 'MTs_Positive': array([0.82861692]),
 'MTs_Negative': array([0.82504856]),
 'MTd_ALT': array([0.66539628]),
 'MTd_CM': array([0.65294455]),
 'readout': array([[9.77459365e-01, 1.11744793e-01, 0.00000000e+00, 5.98203595e-03],
        [1.11132643e-02, 8.82273171e-01, 0.00000000e+00, 5.98203595e-04],
        [0.00000000e+00, 0.00000000e+00, 5.48811636e-01, 0.00000000e+00],
        [0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.00000000e+00]])}

Using the ihmt.run.SingleRun function

Hand parametrized

SingleRun(
    # Pulse
    pw=1e-3,        # in s
    r_tukey=.3,
    fa_sat=200,     # in degree
    offset=7000,    # in Hz
    # Sequence
    FLAG_Signal='ALL',
    N_altern=1,
    np=4,
    nb=10,
    turbo=80,
    N_dummyADC=3,
    dt=1.5e-3,      # in s
    btr=100e-3,     # in s
    btrlast=1e-3,   # in s
    es=6e-3,        # in s
    tr=3,          # in s
    fa_rage=5,      # in degree
    # System
    M0a=1,
    M0b=0.1,
    T1f=1,          # in s
    T2f=0.1,        # in s
    T1b=1,          # in s 
    T1D=0.01,       # in s
    T2b=1e-5,       # in s
    R=10,           # in s^-1
    # poolBound_lineshapeAsymmetry=0,  # in s^-1
    poolBound_lineshapeAsymmetry=-593.83,  # in s^-1
    # Simulator
    output_fullVector=True,
    export_read=True,
    # Output
    outputDir='./output/',
    filePrefix='',
    export=False,
)

{'MT0': array([0.97320366, 0.09829085, 0.        , 1.        ]),
 'MTs_Positive': array([8.62708534e-01, 6.30690264e-02, 2.51624735e-07, 1.00000000e+00]),
 'MTs_Negative': array([ 8.55862142e-01,  6.09918784e-02, -2.62836135e-07,  1.00000000e+00]),
 'MTd_ALT': array([ 8.00473583e-01,  4.39187977e-02, -6.41579854e-08,  1.00000000e+00]),
 'MTd_CM': array([0.79543742, 0.04247663, 0.        , 1.        ]),
 'readout': array([[9.84485836e-01, 5.77155166e-02, 0.00000000e+00, 5.98203595e-03],
        [5.74958916e-03, 9.36302447e-01, 0.00000000e+00, 5.98203595e-04],
        [0.00000000e+00, 0.00000000e+00, 5.48811636e-01, 0.00000000e+00],
        [0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.00000000e+00]])}

Using a configuration object

SingleRun(**default['run'])

{'MT0': array([0.97320366, 0.09829085, 0.        , 1.        ]),
 'MTs_Positive': array([8.62708534e-01, 6.30690264e-02, 2.51624735e-07, 1.00000000e+00]),
 'MTs_Negative': array([ 8.55862142e-01,  6.09918784e-02, -2.62836135e-07,  1.00000000e+00]),
 'MTd_ALT': array([ 8.00473583e-01,  4.39187977e-02, -6.41579854e-08,  1.00000000e+00]),
 'MTd_CM': array([0.79543742, 0.04247663, 0.        , 1.        ]),
 'readout': array([[9.84485836e-01, 5.77155166e-02, 0.00000000e+00, 5.98203595e-03],
        [5.74958916e-03, 9.36302447e-01, 0.00000000e+00, 5.98203595e-04],
        [0.00000000e+00, 0.00000000e+00, 5.48811636e-01, 0.00000000e+00],
        [0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.00000000e+00]])}

From the command line

!python ihmt/run.py ./ihmt/configs/default.yaml

2026-06-16 05:17:45,103 - root - INFO - MT0: [0.9732036610707328, 0.09829085279876039, 0.0, 1.0]
2026-06-16 05:17:45,105 - root - INFO - MTs_Positive: [0.8627085342188335, 0.06306902637436296, 2.516247349066977e-07, 1.0]
2026-06-16 05:17:45,109 - root - INFO - MTs_Negative: [0.8558621416185663, 0.06099187840479833, -2.628361353597496e-07, 1.0]
2026-06-16 05:17:45,109 - root - INFO - MTd_ALT: [0.8004735826952205, 0.04391879772742473, -6.415798544913084e-08, 1.0]
2026-06-16 05:17:45,110 - root - INFO - MTd_CM: [0.7954374236676484, 0.04247663490130794, 0.0, 1.0]
2026-06-16 05:17:45,111 - root - INFO - readout: [[0.984485836436591, 0.05771551658429958, 0.0, 0.005982035946064735], [0.005749589161890545, 0.9363024474696356, 0.0, 0.0005982035946064736], [0.0, 0.0, 0.5488116360940265, 0.0], [0.0, 0.0, 0.0, 1.0]]

Example: Computing derivative maps: MT(s/d)R, ihMT, ihMTR, BP, BPR

Manual Computation

data = SingleRun(**default['run'])

with np.errstate(divide='ignore', invalid='ignore'):
    data['MTs']           =.5 * (data['MTs_Positive'] + data['MTs_Negative'])
    data['ihMT_CM']       = 2 * (data['MTs'] - data['MTd_CM'])
    data['ihMT_ALT']      = 2 * (data['MTs'] - data['MTd_ALT'])
    data['BP']            = 2 * (data['MTd_ALT'] - data['MTd_CM'])
    data['MTsR_Positive'] = 100 * (1 - data['MTs_Positive'] / data['MT0'])
    data['MTsR_Negative'] = 100 * (1 - data['MTs_Negative'] / data['MT0'])
    data['MTsR']          = 100 * (1 - data['MTs'] / data['MT0'])
    data['MTdR_CM']       = 100 * (1 - data['MTd_CM'] / data['MT0'])
    data['MTdR_ALT']      = 100 * (1 - data['MTd_ALT'] / data['MT0'])
    data['ihMTR_CM']      = 100 * data['ihMT_CM'] / data['MT0']
    data['ihMTR_ALT']     = 100 * data['ihMT_ALT'] / data['MT0']
    data['BPR']           = 100 * data['BP'] / data['MT0']

print(CompositeDictionary(data))

Shape: (4,)
          MT0 = [0.9732036610707328, 0.09829085279876039, 0.0, 1.0]
 MTs_Positive = [0.8627085342188335, 0.06306902637436296, 2.516247349066977e-07, 1.0]
 MTs_Negative = [0.8558621416185663, 0.06099187840479833, -2.628361353597496e-07, 1.0]
      MTd_ALT = [0.8004735826952205, 0.04391879772742473, -6.415798544913084e-08, 1.0]
       MTd_CM = [0.7954374236676484, 0.04247663490130794, 0.0, 1.0]
          MTs = [0.8592853379187, 0.062030452389580645, -5.605700226525966e-09, 1.0]
      ihMT_CM = [0.12769582850210326, 0.039107634976545416, -1.1211400453051932e-08, 0.0]
     ihMT_ALT = [0.11762351044695896, 0.036223309324311836, 1.1710457044520975e-07, 0.0]
           BP = [0.010072318055144303, 0.0028843256522335797, -1.2831597089826168e-07, 0.0]
MTsR_Positive = [11.353751662866829, 35.834287140137256, -inf, 0.0]
MTsR_Negative = [12.057241885328052, 37.9475539502415, inf, 0.0]
         MTsR = [11.705496774097435, 36.890920545189374, inf, 0.0]
      MTdR_CM = [18.266088025964, 56.7847529125888, nan, 0.0]
     MTdR_ALT = [17.748605485667014, 55.31751279303315, inf, 0.0]
     ihMTR_CM = [13.12118250373313, 39.78766473479883, -inf, 0.0]
    ihMTR_ALT = [12.086217423139148, 36.85318449568755, inf, 0.0]
          BPR = [1.034965080593983, 2.9344802391112794, -inf, 0.0]

Using ihmt.meta.CompositeSignal

data = CompositeDictionary(SingleRun(**default['run']))[Signal.ALL]

print(data)

Shape: (4,)
          MT0 = [0.9732036610707328, 0.09829085279876039, 0.0, 1.0]
 MTs_Positive = [0.8627085342188335, 0.06306902637436296, 2.516247349066977e-07, 1.0]
 MTs_Negative = [0.8558621416185663, 0.06099187840479833, -2.628361353597496e-07, 1.0]
      MTd_ALT = [0.8004735826952205, 0.04391879772742473, -6.415798544913084e-08, 1.0]
       MTd_CM = [0.7954374236676484, 0.04247663490130794, 0.0, 1.0]
          MTs = [0.8592853379187, 0.062030452389580645, -5.605700226525966e-09, 1.0]
      ihMT_CM = [0.12769582850210326, 0.039107634976545416, -1.1211400453051932e-08, 0.0]
     ihMT_ALT = [0.11762351044695896, 0.036223309324311836, 1.1710457044520975e-07, 0.0]
           BP = [0.010072318055144303, 0.0028843256522335797, -1.2831597089826168e-07, 0.0]
MTsR_Positive = [11.353751662866827, 35.83428714013725, -inf, 0.0]
MTsR_Negative = [12.057241885328054, 37.9475539502415, inf, 0.0]
         MTsR = [11.70549677409744, 36.890920545189374, inf, 0.0]
      MTdR_CM = [18.26608802596401, 56.784752912588786, nan, 0.0]
     MTdR_ALT = [17.748605485667014, 55.317512793033146, inf, 0.0]
     ihMTR_CM = [13.12118250373313, 39.78766473479883, -inf, 0.0]
    ihMTR_ALT = [12.086217423139148, 36.85318449568755, inf, 0.0]
          BPR = [1.034965080593983, 2.93448023911128, -inf, 0.0]

Example: Computing steady-state signals at every readout

Manual computation

#####
# 2 Ways to compute every readout:
# - Iterative propagation
# - Recomputing the matrix power of the propagator
#####

##### Necessary setup
# Keeping the previous flags state of simulator in memory
tmp = simulator.export_readMatrix, simulator.output_vectorSlice
# Making sure the correct flags are turned on
simulator.export_readMatrix, simulator.output_vectorSlice = True, slice(None)
# Simulating the data
data = simulator.SteadyState()
# Restoring simulator flags to their original value
simulator.export_readMatrix, simulator.output_vectorSlice = tmp

##### Recomputing the matrix power of the propagator
readouts = {key: [] for key in data if key != 'readout'}
for i in range(simulator.sequence.N_adc):
    propagator = np.linalg.matrix_power(data['readout'], i - simulator.sequence.N_dummyADC)
    [readouts[key].append(propagator @ data[key]) for key in data.keys() if key != 'readout']

print(CompositeDictionary(readouts).T[Signal.ALL])

Shape: (4, 96)
          MT0 = [[0.9999999989204692, 0.9946158794866504, 0.989346281068416, 0.9841827413287039, 0.9791178232416089, 0.9741449832216156, 0.969258456302484, 0.9644531561604541, 0.9597245880616965, 0.955068773062306, 0.9504821820053664, 0.9459616780478972, 0.9415044666143932, 0.9371080518163928, 0.9327701985017501, 0.9284888992054809, 0.9242623453682204, 0.9200889022703547, 0.9159670872012595, 0.9118955504452637, 0.9078730587200576, 0.9038984807503924, 0.8999707747009421, 0.896088977227914, 0.8922521939400889, 0.8884595910870587, 0.8847103883159815, 0.8810038523587218, 0.8773392915290884, 0.8737160509254626, 0.8701335082476308, 0.8665910701484536, 0.8630881690512431, 0.8596242603726929, 0.8561988200989482, 0.8528113426692194, 0.8494613391272134, 0.8461483355058076, 0.8428718714148599, 0.8396314988059408, 0.836426780891166, 0.8332572911962584, 0.8301226127305351, 0.8270223372587608, 0.8239560646617439, 0.820923402374263, 0.8179239648903722, 0.8149573733274361, 0.8120232550413437, 0.8091212432863524, 0.8062509769138304, 0.803412100104933, 0.8006042621328707, 0.7978271171510025, 0.7950803240034596, 0.7923635460554461, 0.7896764510407182, 0.7870187109240774, 0.7843900017769799, 0.7817900036646241, 0.7792184005430758, 0.7766748801651879, 0.7741591339942199, 0.7716708571242168, 0.7692097482063147, 0.7667755093802624, 0.7643678462105196, 0.7619864676263994, 0.7596310858657684, 0.7573014164218949, 0.7549971779930802, 0.7527180924347614, 0.7504638847138045, 0.7482342828647555, 0.746029017947831, 0.7438478240084746, 0.7416904380383107, 0.7395565999373642, 0.7374460524774182, 0.7353585412664054, 0.7332938147137403, 0.731251623996511, 0.7292317230264562, 0.7272338684176685, 0.7252578194549657, 0.7233033380628859, 0.7213701887752578, 0.7194581387053153, 0.7175669575163177, 0.7156964173926532, 0.7138462930113911, 0.7120163615142684, 0.7102064024800838, 0.7084161978974883, 0.7066455321381468, 0.7048941919302667], [0.09999999989204687, 0.09993878492594421, 0.09982494146121187, 0.09966593798642406, 0.09946826970448946, 0.09923758450904013, 0.09897879266450507, 0.09869616229785896, 0.09839340253736184, 0.0980737358962003, 0.09773996129224682, 0.0973945089151946, 0.09703948799564527, 0.09667672839431389, 0.09630781681074793, 0.09593412830755195, 0.09555685375608153, 0.0951770237311855, 0.09479552931433263, 0.09441314020504088, 0.09403052048879774, 0.09364824236461972, 0.09326679809618676, 0.0928866104163454, 0.09250804158505041, 0.09213140127493481, 0.09175695343616584, 0.09138492227262715, 0.09101549744438753, 0.09064883859654577, 0.09028507930159463, 0.08992433049117413, 0.08956668344327043, 0.08921221238237213, 0.08886097674265583, 0.08851302313779658, 0.08816838707535855, 0.08782709444881247, 0.08748916283595091, 0.08715460262875137, 0.0868234180164961, 0.08649560784113729, 0.08617116634143895, 0.08585008380028958, 0.08553234710771623, 0.08521794025051119, 0.08490684473796982, 0.08459903997201003, 0.08429450356887373, 0.08399321163867923, 0.08369513902828243, 0.08340025953219889, 0.08310854607572396, 0.08281997087385248, 0.08253450556913483, 0.08225212135119855, 0.08197278906031358, 0.08169647927706973, 0.08142316239996891, 0.08115280871249991, 0.08088538844106222, 0.08062087180492704, 0.08035922905927131, 0.08010043053218525, 0.07984444665643853, 0.07959124799668747, 0.07934080527271835, 0.07909308937924417, 0.0788480714027056, 0.0786057226354683, 0.07836601458775821, 0.07812891899763184, 0.07789440783924068, 0.07766245332961452, 0.07743302793416024, 0.07720610437104605, 0.07698165561462052, 0.07675965489799477, 0.07654007571490115, 0.07632289182092564, 0.07610807723419963, 0.07589560623562477, 0.07568545336869585, 0.07547759343897738, 0.07527200151328296, 0.07506865291859968, 0.07486752324079467, 0.07466858832313573, 0.07447182426465393, 0.07427720741837253, 0.07408471438942327, 0.07389432203306823, 0.07370600745264336, 0.07351974799743713, 0.07333552126051676, 0.07315330507651185], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]]
 MTs_Positive = [[0.8286169162485969, 0.8219848769024879, 0.8158843577162456, 0.8102501667388816, 0.8050255059352268, 0.800160885829866, 0.7956131805407836, 0.7913448050429064, 0.7873229988507572, 0.7835192023546118, 0.7799085138251715, 0.7764692166520696, 0.7731823677312796, 0.7700314390916672, 0.7670020058740709, 0.7640814746671127, 0.7612588469795053, 0.7585245133038845, 0.7558700738150946, 0.7532881822577214, 0.7507724100233083, 0.7483171278057016, 0.7459174025607753, 0.7435689077909103, 0.7412678454306655, 0.7390108778330362, 0.7367950685497888, 0.7346178307683784, 0.7324768824150788, 0.7303702070620737, 0.7282960198877817, 0.7262527380368071, 0.7242389548104429, 0.7222534171922783, 0.7202950062775302, 0.7183627202305407, 0.7164556594434435, 0.7145730136113104, 0.712714050475911, 0.7108781060222782, 0.7090645759401923, 0.7072729081869973, 0.7055025965093177, 0.7037531747996819, 0.7020242121800788, 0.7003153087184572, 0.6986260916963212, 0.6969562123561748, 0.6953053430667708, 0.6936731748521598, 0.6920594152375021, 0.6904637863707088, 0.6888860233842579, 0.6873258729661502, 0.6857830921129825, 0.6842574470416093, 0.68274871223891, 0.6812566696318266, 0.6797811078621407, 0.6783218216524735, 0.6768786112517339, 0.6754512819497702, 0.6740396436522942, 0.6726435105083173, 0.6712627005833244, 0.6698970355723045, 0.6685463405475006, 0.6672104437364206, 0.6658891763262165, 0.6645823722910501, 0.663289868239493, 0.6620115032793987, 0.6607471188980079, 0.6594965588553447, 0.6582596690892047, 0.657036297630262, 0.6558262945260097, 0.6546295117724152, 0.6534458032523129, 0.6522750246796887, 0.6511170335491148, 0.6499716890896946, 0.6488388522229498, 0.6477183855241686, 0.6466101531867856, 0.6455140209894232, 0.6444298562652707, 0.6433575278735221, 0.6422969061726235, 0.6412478629951217, 0.6402102716239204, 0.6391840067697889, 0.6381689445499752, 0.6371649624678069, 0.6361719393931631, 0.6351897555437329], [0.05426182065535948, 0.057680590992801636, 0.06062317673317027, 0.06315154450311074, 0.06531964129942872, 0.0671744318984859, 0.06875680207282839, 0.07010234497332464, 0.07124204578974026, 0.07220287784777044, 0.07300832159851776, 0.07367881647453407, 0.07423215429635985, 0.07468382179019964, 0.07504729879937896, 0.075334317920741, 0.07555509055579766, 0.07571850372100077, 0.07583229139954095, 0.07590318372781527, 0.07593703688372613, 0.07593894617309654, 0.07591334448758519, 0.07586408802634927, 0.07579453092893577, 0.07570759025377374, 0.07560580255110004, 0.07549137311761028, 0.0753662188794816, 0.07523200572796238, 0.07509018102511168, 0.07494200190444888, 0.07478855991046025, 0.0746308024505464, 0.07446955147173634, 0.07430551972115718, 0.07413932490281244, 0.07397150200279204, 0.07380251401983717, 0.0736327613075361, 0.07346258970774487, 0.07329229763159525, 0.07312214222422678, 0.07295234473176962, 0.07278309517377299, 0.07261455641092596, 0.07244686768629449, 0.07228014770818075, 0.07211449733390074, 0.07195000190610576, 0.07178673328659602, 0.07162475162675967, 0.07146410690870897, 0.07130484028677778, 0.07114698525520757, 0.07099056866450788, 0.07083561160606908, 0.07068213018207202, 0.07053013617553541, 0.07037963763342073, 0.07023063937404446, 0.07008314342859125, 0.06993714942525546, 0.06979265492343487, 0.06964965570444044, 0.06950814602434971, 0.06936811883390323, 0.06922956596971011, 0.06909247832047646, 0.0689568459714904, 0.06882265833017853, 0.06868990423518542, 0.06855857205110968, 0.06842864975075465, 0.06830012498651117, 0.06817298515228103, 0.06804721743716667, 0.06792280887199502, 0.0677997463696047, 0.06767801675970564, 0.06755760681901568, 0.06743850329728722, 0.06732069293975809, 0.0672041625064914, 0.06708889878900887, 0.06697488862457018, 0.06686211890840513, 0.06675057660416514, 0.06664024875282719, 0.06653112248025214, 0.06642318500357358, 0.06631642363657086, 0.06621082579415954, 0.06610637899611545, 0.0660030708701338, 0.06590088915431085], [1.0491997709711667e-06, 5.758130428961639e-07, 3.160128981561236e-07, 1.7343155566387717e-07, 9.518125581422467e-08, 5.223658072888872e-08, 2.8668043333779113e-08, 1.5733355765625765e-08, 8.634648718982461e-09, 4.738795690561955e-09, 2.600706216052629e-09, 1.427297833431748e-09, 7.833176591591371e-10, 4.29893846104469e-10, 2.359307450273473e-10, 1.2948153818334106e-10, 7.106097481437059e-11, 3.8999089850311134e-11, 2.14031543069272e-11, 1.1746300132757625e-11, 6.446506193910193e-12, 3.5379176113701292e-12, 1.941650352661911e-12, 1.0656003067669269e-12, 5.848138477790537e-13, 3.2095264461006546e-13, 1.7614254599715465e-13, 9.666907885446578e-14, 5.3053115325821824e-14, 2.911616702184935e-14, 1.5979291260048083e-14, 8.769620980049965e-15, 4.812870037985722e-15, 2.6413590798548636e-15, 1.4496085981269602e-15, 7.955620664340253e-16, 4.36613719294002e-16, 2.396186896268393e-16, 1.315055250928124e-16, 7.217176238159044e-17, 3.960870299242996e-17, 2.1737717092837854e-17, 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MTsR_Negative = [[17.495143657444814, 17.71659759254746, 17.895546734256982, 18.037260478822986, 18.1463663037226, 18.226926401505935, 18.282505541753494, 18.316231076695587, 18.330845932101255, 18.328755351322783, 18.312068088839865, 18.282632681573773, 18.242069362418604, 18.19179812128668, 18.133063364643803, 18.06695557498965, 17.994430326867572, 17.916324975531992, 17.833373298077348, 17.74621833433332, 17.65542364583949, 17.561483185414346, 17.464829946929584, 17.365843544597922, 17.264856853121813, 17.162161824176493, 17.05801458069115, 16.952639878041452, 16.846235010384476, 16.73897323079109, 16.631006745405884, 16.522469334459373, 16.41347864644986, 16.30413820609921, 16.19453917166821, 16.08476187281697, 15.974877156332212, 15.864947563656543, 15.755028361185197, 15.645168441691368, 15.535411112959537, 15.425794787706948, 15.316353587120346, 15.207117868800864, 15.098114688564948, 14.989368204371658, 14.880900029615887, 14.772729542123017, 14.66487415439029, 14.557349549928432, 14.450169889949649, 14.34334799411836, 14.23689549861686, 14.130822994371044, 14.025140147924958, 13.919855807143122, 13.81497809364555, 13.710514483642399, 13.606471878626863, 13.502856667201215, 13.399674779152747, 13.2969317327547, 13.19463267614617, 13.092782423537656, 12.991385486894885, 12.890446103672332, 12.789968261095169, 12.689955717427026, 12.590412020604575, 12.491340524573289, 12.392744403616078, 12.294626664929993, 12.196990159673547, 12.099837592680501, 12.003171531009897, 11.906994411481193, 11.811308547325055, 11.716116134063213, 11.621419254716997, 11.52721988443075, 11.433519894586993, 11.340321056478146, 11.247625044593974, 11.15543343957421, 11.063747730870958, 10.972569319159092, 10.881899518528243, 10.791739558485347, 10.702090585793854, 10.612953666171094, 10.5243297858636, 10.436219853117066, 10.348624699555515, 10.261545081482637, 10.174981681116279, 10.088935107765423], [46.57195075283551, 43.05982328903787, 39.99557815137787, 37.31750774561451, 34.973033031612346, 32.917206702897616, 31.111495165694436, 29.522780108277885, 28.122534566745998, 26.88613881210432, 25.79230915095762, 24.822618577702073, 23.96109265499807, 23.193867398958915, 22.508898570660975, 21.89571381876155, 21.3452007203707, 20.849425033234837, 20.401474479528346, 19.99532418847562, 19.625720575770643, 19.288080965891993, 18.978406694653316, 18.69320778350729, 18.429437569618088, 18.184435918539947, 17.955879848914577, 17.741740568376926, 17.54024606275837, 17.349848501428355, 17.169195824025863, 16.997106960977618, 16.832550214581175, 16.674624391094582, 16.52254232889949, 16.375616514782365, 16.233246520858643, 16.094908029612483, 15.96014324474119, 15.828552511661059, 15.699786994216538, 15.573542273828494, 15.449552754426264, 15.327586771388752, 15.207442315668487, 15.088943295552326, 14.971936268337984, 14.856287582776687, 14.741880880604114, 14.628614912005276, 14.51640162555124, 14.40516449811679, 14.29483707463018, 14.185361691297814, 14.076688359262192, 13.96877378854586, 13.861580534666842, 13.755076252522244, 13.64923304407202, 13.544026888045224, 13.43943714136995, 13.335446103321004, 13.232038634510033, 13.129201823830414, 13.026924697335389, 12.925197963782495, 12.824013792238844, 12.723365617720418, 12.623247971343815, 12.523656331910828, 12.424586996233629, 12.326036965845844, 12.2280038480407, 12.13048576943639, 12.033481300494756, 11.93698938961657, 11.841009305610868, 11.74554058748599, 11.65058300064213, 11.556136498662283, 11.462201189997316, 11.368777308931229, 11.275865190289238, 11.183465247418198, 11.091577953029685, 11.000203822545473, 10.909343399632405, 10.81899724365185, 10.729165918783792, 10.639849984615552, 10.55104998801248, 10.462766456109364, 10.374999890283078, 10.2877507609833, 10.201019503314754, 10.114806513276648], [inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]
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          BPR = [[2.4903450511714937, 2.503938435501344, 2.5138187962944425, 2.5204478701338786, 2.5242311469527694, 2.5255245893942253, 2.524640582393138, 2.5218531934180883, 2.5174028173000087, 2.511500273082253, 2.504330414035426, 2.4960553059901693, 2.4868170235353335, 2.476740108425053, 2.4659337297704793, 2.4544935812383497, 2.4425035465398333, 2.4300371609395004, 2.4171588933263286, 2.403925270533804, 2.3903858630543406, 2.3765841490267445, 2.3625582713671522, 2.3483417011318983, 2.333963818625865, 2.3194504223762897, 2.3048241748644736, 2.2901049928241313, 2.2753103889609783, 2.260455771107956, 2.245554704093745, 2.2306191389501007, 2.215659613516291, 2.200685427995785, 2.1857047985816007, 2.1707249918814875, 2.155752442534448, 2.1407928561143916, 2.12585129915626, 2.1109322779114446, 2.0960398072401802, 2.081177470872978, 2.066348474119747, 2.0515556899708915, 2.036801699417458, 2.0220888267131514, 2.0074191702119397, 1.9927946293353413, 1.9782169281542887, 1.9636876360099997, 1.949208185545211, 1.9347798884708127, 1.9204039493515788, 1.9060814776610802, 1.8918134983214172, 1.8776009609199702, 1.8634447477686953, 1.8493456809515043, 1.8353045284880798, 1.8213220097243752, 1.8073988000480357, 1.7935355350139763, 1.7797328139543909, 1.7659912031379836, 1.7523112385366826, 1.738693428248423, 1.7251382546202036, 1.71164617610917, 1.6982176289156221, 1.6848530284164112, 1.671552770424533, 1.658317232297107, 1.645146773911253, 1.6320417385245438, 1.6190024535351593, 1.6060292311551159, 1.5931223690065635, 1.5802821506529525, 1.567508846071761, 1.5548027120780512, 1.5421639927039996, 1.5295929195413098, 1.517089712050487, 1.5046545778425116, 1.4922877129356515, 1.4799893019911878, 1.4677595185310783, 1.4555985251400823, 1.4435064736539491, 1.4314835053366073, 1.419529751047072, 1.407645331397751, 1.3958303569062416, 1.3840849281400232, 1.3724091358567596, 1.3608030611399373], [5.033419210649191, 4.720499008420537, 4.446775684470231, 4.206847369137276, 3.9961116535170507, 3.8106344724095416, 3.64704341076679, 3.5024402468983644, 3.374328782151597, 3.260554919443859, 3.1592566334364824, 3.0688219872091738, 2.9878537391416784, 2.9151393815243045, 2.849625682390977, 2.7903969810609714, 2.7366566282511275, 2.68771107252535, 2.6429561830909827, 2.601865469648686, 2.563979917015344, 2.5288991985127267, 2.496274069897155, 2.465799776638796, 2.437210332986242, 2.4102735525282295, 2.3847867277139776, 2.360572870667779, 2.3374774401561216, 2.31536549014291, 2.2941191843430393, 2.273635628817752, 2.253824981173082, 2.234608800498944, 2.2159186069721, 2.197694624161116, 2.1798846806178376, 2.162443250399647, 2.1453306148148648, 2.1285121299735987, 2.11195758671453, 2.0956406512012853, 2.0795383759811017, 2.0636307726006047, 2.0479004380077046, 2.0323322279554077, 2.0169129714839964, 2.001631221308086, 1.9864770355882928, 1.9714417871396133, 1.9565179966247885, 1.9416991867178157, 1.9269797546009015, 1.9123548604916893, 1.8978203301853358, 1.8833725698518677, 1.8690084915479082, 1.8547254480980513, 1.8405211761679001, 1.826393746500234, 1.8123415204146216, 1.7983631117832424, 1.7844573537953663, 1.770623269908852, 1.7568600484626729, 1.743167020490254, 1.7295436403320996, 1.7159894686953765, 1.7025041578535824, 1.6890874387168344, 1.6757391095385583, 1.6624590260520438, 1.6492470928581822, 1.6361032559064073, 1.6230274959320476, 1.610019822729938, 1.5970802701588078, 1.5842088917853054, 1.571405757087134, 1.558670948144735, 1.5460045567610585, 1.533406681954729, 1.520877427780927, 1.5084169014377085, 1.4960252116229884, 1.4837024671103038, 1.4714487755160253, 1.459264242234398, 1.447148969518912, 1.4351030556922961, 1.4231265944685363, 1.4112196743736467, 1.3993823782521397, 1.3876147828491718, 1.3759169584584885, 1.364288968628407], [-inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]

Using ihmt.trajector.Trajector

##### Recomputing the matrix power of the propagator
readouts = Trajector.readouts(simulator=simulator, stable=True)

print(readouts[Signal.ALL])

Shape: (4, 96)
          MT0 = [[0.9999999989204692, 0.9946158794866504, 0.989346281068416, 0.9841827413287039, 0.9791178232416089, 0.9741449832216156, 0.969258456302484, 0.9644531561604541, 0.9597245880616965, 0.955068773062306, 0.9504821820053664, 0.9459616780478972, 0.9415044666143932, 0.9371080518163928, 0.9327701985017501, 0.9284888992054809, 0.9242623453682204, 0.9200889022703547, 0.9159670872012595, 0.9118955504452637, 0.9078730587200576, 0.9038984807503924, 0.8999707747009421, 0.896088977227914, 0.8922521939400889, 0.8884595910870587, 0.8847103883159815, 0.8810038523587218, 0.8773392915290884, 0.8737160509254626, 0.8701335082476308, 0.8665910701484536, 0.8630881690512431, 0.8596242603726929, 0.8561988200989482, 0.8528113426692194, 0.8494613391272134, 0.8461483355058076, 0.8428718714148599, 0.8396314988059408, 0.836426780891166, 0.8332572911962584, 0.8301226127305351, 0.8270223372587608, 0.8239560646617439, 0.820923402374263, 0.8179239648903722, 0.8149573733274361, 0.8120232550413437, 0.8091212432863524, 0.8062509769138304, 0.803412100104933, 0.8006042621328707, 0.7978271171510025, 0.7950803240034596, 0.7923635460554461, 0.7896764510407182, 0.7870187109240774, 0.7843900017769799, 0.7817900036646241, 0.7792184005430758, 0.7766748801651879, 0.7741591339942199, 0.7716708571242168, 0.7692097482063147, 0.7667755093802624, 0.7643678462105196, 0.7619864676263994, 0.7596310858657684, 0.7573014164218949, 0.7549971779930802, 0.7527180924347614, 0.7504638847138045, 0.7482342828647555, 0.746029017947831, 0.7438478240084746, 0.7416904380383107, 0.7395565999373642, 0.7374460524774182, 0.7353585412664054, 0.7332938147137403, 0.731251623996511, 0.7292317230264562, 0.7272338684176685, 0.7252578194549657, 0.7233033380628859, 0.7213701887752578, 0.7194581387053153, 0.7175669575163177, 0.7156964173926532, 0.7138462930113911, 0.7120163615142684, 0.7102064024800838, 0.7084161978974883, 0.7066455321381468, 0.7048941919302667], [0.09999999989204687, 0.09993878492594421, 0.09982494146121187, 0.09966593798642406, 0.09946826970448946, 0.09923758450904013, 0.09897879266450507, 0.09869616229785896, 0.09839340253736184, 0.0980737358962003, 0.09773996129224682, 0.0973945089151946, 0.09703948799564527, 0.09667672839431389, 0.09630781681074793, 0.09593412830755195, 0.09555685375608153, 0.0951770237311855, 0.09479552931433263, 0.09441314020504088, 0.09403052048879774, 0.09364824236461972, 0.09326679809618676, 0.0928866104163454, 0.09250804158505041, 0.09213140127493481, 0.09175695343616584, 0.09138492227262715, 0.09101549744438753, 0.09064883859654577, 0.09028507930159463, 0.08992433049117413, 0.08956668344327043, 0.08921221238237213, 0.08886097674265583, 0.08851302313779658, 0.08816838707535855, 0.08782709444881247, 0.08748916283595091, 0.08715460262875137, 0.0868234180164961, 0.08649560784113729, 0.08617116634143895, 0.08585008380028958, 0.08553234710771623, 0.08521794025051119, 0.08490684473796982, 0.08459903997201003, 0.08429450356887373, 0.08399321163867923, 0.08369513902828243, 0.08340025953219889, 0.08310854607572396, 0.08281997087385248, 0.08253450556913483, 0.08225212135119855, 0.08197278906031358, 0.08169647927706973, 0.08142316239996891, 0.08115280871249991, 0.08088538844106222, 0.08062087180492704, 0.08035922905927131, 0.08010043053218525, 0.07984444665643853, 0.07959124799668747, 0.07934080527271835, 0.07909308937924417, 0.0788480714027056, 0.0786057226354683, 0.07836601458775821, 0.07812891899763184, 0.07789440783924068, 0.07766245332961452, 0.07743302793416024, 0.07720610437104605, 0.07698165561462052, 0.07675965489799477, 0.07654007571490115, 0.07632289182092564, 0.07610807723419963, 0.07589560623562477, 0.07568545336869585, 0.07547759343897738, 0.07527200151328296, 0.07506865291859968, 0.07486752324079467, 0.07466858832313573, 0.07447182426465393, 0.07427720741837253, 0.07408471438942327, 0.07389432203306823, 0.07370600745264336, 0.07351974799743713, 0.07333552126051676, 0.07315330507651185], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]]
 MTs_Positive = [[0.8286169162485969, 0.8219848769024879, 0.8158843577162456, 0.8102501667388816, 0.8050255059352268, 0.800160885829866, 0.7956131805407836, 0.7913448050429064, 0.7873229988507572, 0.7835192023546118, 0.7799085138251715, 0.7764692166520696, 0.7731823677312796, 0.7700314390916672, 0.7670020058740709, 0.7640814746671127, 0.7612588469795053, 0.7585245133038845, 0.7558700738150946, 0.7532881822577214, 0.7507724100233083, 0.7483171278057016, 0.7459174025607753, 0.7435689077909103, 0.7412678454306655, 0.7390108778330362, 0.7367950685497888, 0.7346178307683784, 0.7324768824150788, 0.7303702070620737, 0.7282960198877817, 0.7262527380368071, 0.7242389548104429, 0.7222534171922783, 0.7202950062775302, 0.7183627202305407, 0.7164556594434435, 0.7145730136113104, 0.712714050475911, 0.7108781060222782, 0.7090645759401923, 0.7072729081869973, 0.7055025965093177, 0.7037531747996819, 0.7020242121800788, 0.7003153087184572, 0.6986260916963212, 0.6969562123561748, 0.6953053430667708, 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 MTs_Negative = [[0.8250485625348865, 0.8184037865264239, 0.8122973549761843, 0.8066631366876248, 0.8014435164911513, 0.7965882940858494, 0.792053725315068, 0.7878016874516216, 0.7837989524516134, 0.7800165542108358, 0.7764292376642529, 0.7730149791419487, 0.7697545687643264, 0.766631246851632, 0.7636303873609139, 0.7607392222673164, 0.7579466015934638, 0.755242784475793, 0.7526192572531332, 0.7500685750821765, 0.7475842240365903, 0.7451605010401964, 0.7427924093273577, 0.7404755674221268, 0.7382061298874938, 0.7359807183222811, 0.7337963612801521, 0.7316504419566756, 0.7295406526396561, 0.7274649550479244, 0.7254215457969304, 0.7234088263280122, 0.7214253767239822, 0.7194699329083709, 0.717541366790663, 0.7156386689765023, 0.7137609337111065, 0.7119073457670586, 0.7100771690249962, 0.7082697365282535, 0.7064844418208301, 0.704720731402718, 0.7029780981580847, 0.7012560756305092, 0.6995542330357275, 0.6978721709165292, 0.6962095173567654, 0.6945659246821844, 0.692941066585147, 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MTsR_Negative = [[17.495143657444814, 17.71659759254746, 17.895546734256982, 18.037260478822986, 18.1463663037226, 18.226926401505935, 18.282505541753494, 18.316231076695587, 18.330845932101255, 18.328755351322783, 18.312068088839865, 18.282632681573773, 18.242069362418604, 18.19179812128668, 18.133063364643803, 18.06695557498965, 17.994430326867572, 17.916324975531992, 17.833373298077348, 17.74621833433332, 17.65542364583949, 17.561483185414346, 17.464829946929584, 17.365843544597922, 17.264856853121813, 17.162161824176493, 17.05801458069115, 16.952639878041452, 16.846235010384476, 16.73897323079109, 16.631006745405884, 16.522469334459373, 16.41347864644986, 16.30413820609921, 16.19453917166821, 16.08476187281697, 15.974877156332212, 15.864947563656543, 15.755028361185197, 15.645168441691368, 15.535411112959537, 15.425794787706948, 15.316353587120346, 15.207117868800864, 15.098114688564948, 14.989368204371658, 14.880900029615887, 14.772729542123017, 14.66487415439029, 14.557349549928432, 14.450169889949649, 14.34334799411836, 14.23689549861686, 14.130822994371044, 14.025140147924958, 13.919855807143122, 13.81497809364555, 13.710514483642399, 13.606471878626863, 13.502856667201215, 13.399674779152747, 13.2969317327547, 13.19463267614617, 13.092782423537656, 12.991385486894885, 12.890446103672332, 12.789968261095169, 12.689955717427026, 12.590412020604575, 12.491340524573289, 12.392744403616078, 12.294626664929993, 12.196990159673547, 12.099837592680501, 12.003171531009897, 11.906994411481193, 11.811308547325055, 11.716116134063213, 11.621419254716997, 11.52721988443075, 11.433519894586993, 11.340321056478146, 11.247625044593974, 11.15543343957421, 11.063747730870958, 10.972569319159092, 10.881899518528243, 10.791739558485347, 10.702090585793854, 10.612953666171094, 10.5243297858636, 10.436219853117066, 10.348624699555515, 10.261545081482637, 10.174981681116279, 10.088935107765423], [46.57195075283551, 43.05982328903787, 39.99557815137787, 37.31750774561451, 34.973033031612346, 32.917206702897616, 31.111495165694436, 29.522780108277885, 28.122534566745998, 26.88613881210432, 25.79230915095762, 24.822618577702073, 23.96109265499807, 23.193867398958915, 22.508898570660975, 21.89571381876155, 21.3452007203707, 20.849425033234837, 20.401474479528346, 19.99532418847562, 19.625720575770643, 19.288080965891993, 18.978406694653316, 18.69320778350729, 18.429437569618088, 18.184435918539947, 17.955879848914577, 17.741740568376926, 17.54024606275837, 17.349848501428355, 17.169195824025863, 16.997106960977618, 16.832550214581175, 16.674624391094582, 16.52254232889949, 16.375616514782365, 16.233246520858643, 16.094908029612483, 15.96014324474119, 15.828552511661059, 15.699786994216538, 15.573542273828494, 15.449552754426264, 15.327586771388752, 15.207442315668487, 15.088943295552326, 14.971936268337984, 14.856287582776687, 14.741880880604114, 14.628614912005276, 14.51640162555124, 14.40516449811679, 14.29483707463018, 14.185361691297814, 14.076688359262192, 13.96877378854586, 13.861580534666842, 13.755076252522244, 13.64923304407202, 13.544026888045224, 13.43943714136995, 13.335446103321004, 13.232038634510033, 13.129201823830414, 13.026924697335389, 12.925197963782495, 12.824013792238844, 12.723365617720418, 12.623247971343815, 12.523656331910828, 12.424586996233629, 12.326036965845844, 12.2280038480407, 12.13048576943639, 12.033481300494756, 11.93698938961657, 11.841009305610868, 11.74554058748599, 11.65058300064213, 11.556136498662283, 11.462201189997316, 11.368777308931229, 11.275865190289238, 11.183465247418198, 11.091577953029685, 11.000203822545473, 10.909343399632405, 10.81899724365185, 10.729165918783792, 10.639849984615552, 10.55104998801248, 10.462766456109364, 10.374999890283078, 10.2877507609833, 10.201019503314754, 10.114806513276648], [inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]
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          BPR = [[2.4903450511714937, 2.503938435501344, 2.5138187962944425, 2.5204478701338786, 2.5242311469527694, 2.5255245893942253, 2.524640582393138, 2.5218531934180883, 2.5174028173000087, 2.511500273082253, 2.504330414035426, 2.4960553059901693, 2.4868170235353335, 2.476740108425053, 2.4659337297704793, 2.4544935812383497, 2.4425035465398333, 2.4300371609395004, 2.4171588933263286, 2.403925270533804, 2.3903858630543406, 2.3765841490267445, 2.3625582713671522, 2.3483417011318983, 2.333963818625865, 2.3194504223762897, 2.3048241748644736, 2.2901049928241313, 2.2753103889609783, 2.260455771107956, 2.245554704093745, 2.2306191389501007, 2.215659613516291, 2.200685427995785, 2.1857047985816007, 2.1707249918814875, 2.155752442534448, 2.1407928561143916, 2.12585129915626, 2.1109322779114446, 2.0960398072401802, 2.081177470872978, 2.066348474119747, 2.0515556899708915, 2.036801699417458, 2.0220888267131514, 2.0074191702119397, 1.9927946293353413, 1.9782169281542887, 1.9636876360099997, 1.949208185545211, 1.9347798884708127, 1.9204039493515788, 1.9060814776610802, 1.8918134983214172, 1.8776009609199702, 1.8634447477686953, 1.8493456809515043, 1.8353045284880798, 1.8213220097243752, 1.8073988000480357, 1.7935355350139763, 1.7797328139543909, 1.7659912031379836, 1.7523112385366826, 1.738693428248423, 1.7251382546202036, 1.71164617610917, 1.6982176289156221, 1.6848530284164112, 1.671552770424533, 1.658317232297107, 1.645146773911253, 1.6320417385245438, 1.6190024535351593, 1.6060292311551159, 1.5931223690065635, 1.5802821506529525, 1.567508846071761, 1.5548027120780512, 1.5421639927039996, 1.5295929195413098, 1.517089712050487, 1.5046545778425116, 1.4922877129356515, 1.4799893019911878, 1.4677595185310783, 1.4555985251400823, 1.4435064736539491, 1.4314835053366073, 1.419529751047072, 1.407645331397751, 1.3958303569062416, 1.3840849281400232, 1.3724091358567596, 1.3608030611399373], [5.033419210649191, 4.720499008420537, 4.446775684470231, 4.206847369137276, 3.9961116535170507, 3.8106344724095416, 3.64704341076679, 3.5024402468983644, 3.374328782151597, 3.260554919443859, 3.1592566334364824, 3.0688219872091738, 2.9878537391416784, 2.9151393815243045, 2.849625682390977, 2.7903969810609714, 2.7366566282511275, 2.68771107252535, 2.6429561830909827, 2.601865469648686, 2.563979917015344, 2.5288991985127267, 2.496274069897155, 2.465799776638796, 2.437210332986242, 2.4102735525282295, 2.3847867277139776, 2.360572870667779, 2.3374774401561216, 2.31536549014291, 2.2941191843430393, 2.273635628817752, 2.253824981173082, 2.234608800498944, 2.2159186069721, 2.197694624161116, 2.1798846806178376, 2.162443250399647, 2.1453306148148648, 2.1285121299735987, 2.11195758671453, 2.0956406512012853, 2.0795383759811017, 2.0636307726006047, 2.0479004380077046, 2.0323322279554077, 2.0169129714839964, 2.001631221308086, 1.9864770355882928, 1.9714417871396133, 1.9565179966247885, 1.9416991867178157, 1.9269797546009015, 1.9123548604916893, 1.8978203301853358, 1.8833725698518677, 1.8690084915479082, 1.8547254480980513, 1.8405211761679001, 1.826393746500234, 1.8123415204146216, 1.7983631117832424, 1.7844573537953663, 1.770623269908852, 1.7568600484626729, 1.743167020490254, 1.7295436403320996, 1.7159894686953765, 1.7025041578535824, 1.6890874387168344, 1.6757391095385583, 1.6624590260520438, 1.6492470928581822, 1.6361032559064073, 1.6230274959320476, 1.610019822729938, 1.5970802701588078, 1.5842088917853054, 1.571405757087134, 1.558670948144735, 1.5460045567610585, 1.533406681954729, 1.520877427780927, 1.5084169014377085, 1.4960252116229884, 1.4837024671103038, 1.4714487755160253, 1.459264242234398, 1.447148969518912, 1.4351030556922961, 1.4231265944685363, 1.4112196743736467, 1.3993823782521397, 1.3876147828491718, 1.3759169584584885, 1.364288968628407], [-inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]

Timing difference using stable=True

print(f'For {simulator.sequence.N_adc} ADC events with {simulator.sequence.N_dummyADC} dummy ADC events:')
print("Stable = False:", end='\t')
%timeit -t -n 100 Trajector.readouts(simulator=simulator, stable=False)
print("Stable = True :", end='\t')
%timeit -t -n 100 Trajector.readouts(simulator=simulator, stable=True)

For 96 ADC events with 0 dummy ADC events:
Stable = False:	2.44 ms ± 533 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)
Stable = True :	3.45 ms ± 410 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)

Value difference using stable=True

# We return Signal.ALL to ensure that we precompute all ratio signal
# Otherwise, our quick helper `print_readouts` will compute things like
# [(ihMT_1 - ihMT_2) / (MT0_1 - MT0_2)] instead of [(ihMTR_1 - ihMTR_2)]
print(Trajector.readouts(simulator=simulator, stable=True)[Signal.ALL] - Trajector.readouts(simulator=simulator, stable=False)[Signal.ALL])

Shape: (4, 96)
MTsR_Positive = [[0.0, 0.0, -1.4210854715202004e-14, -1.4210854715202004e-14, -1.4210854715202004e-14, -2.842170943040401e-14, -1.4210854715202004e-14, 0.0, -1.4210854715202004e-14, 0.0, -2.842170943040401e-14, -1.4210854715202004e-14, -2.842170943040401e-14, -1.4210854715202004e-14, -2.842170943040401e-14, 0.0, -1.4210854715202004e-14, -2.842170943040401e-14, -2.842170943040401e-14, -5.684341886080802e-14, -4.263256414560601e-14, -2.842170943040401e-14, -4.263256414560601e-14, -1.4210854715202004e-14, -2.842170943040401e-14, 0.0, -1.4210854715202004e-14, -1.4210854715202004e-14, -2.842170943040401e-14, -4.263256414560601e-14, -1.4210854715202004e-14, 1.4210854715202004e-14, -1.4210854715202004e-14, -1.4210854715202004e-14, 0.0, -1.4210854715202004e-14, -1.4210854715202004e-14, -5.684341886080802e-14, -4.263256414560601e-14, -1.4210854715202004e-14, 0.0, -1.4210854715202004e-14, 0.0, -2.842170943040401e-14, -2.842170943040401e-14, -2.842170943040401e-14, -4.263256414560601e-14, -2.842170943040401e-14, -2.842170943040401e-14, -4.263256414560601e-14, -1.4210854715202004e-14, -2.842170943040401e-14, -2.842170943040401e-14, -4.263256414560601e-14, -2.842170943040401e-14, -5.684341886080802e-14, -5.684341886080802e-14, -7.105427357601002e-14, -4.263256414560601e-14, -4.263256414560601e-14, -2.842170943040401e-14, -4.263256414560601e-14, -2.842170943040401e-14, -4.263256414560601e-14, -5.684341886080802e-14, -5.684341886080802e-14, -2.842170943040401e-14, -2.842170943040401e-14, 0.0, -1.4210854715202004e-14, -1.4210854715202004e-14, -2.842170943040401e-14, -1.4210854715202004e-14, 0.0, -2.842170943040401e-14, -2.842170943040401e-14, 0.0, 0.0, 0.0, -2.842170943040401e-14, 1.4210854715202004e-14, 0.0, -2.842170943040401e-14, -1.4210854715202004e-14, -2.842170943040401e-14, -1.4210854715202004e-14, -2.842170943040401e-14, -2.842170943040401e-14, -5.684341886080802e-14, -4.263256414560601e-14, -4.263256414560601e-14, -5.684341886080802e-14, -2.842170943040401e-14, -4.263256414560601e-14, -4.263256414560601e-14, -2.842170943040401e-14], [0.0, 0.0, 0.0, 0.0, 0.0, 1.4210854715202004e-14, 1.4210854715202004e-14, 1.4210854715202004e-14, 1.4210854715202004e-14, 2.842170943040401e-14, 1.4210854715202004e-14, 1.4210854715202004e-14, 0.0, -2.842170943040401e-14, 0.0, -2.842170943040401e-14, -1.4210854715202004e-14, -1.4210854715202004e-14, -4.263256414560601e-14, -1.4210854715202004e-14, -1.4210854715202004e-14, 0.0, -1.4210854715202004e-14, -1.4210854715202004e-14, 1.4210854715202004e-14, 1.4210854715202004e-14, 0.0, -1.4210854715202004e-14, 0.0, 2.842170943040401e-14, -2.842170943040401e-14, -2.842170943040401e-14, -2.842170943040401e-14, -1.4210854715202004e-14, -1.4210854715202004e-14, -1.4210854715202004e-14, -1.4210854715202004e-14, 0.0, 0.0, 0.0, -4.263256414560601e-14, -1.4210854715202004e-14, -1.4210854715202004e-14, -4.263256414560601e-14, -4.263256414560601e-14, -4.263256414560601e-14, -4.263256414560601e-14, -2.842170943040401e-14, -5.684341886080802e-14, -4.263256414560601e-14, -2.842170943040401e-14, -4.263256414560601e-14, -2.842170943040401e-14, -5.684341886080802e-14, -4.263256414560601e-14, -4.263256414560601e-14, -4.263256414560601e-14, -4.263256414560601e-14, -2.842170943040401e-14, -2.842170943040401e-14, -4.263256414560601e-14, -4.263256414560601e-14, -4.263256414560601e-14, -2.842170943040401e-14, -2.842170943040401e-14, 0.0, 0.0, 0.0, 2.842170943040401e-14, 2.842170943040401e-14, 2.842170943040401e-14, 4.263256414560601e-14, 5.684341886080802e-14, 4.263256414560601e-14, 5.684341886080802e-14, 5.684341886080802e-14, 5.684341886080802e-14, 4.263256414560601e-14, 4.263256414560601e-14, 5.684341886080802e-14, 7.105427357601002e-14, 4.263256414560601e-14, 8.526512829121202e-14, 8.526512829121202e-14, 8.526512829121202e-14, 8.526512829121202e-14, 5.684341886080802e-14, 2.842170943040401e-14, 5.684341886080802e-14, 2.842170943040401e-14, 4.263256414560601e-14, 2.842170943040401e-14, 0.0, 1.4210854715202004e-14, 0.0, 2.842170943040401e-14], [nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]
          MTs = [[0.0, 0.0, -1.1102230246251565e-16, 1.1102230246251565e-16, 2.220446049250313e-16, 1.1102230246251565e-16, 1.1102230246251565e-16, 2.220446049250313e-16, -1.1102230246251565e-16, 0.0, -1.1102230246251565e-16, 0.0, -2.220446049250313e-16, -1.1102230246251565e-16, -2.220446049250313e-16, 0.0, -3.3306690738754696e-16, -2.220446049250313e-16, -2.220446049250313e-16, -1.1102230246251565e-16, -2.220446049250313e-16, -2.220446049250313e-16, -2.220446049250313e-16, 0.0, -4.440892098500626e-16, -2.220446049250313e-16, -3.3306690738754696e-16, -2.220446049250313e-16, -3.3306690738754696e-16, -2.220446049250313e-16, -4.440892098500626e-16, -2.220446049250313e-16, -4.440892098500626e-16, -3.3306690738754696e-16, -4.440892098500626e-16, -3.3306690738754696e-16, -2.220446049250313e-16, -2.220446049250313e-16, -2.220446049250313e-16, -2.220446049250313e-16, -4.440892098500626e-16, -2.220446049250313e-16, -3.3306690738754696e-16, -2.220446049250313e-16, -3.3306690738754696e-16, 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     ihMTR_CM = [[0.0, 0.0, -3.552713678800501e-14, 0.0, 6.394884621840902e-14, 2.842170943040401e-14, 2.842170943040401e-14, 1.4210854715202004e-14, 2.842170943040401e-14, 2.1316282072803006e-14, 5.684341886080802e-14, 7.105427357601002e-15, 1.4210854715202004e-14, 1.4210854715202004e-14, -1.4210854715202004e-14, 0.0, 0.0, 0.0, -7.105427357601002e-15, 4.973799150320701e-14, 2.1316282072803006e-14, 2.1316282072803006e-14, 4.263256414560601e-14, 3.552713678800501e-14, -7.105427357601002e-15, 7.105427357601002e-15, 2.1316282072803006e-14, 1.4210854715202004e-14, 4.263256414560601e-14, 2.1316282072803006e-14, 0.0, -2.842170943040401e-14, 0.0, 2.4868995751603507e-14, -7.105427357601002e-15, 2.1316282072803006e-14, 4.263256414560601e-14, 4.618527782440651e-14, 7.105427357601002e-14, 3.552713678800501e-14, 4.618527782440651e-14, 3.552713678800501e-14, 7.460698725481052e-14, 9.592326932761353e-14, 7.105427357601002e-14, 4.263256414560601e-14, 7.105427357601002e-14, 3.907985046680551e-14, 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 MTs_Positive = [[0.0, 0.0, -1.1102230246251565e-16, 1.1102230246251565e-16, 1.1102230246251565e-16, 1.1102230246251565e-16, 1.1102230246251565e-16, 2.220446049250313e-16, 0.0, 0.0, -1.1102230246251565e-16, 0.0, -2.220446049250313e-16, -1.1102230246251565e-16, -1.1102230246251565e-16, 0.0, -2.220446049250313e-16, -2.220446049250313e-16, -2.220446049250313e-16, -1.1102230246251565e-16, -1.1102230246251565e-16, -1.1102230246251565e-16, -1.1102230246251565e-16, 0.0, -3.3306690738754696e-16, -2.220446049250313e-16, -2.220446049250313e-16, -1.1102230246251565e-16, -2.220446049250313e-16, -2.220446049250313e-16, -3.3306690738754696e-16, -1.1102230246251565e-16, -4.440892098500626e-16, -3.3306690738754696e-16, -4.440892098500626e-16, -3.3306690738754696e-16, -2.220446049250313e-16, -2.220446049250313e-16, -2.220446049250313e-16, -1.1102230246251565e-16, -3.3306690738754696e-16, -1.1102230246251565e-16, -2.220446049250313e-16, -1.1102230246251565e-16, -3.3306690738754696e-16, 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         MTsR = [[0.0, 0.0, 0.0, -1.4210854715202004e-14, -1.4210854715202004e-14, -1.4210854715202004e-14, -2.842170943040401e-14, 0.0, -1.4210854715202004e-14, 0.0, -1.4210854715202004e-14, -1.4210854715202004e-14, 0.0, -1.4210854715202004e-14, 0.0, 0.0, 0.0, -2.842170943040401e-14, -1.4210854715202004e-14, -5.684341886080802e-14, -1.4210854715202004e-14, -2.842170943040401e-14, -1.4210854715202004e-14, -2.842170943040401e-14, 0.0, 0.0, -2.842170943040401e-14, -1.4210854715202004e-14, 0.0, -1.4210854715202004e-14, 0.0, 1.4210854715202004e-14, -1.4210854715202004e-14, -2.842170943040401e-14, 0.0, -1.4210854715202004e-14, -1.4210854715202004e-14, -5.684341886080802e-14, -2.842170943040401e-14, -1.4210854715202004e-14, 0.0, -1.4210854715202004e-14, 1.4210854715202004e-14, -1.4210854715202004e-14, -1.4210854715202004e-14, -2.842170943040401e-14, -5.684341886080802e-14, -1.4210854715202004e-14, -1.4210854715202004e-14, -4.263256414560601e-14, -2.842170943040401e-14, -1.4210854715202004e-14, 1.4210854715202004e-14, 0.0, -1.4210854715202004e-14, -4.263256414560601e-14, -4.263256414560601e-14, 0.0, -1.4210854715202004e-14, 0.0, 0.0, -2.842170943040401e-14, -1.4210854715202004e-14, -2.842170943040401e-14, -4.263256414560601e-14, 0.0, 0.0, 2.842170943040401e-14, 2.842170943040401e-14, 5.684341886080802e-14, 0.0, 1.4210854715202004e-14, 2.842170943040401e-14, 1.4210854715202004e-14, -1.4210854715202004e-14, 2.842170943040401e-14, 5.684341886080802e-14, 1.4210854715202004e-14, 1.4210854715202004e-14, -1.4210854715202004e-14, 1.4210854715202004e-14, 1.4210854715202004e-14, 1.4210854715202004e-14, 2.842170943040401e-14, 1.4210854715202004e-14, 1.4210854715202004e-14, 2.842170943040401e-14, 0.0, -1.4210854715202004e-14, -2.842170943040401e-14, -2.842170943040401e-14, -1.4210854715202004e-14, 1.4210854715202004e-14, -1.4210854715202004e-14, -1.4210854715202004e-14, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 1.4210854715202004e-14, 1.4210854715202004e-14, 1.4210854715202004e-14, 0.0, 0.0, 1.4210854715202004e-14, 0.0, 0.0, -5.684341886080802e-14, -1.4210854715202004e-14, -2.842170943040401e-14, -2.842170943040401e-14, -2.842170943040401e-14, -2.842170943040401e-14, -1.4210854715202004e-14, -1.4210854715202004e-14, 0.0, 0.0, -1.4210854715202004e-14, 1.4210854715202004e-14, 4.263256414560601e-14, -1.4210854715202004e-14, 0.0, 1.4210854715202004e-14, 2.842170943040401e-14, -1.4210854715202004e-14, -2.842170943040401e-14, -1.4210854715202004e-14, 1.4210854715202004e-14, -2.842170943040401e-14, -2.842170943040401e-14, -2.842170943040401e-14, 0.0, 0.0, 0.0, -2.842170943040401e-14, -2.842170943040401e-14, -1.4210854715202004e-14, -1.4210854715202004e-14, -4.263256414560601e-14, -4.263256414560601e-14, -2.842170943040401e-14, 0.0, -2.842170943040401e-14, -2.842170943040401e-14, -2.842170943040401e-14, -5.684341886080802e-14, -4.263256414560601e-14, -4.263256414560601e-14, -2.842170943040401e-14, -2.842170943040401e-14, -1.4210854715202004e-14, -1.4210854715202004e-14, -1.4210854715202004e-14, -1.4210854715202004e-14, -2.842170943040401e-14, -4.263256414560601e-14, -2.842170943040401e-14, 0.0, 1.4210854715202004e-14, 1.4210854715202004e-14, 4.263256414560601e-14, 5.684341886080802e-14, 8.526512829121202e-14, 7.105427357601002e-14, 5.684341886080802e-14, 7.105427357601002e-14, 7.105427357601002e-14, 7.105427357601002e-14, 7.105427357601002e-14, 7.105427357601002e-14, 7.105427357601002e-14, 7.105427357601002e-14, 9.947598300641403e-14, 7.105427357601002e-14, 9.947598300641403e-14, 8.526512829121202e-14, 1.1368683772161603e-13, 1.1368683772161603e-13, 1.2789769243681803e-13, 1.2789769243681803e-13, 8.526512829121202e-14, 5.684341886080802e-14, 9.947598300641403e-14, 5.684341886080802e-14, 7.105427357601002e-14, 4.263256414560601e-14, 7.105427357601002e-14, 7.105427357601002e-14, 7.105427357601002e-14, 8.526512829121202e-14], [nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]
MTsR_Negative = [[0.0, 0.0, -1.4210854715202004e-14, -1.4210854715202004e-14, -1.4210854715202004e-14, -1.4210854715202004e-14, 0.0, 0.0, 0.0, 0.0, 0.0, -1.4210854715202004e-14, 0.0, -1.4210854715202004e-14, 0.0, 0.0, -1.4210854715202004e-14, -2.842170943040401e-14, -2.842170943040401e-14, -4.263256414560601e-14, 0.0, -2.842170943040401e-14, -1.4210854715202004e-14, 1.4210854715202004e-14, 0.0, 2.842170943040401e-14, 0.0, -2.842170943040401e-14, 0.0, 0.0, -1.4210854715202004e-14, 1.4210854715202004e-14, -1.4210854715202004e-14, 0.0, -1.4210854715202004e-14, -2.842170943040401e-14, -1.4210854715202004e-14, -2.842170943040401e-14, -4.263256414560601e-14, -1.4210854715202004e-14, 1.4210854715202004e-14, 0.0, -1.4210854715202004e-14, -2.842170943040401e-14, -2.842170943040401e-14, 0.0, -2.842170943040401e-14, 1.4210854715202004e-14, 1.4210854715202004e-14, -4.263256414560601e-14, -2.842170943040401e-14, 1.4210854715202004e-14, 0.0, 0.0, 1.4210854715202004e-14, -1.4210854715202004e-14, 0.0, 0.0, 1.4210854715202004e-14, 1.4210854715202004e-14, 2.842170943040401e-14, 1.4210854715202004e-14, -1.4210854715202004e-14, 1.4210854715202004e-14, 2.842170943040401e-14, 4.263256414560601e-14, 2.842170943040401e-14, 5.684341886080802e-14, 8.526512829121202e-14, 9.947598300641403e-14, 2.842170943040401e-14, 5.684341886080802e-14, 7.105427357601002e-14, 4.263256414560601e-14, 2.842170943040401e-14, 7.105427357601002e-14, 7.105427357601002e-14, 5.684341886080802e-14, 8.526512829121202e-14, 5.684341886080802e-14, 7.105427357601002e-14, 5.684341886080802e-14, 5.684341886080802e-14, 5.684341886080802e-14, 4.263256414560601e-14, 2.842170943040401e-14, 4.263256414560601e-14, 4.263256414560601e-14, 4.263256414560601e-14, 2.842170943040401e-14, 1.4210854715202004e-14, 1.4210854715202004e-14, 2.842170943040401e-14, 0.0, -1.4210854715202004e-14, 1.4210854715202004e-14], [0.0, 0.0, 0.0, 0.0, 0.0, 1.4210854715202004e-14, 1.4210854715202004e-14, 1.4210854715202004e-14, 1.4210854715202004e-14, 2.842170943040401e-14, 0.0, 0.0, -1.4210854715202004e-14, -5.684341886080802e-14, -2.842170943040401e-14, -5.684341886080802e-14, -1.4210854715202004e-14, -2.842170943040401e-14, -2.842170943040401e-14, -4.263256414560601e-14, -2.842170943040401e-14, 0.0, -1.4210854715202004e-14, -1.4210854715202004e-14, 2.842170943040401e-14, 1.4210854715202004e-14, 1.4210854715202004e-14, 1.4210854715202004e-14, 2.842170943040401e-14, 1.4210854715202004e-14, 0.0, 0.0, -1.4210854715202004e-14, 0.0, -1.4210854715202004e-14, -1.4210854715202004e-14, -2.842170943040401e-14, 0.0, 0.0, -1.4210854715202004e-14, -1.4210854715202004e-14, 0.0, -1.4210854715202004e-14, -1.4210854715202004e-14, -2.842170943040401e-14, -2.842170943040401e-14, -2.842170943040401e-14, -1.4210854715202004e-14, -1.4210854715202004e-14, -2.842170943040401e-14, -1.4210854715202004e-14, -2.842170943040401e-14, -1.4210854715202004e-14, -2.842170943040401e-14, 0.0, 0.0, 2.842170943040401e-14, 1.4210854715202004e-14, 0.0, 0.0, 4.263256414560601e-14, 0.0, 2.842170943040401e-14, 4.263256414560601e-14, 2.842170943040401e-14, 5.684341886080802e-14, 7.105427357601002e-14, 7.105427357601002e-14, 1.1368683772161603e-13, 9.947598300641403e-14, 8.526512829121202e-14, 7.105427357601002e-14, 9.947598300641403e-14, 9.947598300641403e-14, 1.1368683772161603e-13, 1.1368683772161603e-13, 1.1368683772161603e-13, 1.2789769243681803e-13, 1.1368683772161603e-13, 9.947598300641403e-14, 1.2789769243681803e-13, 1.2789769243681803e-13, 1.5631940186722204e-13, 1.2789769243681803e-13, 1.2789769243681803e-13, 1.4210854715202004e-13, 1.2789769243681803e-13, 7.105427357601002e-14, 1.1368683772161603e-13, 1.1368683772161603e-13, 1.2789769243681803e-13, 1.1368683772161603e-13, 1.1368683772161603e-13, 1.1368683772161603e-13, 9.947598300641403e-14, 9.947598300641403e-14], [nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]
     MTdR_ALT = [[0.0, 0.0, -1.4210854715202004e-14, 0.0, 0.0, -1.4210854715202004e-14, 0.0, 1.4210854715202004e-14, 0.0, 2.842170943040401e-14, 0.0, -1.4210854715202004e-14, 1.4210854715202004e-14, 0.0, 1.4210854715202004e-14, 2.842170943040401e-14, -1.4210854715202004e-14, 0.0, 0.0, -1.4210854715202004e-14, 0.0, 0.0, 0.0, 1.4210854715202004e-14, 0.0, 2.842170943040401e-14, 1.4210854715202004e-14, 2.842170943040401e-14, 2.842170943040401e-14, 2.842170943040401e-14, 1.4210854715202004e-14, 2.842170943040401e-14, 1.4210854715202004e-14, 1.4210854715202004e-14, 1.4210854715202004e-14, 1.4210854715202004e-14, 2.842170943040401e-14, 4.263256414560601e-14, 2.842170943040401e-14, 4.263256414560601e-14, 2.842170943040401e-14, 4.263256414560601e-14, 4.263256414560601e-14, 4.263256414560601e-14, 4.263256414560601e-14, 4.263256414560601e-14, 2.842170943040401e-14, 4.263256414560601e-14, 4.263256414560601e-14, 2.842170943040401e-14, 4.263256414560601e-14, 4.263256414560601e-14, 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          BPR = [[0.0, 0.0, -2.1760371282653068e-14, -2.2648549702353193e-14, 0.0, -2.220446049250313e-14, 0.0, -2.353672812205332e-14, 2.398081733190338e-14, -2.353672812205332e-14, 2.398081733190338e-14, -2.3092638912203256e-14, -2.220446049250313e-14, -4.618527782440651e-14, -4.618527782440651e-14, -4.796163466380676e-14, 1.7763568394002505e-15, -4.707345624410664e-14, -4.707345624410664e-14, -2.2648549702353193e-14, -2.3092638912203256e-14, -2.3092638912203256e-14, 1.3322676295501878e-15, -2.4424906541753444e-14, -2.353672812205332e-14, -2.4424906541753444e-14, -2.398081733190338e-14, -4.929390229335695e-14, -2.398081733190338e-14, -7.505107646466058e-14, -4.929390229335695e-14, -5.10702591327572e-14, -7.549516567451064e-14, -5.0182080713057076e-14, -5.062616992290714e-14, -5.0182080713057076e-14, -5.10702591327572e-14, -7.682743330406083e-14, -5.10702591327572e-14, -5.1958437552457326e-14, -2.531308496145357e-14, -5.284661597215745e-14, -2.531308496145357e-14, 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 MTs_Negative = [[0.0, 0.0, 0.0, 1.1102230246251565e-16, 1.1102230246251565e-16, 0.0, 0.0, 1.1102230246251565e-16, -1.1102230246251565e-16, 0.0, -2.220446049250313e-16, 0.0, -2.220446049250313e-16, -2.220446049250313e-16, -3.3306690738754696e-16, 0.0, -3.3306690738754696e-16, -2.220446049250313e-16, -3.3306690738754696e-16, -2.220446049250313e-16, -4.440892098500626e-16, -3.3306690738754696e-16, -3.3306690738754696e-16, -2.220446049250313e-16, -3.3306690738754696e-16, -3.3306690738754696e-16, -3.3306690738754696e-16, -2.220446049250313e-16, -3.3306690738754696e-16, -3.3306690738754696e-16, -5.551115123125783e-16, -1.1102230246251565e-16, -4.440892098500626e-16, -4.440892098500626e-16, -3.3306690738754696e-16, -2.220446049250313e-16, -3.3306690738754696e-16, -3.3306690738754696e-16, -2.220446049250313e-16, -2.220446049250313e-16, -3.3306690738754696e-16, -2.220446049250313e-16, -3.3306690738754696e-16, -1.1102230246251565e-16, -2.220446049250313e-16, -2.220446049250313e-16, -3.3306690738754696e-16, -2.220446049250313e-16, -4.440892098500626e-16, -3.3306690738754696e-16, -3.3306690738754696e-16, -4.440892098500626e-16, -4.440892098500626e-16, -4.440892098500626e-16, -5.551115123125783e-16, -3.3306690738754696e-16, -6.661338147750939e-16, -5.551115123125783e-16, -6.661338147750939e-16, -5.551115123125783e-16, -6.661338147750939e-16, -4.440892098500626e-16, -5.551115123125783e-16, -4.440892098500626e-16, -6.661338147750939e-16, -6.661338147750939e-16, -7.771561172376096e-16, -7.771561172376096e-16, -8.881784197001252e-16, -8.881784197001252e-16, -7.771561172376096e-16, -6.661338147750939e-16, -7.771561172376096e-16, -6.661338147750939e-16, -6.661338147750939e-16, -6.661338147750939e-16, -7.771561172376096e-16, -7.771561172376096e-16, -8.881784197001252e-16, -6.661338147750939e-16, -8.881784197001252e-16, -8.881784197001252e-16, -8.881784197001252e-16, -7.771561172376096e-16, -8.881784197001252e-16, -7.771561172376096e-16, -8.881784197001252e-16, -7.771561172376096e-16, -8.881784197001252e-16, -6.661338147750939e-16, -6.661338147750939e-16, -4.440892098500626e-16, -6.661338147750939e-16, -5.551115123125783e-16, -5.551115123125783e-16, -3.3306690738754696e-16], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.3877787807814457e-17, 0.0, 0.0, 1.3877787807814457e-17, 1.3877787807814457e-17, 1.3877787807814457e-17, 4.163336342344337e-17, 5.551115123125783e-17, 5.551115123125783e-17, 5.551115123125783e-17, 2.7755575615628914e-17, 2.7755575615628914e-17, 2.7755575615628914e-17, 1.3877787807814457e-17, 2.7755575615628914e-17, 1.3877787807814457e-17, 1.3877787807814457e-17, 2.7755575615628914e-17, 1.3877787807814457e-17, 1.3877787807814457e-17, 1.3877787807814457e-17, 0.0, -1.3877787807814457e-17, 0.0, 1.3877787807814457e-17, 0.0, 0.0, 1.3877787807814457e-17, 1.3877787807814457e-17, 0.0, 1.3877787807814457e-17, 0.0, 0.0, 1.3877787807814457e-17, 0.0, 1.3877787807814457e-17, 0.0, 0.0, 1.3877787807814457e-17, 1.3877787807814457e-17, 1.3877787807814457e-17, 1.3877787807814457e-17, 0.0, 1.3877787807814457e-17, 1.3877787807814457e-17, 1.3877787807814457e-17, 2.7755575615628914e-17, 1.3877787807814457e-17, 1.3877787807814457e-17, 1.3877787807814457e-17, 0.0, 0.0, 1.3877787807814457e-17, 0.0, -1.3877787807814457e-17, 0.0, 0.0, -1.3877787807814457e-17, -2.7755575615628914e-17, -4.163336342344337e-17, -4.163336342344337e-17, -4.163336342344337e-17, -6.938893903907228e-17, -6.938893903907228e-17, -5.551115123125783e-17, -5.551115123125783e-17, -5.551115123125783e-17, -6.938893903907228e-17, -6.938893903907228e-17, -6.938893903907228e-17, -5.551115123125783e-17, -6.938893903907228e-17, -5.551115123125783e-17, -6.938893903907228e-17, -8.326672684688674e-17, -8.326672684688674e-17, -9.71445146547012e-17, -8.326672684688674e-17, -6.938893903907228e-17, -6.938893903907228e-17, -6.938893903907228e-17, -5.551115123125783e-17, -6.938893903907228e-17, -6.938893903907228e-17, -6.938893903907228e-17, -8.326672684688674e-17, -8.326672684688674e-17, -8.326672684688674e-17, -6.938893903907228e-17, -6.938893903907228e-17], [0.0, 0.0, 0.0, 0.0, -1.3234889800848443e-23, -1.3234889800848443e-23, -9.926167350636332e-24, -6.617444900424222e-24, -3.308722450212111e-24, -1.6543612251060553e-24, -1.2407709188295415e-24, -8.271806125530277e-25, -5.169878828456423e-25, -3.101927297073854e-25, -2.0679515313825692e-25, -1.0339757656912846e-25, -6.462348535570529e-26, -3.877409121342317e-26, -2.261821987449685e-26, -1.454028420503369e-26, -8.077935669463161e-27, -4.4428646182047385e-27, -2.4233807008389483e-27, -1.2116903504194741e-27, -7.068193710780266e-28, -4.0389678347315804e-28, -2.271919407036514e-28, -1.3883951931889808e-28, -7.573064690121713e-29, -3.7865323450608567e-29, -2.524354896707238e-29, -1.262177448353619e-29, -7.099748146989106e-30, -3.944304526105059e-30, -2.3665827156630354e-30, -1.3805065841367707e-30, -7.395570986446986e-31, -3.944304526105059e-31, -2.2186712959340957e-31, -1.355854680848614e-31, -7.395570986446986e-32, -4.3140830754274083e-32, -2.465190328815662e-32, -1.4637067577342992e-32, -8.474091755303838e-33, -4.622231866529366e-33, -2.6963019221421302e-33, -1.4444474582904269e-33, -8.185202263645752e-34, -4.574083617919685e-34, -2.6481536735324493e-34, -1.4444474582904269e-34, -7.824090399073146e-35, -4.81482486096809e-35, -2.7083389842945504e-35, -1.4294011305999016e-35, -8.275480229788904e-36, -4.70197740328915e-36, -2.539067797776141e-36, -1.504632769052528e-36, -8.46355932592047e-37, -4.4668785331246925e-37, -2.5860875718090325e-37, -1.3518185034456306e-37, -7.934586868050441e-38, -4.408103815583578e-38, -2.497925495497361e-38, -1.3224311446750734e-38, -7.714181677271262e-39, -4.408103815583578e-39, -2.3877229001077715e-39, -1.3316146942908726e-39, -7.346839692639297e-40, -3.9030085867146265e-40, -2.2958874039497803e-40, -1.2627380721723792e-40, -7.174648137343063e-41, -3.730817031418393e-41, -2.2241409225763497e-41, -1.1838169426616055e-41, -6.636549527042334e-42, -3.766690272105108e-42, -2.0627113394861307e-42, -1.1658803223182478e-42, -6.726232628759122e-43, -3.587324068671532e-43, -2.0739217272007293e-43, -1.0930128021733573e-43, -6.165713243029195e-44, -3.5032461608120427e-44, -1.961817850054744e-44, -1.0860063098517332e-44, -5.955518473380473e-45, -3.2405026987511395e-45, -1.8392042344263224e-45, -9.85287982728387e-46], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]

Example: Point Spread Function (PSF) - WIP

Simulating many experiments

Using the ihmt.run.GridRuns function

sim = simulator.copy()
sim.output_vectorSlice = slice(None)
sim.export_readMatrix = True
data = GridRuns(
    sim,
    ['poolFree_T1', 'flipAngle'],
    {
        'poolFree_T1': [1.0, 1.5, 2.0],
        'flipAngle': (simulator.pulse.flipAngle * np.linspace(.1, 1.5, 15)).astype(Angle)
    },
    safe=True,
)

print('Readout matrix shape:', data['readout'].shape)
print(CompositeDictionary(data))

Readout matrix shape: (3, 15, 4, 4)
Shape: (4, 3, 15)
 MTs_Positive = [[[0.9904119271169727, 0.9655424694671243, 0.9341213987242093, 0.9041729161509892, 0.8799180451323365, 0.8620435041515132, 0.8493879317304119, 0.8403816232949561, 0.8337430229195211, 0.8286169162486072, 0.8244773077364871, 0.8210009721635665, 0.8179803203768445, 0.8152749136781585, 0.8127858356904707], [0.9891476708545726, 0.9610182930764716, 0.9255194819398096, 0.891732820544455, 0.8644102616095338, 0.8443035052406905, 0.8300859993177455, 0.819980260111795, 0.8125395776275807, 0.8068002471082846, 0.8021702844624238, 0.798286264859583, 0.7949149605775017, 0.791898685726215, 0.7891264343424913], [0.9884186831603747, 0.958429788732002, 0.9206053774856128, 0.8846302555401689, 0.8555589777723599, 0.8341800134454235, 0.8190724345508836, 0.8083402291830004, 0.8004425294958325, 0.7943537954853821, 0.7894444370267739, 0.7853281216347682, 0.7817570126546789, 0.7785635978130145, 0.7756299842592068]], [[0.09718718859546474, 0.08998526891322932, 0.08109632763654628, 0.07287826950612493, 0.06645477196003134, 0.061908707160867466, 0.05883530916592035, 0.05675875602583942, 0.05531239149431819, 0.054261820655362177, 0.053468484941771074, 0.05285026085827932, 0.05235588104203463, 0.05195131608488517, 0.051612878104255196], [0.09707811652145655, 0.08961427727677267, 0.08043859015572082, 0.07199433033370375, 0.0654216233019112, 0.06078446638382176, 0.0576553185249797, 0.055542650558678276, 0.054070916555631475, 0.05300101817612125, 0.05219188865998344, 0.051559996863470084, 0.05105323301549308, 0.05063703436816234, 0.05028736079533554], [0.09701551003297565, 0.08940314542711797, 0.08006484286733835, 0.07149229713596875, 0.06483497109026345, 0.06014615993562433, 0.05698540396751248, 0.05485226359631093, 0.05336615005329562, 0.05228529717352547, 0.051467215755083666, 0.05082757651596733, 0.050313792160147565, 0.04989099770464293, 0.0495349534846862]], [[7.85659478087599e-08, 2.758856319166583e-07, 5.098981790091306e-07, 7.12816564281641e-07, 8.570755165583811e-07, 9.463725877239521e-07, 9.969169488141067e-07, 1.0245452926868544e-06, 1.040003536577961e-06, 1.0491997709711667e-06, 1.0550001528657403e-06, 1.0587506575612366e-06, 1.0611281517573699e-06, 1.062519279553949e-06, 1.0631716136508386e-06], [7.847840784372391e-08, 2.747563213369932e-07, 5.057914448227987e-07, 7.042282819774126e-07, 8.438325989730908e-07, 9.292810147600962e-07, 9.77018667006242e-07, 1.0026843197358882e-06, 1.0167444875816832e-06, 1.0248974787751968e-06, 1.029881422408391e-06, 1.0329676039705316e-06, 1.0347871223880494e-06, 1.0356963292813289e-06, 1.0359215142279597e-06], [7.842818201228824e-08, 2.7411395651770343e-07, 5.034590725799817e-07, 6.993530062936996e-07, 8.36316385241668e-07, 9.195810592700463e-07, 9.657259982615667e-07, 9.902777363751534e-07, 1.0035443378549497e-06, 1.0111051269720392e-06, 1.0156256031870495e-06, 1.0183346718254132e-06, 1.0198374566901852e-06, 1.0204731161974005e-06, 1.020455858789017e-06]], [[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]]]
      MTd_ALT = [[[0.9890619026436411, 0.9586620802065079, 0.9149814461905554, 0.865511229991122, 0.816712480382682, 0.7728214665116144, 0.7358283754360964, 0.7060751212820418, 0.6829455270778247, 0.6653962783143583, 0.652289946989293, 0.6425749373513815, 0.6353651817157857, 0.62995907290954, 0.6258249320143213], [0.9876197265979273, 0.9532388192857096, 0.9039108171141876, 0.848163379689076, 0.7933176746591076, 0.7441341089047052, 0.7028080410840449, 0.6696699927989564, 0.6439817063412371, 0.6245411186766746, 0.6100561217084498, 0.5993423678568492, 0.5914079417587325, 0.5854708899163796, 0.5809406109531191], [0.9867892595404432, 0.9501376134234931, 0.897589394993986, 0.8382643245445011, 0.779974636518952, 0.72777948165836, 0.6839904715510128, 0.6489306579830537, 0.621791318594062, 0.6012793223320665, 0.5860141317157631, 0.5747357103937937, 0.5663919282555425, 0.5601552075638447, 0.5554015369930545]], [[0.09678480031832469, 0.08796295494947505, 0.07559015684266313, 0.06203127411241695, 0.049161665327874075, 0.038053367276455606, 0.02907426244305775, 0.02214682514394393, 0.016982266087555174, 0.013230893295917206, 0.010559979379180415, 0.008686534855099296, 0.007385929657335693, 0.006488484628511573, 0.0058707050261330865], [0.09666072198626005, 0.08752501559751598, 0.07478403465534399, 0.0609333729310343, 0.04791559002726624, 0.036800766554530386, 0.02791463530811409, 0.02112939985880512, 0.016116656301583297, 0.012502998208447054, 0.00994550391879868, 0.008159746843565014, 0.006924099227243823, 0.006073399589411938, 0.0054886052973011044], [0.09658960767272691, 0.08727592634915408, 0.07432615532665907, 0.060310032489786954, 0.04720824897981302, 0.03608978168608337, 0.02725644541125285, 0.020551915997791704, 0.01562531383187201, 0.012089783925800901, 0.009596628391503317, 0.007860610923990608, 0.0066618099578121415, 0.005837627827800929, 0.005271547427536673]], [[-1.63502427e-08, -5.94163327046625e-08, -1.1434222719905716e-07, -1.646262732855085e-07, -1.9885094027317485e-07, -2.1337497566217497e-07, -2.1089053085298054e-07, -1.9713866204564438e-07, -1.7801121923998555e-07, -1.579791099678627e-07, -1.39722132466285e-07, -1.2443456016512617e-07, -1.1233722696427511e-07, -1.0313364506364476e-07, -9.632331156316956e-08], [-1.6329284803241805e-08, -5.912064724461819e-08, -1.1312386217982902e-07, -1.617162463951258e-07, -1.938192895547646e-07, -2.0636576219019206e-07, -2.0249910896970819e-07, -1.8810613294935146e-07, -1.6896419289478428e-07, -1.4931545277870064e-07, -1.3161947861499954e-07, -1.1691542131920032e-07, -1.0533905884325852e-07, -9.656077630589567e-08, -9.007756999900981e-08], [-1.6317273148300825e-08, -5.895247439314674e-08, -1.1243187276481404e-07, -1.6006422329024707e-07, -1.9096342390084073e-07, -2.0238792776413452e-07, -1.977371401448123e-07, -1.8298041937949514e-07, -1.6383007614624097e-07, -1.4439849992067847e-07, -1.2702037909138817e-07, -1.1264694126460691e-07, -1.0136577009950164e-07, -9.282848610616745e-08, -8.65306709023058e-08]], [[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]]]
          MT0 = [[[0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692], [0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952], [0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643]], [[0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687], [0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389], [0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301]], [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]]]
       MTd_CM = [[[0.9890511437555202, 0.9585304667397114, 0.9144141041850081, 0.864013482937054, 0.8137538276405042, 0.7679955985379745, 0.7289400438974355, 0.6971379704689502, 0.6721262525047292, 0.6529445530719407, 0.6384762414103742, 0.6276444967968501, 0.6195108267449865, 0.6133128732473258, 0.6084655557340882], [0.9876077025328194, 0.9530906201712053, 0.9032718844068274, 0.8464795708553651, 0.7900000724734222, 0.7387389578144742, 0.6951310793914648, 0.6597396576780591, 0.6319934840904651, 0.6107782346944346, 0.5948208466850755, 0.5829061660457171, 0.573982601065379, 0.5672002640989495, 0.5619093312964443], [0.9867765047840469, 0.9499799223401729, 0.8969095856231164, 0.8364744180648209, 0.776452591231748, 0.7220604876835516, 0.6758654708629336, 0.6384368151952026, 0.6091407085542551, 0.5867743375982473, 0.5699751044930514, 0.5574489271087275, 0.548079853820118, 0.5409682964400399, 0.535427733039411]], [[0.09678606410675371, 0.08794114969699383, 0.07546269308860175, 0.061673293244534896, 0.04845368390448313, 0.036923270475384795, 0.027511271698221023, 0.020191133575859943, 0.014704869217001447, 0.010714183693309178, 0.007882869097867763, 0.005914455058724211, 0.004565503330603097, 0.0036466692909634195, 0.003017670254949276], [0.0966618723312271, 0.08750191094036902, 0.07465219422607802, 0.060568032416699856, 0.047202020767094295, 0.03567569118984325, 0.026376735955096698, 0.019225397482187812, 0.013919522511104848, 0.010093000926643312, 0.00739692187483801, 0.005532626457094636, 0.004260251223865156, 0.003396226552536453, 0.0028060940106509774], [0.0965906928990001, 0.08725208202976605, 0.0741918278913935, 0.05994051260133459, 0.046491508302108124, 0.034967559527911515, 0.02573279197249816, 0.018677253500936155, 0.013473731693254904, 0.009740342955825373, 0.0071209798067696254, 0.005315749610931629, 0.004086820641347773, 0.003253899715454325, 0.002685830915974676]], [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]]]
 MTs_Negative = [[[0.9882042431528718, 0.9586237999811815, 0.9234543195593683, 0.8924193839506441, 0.8692293711397743, 0.8532848059005678, 0.8424936006498276, 0.8349476457763447, 0.8293803867609938, 0.8250485625349024, 0.821519285161347, 0.8185262809149617, 0.8158952094878015, 0.8135066290292565, 0.8112762889464699], [0.9866494190429023, 0.9531971912915326, 0.9134784226965905, 0.8784857025462931, 0.8523802912508479, 0.8344574577666612, 0.8223432048760102, 0.8138820360371006, 0.8076463435487572, 0.8027995564125798, 0.7988549616467704, 0.7955134229624313, 0.7925792080496539, 0.7899182888184633, 0.7874361697182177], [0.9857546814736469, 0.9500939922966561, 0.9077808731926106, 0.8705317286077249, 0.8427646004441591, 0.8237144032721808, 0.8108462618474787, 0.8018636212134189, 0.7952470760064906, 0.7901068783654764, 0.7859256429277812, 0.78238550806491, 0.7792785535519092, 0.7764624421071725, 0.7738368430138691]], [[0.09653940116469611, 0.0879957764806405, 0.07811431864941505, 0.06969570713218629, 0.06365497743205933, 0.059688579450824425, 0.05713928413991892, 0.05545356199253955, 0.05428188281972924, 0.05342804918949153, 0.052782304391137666, 0.05227917836481488, 0.0518766377254387, 0.05154622191251315, 0.05126799943031356], [0.09640584932412734, 0.08755738558513318, 0.07737083733784009, 0.06873609146694235, 0.0625662850203476, 0.058526271561102995, 0.05593310837172315, 0.05421877768729831, 0.05302653380725601, 0.052156605902198255, 0.05149735907420318, 0.05098225490295446, 0.05056860973496116, 0.05022754725748979, 0.04993886071597819], [0.09632936219937638, 0.08730803379523076, 0.07694846496623386, 0.06819114366111316, 0.06194813966966818, 0.05786638677962748, 0.05524835581417994, 0.05351781017334951, 0.05231391135039056, 0.05143486193556922, 0.05076796208789716, 0.05024606778326904, 0.04982612687774832, 0.04947902754827611, 0.04918440718098613]], [[-9.658079450847436e-08, -3.2940915011864785e-07, -5.856047075087526e-07, -7.867699564766618e-07, -9.143645103328844e-07, -9.847029102189422e-07, -1.020906607589596e-06, -1.0397852019794413e-06, -1.0503983481720282e-06, -1.0568565057663241e-06, -1.0609370911617319e-06, -1.063479165157886e-06, -1.064946476954549e-06, -1.065629979251558e-06, -1.0657254460487986e-06], [-9.644814538009342e-08, -3.2777971320025315e-07, -5.800693576147437e-07, -7.760068949854567e-07, -8.988164021104237e-07, -9.656238791676696e-07, -9.99447686383343e-07, -1.0167162519274506e-06, -1.026182233965467e-06, -1.031775122536986e-06, -1.0351726529439026e-06, -1.037155489766853e-06, -1.0381498483537125e-06, -1.0384209342565017e-06, -1.0381462246027828e-06], [-9.637220920879741e-08, -3.268533837722219e-07, -5.769263330088478e-07, -7.698977263021968e-07, -8.89992276658216e-07, -9.547961738888183e-07, -9.872693394566582e-07, -1.0036240453676922e-06, -1.0124388313655997e-06, -1.0175405258869527e-06, -1.0205503018268975e-06, -1.02221568085693e-06, -1.0229415732268453e-06, -1.0229785699704275e-06, -1.0224937620506454e-06]], [[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]]]

Example: Computing derivative maps: MT(s/d)R, ihMT, ihMTR, BP, BPR

data = CompositeDictionary(data)[Signal.ALL]

print(data)

Shape: (4, 3, 15)
 MTs_Positive = [[[0.9904119271169727, 0.9655424694671243, 0.9341213987242093, 0.9041729161509892, 0.8799180451323365, 0.8620435041515132, 0.8493879317304119, 0.8403816232949561, 0.8337430229195211, 0.8286169162486072, 0.8244773077364871, 0.8210009721635665, 0.8179803203768445, 0.8152749136781585, 0.8127858356904707], [0.9891476708545726, 0.9610182930764716, 0.9255194819398096, 0.891732820544455, 0.8644102616095338, 0.8443035052406905, 0.8300859993177455, 0.819980260111795, 0.8125395776275807, 0.8068002471082846, 0.8021702844624238, 0.798286264859583, 0.7949149605775017, 0.791898685726215, 0.7891264343424913], [0.9884186831603747, 0.958429788732002, 0.9206053774856128, 0.8846302555401689, 0.8555589777723599, 0.8341800134454235, 0.8190724345508836, 0.8083402291830004, 0.8004425294958325, 0.7943537954853821, 0.7894444370267739, 0.7853281216347682, 0.7817570126546789, 0.7785635978130145, 0.7756299842592068]], [[0.09718718859546474, 0.08998526891322932, 0.08109632763654628, 0.07287826950612493, 0.06645477196003134, 0.061908707160867466, 0.05883530916592035, 0.05675875602583942, 0.05531239149431819, 0.054261820655362177, 0.053468484941771074, 0.05285026085827932, 0.05235588104203463, 0.05195131608488517, 0.051612878104255196], [0.09707811652145655, 0.08961427727677267, 0.08043859015572082, 0.07199433033370375, 0.0654216233019112, 0.06078446638382176, 0.0576553185249797, 0.055542650558678276, 0.054070916555631475, 0.05300101817612125, 0.05219188865998344, 0.051559996863470084, 0.05105323301549308, 0.05063703436816234, 0.05028736079533554], [0.09701551003297565, 0.08940314542711797, 0.08006484286733835, 0.07149229713596875, 0.06483497109026345, 0.06014615993562433, 0.05698540396751248, 0.05485226359631093, 0.05336615005329562, 0.05228529717352547, 0.051467215755083666, 0.05082757651596733, 0.050313792160147565, 0.04989099770464293, 0.0495349534846862]], [[7.85659478087599e-08, 2.758856319166583e-07, 5.098981790091306e-07, 7.12816564281641e-07, 8.570755165583811e-07, 9.463725877239521e-07, 9.969169488141067e-07, 1.0245452926868544e-06, 1.040003536577961e-06, 1.0491997709711667e-06, 1.0550001528657403e-06, 1.0587506575612366e-06, 1.0611281517573699e-06, 1.062519279553949e-06, 1.0631716136508386e-06], [7.847840784372391e-08, 2.747563213369932e-07, 5.057914448227987e-07, 7.042282819774126e-07, 8.438325989730908e-07, 9.292810147600962e-07, 9.77018667006242e-07, 1.0026843197358882e-06, 1.0167444875816832e-06, 1.0248974787751968e-06, 1.029881422408391e-06, 1.0329676039705316e-06, 1.0347871223880494e-06, 1.0356963292813289e-06, 1.0359215142279597e-06], [7.842818201228824e-08, 2.7411395651770343e-07, 5.034590725799817e-07, 6.993530062936996e-07, 8.36316385241668e-07, 9.195810592700463e-07, 9.657259982615667e-07, 9.902777363751534e-07, 1.0035443378549497e-06, 1.0111051269720392e-06, 1.0156256031870495e-06, 1.0183346718254132e-06, 1.0198374566901852e-06, 1.0204731161974005e-06, 1.020455858789017e-06]], [[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]]]
      MTd_ALT = [[[0.9890619026436411, 0.9586620802065079, 0.9149814461905554, 0.865511229991122, 0.816712480382682, 0.7728214665116144, 0.7358283754360964, 0.7060751212820418, 0.6829455270778247, 0.6653962783143583, 0.652289946989293, 0.6425749373513815, 0.6353651817157857, 0.62995907290954, 0.6258249320143213], [0.9876197265979273, 0.9532388192857096, 0.9039108171141876, 0.848163379689076, 0.7933176746591076, 0.7441341089047052, 0.7028080410840449, 0.6696699927989564, 0.6439817063412371, 0.6245411186766746, 0.6100561217084498, 0.5993423678568492, 0.5914079417587325, 0.5854708899163796, 0.5809406109531191], [0.9867892595404432, 0.9501376134234931, 0.897589394993986, 0.8382643245445011, 0.779974636518952, 0.72777948165836, 0.6839904715510128, 0.6489306579830537, 0.621791318594062, 0.6012793223320665, 0.5860141317157631, 0.5747357103937937, 0.5663919282555425, 0.5601552075638447, 0.5554015369930545]], [[0.09678480031832469, 0.08796295494947505, 0.07559015684266313, 0.06203127411241695, 0.049161665327874075, 0.038053367276455606, 0.02907426244305775, 0.02214682514394393, 0.016982266087555174, 0.013230893295917206, 0.010559979379180415, 0.008686534855099296, 0.007385929657335693, 0.006488484628511573, 0.0058707050261330865], [0.09666072198626005, 0.08752501559751598, 0.07478403465534399, 0.0609333729310343, 0.04791559002726624, 0.036800766554530386, 0.02791463530811409, 0.02112939985880512, 0.016116656301583297, 0.012502998208447054, 0.00994550391879868, 0.008159746843565014, 0.006924099227243823, 0.006073399589411938, 0.0054886052973011044], [0.09658960767272691, 0.08727592634915408, 0.07432615532665907, 0.060310032489786954, 0.04720824897981302, 0.03608978168608337, 0.02725644541125285, 0.020551915997791704, 0.01562531383187201, 0.012089783925800901, 0.009596628391503317, 0.007860610923990608, 0.0066618099578121415, 0.005837627827800929, 0.005271547427536673]], [[-1.63502427e-08, -5.94163327046625e-08, -1.1434222719905716e-07, -1.646262732855085e-07, -1.9885094027317485e-07, -2.1337497566217497e-07, -2.1089053085298054e-07, -1.9713866204564438e-07, -1.7801121923998555e-07, -1.579791099678627e-07, -1.39722132466285e-07, -1.2443456016512617e-07, -1.1233722696427511e-07, -1.0313364506364476e-07, -9.632331156316956e-08], [-1.6329284803241805e-08, -5.912064724461819e-08, -1.1312386217982902e-07, -1.617162463951258e-07, -1.938192895547646e-07, -2.0636576219019206e-07, -2.0249910896970819e-07, -1.8810613294935146e-07, -1.6896419289478428e-07, -1.4931545277870064e-07, -1.3161947861499954e-07, -1.1691542131920032e-07, -1.0533905884325852e-07, -9.656077630589567e-08, -9.007756999900981e-08], [-1.6317273148300825e-08, -5.895247439314674e-08, -1.1243187276481404e-07, -1.6006422329024707e-07, -1.9096342390084073e-07, -2.0238792776413452e-07, -1.977371401448123e-07, -1.8298041937949514e-07, -1.6383007614624097e-07, -1.4439849992067847e-07, -1.2702037909138817e-07, -1.1264694126460691e-07, -1.0136577009950164e-07, -9.282848610616745e-08, -8.65306709023058e-08]], [[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]]]
          MT0 = [[[0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692, 0.9999999989204692], [0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952, 0.9999995770434952], [0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643, 0.9999915704930643]], [[0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687, 0.09999999989204687], [0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389, 0.09999995833647389], [0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301, 0.09999917581869301]], [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]]]
       MTd_CM = [[[0.9890511437555202, 0.9585304667397114, 0.9144141041850081, 0.864013482937054, 0.8137538276405042, 0.7679955985379745, 0.7289400438974355, 0.6971379704689502, 0.6721262525047292, 0.6529445530719407, 0.6384762414103742, 0.6276444967968501, 0.6195108267449865, 0.6133128732473258, 0.6084655557340882], [0.9876077025328194, 0.9530906201712053, 0.9032718844068274, 0.8464795708553651, 0.7900000724734222, 0.7387389578144742, 0.6951310793914648, 0.6597396576780591, 0.6319934840904651, 0.6107782346944346, 0.5948208466850755, 0.5829061660457171, 0.573982601065379, 0.5672002640989495, 0.5619093312964443], [0.9867765047840469, 0.9499799223401729, 0.8969095856231164, 0.8364744180648209, 0.776452591231748, 0.7220604876835516, 0.6758654708629336, 0.6384368151952026, 0.6091407085542551, 0.5867743375982473, 0.5699751044930514, 0.5574489271087275, 0.548079853820118, 0.5409682964400399, 0.535427733039411]], [[0.09678606410675371, 0.08794114969699383, 0.07546269308860175, 0.061673293244534896, 0.04845368390448313, 0.036923270475384795, 0.027511271698221023, 0.020191133575859943, 0.014704869217001447, 0.010714183693309178, 0.007882869097867763, 0.005914455058724211, 0.004565503330603097, 0.0036466692909634195, 0.003017670254949276], [0.0966618723312271, 0.08750191094036902, 0.07465219422607802, 0.060568032416699856, 0.047202020767094295, 0.03567569118984325, 0.026376735955096698, 0.019225397482187812, 0.013919522511104848, 0.010093000926643312, 0.00739692187483801, 0.005532626457094636, 0.004260251223865156, 0.003396226552536453, 0.0028060940106509774], [0.0965906928990001, 0.08725208202976605, 0.0741918278913935, 0.05994051260133459, 0.046491508302108124, 0.034967559527911515, 0.02573279197249816, 0.018677253500936155, 0.013473731693254904, 0.009740342955825373, 0.0071209798067696254, 0.005315749610931629, 0.004086820641347773, 0.003253899715454325, 0.002685830915974676]], [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]]]
 MTs_Negative = [[[0.9882042431528718, 0.9586237999811815, 0.9234543195593683, 0.8924193839506441, 0.8692293711397743, 0.8532848059005678, 0.8424936006498276, 0.8349476457763447, 0.8293803867609938, 0.8250485625349024, 0.821519285161347, 0.8185262809149617, 0.8158952094878015, 0.8135066290292565, 0.8112762889464699], [0.9866494190429023, 0.9531971912915326, 0.9134784226965905, 0.8784857025462931, 0.8523802912508479, 0.8344574577666612, 0.8223432048760102, 0.8138820360371006, 0.8076463435487572, 0.8027995564125798, 0.7988549616467704, 0.7955134229624313, 0.7925792080496539, 0.7899182888184633, 0.7874361697182177], [0.9857546814736469, 0.9500939922966561, 0.9077808731926106, 0.8705317286077249, 0.8427646004441591, 0.8237144032721808, 0.8108462618474787, 0.8018636212134189, 0.7952470760064906, 0.7901068783654764, 0.7859256429277812, 0.78238550806491, 0.7792785535519092, 0.7764624421071725, 0.7738368430138691]], [[0.09653940116469611, 0.0879957764806405, 0.07811431864941505, 0.06969570713218629, 0.06365497743205933, 0.059688579450824425, 0.05713928413991892, 0.05545356199253955, 0.05428188281972924, 0.05342804918949153, 0.052782304391137666, 0.05227917836481488, 0.0518766377254387, 0.05154622191251315, 0.05126799943031356], [0.09640584932412734, 0.08755738558513318, 0.07737083733784009, 0.06873609146694235, 0.0625662850203476, 0.058526271561102995, 0.05593310837172315, 0.05421877768729831, 0.05302653380725601, 0.052156605902198255, 0.05149735907420318, 0.05098225490295446, 0.05056860973496116, 0.05022754725748979, 0.04993886071597819], [0.09632936219937638, 0.08730803379523076, 0.07694846496623386, 0.06819114366111316, 0.06194813966966818, 0.05786638677962748, 0.05524835581417994, 0.05351781017334951, 0.05231391135039056, 0.05143486193556922, 0.05076796208789716, 0.05024606778326904, 0.04982612687774832, 0.04947902754827611, 0.04918440718098613]], [[-9.658079450847436e-08, -3.2940915011864785e-07, -5.856047075087526e-07, -7.867699564766618e-07, -9.143645103328844e-07, -9.847029102189422e-07, -1.020906607589596e-06, -1.0397852019794413e-06, -1.0503983481720282e-06, -1.0568565057663241e-06, -1.0609370911617319e-06, -1.063479165157886e-06, -1.064946476954549e-06, -1.065629979251558e-06, -1.0657254460487986e-06], [-9.644814538009342e-08, -3.2777971320025315e-07, -5.800693576147437e-07, -7.760068949854567e-07, -8.988164021104237e-07, -9.656238791676696e-07, -9.99447686383343e-07, -1.0167162519274506e-06, -1.026182233965467e-06, -1.031775122536986e-06, -1.0351726529439026e-06, -1.037155489766853e-06, -1.0381498483537125e-06, -1.0384209342565017e-06, -1.0381462246027828e-06], [-9.637220920879741e-08, -3.268533837722219e-07, -5.769263330088478e-07, -7.698977263021968e-07, -8.89992276658216e-07, -9.547961738888183e-07, -9.872693394566582e-07, -1.0036240453676922e-06, -1.0124388313655997e-06, -1.0175405258869527e-06, -1.0205503018268975e-06, -1.02221568085693e-06, -1.0229415732268453e-06, -1.0229785699704275e-06, -1.0224937620506454e-06]], [[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]]]
          MTs = [[[0.9893080851349223, 0.962083134724153, 0.9287878591417889, 0.8982961500508166, 0.8745737081360554, 0.8576641550260404, 0.8459407661901197, 0.8376646345356504, 0.8315617048402575, 0.8268327393917548, 0.8229982964489171, 0.819763626539264, 0.8169377649323231, 0.8143907713537075, 0.8120310623184703], [0.9878985449487374, 0.9571077421840021, 0.9194989523182, 0.8851092615453741, 0.8583952764301909, 0.8393804815036758, 0.8262146020968779, 0.8169311480744479, 0.8100929605881689, 0.8047999017604321, 0.8005126230545971, 0.7968998439110071, 0.7937470843135778, 0.7909084872723391, 0.7882813020303545], [0.9870866823170108, 0.9542618905143291, 0.9141931253391117, 0.8775809920739469, 0.8491617891082595, 0.8289472083588021, 0.8149593481991811, 0.8051019251982097, 0.7978448027511615, 0.7922303369254293, 0.7876850399772776, 0.783856814849839, 0.7805177831032941, 0.7775130199600935, 0.774733413636538]], [[0.09686329488008043, 0.08899052269693492, 0.07960532314298066, 0.07128698831915561, 0.06505487469604535, 0.060798643305845945, 0.057987296652919636, 0.056106159009189485, 0.054797137157023716, 0.053844934922426854, 0.05312539466645437, 0.0525647196115471, 0.052116259383736666, 0.051748768998699166, 0.05144043876728438], [0.09674198292279194, 0.08858583143095292, 0.07890471374678046, 0.07036521090032305, 0.06399395416112941, 0.059655368972462375, 0.05679421344835142, 0.0548807141229883, 0.05354872518144374, 0.052578812039159754, 0.051844623867093306, 0.05127112588321227, 0.05081092137522712, 0.05043229081282606, 0.05011311075565686], [0.09667243611617601, 0.08835558961117437, 0.0785066539167861, 0.06984172039854095, 0.06339155537996582, 0.059006273357625906, 0.05611687989084621, 0.054185036884830215, 0.052840030701843094, 0.05186007955454734, 0.05111758892149042, 0.05053682214961819, 0.05006995951894794, 0.04968501262645952, 0.049359680332836164]], [[-9.007423349857226e-09, -2.6761759100994767e-08, -3.7853264249811e-08, -3.697669609751036e-08, -2.8644496887251634e-08, -1.9165161247495035e-08, -1.1994829387744721e-08, -7.619954646293448e-09, -5.197405797033628e-09, -3.828367397578691e-09, -2.9684691479958046e-09, -2.3642537983247396e-09, -1.9091625985895277e-09, -1.5553498488045548e-09, -1.2769161989800088e-09], [-8.984868768184756e-09, -2.6511695931629964e-08, -3.7138956395972496e-08, -3.5889306504022094e-08, -2.749190156866648e-08, -1.8171432203786667e-08, -1.1214509688550546e-08, -7.015966095781212e-09, -4.7188731918919194e-09, -3.438821880894619e-09, -2.6456152677557594e-09, -2.0939428981606965e-09, -1.6813629828315622e-09, -1.3623024875864093e-09, -1.1123551874115529e-09], [-8.972013598254583e-09, -2.6369713627259246e-08, -3.6733630214433085e-08, -3.527236000424862e-08, -2.6837945708273973e-08, -1.7607557309385973e-08, -1.0771670597545751e-08, -6.673154496269403e-09, -4.447246755324987e-09, -3.2176994574567292e-09, -2.462349319924008e-09, -1.9405045157583662e-09, -1.5520582683300436e-09, -1.2527268865135004e-09, -1.0189516308141274e-09]], [[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]]]
      ihMT_CM = [[[0.0005138827588042627, 0.007105335968883075, 0.028747509913561453, 0.0685653342275252, 0.12163976099110241, 0.17933711297613186, 0.23400144458536842, 0.28105332813340045, 0.3188709046710565, 0.34777637263962835, 0.3690441100770858, 0.3842382594848279, 0.3948538763746732, 0.40215579621276354, 0.4071310131687642], [0.0005816848318360712, 0.008034244025593607, 0.032454135822745256, 0.07725938138001798, 0.13679040791353736, 0.2012830473784033, 0.26216704541082625, 0.3143829807927776, 0.3561989529954077, 0.3880433341319951, 0.41138355273904326, 0.42798735573058, 0.4395289664963975, 0.44741644634677913, 0.4527439414678205], [0.0006203550659278356, 0.008563936348312318, 0.034567079431990555, 0.08221314801825197, 0.14541839575302284, 0.21377344135050103, 0.2781877546724951, 0.3333302200060142, 0.37740818839381296, 0.4109119986543641, 0.43541987096845225, 0.45281577548222307, 0.46487585856635216, 0.47308944704010725, 0.47861136119425396]], [[0.00015446154665343936, 0.0020987459998821623, 0.008285260108757825, 0.019227390149241436, 0.03320238158312443, 0.0477507456609223, 0.060952049909397225, 0.07183005086665908, 0.08018453588004454, 0.08626150245823536, 0.09048505113717321, 0.09330052910564578, 0.09510151210626713, 0.0962041994154715, 0.0968455370246702], [0.00016022118312969402, 0.00216784098116779, 0.008505039041404872, 0.019594356967246387, 0.033583866788070224, 0.047959355565238254, 0.06083495498650945, 0.07131063328160098, 0.07925840534067778, 0.08497162222503288, 0.0888954039845106, 0.09147699885223526, 0.09310134030272393, 0.09407212852057922, 0.09461403349001177], [0.00016348643435182275, 0.0022070151628166557, 0.008629652050785197, 0.019802415594412717, 0.0338000941557154, 0.04807742765942878, 0.0607681758366961, 0.07101556676778811, 0.07873259801717639, 0.08423947319744393, 0.08799321822944159, 0.09044214507737312, 0.09196627775520033, 0.09286222582201038, 0.09334769883372297]], [[-1.8014846699714453e-08, -5.3523518201989533e-08, -7.5706528499622e-08, -7.395339219502073e-08, -5.728899377450327e-08, -3.833032249499007e-08, -2.3989658775489443e-08, -1.5239909292586895e-08, -1.0394811594067256e-08, -7.656734795157382e-09, -5.936938295991609e-09, -4.728507596649479e-09, -3.818325197179055e-09, -3.1106996976091096e-09, -2.5538323979600175e-09], [-1.7969737536369512e-08, -5.302339186325993e-08, -7.427791279194499e-08, -7.177861300804419e-08, -5.498380313733296e-08, -3.6342864407573335e-08, -2.242901937710109e-08, -1.4031932191562425e-08, -9.437746383783839e-09, -6.877643761789238e-09, -5.291230535511519e-09, -4.187885796321393e-09, -3.3627259656631244e-09, -2.7246049751728185e-09, -2.2247103748231057e-09], [-1.7944027196509166e-08, -5.273942725451849e-08, -7.346726042886617e-08, -7.054472000849724e-08, -5.3675891416547945e-08, -3.5215114618771946e-08, -2.1543341195091503e-08, -1.3346308992538806e-08, -8.894493510649974e-09, -6.4353989149134585e-09, -4.924698639848016e-09, -3.8810090315167325e-09, -3.104116536660087e-09, -2.5054537730270008e-09, -2.037903261628255e-09]], [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]
     ihMT_ALT = [[[0.0004923649825623322, 0.006842109035290145, 0.02761282590246683, 0.06556984011938938, 0.11572245550674687, 0.169685377028852, 0.2202247815080467, 0.26317902650721736, 0.2972323555248655, 0.322872922154793, 0.3414166989192482, 0.3543773783757651, 0.3631451664330747, 0.368863396888335, 0.372412260608298], [0.0005576367016202344, 0.007737845796584875, 0.03117627040802473, 0.0738917637125962, 0.13015520354216648, 0.19049274519794124, 0.24681312202566597, 0.2945223105509829, 0.3322225084938637, 0.36051756616751507, 0.38091300269229467, 0.3951149521083157, 0.4046782851096906, 0.4108751947119189, 0.4146813821544708], [0.0005948455531352703, 0.008248554181671919, 0.03320746069025127, 0.0786333350588917, 0.13837430517861482, 0.2023354534008841, 0.26193775329633673, 0.3123425344303119, 0.3521069683141991, 0.38190202918672567, 0.4033418165230289, 0.41824220891209074, 0.4282517096955032, 0.4347156247924975, 0.43866375328696705]], [[0.0001569891235114751, 0.00205513549491973, 0.00803033260063507, 0.018511428413477332, 0.03178641873634254, 0.04549055205878068, 0.05782606841972377, 0.0679186677304911, 0.07562974213893708, 0.08122808325301929, 0.08513083057454791, 0.08775636951289562, 0.08946065945280195, 0.09052056874037519, 0.09113946748230259], [0.00016252187306378674, 0.0021216316668738744, 0.008241358182872943, 0.018863675938577504, 0.03215672826772634, 0.04570920483586398, 0.05775915628047466, 0.06750262852836636, 0.0748641377597209, 0.0801516276614254, 0.08379823989658926, 0.08622275807929451, 0.0877736442959666, 0.08871778244682825, 0.0892490109167115], [0.0001656568868982078, 0.002159326524040578, 0.00836099718025407, 0.019063375817507985, 0.032366612800305616, 0.04583298334308507, 0.057720868959186725, 0.06726624177407703, 0.07442943373994217, 0.07954059125749288, 0.0830419210599742, 0.08535242245125516, 0.0868162991222716, 0.08769476959731717, 0.08817626581059898]], [[1.4685638700285548e-08, 6.530914720733546e-08, 1.5297792589849232e-07, 2.5529915437599625e-07, 3.4041288677184644e-07, 3.884196288293599e-07, 3.9779140293047164e-07, 3.7903741479870186e-07, 3.4562762688590384e-07, 3.0830148514056804e-07, 2.735073266365784e-07, 2.4414061273360286e-07, 2.2085612873137117e-07, 2.031565904296804e-07, 1.900927907283791e-07], [1.4688832070114098e-08, 6.521790262597646e-08, 1.5196981156771304e-07, 2.516538797822074e-07, 3.3265477597219627e-07, 3.763886599728108e-07, 3.825691985623153e-07, 3.621803337071405e-07, 3.284906394057847e-07, 2.9175326179561204e-07, 2.5794772669448757e-07, 2.2964295684207925e-07, 2.073153917208539e-07, 1.9039694763661853e-07, 1.7793042962319652e-07], [1.4690519100092485e-08, 6.516552153177499e-08, 1.513964851007619e-07, 2.495837265719969e-07, 3.282509563851335e-07, 3.695607409094971e-07, 3.739309390945331e-07, 3.5261452976645147e-07, 3.1876565878183196e-07, 2.823616009264435e-07, 2.491160595429283e-07, 2.214128734976971e-07, 1.996274236623432e-07, 1.831515184393079e-07, 1.7102343854298333e-07]], [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]
           BP = [[[2.151777624193052e-05, 0.0002632269335929305, 0.0011346840110946221, 0.002995494108135821, 0.0059173054843555395, 0.00965173594727986, 0.013776663077321727, 0.017874301626183087, 0.02163854914619101, 0.024903450484835332, 0.027627411157837622, 0.02986088110906282, 0.03170870994159847, 0.03329239932442851, 0.03471875256046619], [2.404813021583685e-05, 0.0002963982290087319, 0.0012778654147205248, 0.003367617667421774, 0.006635204371370884, 0.010790302180462064, 0.015353923385160284, 0.01986067024179472, 0.023976444501544014, 0.02752576796448003, 0.03047055004674859, 0.03287240362226429, 0.03485068138670688, 0.03654125163486022, 0.038062559313349675], [2.5509512792565303e-05, 0.00031538216664039886, 0.001359618741739288, 0.0035798129593602734, 0.007044090574408024, 0.011437987949616923, 0.016250001376158396, 0.020987685575702297, 0.025301220079613884, 0.029009969467638452, 0.03207805444542333, 0.03457356657013233, 0.03662414887084897, 0.03837382224760977, 0.03994760790728691]], [[-2.5275768580357294e-06, 4.361050496243246e-05, 0.0002549275081227542, 0.0007159617357641035, 0.0014159628467818874, 0.002260193602141622, 0.0031259814896734545, 0.003911383136167977, 0.004554793741107455, 0.005033419205216057, 0.005354220562625304, 0.00554415959275017, 0.005640852653465192, 0.005683630675096306, 0.005706069542367621], [-2.3006899340927145e-06, 4.6209314293915726e-05, 0.00026368085853192835, 0.0007306810286688836, 0.0014271385203438874, 0.0022501507293742756, 0.003075798706034784, 0.0038080047532346173, 0.0043942675809568975, 0.004819994563607485, 0.005097164087921338, 0.005254240772940755, 0.005327696006757334, 0.00535434607375097, 0.005365022573300254], [-2.1704525463850377e-06, 4.768863877607776e-05, 0.00026865487053112647, 0.0007390397769047319, 0.0014334813554097853, 0.0022444443163437133, 0.0030473068775093773, 0.003749324993711098, 0.004303164277234213, 0.0046988819399510565, 0.004951297169467383, 0.005089722626117959, 0.005149978632928737, 0.0051674562246932084, 0.0051714330231239945]], [[-3.27004854e-08, -1.18832665409325e-07, -2.2868445439811432e-07, -3.29252546571017e-07, -3.977018805463497e-07, -4.2674995132434995e-07, -4.217810617059611e-07, -3.9427732409128875e-07, -3.560224384799711e-07, -3.159582199357254e-07, -2.7944426493257e-07, -2.4886912033025234e-07, -2.2467445392855023e-07, -2.0626729012728951e-07, -1.9264662312633912e-07], [-3.265856960648361e-08, -1.1824129448923638e-07, -2.2624772435965803e-07, -3.234324927902516e-07, -3.876385791095292e-07, -4.127315243803841e-07, -4.0499821793941637e-07, -3.762122658987029e-07, -3.3792838578956857e-07, -2.986309055574013e-07, -2.632389572299991e-07, -2.3383084263840064e-07, -2.1067811768651703e-07, -1.9312155261179135e-07, -1.8015513999801963e-07], [-3.263454629660165e-08, -1.1790494878629348e-07, -2.2486374552962807e-07, -3.2012844658049415e-07, -3.8192684780168146e-07, -4.0477585552826904e-07, -3.954742802896246e-07, -3.659608387589903e-07, -3.2766015229248194e-07, -2.8879699984135694e-07, -2.5404075818277633e-07, -2.2529388252921383e-07, -2.027315401990033e-07, -1.856569722123349e-07, -1.730613418046116e-07]], [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]
MTsR_Positive = [[[0.9588071813847137, 3.445752949054281, 6.587860026737786, 9.582708287292817, 12.008195391776482, 13.79564949178841, 15.061206735264761, 15.961837579782582, 16.625697618042764, 17.138308285687515, 17.552269137346414, 17.899902695013765, 18.20196787401204, 18.472508544172697, 18.72141634321018], [1.0851910778808929, 3.8981300454418317, 7.448012660553957, 10.826680229118836, 13.558937278236854, 15.569613765549889, 16.9913649591833, 18.00193930720735, 18.746007870337422, 19.319941165015848, 19.782937625429298, 20.17133974999058, 20.50847032079028, 20.810097933494305, 21.087323189120895], [1.157298488724578, 4.156213210934311, 7.938686219955699, 11.536228740009705, 14.44338102265094, 16.581295476909304, 18.092066101414744, 19.165295684999293, 19.955072311143624, 20.563950844734492, 21.054890828977307, 21.466525838058047, 21.82363974636114, 22.14298392244153, 22.436347750734726]], [[2.8128112996186445, 10.01473098962876, 18.90367227590768, 27.1217304152007, 33.545227968228644, 38.09129277230014, 41.164690770565095, 43.241243912887725, 44.68760844597035, 45.738179286060486, 46.53151500050802, 47.149739084667175, 47.64411890144555, 48.048683859031755, 48.38712184002709], [2.9218430323601865, 10.385685386743972, 19.56137633071222, 28.00563967090713, 34.57834944112234, 39.21550829121567, 42.34465745377161, 44.45732630028537, 45.92906091650871, 46.9989597417765, 47.808089595026345, 48.439981654808214, 48.94674571392099, 49.36294453465484, 49.712618253168046], [2.9836903767356944, 10.596117722796578, 19.93449724775462, 28.50711363302598, 35.16449454762032, 39.85334434688299, 43.0141263655694, 45.14728431786004, 46.63341010924633, 47.714271897277285, 48.532360058248784, 49.172004569195614, 49.685793159564895, 50.108591099691125, 50.46463825412194]], [[-inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf], [-inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf], [-inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf]], [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]
MTsR_Negative = [[[1.1795755780331092, 4.137619898395442, 7.654567944373426, 10.758061508596157, 13.077062792186581, 14.671519317828498, 15.750639844067464, 16.505235332230356, 17.061961234366436, 17.495143657443208, 17.848071395179744, 18.147371820141387, 18.410478963141443, 18.6493370092538, 18.872371017773233], [1.335016364713141, 4.680240554734453, 8.652119094160525, 12.151392589230753, 14.761934822921091, 16.554218929397976, 17.76564473084349, 18.61176197260525, 19.23533148518237, 19.720010403798213, 20.114470047218433, 20.44862405698494, 20.742045672367283, 21.008137708031683, 21.256349723039122], [1.423700903038366, 4.989799881193505, 9.221147459771828, 12.946093317717342, 15.722829540591178, 17.627865316301282, 18.91469030607169, 19.812961941464636, 20.474622039625856, 20.988646136696957, 21.406773205071502, 21.76078967554291, 22.071487745874535, 22.353101264211304, 22.615663386810894]], [[3.460598731086577, 12.004223424365307, 21.885681266258104, 30.304292792575026, 36.34502249922312, 40.311420484739884, 42.86071579839743, 44.546437947596594, 45.718117121671774, 46.57195075283121, 47.21769555188219, 47.72082157874811, 48.12336221855885, 48.45377803184109, 48.73200051434104], [3.594110509779725, 12.44257793535742, 22.62913042672747, 31.263879895166312, 37.43368891232105, 41.473704054778416, 44.066868324561945, 45.781199723237684, 46.97344410001103, 47.84337236751158, 48.50261947017224, 49.01772385603161, 49.431369196364145, 49.772431815934226, 50.06111847772287], [3.66984386548377, 12.691246622344536, 23.050900833674916, 31.808294315595674, 38.05134976113661, 42.1331362924989, 44.75118883544611, 46.48174873922777, 47.685657484577554, 48.56471414441956, 49.2316194886008, 49.75351809461968, 50.173462461243375, 50.52056465146694, 50.81518744698293]], [[inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf], [inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf], [inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf]], [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]
         MTsR = [[[1.0691913797089114, 3.7916864237248546, 7.121213985555585, 10.170384897944487, 12.542629091981524, 14.233584404808454, 15.405923289666106, 16.233536456006476, 16.843829426204593, 17.316725971565376, 17.700170266263086, 18.023637257577576, 18.306223418576735, 18.56092277671324, 18.796893680491706], [1.2101037212970311, 4.2891853000881355, 8.050065877357255, 11.489036409174801, 14.16043605057898, 16.06191634747394, 17.378504845013396, 18.3068506399063, 18.99066967775991, 19.519975784407038, 19.94870383632386, 20.309981903487767, 20.62525799657878, 20.909117820763015, 21.171836456080015], [1.2904996958814792, 4.573006546063908, 8.57991683986377, 12.24116102886353, 15.083105281621059, 17.1045803966053, 18.50337820374321, 19.489128813231957, 20.214847175384747, 20.776298490715718, 21.230832017024397, 21.613657756800492, 21.947563746117837, 22.24804259332643, 22.526005568772803]], [[3.1367050153526037, 11.009477206997033, 20.3946767710829, 28.71301160388785, 34.945125233725875, 39.20135662852001, 42.01270328448126, 43.89384093024216, 45.20286278382106, 46.15506501944585, 46.874605276195105, 47.43528033170764, 47.8837405600022, 48.25123094543642, 48.55956117718405], [3.2579767710699485, 11.414131661050703, 21.095253378719846, 29.634759783036728, 36.006019176721686, 40.34460617299705, 43.20576288916678, 45.119263011761525, 46.45125250825987, 47.42116605464405, 48.155354532599304, 48.728852755419915, 49.18905745514257, 49.56768817529454, 49.88686836544546], [3.326767121109725, 11.64368217257055, 21.49269904071477, 30.157703974310834, 36.607922154378464, 40.993240319690955, 43.88265760050775, 45.81451652854391, 47.15953379691194, 48.13949302084843, 48.88198977342479, 49.462761331907636, 49.929627810404135, 50.31457787557903, 50.639912850552435]], [[inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf], [inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf], [inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf]], [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]
      MTdR_CM = [[[1.0948855176768575, 4.14695322255254, 8.558589482785365, 13.598651613021659, 18.624617148102345, 23.200440063295048, 27.105995531565128, 30.286202877846776, 32.787374676968966, 34.70554462231854, 36.152375790037105, 37.23555025255883, 38.04891725862324, 38.6687126090584, 39.15344436090544], [1.2391879751902053, 4.6908976712746835, 9.672773354829204, 15.35200711204429, 20.999959339076696, 26.126072973094608, 30.48686265981992, 34.02600632806433, 36.80062486036668, 38.92215069728288, 40.51789017314718, 41.7093587410224, 42.601715616484356, 43.27994959999078, 43.809043104024845], [1.321517710644443, 5.0012069729980055, 10.308285380757894, 16.351853080883288, 22.35408636005762, 27.793342565125187, 32.412883187636695, 36.155780305187015, 39.08541566466335, 41.32207161417097, 43.00200908573512, 44.254637383206436, 45.19155260980079, 45.90271434255136, 46.45677535307537]], [[3.213935788762697, 12.05885020807095, 24.53730682993391, 38.32670668888685, 51.5463160432096, 63.076729484755376, 72.4887282720797, 79.80886640234309, 85.29513076712419, 89.28581629512452, 92.11713089362243, 94.08554493489095, 95.4344966644683, 96.35333070509989, 96.98232974179305], [3.3380873960117157, 12.498052603234285, 25.347774671172587, 39.43194234851163, 52.79795956687127, 64.32429394639965, 73.62325305542045, 80.77459450783036, 86.08047168952885, 89.90699486825486, 92.60307504334223, 94.46737123781713, 95.73974700116322, 96.60377203247522, 97.19390482023083], [3.4085110120035154, 12.74719884895704, 25.807560628389993, 40.058993376093596, 53.50810852041303, 65.03215227362406, 74.26699594089266, 81.32259256336312, 86.52615725785188, 90.25957676542711, 92.87896150296221, 94.68420657729266, 95.91314567556284, 96.74607346629143, 97.31414694772653]], [[nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan], [nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan], [nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan]], [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]
     MTdR_ALT = [[[1.0938096288635961, 4.133791875858677, 8.501855282169387, 13.448876907453197, 18.328751873565167, 22.7178532654101, 26.417162376955417, 29.392487795572833, 31.705447218491443, 33.460372096732584, 34.771005230653984, 35.74250619549389, 36.463481759831794, 37.00409264103997, 37.41750673100813], [1.237985568170842, 4.676077753556058, 9.608880057069086, 15.183626157455379, 20.668198980187967, 25.58655763588, 29.719166165859676, 33.03297239596442, 35.60180212823961, 37.5458617169485, 38.99436202642361, 40.065737864729044, 40.85918081013258, 41.45288624547944, 41.90591433341667], [1.320242224253093, 4.985437731739054, 10.240303870620323, 16.172860924099652, 22.001878862401696, 27.221438346773766, 31.600376269796087, 35.10638718053528, 37.82034399675226, 39.871560913699035, 41.39809284324086, 42.52594448267102, 43.36032972995236, 43.98400705641449, 44.459378120637204]], [[3.2151995771930757, 12.037044955566174, 24.40984307573494, 37.968725820618346, 50.838334619054365, 61.94663268246459, 70.92573752555568, 77.85317483214789, 83.01773389411194, 86.76910668979963, 89.44002060941976, 91.31346513552332, 92.61407033469096, 93.5115153644839, 94.1292949675293], [3.3392377414580494, 12.474947936461106, 25.215934186977236, 39.06660168196339, 52.08439000940109, 63.19921811296625, 72.0853530616597, 78.87059133793818, 83.8833369836466, 87.49699658236085, 90.05449193755197, 91.84024975679532, 93.07589788793109, 93.92659788019458, 94.51139241595145], [3.4095962472210175, 12.723354333046956, 25.673232086013698, 39.689470442102284, 52.79136193541677, 63.90992086623073, 72.74332994436764, 79.44791461576236, 84.37455738615083, 87.9101164316387, 90.4032925142275, 92.13932428978958, 93.33813513634296, 94.1623240591652, 94.72840912499676]], [[inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf], [inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf], [inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf]], [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]
     ihMTR_CM = [[[0.051388275935901506, 0.7105335976553505, 2.8747509944595278, 6.85653343015436, 12.163976112241627, 17.93371131697318, 23.400144483798023, 28.10533284368062, 31.88709050152875, 34.777637301506374, 36.90441104754803, 38.4238259899625, 39.48538768009301, 40.21557966469032, 40.71310136082747], [0.058168507786355864, 0.8034247423730816, 3.2454149549438913, 7.725941405738971, 13.679046576995464, 20.12831325124135, 26.216715629613034, 31.438311376316058, 35.61991036521356, 38.80434982575168, 41.13837267364664, 42.79875367506926, 43.952915239811155, 44.74166355845555, 45.27441329588965], [0.06203602952592472, 0.8564008538681692, 3.4567370817882614, 8.221384104039524, 14.541962156873145, 21.37752433703977, 27.819009967786982, 33.333302983910116, 37.74113697855722, 41.0915462469105, 43.54235413742143, 45.281959252811895, 46.487977727365895, 47.30934349844988, 47.861539568605146]], [[0.15446154682018545, 2.0987460021478244, 8.285260117702023, 19.227390169998007, 33.202381618967436, 47.750745712470724, 60.952049975196864, 71.83005094420187, 80.18453596660625, 86.26150255135734, 90.48505123485467, 93.3005292063666, 95.10151220893219, 96.20419951932695, 96.845537129218], [0.1602212498835163, 2.1678418843671596, 8.505042584905508, 19.594365130949818, 33.58388078029916, 47.959375546805205, 60.83498033250736, 71.31066299213767, 79.25843836253794, 84.97165762722163, 88.89544102148587, 91.47703696479444, 93.10137909204131, 94.07216771436137, 94.61407290957074], [0.16348778178755946, 2.207033352772988, 8.629723175350453, 19.802578803565517, 33.80037273206915, 48.07782390786624, 60.768676680769815, 71.01615206963841, 78.73324692187991, 84.24016748915736, 87.99394345907486, 90.44289049077004, 91.96703573031742, 92.8629911814248, 93.3484681943482]], [[-inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf], [-inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf], [-inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf]], [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]
    ihMTR_ALT = [[[0.04923649830938554, 0.6842109042676413, 2.761282593227573, 6.5569840190174045, 11.572245563167284, 16.968537721203262, 22.022478174578616, 26.317902679132725, 29.7232355845737, 32.28729225033443, 34.14166992878181, 35.437737875832646, 36.31451668251012, 36.88633972865345, 37.24122610103286], [0.05576369374764044, 0.7737849069358471, 3.117628359423667, 7.3891794965611535, 13.015525859217973, 19.049282576812104, 24.681322641692553, 29.45224351211626, 33.222264900959416, 36.05177186508293, 38.0913163801995, 39.51151192248255, 40.46784562710761, 41.087536849432865, 41.468155754673305], [0.05948505674322543, 0.8248623713502722, 3.3207740615131103, 7.863399790472243, 13.837547161561254, 20.23371590033693, 26.193996132105745, 31.23451673460664, 35.21099364273503, 38.190524845966635, 40.33452165243291, 41.824573451741074, 42.82553196766907, 43.47192892617614, 43.86674510372881]], [[0.15698912368094978, 2.055135497138313, 8.030332609304066, 18.511428433461, 31.786418770656976, 45.49055210788915, 57.82606848214883, 67.91866780381143, 75.62974222058176, 81.22808334070754, 85.13083066644931, 87.75636960763136, 89.46065954937752, 90.52056883809497, 91.13946758069049], [0.16252194077615795, 2.121632550820806, 8.24136161651479, 18.863683797853326, 32.156741665358794, 45.7092238799384, 57.759180344985836, 67.50265665235334, 74.86416895077346, 80.15166105543362, 83.79827480990535, 86.2227940027508, 87.77368086557703, 88.71781940980009, 89.24904810101197], [0.1656582522225561, 2.1593443209528247, 8.361066090597854, 19.06353293558289, 32.366879562076626, 45.83336109307957, 57.721344687719785, 67.2667961744369, 74.43004717847779, 79.54124682158053, 83.0426054816054, 85.35312591576388, 86.81701465187764, 87.69549236717233, 88.17699254888863]], [[inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf], [inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf], [inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf]], [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]
          BPR = [[[0.0021517776265159625, 0.02632269338770921, 0.11346840123195485, 0.29954941113695494, 0.5917305490743454, 0.9651735957699208, 1.3776663092194061, 1.7874301645478947, 2.1638549169550494, 2.490345051171938, 2.7627411187662267, 2.9860881141298563, 3.1708709975829, 3.3292399360368687, 3.471875259794616], [0.0024048140387154253, 0.02963983543723439, 0.12778659552022428, 0.33676190917781745, 0.6635207177774921, 1.079030674429249, 1.53539298792048, 1.9860678641997942, 2.3976454642541465, 2.7525779606687566, 3.0470562934471386, 3.287241752586711, 3.4850696127035508, 3.6541267090226826, 3.8062575412163535], [0.002550972782699295, 0.03153848251789702, 0.13596302027515123, 0.35798431356728144, 0.704414995311891, 1.1438084367028427, 1.6250138356812383, 2.098786249303475, 2.5301433358221863, 2.9010214009438653, 3.207832484988514, 3.457385801070823, 3.6624457596968303, 3.837414572273729, 3.9947944648763394]], [[-0.0025275768607643276, 0.043610505009511365, 0.25492750839795647, 0.7159617365370066, 1.4159628483104636, 2.2601936045815716, 3.1259814930480494, 3.9113831403904378, 4.554793746024497, 5.03341921064979, 5.354220568405353, 5.544159598735264, 5.640852659554668, 5.683630681231963, 5.706069548527502], [-0.002300690892641665, 0.04620933354635347, 0.2636809683907174, 0.7306813330964915, 1.4271391149403652, 2.2501516668668025, 3.0757999875215143, 3.8080063397843325, 4.394269411764481, 4.819996571788015, 5.097166211580513, 5.254242962043643, 5.327698226464276, 5.354348304561273, 5.365024808558766], [-0.0021704704349966367, 0.047689031820163506, 0.2686570847525989, 0.7390458679826258, 1.4334931699925293, 2.244462814786675, 3.0473319930500256, 3.7493558952015187, 4.3031997434021, 4.698920667576829, 4.951337977469439, 5.089764575006156, 5.150021078439771, 5.1674988142524745, 5.1714756454595605]], [[-inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf], [-inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf], [-inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf]], [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]

Example: $\mathrm{B}_1^+$ correction

Manual computation

# Initialize variables
flipAngle_nominal = simulator.pulse.flipAngle
relative_range = np.linspace(.1, 1.5, 141)
ihMTR_values = []

# Simulate ihMTR throughout the interpolation range
for value in relative_range:
    simulator.pulse.flipAngle = flipAngle_nominal * value
    out = simulator.SteadyState()
    ihMTR_values.append( 100 * (out['MTs_Positive'][0] + out['MTs_Negative'][0] - 2 * out['MTd_CM'][0]) / out['MT0'][0] )
simulator.pulse.flipAngle = flipAngle_nominal

# Generate the interpolator of ihMTR_CM dependency on B1+
interpolator = sp.interpolate.PchipInterpolator(flipAngle_nominal * relative_range, ihMTR_values)

# Correct fake data
FA = np.random.random((2, 2, 3)) * flipAngle_nominal * (max(relative_range) - min(relative_range)) + flipAngle_nominal * min(relative_range)
fake_data = {Signal.ihMTR_CM: interpolator(FA).reshape((2, 2, 3))}
corrected = corrector.apply({'flipAngle': FA}, fake_data)

# Check everything
print('Shape')
print('fake_data:', fake_data[Signal.ihMTR_CM].shape)
print('corrected:', corrected[Signal.ihMTR_CM].shape)

print()

print('Value pairs (original, corrected)')
print(*zip(fake_data[Signal.ihMTR_CM].flatten(), corrected[Signal.ihMTR_CM].flatten()), sep='\n')

Shape
fake_data: (2, 2, 3)
corrected: (2, 2, 3)

Value pairs (original, corrected)
(np.float64(30.70875390364706), np.float64(34.77763730150377))
(np.float64(16.229276149958746), np.float64(34.77763730150377))
(np.float64(0.15692445447949777), np.float64(34.777637301503766))
(np.float64(23.9726161598162), np.float64(34.77763730150377))
(np.float64(27.30581708219862), np.float64(34.777637301503766))
(np.float64(13.536236614553392), np.float64(34.777637301503766))
(np.float64(11.18258008130534), np.float64(34.777637301503766))
(np.float64(26.149900391437274), np.float64(34.777637301503766))
(np.float64(18.415062042792044), np.float64(34.777637301503766))
(np.float64(35.24803762878265), np.float64(34.77763730150378))
(np.float64(13.101720819282113), np.float64(34.777637301503766))
(np.float64(22.08440262247551), np.float64(34.777637301503766))

Using ihmt.corrector.Corrector

# Generate the interpolator of ihMTR_CM dependency on B1+
interpolant = corrector.interpolants[Signal.ihMTR_CM]

# Correct fake data
FA = np.random.random((2, 2, 3)) * (max(corrector.ranges['flipAngle']) - min(corrector.ranges['flipAngle'])) + min(corrector.ranges['flipAngle'])
fake_data = {Signal.ihMTR_CM: interpolant(FA).reshape((2, 2, 3))}
corrected = corrector.apply({'flipAngle': FA}, fake_data)

# Checking everything
print('Shape')
print('fake_data:', fake_data[Signal.ihMTR_CM].shape)
print('corrected:', corrected[Signal.ihMTR_CM].shape)

print()

print('Value pairs (original, corrected)')
print(*list(zip(fake_data[Signal.ihMTR_CM].flatten(), corrected[Signal.ihMTR_CM].flatten())), sep='\n')

Shape
fake_data: (2, 2, 3)
corrected: (2, 2, 3)

Value pairs (original, corrected)
(np.float64(11.087388454074548), np.float64(34.77763730150377))
(np.float64(25.582405678646996), np.float64(34.77763730150377))
(np.float64(18.50520934637333), np.float64(34.77763730150377))
(np.float64(13.195781899906676), np.float64(34.77763730150377))
(np.float64(25.04114139638252), np.float64(34.77763730150377))
(np.float64(13.199758932822961), np.float64(34.77763730150377))
(np.float64(33.56556649210249), np.float64(34.77763730150377))
(np.float64(38.946409741687404), np.float64(34.77763730150377))
(np.float64(1.5358779329656485), np.float64(34.77763730150377))
(np.float64(33.49510903339841), np.float64(34.77763730150377))
(np.float64(24.12238977779215), np.float64(34.77763730150377))
(np.float64(16.48812021531795), np.float64(34.77763730150377))

Visualization

Example: $\mathrm{B}_1^+$ correction

1-Dim $\mathrm{B}_1^+$ correction

# 1D plotting of ihMTR = f(B1+)
x = corrector.ranges['flipAngle']
xb = (x / corrector.simulator.pulse.flipAngle) * simulator.pulse.b1RMS

fig, ax = plt.subplots(1, 1, figsize=(10, 5))
ax.plot(x, ihMTR_values,'k', label=f'Interpolator')

ax.scatter(FA.flatten(), fake_data[Signal.ihMTR_CM].flatten(), label='Random data', alpha=.5)
ax.scatter(FA.flatten(), corrected[Signal.ihMTR_CM].flatten(), label='Corrected data', alpha=.5)

ax.vlines(corrector.simulator.pulse.flipAngle, 0, 50, 'k', 'dashed')
ax.hlines(corrector.nominals[Signal.ihMTR_CM], min(x), max(x), 'k', 'dashed')

ax.set_xlabel('Flip angle [°]')
ax.set_xlim(min(x), max(x))
ax.set_ylim(0, 50)
ax.set_ylabel('ihMTR [%]')

ax.legend()
ax.grid()

fig.suptitle(r'Simulated $\mathrm{B}_1^+$ dependencies of ihMTR')

ax2 = ax.twiny()
ax2.set_xlim(min(xb) * 1e6, max(xb) * 1e6)
ax2.set_xlabel(r'$\mathrm{B}_1^\mathrm{+,rms}$ [µT]')
ax2.grid(linestyle='dotted')

fig.tight_layout()
plt.show()

N-Dim $\mathrm{B}_1^+$ correction

##### Create the data

# Create an N-Dim corrector and retrieve the ihMTR_CM interpolant
nd_corrector = Corrector(simulator, {'poolFree_T1': np.array([.5, 1., 2., 4, 6, 8.]), 'flipAngle': simulator.pulse.flipAngle * np.linspace(.1, 1.5, 141)})
nominals = nd_corrector.nominals
interp = nd_corrector.interpolants[Signal.ihMTR_CM]

# Some fine tuning for the plot
test_interpolate_for_T1 = 1.25
x = nd_corrector.mesh['flipAngle'].T.squeeze()
ranges = np.vstack([test_interpolate_for_T1 * np.ones_like(x), x]).T

# Creating fake data to correct
shape = (5, 5, 5)
T1 = np.random.random(shape) * (max(nd_corrector.ranges['poolFree_T1']) - min(nd_corrector.ranges['poolFree_T1'])) + min(nd_corrector.ranges['poolFree_T1'])
B1 = np.random.random(shape) * (max(nd_corrector.ranges['flipAngle']) - min(nd_corrector.ranges['flipAngle'])) + min(nd_corrector.ranges['flipAngle'])
params = {'flipAngle': B1, 'poolFree_T1': T1}
data = {Signal.ihMTR_CM: interp(np.vstack([T1.flatten(), B1.flatten()]).T).reshape(shape)}
corrected = nd_corrector.apply(params, data)

##### Visualize the results

# 2D plotting of ihMTR = f(B1+) for various values of T1_water
fig, ax = plt.subplots(1, 1, figsize=(10, 5))
ax.plot(x, nd_corrector.simulated[Signal.ihMTR_CM].T, '.', label=nd_corrector.ranges['poolFree_T1'])
ax.plot(x, interp(ranges), color='k', label=r'Interp[$\mathrm{T}_1$=' + f'{test_interpolate_for_T1}]')

ax.scatter(B1.flatten(), data[Signal.ihMTR_CM].flatten(), label='Random data', alpha=.5)
ax.scatter(B1.flatten(), corrected[Signal.ihMTR_CM].flatten(), label='Corrected data', alpha=.5)

ax.vlines(simulator.pulse.flipAngle, 0, 50, 'k', 'dashed')
ax.hlines(nominals[Signal.ihMTR_CM], min(nd_corrector.ranges['flipAngle']), max(nd_corrector.ranges['flipAngle']), 'k', 'dashed')

ax.legend(title=r'$\mathrm{T}_1^{water}$ [s]')
ax.set_xlabel('Flip angle [°]')
ax.set_xlim(min(nd_corrector.ranges['flipAngle']), max(nd_corrector.ranges['flipAngle']))

ax.set_ylim(0, 50)
ax.set_ylabel('ihMTR [%]')

ax.grid()

ax2 = ax.twiny()
ax2.set_xlim(.1e6 * simulator.pulse.b1RMS, 1.5e6 * simulator.pulse.b1RMS)
ax2.set_xlabel(r'$\mathrm{B}_1^\mathrm{+,rms}$ [µT]')
ax2.grid(linestyle='dotted')

fig.suptitle(r'Simulated $\mathrm{B}_1^+$ dependencies of ihMTR')
fig.tight_layout()
plt.show()

Real-world data

# Preparing variables for correction of real-world data
with open('./examples/example_data_config.yaml') as file:
    real_conf = ya.safe_load(file)

real_pulse = Tukey(**real_conf['pulse'])
real_seq = Sequence(Signal.ihMTR_CM, real_pulse, **real_conf['sequence'])
real_sys = System(real_pulse, **real_conf['system'])
real_sim = Simulator(real_sys, real_seq, export_readMatrix=False, output_vectorSlice=slice(1))

real_data = sp.io.loadmat('./examples/example_data.mat')
real_params = {
    'axial'   : {
        'mask'       : real_data['axial']['mask'][0, 0],
        'flipAngle'  : real_data['axial']['flipAngle'][0, 0],
        'poolFree_T1': real_data['axial']['poolFree_T1'][0, 0],
    },
    'sagittal': {
        'mask'       : real_data['sagittal']['mask'][0, 0],
        'flipAngle'  : real_data['sagittal']['flipAngle'][0, 0],
        'poolFree_T1': real_data['sagittal']['poolFree_T1'][0, 0],
    },
    'coronal' : {
        'mask'       : real_data['coronal']['mask'][0, 0],
        'flipAngle'  : real_data['coronal']['flipAngle'][0, 0],
        'poolFree_T1': real_data['coronal']['poolFree_T1'][0, 0],
    },
}
real_ihMTR = {
    'axial'   : {Signal.ihMTR_CM: real_data['axial']['ihMTR_CM'][0, 0]},
    'sagittal': {Signal.ihMTR_CM: real_data['sagittal']['ihMTR_CM'][0, 0]},
    'coronal' : {Signal.ihMTR_CM: real_data['coronal']['ihMTR_CM'][0, 0]},
}

real_cor1D = Corrector.Simple(real_sim)
real_cor2D = Corrector(real_sim, ranges={'flipAngle': real_pulse.flipAngle * np.linspace(.1, 1.5, 141), 'poolFree_T1': np.arange(1, 4102, 100)})

real_axial    = real_cor1D.apply(real_params['axial'], real_ihMTR['axial'])
real_sagittal = real_cor1D.apply(real_params['sagittal'], real_ihMTR['sagittal'])
real_coronal  = real_cor1D.apply(real_params['coronal'], real_ihMTR['coronal'])

real_cor1D_data = {
    'axial'   : real_axial,
    'sagittal': real_sagittal,
    'coronal' : real_coronal,
}

real_axial    = real_cor2D.apply(real_params['axial'], real_ihMTR['axial'])
real_sagittal = real_cor2D.apply(real_params['sagittal'], real_ihMTR['sagittal'])
real_coronal  = real_cor2D.apply(real_params['coronal'], real_ihMTR['coronal'])

real_cor2D_data = {
    'axial'   : real_axial,
    'sagittal': real_sagittal,
    'coronal' : real_coronal,
}

fig, ax = plt.subplots(3, 5, figsize=(20, 10), facecolor='k')
ax = ax.flatten()

c0_0 = ax[0 + 0].imshow(real_cor1D_data['axial'][Signal.ihMTR_CM], cmap='gray', vmin=0, vmax=25)
c0_1 = ax[0 + 1].imshow(real_ihMTR['axial'][Signal.ihMTR_CM], cmap='gray', vmin=0, vmax=25)
c0_2 = ax[0 + 2].imshow(real_cor2D_data['axial'][Signal.ihMTR_CM], cmap='gray', vmin=0, vmax=25)
c0_3 = ax[0 + 3].imshow(real_params['axial']['flipAngle'], cmap='gray', vmin=450, vmax=1400)
c0_4 = ax[0 + 4].imshow(real_params['axial']['poolFree_T1'], cmap='gray', vmin=0, vmax=4000)

c5_0 = ax[5 + 0].imshow(real_cor1D_data['sagittal'][Signal.ihMTR_CM], cmap='gray', vmin=0, vmax=25)
c5_1 = ax[5 + 1].imshow(real_ihMTR['sagittal'][Signal.ihMTR_CM], cmap='gray', vmin=0, vmax=25)
c5_2 = ax[5 + 2].imshow(real_cor2D_data['sagittal'][Signal.ihMTR_CM], cmap='gray', vmin=0, vmax=25)
c5_3 = ax[5 + 3].imshow(real_params['sagittal']['flipAngle'], cmap='gray', vmin=450, vmax=1400)
c5_4 = ax[5 + 4].imshow(real_params['sagittal']['poolFree_T1'], cmap='gray', vmin=0, vmax=4000)

c10_0 = ax[10 + 0].imshow(real_cor1D_data['coronal'][Signal.ihMTR_CM], cmap='gray', vmin=0, vmax=25)
c10_1 = ax[10 + 1].imshow(real_ihMTR['coronal'][Signal.ihMTR_CM], cmap='gray', vmin=0, vmax=25)
c10_2 = ax[10 + 2].imshow(real_cor2D_data['coronal'][Signal.ihMTR_CM], cmap='gray', vmin=0, vmax=25)
c1032 = ax[10 + 3].imshow(real_params['coronal']['flipAngle'], cmap='gray', vmin=450, vmax=1400)
c1042 = ax[10 + 4].imshow(real_params['coronal']['poolFree_T1'], cmap='gray', vmin=0, vmax=4000)

ax[0 + 0].set_title('1D Corrected\n0% → 25%', color='white', fontsize=16)
ax[0 + 1].set_title('Base ihMTR\n0% → 25%'.center(12), color='white', fontsize=16)
ax[0 + 2].set_title('2D Corrected\n0% → 25%', color='white', fontsize=16)
ax[0 + 3].set_title('Saturation Flip Angle\n400° → 1400°'.center(12), color='white', fontsize=16)
ax[0 + 4].set_title(r'Water $\mathrm{T}_1$' '\n0 → 4000 ms'.center(12), color='white', fontsize=16)

[axis.axis('off') for axis in ax]

fig.subplots_adjust(wspace=None, hspace=-.4)
fig.tight_layout()
plt.show()

Example: Steady-state signal with respect to readout

# Generating the data
# pulse = Tukey(duration=1.5e-3, shape=.3, flipAngle=299, offset=7000)
# system = System(pulse=pulse, poolFree_M0=1, poolFree_T1=2, poolFree_T2=5e-3, poolFreeBound_exchangeRate=[60, 10], poolBound_M0=[.6, .4], poolBound_T1=[1, .3], poolBound_T2=[10e-6, 10e-6], poolBound_T1D=[20e-3, 5e-3], poolBound_lineshapeAsymmetry=[600, 600])
# sequence = Sequence(signal=Signal.ALL, pulse=pulse, N_pulsePerOffset=1, N_pulse=4, N_burst=10, N_adc=80, N_dummyADC=0, dt_interPulse=1.5e-3, TR_burst=90e-3, dt_lastBurst=7e-3, es=7e-3, tr=1.5, readout_flipAngle=5)
# simulator = Simulator(system=system, sequence=sequence, output_vectorSlice=slice(None), export_readMatrix=True)
# readouts = Trajector.readouts(simulator=simulator, stable=True)

# Generating the visuals
x = np.array(range(1, simulator.sequence.N_adc + 1))
slices = [0] + list(range(1, len(readouts[Signal.MT0]) - 1, 2))  # Show Zeeman Water and Zeeman Macromolecules only

with np.errstate(divide='ignore', invalid='ignore'):
    fig, axes = plt.subplots(2, 6, sharex=True, figsize=(10, 5))
    axes = axes.flatten()

    axes[0].set_title("$MT_0$")
    axes[0].grid()
    axes[0].set_ylim(0, 1)
    lines = axes[0].plot(x, readouts[Signal.MT0][slices, :].T)
    axes[0].set_xlim(1, simulator.sequence.N_adc)
    axes[0].set_xlabel('# readout')
    axes[0].set_ylabel('Signal [a.u.]')
    axes[0 + 6].set_axis_off()

    axes[1].set_title("$MT_s$")
    axes[1].grid()
    axes[1].set_ylim(0, 1)
    axes[1].plot(x, readouts[Signal.MTs][slices, :].T, linestyle='solid')
    axes[1].plot(x, readouts[Signal.MTs_Positive][slices, :].T, linestyle='dashed')
    axes[1].plot(x, readouts[Signal.MTs_Negative][slices, :].T, linestyle='dotted')
    axes[1 + 6].set_title("$MTR_s$")
    axes[1 + 6].grid()
    axes[1 + 6].set_ylim(0, 40)
    axes[1 + 6].set_ylabel('Signal [%]')
    axes[1 + 6].plot(x, readouts[Signal.MTsR][slices, :].T, linestyle='solid')
    axes[1 + 6].plot(x, readouts[Signal.MTsR_Positive][slices, :].T, linestyle='dashed')
    axes[1 + 6].plot(x, readouts[Signal.MTsR_Negative][slices, :].T, linestyle='dotted')

    axes[2].set_title("$MT_d^{CM}$")
    axes[2].grid()
    axes[2].set_ylim(0, 1)
    axes[2].plot(x, readouts[Signal.MTd_CM][slices, :].T)
    axes[2 + 6].set_title("$MTR_d^{CM}$")
    axes[2 + 6].grid()
    axes[2 + 6].set_ylim(0, 40)
    axes[2 + 6].plot(x, readouts[Signal.MTdR_CM][slices, :].T)

    axes[3].set_title("$MT_d^{ALT}$")
    axes[3].grid()
    axes[3].set_ylim(0, 1)
    axes[3].plot(x, readouts[Signal.MTd_ALT][slices, :].T)
    axes[3 + 6].set_title("$MTR_d^{ALT}$")
    axes[3 + 6].grid()
    axes[3 + 6].set_ylim(0, 40)
    axes[3 + 6].plot(x, readouts[Signal.MTdR_ALT][slices, :].T)

    axes[4].set_title("$ihMT^{CM}$")
    axes[4].grid()
    axes[4].set_ylim(0, .40)
    axes[4].plot(x, readouts[Signal.ihMT_CM][slices, :].T)
    axes[4 + 6].set_title("$ihMTR^{CM}$")
    axes[4 + 6].grid()
    axes[4 + 6].set_ylim(0, 40)
    axes[4 + 6].plot(x, readouts[Signal.ihMTR_CM][slices, :].T)

    axes[5].set_title("$ihMT^{ALT}$")
    axes[5].grid()
    axes[5].set_ylim(0, .40)
    axes[5].plot(x, readouts[Signal.ihMT_ALT][slices, :].T)
    axes[5 + 6].set_title("$ihMTR^{ALT}$")
    axes[5 + 6].grid()
    axes[5 + 6].set_ylim(0, 40)
    axes[5 + 6].plot(x, readouts[Signal.ihMTR_ALT][slices, :].T)

    axes[0 + 6].legend(handles=lines, labels=[*[f'Water #{i+1}' for i in range(simulator.system.N_poolFree)], *[f'Macromolecules #{i+1}' for i in range(simulator.system.N_poolBound)]], title='Zeeman pool', title_fontproperties={'weight':'bold'})
    plt.tight_layout()
    plt.show()

# Generating the data
readouts = Trajector.readouts(simulator=simulator, stable=True)

# Generating the visuals
x = np.array(range(1, simulator.sequence.N_adc + 1))
slices = slice(0, 2)  # Show Zeeman Water and Zeeman Macromolecules only

with np.errstate(divide='ignore', invalid='ignore'):
    fig, axes = plt.subplots(1, 2, sharex=True, figsize=(10, 5))
    axes = axes.flatten()

    axes[0].plot(x, readouts[Signal.MT0][0], color='C0', linestyle='dotted', label='MT0')
    axes[0].plot(x, readouts[Signal.MTs][0], color='C2', linestyle='-.', label='MTs')
    axes[0].plot(x, readouts[Signal.MTd_CM][0], color='k', linestyle='--', label='MTd CM')
    axes[0].plot(x, readouts[Signal.MTd_ALT][0], color='C3', linestyle='--', label='MTd ALT')
    axes[0].plot(x, readouts[Signal.ihMT_CM][0], color='k', linestyle='-', label='ihMT CM')
    axes[0].plot(x, readouts[Signal.ihMT_ALT][0], color='C3', linestyle='-', label='ihMT ALT')
    axes[0].plot(x, readouts[Signal.BP][0], color='C4', linestyle='-', label='BP')

    axes[1].plot(x, readouts[Signal.MTsR][0], color='C2', linestyle='-.', label='MTRs')
    axes[1].plot(x, readouts[Signal.MTdR_CM][0], color='k', linestyle='--', label='MTRd CM')
    axes[1].plot(x, readouts[Signal.MTdR_ALT][0], color='C3', linestyle='--', label='MTRd ALT')
    axes[1].plot(x, readouts[Signal.ihMTR_CM][0], color='k', linestyle='-', label='ihMTR CM')
    axes[1].plot(x, readouts[Signal.ihMTR_ALT][0], color='C3', linestyle='-', label='ihMTR ALT')
    axes[1].plot(x, readouts[Signal.BPR][0], color='C4', linestyle='-', label='BPR')

    axes[0].legend(title='Zeeman water', title_fontproperties={'weight':'bold'}, loc='lower right')
    axes[0].grid()
    axes[0].set_xlabel('# readout')
    axes[0].set_xlim(1, simulator.sequence.N_adc)
    axes[0].set_ylabel('(ih)MT [a.u.]')
    axes[0].set_ylim(0, 1)

    axes[1].legend(title='Zeeman water', title_fontproperties={'weight':'bold'}, loc='upper right')
    axes[1].grid()
    axes[1].set_xlabel('# readout')
    axes[1].set_xlim(1, simulator.sequence.N_adc)
    axes[1].set_ylabel('(ih)MTR [%]')
    axes[1].set_ylim(0, 40)

    plt.tight_layout()
    plt.show()

Exmple: PSF - WIP

Advanced

Sensivity analysis - WIP

Using fixed parameter vectors

Using distribution sampling

Additional Information

Configuration files

Default configurations

3 Teslas

for key, val in default.items():
    print(f'\033[1m{key}\033[0m')
    for kkey, vval in val.items():
        if type(vval) != dict:
            print(str(kkey).rjust(len('poolBound_lineshapeAsymmetry')), ':', repr(vval))
        else:
            print(f'\t\033[1m{kkey}\033[0m')
            for kkkey, vvval in vval.items():
                print('\t\t', kkkey, repr(vvval))
    print()

run
                          pw : 0.001
                     r_tukey : 0.3
                      fa_sat : 200
                      offset : 7000
                 FLAG_Signal : 'ALL'
                    N_altern : 1
                          np : 4
                          nb : 10
                       turbo : 80
                  N_dummyADC : 3
                          dt : 0.0015
                         btr : 0.1
                     btrlast : 0.001
                          es : 0.006
                          tr : 3
                     fa_rage : 5
                         M0a : 1
                         M0b : 0.1
                         T1f : 1
                         T2f : 0.1
                         T1b : 1
                         T1D : 0.01
                         T2b : 1e-05
                           R : 10
poolBound_lineshapeAsymmetry : -593.83
                 export_read : True
           output_fullVector : True
                   outputDir : './output/'
                  filePrefix : ''
                      export : True

log
                     version : 1
    disable_existing_loggers : False
	formatters
		 standard {'format': '%(asctime)s - %(name)s - %(levelname)s - %(message)s'}
		 error {'format': '%(asctime)s - %(name)s - %(levelname)s <PID %(process)d:%(processName)s> %(name)s.%(funcName)s(): %(message)s'}
	handlers
		 root_file_handler {'class': 'logging.FileHandler', 'level': 'INFO', 'formatter': 'standard', 'filename': './output/logs.txt', 'mode': 'w'}
		 debug_root_file_handler {'class': 'logging.FileHandler', 'level': 'DEBUG', 'formatter': 'error', 'filename': './output/logs_debug.txt', 'mode': 'w'}
		 console {'class': 'logging.StreamHandler', 'level': 'INFO', 'formatter': 'standard', 'stream': 'ext://sys.stdout'}
		 error_console {'class': 'logging.StreamHandler', 'level': 'ERROR', 'formatter': 'error', 'stream': 'ext://sys.stderr'}
	root
		 level 'DEBUG'
		 handlers ['console', 'error_console', 'root_file_handler', 'debug_root_file_handler']

7 Teslas

Custom configurations

In a live environment

Stored on file

Loggers

The ihmt.meta.CompositeDictionary class

Optimizing ihmt.run.GridRuns runtime

Test suite

try:
    import coverage
except ImportError as e:
    %pip install coverage

!./run_tests.sh

Collecting coverage
  Downloading coverage-7.14.1-cp314-cp314-manylinux1_x86_64.manylinux_2_28_x86_64.manylinux_2_5_x86_64.whl.metadata (8.6 kB)
Downloading coverage-7.14.1-cp314-cp314-manylinux1_x86_64.manylinux_2_28_x86_64.manylinux_2_5_x86_64.whl (253 kB)
Installing collected packages: coverage
Successfully installed coverage-7.14.1
Note: you may need to restart the kernel to use updated packages.

----------------------------------------------------------------------
Ran 116 tests in 5.069s

Name                            Stmts   Miss Branch BrPart  Cover
-----------------------------------------------------------------
ihmt/__init__.py               9      0      0      0   100%
ihmt/config.py                24      4      2      0    85%
ihmt/corrector.py            113     76     40      0    24%
ihmt/meta.py                 418    204    174     24    46%
ihmt/pulse.py                179     24     20      0    86%
ihmt/run.py                   94     60     38      1    28%
ihmt/sequence.py             210      0     28      0   100%
ihmt/simulator.py            126     17     30     10    81%
ihmt/system.py               336      7     44      6    97%
ihmt/trajector.py             58     29     10      0    43%
ihmt/vectorized/pulse.py     166     79     16      0    48%
-----------------------------------------------------------------
TOTAL                            1733    500    402     41    65%

Contributing new features - WIP

Adding new modules

Modifying existing modules

Notes

• General nomenclature (variable, function, class, and file names) is still open to changes
• Parameter names of ihmt.run.SingleRun should match exactly the names in config files/dict for SingleRun(**config) to work as intended
• new python projects tend to favor .toml over .yaml configuration files, but I'm not too sure if the switch is worth it
  • A generic Configuration object could be implemented and instantiated with Configuration.from_yaml, Configuration.from_toml, and Configuration.from_json

To do

1. Generic - Improve test coverage (currently: 65%, goal: >95%)
2. Notebook - Detail how-tos
3. Generic - Increase logging
4. Trajector - Implement various default trajectory and generic trajectory
5. Trajector - Implement PSF and related
6. Simulator - Solver choice
7. Simulator - Step by step solver
8. Sequence - Add dummy TR attribute
9. Trajector - Use Step by step solver for readouts at every k-space sample point
10. Generic - Numba / Cython