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shared/cgi/breadcrumbs.cgi create mode 100644 shared/footer.shtml create mode 100644 shared/header.shtml create mode 100644 shared/img/grid.png create mode 100644 shared/style.css diff --git a/.htaccess b/.htaccess new file mode 100644 index 0000000..4f2af75 --- /dev/null +++ b/.htaccess @@ -0,0 +1,16 @@ +Options +Includes + +# See Calvin Smith's "Serving XHTML Correctly Using Apache" +# http://protempore.net/~calvins/howto/xhtml-apache/ +# for details on the following code, which works around +# application/xhtml+xml issues with MSIE. +RewriteEngine On +AddType application/xhtml+xml;q=0.8 .shtml +#RewriteBase / +RewriteCond %{REQUEST_URI} \.shtml$ +RewriteCond %{HTTP_USER_AGENT} MSIE [OR] +RewriteCond %{HTTP_ACCEPT} application/xhtml\+xml\s*;\s*q=0\.?0*(\s|,|$) +RewriteRule .* - [T=text/html] + +# If MSIE was intelligent, we could replace the above with a simple +#AddType application/xhtml+xml .shtml diff --git a/_script/build.sh b/_script/build.sh new file mode 100755 index 0000000..b0c6dcb --- /dev/null +++ b/_script/build.sh @@ -0,0 +1,5 @@ +#!/bin/bash + +math.sh . +html_toc.py . +make_tar.sh . diff --git a/_script/clean.sh b/_script/clean.sh new file mode 100755 index 0000000..280cef8 --- /dev/null +++ b/_script/clean.sh @@ -0,0 +1,5 @@ +#!/bin/bash + +make_tar.sh --clean . +html_toc.py --clean +math.sh --clean . diff --git a/_script/html_toc.py b/_script/html_toc.py new file mode 100755 index 0000000..0375ded --- /dev/null +++ b/_script/html_toc.py @@ -0,0 +1,198 @@ +#!/usr/bin/env python + +"""Automatically maintain tables of contents (TOCs) in HTML documents. + +For a similar idea restricted to a single file, see Andrew Hardwick's + HtmlHeadingsToTableOfContents.pl + http://duramecho.com/ComputerPrograms/HtmlHeadingsToTableOfContents/ +""" + +import os.path +from StringIO import StringIO +import sys + +from lxml import etree + + +class ToCTree (object): + def __init__(self, path, index_file='index.html', toc_file='.html_toc', + stack=[]): + self._begin_tag = '' + self._end_tag = '' + self._index_file = index_file + self._toc_file = toc_file + self._stack = stack + self._dir,self._path = self._normalize_path(path) + try: + self._lines = [x.rstrip() for x in open(self._path, 'rb').readlines()] + except IOError: + self._lines = [] + self._etree,self._prefix_lines = self._parse_page() + self._title = self._page_title() + self._descendants = list(self._get_descendants()) + + def _normalize_path(self, path): + if os.path.isdir(path): + dir_ = path + path = os.path.join(dir_, index_file) + else: + dir_ = os.path.dirname(path) + return (dir_, path) + + def _parse_page(self): + lines = ['', + '', + ] + self._lines + [''] + parser = etree.XMLParser(resolve_entities=False, recover=True) + tree = etree.parse(StringIO('\n'.join(lines)), parser=parser) + if len(parser.error_log) > 0: + print >> sys.stderr, '%s: parsing error' % self._path + print >> sys.stderr, '(listed lines offset by +2)' + print >> sys.stderr, parser.error_log + return (tree, 2) + + def _page_title(self): + heading = self._etree.find('.//h1') + if heading is None: + return os.path.basename(self._dir) + return heading.text + + def _heading_nodes(self, path=''): + h1s = self._etree.findall('.//h1') + if len(h1s) == 0: + return [] + elif len(h1s) > 1: + raise ValueError('multiple h1 headings in %s: %s' + % (self._path, [h.text for h in h1s])) + h1 = h1s[0] + h2s = self._etree.findall('.//h2') + h3s = self._etree.findall('.//h3') + if len(h2s) == 0: + return [] + iZ = max([h.sourceline for h in h2s+h3s]) + 1 + lines = [h.sourceline for h in [h1]+h2s+h3s] + if len(set(lines)) < len(lines): + dup_lines = [x for x in lines if lines.count(x) > 1] + if len(dup_lines) > 1: + location = 'lines %s' % ','.join( + [str(x-self._prefix_lines) for x in dup_lines]) + else: + location = 'line %d' % (dup_lines[0] - self._prefix_lines) + raise ValueError('multiple headings on %s of %s' + % (location, self._path)) + nodes = [] + for i2,h2 in enumerate(h2s): + n2 = etree.Element('li') + nodes.append(n2) + n2a = etree.Element('a', href='%s#%s' % (path, h2.get('id'))) + n2a.text = h2.text + n2.append(n2a) + + if i2+1 == len(h2s): + next_h2_line = iZ + else: + next_h2_line = h2s[i2+1].sourceline + _h3s = [h3 for h3 in h3s if + (h3.sourceline > h2.sourceline + and h3.sourceline < next_h2_line)] + if len(_h3s) > 0: + n2ul = etree.Element('ul') + n2.append(n2ul) + for h3 in _h3s: + h3s.remove(h3) + n3 = etree.Element('li') + n2ul.append(n3) + n3a = etree.Element( + 'a', href='%s#%s' % (path, h3.get('id'))) + n3a.text = h3.text + n3.append(n3a) + if len(h3s) > 0: + raise ValueError('misplaced h3 on line %d of %s' + % (h3s[0].sourceline - self._prefix_lines, + self._path)) + return nodes + + def _get_descendants(self): + """Depth first traversal.""" + toc_file_path = os.path.join(self._dir, self._toc_file) + try: + children = open(toc_file_path, 'r').readlines() + except IOError, e: + return + for child_file_name in children: + child_path = os.path.join(self._dir, child_file_name.strip()) + child_tree = ToCTree( + child_path, index_file=self._index_file, + toc_file=self._toc_file, stack=self._stack+[self]) + yield child_tree + for c in child_tree._get_descendants(): + yield c + + def set_tocs(self, clean=False): + self._set_toc(clean=clean) + for d in self._descendants: + d._set_toc(clean=clean) + + def _set_toc(self, clean=False): + lines = list(self._lines) + try: + begin = lines.index(self._begin_tag) + end = lines[begin:].index(self._end_tag) + begin + except ValueError, e: + print >> sys.stderr, '%s\tskip (no tags)' % self._path + return + if clean == True: + toc_lines = [] + else: + toc_lines = self._toc_lines() + lines = lines[:begin+1] + toc_lines + lines[end:] + if lines != self._lines: + print >> sys.stderr, '%s\tupdate' % self._path + open(self._path, 'wb').write('\n'.join(lines)+'\n') + else: + print >> sys.stderr, '%s\tno change' % self._path + + def _toc_lines(self): + toc = etree.Element('ul') + toc.extend(self._heading_nodes()) + stack = [toc] + for d in self._descendants: + while len(stack) > len(d._stack): + stack.pop() + node,node_ul = d._entry(from_=self) + stack[-1].append(node) + if len(d._descendants) > 0: + node.append(node_ul) + stack.append(node_ul) + elif len(node_ul) == 0: + node.remove(node_ul) + text = etree.tostring(toc, pretty_print=True) + return text.splitlines() + + def _entry(self, from_): + path = os.path.relpath(self._dir, start=from_._dir)+os.path.sep + if os.path.sep != '/': + path.replace(os.path.sep, '/') + node = etree.Element('li') + link = etree.Element('a', href=path) + link.text = self._title + node.append(link) + ul = etree.Element('ul') + node.append(ul) + ul.extend(self._heading_nodes(path=path)) + return (node, ul) + + +if __name__ == '__main__': + root = '.' + clean = False + if len(sys.argv) > 1: + root = sys.argv[1] + if '--clean' in sys.argv[1:]: + if root == '--clean': + root = '.' + clean = True + index_file = 'index.shtml' + + tree = ToCTree(path=root) + tree.set_tocs(clean=clean) diff --git a/_script/make_tar.sh b/_script/make_tar.sh new file mode 100755 index 0000000..8c22eaf --- /dev/null +++ b/_script/make_tar.sh @@ -0,0 +1,37 @@ +#!/bin/bash +# +# (re)generate source tarballs for any directory containing a +# .make_tar file. Will *not* include any dot files (e.g. .make_tar) +# .make_tar should contain a relative path to the directory that +# provides the tarball's base name. For example +# $ echo some_dir/src/.make_tar +# ../ +# calls for an output +# some_dir/src/some_dir.tar.gz + +CLEAN=0 +if [ "$1" == '--clean' ]; then + CLEAN=1 +fi + +TAR_OPTS='--create --gzip --verbose --show-transformed-names --no-wildcards-match-slash --dereference' + +find . -name '.make_tar' | while read MAKE_TAR_FILE +do + DIR=$(dirname "$MAKE_TAR_FILE") + REL_DIR=$(cat "$MAKE_TAR_FILE") + TAR_NAME=$(basename $(readlink --canonicalize "$DIR/$REL_DIR")) + OUTPUT="$DIR/$TAR_NAME.tar.gz" + if [ "$CLEAN" == "1" ]; then + rm -vf "$OUTPUT" + else + echo "$OUTPUT" + tar $TAR_OPTS --file "$OUTPUT" --exclude '.[^A--0-^?]*' --exclude "$TAR_NAME.tar.gz" --directory "$DIR" --transform "s,^./,./$TAR_NAME/," . + echo + # See + # Jerry Peek et al.'s "Uniz Power Tools" + # 15.5 Matching All "Dot Files" with Wildcards + # http://docstore.mik.ua/orelly/unix/upt/ch15_05.htm + # for a description of the '.[^A--0-^?]*' expression. + fi +done diff --git a/_script/math.sh b/_script/math.sh new file mode 100755 index 0000000..4b5b916 --- /dev/null +++ b/_script/math.sh @@ -0,0 +1,29 @@ +#!/bin/bash +# +# (re)generate source tarballs for any directory containing a +# .make_tar file. Will *not* include any dot files (e.g. .make_tar) +# .make_tar should contain a relative path to the directory that +# provides the tarball's base name. For example +# $ echo some_dir/src/.make_tar +# ../ +# calls for an output +# some_dir/src/some_dir.tar.gz + +ITEX2MML=itex2MML +CLEAN=0 +if [ "$1" == '--clean' ]; then + CLEAN=1 +fi + +ITEX2MML_OPTS=' --forbid-markup --unicode-entities' + +find . -name '*.itex2MML' | while read ITEX2MML_FILE +do + OUTPUT="${ITEX2MML_FILE/.itex2MML/}" + if [ "$CLEAN" == "1" ]; then + rm -vf "$OUTPUT" + else + echo "$ITEX2MML_FILE" + cat "$ITEX2MML_FILE" | $ITEX2MML $ITEX2MML_OPTS > "$OUTPUT" + fi +done diff --git a/assignments/archive/2d_diffusion/index.shtml b/assignments/archive/2d_diffusion/index.shtml new file mode 100644 index 0000000..f57633c --- /dev/null +++ b/assignments/archive/2d_diffusion/index.shtml @@ -0,0 +1,8 @@ + + +

Assignment #7

+

Due Friday, December 7, 2007

+ +

Write a parallel version of the 2D diffusion equation solver.

+ + diff --git a/assignments/archive/2d_diffusion/index.shtml.2001.05.shtml b/assignments/archive/2d_diffusion/index.shtml.2001.05.shtml new file mode 100644 index 0000000..55da241 --- /dev/null +++ b/assignments/archive/2d_diffusion/index.shtml.2001.05.shtml @@ -0,0 +1,32 @@ + + +

Final Project

+

Due: Wednesday, June 6, 2001

+

Due: Wednesday, May 30, 2001 (for graduating students)

+ +

Transform /content/DiffusionEquation/Codes/2d_parabolic.c">2d_parabolic.c +into a parallel code.

+ +

Estimate the time saving by using multi-processors code versus the +scalar code.

+ +

Hints

+ +

Do not reassign the arrays for the fields — this will save +you lots of aggravation and pain! This should be done to save memory +— the small arrays used in the code will certainly not fill the +memory on our system.

+ +

The /content/DiffusionEquation/Codes/2d_source.c">2d_source.c +code should not need modification — this is why I split those +functions in a separated file — a black box solution .

+ +

Use ideas and snippets of codes from the Poisson equation solver as +much as possible to simplify your work. + +

PS: Graduate students should provide their own project, subject +to instructor approval.

+ + diff --git a/assignments/archive/2d_poisson/index.shtml b/assignments/archive/2d_poisson/index.shtml new file mode 100644 index 0000000..5de0cf3 --- /dev/null +++ b/assignments/archive/2d_poisson/index.shtml @@ -0,0 +1,8 @@ + + +

Assignment #6

+

Due Friday, December 7, 2007

+ +

Write a parallel version of the 2D Poisson equation solver.

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Assignment #1

+

Due Friday, October 12, 2007

+ +

Write a parallel code to compute the average and standard deviation +of a set of numbers.

+ +

References

+ + + + diff --git a/assignments/archive/average_and_standard_deviation/index.shtml.200X.XX.shtml b/assignments/archive/average_and_standard_deviation/index.shtml.200X.XX.shtml new file mode 100644 index 0000000..dd0bef1 --- /dev/null +++ b/assignments/archive/average_and_standard_deviation/index.shtml.200X.XX.shtml @@ -0,0 +1,38 @@ + + +

Point to Point Communication

+

Assignment 1

+ +

Part A

+ +

+Modify the code hop.c to remove the deadlock by sending and receiving +in a red and black scheme, or odd-even scheme, in the processes order +of the send-receive part of the code. +

+ +

Part B

+ +

+Calculate in parallel the average and standard deviation of a set of +numbers. +

+ +

+The program stats.c +calculates the average and standard deviations of set of random +numbers read in from a +file random_number_list. The program works +on a single CPU. The +file random_number_list is generated by the +code + generate_random_data.c. +

+ +

Adapt the stats.c +code to work in parallel. Split the sums in partial sums to be +performed on each node. Perform ALL file I/O from node zero (0). Let +node zero (0) print out the final results. +

+ + diff --git a/assignments/archive/direct_simulation_monte_carlo/index.shtml b/assignments/archive/direct_simulation_monte_carlo/index.shtml new file mode 100644 index 0000000..d10c39e --- /dev/null +++ b/assignments/archive/direct_simulation_monte_carlo/index.shtml @@ -0,0 +1,114 @@ + + +

Direct Simulation Monte Carlo (DSMC)

+ +

Simulation of rarefied gas via Monte Carlo description of +pseudo-molecules, implementing simple short-range interactions +between nearby molecules and simple interactions of the molecules +with the walls of the domain. In its simplest form, the model +assumes

+ +
    +
  • Pseudo-molecules representing groups of molecules located nearby + in space.
    • +
  • Separation of the ballistic motion and collisions among the + pseudo-molecules.
    • +
  • The ballistic motion are simple straight line motions due to the + (constant) velocity of the pseudo-particles during dt.
    • +
  • The volume is divided in small cells for the purpose of finding + nearby pseudo-molecules.
    • +
  • Only the pseudo-particles located in a cell collide.
    • +
  • The pseudo-molecules collisions are modeled via hard sphere + collisions +
      +
    • Hard sphere collisions have isotropic differential cross + section as a function of the impact parameter.
      • +
    • The center-of-mass and relative velocities are conserved + (elastic collisions).
      • +
    • The exit angle is assumed at random in angle ([0, 2π] + in 2 dimensions).
      • +
    • Mc pairs of pseudo-particles collide, depending on + volume displaced by the pseudo-particles during their motion + in dt and the collision cross section.
      • +
    +
    • +
  • The particles bounce specularly on the walls (incidence angle = + outgoing angle).
    • +
+ +

The model is implemented in the +code dsmc_serial.c with header file +dsmc_serial.h. The code +analyze.c analyzes the "speeds" of the +pseudo-particles (output files speed_I +and speed_F). The procedure to follow to run the code +is:

+ +
+gcc dsmc_seria.c -lm -o dsmc_serial
+gcc analyze.c -o analyze
+dsmc_serial
+cat speed_I | analyze > see_I
+cat speed_F | analyze > see_F
+cat see_I | plot_data -p
+cat see_F | plot_data -p
+
+ +

The physical constants are in dsmc_serial.h. All +variables are scaled; no attempt was made to relate the parameters to +those of real gases. The code includes three initial conditions:

+ +
+
INITIAL_CONDITION = 1
+
Initially, the pseudo-particles have random positions and + velocity (speed = 1) in the + + or -x-direction.
+
INITIAL_CONDITION = 2
+
Initially, the pseudo-particles have random positions (90% in + the left half of the volume and 10% in the right half of the + volume), speed at random according to a narrow Gaussian + distribution, and arbitrary direction of the velocity vector + (uniformly distributed).
+
INITIAL_CONDITION = 3
+
Initially, the pseudo-particles have random positions in the + full volume, speed at random according to a narrow Gaussian + distribution, and arbitrary direction of the velocity vector + (uniformly distributed).
+
+ +

Initial conditions 1 and 3 illustrate the thermalization of the +motion, while initial condition 2 is meant to illustrate the +propencity for the pseudo-molecules to transport throughout the entire +volume.

+ +

The codes ran_gauss.c and +ran_int.c illustrate the quality +of rand(), A better routine would be one of +the random +number algorithms implemented by +the GNU Scientific +Library.

+ +

References

+ +
    +
  • DSMC site.
    • +
  • Francis Alexander and Alejandro Garcia, The Direct Simulation + Monte Carlo Method, Computers in Physics, Nov/Dec, 11, + 1997.
    • +
  • Alejandro Garcia, Numerical Methods for Physics, 2nd + Edition, Prentice Hall, 2000.
    • + +
+ + diff --git a/assignments/archive/direct_simulation_monte_carlo/src/.htaccess b/assignments/archive/direct_simulation_monte_carlo/src/.htaccess new file mode 100644 index 0000000..ad0f04a --- /dev/null +++ b/assignments/archive/direct_simulation_monte_carlo/src/.htaccess @@ -0,0 +1 @@ +AddType text/plain .c diff --git a/assignments/archive/direct_simulation_monte_carlo/src/.make_tar b/assignments/archive/direct_simulation_monte_carlo/src/.make_tar new file mode 100644 index 0000000..eb4d905 --- /dev/null +++ b/assignments/archive/direct_simulation_monte_carlo/src/.make_tar @@ -0,0 +1 @@ +../ diff --git a/assignments/archive/direct_simulation_monte_carlo/src/analyze.c b/assignments/archive/direct_simulation_monte_carlo/src/analyze.c new file mode 100755 index 0000000..dd3a5af --- /dev/null +++ b/assignments/archive/direct_simulation_monte_carlo/src/analyze.c @@ -0,0 +1,32 @@ +// +// To analyse velocity data +// + +#include + +int main() +{ + double deltav, x; + int i, j, n, bin[100]; + + deltav = 0.1; + + for ( i=0 ; i<30 ; i++ ) + { + bin[i] = 0; + } + + for ( i=0 ; ; i++ ) + { + if( ( n = scanf( "%lf ", &x ) ) == EOF ) + break; + j = (int)( x/deltav ); + bin[j]++; + } + + for ( i=0 ; i<30 ; i++ ) + { + printf( " %f %d \n", deltav*(i+0.5), bin[i] ); + } + +} diff --git a/assignments/archive/direct_simulation_monte_carlo/src/dsmc_serial.c b/assignments/archive/direct_simulation_monte_carlo/src/dsmc_serial.c new file mode 100755 index 0000000..deae3aa --- /dev/null +++ b/assignments/archive/direct_simulation_monte_carlo/src/dsmc_serial.c @@ -0,0 +1,807 @@ +/* + + Direct Simulation Monte Carlo (DSMC) gas dynamics + + Michel Vallieres + Spring 2002 +*/ + + +#include +#include +#include +#include + + // DSMC header file +#include "./dsmc_serial.h" + + +// +// calculation of density of pseudo-particles +// +int density( int *max_density, int *min_density ) +{ + int ic, icc, np, ip; + int ix, iy, ipoint; + int max_count, min_count, check_count; + double dxp, dyp; + + // blank out image + for ( ipoint=0; ipoint X_MAX || cells[ic].x[ip] < X_MIN || + cells[ic].y[ip] > Y_MAX || cells[ic].y[ip] < Y_MIN ) + { + fprintf( stderr, " Error conditions | %d %d %f %f %f %f \n", + ic, ip, cells[ic].x[ip], cells[ic].y[ip] ); + } + + + if ( ipoint < 0 || ipoint > SIZEX*SIZEY ) + { + fprintf( stderr, " Error %d %d %d %d %d %f %f\n", + ix, iy, ipoint, max_count, min_count, + cells[ic].x[ip], cells[ic].y[ip] ); + exit (1); + } + image[ipoint]++; + check_count++; + } + } + + // density range + max_count = 0; + min_count = N_PART; + for ( ipoint=0 ; ipoint max_count ) + max_count = image[ipoint]; + if ( image[ipoint] < min_count ) + min_count = image[ipoint]; + } + *max_density = max_count; + *min_density = min_count; + + // safety check + if ( check_count != N_PART ) + fprintf( stderr, " Error in density: %d -- %d \n", + check_count, N_PART ); + + printf( "\n Density \n" ); + for( iy=0 ; iy X_MIN+0.5*(X_MAX-X_MIN) ) ok = 1; + if ( x < X_MIN+0.5*(X_MAX-X_MIN) ) ok = 1; + + if ( INITIAL_COND == 1 ) ok = 1; + if ( INITIAL_COND == 3 ) ok = 1; + + if ( ok == 1 ) + { + // particle count + n_tot++; + n_half++; + // which cell + cell_x = (int)(x/dx); + cell_y = (int)(y/dy); + ic = NX*cell_y + cell_x; + cells[ic].n_in_cell++; + ip = cells[ic].n_in_cell-1; + cells[ic].x[ip] = x; + cells[ic].y[ip] = y; + // velocity components -- vx=V_CONSTANT,vy=0 + if ( INITIAL_COND == 1 ) + { + cells[ic].vy[ip] = 0.0; + cells[ic].vx[ip] = V_CONSTANT; + if ( n_tot > N_PART/2 ) + cells[ic].vx[ip] = -V_CONSTANT; + } // narrow gaussian in random directions + else if ( INITIAL_COND == 2 || INITIAL_COND == 3 ) + { + gauss1 = -1.0; + while ( gauss1 < 0.0 ) + { + Gaussian( &gauss1, &gauss2, sigma, amu ); + angle = 2*M_PI*random_num(); + cells[ic].vx[ip] = gauss1*cos(angle); + cells[ic].vy[ip] = gauss1*sin(angle); + } + } + else + { + printf( " Wrong case in initial conditions \n" ); + exit(1); + } + // mass + cells[ic].mass[ip] = MASS_A; + + + if ( cell_x < 0 || cell_x > NX-1 || + cell_y < 0 || cell_y > NY-1 ) + { + fprintf( stderr, " Error in init_pseudo_molecules \n" ); + exit(1); + } + + if ( cells[ic].vx[ip]*cells[ic].vx[ip] + + cells[ic].vy[ip]*cells[ic].vy[ip] < 0.00000001 ) + { + fprintf( stderr, " Error in init_pseudo_molecules - velocities\n" ); + fprintf( stderr, " Velocity components: %f %f \n", + cells[ic].vx[ip], cells[ic].vy[ip] ); + exit(1); + } + + } // ok + } // while +} + + +// +// move of pseudo-particles during a time step (constant velocities) +// +int move() +{ + int ip, np; + int ic, icc, ic_new; + int cell_x, cell_y; + double x, y; + + // scan over cells + for ( icc=0 ; icc X_MAX || cells[ic].x[ip] < X_MIN || + cells[ic].y[ip] > Y_MAX || cells[ic].y[ip] < Y_MIN || + grid_mask[ic_new] == 0 ) + { + // bounce on wall + secular_wall_bounce( n_bounce, ic, ip ); + + // new cell + cell_x = (int)((cells[ic].x[ip]-X_MIN)/dx); + cell_y = (int)((cells[ic].y[ip]-Y_MIN)/dy); + ic_new = NX*cell_y + cell_x; + + } + // inside old cell ? + if ( ic_new != ic ) + { + // move pseudo-molecule + // in new cell + cell_shift++; + signal[ip] = 0; + // transfer to new cell + cells[ic_new].n_in_cell++; + ipoint = cells[ic_new].n_in_cell - 1; + cells[ic_new].x[ipoint]=cells[ic].x[ip]; + cells[ic_new].y[ipoint]=cells[ic].y[ip]; + cells[ic_new].vx[ipoint]=cells[ic].vx[ip]; + cells[ic_new].vy[ipoint]=cells[ic].vy[ip]; + cells[ic_new].mass[ipoint]=cells[ic].mass[ip]; + + } + } + *total_shift = *total_shift + cell_shift; + + // remove the moved pseudo-molecules + if ( cell_shift != 0 ) + { + ipoint = -1; + for ( ip=0; ip X_MAX ) + { + bounce_signal=1; + cells[ic].x[ip] = 2*X_MAX - cells[ic].x[ip]; + cells[ic].vx[ip] = - cells[ic].vx[ip]; + } + if ( cells[ic].x[ip] < X_MIN ) + { + bounce_signal=1; + cells[ic].x[ip] = 2*X_MIN - cells[ic].x[ip]; + cells[ic].vx[ip] = - cells[ic].vx[ip]; + } + if ( cells[ic].y[ip] > Y_MAX ) + { + bounce_signal=1; + cells[ic].y[ip] = 2*Y_MAX - cells[ic].y[ip]; + cells[ic].vy[ip] = - cells[ic].vy[ip]; + } + if ( cells[ic].y[ip] < Y_MIN ) + { + bounce_signal=1; + cells[ic].y[ip] = 2*Y_MIN - cells[ic].y[ip]; + cells[ic].vy[ip] = - cells[ic].vy[ip]; + } + if ( bounce_signal == 1 ) + (*n_bounce)++; +} + + +// +// calculation of kinetic energy ( per cell & total ) +// number of pseudo-particles is calculated as a check +// +int kinetic( int *n_pseudo_mol, double *average_energy ) +{ + double total_energy; + int count; + int ic, icc, ip, np; + + total_energy=0.0; + count=0; + // scan over cells + for ( icc=0 ; icc v_max ) v_max = v_mag; + if ( v_mag < v_min ) v_min = v_mag; + } + } + v_min = sqrt( v_min ); + v_max = sqrt( v_max ); + + // special case: speed of all + // pseudo-molecule are equal + // - requires a reset to allow + // collision pair selection in + // routine collision in first + // time step + if ( INITIAL_COND == 1 && it == 0 ) + { + v_max = 4.0 * v_min; + printf( " Special case: speed of all particles equal\n"); + } + + // return results + *vel_min = v_min; + *vel_max = v_max; +} + + +// +// random collisions of pseudo-particles (hard ball scheme) +// +int collisions( double vel_max, int *n_coll, + int *max_trial_coll, int *max_cell_coll ) +{ + int ic, icc, ip, np; + int max_trial_collisions, n_collisions, max_cell_collisions; + int Mc; + double sigma, Vc; + int count_trials, count, n1, n2; + int n1_store[N_MAX*(N_MAX-1)/2], n2_store[N_MAX*(N_MAX-1)/2]; + int ok, prev; + double v_rel_12_x, v_rel_12_y, v_rel; + double total_mass, angle, aux, cosff, sinff; + double v1x, v1y, v2x, v2y; + double v_cm_12_x, v_cm_12_y; + double e1, e2, e_before, e_after; + double rel_vel_max; + + // max relative velocity + // twice max velocity + rel_vel_max = 2.0*vel_max; + // # of collisions + n_collisions = 0; + max_cell_collisions = 0; + max_trial_collisions = 0; + // cross section + sigma = 4.0*R; + Vc = dx*dy; + // scan over cells + for ( icc=0 ; icc N_MAX*(N_MAX-1)/2 ) + { + printf( " Error \n" ); + printf( " Collisions - Cell: %4d %4d -- No: %3d -- Mc: %3d \n", + icc, ic, np, Mc ); + exit(1); + } + + if ( Mc > max_cell_collisions ) + max_cell_collisions = Mc; + + + if ( Mc > 0 ) + { + // count pairs + count = 0; + count_trials = 0; + while ( count < Mc ) + { + // choose a pair + n1 = np*random_num(); + n2 = np*random_num(); + count_trials++; + + // eliminate repeats & n1=n2 + ok = 1; + if ( n1 == n2 ) + ok = 0; + if ( count > 0 && ok == 1 ) + { + for ( prev=0 ; prev max_trial_collisions ) + max_trial_collisions = count_trials; + } + + *n_coll = n_collisions; + *max_cell_coll = max_cell_collisions; + *max_trial_coll = max_trial_collisions; + +} + + +// +// some statistics printing +// +void echo_results( int it, int n_bounce, int total_shift, int n_coll, + int max_trial_coll, int max_cell_coll, + int n_pseudo_mol, double average_energy, + int max_density, int min_density ) +{ + printf("\n Time step: %d\n", it ); + printf(" Total # pseudo-molecules bouncing on border: %d\n", + n_bounce ); + printf(" Total # pseudo-molecules to shift (inside domain): %d\n", + total_shift ); + printf(" Total # pairs pseudo-molecules colliding: %d\n", n_coll ); + printf( + " Max collisions pairs trial: %d -- Max collisions per cell: %d\n", + max_trial_coll, max_cell_coll ); + printf( + " Final average Kinetic energy (%d pseudo molecules): %f\n", + n_pseudo_mol, average_energy ); + printf(" Max & min density: %d %d \n", max_density, min_density ); +} + + +// +// write speed of particles in file +// +void velocity_statistics( int init_final_case ) +{ + FILE *fp; + int icc, ic, np, ip; + double v_mag; + char fname[100]; + + // either initial speed (1) or + // final speed distribution + strcpy( fname, "./speed_I" ); + if ( init_final_case == 2 ) + strcpy( fname, "./speed_F" ); + if ( init_final_case == 3 ) + strcpy( fname, "./speed_O" ); + // open file + if ( ( fp = fopen( fname, "w" ) ) == NULL ) + { + fprintf( stderr, " Error opening file: speed\n" ); + exit(1); + } + // scan over cells + for ( icc=0 ; icc +#include +#include +#include + + + +// +// random numbers in { 0 - 1 } +// +double random_num() +{ + return (double)rand()/(double)RAND_MAX; +} + + + +// +// Gaussian distributed random numbers +// +double Gaussian ( double *gauss1, double *gauss2 ) +{ + double twou, radius, theta; + + twou = -2.0*log(1.0-random_num()); + radius = sqrt(twou); + theta = 2*M_PI*random_num(); + *gauss1 = radius*cos(theta); + *gauss2 = radius*sin(theta); +} + + + +int main() +{ + int i, j, count, counter[100]; + double deltav, gauss1, gauss2; + + deltav = 0.1; + + for ( j=0; j<100 ; j++ ) + counter[j] = 0; + + count = 0; + for ( i=0; i 100 ) printf( " ----> %d\n", j ); + counter[j]++; + j = (int)( (gauss2+5.0)/deltav ); + if ( j > 100 ) printf( " ----> %d\n", j ); + counter[j]++; + count++; + } + printf( " Check - %d\n", count ); + + count = 0; + for ( j=0; j<100 ; j++ ) + { + printf( "%7.3f %d\n", deltav*j, counter[j] ); + count = count + counter[j]; + } + printf( " Check - %d\n", count ); +} diff --git a/assignments/archive/direct_simulation_monte_carlo/src/ran_int.c b/assignments/archive/direct_simulation_monte_carlo/src/ran_int.c new file mode 100755 index 0000000..9ec9115 --- /dev/null +++ b/assignments/archive/direct_simulation_monte_carlo/src/ran_int.c @@ -0,0 +1,49 @@ +/* + + simple check of random numbers + +*/ + +#define N 100000 + +#include +#include +#include +#include + +double random_num() +{ + return (double)rand()/(double)(RAND_MAX); +} + + +int main() +{ + int i, j, count, counter[100]; + + for ( j=0; j<20 ; j++ ) + counter[j] = 0; + + for ( i=0; if$wb5uc+mNqV?P5_XkjiHOFxT&$diK(C*4si7@~M|!)?f*p|*-pG+( zpLE+>S({eSbYojcFl|iy-Mgwp5}sgGGEAEw_Sg$wMb{Jg*)O9=%@`zH981$0g?5FZ zvq73>V;6;&g6)sU1tNRS(vm1Ty561bd>cx{7CU$K;#u^LRqOf5n9nrB+43U4jPaRJdHFSxVq_dDUpobH(O(gO0O)JnMo!md&v5Ae0$ulod;!&YRa3|YYx$Ah0 z(g&XB!gBg;9flF;*AGU5lhf|IGiYs%C!6Ov8YyZmy)q3L8>b<{Ic4*FlrMLQ z@TvFDT$RTk;5-xzdC2Cu&-(EG98?g6e5FjLFZyIpRV+%|)FQ6#RpMp9$)-th*9Ows 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+ + + + + + + + + + + + + + + + +JSFH + + + \ No newline at end of file diff --git a/assignments/archive/hamiltonian_expectation_value/index.shtml b/assignments/archive/hamiltonian_expectation_value/index.shtml new file mode 100644 index 0000000..6f8acc9 --- /dev/null +++ b/assignments/archive/hamiltonian_expectation_value/index.shtml @@ -0,0 +1,73 @@ + + +

Assignment #2

+

Due Friday, October 19, 2007

+ +

Quantum mechanics in Heisenberg representation deals with +matrices. These matrices can be very large, specially in many-body +systems. In these problems, parallel computers offer the advantage of +large memory (aggregate of memory on each node) and large disk +capacity (/tmp on each node).

+ +

The expectation value of an observable results from +vector–matrix–vector multiplication. For instance, +multiplying the eigenstate and the Hamiltonian matrix yields the +energy. The size of the vector and matrices is the size N of +the basis spanning the Hilbert space.

+ +

In this assignment we will use a (unrealistic) unit +eigenvector, |v> = 1.0/sqrt(N) (v * v = 1), as +eigenvectors and simple Hamiltonian matrices.

+ +

Part A

+ +

The code full_matrix.c is a +sequential code to compute v * H * v for the case +H(i,j) = i+j. The +Maple full_matrix_exact.mw gives +the exact answer for these simple H(i,j) and vector for +any N. + +

Write a parallel code to compute this expectation value +on Np nodes, where the Hamiltonian matrix +H(i,j) is split in Np "horizontal" slices. Each node +will perform a part of the vector–matrix–vector +multiplication.

+ +

Run your parallel code for H(i,j) of size 1000x1000 and +check it against both the sequential code and the Maple result. Run +your parallel code for +H(i,j) of size 3500x3500 and check it against the Maple +result.

+ +

Part B

+ +

In cases where the Hamiltonian matrix is "really large", but +sparse, one could store only the non-zero matrix elements and +corresponding indices. For instance, a 1000 x 1000 H with sparcity 5% +would require to store 1,000,000 8 Byte words in full-storage mode +(8,000,000 Bytes), while requiring 50,000 8 Byte words and twice (2 +indices) 50,000 4 Byte words (integer) in sparse-storage mode (400,000 +Bytes). Larger gains occur for larger matrices. Note that the symmetry +of the H(i,j) matrix reduces these storage requirements by +almost a factor 2).

+ +

The code sparse_matrix_setup.c +calculates a sparse Hamiltonian matrix H(i,j) with random +values ranging from 0.0 to 1.0 placed at random positions in the +matrix. It creates two files: +sparse_Hamiltonian_size, which contains the matrix size +and the number of non-zero matrix elements, +and sparse_Hamiltonian, the Hamiltonian matrix +itself. The latter is in symmetric storage mode, each line containing +i, j, and H(i,j) for half the matrix. Run this +code and copy the two files on /tmp in each node +of abax (with your name to identify your files) using +doscp.

+ +

Write a parallel code to compute the expectation value +of H(i,j) with any number of processes.

+ +

Please clean up /tmp on the nodes once done.

+ + diff --git a/assignments/archive/hamiltonian_expectation_value/sparse_Hamiltonian b/assignments/archive/hamiltonian_expectation_value/sparse_Hamiltonian new file mode 100644 index 0000000..a50730d --- /dev/null +++ b/assignments/archive/hamiltonian_expectation_value/sparse_Hamiltonian @@ -0,0 +1,1012717 @@ +840187 394382 0.783099 +911647 798440 0.197551 +768229 335222 0.277775 +553969 477397 0.628871 +513400 364784 0.952230 +916195 635711 0.717297 +606968 141602 0.016301 +242886 137231 0.804177 +400944 156679 0.129790 +998924 108808 0.218257 +839112 512932 0.612640 +637552 296031 0.524287 +972775 493582 0.292517 +771357 526744 0.769914 +891529 400228 0.283315 +807724 352458 0.919026 +949327 69755 0.525995 +192213 86055 0.663227 +890232 348892 0.064171 +457701 20023 0.063096 +970634 238279 0.902208 +850919 266665 0.539760 +760248 375206 0.512535 +667723 531606 0.039280 +931835 437637 0.930810 +720952 284293 0.738534 +639978 354048 0.687861 +440104 165974 0.880075 +829201 330337 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file mode 100644 index 0000000..eb4d905 --- /dev/null +++ b/assignments/archive/hamiltonian_expectation_value/src/.make_tar @@ -0,0 +1 @@ +../ diff --git a/assignments/archive/hamiltonian_expectation_value/src/full_matrix.c b/assignments/archive/hamiltonian_expectation_value/src/full_matrix.c new file mode 100644 index 0000000..4f9bd77 --- /dev/null +++ b/assignments/archive/hamiltonian_expectation_value/src/full_matrix.c @@ -0,0 +1,52 @@ + // PHYS 405 // + + // code to multiply matrix x vector // + + // assignment 2 - part a // + + // Michel Vallieres, Fall 2007 // + +#include +#include +#include + +#define N 1000 + + +int main( int argc, char * argv[] ) +{ + double H[N][N], v[N]; + double expectation_value, norm, temp; + int i, j; + + // unit vector v*v = 1. + norm = 1.0 / sqrt( (float)N ); + for ( i=0 ; i +#include +#include +#include /* MPI header file */ + +#define N 3500 +#define MaxHeight 400 + + +int main( int argc, char * argv[] ) +{ + double H[MaxHeight][N], v[N]; + double expectation_value, local_value, norm, temp; + int i, j, k, Nh, Nh1, shift; + int rank, size; + + /* init into MPI */ + MPI_Init(&argc, &argv); + /* my rank - my id */ + MPI_Comm_rank(MPI_COMM_WORLD, &rank); + /* how many processes in the virtual machine */ + MPI_Comm_size(MPI_COMM_WORLD, &size); + + //slicing + Nh1 = N / size; + if ( Nh1 > MaxHeight-5 ) + { + if ( rank == 0 ) + { + fprintf( stderr, "\n# processes too small for matrix size\n" ); + fprintf( stderr, "Increase # processes\n\n" ); + } + MPI_Finalize(); + exit(1); + } + Nh = Nh1; + shift = Nh1 * rank; + if ( rank == size-1 ) + Nh = N - shift; + printf("My rank: %d -- Slice and shift: %d %d \n", rank, Nh, shift ); + + // unit vector v*v = 1. + norm = 1.0 / sqrt( (float)N ); + for ( i=0 ; i +#include +#include + + +int main( int argc, char * argv[] ) +{ + double Hij, symm, expectation_value, norm, *v; + int N, Nelements, i, j, element; + FILE *fp; + /* data file size */ + fp = fopen( "sparse_Hamiltonian_size", "r" ); + fscanf( fp, "%d %d\n", &N, &Nelements); + fclose( fp ); + printf( "\nSize: %d and # non-zero elements: %d \n\n", N, Nelements ); + + /* unit vector v*v = 1 */ + v = (double *)malloc( N * sizeof(double) ); + norm = 1.0 / sqrt( (float)N ); + for ( i=0 ; i +#include +#include +#include /* MPI header file */ + + + +int main( int argc, char * argv[] ) +{ + double Hij, symm, local_value, expectation_value, norm, *v; + int N, Nelements, i, j, element, Nlocal, Nshift; + FILE *fp; + int rank, size; + + /* init into MPI */ + MPI_Init(&argc, &argv); + /* my rank - my id */ + MPI_Comm_rank(MPI_COMM_WORLD, &rank); + /* how many processes in the virtual machine */ + MPI_Comm_size(MPI_COMM_WORLD, &size); + + /* data file size */ + fp = fopen( "/tmp/michel_sparse_Hamiltonian_size", "r" ); + fscanf( fp, "%d %d\n", &N, &Nelements); + fclose( fp ); + + /* my data slice */ + Nlocal = Nelements / size; + Nshift = Nlocal * rank; + if ( rank == size-1 ) + Nlocal = Nelements - Nshift; + fprintf( stderr, " Rank, size, H size, non-zero, Nlocal, Nshift: %d %d %d %d %d %d\n", + rank, size, N, Nelements, Nlocal, Nshift ); + + /* unit vector v*v = 1 */ + v = (double *)malloc( N * sizeof(double) ); + norm = 1.0 / sqrt( (float)N ); + for ( i=0 ; i +#include +#include + + /* matrix size */ +#define N 1000000 + /* # non-zero elements */ +#define Nelements 1012717 + + +int main( int argc, char * argv[] ) +{ + double Hij; + int i, j, k, element; + int scan, repeat, kepti[Nelements], keptj[Nelements]; + FILE *fp; + /* data file size */ + fp = fopen( "sparse_Hamiltonian_size", "w" ); + fprintf( fp, "%d %d\n", N, Nelements); + fclose( fp ); + /* data file */ + fp = fopen( "sparse_Hamiltonian", "w" ); + /* initialize random numbers */ + srand( 1.0 ); + /* loop over non-zero Hij */ + element =0; + while ( element i ) + { + k = i; + i = j; + j = k; + } + + /* avoid repetition */ + repeat = 0; + if ( element > 0 ) + { + scan = 0; + while ( scan < element ) + { + if ( i == kepti[scan] && j == keptj[scan] ) + { + repeat = 1; + } + scan++; + if ( repeat == 1 ) + break; + } + } + + if ( repeat == 0 ) + { + /* random value */ + Hij = (float)rand() / (float)RAND_MAX; + + /* store element */ + kepti[element] = i; + keptj[element] = j; + fprintf( fp, "%d %d %f\n", i, j, Hij ); + element++; + } + } + + fclose( fp ); + +} + + diff --git a/assignments/archive/hamiltonian_expectation_value/src/sparse_matrix_setup_old.c b/assignments/archive/hamiltonian_expectation_value/src/sparse_matrix_setup_old.c new file mode 100644 index 0000000..0fc6570 --- /dev/null +++ b/assignments/archive/hamiltonian_expectation_value/src/sparse_matrix_setup_old.c @@ -0,0 +1,57 @@ + + // PHYS 405 // + + // code to generate a sparse Hamiltonian matrix // + // H matrix filled with random numbers at random locations // + + // assignment 2 - part b // + + // Michel Vallieres, Fall 2007 // + +#include +#include +#include + +#define N 1000 +#define Nelements 500000 + + +int main( int argc, char * argv[] ) +{ + double Hij; + int i, j, k, element; + FILE *fp; + /* data file size */ + fp = fopen( "sparse_Hamiltonian_size", "w" ); + fprintf( fp, "%d %d\n", N, Nelements); + fclose( fp ); + /* data file */ + fp = fopen( "sparse_Hamiltonian", "w" ); + /* initialize random numbers */ + srand( 1.0 ); + /* loop over non-zero Hij */ + for ( element=0 ; element i ) + { + k = i; + i = j; + j = k; + } + /* random value */ + Hij = (float)rand() / (float)RAND_MAX; + + /* store element */ + fprintf( fp, "%d %d %f\n", i, j, Hij ); + } + + fclose( fp ); + +} + + diff --git a/assignments/archive/least_squares_fitting/Least_Square_Fit_Linear_Quadratic.mws b/assignments/archive/least_squares_fitting/Least_Square_Fit_Linear_Quadratic.mws new file mode 100755 index 0000000..7fb841d --- /dev/null +++ b/assignments/archive/least_squares_fitting/Least_Square_Fit_Linear_Quadratic.mws @@ -0,0 +1,89 @@ +{VERSION 5 0 "IBM INTEL NT" "5.0" } +{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 +1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 +0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } +{CSTYLE "" -1 256 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 +257 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 +0 0 1 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Tim +es" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } +{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 +2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Outpu +t" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 } +1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 +-1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 +0 1 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 +0 0 0 }2 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" +-1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }2 0 0 -1 -1 -1 0 0 0 0 0 0 +-1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} +{SECT 0 {EXCHG {PARA 259 "" 0 "" {TEXT -1 1 " " }{TEXT 256 16 "Least S +quare fit" }{TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 16 "Michel Vall +ieres" }}{PARA 258 "" 0 "" {TEXT -1 11 "Spring 2002" }}{PARA 0 "" 0 " +" {TEXT 257 10 "Linear Fit" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG +{PARA 0 "> " 0 "" {MPLTEXT 1 0 471 "restart:\n \+ + # standard Deviation\nst_dev := sum( ( y[i] - alpha0 - a +lpha1*x[i] )^2, i=1..N );\n # min +imum conditions\n # first derivat +ives = 0\ndstdev_d1 := diff( st_dev, alpha0 ):\ndstdev_d2 := diff( st_ +dev, alpha1 ):\n # solve equation +s for minimum\neq1 := dstdev_d1 = 0;\neq2 := dstdev_d2 = 0;\nsolve( \{ +eq1,eq2\},\{alpha0,alpha1\} );\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% +'st_devG,&*&%\"NG\"\"\")%'alpha0G\"\"#F(F(-%$sumG6$,,*$)&%\"yG6#%\"iGF ++F(F(*(F+F(F2F(F*F(!\"\"**F+F(F2F(%'alpha1GF(&%\"xGF4F(F7**F+F(F*F(F9F +(F:F(F(*&)F9F+F()F:F+F(F(/F5;F(F'F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 +#>%$eq1G/,&*&%\"NG\"\"\"%'alpha0GF)\"\"#-%$sumG6$,&&%\"yG6#%\"iG!\"#*( +F+F)%'alpha1GF)&%\"xGF2F)F)/F3;F)F(F)\"\"!" }}{PARA 11 "" 1 "" +{XPPMATH 20 "6#>%$eq2G/-%$sumG6$,(*&&%\"xG6#%\"iG\"\"\"&%\"yGF-F/!\"#* +(\"\"#F/%'alpha0GF/F+F/F/*(F4F/%'alpha1GF/)F+F4F/F//F.;F/%\"NG\"\"!" } +}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%'alpha1G*&,&*&%\"NG\"\"\"-%$sumG6 +$*&&%\"xG6#%\"iGF*&%\"yGF1F*/F2;F*F)F*F**&-F,6$F/F5F*-F,6$F3F5F*!\"\"F +*,&*&F)F*-F,6$*$)F/\"\"#F*F5F*F**$)F8FCF*F " +0 "" {MPLTEXT 1 0 837 "restart:\n \+ + # standard Deviation\nst_dev := sum( ( y[i] - alpha0 - alpha1*x[i] - \+ +alpha2*x[i]^2 )^2, i=1..N );\n # \+ +minimum conditions\n # first deri +vatives = 0\ndstdev_d1 := diff( st_dev, alpha0 ):\ndstdev_d2 := diff( \+ +st_dev, alpha1 ):\ndstdev_d3 := diff( st_dev, alpha2 ):\n \+ + # solve equations for minimum\neq1 := dstdev_ +d1 = 0;\neq2 := dstdev_d2 = 0;\neq3 := dstdev_d3 = 0;\nsoln := solve( \+ +\{eq1,eq2,eq3\},\{alpha0,alpha1,alpha2\} ):\n \+ + # display solutions\nassign( soln ): \n`Numerators of the + three alpha coefficients`;\n'alpha0';\nnumer(alpha0);\n'alpha1';\nnum +er(alpha1);\n'alpha2';\nnumer(alpha2);\n`denominator of the alpha coef +ficients (same for all three)`;\ndenom(alpha1);" }}{PARA 11 "" 1 "" +{XPPMATH 20 "6#>%'st_devG,&*&%\"NG\"\"\")%'alpha0G\"\"#F(F(-%$sumG6$,4 +*$)&%\"yG6#%\"iGF+F(F(*(F+F(F2F(F*F(!\"\"**F+F(F2F(%'alpha1GF(&%\"xGF4 +F(F7**F+F(F2F(%'alpha2GF()F:F+F(F7**F+F(F*F(F9F(F:F(F(**F+F(F*F(F=F(F> +F(F(*&)F9F+F(F>F(F(**F+F(F9F()F:\"\"$F(F=F(F(*&)F=F+F()F:\"\"%F(F(/F5; +F(F'F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G/,&*&%\"NG\"\"\"%'alp +ha0GF)\"\"#-%$sumG6$,(&%\"yG6#%\"iG!\"#*(F+F)%'alpha1GF)&%\"xGF2F)F)*( +F+F)%'alpha2GF))F7F+F)F)/F3;F)F(F)\"\"!" }}{PARA 11 "" 1 "" {XPPMATH +20 "6#>%$eq2G/-%$sumG6$,**&&%\"yG6#%\"iG\"\"\"&%\"xGF-F/!\"#*(\"\"#F/F +0F/%'alpha0GF/F/*(F4F/%'alpha1GF/)F0F4F/F/*(F4F/)F0\"\"$F/%'alpha2GF/F +//F.;F/%\"NG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq3G/-%$sumG6$ +,**&&%\"yG6#%\"iG\"\"\")&%\"xGF-\"\"#F/!\"#*(F3F/F0F/%'alpha0GF/F/*(F3 +F/)F1\"\"$F/%'alpha1GF/F/*(F3F/%'alpha2GF/)F1\"\"%F/F//F.;F/%\"NG\"\"! +" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%KNumerators~of~the~three~alpha~co +efficientsG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'alpha0G" }}{PARA 12 " +" 1 "" {XPPMATH 20 "6#,.*(-%$sumG6$&%\"yG6#%\"iG/F+;\"\"\"%\"NGF.-F&6$ +*$)&%\"xGF*\"\"%F.F,F.-F&6$*$)F4\"\"#F.F,F.F.*&F%F.)-F&6$*$)F4\"\"$F.F +,F;F.!\"\"*(-F&6$F4F,F.F0F.-F&6$*&F(F.F4F.F,F.FC*(FEF.F>F.-F&6$*&F(F.F +:F.F,F.F.*&)F7F;F.FKF.FC*(F7F.F>F.FGF.F." }}{PARA 11 "" 1 "" {XPPMATH +20 "6#%'alpha1G" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,.*(%\"NG\"\"\"-%$s +umG6$*$)&%\"xG6#%\"iG\"\"%F&/F/;F&F%F&-F(6$*&&%\"yGF.F&F,F&F1F&!\"\"*( +F%F&-F(6$*$)F,\"\"$F&F1F&-F(6$*&F6F&)F,\"\"#F&F1F&F&*&)-F(6$*$FBF&F1FC +F&F3F&F&*(FFF&-F(6$F,F1F&F?F&F8*(F'F&FJF&-F(6$F6F1F&F&*(F:F&FFF&FMF&F8 +" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'alpha2G" }}{PARA 12 "" 1 "" +{XPPMATH 20 "6#,.*(%\"NG\"\"\"-%$sumG6$*$)&%\"xG6#%\"iG\"\"#F&/F/;F&F% +F&-F(6$*&&%\"yGF.F&F+F&F1F&!\"\"*(F%F&-F(6$*$)F,\"\"$F&F1F&-F(6$*&F6F& +F,F&F1F&F&*&F3F&)-F(6$F,F1F0F&F&*(F:F&FDF&-F(6$F6F1F&F8*(F'F&FDF&F?F&F +8*&)F'F0F&FGF&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%endenominator~of~ +the~alpha~coefficients~(same~for~all~three)G" }}{PARA 11 "" 1 "" +{XPPMATH 20 "6#,,*(%\"NG\"\"\"-%$sumG6$*$)&%\"xG6#%\"iG\"\"%F&/F/;F&F% +F&-F(6$*$)F,\"\"#F&F1F&!\"\"*&F%F&)-F(6$*$)F,\"\"$F&F1F7F&F&*$)F3F?F&F +&**F7F&F;F&F3F&-F(6$F,F1F&F8*&F'F&)FCF7F&F&" }}}{EXCHG {PARA 0 "> " 0 +"" {MPLTEXT 1 0 0 "" }}}}{MARK "2 1 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 +1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 } diff --git a/assignments/archive/least_squares_fitting/PHYS405_PHYS750_405.doc b/assignments/archive/least_squares_fitting/PHYS405_PHYS750_405.doc new file mode 100755 index 0000000000000000000000000000000000000000..322a3a38795d039d7033244e4de21a78bb4b4e2c GIT binary patch literal 20992 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b/assignments/archive/least_squares_fitting/index.shtml new file mode 100644 index 0000000..ba75621 --- /dev/null +++ b/assignments/archive/least_squares_fitting/index.shtml @@ -0,0 +1,46 @@ + + +

Assignment #1

+

Due Wednesday, April 17, 2002

+ +

Purpose

+

Understand and practice message passing under MPI.

+ +

Problem

+

Do a linear and polynomial fit of order 2 to a data set.

+ +

Method

+

Direct minimization of the residual via the least-square fit approach

+ +

To Do

+
    +
  • read the data on node 0
    • +
  • distribute the data on the processes ≠ 0
    • +
  • perform partial sums on the processes ≠ 0
    • +
  • send results back to node 0
    • +
  • use node 0 to calculate global sums and final results for the + polynomial fit coefficients
    • +
  • let the processes ≠ 0 calculate the final fit and residual + functions
    • +
  • node 0 is to store the final fit and residual functions on + file
    • +
+ +

Guide

+ + + +

Data

+ + + + diff --git a/assignments/archive/least_squares_fitting/least_square.c b/assignments/archive/least_squares_fitting/least_square.c new file mode 100644 index 0000000..842666d --- /dev/null +++ b/assignments/archive/least_squares_fitting/least_square.c @@ -0,0 +1,233 @@ +// +// to fit a polynomial through data +// Michel Vallieres +// Spring 2002 +// + + +#include +#include +#include +#include + + +// +// standard deviation +// +int std_dev( double *residuals, double *sigma, int N ) +{ + int k; + double sum; + + sum = 0.0; + for ( k=0 ; kq#gyef4x_9-u-uv!*-_MQUnVd6cX8tpC=9{wzEcFeJD99jITOXW{7K;uHXtKON{8@af+FMLB)@N|3vgi{T~I6(|%O^bfe?g7RhoI+RSadlgS5^^wf)tl|k@87@r1V?wS?G@)8`dp_d)%P&&TYnL;n^Rr(Bp2&}={0J;uP1Su}}QUw4y zj@wH`6xgZ|wW17#1HdLfi)Q`7*FqEJUNF)O0MH=Ut3|!#G4w$as>P!XAa=q10;w0> z-%Hmz;8N8AQqW+dcpEEFg|nf}qYJcwaLj5b7DpdqMiTnz>-w;pjV;Lc^3zeVw+qS% zIL9U}xvSCRxp)KLvG(M z$(_$}cFX&eisgFv#~=L_%=doq!199!Mc6-iP*8wxGx5V-pngzYD<~Xlb!po=(LMo2 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