def test_3d_block_2(): print('============== test_3d_block_2 ================') x, y, z = symbols('x y z') u = IndexedBase('u') v = IndexedBase('v') a = Lambda((x, y, z, v, u), Dot(Curl(u), Curl(v)) + 0.2 * Dot(u, v)) print('> input := {0}'.format(a)) # ... create a finite element space p1 = 2 p2 = 2 p3 = 2 ne1 = 2 ne2 = 2 ne3 = 2 # ... print('> Grid :: [{},{},{}]'.format(ne1, ne2, ne3)) print('> Degree :: [{},{},{}]'.format(p1, p2, p3)) grid_1 = linspace(0., 1., ne1 + 1) grid_2 = linspace(0., 1., ne2 + 1) grid_3 = linspace(0., 1., ne3 + 1) V1 = SplineSpace(p1, grid=grid_1) V2 = SplineSpace(p2, grid=grid_2) V3 = SplineSpace(p3, grid=grid_3) Vx = TensorFemSpace(V1, V2, V3) Vy = TensorFemSpace(V1, V2, V3) Vz = TensorFemSpace(V1, V2, V3) V = VectorFemSpace(Vx, Vy, Vz) # ... # ... create a glt symbol from a string without evaluation expr = glt_symbol(a, space=V) print('> glt symbol := {0}'.format(expr)) # ... # ... symbol_f90 = compile_symbol('symbol_block_2', a, V, backend='fortran') # ... # ... example of symbol evaluation t1 = linspace(-pi, pi, ne1 + 1) t2 = linspace(-pi, pi, ne2 + 1) t3 = linspace(-pi, pi, ne3 + 1) x1 = linspace(0., 1., ne1 + 1) x2 = linspace(0., 1., ne2 + 1) x3 = linspace(0., 1., ne3 + 1) e = zeros((3, 3, ne1 + 1, ne2 + 1, ne3 + 1), order='F') symbol_f90(x1, x2, x3, t1, t2, t3, e) # ... print('')
def test_3d_scalar_4(): print('============== test_3d_scalar_4 ================') x, y, z = symbols('x y z') u = Symbol('u') v = Symbol('v') a = Lambda( (x, y, z, v, u), dx(dx(u)) * dx(dx(v)) + dy(dy(u)) * dy(dy(v)) + dz(dz(u)) * dz(dz(v))) print('> input := {0}'.format(a)) # ... create a finite element space p1 = 2 p2 = 2 p3 = 2 ne1 = 2 ne2 = 2 ne3 = 2 # ... print('> Grid :: [{},{},{}]'.format(ne1, ne2, ne3)) print('> Degree :: [{},{},{}]'.format(p1, p2, p3)) grid_1 = linspace(0., 1., ne1 + 1) grid_2 = linspace(0., 1., ne2 + 1) grid_3 = linspace(0., 1., ne3 + 1) V1 = SplineSpace(p1, grid=grid_1) V2 = SplineSpace(p2, grid=grid_2) V3 = SplineSpace(p3, grid=grid_3) V = TensorFemSpace(V1, V2, V3) # ... # ... create a glt symbol from a string without evaluation expr = glt_symbol(a, space=V) print('> glt symbol := {0}'.format(expr)) # ... # ... symbol_f90 = compile_symbol('symbol_scalar_4', a, V, backend='fortran') # ... # ... example of symbol evaluation t1 = linspace(-pi, pi, ne1 + 1) t2 = linspace(-pi, pi, ne2 + 1) t3 = linspace(-pi, pi, ne3 + 1) x1 = linspace(0., 1., ne1 + 1) x2 = linspace(0., 1., ne2 + 1) x3 = linspace(0., 1., ne3 + 1) e = zeros((ne1 + 1, ne2 + 1, ne3 + 1), order='F') symbol_f90(x1, x2, x3, t1, t2, t3, e) # ... print('')
def test_2d_block_1(): print('============== test_2d_block_1 ================') x, y = symbols('x y') u = IndexedBase('u') v = IndexedBase('v') a = Lambda((x, y, v, u), Rot(u) * Rot(v) + Div(u) * Div(v) + 0.2 * Dot(u, v)) print('> input := {0}'.format(a)) # ... create a finite element space p1 = 2 p2 = 2 ne1 = 8 ne2 = 8 print('> Grid :: [{ne1},{ne2}]'.format(ne1=ne1, ne2=ne2)) print('> Degree :: [{p1},{p2}]'.format(p1=p1, p2=p2)) grid_1 = linspace(0., 1., ne1 + 1) grid_2 = linspace(0., 1., ne2 + 1) V1 = SplineSpace(p1, grid=grid_1) V2 = SplineSpace(p2, grid=grid_2) Vx = TensorFemSpace(V1, V2) Vy = TensorFemSpace(V1, V2) V = VectorFemSpace(Vx, Vy) # ... # ... create a glt symbol from a string without evaluation expr = glt_symbol(a, space=V) print('> glt symbol := {0}'.format(expr)) # ... # ... symbol_f90 = compile_symbol('symbol_block_2', a, V, backend='fortran') # ... # ... example of symbol evaluation t1 = linspace(-pi, pi, ne1 + 1) t2 = linspace(-pi, pi, ne2 + 1) x1 = linspace(0., 1., ne1 + 1) x2 = linspace(0., 1., ne2 + 1) e = zeros((2, 2, ne1 + 1, ne2 + 1), order='F') symbol_f90(x1, x2, t1, t2, e) # ... print('')
def test_2d_scalar_5(): print('============== test_2d_scalar_5 ================') x, y = symbols('x y') u = Symbol('u') v = Symbol('v') a = Lambda((x, y, v, u), dx(dx(u)) * dx(dx(v)) + dy(dy(u)) * dy(dy(v))) print('> input := {0}'.format(a)) # ... create a finite element space p1 = 2 p2 = 2 ne1 = 8 ne2 = 8 print('> Grid :: [{ne1},{ne2}]'.format(ne1=ne1, ne2=ne2)) print('> Degree :: [{p1},{p2}]'.format(p1=p1, p2=p2)) grid_1 = linspace(0., 1., ne1 + 1) grid_2 = linspace(0., 1., ne2 + 1) V1 = SplineSpace(p1, grid=grid_1) V2 = SplineSpace(p2, grid=grid_2) V = TensorFemSpace(V1, V2) # ... # ... create a glt symbol from a string without evaluation expr = glt_symbol(a, space=V) print('> glt symbol := {0}'.format(expr)) # ... # ... symbol_f90 = compile_symbol('symbol_scalar_5', a, V, backend='fortran') # ... # ... example of symbol evaluation t1 = linspace(-pi, pi, ne1 + 1) t2 = linspace(-pi, pi, ne2 + 1) x1 = linspace(0., 1., ne1 + 1) x2 = linspace(0., 1., ne2 + 1) e = zeros((ne1 + 1, ne2 + 1), order='F') symbol_f90(x1, x2, t1, t2, e) # ... print('')
def test_1d_scalar_2(): print('============== test_1d_scalar_2 ================') x = Symbol('x') u = Symbol('u') v = Symbol('v') b = Constant('b') a = Lambda((x, v, u), Dot(Grad(b * u), Grad(v)) + u * v) print('> input := {0}'.format(a)) # ... create a finite element space p = 3 ne = 64 print('> Grid :: {ne}'.format(ne=ne)) print('> Degree :: {p}'.format(p=p)) grid = linspace(0., 1., ne + 1) V = SplineSpace(p, grid=grid) # ... # ... create a glt symbol from a string without evaluation expr = glt_symbol(a, space=V) print('> glt symbol := {0}'.format(expr)) # ... # ... symbol_f90 = compile_symbol('symbol_scalar_2', a, V, d_constants={'b': 0.1}, backend='fortran') # ... # ... example of symbol evaluation t1 = linspace(-pi, pi, ne + 1) x1 = linspace(0., 1., ne + 1) e = zeros(ne + 1) symbol_f90(x1, t1, e) # ... print('')
def test_1d_block_1(): print('============== test_1d_block_1 ================') x = Symbol('x') u0, u1 = symbols('u0 u1') v0, v1 = symbols('v0 v1') a = Lambda((x, v0, v1, u0, u1), dx(u0) * dx(v0) + dx(u1) * v0 + u0 * dx(v1) + u1 * v1) print('> input := {0}'.format(a)) # ... create a finite element space p = 3 ne = 64 print('> Grid :: {ne}'.format(ne=ne)) print('> Degree :: {p}'.format(p=p)) grid = linspace(0., 1., ne + 1) V1 = SplineSpace(p, grid=grid) V2 = SplineSpace(p, grid=grid) V = VectorFemSpace(V1, V2) # ... # ... create a glt symbol from a string without evaluation expr = glt_symbol(a, space=V) print('> glt symbol := {0}'.format(expr)) # ... # ... symbol_f90 = compile_symbol('symbol_block_1', a, V, backend='fortran') # ... # ... example of symbol evaluation t1 = linspace(-pi, pi, ne + 1) x1 = linspace(0., 1., ne + 1) e = zeros((2, 2, ne + 1)) symbol_f90(x1, t1, e) # ... print('')
def test_2d_scalar_2(): print('============== test_2d_scalar_2 ================') x, y = symbols('x y') u = Symbol('u') v = Symbol('v') c = Constant('c') b0 = Constant('b0') b1 = Constant('b1') b = Tuple(b0, b1) a = Lambda((x, y, v, u), c * u * v + Dot(b, Grad(v)) * u + Dot(b, Grad(u)) * v) print('> input := {0}'.format(a)) # ... create a finite element space p1 = 2 p2 = 2 ne1 = 8 ne2 = 8 print('> Grid :: [{ne1},{ne2}]'.format(ne1=ne1, ne2=ne2)) print('> Degree :: [{p1},{p2}]'.format(p1=p1, p2=p2)) grid_1 = linspace(0., 1., ne1 + 1) grid_2 = linspace(0., 1., ne2 + 1) V1 = SplineSpace(p1, grid=grid_1) V2 = SplineSpace(p2, grid=grid_2) V = TensorFemSpace(V1, V2) # ... # ... create a glt symbol from a string without evaluation expr = glt_symbol(a, space=V) print('> glt symbol := {0}'.format(expr)) # ... # ... symbol_f90 = compile_symbol('symbol_scalar_2', a, V, d_constants={ 'b0': 0.1, 'b1': 1., 'c': 0.2 }, backend='fortran') # ... # ... example of symbol evaluation t1 = linspace(-pi, pi, ne1 + 1) t2 = linspace(-pi, pi, ne2 + 1) x1 = linspace(0., 1., ne1 + 1) x2 = linspace(0., 1., ne2 + 1) e = zeros((ne1 + 1, ne2 + 1), order='F') symbol_f90(x1, x2, t1, t2, e) # ... print('')
def test_2d_scalar_3(): print('============== test_2d_scalar_3 ================') x, y = symbols('x y') u = Symbol('u') v = Symbol('v') b = Function('b') a = Lambda((x, y, v, u), Dot(Grad(u), Grad(v)) + b(x, y) * u * v) print('> input := {0}'.format(a)) # ... create a finite element space p1 = 2 p2 = 2 ne1 = 8 ne2 = 8 print('> Grid :: [{ne1},{ne2}]'.format(ne1=ne1, ne2=ne2)) print('> Degree :: [{p1},{p2}]'.format(p1=p1, p2=p2)) grid_1 = linspace(0., 1., ne1 + 1) grid_2 = linspace(0., 1., ne2 + 1) V1 = SplineSpace(p1, grid=grid_1) V2 = SplineSpace(p2, grid=grid_2) V = TensorFemSpace(V1, V2) # ... # ... create a glt symbol from a string without evaluation expr = glt_symbol(a, space=V) print('> glt symbol := {0}'.format(expr)) # ... # ... user defined function def b(x, y): r = 1. + x * y return r # ... # ... create an interactive pyccel context from pyccel.epyccel import ContextPyccel context = ContextPyccel(name='context_scalar_3') context.insert_function(b, ['double', 'double'], kind='function', results=['double']) context.compile() # ... # ... symbol_f90 = compile_symbol('symbol_scalar_3', a, V, context=context, backend='fortran') # ... # ... example of symbol evaluation t1 = linspace(-pi, pi, ne1 + 1) t2 = linspace(-pi, pi, ne2 + 1) x1 = linspace(0., 1., ne1 + 1) x2 = linspace(0., 1., ne2 + 1) e = zeros((ne1 + 1, ne2 + 1), order='F') symbol_f90(x1, x2, t1, t2, e) # ... print('')
def test_3d_block_4(): print('============== test_3d_block_4 ================') """Alfven operator.""" x, y, z = symbols('x y z') u = IndexedBase('u') v = IndexedBase('v') bx = Constant('bx') by = Constant('by') bz = Constant('bz') b = Tuple(bx, by, bz) c0 = Constant('c0') c1 = Constant('c1') c2 = Constant('c2') a = Lambda((x, y, z, v, u), (c0 * Dot(u, v) + c1 * Div(u) * Div(v) + c2 * Dot(Curl(Cross(b, u)), Curl(Cross(b, v))))) print('> input := {0}'.format(a)) # ... create a finite element space p1 = 2 p2 = 2 p3 = 2 ne1 = 2 ne2 = 2 ne3 = 2 # ... print('> Grid :: [{},{},{}]'.format(ne1, ne2, ne3)) print('> Degree :: [{},{},{}]'.format(p1, p2, p3)) grid_1 = linspace(0., 1., ne1 + 1) grid_2 = linspace(0., 1., ne2 + 1) grid_3 = linspace(0., 1., ne3 + 1) V1 = SplineSpace(p1, grid=grid_1) V2 = SplineSpace(p2, grid=grid_2) V3 = SplineSpace(p3, grid=grid_3) Vx = TensorFemSpace(V1, V2, V3) Vy = TensorFemSpace(V1, V2, V3) Vz = TensorFemSpace(V1, V2, V3) V = VectorFemSpace(Vx, Vy, Vz) # ... # ... create a glt symbol from a string without evaluation expr = glt_symbol(a, space=V) print('> glt symbol := {0}'.format(expr)) # ... # ... symbol_f90 = compile_symbol('symbol_block_4', a, V, d_constants={ 'bx': 0.1, 'by': 1., 'bz': 0.2, 'c0': 0.1, 'c1': 1., 'c2': 1. }, backend='fortran') # ... # ... example of symbol evaluation t1 = linspace(-pi, pi, ne1 + 1) t2 = linspace(-pi, pi, ne2 + 1) t3 = linspace(-pi, pi, ne3 + 1) x1 = linspace(0., 1., ne1 + 1) x2 = linspace(0., 1., ne2 + 1) x3 = linspace(0., 1., ne3 + 1) e = zeros((3, 3, ne1 + 1, ne2 + 1, ne3 + 1), order='F') symbol_f90(x1, x2, x3, t1, t2, t3, e) # ... print('')
def test_1d_scalar_3(): print('============== test_1d_scalar_3 ================') x = Symbol('x') u = Symbol('u') v = Symbol('v') b = Function('b') a = Lambda((x, v, u), Dot(Grad(u), Grad(v)) + b(x) * u * v) print('> input := {0}'.format(a)) # ... create a finite element space p = 3 ne = 64 print('> Grid :: {ne}'.format(ne=ne)) print('> Degree :: {p}'.format(p=p)) grid = linspace(0., 1., ne + 1) V = SplineSpace(p, grid=grid) # ... # ... create a glt symbol from a string without evaluation expr = glt_symbol(a, space=V) print('> glt symbol := {0}'.format(expr)) # ... # ... user defined function def b(s): r = 1. + s * (1. - s) return r # ... # ... create an interactive pyccel context from pyccel.epyccel import ContextPyccel context = ContextPyccel(name='context_scalar_3') context.insert_function(b, ['double'], kind='function', results=['double']) context.compile() # ... # ... symbol_f90 = compile_symbol('symbol_scalar_3', a, V, context=context, backend='fortran') # ... # ... example of symbol evaluation t1 = linspace(-pi, pi, ne + 1) x1 = linspace(0., 1., ne + 1) e = zeros(ne + 1) symbol_f90(x1, t1, e) # ... print('')