Add some helpers: basis.derivative_basis() method, field.T and field.…

…H for regular/Hermitian transpose, and dist.IdentityTensor.

dedalus/core/basis.py

@@ -556,6 +556,11 @@ def multiplication_matrix(self, subproblem, arg_basis, coeffs, ncc_comp, arg_com
         matrix = convert @ matrix
         return matrix[:N, :N]
 
+    def derivative_basis(self, order=1):
+        a = self.a + order
+        b = self.b + order
+        return self.clone_with(a=a, b=b)
+
 
 def Legendre(*args, **kw):
     return Jacobi(*args, a=0, b=0, **kw)
@@ -631,9 +636,7 @@ class DifferentiateJacobi(operators.Differentiate, operators.SpectralOperator1D)
 
     @staticmethod
     def _output_basis(input_basis):
-        a = input_basis.a + 1
-        b = input_basis.b + 1
-        return input_basis.clone_with(a=a, b=b)
+        return input_basis.derivative_basis(order=1)
 
     @staticmethod
     @CachedMethod
@@ -1944,6 +1947,10 @@ def radius_multiplication_matrix(self, m, spintotal, order, d):
             operator = R2**(d//2) @ operator
         return operator(self.n_size(m), self.alpha + self.k, abs(m + spintotal)).square.astype(np.float64)
 
+    def derivative_basis(self, order=1):
+        k = self.k + order
+        return self.clone_with(k=k)
+
 
 class AnnulusBasis(PolarBasis):
 
@@ -3924,6 +3931,10 @@ def matrix_dependence(self, matrix_coupling):
     def constant(self):
         return (self.Lmax==0, self.Lmax==0, False)
 
+    def derivative_basis(self, order=1):
+        k = self.k + order
+        return self.clone_with(k=k)
+
     @CachedAttribute
     def constant_mode_value(self):
         # Adjust for SWSH normalization

dedalus/core/distributor.py

@@ -216,6 +216,14 @@ def TensorField(self, *args, **kw):
         from .field import TensorField
         return TensorField(self, *args, **kw)
 
+    def IdentityTensor(self, coordsys):
+        """Identity tensor field."""
+        from .field import TensorField
+        I = TensorField(self, (coordsys, coordsys))
+        for i in range(coordsys.dim):
+            I['g'][i, i] = 1
+        return I
+
     def local_grid(self, basis, scale=None):
         # TODO: remove from bases and do it all here?
         if basis.dim == 1:

dedalus/core/field.py

@@ -247,7 +247,15 @@ def expression_matrices(self, subproblem, vars, **kw):
         """Build expression matrices for a specific subproblem and variables."""
         raise NotImplementedError()
 
+    @property
+    def T(self):
+        from .operators import TransposeComponents
+        return TransposeComponents(self)
 
+    @property
+    def H(self):
+        from .operators import TransposeComponents
+        return TransposeComponents(np.conj(self))
 
 
 class Current(Operand):

dedalus/core/operators.py

@@ -2813,8 +2813,7 @@ def __init__(self, operand, coordsys, out=None):
 
     @staticmethod
     def _output_basis(input_basis):
-        out = input_basis._new_k(input_basis.k + 1)
-        return out
+        return input_basis.derivative_basis(1)
 
     def check_conditions(self):
         """Check that operands are in a proper layout."""
@@ -2962,8 +2961,7 @@ def __init__(self, operand, coordsys, out=None):
 
     @staticmethod
     def _output_basis(input_basis):
-        out = input_basis._new_k(input_basis.k + 1)
-        return out
+        return input_basis.derivative_basis(1)
 
     def check_conditions(self):
         """Check that operands are in a proper layout."""
@@ -3164,8 +3162,7 @@ def __init__(self, operand, index=0, out=None):
 
     @staticmethod
     def _output_basis(input_basis):
-        out = input_basis._new_k(input_basis.k + 1)
-        return out
+        return input_basis.derivative_basis(1)
 
     def check_conditions(self):
         """Check that operands are in a proper layout."""
@@ -3225,8 +3222,7 @@ def __init__(self, operand, index=0, out=None):
 
     @staticmethod
     def _output_basis(input_basis):
-        out = input_basis._new_k(input_basis.k + 1)
-        return out
+        return input_basis.derivative_basis(1)
 
     def check_conditions(self):
         """Check that operands are in a proper layout."""
@@ -3371,8 +3367,7 @@ def __init__(self, operand, index=0, out=None):
 
     @staticmethod
     def _output_basis(input_basis):
-        out = input_basis._new_k(input_basis.k + 1)
-        return out
+        return input_basis.derivative_basis(1)
 
     def check_conditions(self):
         """Check that operands are in a proper layout."""
@@ -3515,8 +3510,7 @@ def __init__(self, operand, index=0, out=None):
 
     @staticmethod
     def _output_basis(input_basis):
-        out = input_basis._new_k(input_basis.k + 1)
-        return out
+        return input_basis.derivative_basis(1)
 
     def check_conditions(self):
         """Check that operands are in a proper layout."""
@@ -3718,8 +3712,7 @@ def __init__(self, operand, coordsys, out=None):
 
     @staticmethod
     def _output_basis(input_basis):
-        out = input_basis._new_k(input_basis.k + 2)
-        return out
+        return input_basis.derivative_basis(2)
 
     def check_conditions(self):
         """Check that operands are in a proper layout."""
@@ -3827,8 +3820,7 @@ def __init__(self, operand, coordsys, out=None):
 
     @staticmethod
     def _output_basis(input_basis):
-        out = input_basis._new_k(input_basis.k + 2)
-        return out
+        return input_basis.derivative_basis(2)
 
     def check_conditions(self):
         """Check that operands are in a proper layout."""

docs/notebooks/dedalus_tutorial_3.ipynb

@@ -179,7 +179,7 @@
     "c = -1.76\n",
     "\n",
     "# Tau polynomials\n",
-    "tau_basis = xbasis.clone_with(a=1.5, b=1.5)\n",
+    "tau_basis = xbasis.derivative_basis(2)\n",
     "p1 = dist.Field(bases=tau_basis)\n",
     "p2 = dist.Field(bases=tau_basis)\n",
     "p1['c'][-1] = 1\n",

docs/notebooks/dedalus_tutorial_4.ipynb

@@ -106,7 +106,7 @@
     "c = -1.76\n",
     "\n",
     "# Tau polynomials\n",
-    "tau_basis = xbasis.clone_with(a=1.5, b=1.5)\n",
+    "tau_basis = xbasis.derivative_basis(2)\n",
     "p1 = dist.Field(bases=tau_basis)\n",
     "p2 = dist.Field(bases=tau_basis)\n",
     "p1['c'][-1] = 1\n",

docs/pages/tau_method.rst

@@ -132,7 +132,7 @@ Here we'll take :math:`P(y)` to be the highest mode in the Chebyshev-U basis, in
 
     # Substitutions
     ex, ey = coords.unit_vector_fields(dist)
-    lift_basis = ybasis.clone_with(a=1/2, b=1/2) # Chebyshev U basis
+    lift_basis = ybasis.derivative_basis(1) # Chebyshev U basis
     lift = lambda A, n: d3.Lift(A, lift_basis, -1) # Shortcut for multiplying by U_{N-1}(y)
     grad_u = d3.grad(u) - ey*lift(tau_u1) # Operator representing G
 

examples/evp_1d_waves_on_a_string/waves_on_a_string.py

@@ -41,7 +41,7 @@
 
 # Substitutions
 dx = lambda A: d3.Differentiate(A, xcoord)
-lift_basis = xbasis.clone_with(a=1/2, b=1/2) # First derivative basis
+lift_basis = xbasis.derivative_basis(1)
 lift = lambda A: d3.Lift(A, lift_basis, -1)
 ux = dx(u) + lift(tau_1) # First-order reduction
 

examples/ivp_2d_rayleigh_benard/rayleigh_benard.py

@@ -61,7 +61,7 @@
 nu = (Rayleigh / Prandtl)**(-1/2)
 x, z = dist.local_grids(xbasis, zbasis)
 ex, ez = coords.unit_vector_fields(dist)
-lift_basis = zbasis.clone_with(a=1/2, b=1/2) # First derivative basis
+lift_basis = zbasis.derivative_basis(1)
 lift = lambda A: d3.Lift(A, lift_basis, -1)
 grad_u = d3.grad(u) + ez*lift(tau_u1) # First-order reduction
 grad_b = d3.grad(b) + ez*lift(tau_b1) # First-order reduction

examples/ivp_shell_convection/shell_convection.py

@@ -65,7 +65,7 @@
 er['g'][2] = 1
 rvec = dist.VectorField(coords, bases=basis.radial_basis)
 rvec['g'][2] = r
-lift_basis = basis.clone_with(k=1) # First derivative basis
+lift_basis = basis.derivative_basis(1)
 lift = lambda A: d3.Lift(A, lift_basis, -1)
 grad_u = d3.grad(u) + rvec*lift(tau_u1) # First-order reduction
 grad_b = d3.grad(b) + rvec*lift(tau_b1) # First-order reduction

examples/lbvp_2d_poisson/poisson.py

@@ -47,7 +47,7 @@
 
 # Substitutions
 dy = lambda A: d3.Differentiate(A, coords['y'])
-lift_basis = ybasis.clone_with(a=3/2, b=3/2) # Natural output basis
+lift_basis = ybasis.derivative_basis(2)
 lift = lambda A, n: d3.Lift(A, lift_basis, n)
 
 # Problem