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MAINT: fix more Sphinx warnings.

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commit 8be148e86f2c65b2bf4c897dac6f2ed89c404d55 1 parent e98c18e
@rgommers rgommers authored
View
8 scipy/cluster/hierarchy.py
@@ -129,13 +129,9 @@
* Mathematica is a registered trademark of The Wolfram Research, Inc.
-Copyright Notice
-----------------
-
-Copyright (C) Damian Eads, 2007-2008. New BSD License.
-
"""
+# Copyright (C) Damian Eads, 2007-2008. New BSD License.
# hierarchy.py (derived from cluster.py, http://scipy-cluster.googlecode.com)
#
@@ -171,6 +167,7 @@
# THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
# (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
import types
import warnings
@@ -178,6 +175,7 @@
import _hierarchy_wrap
import scipy.spatial.distance as distance
+
_cpy_non_euclid_methods = {'single': 0, 'complete': 1, 'average': 2,
'weighted': 6}
_cpy_euclid_methods = {'centroid': 3, 'median': 4, 'ward': 5}
View
15 scipy/interpolate/interpnd.pyx.in
@@ -178,12 +178,12 @@ class LinearNDInterpolator(NDInterpolatorBase):
Notes
-----
The interpolant is constructed by triangulating the input data
- with Qhull [Qhull]_, and on each triangle performing linear
+ with Qhull [1]_, and on each triangle performing linear
barycentric interpolation.
References
----------
- .. [Qhull] http://www.qhull.org/
+ .. [1] http://www.qhull.org/
"""
@@ -509,9 +509,9 @@ cdef ${CDTYPE} _clough_tocher_2d_single_${DTYPE}(qhull.DelaunayInfo_t *d,
Parameters
----------
- d
+ d :
Delaunay info
- isimplex
+ isimplex : int
Triangle to evaluate on
b : shape (3,)
Barycentric coordinates of the point on the triangle
@@ -522,7 +522,7 @@ cdef ${CDTYPE} _clough_tocher_2d_single_${DTYPE}(qhull.DelaunayInfo_t *d,
Returns
-------
- w
+ w :
Value of the interpolant at the given point
References
@@ -758,7 +758,7 @@ class CloughTocher2DInterpolator(NDInterpolatorBase):
Notes
-----
The interpolant is constructed by triangulating the input data
- with Qhull [Qhull]_, and constructing a piecewise cubic
+ with Qhull [1]_, and constructing a piecewise cubic
interpolating Bezier polynomial on each triangle, using a
Clough-Tocher scheme [CT]_. The interpolant is guaranteed to be
continuously differentiable.
@@ -770,8 +770,7 @@ class CloughTocher2DInterpolator(NDInterpolatorBase):
References
----------
-
- .. [Qhull] http://www.qhull.org/
+ .. [1] http://www.qhull.org/
.. [CT] See, for example,
P. Alfeld,
View
17 scipy/sparse/linalg/dsolve/linsolve.py
@@ -22,7 +22,8 @@
def use_solver( **kwargs ):
"""
- Valid keyword arguments with defaults (other ignored):
+ Valid keyword arguments with defaults (other ignored)::
+
useUmfpack = True
assumeSortedIndices = False
@@ -31,8 +32,9 @@ def use_solver( **kwargs ):
based solver to be used.
Umfpack requires a CSR/CSC matrix to have sorted column/row indices. If
- sure that the matrix fulfills this, pass assumeSortedIndices=True
+ sure that the matrix fulfills this, pass ``assumeSortedIndices=True``
to gain some speed.
+
"""
if 'useUmfpack' in kwargs:
globals()['useUmfpack'] = kwargs['useUmfpack']
@@ -42,8 +44,7 @@ def use_solver( **kwargs ):
def spsolve(A, b, permc_spec=None, use_umfpack=True):
- """Solve the sparse linear system Ax=b
- """
+ """Solve the sparse linear system Ax=b """
if isspmatrix( b ):
b = b.toarray()
@@ -105,9 +106,8 @@ def splu(A, permc_spec=None, diag_pivot_thresh=None,
Parameters
----------
- A
+ A : sparse matrix
Sparse matrix to factorize. Should be in CSR or CSC format.
-
permc_spec : str, optional
How to permute the columns of the matrix for sparsity preservation.
(default: 'COLAMD')
@@ -218,12 +218,7 @@ def spilu(A, drop_tol=None, fill_factor=None, drop_rule=None, permc_spec=None,
This function uses the SuperLU library.
- References
- ----------
- .. [SLU] SuperLU http://crd.lbl.gov/~xiaoye/SuperLU/
-
"""
-
if not isspmatrix_csc(A):
A = csc_matrix(A)
warn('splu requires CSC matrix format', SparseEfficiencyWarning)
View
85 scipy/sparse/linalg/eigen/arpack/arpack.py
@@ -1072,47 +1072,40 @@ def eigs(A, k=6, M=None, sigma=None, which='LM', v0=None,
Parameters
----------
- A : An N x N matrix, array, sparse matrix, or LinearOperator representing
- the operation A * x, where A is a real or complex square matrix.
- k : integer
+ A : ndarray, sparse matrix or LinearOperator
+ An array, sparse matrix, or LinearOperator representing
+ the operation ``A * x``, where A is a real or complex square matrix.
+ k : int, optional
The number of eigenvalues and eigenvectors desired.
`k` must be smaller than N. It is not possible to compute all
eigenvectors of a matrix.
-
- Returns
- -------
- w : array
- Array of k eigenvalues.
- v : array
- An array of `k` eigenvectors.
- ``v[:, i]`` is the eigenvector corresponding to the eigenvalue w[i].
-
- Other Parameters
- ----------------
- M : An N x N matrix, array, sparse matrix, or LinearOperator representing
+ M : ndarray, sparse matrix or LinearOperator, optional
+ An array, sparse matrix, or LinearOperator representing
the operation M*x for the generalized eigenvalue problem
- ``A * x = w * M * x``
+ ``A * x = w * M * x``.
M must represent a real, symmetric matrix if A is real, and must
represent a complex, hermitian matrix if A is complex. For best
results, the data type of M should be the same as that of A.
Additionally:
- * If sigma==None, M is positive definite
- * If sigma is specified, M is positive semi-definite
- If sigma==None, eigs requires an operator to compute the solution
- of the linear equation `M * x = b`. This is done internally via a
+
+ - If `sigma` is None, M is positive definite
+ - If sigma is specified, M is positive semi-definite
+
+ If sigma is None, eigs requires an operator to compute the solution
+ of the linear equation ``M * x = b``. This is done internally via a
(sparse) LU decomposition for an explicit matrix M, or via an
iterative solver for a general linear operator. Alternatively,
the user can supply the matrix or operator Minv, which gives
- x = Minv * b = M^-1 * b
- sigma : real or complex
+ ``x = Minv * b = M^-1 * b``.
+ sigma : real or complex, optional
Find eigenvalues near sigma using shift-invert mode. This requires
an operator to compute the solution of the linear system
- `[A - sigma * M] * x = b`, where M is the identity matrix if
+ ``[A - sigma * M] * x = b``, where M is the identity matrix if
unspecified. This is computed internally via a (sparse) LU
decomposition for explicit matrices A & M, or via an iterative
solver if either A or M is a general linear operator.
Alternatively, the user can supply the matrix or operator OPinv,
- which gives x = OPinv * b = [A - sigma * M]^-1 * b.
+ which gives ``x = OPinv * b = [A - sigma * M]^-1 * b``.
For a real matrix A, shift-invert can either be done in imaginary
mode or real mode, specified by the parameter OPpart ('r' or 'i').
Note that when sigma is specified, the keyword 'which' (below)
@@ -1124,12 +1117,12 @@ def eigs(A, k=6, M=None, sigma=None, which='LM', v0=None,
``w'[i] = 1/2i * [1/(w[i]-sigma) - 1/(w[i]-conj(sigma))]``.
- If A is complex, ``w'[i] = 1/(w[i]-sigma)``.
- v0 : ndarray
+ v0 : ndarray, optional
Starting vector for iteration.
- ncv : int
+ ncv : int, optional
The number of Lanczos vectors generated
`ncv` must be greater than `k`; it is recommended that ``ncv > 2*k``.
- which : str, ['LM' | 'SM' | 'LR' | 'SR' | 'LI' | 'SI']
+ which : str, ['LM' | 'SM' | 'LR' | 'SR' | 'LI' | 'SI'], optional
Which `k` eigenvectors and eigenvalues to find:
- 'LM' : largest magnitude
@@ -1143,20 +1136,28 @@ def eigs(A, k=6, M=None, sigma=None, which='LM', v0=None,
(see discussion in 'sigma', above). ARPACK is generally better
at finding large values than small values. If small eigenvalues are
desired, consider using shift-invert mode for better performance.
- maxiter : int
+ maxiter : int, optional
Maximum number of Arnoldi update iterations allowed
- tol : float
+ tol : float, optional
Relative accuracy for eigenvalues (stopping criterion)
The default value of 0 implies machine precision.
- return_eigenvectors : bool
+ return_eigenvectors : bool, optional
Return eigenvectors (True) in addition to eigenvalues
- Minv : N x N matrix, array, sparse matrix, or linear operator
+ Minv : ndarray, sparse matrix or LinearOperator, optional
See notes in M, above.
- OPinv : N x N matrix, array, sparse matrix, or linear operator
+ OPinv : ndarray, sparse matrix or LinearOperator, optional
See notes in sigma, above.
- OPpart : 'r' or 'i'.
+ OPpart : {'r' or 'i'}, optional
See notes in sigma, above
+ Returns
+ -------
+ w : ndarray
+ Array of k eigenvalues.
+ v : ndarray
+ An array of `k` eigenvectors.
+ ``v[:, i]`` is the eigenvector corresponding to the eigenvalue w[i].
+
Raises
------
ArpackNoConvergence
@@ -1319,15 +1320,17 @@ def eigsh(A, k=6, M=None, sigma=None, which='LM', v0=None,
represent a complex, hermitian matrix if A is complex. For best
results, the data type of M should be the same as that of A.
Additionally:
- * If sigma == None, M is symmetric positive definite
- * If sigma is specified, M is symmetric positive semi-definite
- * In buckling mode, M is symmetric indefinite.
- If sigma == None, eigsh requires an operator to compute the solution
- of the linear equation `M * x = b`. This is done internally via a
+
+ - If sigma is None, M is symmetric positive definite
+ - If sigma is specified, M is symmetric positive semi-definite
+ - In buckling mode, M is symmetric indefinite.
+
+ If sigma is None, eigsh requires an operator to compute the solution
+ of the linear equation ``M * x = b``. This is done internally via a
(sparse) LU decomposition for an explicit matrix M, or via an
iterative solver for a general linear operator. Alternatively,
the user can supply the matrix or operator Minv, which gives
- x = Minv * b = M^-1 * b
+ ``x = Minv * b = M^-1 * b``.
sigma : real
Find eigenvalues near sigma using shift-invert mode. This requires
an operator to compute the solution of the linear system
@@ -1336,9 +1339,9 @@ def eigsh(A, k=6, M=None, sigma=None, which='LM', v0=None,
decomposition for explicit matrices A & M, or via an iterative
solver if either A or M is a general linear operator.
Alternatively, the user can supply the matrix or operator OPinv,
- which gives x = OPinv * b = [A - sigma * M]^-1 * b.
+ which gives ``x = OPinv * b = [A - sigma * M]^-1 * b``.
Note that when sigma is specified, the keyword 'which' refers to
- the shifted eigenvalues w'[i] where:
+ the shifted eigenvalues ``w'[i]`` where:
- if mode == 'normal', ``w'[i] = 1 / (w[i] - sigma)``.
- if mode == 'cayley', ``w'[i] = (w[i] + sigma) / (w[i] - sigma)``.
View
50 scipy/spatial/distance.py
@@ -59,56 +59,10 @@
sqeuclidean -- the squared Euclidean distance.
yule -- the Yule dissimilarity (boolean).
+"""
-References
-----------
-
-.. [Sta07] "Statistics toolbox." API Reference Documentation. The MathWorks.
- http://www.mathworks.com/access/helpdesk/help/toolbox/stats/.
- Accessed October 1, 2007.
-
-.. [Mti07] "Hierarchical clustering." API Reference Documentation.
- The Wolfram Research, Inc.
- http://reference.wolfram.com/mathematica/HierarchicalClustering/tutorial/HierarchicalClustering.html.
- Accessed October 1, 2007.
-
-.. [Gow69] Gower, JC and Ross, GJS. "Minimum Spanning Trees and Single Linkage
- Cluster Analysis." Applied Statistics. 18(1): pp. 54--64. 1969.
-
-.. [War63] Ward Jr, JH. "Hierarchical grouping to optimize an objective
- function." Journal of the American Statistical Association. 58(301):
- pp. 236--44. 1963.
-
-.. [Joh66] Johnson, SC. "Hierarchical clustering schemes." Psychometrika.
- 32(2): pp. 241--54. 1966.
-
-.. [Sne62] Sneath, PH and Sokal, RR. "Numerical taxonomy." Nature. 193: pp.
- 855--60. 1962.
-
-.. [Bat95] Batagelj, V. "Comparing resemblance measures." Journal of
- Classification. 12: pp. 73--90. 1995.
-
-.. [Sok58] Sokal, RR and Michener, CD. "A statistical method for evaluating
- systematic relationships." Scientific Bulletins. 38(22):
- pp. 1409--38. 1958.
-
-.. [Ede79] Edelbrock, C. "Mixture model tests of hierarchical clustering
- algorithms: the problem of classifying everybody." Multivariate
- Behavioral Research. 14: pp. 367--84. 1979.
-
-.. [Jai88] Jain, A., and Dubes, R., "Algorithms for Clustering Data."
- Prentice-Hall. Englewood Cliffs, NJ. 1988.
-
-.. [Fis36] Fisher, RA "The use of multiple measurements in taxonomic
- problems." Annals of Eugenics, 7(2): 179-188. 1936
-
-
-Copyright Notice
-----------------
-
-Copyright (C) Damian Eads, 2007-2008. New BSD License.
+# Copyright (C) Damian Eads, 2007-2008. New BSD License.
-"""
import warnings
import numpy as np
View
8 scipy/spatial/kdtree.py
@@ -616,14 +616,14 @@ def query_pairs(self, r, p=2., eps=0):
``1 <= p <= infinity``.
eps : float, optional
Approximate search. Branches of the tree are not explored
- if their nearest points are further than r/(1+eps), and branches
- are added in bulk if their furthest points are nearer than
- ``r * (1+eps)``. `eps` has to be non-negative.
+ if their nearest points are further than ``r/(1+eps)``, and
+ branches are added in bulk if their furthest points are nearer
+ than ``r * (1+eps)``. `eps` has to be non-negative.
Returns
-------
results : set
- Set of pairs ``(i,j)``, with ``i<j`, for which the corresponding
+ Set of pairs ``(i,j)``, with ``i < j`, for which the corresponding
positions are close.
"""
View
690 scipy/spatial/qhull.c
345 additions, 345 deletions not shown
View
22 scipy/spatial/qhull.pyx
@@ -887,9 +887,7 @@ class Delaunay(object):
"""
Delaunay(points)
- Delaunay tesselation in N dimensions
-
- .. versionadded:: 0.9
+ Delaunay tesselation in N dimensions.
Parameters
----------
@@ -899,19 +897,19 @@ class Delaunay(object):
Attributes
----------
points : ndarray of double, shape (npoints, ndim)
- Points in the triangulation
+ Points in the triangulation.
vertices : ndarray of ints, shape (nsimplex, ndim+1)
- Indices of vertices forming simplices in the triangulation
+ Indices of vertices forming simplices in the triangulation.
neighbors : ndarray of ints, shape (nsimplex, ndim+1)
Indices of neighbor simplices for each simplex.
The kth neighbor is opposite to the kth vertex.
For simplices at the boundary, -1 denotes no neighbor.
equations : ndarray of double, shape (nsimplex, ndim+2)
[normal, offset] forming the hyperplane equation of the facet
- on the paraboloid. (See [Qhull]_ documentation for more.)
+ on the paraboloid (see [Qhull]_ documentation for more).
paraboloid_scale, paraboloid_shift : float
- Scale and shift for the extra paraboloid dimension.
- (See [Qhull]_ documentation for more.)
+ Scale and shift for the extra paraboloid dimension
+ (see [Qhull]_ documentation for more).
transform : ndarray of double, shape (nsimplex, ndim+1, ndim)
Affine transform from ``x`` to the barycentric coordinates ``c``.
This is defined by::
@@ -935,13 +933,13 @@ class Delaunay(object):
-----
The tesselation is computed using the Qhull libary [Qhull]_.
+ .. versionadded:: 0.9
+
References
----------
-
.. [Qhull] http://www.qhull.org/
"""
-
def __init__(self, points):
points = np.ascontiguousarray(points).astype(np.double)
vertices, neighbors, equations, paraboloid_scale, paraboloid_shift = \
@@ -1087,7 +1085,7 @@ class Delaunay(object):
Notes
-----
- This uses an algorithm adapted from Qhull's qh_findbestfacet,
+ This uses an algorithm adapted from Qhull's ``qh_findbestfacet``,
which makes use of the connection between a convex hull and a
Delaunay triangulation. After finding the simplex closest to
the point in N+1 dimensions, the algorithm falls back to
@@ -1192,7 +1190,7 @@ def tsearch(tri, xi):
tsearch(tri, xi)
Find simplices containing the given points. This function does the
- same thing as Delaunay.find_simplex.
+ same thing as `Delaunay.find_simplex`.
.. versionadded:: 0.9
View
22 scipy/special/basic.py
@@ -520,24 +520,23 @@ def mathieu_odd_coef(m,q):
fc = specfun.fcoef(kd,m,q,b)
return fc[:km]
+
def lpmn(m,n,z):
"""Associated Legendre functions of the first kind, Pmn(z) and its
- derivative, Pmn'(z) of order m and degree n. Returns two
- arrays of size (m+1,n+1) containing Pmn(z) and Pmn'(z) for
- all orders from 0..m and degrees from 0..n.
-
- z can be complex.
+ derivative, ``Pmn'(z)`` of order m and degree n. Returns two
+ arrays of size ``(m+1, n+1)`` containing ``Pmn(z)`` and ``Pmn'(z)`` for
+ all orders from ``0..m`` and degrees from ``0..n``.
Parameters
----------
m : int
- |m| <= n; the order of the Legendre function
+ ``|m| <= n``; the order of the Legendre function.
n : int
- where `n` >= 0; the degree of the Legendre function. Often
+ where ``n >= 0``; the degree of the Legendre function. Often
called ``l`` (lower case L) in descriptions of the associated
Legendre function
z : float or complex
- input value
+ Input value.
Returns
-------
@@ -570,12 +569,11 @@ def lpmn(m,n,z):
return p,pd
-
def lqmn(m,n,z):
"""Associated Legendre functions of the second kind, Qmn(z) and its
- derivative, Qmn'(z) of order m and degree n. Returns two
- arrays of size (m+1,n+1) containing Qmn(z) and Qmn'(z) for
- all orders from 0..m and degrees from 0..n.
+ derivative, ``Qmn'(z)`` of order m and degree n. Returns two
+ arrays of size ``(m+1, n+1)`` containing ``Qmn(z)`` and ``Qmn'(z)`` for
+ all orders from ``0..m`` and degrees from ``0..n``.
z can be complex.
"""
View
36 scipy/special/cephes_doc.h
@@ -22,7 +22,7 @@
"incomplete beta. Under this definition, you can get the incomplete beta by\n" \
"multiplying the result of the scipy function by beta(a, b)."
#define betaincinv_doc "x=betaincinv(a,b,y) returns x such that betainc(a,b,x) = y."
-#define betaln_doc "y=betaln(a,b) returns the natural logarithm of the absolute value of\nbeta: ln(|beta(x)|)."
+#define betaln_doc "y=betaln(a,b) returns the natural logarithm of the absolute value of\nbeta: ln(abs(beta(x)))."
#define btdtr_doc "y=btdtr(a,b,x) returns the area from zero to x under the beta\ndensity function: gamma(a+b)/(gamma(a)*gamma(b)))*integral(t**(a-1)\n(1-t)**(b-1), t=0..x). SEE ALSO betainc"
#define btdtri_doc "x=btdtri(a,b,p) returns the pth quantile of the beta distribution. It is\neffectively the inverse of btdtr returning the value of x for which \nbtdtr(a,b,x) = p. SEE ALSO betaincinv"
#define cbrt_doc "y=cbrt(x) returns the real cube root of x."
@@ -56,7 +56,7 @@
#define gammainc_doc "y=gammainc(a,x) returns the incomplete gamma integral defined as\n1 / gamma(a) * integral(exp(-t) * t**(a-1), t=0..x). a must be\npositive and x must be >= 0."
#define gammaincc_doc "y=gammaincc(a,x) returns the complemented incomplete gamma integral\ndefined as 1 / gamma(a) * integral(exp(-t) * t**(a-1), t=x..inf) = 1 -\ngammainc(a,x). a must be positive and x must be >= 0."
#define gammainccinv_doc "x=gammainccinv(a,y) returns x such that gammaincc(a,x) = y."
-#define gammaln_doc "y=gammaln(z) returns the base e logarithm of the absolute value of the\ngamma function of z: ln(|gamma(z)|)"
+#define gammaln_doc "y=gammaln(z) returns the base e logarithm of the absolute value of the\ngamma function of z: ln(abs(gamma(z)))"
#define gdtr_doc "y=gdtr(a,b,x) returns the integral from zero to x of the gamma\nprobability density function: a**b / gamma(b) * integral(t**(b-1) exp(-at),t=0..x).\nThe arguments a and b are used differently here than in other definitions."
#define gdtrc_doc "y=gdtrc(a,b,x) returns the integral from x to infinity of the gamma\nprobability density function. SEE gdtr, gdtri"
#define gdtri_doc "x=gdtri(a,b,p) returns pth quantile of the gamma distribution. It is \nthe inverse of the gamma cdf returning the value of x for which \ngdtr(b,a,x) = p."
@@ -71,9 +71,9 @@
#define hyp3f0_doc "(y,err)=hyp3f0(a,b,c,x) returns (y,err) with the hypergeometric function 3F0 in y and an error estimate in err."
#define hyperu_doc "y=hyperu(a,b,x) returns the confluent hypergeometric function of the\nsecond kind U(a,b,x)."
#define i0_doc "y=i0(x) returns the modified Bessel function of order 0 at x."
-#define i0e_doc "y=i0e(x) returns the exponentially scaled modified Bessel function\nof order 0 at x. i0e(x) = exp(-|x|) * i0(x)."
+#define i0e_doc "y=i0e(x) returns the exponentially scaled modified Bessel function\nof order 0 at x. i0e(x) = exp(-abs(x)) * i0(x)."
#define i1_doc "y=i1(x) returns the modified Bessel function of order 1 at x."
-#define i1e_doc "y=i1e(x) returns the exponentially scaled modified Bessel function\nof order 0 at x. i1e(x) = exp(-|x|) * i1(x)."
+#define i1e_doc "y=i1e(x) returns the exponentially scaled modified Bessel function\nof order 0 at x. i1e(x) = exp(-abs(x)) * i1(x)."
#define it2i0k0_doc "(ii0,ik0)=it2i0k0(x) returns the integrals int((i0(t)-1)/t,t=0..x) and \nint(k0(t)/t,t=x..infinitity)."
#define it2j0y0_doc "(ij0,iy0)=it2j0y0(x) returns the integrals int((1-j0(t))/t,t=0..x) and \nint(y0(t)/t,t=x..infinitity)."
#define it2struve0_doc "y=it2struve0(x) returns the integral of the Struve function of order 0 \ndivided by t from x to infinity: integral(H0(t)/t, t=x..inf)."
@@ -104,7 +104,7 @@
#define kv_doc "y=kv(v,z) returns the modified Bessel function of the second kind (sometimes called the third kind) for\nreal order v at complex z."
#define kve_doc "y=kve(v,z) returns the exponentially scaled, modified Bessel function\nof the second kind (sometimes called the third kind) for real order v at complex z: kve(v,z) = kv(v,z) * exp(z)"
#define log1p_doc "y=log1p(x) calculates log(1+x) for use when x is near zero."
-#define lpmv_doc "y=lpmv(m,v,x) returns the associated legendre function of integer order\nm and real degree v (s.t. v>-m-1 or v<m): |x|<=1."
+#define lpmv_doc "y=lpmv(m,v,x) returns the associated legendre function of integer order\nm and real degree v (s.t. v>-m-1 or v<m): ``|x| <= 1``."
#define mathieu_a_doc "lmbda=mathieu_a(m,q) returns the characteristic value for the even solution, \nce_m(z,q), of Mathieu's equation"
#define mathieu_b_doc "lmbda=mathieu_b(m,q) returns the characteristic value for the odd solution, \nse_m(z,q), of Mathieu's equation"
#define mathieu_cem_doc "(y,yp)=mathieu_cem(m,q,x) returns the even Mathieu function, ce_m(x,q), \nof order m and parameter q evaluated at x (given in degrees).\nAlso returns the derivative with respect to x of ce_m(x,q)"
@@ -113,9 +113,9 @@
#define mathieu_modsem1_doc "(y,yp)=mathieu_modsem1(m,q,x) evaluates the odd modified Matheiu function \nof the first kind, Ms1m(x,q), and its derivative at x (given in degrees)\nfor order m and parameter q."
#define mathieu_modsem2_doc "(y,yp)=mathieu_modsem2(m,q,x) evaluates the odd modified Matheiu function\nof the second kind, Ms2m(x,q), and its derivative at x (given in degrees)\nfor order m and parameter q."
#define mathieu_sem_doc "(y,yp)=mathieu_sem(m,q,x) returns the odd Mathieu function, se_m(x,q), \nof order m and parameter q evaluated at x (given in degrees).\nAlso returns the derivative with respect to x of se_m(x,q)."
-#define modfresnelm_doc "(fm,km)=modfresnelp(x) returns the modified fresnel integrals F_-(x) amd K_-(x)\nas fp=integral(exp(-1j*t*t),t=x..inf) and kp=1/sqrt(pi)*exp(1j*(x*x+pi/4))*fp"
+#define modfresnelm_doc "(fm,km)=modfresnelp(x) returns the modified fresnel integrals ``F_-(x)`` and ``K_-(x)``\nas ``fp=integral(exp(-1j*t*t),t=x..inf)`` and ``kp=1/sqrt(pi)*exp(1j*(x*x+pi/4))*fp``"
#define modfresnelp_doc "(fp,kp)=modfresnelp(x) returns the modified fresnel integrals F_+(x) and K_+(x)\nas fp=integral(exp(1j*t*t),t=x..inf) and kp=1/sqrt(pi)*exp(-1j*(x*x+pi/4))*fp"
-#define modstruve_doc "y=modstruve(v,x) returns the modified Struve function Lv(x) of order\nv at x, x must be positive unless v is an integer and it is recommended\nthat |v|<=20."
+#define modstruve_doc "y=modstruve(v,x) returns the modified Struve function Lv(x) of order\nv at x, x must be positive unless v is an integer and it is recommended\nthat ``|v| <= 20``."
#define nbdtr_doc "y=nbdtr(k,n,p) returns the sum of the terms 0 through k of the\nnegative binomial distribution: sum((n+j-1)Cj p**n (1-p)**j,j=0..k).\nIn a sequence of Bernoulli trials this is the probability that k or\nfewer failures precede the nth success."
#define nbdtrc_doc "y=nbdtrc(k,n,p) returns the sum of the terms k+1 to infinity of the\nnegative binomial distribution."
#define nbdtri_doc "p=nbdtri(k,n,y) finds the argument p such that nbdtr(k,n,p)=y."
@@ -123,13 +123,13 @@
#define nbdtrin_doc "n=nbdtrin(k,y,p) finds the argument n such that nbdtr(k,n,p)=y."
#define ndtr_doc "y=ndtr(x) returns the area under the standard Gaussian probability \ndensity function, integrated from minus infinity to x:\n1/sqrt(2*pi) * integral(exp(-t**2 / 2),t=-inf..x)"
#define ndtri_doc "x=ndtri(y) returns the argument x for which the area udnder the\nGaussian probability density function (integrated from minus infinity\nto x) is equal to y."
-#define obl_ang1_doc "(s,sp)=obl_ang1(m,n,c,x) computes the oblate sheroidal angular function \nof the first kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and |x|<1.0."
-#define obl_ang1_cv_doc "(s,sp)=obl_ang1_cv(m,n,c,cv,x) computes the oblate sheroidal angular function \nof the first kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and |x|<1.0. Requires pre-computed\ncharacteristic value."
+#define obl_ang1_doc "(s,sp)=obl_ang1(m,n,c,x) computes the oblate sheroidal angular function \nof the first kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and ``|x| < 1.0``."
+#define obl_ang1_cv_doc "(s,sp)=obl_ang1_cv(m,n,c,cv,x) computes the oblate sheroidal angular function \nof the first kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and ``|x| < 1.0``. Requires pre-computed\ncharacteristic value."
#define obl_cv_doc "cv=obl_cv(m,n,c) computes the characteristic value of oblate spheroidal \nwave functions of order m,n (n>=m) and spheroidal parameter c."
-#define obl_rad1_doc "(s,sp)=obl_rad1(m,n,c,x) computes the oblate sheroidal radial function \nof the first kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and |x|<1.0."
-#define obl_rad1_cv_doc "(s,sp)=obl_rad1_cv(m,n,c,cv,x) computes the oblate sheroidal radial function \nof the first kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and |x|<1.0. Requires pre-computed\ncharacteristic value."
-#define obl_rad2_doc "(s,sp)=obl_rad2(m,n,c,x) computes the oblate sheroidal radial function \nof the second kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and |x|<1.0."
-#define obl_rad2_cv_doc "(s,sp)=obl_rad2_cv(m,n,c,cv,x) computes the oblate sheroidal radial function \nof the second kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and |x|<1.0. Requires pre-computed\ncharacteristic value."
+#define obl_rad1_doc "(s,sp)=obl_rad1(m,n,c,x) computes the oblate sheroidal radial function \nof the first kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and ``|x| < 1.0``."
+#define obl_rad1_cv_doc "(s,sp)=obl_rad1_cv(m,n,c,cv,x) computes the oblate sheroidal radial function \nof the first kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and ``|x| < 1.0``. Requires pre-computed\ncharacteristic value."
+#define obl_rad2_doc "(s,sp)=obl_rad2(m,n,c,x) computes the oblate sheroidal radial function \nof the second kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and ``|x| < 1.0``."
+#define obl_rad2_cv_doc "(s,sp)=obl_rad2_cv(m,n,c,cv,x) computes the oblate sheroidal radial function \nof the second kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and ``|x| < 1.0``. Requires pre-computed\ncharacteristic value."
#define pbdv_doc "(d,dp)=pbdv(v,x) returns (d,dp) with the parabolic cylinder function Dv(x) in \nd and the derivative, Dv'(x) in dp."
#define pbvv_doc "(v,vp)=pbvv(v,x) returns (v,vp) with the parabolic cylinder function Vv(x) in \nv and the derivative, Vv'(x) in vp."
#define pbwa_doc "(w,wp)=pbwa(a,x) returns (w,wp) with the parabolic cylinder function W(a,x) in \nw and the derivative, W'(a,x) in wp. May not be accurate for large (>5) \narguments in a and/or x."
@@ -137,13 +137,13 @@
#define pdtrc_doc "y=pdtrc(k,m) returns the sum of the terms from k+1 to infinity of the\nPoisson distribution: sum(exp(-m) * m**j / j!, j=k+1..inf) = gammainc( k+1, m).\nArguments must both be positive and k an integer."
#define pdtri_doc "m=pdtri(k,y) returns the Poisson variable m such that the sum\nfrom 0 to k of the Poisson density is equal to the given probability\ny: calculated by gammaincinv( k+1, y). k must be a nonnegative integer and\ny between 0 and 1."
#define pdtrik_doc "k=pdtrik(p,m) returns the quantile k such that pdtr(k,m)=p"
-#define pro_ang1_doc "(s,sp)=pro_ang1(m,n,c,x) computes the prolate sheroidal angular function \nof the first kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and |x|<1.0."
-#define pro_ang1_cv_doc "(s,sp)=pro_ang1_cv(m,n,c,cv,x) computes the prolate sheroidal angular function \nof the first kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and |x|<1.0. Requires pre-computed\ncharacteristic value."
+#define pro_ang1_doc "(s,sp)=pro_ang1(m,n,c,x) computes the prolate sheroidal angular function \nof the first kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and ``|x| < 1.0``."
+#define pro_ang1_cv_doc "(s,sp)=pro_ang1_cv(m,n,c,cv,x) computes the prolate sheroidal angular function \nof the first kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and ``|x| < 1.0``. Requires pre-computed\ncharacteristic value."
#define pro_cv_doc "cv=pro_cv(m,n,c) computes the characteristic value of prolate spheroidal \nwave functions of order m,n (n>=m) and spheroidal parameter c."
-#define pro_rad1_doc "(s,sp)=pro_rad1(m,n,c,x) computes the prolate sheroidal radial function \nof the first kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and |x|<1.0."
-#define pro_rad1_cv_doc "(s,sp)=pro_rad1_cv(m,n,c,cv,x) computes the prolate sheroidal radial function \nof the first kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and |x|<1.0. Requires pre-computed\ncharacteristic value."
+#define pro_rad1_doc "(s,sp)=pro_rad1(m,n,c,x) computes the prolate sheroidal radial function \nof the first kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and ``|x| < 1.0``."
+#define pro_rad1_cv_doc "(s,sp)=pro_rad1_cv(m,n,c,cv,x) computes the prolate sheroidal radial function \nof the first kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and ``|x| < 1.0``. Requires pre-computed\ncharacteristic value."
#define pro_rad2_doc "(s,sp)=pro_rad2(m,n,c,x) computes the prolate sheroidal radial function \nof the second kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and |x|<1.0."
-#define pro_rad2_cv_doc "(s,sp)=pro_rad2_cv(m,n,c,cv,x) computes the prolate sheroidal radial function \nof the second kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and |x|<1.0. Requires pre-computed\ncharacteristic value."
+#define pro_rad2_cv_doc "(s,sp)=pro_rad2_cv(m,n,c,cv,x) computes the prolate sheroidal radial function \nof the second kind and its derivative (with respect to x) for mode paramters\nm>=0 and n>=m, spheroidal parameter c and ``|x| < 1.0``. Requires pre-computed\ncharacteristic value."
#define psi_doc "y=psi(z) is the derivative of the logarithm of the gamma function\nevaluated at z (also called the digamma function)."
#define radian_doc "y=radian(d,m,s) returns the angle given in (d)egrees, (m)inutes, and\n(s)econds in radians."
#define rgamma_doc "y=rgamma(z) returns one divided by the gamma function of x."
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