QRMatrix (i.e. QR decomposition, QR factorisation or orthogonal-triangular
decomposition) decomposes a scalar/complex matrix \c A into the following
matrix product:
\verbatim
A = Q*R,
\endverbatim
where
\c Q is a unitary similarity matrix,
\c R is an upper triangular matrix.
Usage
Input types:
- \c A can be a \c SquareMatrix<Type> or \c RectangularMatrix<Type>
Output types:
- \c Q is always of the type of the matrix \c A
- \c R is always of the type of the matrix \c A
Options for the output forms of \c QRMatrix (for an (m-by-n) input matrix
\c A with k = min(m, n)):
- outputTypes::FULL_R: computes only \c R (m-by-n)
- outputTypes::FULL_QR: computes both \c R and \c Q (m-by-m)
- outputTypes::REDUCED_R: computes only reduced \c R (k-by-n)
Options where to store \c R:
- storeMethods::IN_PLACE: replaces input matrix content with \c R
- storeMethods::OUT_OF_PLACE: creates new object of \c R
Options for the computation of column pivoting:
- colPivoting::FALSE: switches off column pivoting
- colPivoting::TRUE: switches on column pivoting
Direct solution of linear systems A x = b is possible by solve() alongside
the following limitations:
- \c A = a scalar square matrix
- output type = outputTypes::FULL_QR
- store method = storeMethods::IN_PLACE
Notes
- QR decomposition is not unique if \c R is not positive diagonal \c R.
- The option combination:
- outputTypes::REDUCED_R
- storeMethods::IN_PLACE
will not modify the rows of input matrix \c A after its nth row.
- Both FULL_R and REDUCED_R QR decompositions execute the same number of
operations. Yet REDUCED_R QR decomposition returns only the first n rows
of \c R if m > n for an input m-by-n matrix \c A.
- For m <= n, FULL_R and REDUCED_R will produce the same matrices
COMP: delay evaluation of fieldToken enumeration types
- lazy evaluation at runTime instead of compile-time to make the code
independent of initialization order.
Otherwise triggers problems on gcc-4.8.5 on some systems where
glibc is the same age, or older.
- replace stringOps::toScalar with a more generic stringOps::evaluate
method that handles scalars, vectors etc.
- improve #eval to handle various mathematical operations.
Previously only handled scalars. Now produce vectors, tensors etc
for the entries. These tokens are streamed directly into the entry.
- ITstream append() would previously have used the append from the
underlying tokenList, which leaves the tokenIndex untouched and
renders the freshly appended tokens effectively invisible if
interspersed with primitiveEntry::read() that itself uses tokenIndex
when building the list.
The new append() method makes this hidden ITstream bi-directionality
easier to manage. For efficiency, we only append lists
(not individual tokens) and support a 'lazy' resizing that allows
the final resizing to occur later when all tokens have been appended.
- The new ITstream seek() method provides a conveniently means to move
to the end of the list or reposition to the middle.
Using rewind() and using seek(0) are identical.
ENH: added OTstream to output directly to a list of tokens
---
BUG: List::newElem resized incorrectly
- had a simple doubling of the List size without checking that this
would indeed be sufficient for the requested index.
Bug was not triggered since primitiveEntry was the only class using
this call, and it added the tokens sequentially.
- allows use of Enum in more situations where a tiny Map/HashTable
replacement is desirable. The new methods can be combined with
null constructed for to have a simple low-weight caching system
for words/integers instead of fitting in a HashTable.
- silently deprecate 'startsWith', 'endsWith' methods
(added in 2016: 2b14360662), in favour of
'starts_with', 'ends_with' methods, corresponding to C++20 and
allowing us to cull then in a few years.
- handle single character versions of starts_with, ends_with.
- add single character version of removeEnd and silently deprecate
removeTrailing which did the same thing.
- drop the const versions of removeRepeated, removeTrailing.
Unused and with potential confusion.
STYLE: use shrink_to_fit(), erase()
- Now accept '/' when reading variables without requiring
a surrounding '{}'
- fix some degenerate parsing cases when the first character is
already bad.
Eg, $"abc" would have previously parsed as a <$"> variable, even
although a double quote is not a valid variable character.
Now emits a warning and parses as a '$' token and a string token.
- add toScalar evaluation, embedded as "${{EXPR}}".
For example,
"repeat ${{5 * 7}} times or ${{ pow(3, 10) }}"
- use direct string concatenation if primitive entry is only a string
type. This prevents spurious quotes from appearing in the expansion.
radius "(2+4)";
angle "3*15";
#eval "$radius*sin(degToRad($angle))";
We want to have
'(2+4)*sin(degToRad(3*15))'
and not
'"(2+4)"*sin(degToRad("3*15"))'
ENH: code refactoring
- refactored expansion code with low-level service routines now
belonging to file-scope. All expansion routines use a common
multi-parameter backend to handle with/without dictionary etc.
This removes a large amount of code duplication.
- add floor/ceil/round methods
- support evaluation of sub-strings
STYLE: add blockMeshDict1.calc, blockMeshDict1.eval test dictionaries
- useful for testing and simple demonstration of equivalence
- SubField and SubList assign from zero
- SubField +=, -=, *=, /= operators
- SubList construct from UList (as per SubField)
Note: constructing an anonymous SubField or SubList with a single
parameter should use '{} instead of '()' to avoid compiler
ambiguities.
- the #eval directive is similar to the #calc directive, but for evaluating
string expressions into scalar values. It uses an internal parser for
the evaluation instead of dynamic code compilation. This can make it
more suitable for 'quick' evaluations.
The evaluation supports the following:
- operations: - + * /
- functions: exp, log, log10, pow, sqrt, cbrt, sqr, mag, magSqr
- trigonometric: sin, cos, tan, asin, acos, atan, atan2, hypot
- hyperbolic: sinh, cosh, tanh
- conversions: degToRad, radToDeg
- constants: pi()
- misc: rand(), rand(seed)
- this largely reverts 3f0f218d88 and 4ee65d12c4.
Consistent addressing with support for wrapped pointer types (eg,
autoPtr, std::unique_ptr) has proven to be less robust than desired.
Thus rescind HashTable iterator '->' dereferencing (from APR-2019).
- relax casting rules
* down-cast of labelToken to boolToken
* up-cast of wordToken to stringToken.
Can use isStringType() test for word or string types
- simplify constructors, move construct etc.
- expose reset() method as public, which resets to UNDEFINED and
clears allocated storage etc.
DEFEATURE: remove assign from word or string pointer.
- This was deprecated 2017-11 and now removed.
For this type of content transfer, move assignment should be used
instead of stealing pointers.
- change contiguous from a series of global functions to separate
templated traits classes:
- is_contiguous
- is_contiguous_label
- is_contiguous_scalar
The static constexpr 'value' and a constexpr conversion operator
allow use in template expressions. The change also makes it much
easier to define general traits and to inherit from them.
The is_contiguous_label and is_contiguous_scalar are special traits
for handling data of homogeneous components of the respective types.
- this is principally for cases where reduced indentation is desired,
such as when streaming to a memory location. If the indentation size
is zero or one, only a single space will be used to separate the
key/value.
This change does not affect the stream allocation size, since the
extra data falls within the padding.
ENH: relocate label/scalar sizes from Istream to IOstream.
- could allow future use for output streams as well?
Due to padding, reorganization has no effect on allocated size
of output streams.
STYLE: add read/write name qualifier to beginRaw, endRaw
- removes ambiguity for bi-directional streams
STYLE: fix inconsistent 'const' qualifier on std::streamsize
- base Ostream was without const, some derived streams with const
- allows full recovery of allocated space, not just addressable range.
This can be particularly useful for code patterns that repeatedly
reuse the same buffer space. For example,
DynamicList<char> buf(1024);
// some loop
{
OListStream os(std::move(buf));
os << ...
os.swap(buf);
}
Can read back from this buffer as a second operation:
{
UIListStream is(buf);
is >> ...
}
