Commit d8302ae1 authored by Blais, Chris's avatar Blais, Chris
Browse files

Standardize figure names

parent 1483c16a

documenting_failures/documented_failures.ipynb

+1 −1
Original line number Diff line number Diff line 
%% Cell type:code id:c8f1b999 tags:



``` python

import sympy as sy

import pandas as pd

import os

import scipy as sp

import numpy as np

import math

import itertools

import sys

module_path = os.path.join(os.path.dirname(os.path.abspath('')))

if module_path not in sys.path:

    sys.path.insert(0, module_path)

else:

    print("path already in sys.path")



import matplotlib.pyplot as plt

from numerical_labelling.labelling import *

```



%% Output



    path already in sys.path



%% Cell type:markdown id:8e4f0a26 tags:



## Linear case

<img src="../fig/membrane_corrected.png" width="50%">

<img src="../fig/ccro_layout.png" width="50%">



%% Cell type:code id:a87b952f tags:



``` python

# generate constraints

def constr_mem_lin():

    """

    constraint equations for membrane example

    """



    m1, m2, m3, m4, m5, m6, m7, m8 = sy.symbols('m1 m2 m3 m4 m5 m6 m7 m8') # overall mass flow rates

    varbs = [

        m1, m2, m3, m4, m5, m6, m7, m8

        ]

    var_labels = [

        'M1', 'M2', 'M3', 'M4', 'M5', 'M6', 'M7', 'M8'

        ]



    # Create a dictionary to store all variables and their values

    var_dict = dict(zip(var_labels, varbs))



    constr = {}

    # mass balance

    constr[0] = m1 - m2

    constr[1] = m2 - m3 + m8

    constr[2] = m3 - m4 - m5

    constr[3] = m5 - m6 - m7

    constr[4] = m7 - m8



    return constr, var_dict

```



%% Cell type:code id:92ba160f tags:



``` python

constr_lin, varbs_lin = constr_mem_lin()

```



%% Cell type:code id:8f31dfa5 tags:



``` python

jac_lin = jacsym(constr_lin.values(), varbs_lin.values())

```



%% Cell type:code id:307d5feb tags:



``` python

jac_lin

```



%% Output



    $\displaystyle \left[\begin{matrix}1 & -1 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 1 & -1 & 0 & 0 & 0 & 0 & 1\\0 & 0 & 1 & -1 & -1 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 1 & -1 & -1 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 1 & -1\end{matrix}\right]$

    Matrix([

    [1, -1,  0,  0,  0,  0,  0,  0],

    [0,  1, -1,  0,  0,  0,  0,  1],

    [0,  0,  1, -1, -1,  0,  0,  0],

    [0,  0,  0,  0,  1, -1, -1,  0],

    [0,  0,  0,  0,  0,  0,  1, -1]])



%% Cell type:code id:7c92dbab tags:



``` python

layout = [True, True, True, False, False, False, False, False]

layout_inv = [not(i) for i in layout]

layout_inv

```



%% Output



    [False, False, False, True, True, True, True, True]



%% Cell type:code id:035143cd tags:



``` python

ju = jac_lin[:,layout_inv]

jm = jac_lin[:, layout]

```



%% Cell type:code id:50a64f26 tags:



``` python

ju.rref()[0]

```



%% Output



    $\displaystyle \left[\begin{matrix}1 & 0 & 1 & 0 & 0\\0 & 1 & -1 & 0 & 0\\0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 1\\0 & 0 & 0 & 0 & 0\end{matrix}\right]$

    Matrix([

    [1, 0,  1, 0, 0],

    [0, 1, -1, 0, 0],

    [0, 0,  0, 1, 0],

    [0, 0,  0, 0, 1],

    [0, 0,  0, 0, 0]])



%% Cell type:code id:1fad065b tags:



``` python

# transfer one measured over:

layout = [False, True, True, False, False, False, False, False]

layout_inv = [not(i) for i in layout]

ju = jac_lin[:,layout_inv]

jm = jac_lin[:, layout]

ju.rref()[0]

```



%% Output



    $\displaystyle \left[\begin{matrix}1 & 0 & 0 & 0 & 0 & 0\\0 & 1 & 0 & 1 & 0 & 0\\0 & 0 & 1 & -1 & 0 & 0\\0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 1\end{matrix}\right]$

    Matrix([

    [1, 0, 0,  0, 0, 0],

    [0, 1, 0,  1, 0, 0],

    [0, 0, 1, -1, 0, 0],

    [0, 0, 0,  0, 1, 0],

    [0, 0, 0,  0, 0, 1]])



%% Cell type:markdown id:21ed7f7f tags:



## bilinear case



%% Cell type:code id:e1d43176 tags:



``` python

import sympy as sy

import pandas as pd

import os

import scipy as sp

import numpy as np

import math

import itertools

import sys

module_path = os.path.join(os.path.dirname(os.path.abspath('')))

if module_path not in sys.path:

    sys.path.insert(0, module_path)

else:

    print("path already in sys.path")



import matplotlib.pyplot as plt

from numerical_labelling.labelling import *

from numerical_labelling.plot_layout import make_pretty_labels

```



%% Output



    path already in sys.path



%% Cell type:code id:a6ff637e tags:



``` python

def constr_spl():

    constr = {}

    m1, m2, m3 = sy.symbols("m1 m2 m3")

    x1, x2, x3 = sy.symbols("x1 x2 x3")

    varbs_sy = [m1, m2, m3, x1, x2, x3]



    constr[0] = m1 - m2 - m3

    constr[1] = x1 - x2

    constr[2] = x1 - x3



    varb_labels = [

        "m1", "m2", "m3",

        "x1", "x2", "x3",

        ]



    varbs = dict(zip(varb_labels,varbs_sy))



    return constr, varbs



def constr_spl_sup(simple_constr = False):

    "include superfluous constraint"

    constr = {}

    m1, m2, m3 = sy.symbols("m1 m2 m3")

    x1, x2, x3 = sy.symbols("x1 x2 x3")

    varbs_sy = [m1, m2, m3, x1, x2, x3]



    constr[0] = m1 - m2 - m3

    constr[1] = x1 - x2

    constr[2] = x1 - x3

    if simple_constr:

        constr[3] = m1 - m2 - m3

    else:

        constr[3] = m1*x1 - m2*x2 - m3*x3



    varb_labels = [

        "m1", "m2", "m3",

        "x1", "x2", "x3",

        ]



    varbs = dict(zip(varb_labels,varbs_sy))



    return constr, varbs

```



%% Cell type:code id:9a97895b tags:



``` python

constr_req, varbs_req = constr_spl()

constr_sup, varbs_sup = constr_spl_sup()

constr_sup_mb, varbs_sup_mb = constr_spl_sup(simple_constr=True)

jac_req = jacsym(constr_req.values(), varbs_req.values())

jac_sup = jacsym(constr_sup.values(), varbs_sup.values())

jac_sup_mb = jacsym(constr_sup_mb.values(), varbs_sup_mb.values())

```



%% Cell type:code id:2701d8e2 tags:



``` python

layout = [

    True, False, False,

    False, True, False

]



bool_measured = np.where(np.array(layout))[0]

bool_unmeasured = np.where(~np.array(layout))[0]

vb_all, vb_m, vb_um = make_pretty_labels(varbs_req, layout)

```



%% Cell type:code id:f55e7793 tags:



``` python

r1, r2, r3, r4 = sy.symbols("r1 r2 r3 r4")

rhs_syms = sy.Matrix([r1, r2, r3, r4])

```



%% Cell type:code id:4c3f3568 tags:



``` python

Ju_req = jac_req[:, list(bool_unmeasured)]

Ju_sup = jac_sup[:, list(bool_unmeasured)]

Ju_sup_mb = jac_sup_mb[:, list(bool_unmeasured)]

rref_req, rhs_req = Ju_req.rref_rhs(rhs_syms[:Ju_req.shape[0],:])

rref_sup, rhs_sup = Ju_sup.rref_rhs(rhs_syms[:Ju_sup.shape[0],:])

rref_sup_mb, rhs_sup_mb = Ju_sup_mb.rref_rhs(rhs_syms[:Ju_sup_mb.shape[0], :])

```



%% Cell type:code id:d4b906cd tags:



``` python

sy.Matrix.vstack(vb_um, rref_req)

```



%% Output



    $\displaystyle \left[\begin{matrix}m_{2} & m_{3} & x_{1} & x_{3}\\- & - & - & -\\1 & 1 & 0 & 0\\0 & 0 & 1 & 0\\0 & 0 & 0 & 1\end{matrix}\right]$

    Matrix([

    [m2, m3, x1, x3],

    [ -,  -,  -,  -],

    [ 1,  1,  0,  0],

    [ 0,  0,  1,  0],

    [ 0,  0,  0,  1]])



%% Cell type:code id:aad07395 tags:



``` python

sy.Matrix.vstack(vb_um, rref_sup)

```



%% Output



    $\displaystyle \left[\begin{matrix}m_{2} & m_{3} & x_{1} & x_{3}\\- & - & - & -\\1 & 0 & 0 & 0\\0 & 1 & 0 & 0\\0 & 0 & 1 & 0\\0 & 0 & 0 & 1\end{matrix}\right]$

    Matrix([

    [m2, m3, x1, x3],

    [ -,  -,  -,  -],

    [ 1,  0,  0,  0],

    [ 0,  1,  0,  0],

    [ 0,  0,  1,  0],

    [ 0,  0,  0,  1]])



%% Cell type:code id:07ba3528 tags:



``` python

sy.Matrix.vstack(vb_um, rref_sup_mb)

```



%% Output



    $\displaystyle \left[\begin{matrix}m_{2} & m_{3} & x_{1} & x_{3}\\- & - & - & -\\1 & 1 & 0 & 0\\0 & 0 & 1 & 0\\0 & 0 & 0 & 1\\0 & 0 & 0 & 0\end{matrix}\right]$

    Matrix([

    [m2, m3, x1, x3],

    [ -,  -,  -,  -],

    [ 1,  1,  0,  0],

    [ 0,  0,  1,  0],

    [ 0,  0,  0,  1],

    [ 0,  0,  0,  0]])



%% Cell type:code id:20d2fb5a tags:



``` python

rhs_req

```



%% Output



    $\displaystyle \left[\begin{matrix}- r_{1}\\r_{2}\\r_{2} - r_{3}\end{matrix}\right]$

    Matrix([

    [    -r1],

    [     r2],

    [r2 - r3]])



%% Cell type:code id:3257c8d7 tags:



``` python

rhs_sup

```



%% Output



    $\displaystyle \left[\begin{matrix}\frac{m_{1} r_{2} - m_{3} r_{2} + m_{3} r_{3} + r_{1} x_{3} - r_{4}}{x_{2} - x_{3}}\\\frac{- m_{1} r_{2} + m_{3} r_{2} - m_{3} r_{3} - r_{1} x_{2} + r_{4}}{x_{2} - x_{3}}\\r_{2}\\r_{2} - r_{3}\end{matrix}\right]$

    Matrix([

    [ (m1*r2 - m3*r2 + m3*r3 + r1*x3 - r4)/(x2 - x3)],

    [(-m1*r2 + m3*r2 - m3*r3 - r1*x2 + r4)/(x2 - x3)],

    [                                             r2],

    [                                        r2 - r3]])



%% Cell type:code id:56de1575 tags:



``` python

rhs_sup_mb

```



%% Output



    $\displaystyle \left[\begin{matrix}- r_{4}\\r_{2}\\r_{2} - r_{3}\\r_{1} - r_{4}\end{matrix}\right]$

    Matrix([

    [    -r4],

    [     r2],

    [r2 - r3],

    [r1 - r4]])



%% Cell type:code id:e4b4c4d8 tags:



``` python

rref_subout, rhs_subout = Ju_sup.subs({'x2':varbs_req['x3']}).rref_rhs(rhs_syms[:4, :])

rhs_subout

```



%% Output



    $\displaystyle \left[\begin{matrix}\frac{m_{1} r_{2} - m_{3} r_{2} + m_{3} r_{3} - r_{4}}{x_{3}}\\r_{2}\\r_{2} - r_{3}\\\frac{m_{1} r_{2} - m_{3} r_{2} + m_{3} r_{3} + r_{1} x_{3} - r_{4}}{x_{3}}\end{matrix}\right]$

    Matrix([

    [        (m1*r2 - m3*r2 + m3*r3 - r4)/x3],

    [                                     r2],

    [                                r2 - r3],

    [(m1*r2 - m3*r2 + m3*r3 + r1*x3 - r4)/x3]])



%% Cell type:code id:224f51bb tags:



``` python

Ju_req

```



%% Output



    $\displaystyle \left[\begin{matrix}-1 & -1 & 0 & 0\\0 & 0 & 1 & 0\\0 & 0 & 1 & -1\end{matrix}\right]$

    Matrix([

    [-1, -1, 0,  0],

    [ 0,  0, 1,  0],

    [ 0,  0, 1, -1]])



%% Cell type:code id:f0f6e228 tags:



``` python

varbs_req['x2']

```



%% Output



    $\displaystyle x_{2}$

    x2



%% Cell type:markdown id:58024a89 tags:



## Bilinear failure: operating point selection



%% Cell type:markdown id:e4747f6d tags:

documenting_failures/soar_comparison.ipynb

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Original line number Diff line number Diff line
@@ -29,7 +29,7 @@ 
   "metadata": {},

   "source": [

    "## Linear case\n",

    "<img src=\"../fig/membrane_corrected.png\" width=\"50%\">"

    "<img src=\"../fig/ccro_layout.png\" width=\"50%\">"

   ]

  },

  {
@@ -1262,7 +1262,7 @@ 
   "metadata": {},

   "source": [

    "## QR factorization\n",

    "<img src=\"../fig/membrane_corrected.png\" width=\"50%\">"

    "<img src=\"../fig/ccro_layout.png\" width=\"50%\">"

   ]

  },

  {

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fig/example_schematic.png

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