def split_linear(core, criterion=None):
"""
"""
if criterion is None:
args = (core.x + core.dx() + core.w, core.dx() + core.w)
mats = (hessian(core.H, core.x), jacobian(core.z, core.w))
criterion = list(zip(mats, args))
movefunc = movesquarematrixcolnrow
else:
movefunc = movematrixcols
# split storage part
nxl = 0
hess = criterion[0][0]
arg = criterion[0][1]
for _ in range(hess.shape[1]):
# hess_row = list(hess[nxl, :].T)
hess_col = list(hess[:, nxl])
# collect line symbols
symbs = free_symbols(hess_col)
# if symbols are not states
if symbs.isdisjoint(arg):
# do nothing and increment counter
nxl += 1
else:
# move the element at the end of states vector
move_stor(core, nxl, core.dims.x() - 1)
hess = movefunc(hess, nxl, core.dims.x() - 1)
# number of linear components
setattr(core.dims, '_xl', nxl)
setattr(core, 'Q', hessian(core.H, core.xl()))
# split dissipative part
nwl = 0
jacz = criterion[1][0]
arg = criterion[1][1]
for _ in range(jacz.shape[1]):
# jacz_row = list(jacz[nwl, :].T)
jacz_col = list(jacz[:, nwl])
# collect line symbols
symbs = free_symbols(jacz_col)
# if symbols are not dissipation variables
if symbs.isdisjoint(arg):
# do nothing and increment counter
nwl += 1
else:
# move the element to end of dissipation variables vector
move_diss(core, nwl, core.dims.w() - 1)
jacz = movefunc(jacz, nwl, core.dims.w() - 1)
# number of linear components
setattr(core.dims, '_wl', nwl)
core.setexpr('Zl', jacobian(core.zl(), core.wl()))
def monovar_multivar(core):
"""
Split core components into monovariate and multivariate components.
"""
from utils.structure import move_stor, move_diss
# split storage part
i = 0
for _ in range(core.dims.x()):
hess = hessian(core.H, core.x)
hess_line = list(hess[i, :].T)
# remove i-th element
hess_line.pop(i)
# if other elements are all 0
if all(el is sympy.sympify(0) for el in hess_line):
# do nothing and increment counter
i += 1
else:
# move the element at the end of states vector
move_stor(core, i, core.dims.x())
# number of separate components
core.dims.xs = i
# number of non-separate components
core.dims.xns = core.dims.x()-i
# split dissipative part
i = 0
for _ in range(core.dims.w()):
Jacz_line = list(core.Jacz[i, :].T)
# remove i-th element
Jacz_line.pop(i)
# if other elements are all 0
if all(el is sympy.sympify(0) for el in Jacz_line):
# do nothing and increment counter
i += 1
else:
# move the element at the end of variables vector
move_diss(core, i, core.dims.w())
# number of separate components
core.dims.ws = i
# number of non-separate components
core.dims.wns = core.dims.w()-i
def linear_nonlinear(core, criterion=None):
"""
1. Detect the number of linear storage component (_nxl) and of linear
dissipative components (_nwl).
2. Sort linear and then nonlinear components.
3. Build matrices Q and Zl.
Parameters
----------
core : pyphs.Core
Core to analyse.
criterion: list of tuples of objects
criterion[0] = (hessH, argx)
criterion[1] = (jacz, argz)
"""
if criterion is None:
args = (core.x + core.dx() + core.w, core.dx() + core.w)
mats = (hessian(core.H, core.x), jacobian(core.z, core.w))
criterion = list(zip(mats, args))
movefunc = movesquarematrixcolnrow
else:
movefunc = movematrixcols
# split storage part
nxl = 0
hess = criterion[0][0]
arg = criterion[0][1]
for _ in range(hess.shape[1]):
# hess_row = list(hess[nxl, :].T)
hess_col = list(hess[:, nxl])
# collect line symbols
symbs = free_symbols(hess_col)
# if symbols are not states
if symbs.isdisjoint(arg):
# do nothing and increment counter
nxl += 1
else:
# move the element at the end of states vector
move_stor(core, nxl, core.dims.x()-1)
hess = movefunc(hess, nxl, core.dims.x()-1)
# split dissipative part
nwl = 0
jacz = criterion[1][0]
arg = criterion[1][1]
for _ in range(jacz.shape[1]):
# jacz_row = list(jacz[nwl, :].T)
jacz_col = list(jacz[:, nwl])
# collect line symbols
symbs = free_symbols(jacz_col)
# if symbols are not dissipation variables
if symbs.isdisjoint(arg):
# do nothing and increment counter
nwl += 1
else:
# move the element to end of dissipation variables vector
move_diss(core, nwl, core.dims.w()-1)
jacz = movefunc(jacz, nwl, core.dims.w()-1)
# number of linear components
setattr(core.dims, '_xl', nxl)
core.setexpr('Q', hessian(core.H, core.xl()))
# number of linear components
setattr(core.dims, '_wl', nwl)
core.setexpr('Zl', jacobian(core.zl(), core.wl()))