def test_HStack(par):
"""Dot-test and inversion for HStack operator with numpy array as input
"""
np.random.seed(0)
G1 = np.random.normal(0, 10, (par['ny'], par['nx'])).astype('float32')
G2 = np.random.normal(0, 10, (par['ny'], par['nx'])).astype('float32')
x = np.ones(2 * par['nx']) + par['imag'] * np.ones(2 * par['nx'])
Hop = HStack([G1, MatrixMult(G2, dtype=par['dtype'])], dtype=par['dtype'])
assert dottest(Hop,
par['ny'],
2 * par['nx'],
complexflag=0 if par['imag'] == 0 else 3)
xlsqr = lsqr(Hop, Hop * x, damp=1e-20, iter_lim=300, show=0)[0]
assert_array_almost_equal(x, xlsqr, decimal=4)
# use numpy matrix directly in the definition of the operator
H1op = HStack([G1, MatrixMult(G2, dtype=par['dtype'])], dtype=par['dtype'])
assert dottest(H1op,
par['ny'],
2 * par['nx'],
complexflag=0 if par['imag'] == 0 else 3)
# use scipy matrix directly in the definition of the operator
G1 = sp_random(par['ny'], par['nx'], density=0.4).astype('float32')
H2op = HStack([G1, MatrixMult(G2, dtype=par['dtype'])], dtype=par['dtype'])
assert dottest(H2op,
par['ny'],
2 * par['nx'],
complexflag=0 if par['imag'] == 0 else 3)
def focusing_wrapper(direct,toff,g0VS,iava,Rop,R1op,Restrop,t):
nr=direct.shape[0]
nsava=iava.shape[0]
nt=t.shape[0]
dt=t[1]-t[0]
# window
directVS_off = direct - toff
idirectVS_off = np.round(directVS_off/dt).astype(np.int)
w = np.zeros((nr, nt))
wi = np.ones((nr, nt))
for ir in range(nr-1):
w[ir, :idirectVS_off[ir]]=1
wi = wi - w
w = np.hstack((np.fliplr(w), w[:, 1:]))
wi = np.hstack((np.fliplr(wi), wi[:, 1:]))
# smoothing
nsmooth=10
if nsmooth>0:
smooth=np.ones(nsmooth)/nsmooth
w = filtfilt(smooth, 1, w)
wi = filtfilt(smooth, 1, wi)
# Input focusing function
fd_plus = np.concatenate((np.fliplr(g0VS.T), np.zeros((nr, nt-1))), axis=-1)
# operators
Wop = Diagonal(w.flatten())
WSop = Diagonal(w[iava].flatten())
WiSop = Diagonal(wi[iava].flatten())
Mop = VStack([HStack([Restrop, -1*WSop*Rop]),
HStack([-1*WSop*R1op, Restrop])])*BlockDiag([Wop, Wop])
Gop = VStack([HStack([Restrop, -1*Rop]),
HStack([-1*R1op, Restrop])])
p0_minus = Rop*fd_plus.flatten()
d = WSop*p0_minus
p0_minus = p0_minus.reshape(nsava, 2*nt-1)
d = np.concatenate((d.reshape(nsava, 2*nt-1), np.zeros((nsava, 2*nt-1))))
# solve
f1 = lsqr(Mop, d.flatten(), iter_lim=10, show=False)[0]
f1 = f1.reshape(2*nr, (2*nt-1))
f1_tot = f1 + np.concatenate((np.zeros((nr, 2*nt-1)), fd_plus))
g = BlockDiag([WiSop,WiSop])*Gop*f1_tot.flatten()
g = g.reshape(2*nsava, (2*nt-1))
f1_minus, f1_plus = f1_tot[:nr], f1_tot[nr:]
g_minus, g_plus = -g[:nsava], np.fliplr(g[nsava:])
return f1_minus, f1_plus, g_minus, g_plus, p0_minus
def test_dense_skinny(par):
"""Dense matrix representation of skinny matrix"""
diag = np.arange(par["nx"]) + par["imag"] * np.arange(par["nx"])
D = np.diag(diag)
Dop = Diagonal(diag, dtype=par["dtype"])
Zop = Zero(par["nx"], 3, dtype=par["dtype"])
Op = HStack([Dop, Zop])
O = np.hstack((D, np.zeros((par["nx"], 3))))
assert_array_equal(Op.todense(), O)
def test_describe():
"""Testing the describe method. As it is is difficult to verify that the
output is correct, at this point we merely test that no error arises when
applying this method to a variety of operators
"""
A = MatrixMult(np.ones((10, 5)))
A.name = "A"
B = Diagonal(np.ones(5))
B.name = "A"
C = MatrixMult(np.ones((10, 5)))
C.name = "C"
AT = A.T
AH = A.H
A3 = 3 * A
D = A + C
E = D * B
F = (A + C) * B + A
G = HStack((A * B, C * B))
H = BlockDiag((F, G))
describe(A)
describe(AT)
describe(AH)
describe(A3)
describe(D)
describe(E)
describe(F)
describe(G)
describe(H)
def test_skinnyregularization(par):
"""Solve inversion with a skinny regularization (rows are smaller than
the number of elements in the model vector)
"""
np.random.seed(10)
d = np.arange(par['nx'] - 1).astype(par['dtype']) + 1.
Dop = Diagonal(d, dtype=par['dtype'])
Regop = HStack([Identity(par['nx'] // 2), Identity(par['nx'] // 2)])
x = np.arange(par['nx'] - 1)
y = Dop * x
xinv = NormalEquationsInversion(Dop, [
Regop,
], y, epsRs=[
1e-4,
])
assert_array_almost_equal(x, xinv, decimal=2)
xinv = RegularizedInversion(Dop, [
Regop,
], y, epsRs=[
1e-4,
])
assert_array_almost_equal(x, xinv, decimal=2)
def test_HStack_incosistent_columns(par):
"""Check error is raised if operators with different number of rows
are passed to VStack
"""
G1 = np.random.normal(0, 10, (par["ny"], par["nx"])).astype(par["dtype"])
G2 = np.random.normal(0, 10, (par["ny"] + 1, par["nx"])).astype(par["dtype"])
with pytest.raises(ValueError):
HStack(
[MatrixMult(G1, dtype=par["dtype"]), MatrixMult(G2, dtype=par["dtype"])],
dtype=par["dtype"],
)
def test_HStack_multiproc(par):
"""Single and multiprocess consistentcy for HStack operator"""
np.random.seed(0)
nproc = 2
G = np.random.normal(0, 10, (par["ny"], par["nx"])).astype(par["dtype"])
x = np.ones(4 * par["nx"]) + par["imag"] * np.ones(4 * par["nx"])
y = np.ones(par["ny"]) + par["imag"] * np.ones(par["ny"])
Hop = HStack([MatrixMult(G, dtype=par["dtype"])] * 4, dtype=par["dtype"])
Hmultiop = HStack(
[MatrixMult(G, dtype=par["dtype"])] * 4, nproc=nproc, dtype=par["dtype"]
)
assert dottest(
Hmultiop, par["ny"], 4 * par["nx"], complexflag=0 if par["imag"] == 0 else 3
)
# forward
assert_array_almost_equal(Hop * x, Hmultiop * x, decimal=4)
# adjoint
assert_array_almost_equal(Hop.H * y, Hmultiop.H * y, decimal=4)
# close pool
Hmultiop.pool.close()
def test_HStack(par):
"""Dot-test and inversion for HStack operator
"""
np.random.seed(10)
G1 = np.random.normal(0, 10, (par['ny'], par['nx'])).astype('float32')
G2 = np.random.normal(0, 10, (par['ny'], par['nx'])).astype('float32')
x = np.ones(2*par['nx']) + par['imag']*np.ones(2*par['nx'])
Hop = HStack([MatrixMult(G1, dtype=par['dtype']),
MatrixMult(G2, dtype=par['dtype'])],
dtype=par['dtype'])
assert dottest(Hop, par['ny'], 2*par['nx'], complexflag=0 if par['imag'] == 0 else 3)
xlsqr = lsqr(Hop, Hop * x, damp=1e-20, iter_lim=300, show=0)[0]
assert_array_almost_equal(x, xlsqr, decimal=4)
def test_HStack(par):
"""Dot-test and inversion for HStack operator
"""
np.random.seed(10)
G1 = da.random.normal(0, 10, (par['ny'], par['nx'])).astype('float32')
G2 = da.random.normal(0, 10, (par['ny'], par['nx'])).astype('float32')
x = da.ones(2 * par['nx']) + par['imag'] * da.ones(2 * par['nx'])
dops = [dMatrixMult(G1, dtype=par['dtype']),
dMatrixMult(G2, dtype=par['dtype'])]
ops = [MatrixMult(G1.compute(), dtype=par['dtype']),
MatrixMult(G2.compute(), dtype=par['dtype'])]
dHop = dHStack(dops, compute=(True, True), dtype=par['dtype'])
Hop = HStack(ops, dtype=par['dtype'])
assert dottest(dHop, par['ny'], 2*par['nx'],
chunks=(par['ny'], 2*par['nx']),
complexflag=0 if par['imag'] == 0 else 3)
dy = dHop * x.ravel()
y = Hop * x.ravel().compute()
assert_array_almost_equal(dy, y, decimal=4)
def test_HStack_rlinear(par):
"""HStack operator applied to mix of R-linear and C-linear operators"""
np.random.seed(0)
if np.dtype(par["dtype"]).kind == "c":
G = (
np.random.normal(0, 10, (par["ny"], par["nx"]))
+ 1j * np.random.normal(0, 10, (par["ny"], par["nx"]))
).astype(par["dtype"])
else:
G = np.random.normal(0, 10, (par["ny"], par["nx"])).astype(par["dtype"])
Rop = Real(dims=(par["ny"],), dtype=par["dtype"])
HSop = HStack([Rop, MatrixMult(G, dtype=par["dtype"])], dtype=par["dtype"])
assert HSop.clinear == False
assert dottest(
HSop, par["ny"], par["nx"] + par["ny"], complexflag=0 if par["imag"] == 0 else 3
)
# forward
x = np.random.randn(par["nx"] + par["ny"]) + par["imag"] * np.random.randn(
par["nx"] + par["ny"]
)
expected = np.sum([np.real(x[: par["ny"]]), G @ x[par["ny"] :]], axis=0)
assert_array_almost_equal(expected, HSop * x, decimal=4)
def Sliding3D(Op, dims, dimsd, nwin, nover, nop,
tapertype='hanning', design=False, nproc=1):
"""3D Sliding transform operator.
Apply a transform operator ``Op`` repeatedly to patches of the model
vector in forward mode and patches of the data vector in adjoint mode.
More specifically, in forward mode the model vector is divided into patches
each patch is transformed, and patches are then recombined in a sliding
window fashion. Both model and data should be 3-dimensional
arrays in nature as they are internally reshaped and interpreted as
3-dimensional arrays. Each patch contains in fact a portion of the
array in the first and second dimensions (and the entire third dimension).
This operator can be used to perform local, overlapping transforms (e.g.,
:obj:`pylops.signalprocessing.FFTND`
or :obj:`pylops.signalprocessing.Radon3D`) of 3-dimensional arrays.
.. note:: The shape of the model has to be consistent with
the number of windows for this operator not to return an error. As the
number of windows depends directly on the choice of ``nwin`` and
``nover``, it is recommended to use ``design=True`` if unsure about the
choice ``dims`` and use the number of windows printed on screen to
define such input parameter.
.. warning:: Depending on the choice of `nwin` and `nover` as well as the
size of the data, sliding windows may not cover the entire first and/or
second dimensions. The start and end indeces of each window can be
displayed using ``design=True`` while defining the best sliding window
approach.
Parameters
----------
Op : :obj:`pylops.LinearOperator`
Transform operator
dims : :obj:`tuple`
Shape of 3-dimensional model. Note that ``dims[0]`` and ``dims[1]``
should be multiple of the model sizes of the transform in the
first and second dimensions
dimsd : :obj:`tuple`
Shape of 3-dimensional data
nwin : :obj:`tuple`
Number of samples of window
nover : :obj:`tuple`
Number of samples of overlapping part of window
nop : :obj:`tuple`
Number of samples in axes of transformed domain associated
to spatial axes in the data
tapertype : :obj:`str`, optional
Type of taper (``hanning``, ``cosine``, ``cosinesquare`` or ``None``)
design : :obj:`bool`, optional
Print number sliding window (``True``) or not (``False``)
Returns
-------
Sop : :obj:`pylops.LinearOperator`
Sliding operator
Raises
------
ValueError
Identified number of windows is not consistent with provided model
shape (``dims``).
"""
# model windows
mwin0_ins, mwin0_ends = _slidingsteps(dims[0],
Op.shape[1]//(nop[1]*dims[2]), 0)
mwin1_ins, mwin1_ends = _slidingsteps(dims[1],
Op.shape[1]//(nop[0]*dims[2]), 0)
# data windows
dwin0_ins, dwin0_ends = _slidingsteps(dimsd[0], nwin[0], nover[0])
dwin1_ins, dwin1_ends = _slidingsteps(dimsd[1], nwin[1], nover[1])
nwins0 = len(dwin0_ins)
nwins1 = len(dwin1_ins)
nwins = nwins0*nwins1
# create tapers
if tapertype is not None:
tap = taper3d(dimsd[2], nwin, nover, tapertype=tapertype)
# check that identified number of windows agrees with mode size
if design:
logging.warning('(%d,%d) windows required...', nwins0, nwins1)
logging.warning('model wins - start0:%s, end0:%s, start1:%s, end1:%s',
str(mwin0_ins), str(mwin0_ends),
str(mwin1_ins), str(mwin1_ends))
logging.warning('data wins - start0:%s, end0:%s, start1:%s, end1:%s',
str(dwin0_ins), str(dwin0_ends),
str(dwin1_ins), str(dwin1_ends))
if nwins*Op.shape[1]//dims[2] != dims[0]*dims[1]:
raise ValueError('Model shape (dims=%s) is not consistent with chosen '
'number of windows. Choose dims[0]=%d and '
'dims[1]=%d for the operator to work with '
'estimated number of windows, or create '
'the operator with design=True to find out the'
'optimal number of windows for the current '
'model size...'
% (str(dims), nwins0*Op.shape[1]//(nop[1]*dims[2]),
nwins1 * Op.shape[1]//(nop[0]*dims[2])))
# transform to apply
if tapertype is None:
OOp = BlockDiag([Op for _ in range(nwins)], nproc=nproc)
else:
OOp = BlockDiag([Diagonal(tap.flatten()) * Op
for _ in range(nwins)], nproc=nproc)
hstack = HStack([Restriction(dimsd[1] * dimsd[2] * nwin[0],
range(win_in, win_end),
dims=(nwin[0], dimsd[1], dimsd[2]),
dir=1).H
for win_in, win_end in zip(dwin1_ins,
dwin1_ends)])
combining1 = BlockDiag([hstack]*nwins0)
combining0 = HStack([Restriction(np.prod(dimsd),
range(win_in, win_end),
dims=dimsd, dir=0).H
for win_in, win_end in zip(dwin0_ins, dwin0_ends)])
Sop = combining0 * combining1 * OOp
return Sop
def Block(ops, dtype=None):
r"""Block operator.
Create a block operator from N lists of M linear operators each.
Parameters
----------
ops : :obj:`list`
List of lists of operators to be combined in block fashion
dtype : :obj:`str`, optional
Type of elements in input array.
Attributes
----------
shape : :obj:`tuple`
Operator shape
explicit : :obj:`bool`
Operator contains a matrix that can be solved explicitly (``True``) or
not (``False``)
Notes
-----
In mathematics, a block or a partitioned matrix is a matrix that is
interpreted as being broken into sections called blocks or submatrices.
Similarly a block operator is composed of N sets of M linear operators
each such that its application in forward mode leads to
.. math::
\begin{bmatrix}
\mathbf{L_{1,1}} & \mathbf{L_{1,2}} & ... & \mathbf{L_{1,M}} \\
\mathbf{L_{2,1}} & \mathbf{L_{2,2}} & ... & \mathbf{L_{2,M}} \\
... & ... & ... & ... \\
\mathbf{L_{N,1}} & \mathbf{L_{N,2}} & ... & \mathbf{L_{N,M}} \\
\end{bmatrix}
\begin{bmatrix}
\mathbf{x}_{1} \\
\mathbf{x}_{2} \\
... \\
\mathbf{x}_{M}
\end{bmatrix} =
\begin{bmatrix}
\mathbf{L_{1,1}} \mathbf{x}_{1} + \mathbf{L_{1,2}} \mathbf{x}_{2} +
\mathbf{L_{1,M}} \mathbf{x}_{M} \\
\mathbf{L_{2,1}} \mathbf{x}_{1} + \mathbf{L_{2,2}} \mathbf{x}_{2} +
\mathbf{L_{2,M}} \mathbf{x}_{M} \\
... \\
\mathbf{L_{N,1}} \mathbf{x}_{1} + \mathbf{L_{N,2}} \mathbf{x}_{2} +
\mathbf{L_{N,M}} \mathbf{x}_{M} \\
\end{bmatrix}
while its application in adjoint mode leads to
.. math::
\begin{bmatrix}
\mathbf{L_{1,1}}^H & \mathbf{L_{2,1}}^H & ... &
\mathbf{L_{N,1}}^H \\
\mathbf{L_{1,2}}^H & \mathbf{L_{2,2}}^H & ... &
\mathbf{L_{N,2}}^H \\
... & ... & ... & ... \\
\mathbf{L_{1,M}}^H & \mathbf{L_{2,M}}^H & ... &
\mathbf{L_{N,M}}^H \\
\end{bmatrix}
\begin{bmatrix}
\mathbf{y}_{1} \\
\mathbf{y}_{2} \\
... \\
\mathbf{y}_{N}
\end{bmatrix} =
\begin{bmatrix}
\mathbf{L_{1,1}}^H \mathbf{y}_{1} +
\mathbf{L_{2,1}}^H \mathbf{y}_{2} +
\mathbf{L_{N,1}}^H \mathbf{y}_{N} \\
\mathbf{L_{1,2}}^H \mathbf{y}_{1} +
\mathbf{L_{2,2}}^H \mathbf{y}_{2} +
\mathbf{L_{N,2}}^H \mathbf{y}_{N} \\
... \\
\mathbf{L_{1,M}}^H \mathbf{y}_{1} +
\mathbf{L_{2,M}}^H \mathbf{y}_{2} +
\mathbf{L_{N,M}}^H \mathbf{y}_{N} \\
\end{bmatrix}
"""
hblocks = [HStack(hblock, dtype=dtype) for hblock in ops]
return VStack(hblocks, dtype=dtype)
def Sliding1D(Op, dim, dimd, nwin, nover, tapertype="hanning", design=False):
r"""1D Sliding transform operator.
Apply a transform operator ``Op`` repeatedly to slices of the model
vector in forward mode and slices of the data vector in adjoint mode.
More specifically, in forward mode the model vector is divided into
slices, each slice is transformed, and slices are then recombined in a
sliding window fashion.
This operator can be used to perform local, overlapping transforms (e.g.,
:obj:`pylops.signalprocessing.FFT`) on 1-dimensional arrays.
.. note:: The shape of the model has to be consistent with
the number of windows for this operator not to return an error. As the
number of windows depends directly on the choice of ``nwin`` and
``nover``, it is recommended to use ``design=True`` if unsure about the
choice ``dims`` and use the number of windows printed on screen to
define such input parameter.
.. warning:: Depending on the choice of `nwin` and `nover` as well as the
size of the data, sliding windows may not cover the entire data.
The start and end indices of each window can be displayed using
``design=True`` while defining the best sliding window approach.
Parameters
----------
Op : :obj:`pylops.LinearOperator`
Transform operator
dim : :obj:`tuple`
Shape of 1-dimensional model.
dimd : :obj:`tuple`
Shape of 1-dimensional data
nwin : :obj:`int`
Number of samples of window
nover : :obj:`int`
Number of samples of overlapping part of window
tapertype : :obj:`str`, optional
Type of taper (``hanning``, ``cosine``, ``cosinesquare`` or ``None``)
design : :obj:`bool`, optional
Print number of sliding window (``True``) or not (``False``)
Returns
-------
Sop : :obj:`pylops.LinearOperator`
Sliding operator
Raises
------
ValueError
Identified number of windows is not consistent with provided model
shape (``dims``).
"""
# model windows
mwin_ins, mwin_ends = _slidingsteps(dim, Op.shape[1], 0)
# data windows
dwin_ins, dwin_ends = _slidingsteps(dimd, nwin, nover)
nwins = len(dwin_ins)
# create tapers
if tapertype is not None:
tap = taper(nwin, nover, tapertype=tapertype)
tapin = tap.copy()
tapin[:nover] = 1
tapend = tap.copy()
tapend[-nover:] = 1
taps = {}
taps[0] = tapin
for i in range(1, nwins - 1):
taps[i] = tap
taps[nwins - 1] = tapend
# check that identified number of windows agrees with mode size
if design:
logging.warning("%d windows required...", nwins)
logging.warning("model wins - start:%s, end:%s", str(mwin_ins), str(mwin_ends))
logging.warning("data wins - start:%s, end:%s", str(dwin_ins), str(dwin_ends))
if nwins * Op.shape[1] != dim:
raise ValueError(
"Model shape (dim=%d) is not consistent with chosen "
"number of windows. Choose dim=%d for the "
"operator to work with estimated number of windows, "
"or create the operator with design=True to find "
"out the optimal number of windows for the current "
"model size..." % (dim, nwins * Op.shape[1])
)
# transform to apply
if tapertype is None:
OOp = BlockDiag([Op for _ in range(nwins)])
else:
OOp = BlockDiag([Diagonal(taps[itap].ravel()) * Op for itap in range(nwins)])
combining = HStack(
[
Restriction(dimd, np.arange(win_in, win_end), dtype=Op.dtype).H
for win_in, win_end in zip(dwin_ins, dwin_ends)
]
)
Sop = combining * OOp
return Sop
def focusing_wrapper(direct, toff, g0VS, iava1, Rop1, R1op1, Restrop1, iava2,
Rop2, R1op2, Restrop2, t):
nsmooth = 10
nr = direct.shape[0]
nsava1 = iava1.shape[0]
nsava2 = iava2.shape[0]
nt = t.shape[0]
dt = t[1] - t[0]
# window
directVS_off = direct - toff
idirectVS_off = np.round(directVS_off / dt).astype(np.int)
w = np.zeros((nr, nt))
wi = np.ones((nr, nt))
for ir in range(nr - 1):
w[ir, :idirectVS_off[ir]] = 1
wi = wi - w
w = np.hstack((np.fliplr(w), w[:, 1:]))
wi = np.hstack((np.fliplr(wi), wi[:, 1:]))
if nsmooth > 0:
smooth = np.ones(nsmooth) / nsmooth
w = filtfilt(smooth, 1, w)
wi = filtfilt(smooth, 1, wi)
# Input focusing function
fd_plus = np.concatenate((np.fliplr(g0VS.T), np.zeros((nr, nt - 1))),
axis=-1)
# operators
Wop = Diagonal(w.flatten())
WSop1 = Diagonal(w[iava1].flatten())
WSop2 = Diagonal(w[iava2].flatten())
WiSop1 = Diagonal(wi[iava1].flatten())
WiSop2 = Diagonal(wi[iava2].flatten())
Mop1 = VStack([
HStack([Restrop1, -1 * WSop1 * Rop1]),
HStack([-1 * WSop1 * R1op1, Restrop1])
]) * BlockDiag([Wop, Wop])
Mop2 = VStack([
HStack([Restrop2, -1 * WSop2 * Rop2]),
HStack([-1 * WSop2 * R1op2, Restrop2])
]) * BlockDiag([Wop, Wop])
Mop = VStack([
HStack([Mop1, Mop1, Zero(Mop1.shape[0], Mop1.shape[1])]),
HStack([Mop2, Zero(Mop2.shape[0], Mop2.shape[1]), Mop2])
])
Gop1 = VStack(
[HStack([Restrop1, -1 * Rop1]),
HStack([-1 * R1op1, Restrop1])])
Gop2 = VStack(
[HStack([Restrop2, -1 * Rop2]),
HStack([-1 * R1op2, Restrop2])])
d1 = WSop1 * Rop1 * fd_plus.flatten()
d1 = np.concatenate(
(d1.reshape(nsava1, 2 * nt - 1), np.zeros((nsava1, 2 * nt - 1))))
d2 = WSop2 * Rop2 * fd_plus.flatten()
d2 = np.concatenate(
(d2.reshape(nsava2, 2 * nt - 1), np.zeros((nsava2, 2 * nt - 1))))
d = np.concatenate((d1, d2))
# solve
comb_f = lsqr(Mop, d.flatten(), iter_lim=10, show=False)[0]
comb_f = comb_f.reshape(6 * nr, (2 * nt - 1))
comb_f_tot = comb_f + np.concatenate((np.zeros(
(nr, 2 * nt - 1)), fd_plus, np.zeros((4 * nr, 2 * nt - 1))))
f1_1 = comb_f_tot[:2 * nr] + comb_f_tot[2 * nr:4 * nr]
f1_2 = comb_f_tot[:2 * nr] + comb_f_tot[4 * nr:]
g_1 = BlockDiag([WiSop1, WiSop1]) * Gop1 * f1_1.flatten()
g_1 = g_1.reshape(2 * nsava1, (2 * nt - 1))
g_2 = BlockDiag([WiSop2, WiSop2]) * Gop2 * f1_2.flatten()
g_2 = g_2.reshape(2 * nsava2, (2 * nt - 1))
f1_1_minus, f1_1_plus = f1_1[:nr], f1_1[nr:]
f1_2_minus, f1_2_plus = f1_2[:nr], f1_2[nr:]
g_1_minus, g_1_plus = -g_1[:nsava1], np.fliplr(g_1[nsava1:])
g_2_minus, g_2_plus = -g_2[:nsava2], np.fliplr(g_2[nsava2:])
return f1_1_minus, f1_1_plus, f1_2_minus, f1_2_plus, g_1_minus, g_1_plus, g_2_minus, g_2_plus
def redatuming_wrapper(toff, W, wav, iava, Rop, R1op, Restrop, Sparseop, vsx,
vsz, x, z, z_current, nt, dt, nfft, nr, ds, dvsx):
from scipy.signal import filtfilt
nava = iava.shape[0]
nvsx = vsx.shape[0]
PUP = np.zeros(shape=(nava, nvsx, nt))
PDOWN = np.zeros(shape=(nava, nvsx, nt))
for ix in range(nvsx):
s = '####### Point ' + str(ix + 1) + ' of ' + str(
nvsx) + ' of current line (z = ' + str(z_current) + ', x = ' + str(
vsx[ix]) + ')'
print(s)
# direct wave
direct = np.loadtxt(path0 + 'Traveltimes/trav_x' + str(vsx[ix]) +
'_z' + str(z_current) + '.dat',
delimiter=',')
f = 2 * np.pi * np.arange(nfft) / (dt * nfft)
g0VS = np.zeros((nfft, nr), dtype=np.complex128)
for it in range(len(W)):
g0VS[it] = W[it] * f[it] * hankel2(0, f[it] * direct + 1e-10) / 4
g0VS = np.fft.irfft(g0VS, nfft, axis=0) / dt
g0VS = np.real(g0VS[:nt])
nr = direct.shape[0]
nsava = iava.shape[0]
# window
directVS_off = direct - toff
idirectVS_off = np.round(directVS_off / dt).astype(np.int)
w = np.zeros((nr, nt))
wi = np.ones((nr, nt))
for ir in range(nr - 1):
w[ir, :idirectVS_off[ir]] = 1
wi = wi - w
w = np.hstack((np.fliplr(w), w[:, 1:]))
wi = np.hstack((np.fliplr(wi), wi[:, 1:]))
# smoothing
nsmooth = 10
if nsmooth > 0:
smooth = np.ones(nsmooth) / nsmooth
w = filtfilt(smooth, 1, w)
wi = filtfilt(smooth, 1, wi)
# Input focusing function
fd_plus = np.concatenate((np.fliplr(g0VS.T), np.zeros((nr, nt - 1))),
axis=-1)
# create operators
Wop = Diagonal(w.flatten())
WSop = Diagonal(w[iava].flatten())
WiSop = Diagonal(wi[iava].flatten())
Mop = VStack([
HStack([Restrop, -1 * WSop * Rop]),
HStack([-1 * WSop * R1op, Restrop])
]) * BlockDiag([Wop, Wop])
Mop_radon = Mop * Sparseop
Gop = VStack(
[HStack([Restrop, -1 * Rop]),
HStack([-1 * R1op, Restrop])])
d = WSop * Rop * fd_plus.flatten()
d = np.concatenate(
(d.reshape(nsava, 2 * nt - 1), np.zeros((nsava, 2 * nt - 1))))
# solve with SPGL1
f = SPGL1(Mop_radon,
d.flatten(),
sigma=1e-5,
iter_lim=35,
opt_tol=0.05,
dec_tol=0.05,
verbosity=1)[0]
# alternatively solve with FISTA
#f = FISTA(Mop_radon, d.flatten(), eps=1e-1, niter=200,
# alpha=2.129944e-04, eigsiter=4, eigstol=1e-3,
# tol=1e-2, returninfo=False, show=True)[0]
# alternatively solve with LSQR
#f = lsqr(Mop_radon, d.flatten(), iter_lim=100, show=True)[0]
f = Sparseop * f
f = f.reshape(2 * nr, (2 * nt - 1))
f_tot = f + np.concatenate((np.zeros((nr, 2 * nt - 1)), fd_plus))
g_1 = BlockDiag([WiSop, WiSop]) * Gop * f_tot.flatten()
g_1 = g_1.reshape(2 * nsava, (2 * nt - 1))
#f1_minus, f1_plus = f_tot[:nr], f_tot[nr:]
g_minus, g_plus = -g_1[:nsava], np.fliplr(g_1[nsava:])
#
PUP[:, ix, :] = g_minus[:, nt - 1:]
PDOWN[:, ix, :] = g_plus[:, nt - 1:]
# save redatumed wavefield (line-by-line)
jt = 2
redatumed = MDD(PDOWN[:, :, ::jt],
PUP[:, :, ::jt],
dt=jt * dt,
dr=dvsx,
wav=wav[::jt],
twosided=True,
adjoint=False,
psf=False,
dtype='complex64',
dottest=False,
**dict(iter_lim=20, show=0))
np.savetxt(path_save + 'Line1_' + str(z_current) + '.dat',
np.diag(redatumed[:, :, (nt + 1) // jt - 1]),
delimiter=',')
# calculate and save angle gathers (line-by-line)
vel_sm = np.loadtxt(path0 + 'vel_sm.dat', delimiter=',')
cp = vel_sm[find_closest(z_current, z), 751 // 2]
irA = np.asarray([7, 15, 24, 35])
nalpha = 201
A = np.zeros((nalpha, len(irA)))
for i in np.arange(0, len(irA)):
ir = irA[i]
anglegath, alpha = AngleGather(np.swapaxes(redatumed, 0, 2), nvsx,
nalpha, dt * jt, ds, ir, cp)
A[:, i] = anglegath
np.savetxt(path_save + 'AngleGather1_' + str(z_current) + '.dat',
A,
delimiter=',')
def Patch2D(Op,
dims,
dimsd,
nwin,
nover,
nop,
tapertype="hanning",
design=False):
"""2D Patch transform operator.
Apply a transform operator ``Op`` repeatedly to patches of the model
vector in forward mode and patches of the data vector in adjoint mode.
More specifically, in forward mode the model vector is divided into
patches, each patch is transformed, and patches are then recombined
together. Both model and data are internally reshaped and
interpreted as 2-dimensional arrays: each patch contains a portion
of the array in both the first and second dimension.
This operator can be used to perform local, overlapping transforms (e.g.,
:obj:`pylops.signalprocessing.FFT2D`
or :obj:`pylops.signalprocessing.Radon2D`) on 2-dimensional arrays.
.. note:: The shape of the model has to be consistent with
the number of windows for this operator not to return an error. As the
number of windows depends directly on the choice of ``nwin`` and
``nover``, it is recommended to use ``design=True`` if unsure about the
choice ``dims`` and use the number of windows printed on screen to
define such input parameter.
.. warning:: Depending on the choice of `nwin` and `nover` as well as the
size of the data, patches may not cover the entire size of the data.
The start and end indices of each window can be displayed using
``design=True`` while defining the best patching approach.
Parameters
----------
Op : :obj:`pylops.LinearOperator`
Transform operator
dims : :obj:`tuple`
Shape of 2-dimensional model. Note that ``dims[0]`` and ``dims[1]``
should be multiple of the model size of the transform in their
respective dimensions
dimsd : :obj:`tuple`
Shape of 2-dimensional data
nwin : :obj:`tuple`
Number of samples of window
nover : :obj:`tuple`
Number of samples of overlapping part of window
nop : :obj:`tuple`
Size of model in the transformed domain
tapertype : :obj:`str`, optional
Type of taper (``hanning``, ``cosine``, ``cosinesquare`` or ``None``)
design : :obj:`bool`, optional
Print number of sliding window (``True``) or not (``False``)
Returns
-------
Sop : :obj:`pylops.LinearOperator`
Sliding operator
Raises
------
ValueError
Identified number of windows is not consistent with provided model
shape (``dims``).
See Also
--------
Sliding2d: 2D Sliding transform operator.
"""
# model windows
mwin0_ins, mwin0_ends = _slidingsteps(dims[0], nop[0], 0)
mwin1_ins, mwin1_ends = _slidingsteps(dims[1], nop[1], 0)
# data windows
dwin0_ins, dwin0_ends = _slidingsteps(dimsd[0], nwin[0], nover[0])
dwin1_ins, dwin1_ends = _slidingsteps(dimsd[1], nwin[1], nover[1])
nwins0 = len(dwin0_ins)
nwins1 = len(dwin1_ins)
nwins = nwins0 * nwins1
# create tapers
if tapertype is not None:
tap = taper2d(nwin[1], nwin[0], nover,
tapertype=tapertype).astype(Op.dtype)
taps = {itap: tap for itap in range(nwins)}
# topmost tapers
taptop = tap.copy()
taptop[:nover[0]] = tap[nwin[0] // 2]
for itap in range(0, nwins1):
taps[itap] = taptop
# bottommost tapers
tapbottom = tap.copy()
tapbottom[-nover[0]:] = tap[nwin[0] // 2]
for itap in range(nwins - nwins1, nwins):
taps[itap] = tapbottom
# leftmost tapers
tapleft = tap.copy()
tapleft[:, :nover[1]] = tap[:, nwin[1] // 2][:, np.newaxis]
for itap in range(0, nwins, nwins1):
taps[itap] = tapleft
# rightmost tapers
tapright = tap.copy()
tapright[:, -nover[1]:] = tap[:, nwin[1] // 2][:, np.newaxis]
for itap in range(nwins1 - 1, nwins, nwins1):
taps[itap] = tapright
# lefttopcorner taper
taplefttop = tap.copy()
taplefttop[:, :nover[1]] = tap[:, nwin[1] // 2][:, np.newaxis]
taplefttop[:nover[0]] = taplefttop[nwin[0] // 2]
taps[0] = taplefttop
# righttopcorner taper
taprighttop = tap.copy()
taprighttop[:, -nover[1]:] = tap[:, nwin[1] // 2][:, np.newaxis]
taprighttop[:nover[0]] = taprighttop[nwin[0] // 2]
taps[nwins1 - 1] = taprighttop
# leftbottomcorner taper
tapleftbottom = tap.copy()
tapleftbottom[:, :nover[1]] = tap[:, nwin[1] // 2][:, np.newaxis]
tapleftbottom[-nover[0]:] = tapleftbottom[nwin[0] // 2]
taps[nwins - nwins1] = tapleftbottom
# rightbottomcorner taper
taprightbottom = tap.copy()
taprightbottom[:, -nover[1]:] = tap[:, nwin[1] // 2][:, np.newaxis]
taprightbottom[-nover[0]:] = taprightbottom[nwin[0] // 2]
taps[nwins - 1] = taprightbottom
# check that identified number of windows agrees with mode size
if design:
logging.warning("%d-%d windows required...", nwins0, nwins1)
logging.warning(
"model wins - start:%s, end:%s / start:%s, end:%s",
str(mwin0_ins),
str(mwin0_ends),
str(mwin1_ins),
str(mwin1_ends),
)
logging.warning(
"data wins - start:%s, end:%s / start:%s, end:%s",
str(dwin0_ins),
str(dwin0_ends),
str(dwin1_ins),
str(dwin1_ends),
)
if nwins0 * nop[0] != dims[0] or nwins1 * nop[1] != dims[1]:
raise ValueError("Model shape (dims=%s) is not consistent with chosen "
"number of windows. Choose dims[0]=%d and "
"dims[1]=%d for the operator to work with "
"estimated number of windows, or create "
"the operator with design=True to find out the"
"optimal number of windows for the current "
"model size..." %
(str(dims), nwins0 * nop[0], nwins1 * nop[1]))
# transform to apply
if tapertype is None:
OOp = BlockDiag([Op for _ in range(nwins)])
else:
OOp = BlockDiag([
Diagonal(taps[itap].ravel(), dtype=Op.dtype) * Op
for itap in range(nwins)
])
hstack = HStack([
Restriction(
dimsd[1] * nwin[0],
range(win_in, win_end),
dims=(nwin[0], dimsd[1]),
dir=1,
dtype=Op.dtype,
).H for win_in, win_end in zip(dwin1_ins, dwin1_ends)
])
combining1 = BlockDiag([hstack] * nwins0)
combining0 = HStack([
Restriction(
np.prod(dimsd),
range(win_in, win_end),
dims=dimsd,
dir=0,
dtype=Op.dtype,
).H for win_in, win_end in zip(dwin0_ins, dwin0_ends)
])
Pop = combining0 * combining1 * OOp
return Pop
def Sliding2D(Op, dims, dimsd, nwin, nover, tapertype='hanning', design=False):
"""2D Sliding transform operator.
Apply a transform operator ``Op`` repeatedly to patches of the model
vector in forward mode and patches of the data vector in adjoint mode.
More specifically, in forward mode the model vector is divided into patches
each patch is transformed, and patches are then recombined in a sliding
window fashion. Both model and data should be 2-dimensional
arrays in nature as they are internally reshaped and interpreted as
2-dimensional arrays. Each patch contains in fact a portion of the
array in the first dimension (and the entire second dimension).
This operator can be used to perform local, overlapping transforms (e.g.,
:obj:`pylops.signalprocessing.FFT2`
or :obj:`pylops.signalprocessing.Radon2D`) of 2-dimensional arrays.
.. note:: The shape of the model has to be consistent with
the number of windows for this operator not to return an error. As the
number of windows depends directly on the choice of ``nwin`` and
``nover``, it is recommended to use ``design=True`` if unsure about the
choice ``dims`` and use the number of windows printed on screen to
define such input parameter.
.. warning:: Depending on the choice of `nwin` and `nover` as well as the
size of the data, sliding windows may not cover the entire first dimension.
The start and end indeces of each window can be displayed using
``design=True`` while defining the best sliding window approach.
Parameters
----------
Op : :obj:`pylops.LinearOperator`
Transform operator
dims : :obj:`tuple`
Shape of 2-dimensional model. Note that ``dims[0]`` should be multiple
of the model size of the transform in the first dimension
dimsd : :obj:`tuple`
Shape of 2-dimensional data
nwin : :obj:`int`
Number of samples of window
nover : :obj:`int`
Number of samples of overlapping part of window
tapertype : :obj:`str`, optional
Type of taper (``hanning``, ``cosine``, ``cosinesquare`` or ``None``)
design : :obj:`bool`, optional
Print number of sliding window (``True``) or not (``False``)
Returns
-------
Sop : :obj:`pylops.LinearOperator`
Sliding operator
Raises
------
ValueError
Identified number of windows is not consistent with provided model
shape (``dims``).
"""
# model windows
mwin_ins, mwin_ends = _slidingsteps(dims[0], Op.shape[1] // dims[1], 0)
# data windows
dwin_ins, dwin_ends = _slidingsteps(dimsd[0], nwin, nover)
nwins = len(dwin_ins)
# create tapers
if tapertype is not None:
tap = taper2d(dimsd[1], nwin, nover, tapertype=tapertype)
tapin = tap.copy()
tapin[:nover] = 1
tapend = tap.copy()
tapend[-nover:] = 1
taps = {}
taps[0] = tapin
for i in range(1, nwins - 1):
taps[i] = tap
taps[nwins - 1] = tapend
# check that identified number of windows agrees with mode size
if design:
logging.warning('%d windows required...', nwins)
logging.warning('model wins - start:%s, end:%s', str(mwin_ins),
str(mwin_ends))
logging.warning('data wins - start:%s, end:%s', str(dwin_ins),
str(dwin_ends))
if nwins * Op.shape[1] // dims[1] != dims[0]:
raise ValueError('Model shape (dims=%s) is not consistent with chosen '
'number of windows. Choose dims[0]=%d for the '
'operator to work with estimated number of windows, '
'or create the operator with design=True to find '
'out the optimal number of windows for the current '
'model size...' %
(str(dims), nwins * Op.shape[1] // dims[1]))
# transform to apply
if tapertype is None:
OOp = BlockDiag([Op for _ in range(nwins)])
else:
OOp = BlockDiag(
[Diagonal(taps[itap].flatten()) * Op for itap in range(nwins)])
combining = HStack([
Restriction(np.prod(dimsd), range(win_in, win_end), dims=dimsd).H
for win_in, win_end in zip(dwin_ins, dwin_ends)
])
Sop = combining * OOp
return Sop