## mathphysics

I will try to collect my notes and solutions on math and physics, and links to them here.

## Open-source; PayPal only

From the beginning of 2016, I decided to cease all explicit crowdfunding for any of my materials on physics, math. I failed to raise any funds from previous crowdfunding efforts. I decided that if I was going to live in abundance, I must lose a scarcity attitude. I am committed to keeping all of my material open-sourced. I give all my stuff for free.

In the beginning of 2017, I received a very generous donation from a reader from Norway who found these notes useful, through PayPal. If you find these notes useful, feel free to donate directly and easily through PayPal, which won’t go through a 3rd. party such as indiegogo, kickstarter, patreon.

Otherwise, under the open-source MIT license, feel free to copy, edit, paste, make your own versions, share, use as you wish.

### Algebraic Geometry

#### (symbolic computational) Algebraic Geometry with Sage Math on a jupyter notebook

cf.

https://github.com/ernestyalumni/mathphysics/blob/master/AG_sage.ipynb

http://nbviewer.jupyter.org/github/ernestyalumni/mathphysics/blob/master/AG_sage.ipynb

I did a Google search for “Sage Math groebner” and I came across Martin Albrecht’s slides on “Groebner Bases” (22 October 2013).  I implemented fully on Sage Math all the topics on the slides up to the F4 algorithm.  In particular, I implemented in Sage Math/Python the generalized division algorithm, and Buchberger’s Algorithm with and without the first criterion (I did plenty of Google searches and couldn’t find someone who had a working implementation on Sage Math/Python).  Another bonus is the interactivity of having it on a jupyter notebook.  If this jupyter notebook helps yourself (reader), students/colleagues, that’d be good, as I quickly picked up the basic and foundations of using computational algebraic geometry quickly (over the weekend) from looking at the slides and working it out running Sage Math on a jupyter notebook.

I’ll update the github file as much as I can as I’m going through Cox, Little, O’Shea (2015), Ideals, Varieties, and Algorithms, and implementing what I need from there.

# Algebraic Geometry and Algebraic Topology dump (AGDT_dump.tex and DGDT_dump.pdf)

20171002 – I’ve consolidated by notes on Algebraic Geometry and Algebraic Topology.  Because central extensions of groups, Lie group, Lie algebras play an important role in Conformal Field Theory, I include notes on Conformal Field Theory (CFT) in these notes.

Of note, I compare 2 definitions of semi-direct product and show how they’re related and the same.

# Differential Geometry and Differential Topology dump (DGDT_dump.tex and DGDT_dump.pdf)

I continue to take notes on differential geometry and differential topology and its relation to physics, with an emphasis on topological quantum field theory.  I dump all my note and thoughts immediately in the LaTeX and compiled pdf file here and here.  I don’t try to polish or organize these notes in any way, as I am learning at my own pace.  I’ve put this out there, with a permanent home on github, to invite any one to copy, edit, reorganize, and use these notes in anyway they’d like (the power of crowdsourcing).

## Manifolds

20171203 update

I added notes on immersions, submersions, and some immersed submanifolds.  Absil, Mahony, and Sepulchre (2008)’s book Optimization algorithms on Matrix Manifolds had clearer, more concise, and more to the point definitions in its manifolds review than many of these classic pure math textbooks (Lees).

I finally understood clearly immersions, submersions, and their differences after writing (and drawing) this down:

### Holonomy

#### 20170423 update.

I have been reviewing holonomy by reading Conlon (2008), Clarke and Santoro (2012, 1206.3170 [math.DG]), and Schreiber and Waldorf (2007, 0705.0452 [math.DG]) concurrently.  I’ve already put these notes on my github repository mathphysics , in DGDT_dump.tex and DGDT_dump.pdf.

## Computational Physics (CompPhys), Computational Fluid Dynamics (CFD)

I went through Ch.10 of Hjorth-Jensen (2015) and wrote up as many C++ scripts to illustrate all the (serial) PDE solvers: forward, backward Euler, Crank-Nicolson, Jacobi method.

`Cpp/progs/ch10pde` of CompPhys github repository

# Lid-driven cavity with incompressible, viscous fluid on a 512×512 staggered grid, in CUDA C++11, with finite difference method for 2-dim., unsteady Navier-Stokes equations solver

Compare this with pp. 69 of Ch. 5, Example Applications of Griebel, Dornsheifer, Neunhoeffer.

Michael Griebel, Thomas Dornsheifer, Tilman Neunhoeffer.  Numerical Simulation in Fluid Dynamics: A Practical Introduction (Monographs on Mathematical Modeling and Computation).  SIAM.  1997.

## Cantera installation tips (on Fedora Linux, namely Fedora 23 Workstation Linux)

I spent an obscene amount of time documenting my installation on Fedora 23 Workstation Linux of Cantera on my github repository subdirectory `cantera_install_tips` in Markdown. I’ll try copying markdown in here, in wordpress. Otherwise, go here: `github:Propulsion/cantera_stuff/cantera_install_tips/`

# Cantera Installation Tips

Installing Cantera on Fedora Linux, straight, directly from the github repository, all the way to being compiled with `scons`, was nontrivial, mostly because of the installation prerequisites, which, in retrospect, can be easily installed if one knows what they are with respect to what it is in terms of Fedora/CentOS/RedHat `dnf`.

codename directory reference webpage (if any) Description
`cantera_install_success` `./` None A verbose, but complete Terminal log of cantera installation on Fedora Workstation 23 Linux, from `git clone`, cloning the githb repository for cantera, directly, all the way to a successful `scons install`.
`ClassThermoPhaseExam.cpp` `./` Computing Thermodynamic Properties, Class ThermoPhase, Cantera C++ Interface User’s Guide Simple, complete program creates object representing gas mixture and prints its temperature
`chemeqex.cpp` `./` Chemical Equilibrium Example Program, Cantera C++ Interface User’s Guide `equilibrate` method called to set gas to state of chemical equilibrium, holding temperature and pressure fixed.
`verysimplecppprog.cpp` `./`

## Installation Prerequisites, ala Fedora Linux, Fedora/CentOS/RedHat `dnf`

While Cantera mainpage’s Cantera Compilation Guide gave the packages in terms of Ubuntu/Debian’s package manager:

```g++ python scons libboost-all-dev libsundials-serial-dev
```

and for the python module

```cython python-dev python-numpy python-numpy-dev
```

for other Linux distributions/flavors, the same libraries have different names for different package managers and some libraries were already installed with the “stock” OS and some aren’t (as I found in my situation. For example, Cantera’s mainpage, for Ubuntu/Debian installation (compilation), it’s neglected that `boost` is already installed (which I found wasn’t for Fedora 23 Workstation Linux).

### Installation Prerequisites for Fedora 23 Workstation Linux (make sure to do these `dnf install`s and installation with `scons` will go more smoothly).

I found that you can’t get away from `dnf install` on an administrator account – be sure to be on a `sudo` or `admin` account to be able to do `dnf install`s. Also, I found that compiling Cantera had to be done on a `sudo`-enabled or administrator account, in particular, access is needed to be granted to accessing root directories such as `/opt/`, etc. (more on that later).

Also, in general, you’d want to install the developer version of the libraries as well, usually suffixed with `-devel`, mostly because the header files will be placed in the right `/usr/*` subdirectory so to be included in the system (when compiling C++ files or installing).

• `g++` and `gcc` – For something else (namely CUDA Toolkit), I successfully installed, by `dnf install`, gcc 5, the C++ compiler that has compatibility with the new C++11/C++14 standard. The C++11 standard is necessary for compiling C++ files using Cantera (so the flag `-std=c++11` is needed with `g++`).
• `scons` – be sure to install `scons` – it seems like there is a push to use scons, a Python program, for installation and (package) compilation, as opposed to (old-school) CMake, or Make.
• `boost`Boost is free peer-reviewed portable C++ source libraries.
```sudo dnf install boost.x86_64
sudo dnf install boost-devel.x86_64
```
• `lapack``lapack`, Linear Algebra PACkage. Don’t take it for granted that `lapack` is already installed (I had to troubleshoot this myself, beyond the Cantera main page documentation, and find where it is). I had to install it because I found it was missing through the Cantera `scons build`
```dnf list lapack*  # find lapack in dnf
sudo dnf install lapack.x86_64
sudo dnf install lapack-devel.x86_64
```
• `blas``blas`, Basic Linear Algebra Subprograms. Don’t take it for granted that `blas` is already installed (I had to troubleshoot this myself, beyond the Cantera main page documentation, and find where it is). I had to install it because I found it was missing through the Cantera `scons build`
```dnf list blas*  # find blas in dnf
sudo dnf install blas.x86_64
sudo dnf install blas-devel.x86_64
```
• `python-devel` – Following the spirit of how you’d want to install the developer’s version of the library concurrent with the library itself, in that you’d want the headers and symbolic links to be installed and saved onto the respective root `/usr/*` subdirectories (so that your system will know how to include the files), you’d want to install the Python developer’s libraries.
```sudo dnf install python-devel
```

On this note, for Fedora Linux, I did not find with `dnf list` `python-numpy` nor `python-numpy-dev` which, supposedly, is found in Ubuntu/Debian – this is an example of how Fedora/CentOS/RedHat package manager is different from Ubuntu/Debian.
`sundial`sundial has (essential) non-linear solvers.

```sudo dnf install sundials.x86_64
sudo dnf install sundials-devel.x86_64
```

## Clean install, from `git clone` to `scons install`

• `git clone https://github.com/Cantera/cantera.git`
```git clone https://github.com/Cantera/cantera.git
```

`scons build -j12`

```scons build -j12
```

`scons build` by itself is ok; I added the flag `-j12` (correct me if I’m wrong) to optimize the compilation on 12 cores. So if you’re on a quad-core CPU processor, then you’d do `-j4`.
`scons test`
In my experience, if all the necessary libraries and prerequisite software are installed, then `scons test` should result in all tests being passed, none failed.
`sudo scons install`

```sudo scons install
```

There’s no getting around not using sudo for scons install.

A successful `sudo scons install` should end up looking like this at the very end:

```Cantera has been successfully installed.

File locations:

applications                /usr/local/bin
library files               /usr/local/lib64
samples                     /usr/local/share/cantera/samples
data files                  /usr/local/share/cantera/data
Python 2 package (cantera)  /usr/local/lib64/python2.7/site-packages
Python 2 samples            /usr/local/lib64/python2.7/site-packages/cantera/examples
setup script                /usr/local/bin/setup_cantera

The setup script configures the environment for Cantera. It is recommended that
you run this script by typing:

source /usr/local/bin/setup_cantera

before using Cantera, or else include its contents in your shell login script.

scons: done building targets.
```

Knowing where all the files were installed is good to know.

## Compiling very simple C++ programs as a sanity check (that Cantera was installed)

The Cantera main page, C++ Interface User’s Guide, under Compiling Cantera C++ Programs gave the tips of using 3 ways, `pkg-config`, `SCons`, `Make` as ways to compile C++ programs.

However, a brief peruse of `Cantera.mak`, you’ll see that the flags included are daunting, numerous, and complicated:

```# Required Cantera libraries

CANTERA_CORE_LIBS_DEP = /usr/local/lib64/libcantera.a

CANTERA_EXTRA_LIBDIRS=

CANTERA_CORE_FTN=-L/usr/local/lib64 -lcantera_fortran -lcantera

CANTERA_FORTRAN_MODS=\$(CANTERA_INSTALL_ROOT)/include/cantera

###############################################################################
#            BOOST
###############################################################################

CANTERA_BOOST_INCLUDES=

###############################################################################
###############################################################################

CANTERA_SUNDIALS_INCLUDE=
CANTERA_SUNDIALS_LIBS= -lsundials_cvodes -lsundials_ida -lsundials_nvecserial
```

Do you need `sundials` all the time? Does anyone (still) program in Fortran (2016)? Do we really need to include the `/usr/local/lib64` directory every time? What’s the most minimal number of flags needed?

Thus, in this repository’s subdirectory, I included the simple programs that I was able to compile without a complicated Makefile such as `Cantera.mak`.

I found these compilation commands worked:

```g++ -std=c++11 verysimplecppprog.cpp -o verysimplecppprog -lcantera -l pthread
```
```g++ -std=c++11 chemeqex.cpp -o chemeqex -lcantera -l pthread
```
```g++ -std=c++11 ClassThermoPhaseExam.cpp -o ClassThermoPhaseExam -lcantera -l pthread
```

These flags also worked, but seemed unnecessary:

```g++ -std=c++11 chemeqex.cpp -o chemeqex -lcantera -L/usr/local/lib64 -lsundials_cvodes -lsundials_ida -lsundials_nvecserial -L/usr/local/lib -l pthread
```

## Troubleshooting installation/(installation) errors that pop up

• `fatal error: Python.h: No such file or directory`
```fatal error: Python.h: No such file or directory
scons: *** [build/temp-py/_cantera2.os] Error 1
```

I found that I had to `dnf install` `python-devel` to get the header files installed onto the appropriate `/usr/*` root subdirectories.
`scons: *** [/usr/local/include/cantera/Edge.h] /usr/local/include/cantera/Edge.h: Permission denied`
Do `sudo scons install`
`error: could not create`/usr/local/lib64/python2.7′: Permission denied`Do`sudo scons install`-`scons: *** [/opt/cantera] /opt/cantera: Permission denied`

```scons: *** [/opt/cantera] /opt/cantera: Permission denied
scons: building terminated because of errors.
```

Do `sudo scons install`

## Troubleshooting C++ compilation/(C++ compilation) errors that pop up

I realized that I needed to include the Cantera library in this way:

```-lcantera
```

when compiling with g++.
`Package cantera was not found in the pkg-config search path.`

```Package cantera was not found in the pkg-config search path.
Perhaps you should add the directory containing `cantera.pc'
to the PKG_CONFIG_PATH environment variable
No package 'cantera' found
verysimplecppprog.cpp:9:29: fatal error: cantera/Cantera.h: No such file or directory
compilation terminated.
```

In my experience, I found that pkg-config, even though installed, didn’t work in compiling a simple program.
`/usr/lib64/libpthread.so.0: error adding symbols: DSO missing from command line`

I Google searched for this webpage:
cf. “error adding symbols: DSO missing from command line” while compiling g13-driver, ask ubuntu

From this page, I saw the use of the line `LIBS = -lusb-1.0 -l pthread`, and the idea of using the flag `-l pthread` ended up being the solution.
`/usr/include/c++/5.3.1/bits/c++0x_warning.h:32:2: error: #error This file requires compiler and library support for the ISO C++ 2011 standard. This support must be enabled with the -std=c++11 or -std=gnu++11 compiler options.`
You must include the `-std=c++11` to use the new C++11 standard. Indeed:

```/usr/include/c++/5.3.1/bits/c++0x_warning.h:32:2: error: #error This file requires compiler and library support for the ISO C++ 2011 standard. This support must be enabled with the -std=c++11 or -std=gnu++11 compiler options.
#error This file requires compiler and library support \
^
In file included from /usr/local/include/cantera/base/fmt.h:2:0,
from /usr/local/include/cantera/base/ctexceptions.h:14,
from /usr/local/include/cantera/thermo/Phase.h:12,
from /usr/local/include/cantera/thermo/ThermoPhase.h:14,
from /usr/local/include/cantera/thermo.h:12,
```

So you’ll have to compile like this:

```g++ -std=c++11
```

and include this flag in Makefiles.
usr/bin/ld: cannot find -l
include the `-lcantera` flag in C++ compilation.

```dnf list boost-*
```

```sudo dnf install boost-devel.x86_64

```

```dnf list lapack*  # find lapack in dnf
sudo dnf install lapack-devel.x86_64
```

```sudo dnf install python-devel
```

```sudo dnf install sundials.x86_64
sudo dnf install sundials-devel.x86_64
```

```git clone https://github.com/Cantera/cantera.git
```

```fatal error: Python.h: No such file or directory
scons: *** [build/temp-py/_cantera2.os] Error 1
```

### Successful installation/compilation (what we want, what it should look like)

```scons build
```

```scons test
```

```scons test success
```

```sudo scons install
```

There’s no way, I found, of getting away from having to use `sudo` for scons install – you’ll have to be on a sudo enabled or administrator account logged in.

It troubleshoots

```scons: *** [/usr/local/include/cantera/Edge.h] /usr/local/include/cantera/Edge.h: Permission denied
error: could not create `/usr/local/lib64/python2.7': Permission denied
```

## Hillis/Steele and Blelloch (i.e. Prefix) scan(s) methods implemented in parallel on the GPU w/ CUDA C++11

In the subdirectory scan in Lesson Code Snippets 3 is an implementation in CUDA C++11 and C++11, with global memory, of the Hillis/Steele (inclusive) scan, Blelloch (prefix; exclusive) scan(s), each in both parallel and serial implementation.

As you can see, for large float arrays, running parallel implementations in CUDA C++11, where I used the GeForce GTX 980 Ti smokes being run serially on the CPU (I use for a CPU the Intel® Xeon(R) CPU E5-1650 v3 @ 3.50GHz × 12.

I have a thorough write up on the README.md of my fork of Udacity’s cs344 on github.

Note that I was learning about the Hillis/Steele and Blelloch (i.e. Prefix) scan(s) methods in conjunction with Udacity’s cs344, Lesson 3 – Fundamental GPU Algorithms (Reduce, Scan, Histogram), i.e. Unit 3.. I have a writeup of the notes I took related to these scans, formulating them mathematically, on my big CompPhys.pdf, Computational Physics notes.

## I accidentally `dnf update` on Fedora 23 w/ NVidia GTX 980 Ti & prop. drivers & new kernel trashed my video output for the 2nd time; here’s how I recovered my system; Fedora Linux installation, including install of CUDA

20161031. Note that another, similar (i.e. only a few minor changes), version of this post, in Markdown format, is on my MLGrabbag github repository, MLGrabbag README.md

Oops.  I was on an administrator account and I accidentally ran

``` dnf update ```

<!–

–>

//platform.instagram.com/en_US/embeds.js

I had done this before and written about this before, in the post Fedora 23 workstation (Linux)+NVIDIA GeForce GTX 980 Ti: my experience, log of what I do (and find out).

### Fix

I relied upon 2 webpages for the critical, almost life-saving, terminal commands to recover video output and the previous, working “good” kernel – they were such a life-saver that they’re worth repeating and I’ve saved a html copy of the 2 pages onto the MLgrabbag github repository:

#### See what video card is there and all kernels installed and present, respectively

```lspci | grep VGA
lspci | grep -E "VGA|3D"
lspci | grep -i "VGA"

uname -a
```

#### Remove the offending kernel that was automatically installed by `dnf install`

Critical commands:

```rpm -qa | grep ^kernel

uname -r

sudo yum remove kernel-core-4.7.9-100.fc23.x86_64 kernel-devel-4.7.9-100.fc23.x86_64 kernel-modules-4.7.9-100.fc23.x86_64 kernel-4.7.9-100.fc23.x86_64 kernel-headers-4.7.9-100.fc23.x86_64
```

#### Install NVidia drivers to, at least, recover video output

While at the terminal prompt (in low-resolution), change to the directory where you had downloaded the NVidia drivers (hopefully it’s there somewhere already on your hard drive because you wouldn’t have web browser capability without video output):

```sudo sh ./NVIDIA-Linux-x86_64-361.42.run
reboot

dnf install gcc
dnf install dkms acpid

echo "blacklist nouveau" >> /etc/modprobe.d/blacklist.conf

cd /etc/sysconfig
grub2-mkconfig -o /boot/efi/EFI/fedora/grub.cfg

dnf list xorg-x11-drv-nouveau

dnf remove xorg-x11-drv-nouveau
cd /boot

## Backup old initramfs nouveau image ##
mv /boot/initramfs-\$(uname -r).img /boot/initramfs-\$(uname -r)-nouveau20161031.img
```

(the last command, with the output file name, the output file’s name is arbitrary)

```## Create new initramfs image ##
dracut /boot/initramfs-\$(uname -r).img \$(uname -r)
systemctl set-default multi-user.target
```

At this point, you’ll notice that `dnf update` and its subsequent removal would’ve trashed your C++ setup.

For at this point, I tried to do a `make` of a C++ project I had:

```[topolo@localhost MacCor1d_gfx]\$ make
/usr/local/cuda/bin/nvcc -std=c++11 -g -G -Xcompiler "-Wall -Wno-deprecated-declarations" -L/usr/local/cuda/samples/common/lib/linux/x86_64 -lglut -lGL -lGLU -dc main.cu -o main.o
gcc: error trying to exec 'cc1plus': execvp: No such file or directoryMakefile:21: recipe for target 'main.o' failedmake: *** [main.o] Error 1
```

So you’ll have to do

```dnf install gcc-c++
```

## Might as well, while we’re at it, updateNVidia proprietary drivers and CUDA Toolkit

### Updating the NVidia proprietary driver – similar to installing, but remember you have to go into the low-resolution, no video driver, terminal, command line, prompt

```chmod +x NVIDIA-Linux-x86_64-367.57.run
systemctl set-default multi-user.target
reboot

./NVIDIA-Linux-x86_64-367.57.run
systemctl set-default graphical.target
reboot
```

### Update to CUDA Toolkit (9.0)

Try  to use package manager on Linux distribution as much as possible (as general principle).

Remember to do Post-Installation Actions which must be done manually.  Usually, go to your bash profile, `~/.bashrc` , and add the following environment variables:

```LD_LIBRARY_PATH=/usr/local/cuda-9.0/lib64\${LD_LIBRARY_PATH:+:\${LD_LIBRARY_PATH})
```

What I did was use emacs on `~/.bashrc` and added these lines manually:
```PATH=/usr/local/cuda-9.0/bin:\$PATH

LD_LIBRARY_PATH=/usr/local/cuda-9.0/lib64:/usr/lib/x86_64-linux-gpu```

### Updating CUDA Toolkit (8.0)

Then follow the instructions. If the driver is updated already, before using the “`.run`” installation, then choose no to installing drivers – otherwise, I had chosen yes and the default for all the options.

The Linux installation guide for CUDA Toolkit 8.0 is actually very thorough, comprehensive, and easy to use. Let’s look at the Post-Installation Actions, the Environment Setup:

The `PATH` variable needs to include `/usr/local/cuda-8.0/bin`

To add this path to the `PATH` variable:

```\$ export PATH=/usr/local/cuda-8.0/bin\${PATH:+:\${PATH}}
```

In addition, when using the runfile installation method, the `LD_LIBRARY_PATH` variable needs to contain `/usr/local/cuda-8.0/lib64` on a 64-bit system, or `/usr/local/cuda-8.0/lib` on a 32-bit system

To change the environment variables for 64-bit operating systems:

```\$ export LD_LIBRARY_PATH=/usr/local/cuda-8.0/lib64\
\${LD_LIBRARY_PATH:+:\${LD_LIBRARY_PATH}}
```

Indeed, prior to adding the `PATH` variable, I was getting errors when I type `nvcc` at the command line. After doing this:

```[propdev@localhost ~]\$ export PATH=/usr/local/cuda-8.0/bin\${PATH:+:\${PATH}}
[propdev@localhost ~]\$ env | grep '^PATH'
PATH=/usr/local/cuda-8.0/bin:/home/propdev/anaconda2/bin:/home/propdev/anaconda2/bin:/usr/local/bin:/usr/local/sbin:/usr/bin:/usr/sbin:/home/propdev/.local/bin:/home/propdev/bin
[propdev@localhost ~]\$ nvcc
nvcc warning : The 'compute_20', 'sm_20', and 'sm_21' architectures are deprecated, and may be removed in a future release (Use -Wno-deprecated-gpu-targets to suppress warning).
nvcc fatal : No input files specified; use option --help for more information
[propdev@localhost ~]\$ nvcc -V
nvcc: NVIDIA (R) Cuda compiler driver
Built on Sun_Sep__4_22:14:01_CDT_2016
Cuda compilation tools, release 8.0, V8.0.44
```

I obtain what I desired – I can use `nvcc` at the command line.

To get the samples that use OpenGL, be sure to have glut and/or freeglut installed:

```dnf install freeglut freeglut-devel
```

Now for some bloody reason (please let me know), the command

```\$ export LD_LIBRARY_PATH=/usr/local/cuda-8.0/lib64\
\${LD_LIBRARY_PATH:+:\${LD_LIBRARY_PATH}}
```

still didn’t help me to allow my CUDA programs utilize the libraries in that `lib64` subdirectory of the CUDA Toolkit. It seems like the programs, or the OS, wasn’t seeing the link that should be there in `/usr/lib64`.

What did work was in here, libcublas.so.7.0: cannot open shared object file, with the solution at the end, from
atv, with an answer originally from txbob (most likely Robert Cravello of github)

Solved. Finally I did:

```sudo echo "/usr/local/cuda-7.0/lib64" > /etc/ld.so.conf.d/cuda.conf
sudo ldconfig
```

Thanks a lot txbob!

This is what I did:

```[root@localhost ~]# sudo echo "/usr/local/cuda-8.0/lib64" > /etc/ld.so.conf.d/cuda.conf
[root@localhost ~]# sudo ldconfig
ldconfig: /usr/local/cuda-7.5/lib64/libcudnn.so.5 is not a symbolic link
```

and it worked; C++ programs compile with my make files.

Also, files, including in the Samples for the 8.0 Toolkit, using `nvrtc` compiled and worked.

#### Fun Nvidia video card version information, details

Doing

```nvidia-smi
```

at the command prompt gave me this:

```<br />[propdev@localhost ~]\$ nvidia-smi
Mon Oct 31 15:28:30 2016
+-----------------------------------------------------------------------------+
| NVIDIA-SMI 367.57 Driver Version: 367.57 |
|-------------------------------+----------------------+----------------------+
| GPU Name Persistence-M| Bus-Id Disp.A | Volatile Uncorr. ECC |
| Fan Temp Perf Pwr:Usage/Cap| Memory-Usage | GPU-Util Compute M. |
|===============================+======================+======================|
| 0 GeForce GTX 980 Ti Off | 0000:03:00.0 On | N/A |
| 0% 50C P8 22W / 275W | 423MiB / 6077MiB | 1% Default |
+-------------------------------+----------------------+----------------------+

+-----------------------------------------------------------------------------+
| Processes: GPU Memory |
| GPU PID Type Process name Usage |
|=============================================================================|
| 0 1349 G /usr/libexec/Xorg 50MiB |
| 0 19440 G /usr/libexec/Xorg 162MiB |
| 0 19645 G /usr/bin/gnome-shell 127MiB |
| 0 24621 G /usr/libexec/Xorg 6MiB |
+-----------------------------------------------------------------------------+
```

## C++, C++11/C++14

Posts, notes, resources on C++, C++11/C++14.

## C++11 timing code execution

cf. Solarian programmer gave an excellent write up in C++11 timing code performance

## C++11/14 version – the classic algorithm of binary search, using C++11/14 vector library

I implemented the classic algorithm of binary search using C++11/14 vector(s) (library) in vectors_binarysearch.cpp, inside the folder ../Cpp14 of my CompPhys github repository

### functor

C++ Tutorial – Functors(Function Objects) – 2016

My implementation of the examples above for functors here on github:

`functors.cpp`

## C++ templates, class templates and how to put them into header files; Useful links related to splitting up header files for declaration, split to `.cpp` files for definitions

While I already wrote about it in the README.md of my github repository folder `Cpp`, for `CompPhys`Useful links related to splitting up header files for declaration, split to .cpp files for definitions, github repo CompPhys, folder cpp, I had to look it up again, and so I’ll reiterate that material here.

, had an excellent article detailing how understandably confusing it is to split up templates to header files for C++.  The examples and options are comprehensive and crystal-clear.

Gives the reason why.

## virtual method tables, vtables, for C++ inherited classes and keyword virtual

I put together some basic, pedagogical C++ scripts, collected reading material (because a lot of great explanations on old websites are being lost as old websites get deleted, and being cache’ed only in the Wayback machine website; I’ll reproduce what I can in this following github repository), and gdb‘ed thoroughly the memory layouts of these vtables and class data members, and class object instances (pointers to a new class instance) here:

https://github.com/ernestyalumni/HrdwCCppCUDA/tree/master/Cppcls

## Texture Object API

struct cudaResourceDesc resDesc

struct myStruct myVariable;

struct Leopard leopard;
leopard.base.animal.weight = 44;

Struct declaration
http://en.cppreference.com/w/c/language/struct

struct inherit copy from another struct declare c c++

http://stackoverflow.com/questions/1114349/struct-inheritance-in-c

Typesafe inheritance in C
http://www.deleveld.dds.nl/inherit.htm

Difference between ‘struct’ and ‘typedef struct’ in C++?
http://stackoverflow.com/questions/612328/difference-between-struct-and-typedef-struct-in-c

typedef struct

useful

typedef struct vs struct definitions [duplicate]
http://stackoverflow.com/questions/1675351/typedef-struct-vs-struct-definitions

how to declare an instance of a struct C++

Proper way to initialize C++ structs

http://stackoverflow.com/questions/5914422/proper-way-to-initialize-c-structs

## Abstract Algebra

I reviewed a little about rings and polynomial rings over this past weekend and I wanted to try to collect the resources I come across here. My aim for abstract algebra is to apply to (of course) topological field theory AND (unprecedentedly) to aerospace engineering, namely combustion CFD (computational fluid dynamics).

Cornell Math 4320 Solutions (probably more “around” this link

Using Sage Math for Abstract Algebra, especially in conjunction with jupyter notebooks, should be the way forward in the 21st century, and from there, digging deeper into various C/C++ libraries. The jupyter notebook I keep is in my qSApoly github repository:

https://github.com/ernestyalumni/qSApoly/blob/master/AbstractAlgebra.ipynb

### Givaro – C++ library for arithmetic and algebraic computations

https://github.com/linbox-team/givaro

http://givaro.forge.imag.fr/