Difference between revisions of "Example:compound nomograph 2"

Compound nomograph example 2

In this example we construct compound nomograph for solving equation

$q = u^v + w. \,$

This example is taken from [1]. The equation is split into two equations that each are blocks:

 $\log (r) = v \log (u) \,\,\,\,\,\,\,$ type 2 $q-w-r=0 \,\,\,\,\,\,\,$ type 1

Because one equation has r and other log(r), we need to use ladders, that are type 6. Ladders are not generally elegant choice and we use them because there is no other choice (if we forget "contour" = type 5.)

1. Epstein: Nomography, p. 66

Simple example

Compound nomograph: example 2
Generated portable document file (pdf): File:Ex compound nomo 2.pdf

Source code of simple compound nomograph example

"""
ex_compound_nomo_2.py

Compound nomograph: q = u**v+w

This program is free software: you can redistribute it and/or modify
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program.  If not, see <http://www.gnu.org/licenses/>.
"""
from pynomo.nomographer import *

# N
u_params={
'u_min':1.0,
'u_max':10.0,
'function':lambda u:log(u),
'title':r'$u$',
'tick_levels':3,
'tick_text_levels':1,
'tick_side':'left',
}

v_params={
'u_min':0.1,
'u_max':20.0,
'function':lambda v:1.0/v,
'title':r'$v$',
'scale_type':'log',
'tick_levels':0,
'tick_text_levels':0,
'extra_params':[{
'u_min':0.1,
'u_max':0.9,
'tick_levels':3,
'tick_text_levels':2,
'tick_side':'left'
},
{
'u_min':1.0,
'u_max':20.0,
'tick_levels':4,
'tick_text_levels':2,
'tick_side':'right'
}
]
}

R_params={
'u_min':1.0,
'u_max':10.0,
'function':lambda r:log(r),
'title':r'',
'tick_levels':0,
'tick_text_levels':0,
'tag':'ra',
}

block_params_1={
'block_type':'type_2',
'width':10.0,
'height':10.0,
'f1_params':u_params,
'f2_params':v_params,
'f3_params':R_params,
}
R_params_a={
'u_min':1.0,
'u_max':10.0,
'function':lambda u:log(u),
'title':'r',
'tick_levels':3,
'tick_text_levels':2,
'tick_side':'left',
'tag':'ra',
}

R_params_b={
'u_min':0.0,
'u_max':10.0,
'function':lambda u:u,
'title':'r',
'tick_levels':3,
'tick_text_levels':2,
'tag':'rb'
}

block_params_2={
'block_type':'type_6',
'f1_params':R_params_a,
'f2_params':R_params_b,
'width':5.0,
'height':10.0,
'mirror_x':True,
}
# type 1: q-w-r=0
r_params_c={
'u_min':0.0,
'u_max':10.0,
'function':lambda u:-u,
'title':r'$r$',
'tick_levels':2,
'tick_text_levels':1,
'tag':'rb'
}

w_params={
'u_min':-10.0,
'u_max':10.0,
'function':lambda u:-u,
'title':r'$w$',
'tick_levels':2,
'tick_text_levels':1,
}

q_params={
'u_min':0.0,
'u_max':10.0,
'function':lambda u:u,
'title':r'$q$',
'tick_levels':2,
'tick_text_levels':1,
}

block_params_3={
'block_type':'type_1',
'width':10.0,
'height':10.0,
'f1_params':r_params_c,
'f2_params':w_params,
'f3_params':q_params,
'mirror_x':False
}

main_params={
'filename':'ex_compound_nomo_2.pdf',
'paper_height':13.0,
'paper_width':20.0,
'block_params':[block_params_1,block_params_2,block_params_3],
'transformations':[('rotate',0.01),('scale paper',)],
}
Nomographer(main_params)