Change-Id: I53f1a245509a216f31e1824486a13c4bac548a7f

This is consistent with how NULL LossFunctions are treated everywhere
else.

Change-Id: Ic91e39ccb13137fcad7f85e78613a29ecde30d67

Before this change, the default step size
for a function F(x) at x was

step_size = |x| * relative_step_size

if step_size was exactly zero, then to prevent
division by zero we would fall back to relative_step_size.

This however is not good enough, as values of x say 1e-64
would lead to step sizes ~ 1e-70 and dividing by such numbers
leads to inaccurate results. For even smaller numbers, like
1e-300, which I have observed can occur as the optimization
algorithm makes progress, this leads to NaNs.

The key change in this CL is to change the fallback mechanism
to be

step_size = max(|x| * relative_step_size, min_step_size)

where

min_step_size = sqrt(DBL_EPSILON)

This is the recommended minimum value for the step size
for double precision arithmetic on the interwebs.

This results in a small loss of precision in the transcendental
functions test, but that is unavoidable as we are not taking
sufficiently small steps anymore.

On the whole though this will improve the numerical performance
of the algorithm.

To validate this approach, one of the parameter values for the
EasyFunctorTest has been set to 1e-64, which causes the test
to start failing without the corrected fallback logic.

This change should also address some if not all of

https://github.com/ceres-solver/ceres-solver/issues/121

Change-Id: I4a9013ef358626c1ba7b8abad60b3904163d63f6

Change-Id: Ic112d31e2b8d7ecd28816fdc76e27adb1da27ac5

Change-Id: I2fc4b203e984beaa7af96fb3cbe8ce14e5bca614

Change-Id: I1fb5f2504424506e1bba244bcb8efb25329564d1

Change-Id: I3594ed46e78243034389cad158243e11dd1dc2b0

Change-Id: I6592b61451ead8f0407bec134fcf4b56ba22ffb9

The test makes sure the Rosenbrock function is correctly minimized from the
canonical starting point using the default settings.

Change-Id: Iea820f976707bde37162981c5db87fac5167ba9e

Change-Id: Id3b25a177aa92032f7f99b0a381c4f97d07d73b2

I think this is all of the cases. These cases arise because pow(a,b) is limited
to real valued results, if the argument and result were complex valued then
these cases would disappear.

NOTE: Since there is so much special casing here, it is worth checking to see
if cpow() is implemented in terms of pow(), and what might be the consequences
of using cpow() on the type std::complex<Jet<double, N> >. It is *possible*
that a separate implementation of cpow might be required also.

Also some comment fixes.

Change-Id: Ia1e38df4cdcb548f778304c2854cacba6e1556ff

Change-Id: Iffcde8f168b7cd68e56f351c43088d7aef1e5e2f

Change-Id: Iec7c12e971b331d1847f9aa91349317eb6524856

Change-Id: I5a9683333fbab189058076cb2053f8f7afc7096a

Change-Id: Id3bd3c7490d679b87259bb0fbf0b2dbc7e831a07

Change-Id: Ife7f6f3aca06322fa414ef747008d2b4dc468a57

Change-Id: I58685b81e119360a5b9085bb44efc55131ec9117

Change-Id: I78fae5be517e3ee4756ea3ce448c1173c39857d6

Change-Id: If64a1e2bd10637eac8ed74a5c43cfa133c7aa575

Change-Id: Ib14e8f4b2de686ab6494de270458392f81a0b946

- Include example use of new find_dependency() macro in CMake 3.x to
  find dependencies in <Project>Config.cmake files.
- Also fix typo in NNLS modeling docs.

Change-Id: Ie9862b69c0451ee8775826f2957f5e182d937439

Change-Id: I5ba9d264cce7b9a986b28fb24f27200d5c5f328d

The code seemed to imply that its possible to call the Write
method with a null pointer which is never the case. There would
be no point to calling Write.

Thanks to Michael Vitus for pointing this out.

Change-Id: Ic9a276856d0a7e65d53a1cc8742d4831c1a52615

Eigen upstream was broken a little while ago, and it seemed to be
the case that we needed a fix for using the LLT factorization on
ARM.

This has been fixed and AFAIK there are no stable eigen releases
with this bug in it.

For full gore, see

http://eigen.tuxfamily.org/bz/show_bug.cgi?id=992

In light of the fix, the extra layer of indirection introduced earlier
is not needed and we are reverting to normal programming.

Change-Id: I16929d2145253b38339b573b27b6b8fabd523704

Change-Id: I4b1e9ac6c1c74e96f51e57e0cbeaa3d3d649f770

- A lot of users find the CMake package installation process confusing,
  particularly the use of imported targets when exporting their own
  projects which use Ceres.
- This patch adds a brief description of the overall process and the
  main bear-trap users are ensnared by.

Change-Id: I44c022bbd18a393868bf88ea9ddd807c5e08abc9

The call to llt in backsubstitute seems to be using one
of the fixed size specializations which is best done with
an inline call to llt/ldlt rather than introducing yet another
variant of the SolverUpperTriangularUsingCholesky and calling it.

Also change the way SolverUpperTriangularUsingCholesky handles
error. It always computes the solution even if it is garbage
and then returns the error code.

This ensures that the previous code that depends on unconditional
computation still works.

Change-Id: Idb1e6efdae9a3775a072e3b87cde02e0bbddb319

When solving a linear system using Eigen's dense Cholesky factorization
if the right hand side of the linear system is the same vector
that will store the solution, call solveInPlace instead of solve.

Change-Id: I3e6d2f21ff420c25217cd87ee5d269fdfabbf19a

CERES_EIGEN_VERSION was being defined by the CMakeList.txt file
but it is needed by the android build too. So this change
directly constructs the CERES_EIGEN_VERSION string out of the
raw Eigen version numbers.

Change-Id: I65309805a59076c3082141d9042ab7e0e1b972bc

It seems that Eigen's LLT factorization is broken on ARM.
This patch enables the use of LDLT factorization instead of LLT
factorization. The switch is controlled at compile time using a
preprocessor define - CERES_USE_EIGEN_LDLT.

By default we continue to use LLT factorization though.

To make the switching easier without introducing the Cholesky factorization
based inversion and linear system solve routines have been abstracted into
two new functions.

Android.mk has been updated to enable the LDLT factorization, but
the cmake file has not been updated as I will leave it to Alex's
capable hands to do proper detection of ARM as a target platform.

Change-Id: Iffe3abd2ce894de2a388b454df3da909b482d5e5

Change-Id: I0a41e88e0669364d21ef86146f0b572f0f08ece5

- Previously, if Ceres was already installed to the same location as one
  of the depenedencies (e.g. /usr/local) then as the BUILD_DIR/config
  path was necessarily added to the include_directories() list *after*
  the INCLUDE_DIRS for the dependencies, the config.h for the
  *installed* version of Ceres would be used instead of the locally
  configured version, as it would appear first on the path.
- Forcing the location of the locally configured config.h to the front
  of the include_directories() list ensures that it is found first
  (and is thus used) even if an installed version of Ceres also exists
  on the path.

Change-Id: I7b4f97a3ad0120bd11551f9b8eb6bffc66966eb4

Change-Id: I9d6707bc686b6c74d878d8c36bbe5e95a805c6f7

- On MSVC, a Ceres dependency such as glog, may be named glog.lib, or
  libglog.lib.  By default, CMake assumes no prefix for libraries on
  MSVC when using find_library(), thus find_library(glog) would fail
  if glog was named libglog.lib.
- This patch caches & updates CMAKE_FIND_LIBRARY_PREFIXES in all of
  Ceres' find_package scripts to include lib & "" (no prefix) on MSVC
  and then returns CMAKE_FIND_LIBRARY_PREFIXES to its original state
  before returning.

Change-Id: Ic82799e3b786cfb7228a51183bc189578b072bbe

- MinGW produces code that segfaults when performing matrix
  multiplications in Eigen when compiled with -O3 (see below), as such
  force the use of -O2 which works.
- http://eigen.tuxfamily.org/bz/show_bug.cgi?id=556

Change-Id: I420e965d5033944374a5cc93490546c25e46bce5

- Previous tolerance of 2.0 * std::numeric_limits<double>::epsilon()
  was too tight for Cygwin, worked on all other known platforms.

Change-Id: Ia79ad8961272dbb608d8e8ddd3f6d52e5f0735f4

In cmake 3.0, it is required to use full path for compilers. And it
seems like there's no need to force the compiler. Instead we can just
use set(CMAKE_C_COMPIER clang) so that we don't need to specify full
path of clang and clang++.

Change-Id: I9f6a625068e9d37a4bf5a595bafd82cbc13fdde4

- Reported by Simeon (s1m3mu3@gmail.com) on Ceres mailing list.

Change-Id: If23491128fb6320d9b643eb3d5db7d9e67ffcf0b

Change-Id: I841aeddb0f0c2b0d905fc0520553f263db7e7959

- Add missing gflags threading dependency.
- Also add optional gflags Shlwapi dependency on Windows.
- Add check_cxx_source_compiles() with CMAKE_BUILD_TYPE to fix
  namespace test builds on Windows with NMake generators.
- Add namespace regex on gflags.h when check_cxx_source_compiles()
  fails on Windows using Visual Studio generator.

Change-Id: I6570c566e5a29c665d621a54935c16d16bac7117