summaryrefslogtreecommitdiff
diff options
context:
space:
mode:
Diffstat
-rw-r--r--doc/release/1.5.0-notes.rst (renamed from doc/release/2.0.0-notes.rst)32
-rw-r--r--numpy/polynomial/chebyshev.py45
-rw-r--r--numpy/polynomial/polynomial.py42
-rw-r--r--numpy/polynomial/polytemplate.py106
-rw-r--r--numpy/polynomial/tests/test_chebyshev.py47
-rw-r--r--numpy/polynomial/tests/test_polynomial.py47
6 files changed, 229 insertions, 90 deletions
diff --git a/doc/release/2.0.0-notes.rst b/doc/release/1.5.0-notes.rst
index 68314c488..abccfdd2e 100644
--- a/doc/release/2.0.0-notes.rst
+++ b/doc/release/1.5.0-notes.rst
@@ -1,5 +1,5 @@
=========================
-NumPy 2.0.0 Release Notes
+NumPy 1.5.0 Release Notes
=========================
@@ -73,30 +73,32 @@ Changes
polynomial.polynomial
---------------------
-* The polyint and polyder functions now check that the specified number integrations or
- derivations is a non-negative integer. The number 0 is a valid value for both
- functions.
+* The polyint and polyder functions now check that the specified number
+ integrations or derivations is a non-negative integer. The number 0 is
+ a valid value for both functions.
* A degree method has been added to the Polynomial class.
-* A cutdeg method has been added to the Polynomial class. It operates like
+* A trimdeg method has been added to the Polynomial class. It operates like
truncate except that the argument is the desired degree of the result,
not the number of coefficients.
-* The fit class function of the Polynomial class now uses None as the default
- domain for the fit. The default Polynomial domain can be specified by using
- [] as the domain value.
+* Polynomial.fit now uses None as the default domain for the fit. The default
+ Polynomial domain can be specified by using [] as the domain value.
+* Weights can be used in both polyfit and Polynomial.fit
+* A linspace method has been added to the Polynomial class to ease plotting.
polynomial.chebyshev
--------------------
-* The chebint and chebder functions now check that the specified number integrations or
- derivations is a non-negative integer. The number 0 is a valid value for both
- functions.
+* The chebint and chebder functions now check that the specified number
+ integrations or derivations is a non-negative integer. The number 0 is
+ a valid value for both functions.
* A degree method has been added to the Chebyshev class.
-* A cutdeg method has been added to the Chebyshev class. It operates like
+* A trimdeg method has been added to the Chebyshev class. It operates like
truncate except that the argument is the desired degree of the result,
not the number of coefficients.
-* The fit class function of the Chebyshev class now uses None as the default
- domain for the fit. The default Chebyshev domain can be specified by using
- [] as the domain value.
+* Chebyshev.fit now uses None as the default domain for the fit. The default
+ Chebyshev domain can be specified by using [] as the domain value.
+* Weights can be used in both chebfit and Chebyshev.fit
+* A linspace method has been added to the Chebyshev class to ease plotting.
histogram
---------
diff --git a/numpy/polynomial/chebyshev.py b/numpy/polynomial/chebyshev.py
index 2b6d7b4bb..99edecca1 100644
--- a/numpy/polynomial/chebyshev.py
+++ b/numpy/polynomial/chebyshev.py
@@ -1046,7 +1046,8 @@ def chebvander(x, deg) :
Parameters
----------
x : array_like
- Array of points. The values are converted to double or complex doubles.
+ Array of points. The values are converted to double or complex
+ doubles.
deg : integer
Degree of the resulting matrix.
@@ -1059,15 +1060,15 @@ def chebvander(x, deg) :
"""
x = np.asarray(x) + 0.0
order = int(deg) + 1
- v = np.ones(x.shape + (order,), dtype=x.dtype)
+ v = np.ones((order,) + x.shape, dtype=x.dtype)
if order > 1 :
x2 = 2*x
- v[...,1] = x
+ v[1] = x
for i in range(2, order) :
- v[...,i] = x2*v[...,i-1] - v[...,i-2]
- return v
+ v[i] = v[i-1]*x2 - v[i-2]
+ return np.rollaxis(v, 0, v.ndim)
-def chebfit(x, y, deg, rcond=None, full=False):
+def chebfit(x, y, deg, rcond=None, full=False, w=None):
"""
Least squares fit of Chebyshev series to data.
@@ -1094,6 +1095,12 @@ def chebfit(x, y, deg, rcond=None, full=False):
Switch determining nature of return value. When it is False (the
default) just the coefficients are returned, when True diagnostic
information from the singular value decomposition is also returned.
+ w : array_like, shape (`M`,), optional
+ Weights. If not None, the contribution of each point
+ ``(x[i],y[i])`` to the fit is weighted by `w[i]`. Ideally the
+ weights are chosen so that the errors of the products ``w[i]*y[i]``
+ all have the same variance. The default value is None.
+ .. versionadded:: 1.5.0
Returns
-------
@@ -1176,17 +1183,33 @@ def chebfit(x, y, deg, rcond=None, full=False):
raise TypeError, "expected non-empty vector for x"
if y.ndim < 1 or y.ndim > 2 :
raise TypeError, "expected 1D or 2D array for y"
- if x.shape[0] != y.shape[0] :
+ if len(x) != len(y):
raise TypeError, "expected x and y to have same length"
+ # set up the least squares matrices
+ lhs = chebvander(x, deg)
+ rhs = y
+ if w is not None:
+ w = np.asarray(w) + 0.0
+ if w.ndim != 1:
+ raise TypeError, "expected 1D vector for w"
+ if len(x) != len(w):
+ raise TypeError, "expected x and w to have same length"
+ # apply weights
+ if rhs.ndim == 2:
+ lhs *= w[:, np.newaxis]
+ rhs *= w[:, np.newaxis]
+ else:
+ lhs *= w[:, np.newaxis]
+ rhs *= w
+
# set rcond
if rcond is None :
rcond = len(x)*np.finfo(x.dtype).eps
- # set up the design matrix and solve the least squares equation
- A = chebvander(x, deg)
- scl = np.sqrt((A*A).sum(0))
- c, resids, rank, s = la.lstsq(A/scl, y, rcond)
+ # scale the design matrix and solve the least squares equation
+ scl = np.sqrt((lhs*lhs).sum(0))
+ c, resids, rank, s = la.lstsq(lhs/scl, rhs, rcond)
c = (c.T/scl).T
# warn on rank reduction
diff --git a/numpy/polynomial/polynomial.py b/numpy/polynomial/polynomial.py
index 9f98ad4ca..3144d9985 100644
--- a/numpy/polynomial/polynomial.py
+++ b/numpy/polynomial/polynomial.py
@@ -646,14 +646,14 @@ def polyvander(x, deg) :
"""
x = np.asarray(x) + 0.0
order = int(deg) + 1
- v = np.ones(x.shape + (order,), dtype=x.dtype)
+ v = np.ones((order,) + x.shape, dtype=x.dtype)
if order > 1 :
- v[...,1] = x
+ v[1] = x
for i in range(2, order) :
- v[...,i] = x*v[...,i-1]
- return v
+ v[i] = v[i-1]*x
+ return np.rollaxis(v, 0, v.ndim)
-def polyfit(x, y, deg, rcond=None, full=False):
+def polyfit(x, y, deg, rcond=None, full=False, w=None):
"""
Least-squares fit of a polynomial to data.
@@ -684,6 +684,12 @@ def polyfit(x, y, deg, rcond=None, full=False):
(the default) just the coefficients are returned; when ``True``,
diagnostic information from the singular value decomposition (used
to solve the fit's matrix equation) is also returned.
+ w : array_like, shape (`M`,), optional
+ Weights. If not None, the contribution of each point
+ ``(x[i],y[i])`` to the fit is weighted by `w[i]`. Ideally the
+ weights are chosen so that the errors of the products ``w[i]*y[i]``
+ all have the same variance. The default value is None.
+ .. versionadded:: 1.5.0
Returns
-------
@@ -787,17 +793,33 @@ def polyfit(x, y, deg, rcond=None, full=False):
raise TypeError, "expected non-empty vector for x"
if y.ndim < 1 or y.ndim > 2 :
raise TypeError, "expected 1D or 2D array for y"
- if x.shape[0] != y.shape[0] :
+ if len(x) != len(y):
raise TypeError, "expected x and y to have same length"
+ # set up the least squares matrices
+ lhs = polyvander(x, deg)
+ rhs = y
+ if w is not None:
+ w = np.asarray(w) + 0.0
+ if w.ndim != 1:
+ raise TypeError, "expected 1D vector for w"
+ if len(x) != len(w):
+ raise TypeError, "expected x and w to have same length"
+ # apply weights
+ if rhs.ndim == 2:
+ lhs *= w[:, np.newaxis]
+ rhs *= w[:, np.newaxis]
+ else:
+ lhs *= w[:, np.newaxis]
+ rhs *= w
+
# set rcond
if rcond is None :
rcond = len(x)*np.finfo(x.dtype).eps
- # set up the design matrix and solve the least squares equation
- A = polyvander(x, deg)
- scl = np.sqrt((A*A).sum(0))
- c, resids, rank, s = la.lstsq(A/scl, y, rcond)
+ # scale the design matrix and solve the least squares equation
+ scl = np.sqrt((lhs*lhs).sum(0))
+ c, resids, rank, s = la.lstsq(lhs/scl, rhs, rcond)
c = (c.T/scl).T
# warn on rank reduction
diff --git a/numpy/polynomial/polytemplate.py b/numpy/polynomial/polytemplate.py
index 1f17593dd..75b1b4eb1 100644
--- a/numpy/polynomial/polytemplate.py
+++ b/numpy/polynomial/polytemplate.py
@@ -322,13 +322,13 @@ class $name(pu.PolyBase) :
squares where the coefficients of the high degree terms may be very
small.
- Parameters:
- -----------
+ Parameters
+ ----------
deg : non-negative int
The series is reduced to degree `deg` by discarding the high
order terms. The value of `deg` must be a non-negative integer.
- Returns:
+ Returns
-------
new_instance : $name
New instance of $name with reduced degree.
@@ -343,8 +343,8 @@ class $name(pu.PolyBase) :
def convert(self, domain=None, kind=None) :
"""Convert to different class and/or domain.
- Parameters:
- -----------
+ Parameters
+ ----------
domain : {None, array_like}
The domain of the new series type instance. If the value is is
``None``, then the default domain of `kind` is used.
@@ -353,17 +353,17 @@ class $name(pu.PolyBase) :
should be converted. If kind is ``None``, then the class of the
current instance is used.
- Returns:
- --------
+ Returns
+ -------
new_series_instance : `kind`
The returned class can be of different type than the current
instance and/or have a different domain.
- Examples:
- ---------
+ Examples
+ --------
- Notes:
- ------
+ Notes
+ -----
Conversion between domains and class types can result in
numerically ill defined series.
@@ -385,8 +385,8 @@ class $name(pu.PolyBase) :
separately, then the linear function must be substituted for the
``x`` in the standard representation of the base polynomials.
- Returns:
- --------
+ Returns
+ -------
off, scl : floats or complex
The mapping function is defined by ``off + scl*x``.
@@ -411,12 +411,12 @@ class $name(pu.PolyBase) :
``[0]``. A new $name instance is returned with the new coefficients.
The current instance remains unchanged.
- Parameters:
- -----------
+ Parameters
+ ----------
tol : non-negative number.
All trailing coefficients less than `tol` will be removed.
- Returns:
+ Returns
-------
new_instance : $name
Contains the new set of coefficients.
@@ -432,13 +432,13 @@ class $name(pu.PolyBase) :
can be useful in least squares where the coefficients of the
high degree terms may be very small.
- Parameters:
- -----------
+ Parameters
+ ----------
size : positive int
The series is reduced to length `size` by discarding the high
degree terms. The value of `size` must be a positive integer.
- Returns:
+ Returns
-------
new_instance : $name
New instance of $name with truncated coefficients.
@@ -458,8 +458,8 @@ class $name(pu.PolyBase) :
A new instance of $name is returned that has the same
coefficients and domain as the current instance.
- Returns:
- --------
+ Returns
+ -------
new_instance : $name
New instance of $name with the same coefficients and domain.
@@ -472,8 +472,8 @@ class $name(pu.PolyBase) :
Return an instance of $name that is the definite integral of the
current series. Refer to `${nick}int` for full documentation.
- Parameters:
- -----------
+ Parameters
+ ----------
m : non-negative int
The number of integrations to perform.
k : array_like
@@ -484,8 +484,8 @@ class $name(pu.PolyBase) :
lbnd : Scalar
The lower bound of the definite integral.
- Returns:
- --------
+ Returns
+ -------
integral : $name
The integral of the series using the same domain.
@@ -509,13 +509,13 @@ class $name(pu.PolyBase) :
Return an instance of $name that is the derivative of the current
series. Refer to `${nick}der` for full documentation.
- Parameters:
- -----------
+ Parameters
+ ----------
m : non-negative int
The number of integrations to perform.
- Returns:
- --------
+ Returns
+ -------
derivative : $name
The derivative of the series using the same domain.
@@ -545,8 +545,35 @@ class $name(pu.PolyBase) :
roots = ${nick}roots(self.coef)
return pu.mapdomain(roots, $domain, self.domain)
+ def linspace(self, n):
+ """Return x,y values at equally spaced points in domain.
+
+ Returns x, y values at `n` equally spaced points across domain.
+ Here y is the value of the polynomial at the points x. This is
+ intended as a plotting aid.
+
+ Paramters
+ ---------
+ n : int
+ Number of point pairs to return.
+
+ Returns
+ -------
+ x, y : ndarrays
+ ``x`` is equal to linspace(self.domain[0], self.domain[1], n)
+ ``y`` is the polynomial evaluated at ``x``.
+
+ .. versionadded:: 1.5.0
+
+ """
+ x = np.linspace(self.domain[0], self.domain[1], n)
+ y = self(x)
+ return x, y
+
+
+
@staticmethod
- def fit(x, y, deg, domain=None, rcond=None, full=False) :
+ def fit(x, y, deg, domain=None, rcond=None, full=False, w=None) :
"""Least squares fit to data.
Return a `$name` instance that is the least squares fit to the data
@@ -565,12 +592,12 @@ class $name(pu.PolyBase) :
passing in a 2D-array that contains one dataset per column.
deg : int
Degree of the fitting polynomial
- domain : {None, [], [beg, end]}, optional
+ domain : {None, [beg, end], []}, optional
Domain to use for the returned $name instance. If ``None``,
- then a minimal domain that covers the points `x` is chosen.
- If ``[]`` the default domain ``$domain`` is used. The
- default value is $domain in numpy 1.4.x and ``None`` in
- numpy 2.0.0. The keyword value ``[]`` was added in numpy 2.0.0.
+ then a minimal domain that covers the points `x` is chosen. If
+ ``[]`` the default domain ``$domain`` is used. The default
+ value is $domain in numpy 1.4.x and ``None`` in later versions.
+ The ``'[]`` value was added in numpy 1.5.0.
rcond : float, optional
Relative condition number of the fit. Singular values smaller
than this relative to the largest singular value will be
@@ -582,6 +609,13 @@ class $name(pu.PolyBase) :
(the default) just the coefficients are returned, when True
diagnostic information from the singular value decomposition is
also returned.
+ w : array_like, shape (M,), optional
+ Weights. If not None the contribution of each point
+ ``(x[i],y[i])`` to the fit is weighted by `w[i]`. Ideally the
+ weights are chosen so that the errors of the products
+ ``w[i]*y[i]`` all have the same variance. The default value is
+ None.
+ .. versionadded:: 1.5.0
Returns
-------
@@ -605,7 +639,7 @@ class $name(pu.PolyBase) :
elif domain == [] :
domain = $domain
xnew = pu.mapdomain(x, domain, $domain)
- res = ${nick}fit(xnew, y, deg, rcond=None, full=full)
+ res = ${nick}fit(xnew, y, deg, w=w, rcond=rcond, full=full)
if full :
[coef, status] = res
return $name(coef, domain=domain), status
diff --git a/numpy/polynomial/tests/test_chebyshev.py b/numpy/polynomial/tests/test_chebyshev.py
index a893921ce..981481ff1 100644
--- a/numpy/polynomial/tests/test_chebyshev.py
+++ b/numpy/polynomial/tests/test_chebyshev.py
@@ -283,18 +283,33 @@ class TestMisc(TestCase) :
assert_raises(TypeError, ch.chebfit, [1], [[[1]]], 0)
assert_raises(TypeError, ch.chebfit, [1, 2], [1], 0)
assert_raises(TypeError, ch.chebfit, [1], [1, 2], 0)
+ assert_raises(TypeError, ch.chebfit, [1], [1], 0, w=[[1]])
+ assert_raises(TypeError, ch.chebfit, [1], [1], 0, w=[1,1])
# Test fit
x = np.linspace(0,2)
y = f(x)
- coef = ch.chebfit(x, y, 3)
- assert_equal(len(coef), 4)
- assert_almost_equal(ch.chebval(x, coef), y)
- coef = ch.chebfit(x, y, 4)
- assert_equal(len(coef), 5)
- assert_almost_equal(ch.chebval(x, coef), y)
- coef2d = ch.chebfit(x, np.array([y,y]).T, 4)
- assert_almost_equal(coef2d, np.array([coef,coef]).T)
+ #
+ coef3 = ch.chebfit(x, y, 3)
+ assert_equal(len(coef3), 4)
+ assert_almost_equal(ch.chebval(x, coef3), y)
+ #
+ coef4 = ch.chebfit(x, y, 4)
+ assert_equal(len(coef4), 5)
+ assert_almost_equal(ch.chebval(x, coef4), y)
+ #
+ coef2d = ch.chebfit(x, np.array([y,y]).T, 3)
+ assert_almost_equal(coef2d, np.array([coef3,coef3]).T)
+ # test weighting
+ w = np.zeros_like(x)
+ yw = y.copy()
+ w[1::2] = 1
+ y[0::2] = 0
+ wcoef3 = ch.chebfit(x, yw, 3, w=w)
+ assert_almost_equal(wcoef3, coef3)
+ #
+ wcoef2d = ch.chebfit(x, np.array([yw,yw]).T, 3, w=w)
+ assert_almost_equal(wcoef2d, np.array([coef3,coef3]).T)
def test_chebtrim(self) :
coef = [2, -1, 1, 0]
@@ -402,7 +417,7 @@ class TestChebyshevClass(TestCase) :
def test_degree(self) :
assert_equal(self.p1.degree(), 2)
- def test_cutdeg(self) :
+ def test_trimdeg(self) :
assert_raises(ValueError, self.p1.cutdeg, .5)
assert_raises(ValueError, self.p1.cutdeg, -1)
assert_equal(len(self.p1.cutdeg(3)), 3)
@@ -459,6 +474,13 @@ class TestChebyshevClass(TestCase) :
tgt = [0, .5, 1]
assert_almost_equal(res, tgt)
+ def test_linspace(self):
+ xdes = np.linspace(0, 1, 20)
+ ydes = self.p2(xdes)
+ xres, yres = self.p2.linspace(20)
+ assert_almost_equal(xres, xdes)
+ assert_almost_equal(yres, ydes)
+
def test_fromroots(self) :
roots = [0, .5, 1]
p = ch.Chebyshev.fromroots(roots, domain=[0, 1])
@@ -483,6 +505,13 @@ class TestChebyshevClass(TestCase) :
p = ch.Chebyshev.fit(x, y, 3, [])
assert_almost_equal(p(x), y)
assert_almost_equal(p.domain, [-1, 1])
+ # test that fit accepts weights.
+ w = np.zeros_like(x)
+ yw = y.copy()
+ w[1::2] = 1
+ yw[0::2] = 0
+ p = ch.Chebyshev.fit(x, yw, 3, w=w)
+ assert_almost_equal(p(x), y)
def test_identity(self) :
x = np.linspace(0,3)
diff --git a/numpy/polynomial/tests/test_polynomial.py b/numpy/polynomial/tests/test_polynomial.py
index 1b8c0f8a5..4bfbc46d9 100644
--- a/numpy/polynomial/tests/test_polynomial.py
+++ b/numpy/polynomial/tests/test_polynomial.py
@@ -263,18 +263,33 @@ class TestMisc(TestCase) :
assert_raises(TypeError, poly.polyfit, [1], [[[1]]], 0)
assert_raises(TypeError, poly.polyfit, [1, 2], [1], 0)
assert_raises(TypeError, poly.polyfit, [1], [1, 2], 0)
+ assert_raises(TypeError, poly.polyfit, [1], [1], 0, w=[[1]])
+ assert_raises(TypeError, poly.polyfit, [1], [1], 0, w=[1,1])
# Test fit
x = np.linspace(0,2)
y = f(x)
- coef = poly.polyfit(x, y, 3)
- assert_equal(len(coef), 4)
- assert_almost_equal(poly.polyval(x, coef), y)
- coef = poly.polyfit(x, y, 4)
- assert_equal(len(coef), 5)
- assert_almost_equal(poly.polyval(x, coef), y)
- coef2d = poly.polyfit(x, np.array([y,y]).T, 4)
- assert_almost_equal(coef2d, np.array([coef,coef]).T)
+ #
+ coef3 = poly.polyfit(x, y, 3)
+ assert_equal(len(coef3), 4)
+ assert_almost_equal(poly.polyval(x, coef3), y)
+ #
+ coef4 = poly.polyfit(x, y, 4)
+ assert_equal(len(coef4), 5)
+ assert_almost_equal(poly.polyval(x, coef4), y)
+ #
+ coef2d = poly.polyfit(x, np.array([y,y]).T, 3)
+ assert_almost_equal(coef2d, np.array([coef3,coef3]).T)
+ # test weighting
+ w = np.zeros_like(x)
+ yw = y.copy()
+ w[1::2] = 1
+ yw[0::2] = 0
+ wcoef3 = poly.polyfit(x, yw, 3, w=w)
+ assert_almost_equal(wcoef3, coef3)
+ #
+ wcoef2d = poly.polyfit(x, np.array([yw,yw]).T, 3, w=w)
+ assert_almost_equal(wcoef2d, np.array([coef3,coef3]).T)
def test_polytrim(self) :
coef = [2, -1, 1, 0]
@@ -373,7 +388,7 @@ class TestPolynomialClass(TestCase) :
def test_degree(self) :
assert_equal(self.p1.degree(), 2)
- def test_cutdeg(self) :
+ def test_trimdeg(self) :
assert_raises(ValueError, self.p1.cutdeg, .5)
assert_raises(ValueError, self.p1.cutdeg, -1)
assert_equal(len(self.p1.cutdeg(3)), 3)
@@ -430,6 +445,13 @@ class TestPolynomialClass(TestCase) :
tgt = [0, .5, 1]
assert_almost_equal(res, tgt)
+ def test_linspace(self):
+ xdes = np.linspace(0, 1, 20)
+ ydes = self.p2(xdes)
+ xres, yres = self.p2.linspace(20)
+ assert_almost_equal(xres, xdes)
+ assert_almost_equal(yres, ydes)
+
def test_fromroots(self) :
roots = [0, .5, 1]
p = poly.Polynomial.fromroots(roots, domain=[0, 1])
@@ -454,6 +476,13 @@ class TestPolynomialClass(TestCase) :
p = poly.Polynomial.fit(x, y, 3, [])
assert_almost_equal(p(x), y)
assert_almost_equal(p.domain, [-1, 1])
+ # test that fit accepts weights.
+ w = np.zeros_like(x)
+ yw = y.copy()
+ w[1::2] = 1
+ yw[0::2] = 0
+ p = poly.Polynomial.fit(x, yw, 3, w=w)
+ assert_almost_equal(p(x), y)
def test_identity(self) :
x = np.linspace(0,3)
View Lorry Controller Status