def mpc_to_str(z, dps, **kwargs):
re, im = z
rs = to_str(re, dps)
if im[0]:
return rs + " - " + to_str(mpf_neg(im), dps, **kwargs) + "j"
else:
return rs + " + " + to_str(im, dps, **kwargs) + "j"
def mpc_to_str(z, dps, **kwargs):
re, im = z
rs = to_str(re, dps)
if im[0]:
return rs + " - " + to_str(mpf_neg(im), dps, **kwargs) + "j"
else:
return rs + " + " + to_str(im, dps, **kwargs) + "j"
def nstr(x, n=6):
"""
Convert an ``mpf`` or ``mpc`` to a decimal string literal with *n*
significant digits. The small default value for *n* is chosen to
make this function useful for printing collections of numbers
(lists, matrices, etc).
If *x* is a list or tuple, :func:`nstr` is applied recursively
to each element. For unrecognized classes, :func:`nstr`
simply returns ``str(x)``.
The companion function :func:`nprint` prints the result
instead of returning it.
>>> from sympy.mpmath import *
>>> nstr([+pi, ldexp(1,-500)])
'[3.14159, 3.05494e-151]'
>>> nprint([+pi, ldexp(1,-500)])
[3.14159, 3.05494e-151]
"""
if isinstance(x, list):
return "[%s]" % (", ".join(nstr(c, n) for c in x))
if isinstance(x, tuple):
return "(%s)" % (", ".join(nstr(c, n) for c in x))
if isinstance(x, mpf):
return to_str(x._mpf_, n)
if isinstance(x, mpc):
return "(" + complex_to_str(x._mpc_[0], x._mpc_[1], n) + ")"
if isinstance(x, basestring):
return repr(x)
from matrices import matrix
if isinstance(x, matrix):
return x.__nstr__(n)
return str(x)
def nstr(x, n=6):
"""Convert an mpf or mpc to a decimal string literal with n significant
digits. The small default value for n is chosen to make this function
useful for printing collections of numbers.
If x is a list or tuple, the function is applied to each element.
For unrecognized classes, this simply returns str(x).
There is also a companion function nprint that prints the string
instead of returning it.
>>> nstr([+pi, ldexp(1,-500)])
'[3.14159, 3.05494e-151]'
>>> print([+pi, ldexp(1,-500)])
[3.14159, 3.05494e-151]
"""
if isinstance(x, list):
return "[%s]" % (", ".join(nstr(c, n) for c in x))
if isinstance(x, tuple):
return "(%s)" % (", ".join(nstr(c, n) for c in x))
if isinstance(x, mpf):
return to_str(x._mpf_, n)
if isinstance(x, mpc):
return "(" + complex_to_str(x._mpc_[0], x._mpc_[1], n) + ")"
if isinstance(x, basestring):
return repr(x)
from matrices import matrix
if isinstance(x, matrix):
return x.__nstr__(n)
return str(x)
def mpi_str(s, prec):
sa, sb = s
dps = prec_to_dps(prec) + 5
return "[%s, %s]" % (to_str(sa, dps), to_str(sb, dps))
def mpi_str(s, prec):
sa, sb = s
dps = prec_to_dps(prec) + 5
return "[%s, %s]" % (to_str(sa, dps), to_str(sb, dps))
def complex_to_str(re, im, dps):
rs = to_str(re, dps)
if im[0]:
return rs + " - " + to_str(mpf_neg(im), dps) + "j"
else:
return rs + " + " + to_str(im, dps) + "j"
def complex_to_str(re, im, dps):
rs = to_str(re, dps)
if im[0]:
return rs + " - " + to_str(mpf_neg(im), dps) + "j"
else:
return rs + " + " + to_str(im, dps) + "j"
def mpi_to_str(x,
dps,
use_spaces=True,
brackets='[]',
mode='brackets',
error_dps=4,
**kwargs):
"""
Convert a mpi interval to a string.
**Arguments**
*dps*
decimal places to use for printing
*use_spaces*
use spaces for more readable output, defaults to true
*brackets*
pair of strings (or two-character string) giving left and right brackets
*mode*
mode of display: 'plusminus', 'percent', 'brackets' (default) or 'diff'
*error_dps*
limit the error to *error_dps* digits (mode 'plusminus and 'percent')
Additional keyword arguments are forwarded to the mpf-to-string conversion
for the components of the output.
**Examples**
>>> from mpmath import mpi, mp
>>> mp.dps = 30
>>> x = mpi(1, 2)
>>> mpi_to_str(x, mode='plusminus')
'1.5 +- 5.0e-1'
>>> mpi_to_str(x, mode='percent')
'1.5 (33.33%)'
>>> mpi_to_str(x, mode='brackets')
'[1.0, 2.0]'
>>> mpi_to_str(x, mode='brackets' , brackets=('<', '>'))
'<1.0, 2.0>'
>>> x = mpi('5.2582327113062393041', '5.2582327113062749951')
>>> mpi_to_str(x, mode='diff')
'5.2582327113062[4, 7]'
>>> mpi_to_str(mpi(0), mode='percent')
'0.0 (0%)'
"""
prec = dps_to_prec(dps)
wp = prec + 20
a, b = x
mid = mpi_mid(x, prec)
delta = mpi_delta(x, prec)
a_str = to_str(a, dps, **kwargs)
b_str = to_str(b, dps, **kwargs)
mid_str = to_str(mid, dps, **kwargs)
sp = ""
if use_spaces:
sp = " "
br1, br2 = brackets
if mode == 'plusminus':
delta_str = to_str(mpf_shift(delta, -1), dps, **kwargs)
s = mid_str + sp + "+-" + sp + delta_str
elif mode == 'percent':
if mid == fzero:
p = fzero
else:
# p = 100 * delta(x) / (2*mid(x))
p = mpf_mul(delta, from_int(100))
p = mpf_div(p, mpf_mul(mid, from_int(2)), wp)
s = mid_str + sp + "(" + to_str(p, error_dps) + "%)"
elif mode == 'brackets':
s = br1 + a_str + "," + sp + b_str + br2
elif mode == 'diff':
# use more digits if str(x.a) and str(x.b) are equal
if a_str == b_str:
a_str = to_str(a, dps + 3, **kwargs)
b_str = to_str(b, dps + 3, **kwargs)
# separate mantissa and exponent
a = a_str.split('e')
if len(a) == 1:
a.append('')
b = b_str.split('e')
if len(b) == 1:
b.append('')
if a[1] == b[1]:
if a[0] != b[0]:
for i in xrange(len(a[0]) + 1):
if a[0][i] != b[0][i]:
break
s = (a[0][:i] + br1 + a[0][i:] + ',' + sp + b[0][i:] + br2 +
'e' * min(len(a[1]), 1) + a[1])
else: # no difference
s = a[0] + br1 + br2 + 'e' * min(len(a[1]), 1) + a[1]
else:
s = br1 + 'e'.join(a) + ',' + sp + 'e'.join(b) + br2
else:
raise ValueError("'%s' is unknown mode for printing mpi" % mode)
return s
def mpi_to_str(x, dps, use_spaces=True, brackets='[]', mode='brackets', error_dps=4, **kwargs):
"""
Convert a mpi interval to a string.
**Arguments**
*dps*
decimal places to use for printing
*use_spaces*
use spaces for more readable output, defaults to true
*brackets*
pair of strings (or two-character string) giving left and right brackets
*mode*
mode of display: 'plusminus', 'percent', 'brackets' (default) or 'diff'
*error_dps*
limit the error to *error_dps* digits (mode 'plusminus and 'percent')
Additional keyword arguments are forwarded to the mpf-to-string conversion
for the components of the output.
**Examples**
>>> from mpmath import mpi, mp
>>> mp.dps = 30
>>> x = mpi(1, 2)
>>> mpi_to_str(x, mode='plusminus')
'1.5 +- 5.0e-1'
>>> mpi_to_str(x, mode='percent')
'1.5 (33.33%)'
>>> mpi_to_str(x, mode='brackets')
'[1.0, 2.0]'
>>> mpi_to_str(x, mode='brackets' , brackets=('<', '>'))
'<1.0, 2.0>'
>>> x = mpi('5.2582327113062393041', '5.2582327113062749951')
>>> mpi_to_str(x, mode='diff')
'5.2582327113062[4, 7]'
>>> mpi_to_str(mpi(0), mode='percent')
'0.0 (0%)'
"""
prec = dps_to_prec(dps)
wp = prec + 20
a, b = x
mid = mpi_mid(x, prec)
delta = mpi_delta(x, prec)
a_str = to_str(a, dps, **kwargs)
b_str = to_str(b, dps, **kwargs)
mid_str = to_str(mid, dps, **kwargs)
sp = ""
if use_spaces:
sp = " "
br1, br2 = brackets
if mode == 'plusminus':
delta_str = to_str(mpf_shift(delta,-1), dps, **kwargs)
s = mid_str + sp + "+-" + sp + delta_str
elif mode == 'percent':
if mid == fzero:
p = fzero
else:
# p = 100 * delta(x) / (2*mid(x))
p = mpf_mul(delta, from_int(100))
p = mpf_div(p, mpf_mul(mid, from_int(2)), wp)
s = mid_str + sp + "(" + to_str(p, error_dps) + "%)"
elif mode == 'brackets':
s = br1 + a_str + "," + sp + b_str + br2
elif mode == 'diff':
# use more digits if str(x.a) and str(x.b) are equal
if a_str == b_str:
a_str = to_str(a, dps+3, **kwargs)
b_str = to_str(b, dps+3, **kwargs)
# separate mantissa and exponent
a = a_str.split('e')
if len(a) == 1:
a.append('')
b = b_str.split('e')
if len(b) == 1:
b.append('')
if a[1] == b[1]:
if a[0] != b[0]:
for i in xrange(len(a[0]) + 1):
if a[0][i] != b[0][i]:
break
s = (a[0][:i] + br1 + a[0][i:] + ',' + sp + b[0][i:] + br2
+ 'e'*min(len(a[1]), 1) + a[1])
else: # no difference
s = a[0] + br1 + br2 + 'e'*min(len(a[1]), 1) + a[1]
else:
s = br1 + 'e'.join(a) + ',' + sp + 'e'.join(b) + br2
else:
raise ValueError("'%s' is unknown mode for printing mpi" % mode)
return s
def __str__(s): return to_str(s._mpf_, mp.dps) def __hash__(s): return mpf_hash(s._mpf_)
def __repr__(s): return "mpf('%s')" % to_str(s._mpf_, repr_dps(mp.prec))
def __str__(s): return to_str(s._mpf_, mp.dps)
def __str__(s): return to_str(s._mpf_, mp.dps) def __hash__(s): return mpf_hash(s._mpf_)
def __repr__(s): return "mpf('%s')" % to_str(s._mpf_, repr_dps(mp.prec))
def __str__(s): return to_str(s._mpf_, mp.dps)