/usr/lib/python-escript-mpi/esys/downunder/regularizations.py is in python-escript-mpi 5.1-5.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 | ##############################################################################
#
# Copyright (c) 2003-2017 by The University of Queensland
# http://www.uq.edu.au
#
# Primary Business: Queensland, Australia
# Licensed under the Apache License, version 2.0
# http://www.apache.org/licenses/LICENSE-2.0
#
# Development until 2012 by Earth Systems Science Computational Center (ESSCC)
# Development 2012-2013 by School of Earth Sciences
# Development from 2014 by Centre for Geoscience Computing (GeoComp)
#
##############################################################################
from __future__ import print_function, division
__copyright__="""Copyright (c) 2003-2017 by The University of Queensland
http://www.uq.edu.au
Primary Business: Queensland, Australia"""
__license__="""Licensed under the Apache License, version 2.0
http://www.apache.org/licenses/LICENSE-2.0"""
__url__="https://launchpad.net/escript-finley"
__all__ = ['Regularization']
import logging
import numpy as np
from esys.escript import Function, outer, Data, Scalar, grad, inner, integrate, interpolate, kronecker, boundingBoxEdgeLengths, vol, sqrt, length,Lsup, transpose
from esys.escript.linearPDEs import LinearPDE, IllegalCoefficientValue,SolverOptions
from esys.escript.pdetools import ArithmeticTuple
from .coordinates import makeTransformation
from .costfunctions import CostFunction
class Regularization(CostFunction):
"""
The regularization term for the level set function ``m`` within the cost
function J for an inversion:
*J(m)=1/2 * sum_k integrate( mu[k] * ( w0[k] * m_k**2 * w1[k,i] * m_{k,i}**2) + sum_l<k mu_c[l,k] wc[l,k] * | curl(m_k) x curl(m_l) |^2*
where w0[k], w1[k,i] and wc[k,l] are non-negative weighting factors and
mu[k] and mu_c[l,k] are trade-off factors which may be altered
during the inversion. The weighting factors are normalized such that their
integrals over the domain are constant:
*integrate(w0[k] + inner(w1[k,:],1/L[:]**2))=scale[k]* volume(domain)*
*integrate(wc[l,k]*1/L**4)=scale_c[k]* volume(domain) *
"""
def __init__(self, domain, numLevelSets=1,
w0=None, w1=None, wc=None,
location_of_set_m=Data(),
useDiagonalHessianApproximation=False, tol=1e-8,
coordinates=None,
scale=None, scale_c=None):
"""
initialization.
:param domain: domain
:type domain: `Domain`
:param numLevelSets: number of level sets
:type numLevelSets: ``int``
:param w0: weighting factor for the m**2 term. If not set zero is assumed.
:type w0: ``Scalar`` if ``numLevelSets`` == 1 or `Data` object of shape
(``numLevelSets`` ,) if ``numLevelSets`` > 1
:param w1: weighting factor for the grad(m_i) terms. If not set zero is assumed
:type w1: ``Vector`` if ``numLevelSets`` == 1 or `Data` object of shape
(``numLevelSets`` , DIM) if ``numLevelSets`` > 1
:param wc: weighting factor for the cross gradient terms. If not set
zero is assumed. Used for the case if ``numLevelSets`` > 1
only. Only values ``wc[l,k]`` in the lower triangle (l<k)
are used.
:type wc: `Data` object of shape (``numLevelSets`` , ``numLevelSets``)
:param location_of_set_m: marks location of zero values of the level
set function ``m`` by a positive entry.
:type location_of_set_m: ``Scalar`` if ``numLevelSets`` == 1 or `Data`
object of shape (``numLevelSets`` ,) if ``numLevelSets`` > 1
:param useDiagonalHessianApproximation: if True cross gradient terms
between level set components are ignored when calculating
approximations of the inverse of the Hessian Operator.
This can speed-up the calculation of the inverse but may
lead to an increase of the number of iteration steps in the
inversion.
:type useDiagonalHessianApproximation: ``bool``
:param tol: tolerance when solving the PDE for the inverse of the
Hessian Operator
:type tol: positive ``float``
:param coordinates: defines coordinate system to be used
:type coordinates: ReferenceSystem` or `SpatialCoordinateTransformation`
:param scale: weighting factor for level set function variation terms.
If not set one is used.
:type scale: ``Scalar`` if ``numLevelSets`` == 1 or `Data` object of
shape (``numLevelSets`` ,) if ``numLevelSets`` > 1
:param scale_c: scale for the cross gradient terms. If not set
one is assumed. Used for the case if ``numLevelSets`` > 1
only. Only values ``scale_c[l,k]`` in the lower triangle
(l<k) are used.
:type scale_c: `Data` object of shape (``numLevelSets``,``numLevelSets``)
"""
if w0 is None and w1 is None:
raise ValueError("Values for w0 or for w1 must be given.")
if wc is None and numLevelSets>1:
raise ValueError("Values for wc must be given.")
self.logger = logging.getLogger('inv.%s'%self.__class__.__name__)
self.__domain=domain
DIM=self.__domain.getDim()
self.__numLevelSets=numLevelSets
self.__trafo=makeTransformation(domain, coordinates)
self.__pde=LinearPDE(self.__domain, numEquations=self.__numLevelSets, numSolutions=self.__numLevelSets)
self.__pde.getSolverOptions().setTolerance(tol)
self.__pde.setSymmetryOn()
self.__pde.setValue(A=self.__pde.createCoefficient('A'), D=self.__pde.createCoefficient('D'), )
try:
self.__pde.setValue(q=location_of_set_m)
except IllegalCoefficientValue:
raise ValueError("Unable to set location of fixed level set function.")
# =========== check the shape of the scales: ========================
if scale is None:
if numLevelSets == 1 :
scale = 1.
else:
scale = np.ones((numLevelSets,))
else:
scale=np.asarray(scale)
if numLevelSets == 1:
if scale.shape == ():
if not scale > 0 :
raise ValueError("Value for scale must be positive.")
else:
raise ValueError("Unexpected shape %s for scale."%scale.shape)
else:
if scale.shape is (numLevelSets,):
if not min(scale) > 0:
raise ValueError("All values for scale must be positive.")
else:
raise ValueError("Unexpected shape %s for scale."%scale.shape)
if scale_c is None or numLevelSets < 2:
scale_c = np.ones((numLevelSets,numLevelSets))
else:
scale_c=np.asarray(scale_c)
if scale_c.shape == (numLevelSets,numLevelSets):
if not all( [ [ scale_c[l,k] > 0. for l in range(k) ] for k in range(1,numLevelSets) ]):
raise ValueError("All values in the lower triangle of scale_c must be positive.")
else:
raise ValueError("Unexpected shape %s for scale."%scale_c.shape)
# ===== check the shape of the weights: =============================
if w0 is not None:
w0 = interpolate(w0,self.__pde.getFunctionSpaceForCoefficient('D'))
s0=w0.getShape()
if numLevelSets == 1:
if not s0 == () :
raise ValueError("Unexpected shape %s for weight w0."%(s0,))
else:
if not s0 == (numLevelSets,):
raise ValueError("Unexpected shape %s for weight w0."%(s0,))
if not self.__trafo.isCartesian():
w0*=self.__trafo.getVolumeFactor()
if not w1 is None:
w1 = interpolate(w1,self.__pde.getFunctionSpaceForCoefficient('A'))
s1=w1.getShape()
if numLevelSets == 1 :
if not s1 == (DIM,) :
raise ValueError("Unexpected shape %s for weight w1."%(s1,))
else:
if not s1 == (numLevelSets,DIM):
raise ValueError("Unexpected shape %s for weight w1."%(s1,))
if not self.__trafo.isCartesian():
f=self.__trafo.getScalingFactors()**2*self.__trafo.getVolumeFactor()
if numLevelSets == 1:
w1*=f
else:
for i in range(numLevelSets): w1[i,:]*=f
if numLevelSets == 1:
wc=None
else:
wc = interpolate(wc,self.__pde.getFunctionSpaceForCoefficient('A'))
sc=wc.getShape()
if not sc == (numLevelSets, numLevelSets):
raise ValueError("Unexpected shape %s for weight wc."%(sc,))
if not self.__trafo.isCartesian():
raise ValueError("Non-cartesian coordinates for cross-gradient term is not supported yet.")
# ============= now we rescale weights: =============================
L2s=np.asarray(boundingBoxEdgeLengths(domain))**2
L4=1/np.sum(1/L2s)**2
if numLevelSets == 1:
A=0
if w0 is not None:
A = integrate(w0)
if w1 is not None:
A += integrate(inner(w1, 1/L2s))
if A > 0:
f = scale/A
if w0 is not None:
w0*=f
if w1 is not None:
w1*=f
else:
raise ValueError("Non-positive weighting factor detected.")
else: # numLevelSets > 1
for k in range(numLevelSets):
A=0
if w0 is not None:
A = integrate(w0[k])
if w1 is not None:
A += integrate(inner(w1[k,:], 1/L2s))
if A > 0:
f = scale[k]/A
if w0 is not None:
w0[k]*=f
if w1 is not None:
w1[k,:]*=f
else:
raise ValueError("Non-positive weighting factor for level set component %d detected."%k)
# and now the cross-gradient:
if wc is not None:
for l in range(k):
A = integrate(wc[l,k])/L4
if A > 0:
f = scale_c[l,k]/A
wc[l,k]*=f
# else:
# raise ValueError("Non-positive weighting factor for cross-gradient level set components %d and %d detected."%(l,k))
self.__w0=w0
self.__w1=w1
self.__wc=wc
self.__pde_is_set=False
if self.__numLevelSets > 1:
self.__useDiagonalHessianApproximation=useDiagonalHessianApproximation
else:
self.__useDiagonalHessianApproximation=True
self._update_Hessian=True
self.__num_tradeoff_factors=numLevelSets+((numLevelSets-1)*numLevelSets)//2
self.setTradeOffFactors()
self.__vol_d=vol(self.__domain)
def getDomain(self):
"""
returns the domain of the regularization term
:rtype: ``Domain``
"""
return self.__domain
def getCoordinateTransformation(self):
"""
returns the coordinate transformation being used
:rtype: `CoordinateTransformation`
"""
return self.__trafo
def getNumLevelSets(self):
"""
returns the number of level set functions
:rtype: ``int``
"""
return self.__numLevelSets
def getPDE(self):
"""
returns the linear PDE to be solved for the Hessian Operator inverse
:rtype: `LinearPDE`
"""
return self.__pde
def getDualProduct(self, m, r):
"""
returns the dual product of a gradient represented by X=r[1] and Y=r[0]
with a level set function m:
*Y_i*m_i + X_ij*m_{i,j}*
:type m: `Data`
:type r: `ArithmeticTuple`
:rtype: ``float``
"""
A=0
if not r[0].isEmpty(): A+=integrate(inner(r[0], m))
if not r[1].isEmpty(): A+=integrate(inner(r[1], grad(m)))
return A
def getNumTradeOffFactors(self):
"""
returns the number of trade-off factors being used.
:rtype: ``int``
"""
return self.__num_tradeoff_factors
def setTradeOffFactors(self, mu=None):
"""
sets the trade-off factors for the level-set variation and the
cross-gradient.
:param mu: new values for the trade-off factors where values
mu[:numLevelSets] are the trade-off factors for the
level-set variation and the remaining values for
the cross-gradient part with
mu_c[l,k]=mu[numLevelSets+l+((k-1)*k)/2] (l<k).
If no values for mu are given ones are used.
Values must be positive.
:type mu: ``list`` of ``float`` or ```numpy.array```
"""
numLS=self.getNumLevelSets()
numTF=self.getNumTradeOffFactors()
if mu is None:
mu = np.ones((numTF,))
else:
mu = np.asarray(mu)
if mu.shape == (numTF,):
self.setTradeOffFactorsForVariation(mu[:numLS])
mu_c2=np.zeros((numLS,numLS))
for k in range(numLS):
for l in range(k):
mu_c2[l,k] = mu[numLS+l+((k-1)*k)//2]
self.setTradeOffFactorsForCrossGradient(mu_c2)
elif mu.shape == () and numLS ==1:
self.setTradeOffFactorsForVariation(mu)
else:
raise ValueError("Unexpected shape %s for mu."%(mu.shape,))
def setTradeOffFactorsForVariation(self, mu=None):
"""
sets the trade-off factors for the level-set variation part.
:param mu: new values for the trade-off factors. Values must be positive.
:type mu: ``float``, ``list`` of ``float`` or ```numpy.array```
"""
numLS=self.getNumLevelSets()
if mu is None:
if numLS == 1:
mu = 1.
else:
mu = np.ones((numLS,))
if type(mu) == list:
#this is a fix for older versions of numpy where passing in an a list of ints causes
#this code to break.
mu=np.asarray([float(i) for i in mu])
else:
mu=np.asarray(mu)
if numLS == 1:
if mu.shape == (1,): mu=mu[0]
if mu.shape == ():
if mu > 0:
self.__mu= mu
self._new_mu=True
else:
raise ValueError("Value for trade-off factor must be positive.")
else:
raise ValueError("Unexpected shape %s for mu."%str(mu.shape))
else:
if mu.shape == (numLS,):
if min(mu) > 0:
self.__mu= mu
self._new_mu=True
else:
raise ValueError("All values for mu must be positive.")
else:
raise ValueError("Unexpected shape %s for trade-off factor."%str(mu.shape))
def setTradeOffFactorsForCrossGradient(self, mu_c=None):
"""
sets the trade-off factors for the cross-gradient terms.
:param mu_c: new values for the trade-off factors for the cross-gradient
terms. Values must be positive. If no value is given ones
are used. Only value mu_c[l,k] for l<k are used.
:type mu_c: ``float``, ``list`` of ``float`` or ``numpy.array``
"""
numLS=self.getNumLevelSets()
if mu_c is None or numLS < 2:
self.__mu_c = np.ones((numLS,numLS))
elif isinstance(mu_c, float) or isinstance(mu_c, int):
self.__mu_c = np.zeros((numLS,numLS))
self.__mu_c[:,:]=mu_c
else:
mu_c=np.asarray(mu_c)
if mu_c.shape == (numLS,numLS):
if not all( [ [ mu_c[l,k] > 0. for l in range(k) ] for k in range(1,numLS) ]):
raise ValueError("All trade-off factors in the lower triangle of mu_c must be positive.")
else:
self.__mu_c = mu_c
self._new_mu=True
else:
raise ValueError("Unexpected shape %s for mu."%(mu_c.shape,))
def getArguments(self, m):
"""
"""
return grad(m),
def getValue(self, m, grad_m):
"""
returns the value of the cost function J with respect to m.
This equation is specified in the inversion cookbook.
:rtype: ``float``
"""
mu=self.__mu
mu_c=self.__mu_c
DIM=self.getDomain().getDim()
numLS=self.getNumLevelSets()
A=0
if self.__w0 is not None:
r = inner(integrate(m**2 * self.__w0), mu)
self.logger.debug("J_R[m^2] = %e"%r)
A += r
if self.__w1 is not None:
if numLS == 1:
r = integrate(inner(grad_m**2, self.__w1))*mu
self.logger.debug("J_R[grad(m)] = %e"%r)
A += r
else:
for k in range(numLS):
r = mu[k]*integrate(inner(grad_m[k,:]**2,self.__w1[k,:]))
self.logger.debug("J_R[grad(m)][%d] = %e"%(k,r))
A += r
if numLS > 1:
for k in range(numLS):
gk=grad_m[k,:]
len_gk=length(gk)
for l in range(k):
gl=grad_m[l,:]
r = mu_c[l,k] * integrate( self.__wc[l,k] * ( ( len_gk * length(gl) )**2 - inner(gk, gl)**2 ) )
self.logger.debug("J_R[cross][%d,%d] = %e"%(l,k,r))
A += r
return A/2
def getGradient(self, m, grad_m):
"""
returns the gradient of the cost function J with respect to m.
:note: This implementation returns Y_k=dPsi/dm_k and X_kj=dPsi/dm_kj
"""
mu=self.__mu
mu_c=self.__mu_c
DIM=self.getDomain().getDim()
numLS=self.getNumLevelSets()
grad_m=grad(m, Function(m.getDomain()))
if self.__w0 is not None:
Y = m * self.__w0 * mu
else:
if numLS == 1:
Y = Scalar(0, grad_m.getFunctionSpace())
else:
Y = Data(0, (numLS,) , grad_m.getFunctionSpace())
if self.__w1 is not None:
if numLS == 1:
X=grad_m* self.__w1*mu
else:
X=grad_m*self.__w1
for k in range(numLS):
X[k,:]*=mu[k]
else:
X = Data(0, grad_m.getShape(), grad_m.getFunctionSpace())
# cross gradient terms:
if numLS > 1:
for k in range(numLS):
grad_m_k=grad_m[k,:]
l2_grad_m_k = length(grad_m_k)**2
for l in range(k):
grad_m_l=grad_m[l,:]
l2_grad_m_l = length(grad_m_l)**2
grad_m_lk = inner(grad_m_l, grad_m_k)
f = mu_c[l,k]* self.__wc[l,k]
X[l,:] += f * (l2_grad_m_k*grad_m_l - grad_m_lk*grad_m_k)
X[k,:] += f * (l2_grad_m_l*grad_m_k - grad_m_lk*grad_m_l)
return ArithmeticTuple(Y, X)
def getInverseHessianApproximation(self, m, r, grad_m, solve=True):
"""
"""
if self._new_mu or self._update_Hessian:
self._new_mu=False
self._update_Hessian=False
mu=self.__mu
mu_c=self.__mu_c
DIM=self.getDomain().getDim()
numLS=self.getNumLevelSets()
if self.__w0 is not None:
if numLS == 1:
D=self.__w0 * mu
else:
D=self.getPDE().getCoefficient("D")
D.setToZero()
for k in range(numLS): D[k,k]=self.__w0[k] * mu[k]
self.getPDE().setValue(D=D)
A=self.getPDE().getCoefficient("A")
A.setToZero()
if self.__w1 is not None:
if numLS == 1:
for i in range(DIM): A[i,i]=self.__w1[i] * mu
else:
for k in range(numLS):
for i in range(DIM): A[k,i,k,i]=self.__w1[k,i] * mu[k]
if numLS > 1:
# this could be make faster by creating caches for grad_m_k, l2_grad_m_k and o_kk
for k in range(numLS):
grad_m_k=grad_m[k,:]
l2_grad_m_k = length(grad_m_k)**2
o_kk=outer(grad_m_k, grad_m_k)
for l in range(k):
grad_m_l=grad_m[l,:]
l2_grad_m_l = length(grad_m_l)**2
i_lk = inner(grad_m_l, grad_m_k)
o_lk = outer(grad_m_l, grad_m_k)
o_kl = outer(grad_m_k, grad_m_l)
o_ll=outer(grad_m_l, grad_m_l)
f= mu_c[l,k]* self.__wc[l,k]
Z=f * (2*o_lk - o_kl - i_lk*kronecker(DIM))
A[l,:,l,:] += f * (l2_grad_m_k*kronecker(DIM) - o_kk)
A[l,:,k,:] += Z
A[k,:,l,:] += transpose(Z)
A[k,:,k,:] += f * (l2_grad_m_l*kronecker(DIM) - o_ll)
self.getPDE().setValue(A=A)
#self.getPDE().resetRightHandSideCoefficients()
#self.getPDE().setValue(X=r[1])
#print "X only: ",self.getPDE().getSolution()
#self.getPDE().resetRightHandSideCoefficients()
#self.getPDE().setValue(Y=r[0])
#print "Y only: ",self.getPDE().getSolution()
self.getPDE().resetRightHandSideCoefficients()
self.getPDE().setValue(X=r[1], Y=r[0])
if not solve:
return self.getPDE()
return self.getPDE().getSolution()
def updateHessian(self):
"""
notifies the class to recalculate the Hessian operator.
"""
if not self.__useDiagonalHessianApproximation:
self._update_Hessian=True
def getNorm(self, m):
"""
returns the norm of ``m``.
:param m: level set function
:type m: `Data`
:rtype: ``float``
"""
return sqrt(integrate(length(m)**2)/self.__vol_d)
|