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Remove external libraries ulab replaces
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# The MIT License (MIT)
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#
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# Copyright (c) 2019 Nick Lee
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#
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# Permission is hereby granted, free of charge, to any person obtaining a copy of
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# this software and associated documentation files (the "Software"), to deal in
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# the Software without restriction, including without limitation the rights to
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# use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
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# the Software, and to permit persons to whom the Software is furnished to do so,
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# subject to the following conditions:
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#
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# The above copyright notice and this permission notice shall be included in all
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# copies or substantial portions of the Software.
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#
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# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
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# FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
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# COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
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# IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
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# CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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def _dot(a, b):
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s = 0
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for i in range(0, len(b)):
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s += a[i] * b[i]
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return s
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def mul(A, b):
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return [_dot(row, b) for row in A]
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def _height(A):
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return len(A)
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def _width(A):
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return len(A[0])
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def _max_magnitude_row(A, column):
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first_row = column
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max_row = first_row
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max_value = A[first_row][column]
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for i in range(first_row+1, _height(A)):
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if abs(A[i][column]) > abs(max_value):
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max_row = i
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max_value = A[i][column]
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return max_row
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def _subtract_rows_below(A, row, column, pivot_value):
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# Fill in factors where entries will become zero.
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for i in range(row+1, _height(A)):
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A[i][column] /= pivot_value
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for i in range(row+1, _height(A)):
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for j in range(column+1, _width(A)):
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A[i][j] -= (A[i][column] * A[row][j])
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def lu(A):
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P = None
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for pivot_column in range(0, _width(A)-1):
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pivot_row = pivot_column
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max_row = _max_magnitude_row(A, pivot_column)
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pivot_value = A[max_row][pivot_column]
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if max_row != pivot_row:
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A[pivot_row], A[max_row] = A[max_row], A[pivot_row]
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if P is None:
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P = list(range(0, _height(A)))
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P[pivot_row], P[max_row] = P[max_row], P[pivot_row]
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_subtract_rows_below(A, pivot_row, pivot_column, pivot_value)
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return P,A
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def _forward_substitute(A, b):
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for i in range(1, len(b)):
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for j in range(0, i):
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b[i] = b[i] - (b[j] * A[i][j])
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def _backward_substitute(A, b):
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size = len(b)
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b[-1] = b[-1] / A[-1][-1]
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for i in range(size-2, -1, -1):
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for j in range(i+1, size):
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b[i] = b[i] - (b[j] * A[i][j])
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b[i] = b[i] / A[i][i]
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def solve(PLU, b):
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P, LU = PLU
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x = b[:] if P is None else [b[i] for i in P] # permutation
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_forward_substitute(LU, x)
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_backward_substitute(LU, x)
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return x
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@ -1,674 +0,0 @@
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GNU GENERAL PUBLIC LICENSE
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Version 3, 29 June 2007
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Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/>
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Everyone is permitted to copy and distribute verbatim copies
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of this license document, but changing it is not allowed.
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Preamble
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The GNU General Public License is a free, copyleft license for
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software and other kinds of works.
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The licenses for most software and other practical works are designed
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to take away your freedom to share and change the works. By contrast,
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the GNU General Public License is intended to guarantee your freedom to
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share and change all versions of a program--to make sure it remains free
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software for all its users. We, the Free Software Foundation, use the
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GNU General Public License for most of our software; it applies also to
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any other work released this way by its authors. You can apply it to
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When we speak of free software, we are referring to freedom, not
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TERMS AND CONDITIONS
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conveying of source, or (2) access to copy the
|
|
||||||
Corresponding Source from a network server at no charge.
|
|
||||||
|
|
||||||
c) Convey individual copies of the object code with a copy of the
|
|
||||||
written offer to provide the Corresponding Source. This
|
|
||||||
alternative is allowed only occasionally and noncommercially, and
|
|
||||||
only if you received the object code with such an offer, in accord
|
|
||||||
with subsection 6b.
|
|
||||||
|
|
||||||
d) Convey the object code by offering access from a designated
|
|
||||||
place (gratis or for a charge), and offer equivalent access to the
|
|
||||||
Corresponding Source in the same way through the same place at no
|
|
||||||
further charge. You need not require recipients to copy the
|
|
||||||
Corresponding Source along with the object code. If the place to
|
|
||||||
copy the object code is a network server, the Corresponding Source
|
|
||||||
may be on a different server (operated by you or a third party)
|
|
||||||
that supports equivalent copying facilities, provided you maintain
|
|
||||||
clear directions next to the object code saying where to find the
|
|
||||||
Corresponding Source. Regardless of what server hosts the
|
|
||||||
Corresponding Source, you remain obligated to ensure that it is
|
|
||||||
available for as long as needed to satisfy these requirements.
|
|
||||||
|
|
||||||
e) Convey the object code using peer-to-peer transmission, provided
|
|
||||||
you inform other peers where the object code and Corresponding
|
|
||||||
Source of the work are being offered to the general public at no
|
|
||||||
charge under subsection 6d.
|
|
||||||
|
|
||||||
A separable portion of the object code, whose source code is excluded
|
|
||||||
from the Corresponding Source as a System Library, need not be
|
|
||||||
included in conveying the object code work.
|
|
||||||
|
|
||||||
A "User Product" is either (1) a "consumer product", which means any
|
|
||||||
tangible personal property which is normally used for personal, family,
|
|
||||||
or household purposes, or (2) anything designed or sold for incorporation
|
|
||||||
into a dwelling. In determining whether a product is a consumer product,
|
|
||||||
doubtful cases shall be resolved in favor of coverage. For a particular
|
|
||||||
product received by a particular user, "normally used" refers to a
|
|
||||||
typical or common use of that class of product, regardless of the status
|
|
||||||
of the particular user or of the way in which the particular user
|
|
||||||
actually uses, or expects or is expected to use, the product. A product
|
|
||||||
is a consumer product regardless of whether the product has substantial
|
|
||||||
commercial, industrial or non-consumer uses, unless such uses represent
|
|
||||||
the only significant mode of use of the product.
|
|
||||||
|
|
||||||
"Installation Information" for a User Product means any methods,
|
|
||||||
procedures, authorization keys, or other information required to install
|
|
||||||
and execute modified versions of a covered work in that User Product from
|
|
||||||
a modified version of its Corresponding Source. The information must
|
|
||||||
suffice to ensure that the continued functioning of the modified object
|
|
||||||
code is in no case prevented or interfered with solely because
|
|
||||||
modification has been made.
|
|
||||||
|
|
||||||
If you convey an object code work under this section in, or with, or
|
|
||||||
specifically for use in, a User Product, and the conveying occurs as
|
|
||||||
part of a transaction in which the right of possession and use of the
|
|
||||||
User Product is transferred to the recipient in perpetuity or for a
|
|
||||||
fixed term (regardless of how the transaction is characterized), the
|
|
||||||
Corresponding Source conveyed under this section must be accompanied
|
|
||||||
by the Installation Information. But this requirement does not apply
|
|
||||||
if neither you nor any third party retains the ability to install
|
|
||||||
modified object code on the User Product (for example, the work has
|
|
||||||
been installed in ROM).
|
|
||||||
|
|
||||||
The requirement to provide Installation Information does not include a
|
|
||||||
requirement to continue to provide support service, warranty, or updates
|
|
||||||
for a work that has been modified or installed by the recipient, or for
|
|
||||||
the User Product in which it has been modified or installed. Access to a
|
|
||||||
network may be denied when the modification itself materially and
|
|
||||||
adversely affects the operation of the network or violates the rules and
|
|
||||||
protocols for communication across the network.
|
|
||||||
|
|
||||||
Corresponding Source conveyed, and Installation Information provided,
|
|
||||||
in accord with this section must be in a format that is publicly
|
|
||||||
documented (and with an implementation available to the public in
|
|
||||||
source code form), and must require no special password or key for
|
|
||||||
unpacking, reading or copying.
|
|
||||||
|
|
||||||
7. Additional Terms.
|
|
||||||
|
|
||||||
"Additional permissions" are terms that supplement the terms of this
|
|
||||||
License by making exceptions from one or more of its conditions.
|
|
||||||
Additional permissions that are applicable to the entire Program shall
|
|
||||||
be treated as though they were included in this License, to the extent
|
|
||||||
that they are valid under applicable law. If additional permissions
|
|
||||||
apply only to part of the Program, that part may be used separately
|
|
||||||
under those permissions, but the entire Program remains governed by
|
|
||||||
this License without regard to the additional permissions.
|
|
||||||
|
|
||||||
When you convey a copy of a covered work, you may at your option
|
|
||||||
remove any additional permissions from that copy, or from any part of
|
|
||||||
it. (Additional permissions may be written to require their own
|
|
||||||
removal in certain cases when you modify the work.) You may place
|
|
||||||
additional permissions on material, added by you to a covered work,
|
|
||||||
for which you have or can give appropriate copyright permission.
|
|
||||||
|
|
||||||
Notwithstanding any other provision of this License, for material you
|
|
||||||
add to a covered work, you may (if authorized by the copyright holders of
|
|
||||||
that material) supplement the terms of this License with terms:
|
|
||||||
|
|
||||||
a) Disclaiming warranty or limiting liability differently from the
|
|
||||||
terms of sections 15 and 16 of this License; or
|
|
||||||
|
|
||||||
b) Requiring preservation of specified reasonable legal notices or
|
|
||||||
author attributions in that material or in the Appropriate Legal
|
|
||||||
Notices displayed by works containing it; or
|
|
||||||
|
|
||||||
c) Prohibiting misrepresentation of the origin of that material, or
|
|
||||||
requiring that modified versions of such material be marked in
|
|
||||||
reasonable ways as different from the original version; or
|
|
||||||
|
|
||||||
d) Limiting the use for publicity purposes of names of licensors or
|
|
||||||
authors of the material; or
|
|
||||||
|
|
||||||
e) Declining to grant rights under trademark law for use of some
|
|
||||||
trade names, trademarks, or service marks; or
|
|
||||||
|
|
||||||
f) Requiring indemnification of licensors and authors of that
|
|
||||||
material by anyone who conveys the material (or modified versions of
|
|
||||||
it) with contractual assumptions of liability to the recipient, for
|
|
||||||
any liability that these contractual assumptions directly impose on
|
|
||||||
those licensors and authors.
|
|
||||||
|
|
||||||
All other non-permissive additional terms are considered "further
|
|
||||||
restrictions" within the meaning of section 10. If the Program as you
|
|
||||||
received it, or any part of it, contains a notice stating that it is
|
|
||||||
governed by this License along with a term that is a further
|
|
||||||
restriction, you may remove that term. If a license document contains
|
|
||||||
a further restriction but permits relicensing or conveying under this
|
|
||||||
License, you may add to a covered work material governed by the terms
|
|
||||||
of that license document, provided that the further restriction does
|
|
||||||
not survive such relicensing or conveying.
|
|
||||||
|
|
||||||
If you add terms to a covered work in accord with this section, you
|
|
||||||
must place, in the relevant source files, a statement of the
|
|
||||||
additional terms that apply to those files, or a notice indicating
|
|
||||||
where to find the applicable terms.
|
|
||||||
|
|
||||||
Additional terms, permissive or non-permissive, may be stated in the
|
|
||||||
form of a separately written license, or stated as exceptions;
|
|
||||||
the above requirements apply either way.
|
|
||||||
|
|
||||||
8. Termination.
|
|
||||||
|
|
||||||
You may not propagate or modify a covered work except as expressly
|
|
||||||
provided under this License. Any attempt otherwise to propagate or
|
|
||||||
modify it is void, and will automatically terminate your rights under
|
|
||||||
this License (including any patent licenses granted under the third
|
|
||||||
paragraph of section 11).
|
|
||||||
|
|
||||||
However, if you cease all violation of this License, then your
|
|
||||||
license from a particular copyright holder is reinstated (a)
|
|
||||||
provisionally, unless and until the copyright holder explicitly and
|
|
||||||
finally terminates your license, and (b) permanently, if the copyright
|
|
||||||
holder fails to notify you of the violation by some reasonable means
|
|
||||||
prior to 60 days after the cessation.
|
|
||||||
|
|
||||||
Moreover, your license from a particular copyright holder is
|
|
||||||
reinstated permanently if the copyright holder notifies you of the
|
|
||||||
violation by some reasonable means, this is the first time you have
|
|
||||||
received notice of violation of this License (for any work) from that
|
|
||||||
copyright holder, and you cure the violation prior to 30 days after
|
|
||||||
your receipt of the notice.
|
|
||||||
|
|
||||||
Termination of your rights under this section does not terminate the
|
|
||||||
licenses of parties who have received copies or rights from you under
|
|
||||||
this License. If your rights have been terminated and not permanently
|
|
||||||
reinstated, you do not qualify to receive new licenses for the same
|
|
||||||
material under section 10.
|
|
||||||
|
|
||||||
9. Acceptance Not Required for Having Copies.
|
|
||||||
|
|
||||||
You are not required to accept this License in order to receive or
|
|
||||||
run a copy of the Program. Ancillary propagation of a covered work
|
|
||||||
occurring solely as a consequence of using peer-to-peer transmission
|
|
||||||
to receive a copy likewise does not require acceptance. However,
|
|
||||||
nothing other than this License grants you permission to propagate or
|
|
||||||
modify any covered work. These actions infringe copyright if you do
|
|
||||||
not accept this License. Therefore, by modifying or propagating a
|
|
||||||
covered work, you indicate your acceptance of this License to do so.
|
|
||||||
|
|
||||||
10. Automatic Licensing of Downstream Recipients.
|
|
||||||
|
|
||||||
Each time you convey a covered work, the recipient automatically
|
|
||||||
receives a license from the original licensors, to run, modify and
|
|
||||||
propagate that work, subject to this License. You are not responsible
|
|
||||||
for enforcing compliance by third parties with this License.
|
|
||||||
|
|
||||||
An "entity transaction" is a transaction transferring control of an
|
|
||||||
organization, or substantially all assets of one, or subdividing an
|
|
||||||
organization, or merging organizations. If propagation of a covered
|
|
||||||
work results from an entity transaction, each party to that
|
|
||||||
transaction who receives a copy of the work also receives whatever
|
|
||||||
licenses to the work the party's predecessor in interest had or could
|
|
||||||
give under the previous paragraph, plus a right to possession of the
|
|
||||||
Corresponding Source of the work from the predecessor in interest, if
|
|
||||||
the predecessor has it or can get it with reasonable efforts.
|
|
||||||
|
|
||||||
You may not impose any further restrictions on the exercise of the
|
|
||||||
rights granted or affirmed under this License. For example, you may
|
|
||||||
not impose a license fee, royalty, or other charge for exercise of
|
|
||||||
rights granted under this License, and you may not initiate litigation
|
|
||||||
(including a cross-claim or counterclaim in a lawsuit) alleging that
|
|
||||||
any patent claim is infringed by making, using, selling, offering for
|
|
||||||
sale, or importing the Program or any portion of it.
|
|
||||||
|
|
||||||
11. Patents.
|
|
||||||
|
|
||||||
A "contributor" is a copyright holder who authorizes use under this
|
|
||||||
License of the Program or a work on which the Program is based. The
|
|
||||||
work thus licensed is called the contributor's "contributor version".
|
|
||||||
|
|
||||||
A contributor's "essential patent claims" are all patent claims
|
|
||||||
owned or controlled by the contributor, whether already acquired or
|
|
||||||
hereafter acquired, that would be infringed by some manner, permitted
|
|
||||||
by this License, of making, using, or selling its contributor version,
|
|
||||||
but do not include claims that would be infringed only as a
|
|
||||||
consequence of further modification of the contributor version. For
|
|
||||||
purposes of this definition, "control" includes the right to grant
|
|
||||||
patent sublicenses in a manner consistent with the requirements of
|
|
||||||
this License.
|
|
||||||
|
|
||||||
Each contributor grants you a non-exclusive, worldwide, royalty-free
|
|
||||||
patent license under the contributor's essential patent claims, to
|
|
||||||
make, use, sell, offer for sale, import and otherwise run, modify and
|
|
||||||
propagate the contents of its contributor version.
|
|
||||||
|
|
||||||
In the following three paragraphs, a "patent license" is any express
|
|
||||||
agreement or commitment, however denominated, not to enforce a patent
|
|
||||||
(such as an express permission to practice a patent or covenant not to
|
|
||||||
sue for patent infringement). To "grant" such a patent license to a
|
|
||||||
party means to make such an agreement or commitment not to enforce a
|
|
||||||
patent against the party.
|
|
||||||
|
|
||||||
If you convey a covered work, knowingly relying on a patent license,
|
|
||||||
and the Corresponding Source of the work is not available for anyone
|
|
||||||
to copy, free of charge and under the terms of this License, through a
|
|
||||||
publicly available network server or other readily accessible means,
|
|
||||||
then you must either (1) cause the Corresponding Source to be so
|
|
||||||
available, or (2) arrange to deprive yourself of the benefit of the
|
|
||||||
patent license for this particular work, or (3) arrange, in a manner
|
|
||||||
consistent with the requirements of this License, to extend the patent
|
|
||||||
license to downstream recipients. "Knowingly relying" means you have
|
|
||||||
actual knowledge that, but for the patent license, your conveying the
|
|
||||||
covered work in a country, or your recipient's use of the covered work
|
|
||||||
in a country, would infringe one or more identifiable patents in that
|
|
||||||
country that you have reason to believe are valid.
|
|
||||||
|
|
||||||
If, pursuant to or in connection with a single transaction or
|
|
||||||
arrangement, you convey, or propagate by procuring conveyance of, a
|
|
||||||
covered work, and grant a patent license to some of the parties
|
|
||||||
receiving the covered work authorizing them to use, propagate, modify
|
|
||||||
or convey a specific copy of the covered work, then the patent license
|
|
||||||
you grant is automatically extended to all recipients of the covered
|
|
||||||
work and works based on it.
|
|
||||||
|
|
||||||
A patent license is "discriminatory" if it does not include within
|
|
||||||
the scope of its coverage, prohibits the exercise of, or is
|
|
||||||
conditioned on the non-exercise of one or more of the rights that are
|
|
||||||
specifically granted under this License. You may not convey a covered
|
|
||||||
work if you are a party to an arrangement with a third party that is
|
|
||||||
in the business of distributing software, under which you make payment
|
|
||||||
to the third party based on the extent of your activity of conveying
|
|
||||||
the work, and under which the third party grants, to any of the
|
|
||||||
parties who would receive the covered work from you, a discriminatory
|
|
||||||
patent license (a) in connection with copies of the covered work
|
|
||||||
conveyed by you (or copies made from those copies), or (b) primarily
|
|
||||||
for and in connection with specific products or compilations that
|
|
||||||
contain the covered work, unless you entered into that arrangement,
|
|
||||||
or that patent license was granted, prior to 28 March 2007.
|
|
||||||
|
|
||||||
Nothing in this License shall be construed as excluding or limiting
|
|
||||||
any implied license or other defenses to infringement that may
|
|
||||||
otherwise be available to you under applicable patent law.
|
|
||||||
|
|
||||||
12. No Surrender of Others' Freedom.
|
|
||||||
|
|
||||||
If conditions are imposed on you (whether by court order, agreement or
|
|
||||||
otherwise) that contradict the conditions of this License, they do not
|
|
||||||
excuse you from the conditions of this License. If you cannot convey a
|
|
||||||
covered work so as to satisfy simultaneously your obligations under this
|
|
||||||
License and any other pertinent obligations, then as a consequence you may
|
|
||||||
not convey it at all. For example, if you agree to terms that obligate you
|
|
||||||
to collect a royalty for further conveying from those to whom you convey
|
|
||||||
the Program, the only way you could satisfy both those terms and this
|
|
||||||
License would be to refrain entirely from conveying the Program.
|
|
||||||
|
|
||||||
13. Use with the GNU Affero General Public License.
|
|
||||||
|
|
||||||
Notwithstanding any other provision of this License, you have
|
|
||||||
permission to link or combine any covered work with a work licensed
|
|
||||||
under version 3 of the GNU Affero General Public License into a single
|
|
||||||
combined work, and to convey the resulting work. The terms of this
|
|
||||||
License will continue to apply to the part which is the covered work,
|
|
||||||
but the special requirements of the GNU Affero General Public License,
|
|
||||||
section 13, concerning interaction through a network will apply to the
|
|
||||||
combination as such.
|
|
||||||
|
|
||||||
14. Revised Versions of this License.
|
|
||||||
|
|
||||||
The Free Software Foundation may publish revised and/or new versions of
|
|
||||||
the GNU General Public License from time to time. Such new versions will
|
|
||||||
be similar in spirit to the present version, but may differ in detail to
|
|
||||||
address new problems or concerns.
|
|
||||||
|
|
||||||
Each version is given a distinguishing version number. If the
|
|
||||||
Program specifies that a certain numbered version of the GNU General
|
|
||||||
Public License "or any later version" applies to it, you have the
|
|
||||||
option of following the terms and conditions either of that numbered
|
|
||||||
version or of any later version published by the Free Software
|
|
||||||
Foundation. If the Program does not specify a version number of the
|
|
||||||
GNU General Public License, you may choose any version ever published
|
|
||||||
by the Free Software Foundation.
|
|
||||||
|
|
||||||
If the Program specifies that a proxy can decide which future
|
|
||||||
versions of the GNU General Public License can be used, that proxy's
|
|
||||||
public statement of acceptance of a version permanently authorizes you
|
|
||||||
to choose that version for the Program.
|
|
||||||
|
|
||||||
Later license versions may give you additional or different
|
|
||||||
permissions. However, no additional obligations are imposed on any
|
|
||||||
author or copyright holder as a result of your choosing to follow a
|
|
||||||
later version.
|
|
||||||
|
|
||||||
15. Disclaimer of Warranty.
|
|
||||||
|
|
||||||
THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
|
|
||||||
APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
|
|
||||||
HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
|
|
||||||
OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
|
|
||||||
THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
|
|
||||||
PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
|
|
||||||
IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
|
|
||||||
ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
|
|
||||||
|
|
||||||
16. Limitation of Liability.
|
|
||||||
|
|
||||||
IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
|
|
||||||
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
|
|
||||||
THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
|
|
||||||
GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
|
|
||||||
USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
|
|
||||||
DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
|
|
||||||
PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
|
|
||||||
EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
|
|
||||||
SUCH DAMAGES.
|
|
||||||
|
|
||||||
17. Interpretation of Sections 15 and 16.
|
|
||||||
|
|
||||||
If the disclaimer of warranty and limitation of liability provided
|
|
||||||
above cannot be given local legal effect according to their terms,
|
|
||||||
reviewing courts shall apply local law that most closely approximates
|
|
||||||
an absolute waiver of all civil liability in connection with the
|
|
||||||
Program, unless a warranty or assumption of liability accompanies a
|
|
||||||
copy of the Program in return for a fee.
|
|
||||||
|
|
||||||
END OF TERMS AND CONDITIONS
|
|
||||||
|
|
||||||
How to Apply These Terms to Your New Programs
|
|
||||||
|
|
||||||
If you develop a new program, and you want it to be of the greatest
|
|
||||||
possible use to the public, the best way to achieve this is to make it
|
|
||||||
free software which everyone can redistribute and change under these terms.
|
|
||||||
|
|
||||||
To do so, attach the following notices to the program. It is safest
|
|
||||||
to attach them to the start of each source file to most effectively
|
|
||||||
state the exclusion of warranty; and each file should have at least
|
|
||||||
the "copyright" line and a pointer to where the full notice is found.
|
|
||||||
|
|
||||||
<one line to give the program's name and a brief idea of what it does.>
|
|
||||||
Copyright (C) <year> <name of author>
|
|
||||||
|
|
||||||
This program is free software: you can redistribute it and/or modify
|
|
||||||
it under the terms of the GNU General Public License as published by
|
|
||||||
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 <https://www.gnu.org/licenses/>.
|
|
||||||
|
|
||||||
Also add information on how to contact you by electronic and paper mail.
|
|
||||||
|
|
||||||
If the program does terminal interaction, make it output a short
|
|
||||||
notice like this when it starts in an interactive mode:
|
|
||||||
|
|
||||||
<program> Copyright (C) <year> <name of author>
|
|
||||||
This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
|
|
||||||
This is free software, and you are welcome to redistribute it
|
|
||||||
under certain conditions; type `show c' for details.
|
|
||||||
|
|
||||||
The hypothetical commands `show w' and `show c' should show the appropriate
|
|
||||||
parts of the General Public License. Of course, your program's commands
|
|
||||||
might be different; for a GUI interface, you would use an "about box".
|
|
||||||
|
|
||||||
You should also get your employer (if you work as a programmer) or school,
|
|
||||||
if any, to sign a "copyright disclaimer" for the program, if necessary.
|
|
||||||
For more information on this, and how to apply and follow the GNU GPL, see
|
|
||||||
<https://www.gnu.org/licenses/>.
|
|
||||||
|
|
||||||
The GNU General Public License does not permit incorporating your program
|
|
||||||
into proprietary programs. If your program is a subroutine library, you
|
|
||||||
may consider it more useful to permit linking proprietary applications with
|
|
||||||
the library. If this is what you want to do, use the GNU Lesser General
|
|
||||||
Public License instead of this License. But first, please read
|
|
||||||
<https://www.gnu.org/licenses/why-not-lgpl.html>.
|
|
||||||
@ -1,173 +0,0 @@
|
|||||||
# OpenRV - Robot Vision routines for OpenMV
|
|
||||||
|
|
||||||
[OpenMV](https://openmv.io) is a small camera board for machine vision. I use it
|
|
||||||
to direct my robot. [The software
|
|
||||||
library](http://docs.openmv.io/library/index.html) is adequate, but lacks some
|
|
||||||
algorithms I need. Out comes this project, in which I implement a few missing
|
|
||||||
pieces myself. I hope it could save time for someone who tries to do the same.
|
|
||||||
|
|
||||||
**Everything is tested on OpenMV Cam H7**
|
|
||||||
|
|
||||||
## Prerequisites
|
|
||||||
|
|
||||||
Vector and matrix are mainstay in machine vision. Finding no satisfactory
|
|
||||||
libraries, I have again implemented my own.
|
|
||||||
|
|
||||||
#### Vector Operations on MicroPython
|
|
||||||
|
|
||||||
- [Project](https://gitlab.com/nickoala/micropython-vec)
|
|
||||||
- [Package](https://pypi.org/project/micropython-vec/)
|
|
||||||
|
|
||||||
#### Fast Matrix Multiplication and Linear Solver on MicroPython
|
|
||||||
|
|
||||||
- [Project](https://gitlab.com/nickoala/micropython-mtx)
|
|
||||||
- [Package](https://pypi.org/project/micropython-mtx/)
|
|
||||||
|
|
||||||
Along with this project's `rv` package, the OpenMV camera's SD card should
|
|
||||||
contain:
|
|
||||||
|
|
||||||
```
|
|
||||||
/
|
|
||||||
├── mtx.py
|
|
||||||
├── rv
|
|
||||||
│ ├── __init__.py
|
|
||||||
│ ├── moments.py
|
|
||||||
│ ├── planar.py
|
|
||||||
│ └── quickshiftpp.py
|
|
||||||
└── vec
|
|
||||||
├── distance.py
|
|
||||||
└── __init__.py
|
|
||||||
```
|
|
||||||
|
|
||||||
**In addition, you need some theoretical backgrounds to use vision algorithms
|
|
||||||
effectively. This page does not give you those backgrounds. Study them
|
|
||||||
yourself.**
|
|
||||||
|
|
||||||
## Hu moments
|
|
||||||
|
|
||||||
[Hu moments](https://docs.opencv.org/2.4/modules/imgproc/doc/structural_analysis_and_shape_descriptors.html#humoments)
|
|
||||||
[is a shape descriptor](https://www.pyimagesearch.com/2014/10/27/opencv-shape-descriptor-hu-moments-example/)
|
|
||||||
[invariant to translation, scale, and rotation](https://www.learnopencv.com/shape-matching-using-hu-moments-c-python/).
|
|
||||||
That means it can recognize the same shape no matter its location, size, and orientation in the picture.
|
|
||||||
|
|
||||||
#### Usage
|
|
||||||
|
|
||||||
The last element of Hu moments is somewhat of an oddball. It indicates
|
|
||||||
reflection rather than the general shape. For matching, the last element should
|
|
||||||
be dropped.
|
|
||||||
|
|
||||||
Use the function `vec.distance.euclidean()` to see how close two vectors are.
|
|
||||||
|
|
||||||
```python
|
|
||||||
import rv.moments
|
|
||||||
import vec.distance
|
|
||||||
import image
|
|
||||||
|
|
||||||
a = image.Image('/images/a.pgm')
|
|
||||||
b = image.Image('/images/b.pgm')
|
|
||||||
|
|
||||||
ha = rv.moments.hu(a)
|
|
||||||
hb = rv.moments.hu(b)
|
|
||||||
|
|
||||||
print(vec.distance.euclidean(ha[:-1], hb[:-1]))
|
|
||||||
```
|
|
||||||
|
|
||||||
**Remark:** Although accepting gray-level images, this implementation treats
|
|
||||||
pixels as either 0 or 1. Pixels having a non-zero brightness are treated as 1.
|
|
||||||
This speeds up calculation.
|
|
||||||
|
|
||||||
**More:** [test_moments.py](test/test_moments.py)
|
|
||||||
|
|
||||||
## Planar homography
|
|
||||||
|
|
||||||
Map points from one coordinate system to another. For example, a red ball sits
|
|
||||||
at (90, 50) on the image and you know it is on the floor (not floating in air),
|
|
||||||
planar homography can map the image point (90, 50) to a position on the floor,
|
|
||||||
telling you how far the red ball is in front of the robot and how much left or
|
|
||||||
right. In this case, points are essentially mapped from the *image coordinate
|
|
||||||
system* to the *floor coordinate system*.
|
|
||||||
|
|
||||||
Once you can map points, finding out the size of objects is straight-forward.
|
|
||||||
|
|
||||||
#### Usage
|
|
||||||
|
|
||||||
It works only when two coordinate systems (i.e. the two planes) are fixed
|
|
||||||
relative to each other. In other words, the camera's height and orientation
|
|
||||||
relative to the floor cannot change.
|
|
||||||
|
|
||||||
**[First, you have to calibrate for a homography matrix, which is a very long
|
|
||||||
story. I have devoted an entire directory to discuss the process. Take a look
|
|
||||||
there.](homography)**
|
|
||||||
|
|
||||||
Once you have the matrix, the rest is easy.
|
|
||||||
|
|
||||||
```python
|
|
||||||
import rv.planar
|
|
||||||
|
|
||||||
H = [[ 3.14916496e+01, -9.79038178e+02, 1.03951636e+05],
|
|
||||||
[ 7.57939015e+02, -3.31912533e+01, -5.86807545e+04],
|
|
||||||
[ 2.06572544e-01, 2.03579263e+00, 1.00000000e+00]]
|
|
||||||
|
|
||||||
p = rv.planar.Planar(H)
|
|
||||||
|
|
||||||
image_points = [[83, 109],
|
|
||||||
[70, 100],
|
|
||||||
[51, 92]]
|
|
||||||
|
|
||||||
print(p.project(image_points))
|
|
||||||
```
|
|
||||||
|
|
||||||
**More:** [test_planar.py](test/test_planar.py)
|
|
||||||
|
|
||||||
## Quickshift++
|
|
||||||
|
|
||||||
[The latest member](https://github.com/google/quickshift) [of the
|
|
||||||
Meanshift](http://www.chioka.in/meanshift-algorithm-for-the-rest-of-us-python/)
|
|
||||||
[family of clustering
|
|
||||||
algorithms](https://github.com/Nick-Ol/MedoidShift-and-QuickShift), Quickshift++
|
|
||||||
accepts a bunch of points and group them. I use it to "discover" the colors of
|
|
||||||
disks on the floor, before using colors to pick out the disks. This saves me
|
|
||||||
from hard-coding the colors beforehand, and makes the robot adaptive.
|
|
||||||
|
|
||||||
It is not optimized to handle a large number of points. OpenMV's limited memory
|
|
||||||
precludes handling a lot of points anyway. Don't expect to use it to segment an
|
|
||||||
entire image.
|
|
||||||
|
|
||||||
#### Usage
|
|
||||||
|
|
||||||
```python
|
|
||||||
import rv.quickshiftpp
|
|
||||||
|
|
||||||
points = [
|
|
||||||
# cluster 1
|
|
||||||
[1, 1],
|
|
||||||
[1.0, 1.2],
|
|
||||||
[0.9, 1.1],
|
|
||||||
[0.95, 0.99],
|
|
||||||
|
|
||||||
# cluster 2
|
|
||||||
[3.3, 3.0],
|
|
||||||
|
|
||||||
# cluster 3
|
|
||||||
[5.0, 8.2],
|
|
||||||
[5.5, 7.9],
|
|
||||||
[4.8, 8.1],
|
|
||||||
[5.1, 7.7],
|
|
||||||
]
|
|
||||||
|
|
||||||
print(rv.quickshiftpp.cluster(points,
|
|
||||||
k=2,
|
|
||||||
beta=0.2))
|
|
||||||
```
|
|
||||||
|
|
||||||
The parameter `k` determines how density is estimated. It uses *distance to the
|
|
||||||
k-th nearest neighbor* to estimate density around each point.
|
|
||||||
|
|
||||||
The parameter `beta` determines how much density is allowed to vary within
|
|
||||||
cluster cores. Here is not the place to explain what "cluster core" means. Some
|
|
||||||
theoretical understanding cannot be avoided.
|
|
||||||
|
|
||||||
In short, use `k` and `beta` to tune the clustering.
|
|
||||||
|
|
||||||
**More:** [test_quickshiftpp.py](test/test_quickshiftpp.py) and
|
|
||||||
[test_quickshiftpp_colors.py](test/test_quickshiftpp_colors.py)
|
|
||||||
@ -1 +0,0 @@
|
|||||||
|
|
||||||
@ -1,86 +0,0 @@
|
|||||||
import math
|
|
||||||
|
|
||||||
def _sum(img, roi, f):
|
|
||||||
x, y, w, h = roi or (0, 0, img.width(), img.height())
|
|
||||||
s = 0
|
|
||||||
for i in range(x, x + w):
|
|
||||||
for j in range(y, y + h):
|
|
||||||
if img.get_pixel(i,j) != 0:
|
|
||||||
s += f(i, j)
|
|
||||||
return s
|
|
||||||
|
|
||||||
def centroid(img, roi=None, return_intermediate=False):
|
|
||||||
m10 = _sum(img, roi, lambda x,y: x)
|
|
||||||
m01 = _sum(img, roi, lambda x,y: y)
|
|
||||||
m00 = _sum(img, roi, lambda x,y: 1)
|
|
||||||
|
|
||||||
c = [0, 0] if m00 == 0 else [float(m10 / m00), float(m01 / m00)]
|
|
||||||
|
|
||||||
return [m00, c] if return_intermediate else c
|
|
||||||
|
|
||||||
def central(img, roi=None, return_intermediate=False):
|
|
||||||
results = centroid(img, roi, return_intermediate=True)
|
|
||||||
cx, cy = results[-1]
|
|
||||||
|
|
||||||
u20 = _sum(img, roi, lambda x,y: (x-cx)**2)
|
|
||||||
u11 = _sum(img, roi, lambda x,y: (x-cx) * (y-cy))
|
|
||||||
u02 = _sum(img, roi, lambda x,y: (y-cy)**2)
|
|
||||||
|
|
||||||
u30 = _sum(img, roi, lambda x,y: (x-cx)**3)
|
|
||||||
u21 = _sum(img, roi, lambda x,y: (x-cx)**2 * (y-cy))
|
|
||||||
u12 = _sum(img, roi, lambda x,y: (x-cx) * (y-cy)**2)
|
|
||||||
u03 = _sum(img, roi, lambda x,y: (y-cy)**3)
|
|
||||||
|
|
||||||
us = [u20, u11, u02, u30, u21, u12, u03]
|
|
||||||
|
|
||||||
return (results + [us]) if return_intermediate else us
|
|
||||||
|
|
||||||
def normalized_central(img, roi=None, return_intermediate=False):
|
|
||||||
results = central(img, roi, return_intermediate=True)
|
|
||||||
m00, _, [u20, u11, u02, u30, u21, u12, u03] = results
|
|
||||||
|
|
||||||
if m00 == 0:
|
|
||||||
ns = [0, 0, 0, 0, 0, 0, 0]
|
|
||||||
else:
|
|
||||||
m2 = m00**2
|
|
||||||
m3 = m00**2.5
|
|
||||||
n20, n11, n02 = u20/m2, u11/m2, u02/m2
|
|
||||||
n30, n21, n12, n03 = u30/m3, u21/m3, u12/m3, u03/m3
|
|
||||||
|
|
||||||
ns = [n20, n11, n02, n30, n21, n12, n03]
|
|
||||||
|
|
||||||
return (results + [ns]) if return_intermediate else ns
|
|
||||||
|
|
||||||
def hu(img, roi=None, return_intermediate=False):
|
|
||||||
results = normalized_central(img, roi, return_intermediate=True)
|
|
||||||
n20, n11, n02, n30, n21, n12, n03 = results[-1]
|
|
||||||
|
|
||||||
h0 = n20 + n02
|
|
||||||
|
|
||||||
h1 = (n20 - n02)**2 + 4 * n11 * n11
|
|
||||||
|
|
||||||
_n30_3n12 = n30 - 3 * n12
|
|
||||||
_3n21_n03 = 3 * n21 - n03
|
|
||||||
|
|
||||||
h2 = _n30_3n12**2 + _3n21_n03**2
|
|
||||||
|
|
||||||
n3012 = n30 + n12
|
|
||||||
n3012_2 = n3012 * n3012
|
|
||||||
|
|
||||||
n2103 = n21 + n03
|
|
||||||
n2103_2 = n2103 * n2103
|
|
||||||
|
|
||||||
h3 = n3012_2 + n2103_2
|
|
||||||
|
|
||||||
h4 = (_n30_3n12 * n3012 * ( n3012_2 - 3 * n2103_2 )
|
|
||||||
+ _3n21_n03 * n2103 * ( 3 * n3012_2 - n2103_2 ))
|
|
||||||
|
|
||||||
h5 = ( n20 - n02 ) * ( n3012_2 - n2103_2 ) + 4 * n11 * n3012 * n2103
|
|
||||||
|
|
||||||
h6 = (_3n21_n03 * n2103 * ( 3 * n3012_2 - n2103_2 )
|
|
||||||
- _n30_3n12 * n2103 * ( 3 * n3012_2 - n2103_2 ))
|
|
||||||
|
|
||||||
hs = [0 if h == 0 else math.copysign(math.log10(math.fabs(h)), h)
|
|
||||||
for h in [h0, h1, h2, h3, h4, h5, h6]]
|
|
||||||
|
|
||||||
return (results + [hs]) if return_intermediate else hs
|
|
||||||
@ -1,20 +0,0 @@
|
|||||||
import mtx, vec
|
|
||||||
|
|
||||||
class Planar(object):
|
|
||||||
def __init__(self, H, offset=[0,0]):
|
|
||||||
self.H = H
|
|
||||||
self.H_ = None # LU factorization of H
|
|
||||||
self.offset = offset
|
|
||||||
|
|
||||||
def project(self, points, reverse=False):
|
|
||||||
if reverse:
|
|
||||||
if self.H_ is None:
|
|
||||||
self.H_ = mtx.lu([r[:] for r in self.H])
|
|
||||||
|
|
||||||
qs = [mtx.solve(self.H_,
|
|
||||||
vec.sub(p, self.offset)+[1]) for p in points]
|
|
||||||
return [vec.div(q[:-1], q[-1]) for q in qs]
|
|
||||||
else:
|
|
||||||
qs = [mtx.mul(self.H, p+[1]) for p in points]
|
|
||||||
return [vec.add(self.offset,
|
|
||||||
vec.div(q[:-1], q[-1])) for q in qs]
|
|
||||||
@ -1,162 +0,0 @@
|
|||||||
import vec.distance
|
|
||||||
|
|
||||||
def distance_to_kth_nearest_neighbor(points, i, k):
|
|
||||||
fix = points[i]
|
|
||||||
d = [vec.distance.euclidean(fix, p) for p in points]
|
|
||||||
d.sort()
|
|
||||||
return d[k]
|
|
||||||
# Smallest distance is always to the point itself.
|
|
||||||
# First element can be ignored.
|
|
||||||
# Distance to k-th nearest neighbor is at index == k.
|
|
||||||
|
|
||||||
def calculate_threshold(r, d, beta):
|
|
||||||
return r / (1 - beta)**(1 / d)
|
|
||||||
|
|
||||||
def find_threshold_position(threshold, ascending):
|
|
||||||
lower = 0
|
|
||||||
upper = len(ascending) - 1
|
|
||||||
|
|
||||||
if ascending[upper][0] <= threshold:
|
|
||||||
return upper
|
|
||||||
|
|
||||||
# binary search
|
|
||||||
while upper - lower > 1:
|
|
||||||
i = (upper + lower) // 2
|
|
||||||
r = ascending[i][0]
|
|
||||||
|
|
||||||
if r == threshold:
|
|
||||||
# push `i` to last element equal to threshold
|
|
||||||
while i+1 < len(ascending) and ascending[i+1][0] == threshold:
|
|
||||||
i += 1
|
|
||||||
return i
|
|
||||||
elif r < threshold:
|
|
||||||
lower = i
|
|
||||||
else:
|
|
||||||
upper = i
|
|
||||||
|
|
||||||
if ascending[upper][0] <= threshold:
|
|
||||||
return upper
|
|
||||||
else:
|
|
||||||
return lower
|
|
||||||
|
|
||||||
def in_which(x, sets):
|
|
||||||
for s in sets:
|
|
||||||
if x in s:
|
|
||||||
return s
|
|
||||||
return None
|
|
||||||
|
|
||||||
def form_cluster_core(core_set,
|
|
||||||
existing_cores,
|
|
||||||
points,
|
|
||||||
sorted_radii,
|
|
||||||
seed_position,
|
|
||||||
threshold_position):
|
|
||||||
|
|
||||||
def include(current_position):
|
|
||||||
current_radius, current_index = sorted_radii[current_position]
|
|
||||||
|
|
||||||
core_set.add(current_index)
|
|
||||||
|
|
||||||
for other_position in range(0, threshold_position + 1):
|
|
||||||
other_radius, other_index = sorted_radii[other_position]
|
|
||||||
|
|
||||||
if other_index == current_index or other_index in core_set:
|
|
||||||
continue
|
|
||||||
|
|
||||||
distance = vec.distance.euclidean(
|
|
||||||
points[current_index], points[other_index])
|
|
||||||
|
|
||||||
if distance <= min(current_radius, other_radius):
|
|
||||||
# Connect current point to the other point
|
|
||||||
|
|
||||||
if in_which(other_index, existing_cores) is not None:
|
|
||||||
# The other point is already in another core.
|
|
||||||
# Current set will not be disjoint from existing cores.
|
|
||||||
# Current set cannot form a new core.
|
|
||||||
return False
|
|
||||||
else:
|
|
||||||
# Continue making connections, starting from new point.
|
|
||||||
clean = include(other_position)
|
|
||||||
if not clean:
|
|
||||||
return False
|
|
||||||
return True
|
|
||||||
|
|
||||||
return include(seed_position)
|
|
||||||
|
|
||||||
def assign_cluster(clusters,
|
|
||||||
points,
|
|
||||||
sorted_radii,
|
|
||||||
position):
|
|
||||||
|
|
||||||
def find_cluster_to_belong(current_position):
|
|
||||||
_, current_index = sorted_radii[current_position]
|
|
||||||
|
|
||||||
cluster_set = in_which(current_index, clusters)
|
|
||||||
if cluster_set is not None:
|
|
||||||
# already belong to a cluster
|
|
||||||
return cluster_set
|
|
||||||
|
|
||||||
nearest_neighbor_distance = None
|
|
||||||
nearest_neighbor_position = None
|
|
||||||
|
|
||||||
# find nearest neighbor
|
|
||||||
for i in range(0, current_position):
|
|
||||||
_, other_index = sorted_radii[i]
|
|
||||||
|
|
||||||
distance = vec.distance.euclidean(
|
|
||||||
points[current_index], points[other_index])
|
|
||||||
|
|
||||||
if nearest_neighbor_distance is None \
|
|
||||||
or distance < nearest_neighbor_distance:
|
|
||||||
nearest_neighbor_distance = distance
|
|
||||||
nearest_neighbor_position = i
|
|
||||||
|
|
||||||
# join nearest neighbor's cluster
|
|
||||||
cluster_set = find_cluster_to_belong(nearest_neighbor_position)
|
|
||||||
cluster_set.add(current_index)
|
|
||||||
return cluster_set
|
|
||||||
|
|
||||||
find_cluster_to_belong(position)
|
|
||||||
|
|
||||||
def cluster(points,
|
|
||||||
k,
|
|
||||||
beta,
|
|
||||||
return_modes=False):
|
|
||||||
dimension = len(points[0])
|
|
||||||
|
|
||||||
sorted_radii = [(distance_to_kth_nearest_neighbor(points, i, k=k), i)
|
|
||||||
for i in range(0, len(points))]
|
|
||||||
sorted_radii.sort()
|
|
||||||
# smallest radius first, i.e. highest density first.
|
|
||||||
|
|
||||||
modes = []
|
|
||||||
clusters = []
|
|
||||||
proposed_core = set()
|
|
||||||
|
|
||||||
for position in range(0, len(sorted_radii)):
|
|
||||||
radius, index = sorted_radii[position]
|
|
||||||
|
|
||||||
threshold = calculate_threshold(radius, dimension, beta)
|
|
||||||
threshold_position = find_threshold_position(threshold, sorted_radii)
|
|
||||||
|
|
||||||
if form_cluster_core(proposed_core,
|
|
||||||
clusters,
|
|
||||||
points,
|
|
||||||
sorted_radii,
|
|
||||||
seed_position=position,
|
|
||||||
threshold_position=threshold_position):
|
|
||||||
clusters.append(proposed_core)
|
|
||||||
proposed_core = set()
|
|
||||||
|
|
||||||
if return_modes:
|
|
||||||
modes.append(index)
|
|
||||||
else:
|
|
||||||
proposed_core.clear()
|
|
||||||
|
|
||||||
for position in range(0, len(sorted_radii)):
|
|
||||||
assign_cluster(clusters,
|
|
||||||
points,
|
|
||||||
sorted_radii,
|
|
||||||
position=position)
|
|
||||||
|
|
||||||
return (clusters, modes) if return_modes else clusters
|
|
||||||
@ -1,173 +0,0 @@
|
|||||||
'''
|
|
||||||
|
|
||||||
Part of the micro-linalg project to provide a small
|
|
||||||
matrix / linear algebra package for Micropython (Python3)
|
|
||||||
|
|
||||||
The MIT License (MIT)
|
|
||||||
|
|
||||||
Copyright (c) 2015 Jamie Lawson
|
|
||||||
|
|
||||||
Permission is hereby granted, free of charge, to any person obtaining a copy
|
|
||||||
of this software and associated documentation files (the "Software"), to deal
|
|
||||||
in the Software without restriction, including without limitation the rights
|
|
||||||
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
|
|
||||||
copies of the Software, and to permit persons to whom the Software is
|
|
||||||
furnished to do so, subject to the following conditions:
|
|
||||||
|
|
||||||
The above copyright notice and this permission notice shall be included in all
|
|
||||||
copies or substantial portions of the Software.
|
|
||||||
|
|
||||||
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
|
||||||
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
|
||||||
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
|
|
||||||
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
|
||||||
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
|
|
||||||
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
|
|
||||||
SOFTWARE.
|
|
||||||
'''
|
|
||||||
import math
|
|
||||||
import umatrix
|
|
||||||
|
|
||||||
|
|
||||||
def zeros(m, n, dtype=umatrix.ddtype):
|
|
||||||
return umatrix.matrix([[0 for i in range(n)] for j in range(m)], dtype=dtype)
|
|
||||||
|
|
||||||
|
|
||||||
def ones(m, n, dtype=umatrix.ddtype):
|
|
||||||
return zeros(m, n, dtype) + 1
|
|
||||||
|
|
||||||
|
|
||||||
def eye(m, dtype=umatrix.ddtype):
|
|
||||||
Z = zeros(m, m, dtype=dtype)
|
|
||||||
for i in range(m):
|
|
||||||
Z[i, i] = 1
|
|
||||||
return Z
|
|
||||||
|
|
||||||
def det_inv(x):
|
|
||||||
''' Return (det(x) and inv(x))
|
|
||||||
|
|
||||||
Operates on a copy of x
|
|
||||||
Using elementary row operations convert X to an upper matrix
|
|
||||||
the product of the diagonal = det(X)
|
|
||||||
Continue to convert X to the identity matrix
|
|
||||||
All the operation carried out on the original identity matrix
|
|
||||||
makes it the inverse of X
|
|
||||||
'''
|
|
||||||
if not x.is_square:
|
|
||||||
raise ValueError('Matrix must be square')
|
|
||||||
else:
|
|
||||||
# divide each row element by [0] to give a one in the first position
|
|
||||||
# (may have to find a row to switch with if first element is 0)
|
|
||||||
x = x.copy()
|
|
||||||
inverse = eye(len(x), dtype=float)
|
|
||||||
sign = 1
|
|
||||||
factors = []
|
|
||||||
p = 0
|
|
||||||
while p < len(x):
|
|
||||||
d = x[p, p]
|
|
||||||
if abs(d) < umatrix.flt_eps:
|
|
||||||
# pivot == 0 need to swap a row
|
|
||||||
# check if swap row also has a zero at the same position
|
|
||||||
np = 1
|
|
||||||
while (p + np) < len(x) and abs(x[p + np, p]) < umatrix.flt_eps:
|
|
||||||
np += 1
|
|
||||||
if (p + np) == len(x):
|
|
||||||
# singular
|
|
||||||
return [0, []]
|
|
||||||
# swap rows
|
|
||||||
z = x[p + np]
|
|
||||||
x[p + np, :] = x[p]
|
|
||||||
x[p, :] = z
|
|
||||||
# do identity
|
|
||||||
z = inverse[p + np]
|
|
||||||
inverse[p + np, :] = inverse[p]
|
|
||||||
inverse[p, :] = z
|
|
||||||
# change sign of det
|
|
||||||
sign = -sign
|
|
||||||
continue
|
|
||||||
factors.append(d)
|
|
||||||
# change target row
|
|
||||||
for n in range(p, len(x)):
|
|
||||||
x[p, n] = x[p, n] / d
|
|
||||||
# need to do the entire row for the inverse
|
|
||||||
for n in range(len(x)):
|
|
||||||
inverse[p, n] = inverse[p, n] / d
|
|
||||||
# eliminate position in the following rows
|
|
||||||
for i in range(p + 1, len(x)):
|
|
||||||
# multiplier is that column entry
|
|
||||||
t = x[i, p]
|
|
||||||
for j in range(p, len(x)):
|
|
||||||
x[i, j] = x[i, j] - (t * x[p, j])
|
|
||||||
for j in range(len(x)):
|
|
||||||
inverse[i, j] = inverse[i, j] - (t * inverse[p, j])
|
|
||||||
p = p + 1
|
|
||||||
s = sign
|
|
||||||
for i in factors:
|
|
||||||
s = s * i # determinant
|
|
||||||
# travel through the rows eliminating upper diagonal non-zero values
|
|
||||||
for i in range(len(x) - 1):
|
|
||||||
# final row should already be all zeros
|
|
||||||
# except for the final position
|
|
||||||
for p in range(i + 1, len(x)):
|
|
||||||
# multiplier is that column entry
|
|
||||||
t = x[i, p]
|
|
||||||
for j in range(i + 1, len(x)):
|
|
||||||
x[i, j] = x[i, j] - (t * x[p, j])
|
|
||||||
for j in range(len(x)):
|
|
||||||
inverse[i, j] = inverse[i, j] - (t * inverse[p, j])
|
|
||||||
return (s, inverse)
|
|
||||||
|
|
||||||
|
|
||||||
def pinv(X):
|
|
||||||
''' Calculates the pseudo inverse Adagger = (A'A)^-1.A' '''
|
|
||||||
Xt = X.transpose()
|
|
||||||
d, Z = det_inv(dot(Xt, X))
|
|
||||||
return dot(Z, Xt)
|
|
||||||
|
|
||||||
|
|
||||||
def dot(X, Y):
|
|
||||||
''' Dot product '''
|
|
||||||
if X.size(2) == Y.size(1):
|
|
||||||
Z = []
|
|
||||||
for k in range(X.size(1)):
|
|
||||||
for j in range(Y.size(2)):
|
|
||||||
Z.append(sum([X[k, i] * Y[i, j] for i in range(Y.size(1))]))
|
|
||||||
return umatrix.matrix(Z, cstride=1, rstride=Y.size(2))
|
|
||||||
else:
|
|
||||||
raise ValueError('shapes not aligned')
|
|
||||||
|
|
||||||
|
|
||||||
def cross(X, Y, axis=1):
|
|
||||||
''' Cross product
|
|
||||||
axis=1 Numpy default
|
|
||||||
axis=0 MATLAB, Octave, SciLab default
|
|
||||||
'''
|
|
||||||
if axis == 0:
|
|
||||||
X = X.T
|
|
||||||
Y = Y.T
|
|
||||||
if (X.n in (2, 3)) and (Y.n in (2, 3)):
|
|
||||||
if X.m == Y.m:
|
|
||||||
Z = []
|
|
||||||
for k in range(min(X.m, Y.m)):
|
|
||||||
z = X[k, 0] * Y[k, 1] - X[k, 1] * Y[k, 0]
|
|
||||||
if (X.n == 3) and (Y.n == 3):
|
|
||||||
Z.append([X[k, 1] * Y[k, 2] - X[k, 2] * Y[k, 1],
|
|
||||||
X[k, 2] * Y[k, 0] - X[k, 0] * Y[k, 2], z])
|
|
||||||
else:
|
|
||||||
Z.append([z])
|
|
||||||
if axis == 0:
|
|
||||||
return umatrix.matrix(Z).T
|
|
||||||
else:
|
|
||||||
return umatrix.matrix(Z)
|
|
||||||
else:
|
|
||||||
raise ValueError('shape mismatch')
|
|
||||||
else:
|
|
||||||
raise ValueError('incompatible dimensions for cross product'
|
|
||||||
' (must be 2 or 3)')
|
|
||||||
|
|
||||||
def eps(x = 0):
|
|
||||||
# ref. numpy.spacing(), Octave/MATLAB eps() function
|
|
||||||
if x:
|
|
||||||
return 2**(math.floor(math.log(abs(x))/math.log(2)))*umatrix.flt_eps
|
|
||||||
else:
|
|
||||||
return umatrix.flt_eps
|
|
||||||
@ -1,473 +0,0 @@
|
|||||||
'''
|
|
||||||
|
|
||||||
Part of the micro-linalg project to provide a small
|
|
||||||
matrix / linear algebra package for MicroPython (Python3)
|
|
||||||
|
|
||||||
The MIT License (MIT)
|
|
||||||
|
|
||||||
Copyright (c) 2015 Jamie Lawson
|
|
||||||
|
|
||||||
Permission is hereby granted, free of charge, to any person obtaining a copy
|
|
||||||
of this software and associated documentation files (the "Software"), to deal
|
|
||||||
in the Software without restriction, including without limitation the rights
|
|
||||||
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
|
|
||||||
copies of the Software, and to permit persons to whom the Software is
|
|
||||||
furnished to do so, subject to the following conditions:
|
|
||||||
|
|
||||||
The above copyright notice and this permission notice shall be included in all
|
|
||||||
copies or substantial portions of the Software.
|
|
||||||
|
|
||||||
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
|
||||||
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
|
||||||
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
|
|
||||||
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
|
||||||
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
|
|
||||||
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
|
|
||||||
SOFTWARE.
|
|
||||||
'''
|
|
||||||
|
|
||||||
import sys
|
|
||||||
|
|
||||||
stypes = [bool, int]
|
|
||||||
ddtype = int
|
|
||||||
estypes = []
|
|
||||||
flt_eps = 1
|
|
||||||
|
|
||||||
|
|
||||||
class matrix(object):
|
|
||||||
|
|
||||||
def __init__(self, data, cstride=0, rstride=0, dtype=None):
|
|
||||||
''' Builds a matrix representation of 'data'.
|
|
||||||
'data' can be a list (columns) of lists (rows)
|
|
||||||
[[1,2,3],[4,5,6]] or
|
|
||||||
a simple list organized as determined by rstride and cstride:
|
|
||||||
[1,2,3,4,5,6] cstride=1, rstride=3.
|
|
||||||
Elements will be of highest type included in 'data' or
|
|
||||||
'dtype' can be used to force the type.
|
|
||||||
'''
|
|
||||||
if cstride != 0:
|
|
||||||
if cstride == 1:
|
|
||||||
self.n = rstride
|
|
||||||
self.m = int(len(data) / self.n)
|
|
||||||
else:
|
|
||||||
self.m = cstride
|
|
||||||
self.n = int(len(data) / self.m)
|
|
||||||
self.cstride = cstride
|
|
||||||
self.rstride = rstride
|
|
||||||
self.data = data
|
|
||||||
else:
|
|
||||||
# else determine shape from list passed in
|
|
||||||
self.n = 1
|
|
||||||
if type(data) == int:
|
|
||||||
self.m = 1
|
|
||||||
else: # it is a list
|
|
||||||
self.m = len(data)
|
|
||||||
# is data[0] a list
|
|
||||||
if (type(data[0]) == list):
|
|
||||||
self.n = len(data[0])
|
|
||||||
self.data = [data[i][j]
|
|
||||||
for i in range(self.m) for j in range(self.n)]
|
|
||||||
self.cstride = 1
|
|
||||||
self.rstride = self.n
|
|
||||||
# ensure all elements are of the same type
|
|
||||||
if dtype is None:
|
|
||||||
self.dtype = stypes[max([stypes.index(type(i)) for i in self.data])]
|
|
||||||
else:
|
|
||||||
if dtype in stypes:
|
|
||||||
self.dtype = dtype
|
|
||||||
else:
|
|
||||||
raise TypeError('unsupported type', dtype)
|
|
||||||
self.data = [self.dtype(i) for i in self.data]
|
|
||||||
|
|
||||||
def __len__(self):
|
|
||||||
return self.m
|
|
||||||
|
|
||||||
def __eq__(self, other):
|
|
||||||
if self.shape == other.shape:
|
|
||||||
res = all([self.data[i] == other.data[i] for i in range(self.size())])
|
|
||||||
return res and (self.shape == other.shape)
|
|
||||||
else:
|
|
||||||
raise ValueError('shapes not equal')
|
|
||||||
|
|
||||||
def __ne__(self, other):
|
|
||||||
return not __eq__(other)
|
|
||||||
|
|
||||||
def __iter__(self):
|
|
||||||
self.cur = 0
|
|
||||||
# determine proper axis
|
|
||||||
if self.m == 1:
|
|
||||||
self.cnt_lim = self.n
|
|
||||||
else:
|
|
||||||
self.cnt_lim = self.m
|
|
||||||
return self
|
|
||||||
|
|
||||||
def __next__(self):
|
|
||||||
'''
|
|
||||||
Returns a matrix if m > 1
|
|
||||||
else the next numeric element of the vector.
|
|
||||||
(Numpy returns vectors if selected via slice)
|
|
||||||
'''
|
|
||||||
if self.cur >= self.cnt_lim:
|
|
||||||
raise StopIteration
|
|
||||||
self.cur = self.cur + 1
|
|
||||||
if self.m == 1:
|
|
||||||
return self.data[self.cur - 1]
|
|
||||||
else:
|
|
||||||
return self[self.cur - 1]
|
|
||||||
|
|
||||||
def slice_to_offset(self, r0, r1, c0, c1):
|
|
||||||
# check values and limit them
|
|
||||||
nd = [self.data[i * self.rstride + j * self.cstride]
|
|
||||||
for i in range(r0, r1) for j in range(c0, c1)]
|
|
||||||
return matrix(nd, cstride=1, rstride=(c1 - c0))
|
|
||||||
|
|
||||||
def slice_indices(self, index, axis=0):
|
|
||||||
# handles the unsupported slice.indices() method in uPy.
|
|
||||||
# If implemented:
|
|
||||||
# midx = index.indices(self.m)
|
|
||||||
# should work.
|
|
||||||
if isinstance(index.start, type(None)):
|
|
||||||
s0 = 0
|
|
||||||
else:
|
|
||||||
s0 = min(int(index.start), self.shape[axis])
|
|
||||||
if isinstance(index.stop, type(None)):
|
|
||||||
p0 = self.shape[axis]
|
|
||||||
else:
|
|
||||||
p0 = min(int(index.stop), self.shape[axis])
|
|
||||||
return (s0, p0)
|
|
||||||
|
|
||||||
def __getitem__(self, index):
|
|
||||||
if type(index) == tuple:
|
|
||||||
# int and int
|
|
||||||
# int and slice
|
|
||||||
# slice and int
|
|
||||||
# slice and slice
|
|
||||||
if isinstance(index[0], int):
|
|
||||||
s0 = index[0]
|
|
||||||
p0 = s0 + 1
|
|
||||||
else: # row slice
|
|
||||||
s0, p0 = self.slice_indices(index[0], 0)
|
|
||||||
if isinstance(index[1], int):
|
|
||||||
s1 = index[1]
|
|
||||||
p1 = s1 + 1
|
|
||||||
else: # column slice
|
|
||||||
s1, p1 = self.slice_indices(index[1], 1)
|
|
||||||
elif type(index) == list:
|
|
||||||
# list of indices etc
|
|
||||||
raise NotImplementedError('Fancy indexing')
|
|
||||||
else:
|
|
||||||
# type is int? This will default to returning a row
|
|
||||||
s0 = index
|
|
||||||
p0 = s0 + 1
|
|
||||||
s1 = 0
|
|
||||||
p1 = self.n
|
|
||||||
# resultant matrix
|
|
||||||
z = self.slice_to_offset(s0, p0, s1, p1)
|
|
||||||
# if it's a single entry then return that entry as int, float etc.
|
|
||||||
if (p0 == s0 + 1) and (p1 == s1 + 1):
|
|
||||||
return z.data[0]
|
|
||||||
else:
|
|
||||||
return z
|
|
||||||
|
|
||||||
def __setitem__(self, index, val):
|
|
||||||
if type(index) != tuple:
|
|
||||||
# need to make it a slice without the slice function
|
|
||||||
raise NotImplementedError('Need to use the slice [1,:] format.')
|
|
||||||
# int and int => single entry gets changed
|
|
||||||
# combinations of int and slice => row and columns take on elements from val
|
|
||||||
if isinstance(index[0], int):
|
|
||||||
s0 = index[0]
|
|
||||||
p0 = s0 + 1
|
|
||||||
else: # slice
|
|
||||||
s0, p0 = self.slice_indices(index[0], 0)
|
|
||||||
if isinstance(index[1], int):
|
|
||||||
s1 = index[1]
|
|
||||||
p1 = s1 + 1
|
|
||||||
else: # slice
|
|
||||||
s1, p1 = self.slice_indices(index[1], 1)
|
|
||||||
if type(val) == matrix:
|
|
||||||
val = val.data
|
|
||||||
elif type(val) not in [list, tuple]:
|
|
||||||
val = [val]
|
|
||||||
if not all([type(i) in stypes for i in val]):
|
|
||||||
raise ValueError('Non numeric entry')
|
|
||||||
else:
|
|
||||||
# assign list values wrapping as necessary to fill destination
|
|
||||||
k = 0
|
|
||||||
for i in range(s0, p0):
|
|
||||||
for j in range(s1, p1):
|
|
||||||
self.data[i * self.rstride + j * self.cstride] = (self.dtype(val[k]))
|
|
||||||
k = (k + 1) % len(val)
|
|
||||||
|
|
||||||
# there is also __delitem__
|
|
||||||
|
|
||||||
# def __str__(self):
|
|
||||||
def __repr__(self):
|
|
||||||
# things that use __str__ will fallback to __repr__
|
|
||||||
# find max string field size for formatting
|
|
||||||
l = 0
|
|
||||||
for i in self.data:
|
|
||||||
l = max(l, len(repr(i)))
|
|
||||||
s = 'mat(['
|
|
||||||
r = 0
|
|
||||||
for i in range(self.m):
|
|
||||||
c = 0
|
|
||||||
s = s + '['
|
|
||||||
for j in range(self.n):
|
|
||||||
s1 = repr(self.data[r + c])
|
|
||||||
s = s + s1 + ' ' * (l - len(s1))
|
|
||||||
if (j < (self.n - 1)):
|
|
||||||
s = s + ', '
|
|
||||||
c = c + self.cstride
|
|
||||||
if (i < (self.m - 1)):
|
|
||||||
s = s + '],\n '
|
|
||||||
else:
|
|
||||||
s = s + ']'
|
|
||||||
r = r + self.rstride
|
|
||||||
s = s + '])'
|
|
||||||
return s
|
|
||||||
|
|
||||||
# Reflected operations are not yet implemented in MicroPython
|
|
||||||
# __rmul__ for example will not be invoked
|
|
||||||
|
|
||||||
def __neg__(self):
|
|
||||||
ndat =[self.data[i] * (-1) for i in range(len(self.data))]
|
|
||||||
return matrix(ndat, cstride=self.cstride, rstride=self.rstride)
|
|
||||||
|
|
||||||
def __do_op__(self, a, b, op):
|
|
||||||
if op == '+':
|
|
||||||
return (a + b)
|
|
||||||
elif op == '-':
|
|
||||||
return (a - b)
|
|
||||||
elif op == '*':
|
|
||||||
return (a * b)
|
|
||||||
elif op == '**':
|
|
||||||
return (a ** b)
|
|
||||||
elif op == '/':
|
|
||||||
try:
|
|
||||||
return (a / b)
|
|
||||||
except ZeroDivisionError:
|
|
||||||
raise ZeroDivisionError('division by zero')
|
|
||||||
elif op == '//':
|
|
||||||
try:
|
|
||||||
return (a // b)
|
|
||||||
except ZeroDivisionError:
|
|
||||||
raise ZeroDivisionError('division by zero')
|
|
||||||
else:
|
|
||||||
raise NotImplementedError('Unknown operator ', op)
|
|
||||||
|
|
||||||
def __OP__(self, a, op):
|
|
||||||
if type(a) in stypes:
|
|
||||||
# matrix - scaler elementwise operation
|
|
||||||
ndat = [self.__do_op__(self.data[i], a, op) for i in range(len(self.data))]
|
|
||||||
return matrix(ndat, cstride=self.cstride, rstride=self.rstride)
|
|
||||||
elif (type(a) == list):
|
|
||||||
# matrix - list elementwise operation
|
|
||||||
# hack - convert list to matrix and resubmit then it gets handled below
|
|
||||||
# if self.n = 1 try transpose otherwise broadcast error to match numpy
|
|
||||||
if (self.n == 1) and (len(a) == self.m):
|
|
||||||
return self.__OP__(matrix([a]).T, op)
|
|
||||||
elif len(a) == self.n:
|
|
||||||
return self.__OP__(matrix([a]), op)
|
|
||||||
else:
|
|
||||||
raise ValueError('could not be broadcast')
|
|
||||||
elif (type(a) == matrix):
|
|
||||||
if (self.m == a.m) and (self.n == a.n):
|
|
||||||
# matrix - matrix elementwise operation
|
|
||||||
# use matrix indices to handle views
|
|
||||||
ndat = [self.__do_op__(self[i, j], a[i, j], op) for i in range(self.m) for j in range(self.n)]
|
|
||||||
return matrix(ndat, cstride=1, rstride=self.n)
|
|
||||||
# generalize the following two elif for > 2 dimensions?
|
|
||||||
elif (self.m == a.m):
|
|
||||||
# m==m n!=n => column-wise row operation
|
|
||||||
Y = self.copy()
|
|
||||||
for i in range(self.n):
|
|
||||||
# this call _OP_ once for each row and __do_op__ for each element
|
|
||||||
for j in range(self.m):
|
|
||||||
Y[j, i] = self.__do_op__(Y[j, i], a[j, 0], op)
|
|
||||||
return Y
|
|
||||||
elif (self.n == a.n):
|
|
||||||
# m!=m n==n => row-wise col operation
|
|
||||||
Y = self.copy()
|
|
||||||
for i in range(self.m):
|
|
||||||
# this call _OP_ once for each col and __do_op__ for each element
|
|
||||||
for j in range(self.n):
|
|
||||||
Y[i, j] = self.__do_op__(Y[i, j], a[0, j], op)
|
|
||||||
return Y
|
|
||||||
else:
|
|
||||||
raise ValueError('could not be broadcast')
|
|
||||||
raise NotImplementedError('__OP__ matrix + ', type(a))
|
|
||||||
|
|
||||||
def __add__(self, a):
|
|
||||||
''' matrix - scaler elementwise addition'''
|
|
||||||
return self.__OP__(a, '+')
|
|
||||||
|
|
||||||
def __radd__(self, a):
|
|
||||||
''' scaler - matrix elementwise addition'''
|
|
||||||
''' commutative '''
|
|
||||||
return self.__add__(a)
|
|
||||||
|
|
||||||
def __sub__(self, a):
|
|
||||||
''' matrix - scaler elementwise subtraction '''
|
|
||||||
if type(a) in estypes:
|
|
||||||
return self.__add__(-a)
|
|
||||||
raise NotImplementedError('__sub__ matrix -', type(a))
|
|
||||||
|
|
||||||
def __rsub__(self, a):
|
|
||||||
''' scaler - matrix elementwise subtraction '''
|
|
||||||
self = -self
|
|
||||||
return self.__add__(a)
|
|
||||||
|
|
||||||
def __mul__(self, a):
|
|
||||||
''' matrix scaler elementwise multiplication '''
|
|
||||||
return self.__OP__(a, '*')
|
|
||||||
|
|
||||||
def __rmul__(self, a):
|
|
||||||
''' scaler * matrix elementwise multiplication
|
|
||||||
commutative
|
|
||||||
'''
|
|
||||||
return self.__mul__(a)
|
|
||||||
|
|
||||||
def __truediv__(self, a):
|
|
||||||
''' matrix / scaler elementwise division '''
|
|
||||||
return self.__OP__(a, '/')
|
|
||||||
|
|
||||||
def __rtruediv__(self, a):
|
|
||||||
''' scaler / matrix elementwise division '''
|
|
||||||
return self.__OP__(a, '/')
|
|
||||||
|
|
||||||
def __floordiv__(self, a):
|
|
||||||
''' matrix // scaler elementwise integer division '''
|
|
||||||
return self.__OP__(a, '//')
|
|
||||||
|
|
||||||
def __rfloordiv__(self, a):
|
|
||||||
''' scaler // matrix elementwise integer division '''
|
|
||||||
return self.__OP__(a, '//')
|
|
||||||
|
|
||||||
def __pow__(self, a):
|
|
||||||
''' matrix ** scaler elementwise power '''
|
|
||||||
return self.__OP__(a, '**')
|
|
||||||
|
|
||||||
def __rpow__(self, a):
|
|
||||||
''' scaler ** matrix elementwise power '''
|
|
||||||
return self.__OP__(a, '**')
|
|
||||||
|
|
||||||
def copy(self):
|
|
||||||
""" Return a copy of matrix, not just a view """
|
|
||||||
return matrix([i for i in self.data],
|
|
||||||
cstride=self.cstride, rstride=self.rstride)
|
|
||||||
|
|
||||||
def size(self, axis=0):
|
|
||||||
""" 0 entries
|
|
||||||
1 rows
|
|
||||||
2 columns
|
|
||||||
"""
|
|
||||||
return [self.m * self.n, self.m, self.n][axis]
|
|
||||||
|
|
||||||
@property
|
|
||||||
def shape(self):
|
|
||||||
return (self.m, self.n)
|
|
||||||
|
|
||||||
@shape.setter
|
|
||||||
def shape(self, nshape):
|
|
||||||
""" check for proper length """
|
|
||||||
if (nshape[0] * nshape[1]) == self.size():
|
|
||||||
self.m, self.n = nshape
|
|
||||||
self.cstride = 1
|
|
||||||
self.rstride = self.n
|
|
||||||
else:
|
|
||||||
raise ValueError('total size of new matrix must be unchanged')
|
|
||||||
return self
|
|
||||||
|
|
||||||
@property
|
|
||||||
def is_square(self):
|
|
||||||
return self.m == self.n
|
|
||||||
|
|
||||||
def reshape(self, nshape):
|
|
||||||
""" check for proper length """
|
|
||||||
X = self.copy()
|
|
||||||
X.shape = nshape
|
|
||||||
return X
|
|
||||||
|
|
||||||
@property
|
|
||||||
def T(self):
|
|
||||||
return self.transpose()
|
|
||||||
|
|
||||||
def transpose(self):
|
|
||||||
""" Return a view """
|
|
||||||
X = matrix(self.data, cstride=self.rstride, rstride=self.cstride)
|
|
||||||
if self.cstride == self.rstride:
|
|
||||||
# handle column vector
|
|
||||||
X.shape = (self.n, self.m)
|
|
||||||
return X
|
|
||||||
|
|
||||||
def reciprocal(self, n=1):
|
|
||||||
return matrix([n / i for i in self.data], cstride=self.cstride, rstride=self.rstride)
|
|
||||||
|
|
||||||
def apply(self, func, *args, **kwargs):
|
|
||||||
""" call a scalar function on each element, returns a new matrix
|
|
||||||
passes *args and **kwargs to func unmodified
|
|
||||||
note: this is not useful for matrix-matrix operations
|
|
||||||
e.g.
|
|
||||||
y = x.apply(math.sin)
|
|
||||||
y = x.apply(lambda a,b: a>b, 5) # equivalent to y = x > 5
|
|
||||||
y = x.apply(operators.gt, 5) # equivalent to y = x > 5 (not in micropython)
|
|
||||||
"""
|
|
||||||
return matrix([func(i, *args, **kwargs) for i in self.data],
|
|
||||||
cstride=self.cstride, rstride=self.rstride)
|
|
||||||
|
|
||||||
def matrix_isclose(x, y, rtol=1E-05, atol=flt_eps):
|
|
||||||
''' Returns a matrix indicating equal elements within tol'''
|
|
||||||
for i in range(x.size()):
|
|
||||||
try:
|
|
||||||
data = [abs(x.data[i] - y.data[i]) <= atol+rtol*abs(y.data[i]) for i in range(len(x.data))]
|
|
||||||
except (AttributeError, IndexError):
|
|
||||||
data = [False for i in range(len(x.data))]
|
|
||||||
return matrix(data, cstride=x.cstride, rstride=x.rstride, dtype=bool)
|
|
||||||
|
|
||||||
|
|
||||||
def matrix_equal(x, y, tol=0):
|
|
||||||
''' Matrix equality test with tolerance same shape'''
|
|
||||||
res = False
|
|
||||||
if type(y) == matrix:
|
|
||||||
if x.shape == y.shape:
|
|
||||||
res = all([abs(x.data[i] - y.data[i]) <= tol for i in range(x.size())])
|
|
||||||
return res
|
|
||||||
|
|
||||||
|
|
||||||
def matrix_equiv(x, y):
|
|
||||||
''' Returns a boolean indicating if X and Y share the same data and are broadcastable'''
|
|
||||||
res = False
|
|
||||||
if type(y) == matrix:
|
|
||||||
if x.size() == y.size():
|
|
||||||
res = all([x.data[i] == y.data[i] for i in range(len(x.data))])
|
|
||||||
return res
|
|
||||||
|
|
||||||
def fp_eps():
|
|
||||||
''' Determine floating point resolution '''
|
|
||||||
e = 1
|
|
||||||
while 1 + e > 1:
|
|
||||||
e = e / 2
|
|
||||||
return 2 * e
|
|
||||||
|
|
||||||
flt_eps = fp_eps()
|
|
||||||
try:
|
|
||||||
if sys.implementation.name == 'micropython' and sys.platform == 'linux':
|
|
||||||
# force this as there seems to be some interaction with
|
|
||||||
# some operations done using the C library with a smaller epsilon (doubles)
|
|
||||||
flt_eps = 1.19E-7 # single precision IEEE 2**-23 double 2.22E-16 == 2**-52
|
|
||||||
except:
|
|
||||||
pass
|
|
||||||
# Determine supported types
|
|
||||||
try:
|
|
||||||
stypes.append(float)
|
|
||||||
ddtype = float
|
|
||||||
except:
|
|
||||||
pass
|
|
||||||
try:
|
|
||||||
stypes.append(complex)
|
|
||||||
except:
|
|
||||||
pass
|
|
||||||
# extended types
|
|
||||||
estypes = [matrix]
|
|
||||||
estypes.extend(stypes)
|
|
||||||
@ -1,20 +0,0 @@
|
|||||||
The MIT License (MIT)
|
|
||||||
|
|
||||||
Copyright (c) 2019 Nick Lee
|
|
||||||
|
|
||||||
Permission is hereby granted, free of charge, to any person obtaining a copy of
|
|
||||||
this software and associated documentation files (the "Software"), to deal in
|
|
||||||
the Software without restriction, including without limitation the rights to
|
|
||||||
use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
|
|
||||||
the Software, and to permit persons to whom the Software is furnished to do so,
|
|
||||||
subject to the following conditions:
|
|
||||||
|
|
||||||
The above copyright notice and this permission notice shall be included in all
|
|
||||||
copies or substantial portions of the Software.
|
|
||||||
|
|
||||||
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
|
||||||
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
|
|
||||||
FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
|
|
||||||
COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
|
|
||||||
IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
|
|
||||||
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
|
|
||||||
@ -1,28 +0,0 @@
|
|||||||
# Vector Operations on MicroPython
|
|
||||||
|
|
||||||
Nothing fancy. Treating list as vector, this library performs common
|
|
||||||
operations. I personally use it on [OpenMV](https://openmv.io) for robot vision.
|
|
||||||
|
|
||||||
```python
|
|
||||||
import vec
|
|
||||||
|
|
||||||
a = [1, 2, 3]
|
|
||||||
b = [4, 5, 6]
|
|
||||||
|
|
||||||
vec.add(a, b) # [5, 7, 9]
|
|
||||||
vec.sub(a, b) # [-3, -3, -3]
|
|
||||||
vec.dot(a, b) # 32
|
|
||||||
|
|
||||||
vec.mul(a, 2) # [2, 4, 6]
|
|
||||||
vec.div(a, 2) # [0.5, 1.0, 1.5]
|
|
||||||
```
|
|
||||||
|
|
||||||
```python
|
|
||||||
import vec.distance
|
|
||||||
|
|
||||||
a = [2, 3]
|
|
||||||
b = [5, 7]
|
|
||||||
|
|
||||||
vec.distance.manhattan(a, b) # 7
|
|
||||||
vec.distance.euclidean(a, b) # 5
|
|
||||||
```
|
|
||||||
@ -1,17 +0,0 @@
|
|||||||
def add(a, b):
|
|
||||||
return [a[i] + b[i] for i in range(0, min(len(a), len(b)))]
|
|
||||||
|
|
||||||
def sub(a, b):
|
|
||||||
return [a[i] - b[i] for i in range(0, min(len(a), len(b)))]
|
|
||||||
|
|
||||||
def mul(a, n):
|
|
||||||
return [a[i] * n for i in range(0, len(a))]
|
|
||||||
|
|
||||||
def div(a, n):
|
|
||||||
return [a[i] / n for i in range(0, len(a))]
|
|
||||||
|
|
||||||
def dot(a, b):
|
|
||||||
s = 0
|
|
||||||
for i in range(0, min(len(a), len(b))):
|
|
||||||
s += a[i] * b[i]
|
|
||||||
return s
|
|
||||||
@ -1,13 +0,0 @@
|
|||||||
import math
|
|
||||||
|
|
||||||
def manhattan(a, b):
|
|
||||||
s = 0
|
|
||||||
for i in range(0, min(len(a), len(b))):
|
|
||||||
s += abs(a[i] - b[i])
|
|
||||||
return s
|
|
||||||
|
|
||||||
def euclidean(a, b):
|
|
||||||
s = 0
|
|
||||||
for i in range(0, min(len(a), len(b))):
|
|
||||||
s += (a[i] - b[i])**2
|
|
||||||
return math.sqrt(s)
|
|
||||||
Loading…
Reference in New Issue
Block a user