From 47058eb41ed447057222d3d1145046f053407ec1 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Mon, 18 Jun 2018 19:46:20 +0800
Subject: [PATCH 01/18] Add Gauss-Legendre and Chebyshev-Gauss quadurature

---
 modepy/__init__.py                |  3 +--
 modepy/quadrature/jacobi_gauss.py | 18 +++++++++++-------
 2 files changed, 12 insertions(+), 9 deletions(-)

diff --git a/modepy/__init__.py b/modepy/__init__.py
index 72ee409..c2587b9 100644
--- a/modepy/__init__.py
+++ b/modepy/__init__.py
@@ -34,8 +34,7 @@ from modepy.matrices import (vandermonde,
         inverse_mass_matrix, mass_matrix,
         modal_face_mass_matrix, nodal_face_mass_matrix)
 from modepy.quadrature import Quadrature, QuadratureRuleUnavailable
-from modepy.quadrature.jacobi_gauss import (
-        JacobiGaussQuadrature, LegendreGaussQuadrature)
+from modepy.quadrature.jacobi_gauss import JacobiGaussQuadrature
 from modepy.quadrature.xiao_gimbutas import XiaoGimbutasSimplexQuadrature
 from modepy.quadrature.vioreanu_rokhlin import VioreanuRokhlinSimplexQuadrature
 from modepy.quadrature.grundmann_moeller import GrundmannMoellerSimplexQuadrature
diff --git a/modepy/quadrature/jacobi_gauss.py b/modepy/quadrature/jacobi_gauss.py
index ab268e1..115a28b 100644
--- a/modepy/quadrature/jacobi_gauss.py
+++ b/modepy/quadrature/jacobi_gauss.py
@@ -118,18 +118,22 @@ class JacobiGaussQuadrature(Quadrature):
         return nodes, weights
 
 
-class LegendreGaussQuadrature(JacobiGaussQuadrature):
-    """An Gauss quadrature associated with weight 1.
+class GaussLegendreQuadrature(JacobiGaussQuadrature):
+    """Gauss–Legendre quadrature is a special case of Gauss–Jacobi quadrature
+    with α = β = 0.5.
+    """
 
-    Integrates on the interval (-1,1).
-    The quadrature rule is exact up to degree :math:`2N+1`.
+    def __init__(self, N):  # noqa
+        JacobiGaussQuadrature.__init__(self, 0.5, 0.5, N)
 
-    Inherits from :class:`modepy.Quadrature`. See there for the interface
-    to obtain nodes and weights.
+
+class ChebyshevGaussQuadrature(JacobiGaussQuadrature):
+    """Chebyshev-Gauss quadrature is a special case of Gauss–Jacobi quadrature
+    with α = β = 1.
     """
 
     def __init__(self, N):  # noqa
-        JacobiGaussQuadrature.__init__(self, 0, 0, N)
+        JacobiGaussQuadrature.__init__(self, 1, 1, N)
 
 
 def jacobi_gauss_lobatto_nodes(alpha, beta, N):  # noqa
-- 
GitLab


From 798ab9421ddf7292c48d5ca59ec2cb819cd6e0ac Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Mon, 18 Jun 2018 19:54:31 +0800
Subject: [PATCH 02/18] Add Gauss-Gengenbauer quadrature

---
 modepy/__init__.py                | 4 +++-
 modepy/quadrature/jacobi_gauss.py | 9 +++++++++
 2 files changed, 12 insertions(+), 1 deletion(-)

diff --git a/modepy/__init__.py b/modepy/__init__.py
index c2587b9..8417bd1 100644
--- a/modepy/__init__.py
+++ b/modepy/__init__.py
@@ -34,7 +34,9 @@ from modepy.matrices import (vandermonde,
         inverse_mass_matrix, mass_matrix,
         modal_face_mass_matrix, nodal_face_mass_matrix)
 from modepy.quadrature import Quadrature, QuadratureRuleUnavailable
-from modepy.quadrature.jacobi_gauss import JacobiGaussQuadrature
+from modepy.quadrature.jacobi_gauss import (
+        JacobiGaussQuadrature, GaussLegendreQuadrature, ChebyshevGaussQuadrature,
+        GaussGegenbauerQuadrature)
 from modepy.quadrature.xiao_gimbutas import XiaoGimbutasSimplexQuadrature
 from modepy.quadrature.vioreanu_rokhlin import VioreanuRokhlinSimplexQuadrature
 from modepy.quadrature.grundmann_moeller import GrundmannMoellerSimplexQuadrature
diff --git a/modepy/quadrature/jacobi_gauss.py b/modepy/quadrature/jacobi_gauss.py
index 115a28b..63add78 100644
--- a/modepy/quadrature/jacobi_gauss.py
+++ b/modepy/quadrature/jacobi_gauss.py
@@ -136,6 +136,15 @@ class ChebyshevGaussQuadrature(JacobiGaussQuadrature):
         JacobiGaussQuadrature.__init__(self, 1, 1, N)
 
 
+class GaussGegenbauerQuadrature(JacobiGaussQuadrature):
+    """Gauss-Gegenbauer quadrature is a special case of Gauss–Jacobi quadrature
+    with α = β.
+    """
+
+    def __init__(self, alpha, N):  # noqa
+        JacobiGaussQuadrature.__init__(self, alpha, alpha, N)
+
+
 def jacobi_gauss_lobatto_nodes(alpha, beta, N):  # noqa
     """Compute the Gauss-Lobatto quadrature
     nodes corresponding to the :class:`JacobiGaussQuadrature`
-- 
GitLab


From ad78f308f10a5cbdf10b9331574ac9c478d96414 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Mon, 18 Jun 2018 21:29:09 +0800
Subject: [PATCH 03/18] Bug fixes

---
 modepy/quadrature/jacobi_gauss.py | 16 ++++++++++------
 1 file changed, 10 insertions(+), 6 deletions(-)

diff --git a/modepy/quadrature/jacobi_gauss.py b/modepy/quadrature/jacobi_gauss.py
index 63add78..613804a 100644
--- a/modepy/quadrature/jacobi_gauss.py
+++ b/modepy/quadrature/jacobi_gauss.py
@@ -120,20 +120,24 @@ class JacobiGaussQuadrature(Quadrature):
 
 class GaussLegendreQuadrature(JacobiGaussQuadrature):
     """Gauss–Legendre quadrature is a special case of Gauss–Jacobi quadrature
-    with α = β = 0.5.
+    with α = β = 0.
     """
 
     def __init__(self, N):  # noqa
-        JacobiGaussQuadrature.__init__(self, 0.5, 0.5, N)
+        JacobiGaussQuadrature.__init__(self, 0, 0, N)
 
 
 class ChebyshevGaussQuadrature(JacobiGaussQuadrature):
-    """Chebyshev-Gauss quadrature is a special case of Gauss–Jacobi quadrature
-    with α = β = 1.
+    """Chebyshev-Gauss quadrature of the first/second kind are special cases
+    of Gauss–Jacobi quadrature with α = β = -0.5/0.5.
     """
 
-    def __init__(self, N):  # noqa
-        JacobiGaussQuadrature.__init__(self, 1, 1, N)
+    def __init__(self, N, kind=1):  # noqa
+        if kind == 1:
+            # FIXME: division by zero
+            JacobiGaussQuadrature.__init__(self, -0.5, -0.5, N)
+        elif kind == 2:
+            JacobiGaussQuadrature.__init__(self, 0.5, 0.5, N)
 
 
 class GaussGegenbauerQuadrature(JacobiGaussQuadrature):
-- 
GitLab


From 735e85cf01c0fcec0146e0a70a8255e27581d61e Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Sat, 26 Jan 2019 20:58:58 -0600
Subject: [PATCH 04/18] Fix module interface

---
 modepy/__init__.py                | 5 ++++-
 modepy/quadrature/jacobi_gauss.py | 2 +-
 2 files changed, 5 insertions(+), 2 deletions(-)

diff --git a/modepy/__init__.py b/modepy/__init__.py
index 8417bd1..02c7298 100644
--- a/modepy/__init__.py
+++ b/modepy/__init__.py
@@ -35,7 +35,7 @@ from modepy.matrices import (vandermonde,
         modal_face_mass_matrix, nodal_face_mass_matrix)
 from modepy.quadrature import Quadrature, QuadratureRuleUnavailable
 from modepy.quadrature.jacobi_gauss import (
-        JacobiGaussQuadrature, GaussLegendreQuadrature, ChebyshevGaussQuadrature,
+        JacobiGaussQuadrature, LegendreGaussQuadrature, ChebyshevGaussQuadrature,
         GaussGegenbauerQuadrature)
 from modepy.quadrature.xiao_gimbutas import XiaoGimbutasSimplexQuadrature
 from modepy.quadrature.vioreanu_rokhlin import VioreanuRokhlinSimplexQuadrature
@@ -43,6 +43,8 @@ from modepy.quadrature.grundmann_moeller import GrundmannMoellerSimplexQuadratur
 
 from modepy.version import VERSION_TEXT as __version__  # noqa: N811
 
+GaussLegendreQuadrature = LegendreGaussQuadrature
+
 __all__ = [
         "__version__",
 
@@ -60,6 +62,7 @@ __all__ = [
 
         "Quadrature", "QuadratureRuleUnavailable",
         "JacobiGaussQuadrature", "LegendreGaussQuadrature",
+        "GaussLegendreQuadrature", "ChebyshevGaussQuadrature",
         "XiaoGimbutasSimplexQuadrature", "GrundmannMoellerSimplexQuadrature",
         "VioreanuRokhlinSimplexQuadrature",
         ]
diff --git a/modepy/quadrature/jacobi_gauss.py b/modepy/quadrature/jacobi_gauss.py
index 613804a..c04aa02 100644
--- a/modepy/quadrature/jacobi_gauss.py
+++ b/modepy/quadrature/jacobi_gauss.py
@@ -118,7 +118,7 @@ class JacobiGaussQuadrature(Quadrature):
         return nodes, weights
 
 
-class GaussLegendreQuadrature(JacobiGaussQuadrature):
+class LegendreGaussQuadrature(JacobiGaussQuadrature):
     """Gauss–Legendre quadrature is a special case of Gauss–Jacobi quadrature
     with α = β = 0.
     """
-- 
GitLab


From a14b550ba46f926ac2fa1f851b564dfa6bc2bebf Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Sat, 26 Jan 2019 21:12:41 -0600
Subject: [PATCH 05/18] Add back mis-removed docstring

---
 modepy/quadrature/jacobi_gauss.py | 12 ++++++++++--
 1 file changed, 10 insertions(+), 2 deletions(-)

diff --git a/modepy/quadrature/jacobi_gauss.py b/modepy/quadrature/jacobi_gauss.py
index c04aa02..f5bc4d2 100644
--- a/modepy/quadrature/jacobi_gauss.py
+++ b/modepy/quadrature/jacobi_gauss.py
@@ -119,8 +119,16 @@ class JacobiGaussQuadrature(Quadrature):
 
 
 class LegendreGaussQuadrature(JacobiGaussQuadrature):
-    """Gauss–Legendre quadrature is a special case of Gauss–Jacobi quadrature
-    with α = β = 0.
+    """An Gauss quadrature associated with weight 1.
+
+    Integrates on the interval (-1,1).
+    The quadrature rule is exact up to degree :math:`2N+1`.
+
+    Inherits from :class:`modepy.Quadrature`. See there for the interface
+    to obtain nodes and weights.
+
+    (NOTE: Gauss–Legendre quadrature is a special case of Gauss–Jacobi
+    quadrature with α = β = 0.)
     """
 
     def __init__(self, N):  # noqa
-- 
GitLab


From d0771055b030054c0fa20b761f503cd3d379cd30 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Sat, 26 Jan 2019 23:21:44 -0600
Subject: [PATCH 06/18] Document new quad rules

---
 doc/quadrature.rst | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/doc/quadrature.rst b/doc/quadrature.rst
index 95d406c..4200ff0 100644
--- a/doc/quadrature.rst
+++ b/doc/quadrature.rst
@@ -25,6 +25,10 @@ Jacobi-Gauss quadrature in one dimension
 
 .. autoclass:: LegendreGaussQuadrature
 
+.. autoclass:: ChebyshevGaussQuadrature
+
+.. autoclass:: GaussGegenbauerQuadrature
+
 .. currentmodule:: modepy.quadrature.jacobi_gauss
 
 .. autofunction:: jacobi_gauss_lobatto_nodes
-- 
GitLab


From 3c46ed7a7922f8bb5aac993b4b2634da4ee257c1 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20Kl=C3=B6ckner?= <inform@tiker.net>
Date: Sun, 27 Jan 2019 20:54:11 +0100
Subject: [PATCH 07/18] Add versionadded markers to new Gauss shortcuts

---
 modepy/quadrature/jacobi_gauss.py | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/modepy/quadrature/jacobi_gauss.py b/modepy/quadrature/jacobi_gauss.py
index f5bc4d2..4e7ac83 100644
--- a/modepy/quadrature/jacobi_gauss.py
+++ b/modepy/quadrature/jacobi_gauss.py
@@ -138,6 +138,8 @@ class LegendreGaussQuadrature(JacobiGaussQuadrature):
 class ChebyshevGaussQuadrature(JacobiGaussQuadrature):
     """Chebyshev-Gauss quadrature of the first/second kind are special cases
     of Gauss–Jacobi quadrature with α = β = -0.5/0.5.
+
+    .. versionadded:: 2019.1
     """
 
     def __init__(self, N, kind=1):  # noqa
@@ -151,6 +153,8 @@ class ChebyshevGaussQuadrature(JacobiGaussQuadrature):
 class GaussGegenbauerQuadrature(JacobiGaussQuadrature):
     """Gauss-Gegenbauer quadrature is a special case of Gauss–Jacobi quadrature
     with α = β.
+
+    .. versionadded:: 2019.1
     """
 
     def __init__(self, alpha, N):  # noqa
-- 
GitLab


From cca1ace324f6b0abbf590d5b97da29e9893ec04c Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Tue, 27 Aug 2019 10:22:54 -0500
Subject: [PATCH 08/18] Add scipy backend to jacobi_gauss

---
 modepy/quadrature/jacobi_gauss.py | 38 +++++++++++++++++++------------
 1 file changed, 24 insertions(+), 14 deletions(-)

diff --git a/modepy/quadrature/jacobi_gauss.py b/modepy/quadrature/jacobi_gauss.py
index 4e7ac83..23dc067 100644
--- a/modepy/quadrature/jacobi_gauss.py
+++ b/modepy/quadrature/jacobi_gauss.py
@@ -27,11 +27,13 @@ from six.moves import range
 import numpy as np
 import numpy.linalg as la
 from modepy.quadrature import Quadrature
+from scipy.special.orthogonal import roots_jacobi
 
 
 class JacobiGaussQuadrature(Quadrature):
     r"""An Gauss quadrature of order *N* associated with the
     Jacobi weight :math:`(1-x)^\alpha(1+x)^\beta`.
+    The sample points are the roots of the (N+1)-th degree Jacobi polynomial.
 
     Assumes :math:`\alpha,\beta > -1` with
     :math:`(\alpha,\beta)\not\in\{(-1/2,-1/2)\}`.
@@ -42,8 +44,16 @@ class JacobiGaussQuadrature(Quadrature):
     Inherits from :class:`modepy.Quadrature`. See there for the interface
     to obtain nodes and weights.
     """
-    def __init__(self, alpha, beta, N):  # noqa
-        x, w = self.compute_weights_and_nodes(N, alpha, beta)
+    def __init__(self, alpha, beta, N, backend=None):  # noqa
+        # default backend
+        if backend is None:
+            backend = 'builtin'
+        if backend == 'builtin':
+            x, w = self.compute_weights_and_nodes(N, alpha, beta)
+        elif backend== 'scipy':
+            x, w = roots_jacobi(N + 1, alpha, beta)
+        else:
+            raise NotImplementedError("Unsupported backend: %s" % backend)
         Quadrature.__init__(self, x, w)
 
     @staticmethod
@@ -131,8 +141,8 @@ class LegendreGaussQuadrature(JacobiGaussQuadrature):
     quadrature with α = β = 0.)
     """
 
-    def __init__(self, N):  # noqa
-        JacobiGaussQuadrature.__init__(self, 0, 0, N)
+    def __init__(self, N, backend=None):  # noqa
+        JacobiGaussQuadrature.__init__(self, 0, 0, N, backend)
 
 
 class ChebyshevGaussQuadrature(JacobiGaussQuadrature):
@@ -142,12 +152,12 @@ class ChebyshevGaussQuadrature(JacobiGaussQuadrature):
     .. versionadded:: 2019.1
     """
 
-    def __init__(self, N, kind=1):  # noqa
+    def __init__(self, N, kind=1, backend=None):  # noqa
         if kind == 1:
-            # FIXME: division by zero
-            JacobiGaussQuadrature.__init__(self, -0.5, -0.5, N)
+            # FIXME: division by zero using built-in backend
+            JacobiGaussQuadrature.__init__(self, -0.5, -0.5, N, backend='scipy')
         elif kind == 2:
-            JacobiGaussQuadrature.__init__(self, 0.5, 0.5, N)
+            JacobiGaussQuadrature.__init__(self, 0.5, 0.5, N, backend=backend)
 
 
 class GaussGegenbauerQuadrature(JacobiGaussQuadrature):
@@ -157,11 +167,11 @@ class GaussGegenbauerQuadrature(JacobiGaussQuadrature):
     .. versionadded:: 2019.1
     """
 
-    def __init__(self, alpha, N):  # noqa
-        JacobiGaussQuadrature.__init__(self, alpha, alpha, N)
+    def __init__(self, alpha, N, backend=None):  # noqa
+        JacobiGaussQuadrature.__init__(self, alpha, alpha, N, backend)
 
 
-def jacobi_gauss_lobatto_nodes(alpha, beta, N):  # noqa
+def jacobi_gauss_lobatto_nodes(alpha, beta, N, backend=None):  # noqa
     """Compute the Gauss-Lobatto quadrature
     nodes corresponding to the :class:`JacobiGaussQuadrature`
     with the same parameters.
@@ -177,14 +187,14 @@ def jacobi_gauss_lobatto_nodes(alpha, beta, N):  # noqa
         return x
 
     x[1:-1] = np.array(
-            JacobiGaussQuadrature(alpha+1, beta+1, N-2).nodes
+            JacobiGaussQuadrature(alpha+1, beta+1, N-2, backend).nodes
             ).real
     return x
 
 
-def legendre_gauss_lobatto_nodes(N):  # noqa
+def legendre_gauss_lobatto_nodes(N, backend=None):  # noqa
     """Compute the Legendre-Gauss-Lobatto quadrature nodes.
 
     Exact to degree :math:`2N-1`.
     """
-    return jacobi_gauss_lobatto_nodes(0, 0, N)
+    return jacobi_gauss_lobatto_nodes(0, 0, N, backend)
-- 
GitLab


From da46bf250c11b722d606acc6f1ffca41d5c16137 Mon Sep 17 00:00:00 2001
From: Xiaoyu Wei <wxy0516@gmail.com>
Date: Tue, 27 Aug 2019 17:58:31 +0200
Subject: [PATCH 09/18] Update jacobi_gauss.py

---
 modepy/quadrature/jacobi_gauss.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/modepy/quadrature/jacobi_gauss.py b/modepy/quadrature/jacobi_gauss.py
index 94747a6..ba1c24b 100644
--- a/modepy/quadrature/jacobi_gauss.py
+++ b/modepy/quadrature/jacobi_gauss.py
@@ -32,7 +32,7 @@ from scipy.special.orthogonal import roots_jacobi
 
 class JacobiGaussQuadrature(Quadrature):
     r"""An Gauss quadrature of order *N* associated with the
-    Jacobi weight :math:`(1-x)^\alpha(1+x)^\beta`.
+    Jacobi weight :math:`(1-x)^\alpha (1+x)^\beta`.
     The sample points are the roots of the (N+1)-th degree Jacobi polynomial.
 
     Assumes :math:`\alpha, \beta > -1` with
-- 
GitLab


From 1f235c15daa98ee1ad56a98bf8d83c2e4e0b3d34 Mon Sep 17 00:00:00 2001
From: Xiaoyu Wei <wxy0516@gmail.com>
Date: Tue, 27 Aug 2019 17:59:28 +0200
Subject: [PATCH 10/18] Update jacobi_gauss.py

---
 modepy/quadrature/jacobi_gauss.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/modepy/quadrature/jacobi_gauss.py b/modepy/quadrature/jacobi_gauss.py
index ba1c24b..60eb252 100644
--- a/modepy/quadrature/jacobi_gauss.py
+++ b/modepy/quadrature/jacobi_gauss.py
@@ -32,7 +32,7 @@ from scipy.special.orthogonal import roots_jacobi
 
 class JacobiGaussQuadrature(Quadrature):
     r"""An Gauss quadrature of order *N* associated with the
-    Jacobi weight :math:`(1-x)^\alpha (1+x)^\beta`.
+    Jacobi weight :math:`(1 - x)^\alpha (1 + x)^\beta`.
     The sample points are the roots of the (N+1)-th degree Jacobi polynomial.
 
     Assumes :math:`\alpha, \beta > -1` with
-- 
GitLab


From 0d09984ccc4a2ac26a40610fa1e910f813d2523b Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Tue, 27 Aug 2019 11:05:29 -0500
Subject: [PATCH 11/18] Make scipy optional

---
 modepy/quadrature/jacobi_gauss.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/modepy/quadrature/jacobi_gauss.py b/modepy/quadrature/jacobi_gauss.py
index 60eb252..aebefd5 100644
--- a/modepy/quadrature/jacobi_gauss.py
+++ b/modepy/quadrature/jacobi_gauss.py
@@ -27,7 +27,6 @@ from six.moves import range
 import numpy as np
 import numpy.linalg as la
 from modepy.quadrature import Quadrature
-from scipy.special.orthogonal import roots_jacobi
 
 
 class JacobiGaussQuadrature(Quadrature):
@@ -51,6 +50,7 @@ class JacobiGaussQuadrature(Quadrature):
         if backend == 'builtin':
             x, w = self.compute_weights_and_nodes(N, alpha, beta)
         elif backend== 'scipy':
+            from scipy.special.orthogonal import roots_jacobi
             x, w = roots_jacobi(N + 1, alpha, beta)
         else:
             raise NotImplementedError("Unsupported backend: %s" % backend)
-- 
GitLab


From 3972f7c0ea780b4479f45782e9cd1db2cb4b2b6f Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Tue, 27 Aug 2019 11:10:16 -0500
Subject: [PATCH 12/18] Document changes

---
 modepy/quadrature/jacobi_gauss.py | 11 +++++++----
 1 file changed, 7 insertions(+), 4 deletions(-)

diff --git a/modepy/quadrature/jacobi_gauss.py b/modepy/quadrature/jacobi_gauss.py
index aebefd5..82f89fa 100644
--- a/modepy/quadrature/jacobi_gauss.py
+++ b/modepy/quadrature/jacobi_gauss.py
@@ -31,12 +31,15 @@ from modepy.quadrature import Quadrature
 
 class JacobiGaussQuadrature(Quadrature):
     r"""An Gauss quadrature of order *N* associated with the
-    Jacobi weight :math:`(1 - x)^\alpha (1 + x)^\beta`.
-    The sample points are the roots of the (N+1)-th degree Jacobi polynomial.
-
-    Assumes :math:`\alpha, \beta > -1` with
+    Jacobi weight :math:`(1 - x)^\alpha (1 + x)^\beta`,
+    where :math:`\alpha, \beta > -1`.
+    In addition, the builtin backend assumes
     :math:`(\alpha, \beta) \not \in \{(-1/2, -1/2)\}`.
 
+    The sample points are the roots of the (N+1)-th degree Jacobi polynomial.
+    Nodes and weights can be obtained from one of the supported backends
+    (builtin, scipy).
+
     Integrates on the interval :math:`(-1, 1)`.
     The quadrature rule is exact up to degree :math:`2N + 1`.
 
-- 
GitLab


From acfa329c15a0e2ceaacc3565eeee09d1e5997ccd Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Tue, 27 Aug 2019 18:50:29 -0500
Subject: [PATCH 13/18] Test scipy backend

---
 .gitlab-ci.yml          | 8 ++++----
 test/test_quadrature.py | 5 +++--
 2 files changed, 7 insertions(+), 6 deletions(-)

diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
index 417d83d..2072e96 100644
--- a/.gitlab-ci.yml
+++ b/.gitlab-ci.yml
@@ -1,7 +1,7 @@
 Python 2.6:
   script:
   - py_version=2.6
-  - EXTRA_INSTALL=numpy
+  - EXTRA_INSTALL="numpy scipy"
   - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/build-and-test-py-project.sh
   - ". ./build-and-test-py-project.sh"
   tags:
@@ -15,7 +15,7 @@ Python 2.6:
 Python 2.7:
   script:
   - py_version=2.7
-  - EXTRA_INSTALL=numpy
+  - EXTRA_INSTALL="numpy scipy"
   - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/build-and-test-py-project.sh
   - ". ./build-and-test-py-project.sh"
   tags:
@@ -29,7 +29,7 @@ Python 2.7:
 Python 3:
   script:
   - py_version=3
-  - EXTRA_INSTALL=numpy
+  - EXTRA_INSTALL="numpy scipy"
   - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/build-and-test-py-project.sh
   - ". ./build-and-test-py-project.sh"
   tags:
@@ -42,7 +42,7 @@ Python 3:
 
 Documentation:
   script:
-  - EXTRA_INSTALL="numpy"
+  - EXTRA_INSTALL="numpy scipy"
   - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/build-docs.sh
   - ". ./build-docs.sh"
   tags:
diff --git a/test/test_quadrature.py b/test/test_quadrature.py
index 07ba925..5580b7b 100644
--- a/test/test_quadrature.py
+++ b/test/test_quadrature.py
@@ -47,11 +47,12 @@ def test_transformed_quadrature():
     assert abs(result - 1) < 1.0e-9
 
 
-def test_gauss_quadrature():
+@pytest.mark.parametrize("backend", [None, "builtin", "scipy"])
+def test_gauss_quadrature(backend):
     from modepy.quadrature.jacobi_gauss import LegendreGaussQuadrature
 
     for s in range(9 + 1):
-        quad = LegendreGaussQuadrature(s)
+        quad = LegendreGaussQuadrature(s, backend)
         for deg in range(quad.exact_to + 1):
             def f(x):
                 return x**deg
-- 
GitLab


From 2c3f5aea37e6082fdc3267775fa97835ccfd1cee Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Tue, 27 Aug 2019 19:05:46 -0500
Subject: [PATCH 14/18] Pin wheel version for Python 2.6

---
 .gitlab-ci.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
index 2072e96..bd1a1fe 100644
--- a/.gitlab-ci.yml
+++ b/.gitlab-ci.yml
@@ -1,7 +1,7 @@
 Python 2.6:
   script:
   - py_version=2.6
-  - EXTRA_INSTALL="numpy scipy"
+  - EXTRA_INSTALL="numpy scipy wheel==0.29.0"
   - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/build-and-test-py-project.sh
   - ". ./build-and-test-py-project.sh"
   tags:
-- 
GitLab


From 1373aedcc5e6f02f9a5f398cf986ca891efa233f Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Tue, 27 Aug 2019 19:07:31 -0500
Subject: [PATCH 15/18] Fix installation order

---
 .gitlab-ci.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
index bd1a1fe..4408e6d 100644
--- a/.gitlab-ci.yml
+++ b/.gitlab-ci.yml
@@ -1,7 +1,7 @@
 Python 2.6:
   script:
   - py_version=2.6
-  - EXTRA_INSTALL="numpy scipy wheel==0.29.0"
+  - EXTRA_INSTALL="wheel==0.29.0 numpy scipy"
   - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/build-and-test-py-project.sh
   - ". ./build-and-test-py-project.sh"
   tags:
-- 
GitLab


From 54426ee7ce5c75bf8d4f52a2c368b7da42be390c Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Tue, 27 Aug 2019 19:19:19 -0500
Subject: [PATCH 16/18] Skip testing scipy on Python 2.6

---
 .gitlab-ci.yml          |  2 +-
 test/test_quadrature.py | 10 +++++++++-
 2 files changed, 10 insertions(+), 2 deletions(-)

diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
index 4408e6d..1e4005b 100644
--- a/.gitlab-ci.yml
+++ b/.gitlab-ci.yml
@@ -1,7 +1,7 @@
 Python 2.6:
   script:
   - py_version=2.6
-  - EXTRA_INSTALL="wheel==0.29.0 numpy scipy"
+  - EXTRA_INSTALL="numpy"
   - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/build-and-test-py-project.sh
   - ". ./build-and-test-py-project.sh"
   tags:
diff --git a/test/test_quadrature.py b/test/test_quadrature.py
index 5580b7b..fd14ce0 100644
--- a/test/test_quadrature.py
+++ b/test/test_quadrature.py
@@ -47,7 +47,15 @@ def test_transformed_quadrature():
     assert abs(result - 1) < 1.0e-9
 
 
-@pytest.mark.parametrize("backend", [None, "builtin", "scipy"])
+try:
+    import scipy  # noqa
+except ImportError:
+    BACKENDS = [None, "builtin"]
+else:
+    BACKENDS = [None, "builtin", "scipy"]
+
+
+@pytest.mark.parametrize("backend", BACKENDS)
 def test_gauss_quadrature(backend):
     from modepy.quadrature.jacobi_gauss import LegendreGaussQuadrature
 
-- 
GitLab


From 8dbe557b4a3d2e921f97deb80ec42bbefb44bc17 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Tue, 27 Aug 2019 20:09:38 -0500
Subject: [PATCH 17/18] Remove Py2.6 CI job

---
 .gitlab-ci.yml | 14 --------------
 1 file changed, 14 deletions(-)

diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
index 1e4005b..b51b948 100644
--- a/.gitlab-ci.yml
+++ b/.gitlab-ci.yml
@@ -1,17 +1,3 @@
-Python 2.6:
-  script:
-  - py_version=2.6
-  - EXTRA_INSTALL="numpy"
-  - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/build-and-test-py-project.sh
-  - ". ./build-and-test-py-project.sh"
-  tags:
-  - python2.6
-  except:
-  - tags
-  artifacts:
-    reports:
-      junit: test/pytest.xml
-
 Python 2.7:
   script:
   - py_version=2.7
-- 
GitLab


From e28228fe827fb4ca16e25c835a2d92e0316533a0 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20Kl=C3=B6ckner?= <inform@tiker.net>
Date: Wed, 28 Aug 2019 05:27:18 +0200
Subject: [PATCH 18/18] Tweak JacobiGaussQuadrature docs

---
 modepy/quadrature/jacobi_gauss.py | 8 ++++++--
 1 file changed, 6 insertions(+), 2 deletions(-)

diff --git a/modepy/quadrature/jacobi_gauss.py b/modepy/quadrature/jacobi_gauss.py
index 82f89fa..2235983 100644
--- a/modepy/quadrature/jacobi_gauss.py
+++ b/modepy/quadrature/jacobi_gauss.py
@@ -33,8 +33,12 @@ class JacobiGaussQuadrature(Quadrature):
     r"""An Gauss quadrature of order *N* associated with the
     Jacobi weight :math:`(1 - x)^\alpha (1 + x)^\beta`,
     where :math:`\alpha, \beta > -1`.
-    In addition, the builtin backend assumes
-    :math:`(\alpha, \beta) \not \in \{(-1/2, -1/2)\}`.
+
+    :arg backend: Either ``"builtin"`` or ``"scipy"``.
+    
+    When the ``"builtin"`` back-end is in use, there is an additional requirement
+    that :math:`(\alpha, \beta) \not \in \{(-1/2, -1/2)\}`. The ``"scipy"``
+    backend has no such restriction.
 
     The sample points are the roots of the (N+1)-th degree Jacobi polynomial.
     Nodes and weights can be obtained from one of the supported backends
-- 
GitLab