File: [local] / OpenXM / src / sage / asir.py (download)
Revision 1.1, Sat Sep 8 05:35:35 2018 UTC (5 years, 8 months ago) by takayama
Branch: MAIN
The initial version of asir module to call asir from sagemath.
|
# $OpenXM: OpenXM/src/sage/asir.py,v 1.1 2018/09/08 05:35:35 takayama Exp $
from __future__ import print_function
from __future__ import absolute_import
import os
from .expect import Expect, ExpectElement
from sage.misc.misc import verbose
class Asir(Expect):
r"""
Interface to the Asir interpreter.
EXAMPLES::
sage: asir.eval("a = [ 1, 1, 2; 3, 5, 8; 13, 21, 33 ]") # optional - asir
'a =\n\n 1 1 2\n 3 5 8\n 13 21 33\n\n's
sage: asir.eval("b = [ 1; 3; 13]") # optional - asir
'b =\n\n 1\n 3\n 13\n\n'
sage: asir.eval("c=a \\ b") # solves linear equation: a*c = b # optional - asir; random output
'c =\n\n 1\n 7.21645e-16\n -7.21645e-16\n\n'
sage: asir.eval("c") # optional - asir; random output
'c =\n\n 1\n 7.21645e-16\n -7.21645e-16\n\n'
"""
def __init__(self, maxread=None, script_subdirectory=None, logfile=None,
server=None, server_tmpdir=None, seed=None, command=None):
"""
EXAMPLES::
sage: asir == loads(dumps(asir))
True
"""
if command is None:
import os
command = os.getenv('SAGE_ASIR_COMMAND') or 'openxm ox_texmacs --view sage --quiet --noCopyright'
if server is None:
import os
server = os.getenv('SAGE_ASIR_SERVER') or None
Expect.__init__(self,
name = 'asir',
# We want the prompt sequence to be unique to avoid confusion with syntax error messages containing >>>
# prompt = 'asir\:\d+> ',
prompt = 'asir>',
# prompt = '',
# We don't want any pagination of output
# command = command + " --no-line-editing --silent --eval 'PS2(PS1());more off' --persist",
command = 'openxm ox_texmacs --view sage --quiet --noCopyright',
# command = "openxm asir -quiet",
maxread = maxread,
server = server,
server_tmpdir = server_tmpdir,
script_subdirectory = script_subdirectory,
restart_on_ctrlc = False,
verbose_start = False,
logfile = logfile,
eval_using_file_cutoff=100)
self._seed = seed
def set_seed(self, seed=None):
"""
Sets the seed for the random number generator
for this asir interpreter.
EXAMPLES::
sage: o = Asir() # optional - asir
sage: o.set_seed(1) # optional - asir
1
sage: [o.rand() for i in range(5)] # optional - asir
[ 0.134364, 0.847434, 0.763775, 0.255069, 0.495435]
"""
if seed is None:
seed = self.rand_seed()
self.eval("rand('state',%d)" % seed)
self._seed = seed
return seed
def __reduce__(self):
"""
EXAMPLES::
sage: asir.__reduce__()
(<function reduce_load_Asir at 0x...>, ())
"""
return reduce_load_Asir, tuple([])
def _read_in_file_command(self, filename):
"""
EXAMPLES::
sage: filename = tmp_filename()
sage: asir._read_in_file_command(filename)
'source("...");'
"""
return 'source("%s");'%filename
def _quit_string(self):
"""
EXAMPLES::
sage: asir._quit_string()
'quit;'
"""
return '!quit;'
def _install_hints(self):
"""
Returns hints on how to install Asir.
EXAMPLES::
sage: print(asir._install_hints())
You must get ...
"""
return """
You must get the program "asir" in order to use Asir
from Sage. You can read all about Asir at
http://www.gnu.org/software/asir/
LINUX:
Do apt-get install asir as root on your machine (Ubuntu/Debian).
Other Linux systems have asir too.
OS X:
* This website has details on OS X builds of Asir:
http://wiki.asir.org/Asir_for_MacOS_X
* Darwin ports and fink have Asir as well.
"""
def _eval_line(self, line, reformat=True, allow_use_file=False,
wait_for_prompt=True, restart_if_needed=False):
"""
EXAMPLES::
sage: print(asir._eval_line('2+2')) #optional - asir
ans = 4
"""
from pexpect.exceptions import EOF
if not wait_for_prompt:
return Expect._eval_line(self, line)
if line == '':
return ''
if self._expect is None:
self._start()
if allow_use_file and len(line)>3000:
return self._eval_line_using_file(line)
try:
E = self._expect
# debug
# self._synchronize(cmd='1+%s\n')
verbose("in = '%s'"%line,level=3)
E.sendline(line)
E.expect(self._prompt)
out = E.before
# debug
verbose("out = '%s'"%out,level=3)
except EOF:
if self._quit_string() in line:
return ''
except KeyboardInterrupt:
self._keyboard_interrupt()
try:
if reformat:
if 'syntax error' in out:
raise SyntaxError(out)
out = "\n".join(out.splitlines()[1:])
return out
except NameError:
return ''
def _keyboard_interrupt(self):
print("CntrlC: Interrupting %s..."%self)
if self._restart_on_ctrlc:
try:
self._expect.close(force=1)
except pexpect.ExceptionPexpect as msg:
raise RuntimeError( "THIS IS A BUG -- PLEASE REPORT. This should never happen.\n" + msg)
self._start()
raise KeyboardInterrupt("Restarting %s (WARNING: all variables defined in previous session are now invalid)"%self)
else:
self._expect.send('\003') # control-c
raise KeyboardInterrupt("Ctrl-c pressed while running %s"%self)
def quit(self, verbose=False):
"""
EXAMPLES::
sage: o = Asir()
sage: o._start() # optional - asir
sage: o.quit(True) # optional - asir
Exiting spawned Asir process.
"""
# Don't bother, since it just hangs in some cases, and it
# isn't necessary, since asir behaves well with respect
# to signals.
if not self._expect is None:
if verbose:
print("Exiting spawned %s process." % self)
return
def _start(self):
"""
Starts the Asir process.
EXAMPLES::
sage: o = Asir() # optional - asir
sage: o.is_running() # optional - asir
False
sage: o._start() # optional - asir
sage: o.is_running() # optional - asir
True
"""
Expect._start(self)
# self.eval("page_screen_output=0;")
# self.eval("format none;")
# set random seed
# self.set_seed(self._seed)
def _equality_symbol(self):
"""
EXAMPLES::
sage: asir('0 == 1') # optional - asir
0
sage: asir('1 == 1') # optional - asir
1
"""
return '=='
def _true_symbol(self):
"""
EXAMPLES::
sage: asir('1 == 1') # optional - asir
1
"""
return '1'
def _false_symbol(self):
"""
EXAMPLES::
sage: asir('0 == 1') # optional - asir
0
"""
return '0'
def set(self, var, value):
"""
Set the variable ``var`` to the given ``value``.
EXAMPLES::
sage: asir.set('x', '2') # optional - asir
sage: asir.get('x') # optional - asir
' 2'
"""
cmd = '%s=%s;'%(var,value)
out = self.eval(cmd)
if out.find("error") != -1 or out.find("Error") != -1:
raise TypeError("Error executing code in Asir\nCODE:\n\t%s\nAsir ERROR:\n\t%s"%(cmd, out))
def get(self, var):
"""
Get the value of the variable ``var``.
EXAMPLES::
sage: asir.set('x', '2') # optional - asir
sage: asir.get('x') # optional - asir
' 2'
"""
s = self.eval('%s;'%var)
i = s.find('=')
return s[i+1:]
def clear(self, var):
"""
Clear the variable named var.
EXAMPLES::
sage: asir.set('x', '2') # optional - asir
sage: asir.clear('x') # optional - asir
sage: asir.get('x') # optional - asir
"error: 'x' undefined near line ... column 1"
"""
self.eval('clear %s'%var)
def console(self):
"""
Spawn a new Asir command-line session.
This requires that the optional asir program be installed and in
your PATH, but no optional Sage packages need be installed.
EXAMPLES::
sage: asir_console() # not tested
GNU Asir, version 2.1.73 (i386-apple-darwin8.5.3).
Copyright (C) 2006 John W. Eaton.
...
asir:1> 2+3
ans = 5
asir:2> [ctl-d]
Pressing ctrl-d exits the asir console and returns you to Sage.
asir, like Sage, remembers its history from one session to
another.
"""
asir_console()
def version(self):
"""
Return the version of Asir.
OUTPUT: string
EXAMPLES::
sage: v = asir.version() # optional - asir
sage: v # optional - asir; random
'2.13.7'
sage: import re
sage: assert re.match("\d+\.\d+\.\d+", v) is not None # optional - asir
"""
return str(self("version()")).strip()
def solve_linear_system(self, A, b):
r"""
Use asir to compute a solution x to A\*x = b, as a list.
INPUT:
- ``A`` -- mxn matrix A with entries in `\QQ` or `\RR`
- ``b`` -- m-vector b entries in `\QQ` or `\RR` (resp)
OUTPUT: A list x (if it exists) which solves M\*x = b
EXAMPLES::
sage: M33 = MatrixSpace(QQ,3,3)
sage: A = M33([1,2,3,4,5,6,7,8,0])
sage: V3 = VectorSpace(QQ,3)
sage: b = V3([1,2,3])
sage: asir.solve_linear_system(A,b) # optional - asir (and output is slightly random in low order bits)
[-0.33333299999999999, 0.66666700000000001, -3.5236600000000002e-18]
AUTHORS:
- David Joyner and William Stein
"""
m = A.nrows()
if m != len(b):
raise ValueError("dimensions of A and b must be compatible")
from sage.matrix.all import MatrixSpace
from sage.rings.all import QQ
MS = MatrixSpace(QQ,m,1)
b = MS(list(b)) # converted b to a "column vector"
sA = self.sage2asir_matrix_string(A)
sb = self.sage2asir_matrix_string(b)
self.eval("a = " + sA )
self.eval("b = " + sb )
soln = asir.eval("c = a \\ b")
soln = soln.replace("\n\n ","[")
soln = soln.replace("\n\n","]")
soln = soln.replace("\n",",")
sol = soln[3:]
return eval(sol)
def sage2asir_matrix_string(self, A):
"""
Return an asir matrix from a Sage matrix.
INPUT: A Sage matrix with entries in the rationals or reals.
OUTPUT: A string that evaluates to an Asir matrix.
EXAMPLES::
sage: M33 = MatrixSpace(QQ,3,3)
sage: A = M33([1,2,3,4,5,6,7,8,0])
sage: asir.sage2asir_matrix_string(A) # optional - asir
'[1, 2, 3; 4, 5, 6; 7, 8, 0]'
AUTHORS:
- David Joyner and William Stein
"""
return str(A.rows()).replace('), (', '; ').replace('(', '').replace(')','')
def de_system_plot(self, f, ics, trange):
r"""
Plots (using asir's interface to gnuplot) the solution to a
`2\times 2` system of differential equations.
INPUT:
- ``f`` - a pair of strings representing the
differential equations; The independent variable must be called x
and the dependent variable must be called y.
- ``ics`` - a pair [x0,y0] such that x(t0) = x0, y(t0)
= y0
- ``trange`` - a pair [t0,t1]
OUTPUT: a gnuplot window appears
EXAMPLES::
sage: asir.de_system_plot(['x+y','x-y'], [1,-1], [0,2]) # not tested -- does this actually work (on OS X it fails for me -- William Stein, 2007-10)
This should yield the two plots `(t,x(t)), (t,y(t))` on the
same graph (the `t`-axis is the horizontal axis) of the
system of ODEs
.. math::
x' = x+y, x(0) = 1;\qquad y' = x-y, y(0) = -1, \quad\text{for}\quad 0 < t < 2.
"""
eqn1 = f[0].replace('x','x(1)').replace('y','x(2)')
eqn2 = f[1].replace('x','x(1)').replace('y','x(2)')
fcn = "function xdot = f(x,t) xdot(1) = %s; xdot(2) = %s; endfunction"%(eqn1, eqn2)
self.eval(fcn)
x0_eqn = "x0 = [%s; %s]"%(ics[0], ics[1])
self.eval(x0_eqn)
t_eqn = "t = linspace(%s, %s, 200)'"%(trange[0], trange[1])
self.eval(t_eqn)
x_eqn = 'x = lsode("f",x0,t);'
self.eval(x_eqn)
self.eval("plot(t,x)")
def _object_class(self):
"""
EXAMPLES::
sage: asir._object_class()
<class 'sage.interfaces.asir.AsirElement'>
"""
return AsirElement
asir_functions = set()
def to_complex(asir_string, R):
r"""
Helper function to convert asir complex number
TESTS::
sage: from sage.interfaces.asir import to_complex
sage: to_complex('(0,1)', CDF)
1.0*I
sage: to_complex('(1.3231,-0.2)', CDF)
1.3231 - 0.2*I
"""
real, imag = asir_string.strip('() ').split(',')
return R(float(real), float(imag))
class AsirElement(ExpectElement):
def _get_sage_ring(self):
r"""
TESTS::
sage: asir('1')._get_sage_ring() # optional - asir
Real Double Field
sage: asir('I')._get_sage_ring() # optional - asir
Complex Double Field
sage: asir('[]')._get_sage_ring() # optional - asir
Real Double Field
"""
if self.isinteger():
import sage.rings.integer_ring
return sage.rings.integer_ring.ZZ
elif self.isreal():
import sage.rings.real_double
return sage.rings.real_double.RDF
elif self.iscomplex():
import sage.rings.complex_double
return sage.rings.complex_double.CDF
else:
raise TypeError("no Sage ring associated to this element.")
def __nonzero__(self):
r"""
Test whether this element is nonzero.
EXAMPLES::
sage: bool(asir('0')) # optional - asir
False
sage: bool(asir('[]')) # optional - asir
False
sage: bool(asir('[0,0]')) # optional - asir
False
sage: bool(asir('[0,0,0;0,0,0]')) # optional - asir
False
sage: bool(asir('0.1')) # optional - asir
True
sage: bool(asir('[0,1,0]')) # optional - asir
True
sage: bool(asir('[0,0,-0.1;0,0,0]')) # optional - asir
True
"""
return str(self) != ' [](0x0)' and any(x != '0' for x in str(self).split())
def _matrix_(self, R=None):
r"""
Return Sage matrix from this asir element.
EXAMPLES::
sage: A = asir('[1,2;3,4.5]') # optional - asir
sage: matrix(A) # optional - asir
[1.0 2.0]
[3.0 4.5]
sage: _.base_ring() # optional - asir
Real Double Field
sage: A = asir('[I,1;-1,0]') # optional - asir
sage: matrix(A) # optional - asir
[1.0*I 1.0]
[ -1.0 0.0]
sage: _.base_ring() # optional - asir
Complex Double Field
sage: A = asir('[1,2;3,4]') # optional - asir
sage: matrix(ZZ, A) # optional - asir
[1 2]
[3 4]
sage: A = asir('[1,2;3,4.5]') # optional - asir
sage: matrix(RR, A) # optional - asir
[1.00000000000000 2.00000000000000]
[3.00000000000000 4.50000000000000]
"""
if not self.ismatrix():
raise TypeError('not an asir matrix')
if R is None:
R = self._get_sage_ring()
s = str(self).strip('\n ')
w = [u.strip().split(' ') for u in s.split('\n')]
nrows = len(w)
ncols = len(w[0])
if self.iscomplex():
w = [[to_complex(x,R) for x in row] for row in w]
from sage.matrix.all import MatrixSpace
return MatrixSpace(R, nrows, ncols)(w)
def _vector_(self, R=None):
r"""
Return Sage vector from this asir element.
EXAMPLES::
sage: A = asir('[1,2,3,4]') # optional - asir
sage: vector(ZZ, A) # optional - asir
(1, 2, 3, 4)
sage: A = asir('[1,2.3,4.5]') # optional - asir
sage: vector(A) # optional - asir
(1.0, 2.3, 4.5)
sage: A = asir('[1,I]') # optional - asir
sage: vector(A) # optional - asir
(1.0, 1.0*I)
"""
oc = self.parent()
if not self.isvector():
raise TypeError('not an asir vector')
if R is None:
R = self._get_sage_ring()
s = str(self).strip('\n ')
w = s.strip().split(' ')
nrows = len(w)
if self.iscomplex():
w = [to_complex(x, R) for x in w]
from sage.modules.free_module import FreeModule
return FreeModule(R, nrows)(w)
def _scalar_(self):
"""
Return Sage scalar from this asir element.
EXAMPLES::
sage: A = asir('2833') # optional - asir
sage: As = A.sage(); As # optional - asir
2833.0
sage: As.parent() # optional - asir
Real Double Field
sage: B = sqrt(A) # optional - asir
sage: Bs = B.sage(); Bs # optional - asir
53.2259
sage: Bs.parent() # optional - asir
Real Double Field
sage: C = sqrt(-A) # optional - asir
sage: Cs = C.sage(); Cs # optional - asir
53.2259*I
sage: Cs.parent() # optional - asir
Complex Double Field
"""
if not self.isscalar():
raise TypeError("not an asir scalar")
R = self._get_sage_ring()
if self.iscomplex():
return to_complex(str(self), R)
else:
return R(str(self))
def _sage_(self):
"""
Try to parse the asir object and return a sage object.
EXAMPLES::
sage: A = asir('2833') # optional - asir
sage: A.sage() # optional - asir
2833.0
sage: B = sqrt(A) # optional - asir
sage: B.sage() # optional - asir
53.2259
sage: C = sqrt(-A) # optional - asir
sage: C.sage() # optional - asir
53.2259*I
sage: A = asir('[1,2,3,4]') # optional - asir
sage: A.sage() # optional - asir
(1.0, 2.0, 3.0, 4.0)
sage: A = asir('[1,2.3,4.5]') # optional - asir
sage: A.sage() # optional - asir
(1.0, 2.3, 4.5)
sage: A = asir('[1,2.3+I,4.5]') # optional - asir
sage: A.sage() # optional - asir
(1.0, 2.3 + 1.0*I, 4.5)
"""
if self.isscalar():
return self._scalar_()
elif self.isvector():
return self._vector_()
elif self.ismatrix():
return self._matrix_()
else:
raise NotImplementedError('asir type is not recognized')
# An instance
asir = Asir()
def reduce_load_Asir():
"""
EXAMPLES::
sage: from sage.interfaces.asir import reduce_load_Asir
sage: reduce_load_Asir()
Asir
"""
return asir
def asir_console():
"""
Spawn a new Asir command-line session.
This requires that the optional asir program be installed and in
your PATH, but no optional Sage packages need be installed.
EXAMPLES::
sage: asir_console() # not tested
GNU Asir, version 2.1.73 (i386-apple-darwin8.5.3).
Copyright (C) 2006 John W. Eaton.
...
asir:1> 2+3
ans = 5
asir:2> [ctl-d]
Pressing ctrl-d exits the asir console and returns you to Sage.
asir, like Sage, remembers its history from one session to
another.
"""
from sage.repl.rich_output.display_manager import get_display_manager
if not get_display_manager().is_in_terminal():
raise RuntimeError('Can use the console only in the terminal. Try %%asir magics instead.')
os.system('openxm asir') # with asir prompt
# os.system('openxm asir -quiet')
def asir_version():
"""
DEPRECATED: Return the version of Asir installed.
EXAMPLES::
sage: asir_version() # optional - asir
doctest:...: DeprecationWarning: This has been deprecated. Use
asir.version() instead
See http://trac.sagemath.org/21135 for details.
'...'
"""
from sage.misc.superseded import deprecation
deprecation(21135, "This has been deprecated. Use asir.version() instead")
return asir.version()
![[BACK]](/icons/cvsweb/back.gif){kind=icon}
Return to asir.py CVS log ![[TXT]](/icons/cvsweb/text.gif){kind=icon}
![[DIR]](/icons/cvsweb/dir.gif){kind=icon}
Up to [local] / OpenXM / src / sage