Use SemiNorm (#325)

Use H^1 and H^2 `SemiNorm` from SymPDE. Previously the class `Norm` was used for all seminorms, which was not mathematically correct. --------- Co-authored-by: Yaman Güçlü <[email protected]>
pyccel · Aug 31, 2023 · 02d1bf7 · 02d1bf7
1 parent a623184
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diff --git a/psydac/api/ast/tests/poisson.py b/psydac/api/ast/tests/poisson.py
@@ -1,27 +1,25 @@
 # -*- coding: UTF-8 -*-
-
+import os
 
 from sympy import symbols
-from sympy import sin,pi
+from sympy import sin, pi
 
 from sympde.calculus import grad, dot
-
 from sympde.topology import ScalarFunctionSpace
-from sympde.topology import elements_of,LogicalExpr
+from sympde.topology import elements_of, LogicalExpr
 from sympde.topology import Square
-from sympde.topology import IdentityMapping,Mapping ,PolarMapping
+from sympde.topology import Mapping, IdentityMapping, PolarMapping
 from sympde.expr     import integral
 from sympde.expr     import LinearForm
 from sympde.expr     import BilinearForm
-from sympde.expr     import Norm
+from sympde.expr     import Norm, SemiNorm
 from sympde.expr.evaluation import TerminalExpr
 
 from psydac.api.ast.fem          import AST
 from psydac.api.ast.parser       import parse
 from psydac.api.discretization   import discretize
 from psydac.api.printing.pycode  import pycode
 
-import os
 # ...
 try:
     mesh_dir = os.environ['PSYDAC_MESH_DIR']
@@ -32,6 +30,7 @@
     mesh_dir = os.path.join(base_dir, 'mesh')
     filename = os.path.join(mesh_dir, 'identity_2d.h5')
 
+
 def test_codegen():
     domain  = Square()
     M       = Mapping('M',2)
@@ -51,22 +50,22 @@ def test_codegen():
     Vh = discretize(V, domain_h)
 
     error  = u - sin(pi*x)*sin(pi*y)
-    l2norm = LogicalExpr(M, Norm(error, domain, kind='l2'))
-    h1norm = LogicalExpr(M, Norm(error, domain, kind='h1'))
+    l2norm = LogicalExpr(M,     Norm(error, domain, kind='l2'))
+    h1norm = LogicalExpr(M, SemiNorm(error, domain, kind='h1'))
 
     ast_b = AST(b, TerminalExpr(b)[0],[Vh, Vh])
-    ast_b = parse(ast_b.expr, settings={'dim':2,'nderiv':1,'mapping':M,'target':domain.logical_domain})
+    ast_b = parse(ast_b.expr, settings={'dim':2, 'nderiv':1, 'mapping':M, 'target':domain.logical_domain})
     print(pycode(ast_b))
 
     print('==============================================================================================================')
     ast_l = AST(l, TerminalExpr(l)[0], Vh)
-    ast_l = parse(ast_l.expr, settings={'dim':2,'nderiv':1,'mapping':M,'target':domain.logical_domain})
+    ast_l = parse(ast_l.expr, settings={'dim':2, 'nderiv':1, 'mapping':M, 'target':domain.logical_domain})
     print(pycode(ast_l))
 
 
     print('==============================================================================================================')
     ast_l2norm = AST(l2norm, TerminalExpr(l2norm)[0], Vh)
-    ast_l2norm = parse(ast_l2norm.expr, settings={'dim':2,'nderiv':1,'mapping':M, 'target':domain.logical_domain})
+    ast_l2norm = parse(ast_l2norm.expr, settings={'dim':2, 'nderiv':1, 'mapping':M, 'target':domain.logical_domain})
     print(pycode(ast_l2norm))
-test_codegen()
 
+test_codegen()
diff --git a/psydac/api/ast/tests/system_1.py b/psydac/api/ast/tests/system_1.py
@@ -1,4 +1,5 @@
 # -*- coding: UTF-8 -*-
+import os
 
 from sympy import pi, sin, Tuple, Matrix
 
@@ -10,8 +11,7 @@
 from sympde.expr     import integral
 from sympde.expr     import LinearForm
 from sympde.expr     import BilinearForm
-from sympde.expr     import Norm
-
+from sympde.expr     import Norm, SemiNorm
 from sympde.expr.evaluation import TerminalExpr
 
 from psydac.api.ast.fem          import AST
@@ -20,7 +20,6 @@
 from psydac.api.printing.pycode  import pycode
 
 
-import os
 # ...
 try:
     mesh_dir = os.environ['PSYDAC_MESH_DIR']
@@ -39,7 +38,7 @@ def test_codegen():
 
     x,y = domain.coordinates
 
-    f   = Tuple(2*pi**2*sin(pi*x)*sin(pi*y),
+    f = Tuple(2*pi**2*sin(pi*x)*sin(pi*y),
               2*pi**2*sin(pi*x)*sin(pi*y))
 
     Fe = Tuple(sin(pi*x)*sin(pi*y), sin(pi*x)*sin(pi*y))
@@ -50,12 +49,12 @@ def test_codegen():
 
     int_0 = lambda expr: integral(domain , expr)
 
-    b = BilinearForm((u,v), int_0(inner(grad(v), grad(u))))
+    b = BilinearForm((u, v), int_0(inner(grad(v), grad(u))))
     l = LinearForm(v, int_0(dot(f, v)))
 
     error = Matrix([F[0]-Fe[0], F[1]-Fe[1]])
-    l2norm_F = Norm(error, domain, kind='l2')
-    h1norm_F = Norm(error, domain, kind='h1')
+    l2norm_F =     Norm(error, domain, kind='l2')
+    h1norm_F = SemiNorm(error, domain, kind='h1')
 
     # Create computational domain from topological domain
     domain_h = discretize(domain, filename=filename)
@@ -64,17 +63,16 @@ def test_codegen():
     Vh = discretize(V, domain_h)
 
     print('============================================BilinearForm=========================================')
-    ast_b    = AST(b, TerminalExpr(b)[0], [Vh, Vh])
-    stmt_b = parse(ast_b.expr, settings={'dim':2,'nderiv':1, 'mapping':Vh.symbolic_mapping})
+    ast_b  = AST(b, TerminalExpr(b)[0], [Vh, Vh])
+    stmt_b = parse(ast_b.expr, settings={'dim':2, 'nderiv':1, 'mapping':Vh.symbolic_mapping})
     print(pycode(stmt_b))
 
     print('============================================LinearForm===========================================')
-    ast_l    = AST(l, TerminalExpr(l)[0], Vh)
-    stmt_l = parse(ast_l.expr, settings={'dim':2,'nderiv':1, 'mapping':Vh.symbolic_mapping})
+    ast_l  = AST(l, TerminalExpr(l)[0], Vh)
+    stmt_l = parse(ast_l.expr, settings={'dim':2, 'nderiv':1, 'mapping':Vh.symbolic_mapping})
     print(pycode(stmt_l))
 
-    print('============================================Norm===========================================')
+    print('============================================SemiNorm===========================================')
     ast_norm = AST(h1norm_F, TerminalExpr(h1norm_F)[0], Vh)
-    stmt_n = parse(ast_norm.expr, settings={'dim':2,'nderiv':1, 'mapping':Vh.symbolic_mapping})
+    stmt_n = parse(ast_norm.expr, settings={'dim':2, 'nderiv':1, 'mapping':Vh.symbolic_mapping})
     print(pycode(stmt_n))
-
diff --git a/psydac/api/discretization.py b/psydac/api/discretization.py
@@ -3,6 +3,7 @@
 # TODO: - init_fem is called whenever we call discretize. we should check that
 #         nderiv has not been changed. shall we add nquads too?
 import os
+
 from sympy import Expr as sym_Expr
 import numpy as np
 
@@ -11,7 +12,7 @@
 from sympde.expr     import LinearForm as sym_LinearForm
 from sympde.expr     import Functional as sym_Functional
 from sympde.expr     import Equation as sym_Equation
-from sympde.expr     import Norm as sym_Norm
+from sympde.expr     import Norm as sym_Norm, SemiNorm as sym_SemiNorm
 from sympde.expr     import TerminalExpr
 
 from sympde.topology import BasicFunctionSpace
@@ -39,9 +40,8 @@
 from psydac.fem.vector       import ProductFemSpace, VectorFemSpace
 from psydac.cad.geometry     import Geometry
 from psydac.mapping.discrete import NurbsMapping
-
-from psydac.linalg.stencil     import StencilVectorSpace
-from psydac.linalg.block       import BlockVectorSpace
+from psydac.linalg.stencil   import StencilVectorSpace
+from psydac.linalg.block     import BlockVectorSpace
 
 __all__ = ('discretize', 'discretize_derham', 'reduce_space_degrees', 'discretize_space', 'discretize_domain')
 
@@ -445,7 +445,7 @@ def discretize(a, *args, **kwargs):
         kwargs['symbolic_mapping'] = mapping
 
     if isinstance(a, sym_BasicForm):
-        if isinstance(a, sym_Norm):
+        if isinstance(a, (sym_Norm, sym_SemiNorm)):
             kernel_expr = TerminalExpr(a, domain)
             if not mapping is None:
                 kernel_expr = tuple(LogicalExpr(i, domain) for i in kernel_expr)

diff --git a/psydac/api/fem.py b/psydac/api/fem.py
@@ -10,6 +10,7 @@
 from sympde.expr          import LinearForm as sym_LinearForm
 from sympde.expr          import Functional as sym_Functional
 from sympde.expr          import Norm as sym_Norm
+from sympde.expr          import SemiNorm as sym_SemiNorm
 from sympde.topology      import Boundary, Interface
 from sympde.topology      import VectorFunctionSpace
 from sympde.topology      import ProductSpace
@@ -1525,7 +1526,7 @@ def assemble(self, **kwargs):
 
         Example
         --------------
-        n = Norm(1.0j*v, domain, kind='l2')
+        n = SemiNorm(1.0j*v, domain, kind='l2')
         nh = discretize(n, domain_h,      Vh , **kwargs)
         fh = FemField(Vh)
         fh.coeffs[:] = 1
@@ -1555,7 +1556,7 @@ def assemble(self, **kwargs):
                 args += (v, )
 
         v = self._func(*args)
-        if isinstance(self.expr, sym_Norm):
+        if isinstance(self.expr, (sym_Norm, sym_SemiNorm)):
             if not( self.comm is None ):
                 v = self.comm.allreduce(sendobj=v)
 

diff --git a/psydac/api/tests/test_2d_biharmonic.py b/psydac/api/tests/test_2d_biharmonic.py
@@ -13,7 +13,7 @@
 from sympde.topology import Square
 from sympde.topology import Union
 from sympde.expr     import BilinearForm, LinearForm, integral
-from sympde.expr     import Norm
+from sympde.expr     import Norm, SemiNorm
 from sympde.expr     import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -74,9 +74,9 @@ def run_biharmonic_2d_dir(solution, f, dir_zero_boundary, ncells, degree, backen
 
     # Error norms
     error  = u - solution
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
-    h2norm = Norm(error, domain, kind='h2')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
+    h2norm = SemiNorm(error, domain, kind='h2')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization

diff --git a/psydac/api/tests/test_2d_complex.py b/psydac/api/tests/test_2d_complex.py
@@ -17,7 +17,7 @@
 from sympde.topology import Domain, Square
 from sympde.topology import IdentityMapping, AffineMapping, PolarMapping
 from sympde.expr     import BilinearForm, LinearForm, integral
-from sympde.expr     import Norm
+from sympde.expr     import Norm, SemiNorm
 from sympde.expr     import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -87,9 +87,9 @@ def run_biharmonic_2d_dir(solution, f, dir_zero_boundary, ncells=None, degree=No
 
     # Error norms
     error  = u - solution
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
-    h2norm = Norm(error, domain, kind='h2')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
+    h2norm = SemiNorm(error, domain, kind='h2')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization
@@ -170,8 +170,8 @@ def run_poisson_2d(solution, f, domain, ncells=None, degree=None, filename=None,
 
     equation = find(u, forall=v, lhs=1j*a(u,v), rhs=1j*l(v), bc=bc)
 
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization
@@ -223,8 +223,8 @@ def run_helmholtz_2d(solution, kappa, e_w_0, dx_e_w_0, domain, ncells=None, degr
 
     equation = find(u, forall=v, lhs=a(u,v), rhs=l(v))
 
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization

diff --git a/psydac/api/tests/test_2d_laplace.py b/psydac/api/tests/test_2d_laplace.py
@@ -13,7 +13,7 @@
 from sympde.topology import Square
 from sympde.topology import Union
 from sympde.expr     import BilinearForm, LinearForm, integral
-from sympde.expr     import Norm
+from sympde.expr     import Norm, SemiNorm
 from sympde.expr     import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -78,8 +78,8 @@ def run_laplace_2d(solution, f, dir_zero_boundary, dir_nonzero_boundary,
 
     # Error norms
     error  = u - solution
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization

diff --git a/psydac/api/tests/test_2d_mapping_biharmonic.py b/psydac/api/tests/test_2d_mapping_biharmonic.py
@@ -29,7 +29,7 @@
 from sympde.topology import Domain,Square
 from sympde.topology import Union
 from sympde.expr import BilinearForm, LinearForm, integral
-from sympde.expr import Norm
+from sympde.expr import Norm, SemiNorm
 from sympde.expr import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -100,9 +100,9 @@ def run_biharmonic_2d_dir(filename, solution, f, dir_zero_boundary,
 
     # Error norms
     error  = u - solution
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
-    h2norm = Norm(error, domain, kind='h2')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
+    h2norm = SemiNorm(error, domain, kind='h2')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization

diff --git a/psydac/api/tests/test_2d_mapping_laplace.py b/psydac/api/tests/test_2d_mapping_laplace.py
@@ -29,7 +29,7 @@
 from sympde.topology import Domain,Square
 from sympde.topology import Union
 from sympde.expr import BilinearForm, LinearForm, integral
-from sympde.expr import Norm
+from sympde.expr import Norm, SemiNorm
 from sympde.expr import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -101,8 +101,8 @@ def run_laplace_2d(filename, solution, f, dir_zero_boundary,
 
     # Error norms
     error  = u - solution
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization

diff --git a/psydac/api/tests/test_2d_mapping_poisson.py b/psydac/api/tests/test_2d_mapping_poisson.py
@@ -29,7 +29,7 @@
 from sympde.topology import Domain
 from sympde.topology import Union
 from sympde.expr import BilinearForm, LinearForm, integral
-from sympde.expr import Norm
+from sympde.expr import Norm, SemiNorm
 from sympde.expr import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -106,8 +106,8 @@ def run_poisson_2d(filename, solution, f, dir_zero_boundary,
 
     # Error norms
     error  = u - solution
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization

diff --git a/psydac/api/tests/test_2d_multipatch_mapping_poisson.py b/psydac/api/tests/test_2d_multipatch_mapping_poisson.py
@@ -16,7 +16,7 @@
 from sympde.topology      import IdentityMapping, PolarMapping, AffineMapping
 from sympde.expr.expr     import LinearForm, BilinearForm
 from sympde.expr.expr     import integral
-from sympde.expr.expr     import Norm
+from sympde.expr.expr     import Norm, SemiNorm
 from sympde.expr.equation import find, EssentialBC
 
 from psydac.api.discretization     import discretize
@@ -76,8 +76,8 @@ def run_poisson_2d(solution, f, domain, ncells=None, degree=None, filename=None,
 
     equation = find(u, forall=v, lhs=a(u,v), rhs=l(v))
 
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization

diff --git a/psydac/api/tests/test_2d_multipatch_poisson.py b/psydac/api/tests/test_2d_multipatch_poisson.py
@@ -11,7 +11,7 @@
 from sympde.topology      import IdentityMapping, AffineMapping
 from sympde.expr.expr     import LinearForm, BilinearForm
 from sympde.expr.expr     import integral
-from sympde.expr.expr     import Norm
+from sympde.expr.expr     import Norm, SemiNorm
 from sympde.expr.equation import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -53,8 +53,8 @@ def run_poisson_2d(solution, f, domain, ncells, degree):
 
     equation = find(u, forall=v, lhs=a(u,v), rhs=l(v), bc=bc)
 
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization