Add test_lt_pdf

test/test_gprinter.py

@@ -8,16 +8,16 @@
 
 # Make SymPy available to this program:
 import sympy 
-from sympy import symbols
+from sympy import symbols, simplify, sin, cos
 
 # Make GAlgebra available to this program:
 from galgebra.ga import Ga  
 # from galgebra.mv import *
 from galgebra.printer import Fmt, GaPrinter, Format
 # Fmt:       sets the way that a multivector's basis expansion is output.
 # GaPrinter: makes GA output a little more readable.
-# Format:    turns on latex printer.
-from galgebra.gprinter import gFormat, gprint, gxpdf
+# Format:    turns on latex gprinter.
+from galgebra.gprinter import gFormat, gprint, gxpdf, gPrint_Function
 
 ROOT = Path(__file__).parent.parent
 DIR_TEST = ROOT / 'test'
@@ -26,7 +26,130 @@
 DIR_DIFF = DIR_TEST / 'diff'
 
 
+def lin_tran():
+    gFormat()
+    gPrint_Function()
+    (x, y, z) = xyz = symbols('x,y,z',real=True)
+    (o3d, ex, ey, ez) = Ga.build('e_x e_y e_z', g=[1, 1, 1], coords=xyz)
+    grad = o3d.grad
+    (u, v) = uv = symbols('u,v',real=True)
+    (g2d, eu, ev) = Ga.build('e_u e_v', coords=uv)
+    grad_uv = g2d.grad
+    v_xyz = o3d.mv('v','vector')
+    A_xyz = o3d.mv('A','vector',f=True)
+    A_uv = g2d.mv('A','vector',f=True)
+    # gprint(r'\text{3d orthogonal ($A$ is vector function)}')
+    gprint('A =', A_xyz)
+    gprint('A^{2} =', A_xyz * A_xyz)
+    gprint(r'\nabla \cdot A =', grad | A_xyz)
+    gprint(r'\nabla A =', grad * A_xyz)
+    gprint('v|(grad*A) =',v_xyz|(grad*A_xyz))
+    gprint(r'\text{2d general ($A$ is vector function)}')
+    gprint('A =', A_uv)
+    gprint('A^{2} =', A_uv * A_uv)
+    gprint(r'\nabla \cdot A =', grad_uv | A_uv)
+    gprint(r'\nabla A =', grad_uv * A_uv)
+    A = o3d.lt('A')
+    gprint(r'\text{3d orthogonal ($A$, $B$ are linear transformations)}')
+    gprint('A =', A)
+    gprint(r'\f{mat}{A} =', A.matrix())
+    gprint('\\f{\\det}{A} =', A.det())
+    gprint('\\overline{A} =', A.adj())
+    gprint('\\f{\\Tr}{A} =', A.tr())
+    gprint('\\f{A}{e_x \\wedge e_y} =', A(ex^ey))
+    gprint('\\f{A}{e_x} \\wedge \\f{A}{e_y} =', A(ex)^A(ey))
+    B = o3d.lt('B')
+    gprint('g =', o3d.g)
+    gprint('g^{-1} =', o3d.g_inv)
+
+    gprint('A + B =', A + B)
+    gprint('AB =', A * B)
+    gprint('A - B =', A - B)
+    gprint('General Symmetric Linear Transformation')
+    Asym = o3d.lt('A',mode='s')
+    gprint('A =', Asym)
+    gprint('General Antisymmetric Linear Transformation')
+    Aasym = o3d.lt('A',mode='a')
+    gprint('A =', Aasym)
+    gprint(r'\text{2d general ($A,\\;B$ are linear transformations)}')
+    A2d = g2d.lt('A')
+    gprint('g =', g2d.g)
+    gprint('g^{-1} =', g2d.g_inv)
+    gprint('gg^{-1} =', simplify(g2d.g * g2d.g_inv))
+    gprint('A =', A2d)
+    gprint(r'\f{mat}{A} =', A2d.matrix())
+    gprint('\\f{\\det}{A} =', A2d.det())
+    A2d_adj = A2d.adj()
+    gprint('\\overline{A} =', A2d_adj)
+    gprint('\\f{mat}{\\overline{A}} =', simplify(A2d_adj.matrix()))
+    gprint('\\f{\\Tr}{A} =', A2d.tr())
+    gprint('\\f{A}{e_u \\wedge e_v} =', A2d(eu^ev))
+    gprint('\\f{A}{e_u} \\wedge \\f{A}{e_v} =', A2d(eu)^A2d(ev))
+    B2d = g2d.lt('B')
+
+    gprint('B =', B2d)
+    gprint('A + B =', A2d + B2d)
+    gprint('A - B =', A2d - B2d)
+    gprint('AB =', A2d * B2d)
+    a = g2d.mv('a','vector')
+    b = g2d.mv('b','vector')
+    gprint(r'a|\f{\overline{A}}{b}-b|\f{\underline{A}}{a} =',((a|A2d.adj()(b))-(b|A2d(a))).simplify())
+    m4d = Ga('e_t e_x e_y e_z', g=[1, -1, -1, -1],coords=symbols('t,x,y,z',real=True))
+    T = m4d.lt('T')
+    gprint('g =', m4d.g)
+    gprint(r'\underline{T} =',T)
+    gprint(r'\overline{T} =',T.adj())
+    gprint(r'\f{\det}{\underline{T}} =',T.det())
+    gprint(r'\f{\mbox{tr}}{\underline{T}} =',T.tr())
+    a = m4d.mv('a','vector')
+    b = m4d.mv('b','vector')
+    gprint(r'a|\f{\overline{T}}{b}-b|\f{\underline{T}}{a} =',((a|T.adj()(b))-(b|T(a))).simplify())
+    coords = (r, th, phi) = symbols('r,theta,phi', real=True)
+    (sp3d, er, eth, ephi) = Ga.build('e_r e_th e_ph', g=[1, r**2, r**2*sin(th)**2], coords=coords)
+    grad = sp3d.grad
+    sm_coords = (u, v) = symbols('u,v', real=True)
+    smap = [1, u, v]  # Coordinate map for sphere of r = 1
+    sph2d = sp3d.sm(smap,sm_coords,norm=True)
+    (eu, ev) = sph2d.mv()
+    grad_uv = sph2d.grad
+    F = sph2d.mv('F','vector',f=True)
+    f = sph2d.mv('f','scalar',f=True)
+    gprint('f =',f)
+    gprint(r'\nabla f =',grad_uv * f)
+    gprint('F =',F)
+    gprint(r'\nabla F =',grad_uv * F)
+    tp = (th,phi) = symbols('theta,phi',real=True)
+    smap = [sin(th)*cos(phi),sin(th)*sin(phi),cos(th)]
+    sph2dr = o3d.sm(smap,tp,norm=True)
+    (eth, ephi) = sph2dr.mv()
+    grad_tp = sph2dr.grad
+    F = sph2dr.mv('F','vector',f=True)
+    f = sph2dr.mv('f','scalar',f=True)
+    gprint('f =',f)
+    gprint(r'\nabla f =',grad_tp * f)
+    gprint('F =',F)
+    gprint(r'\nabla F =',grad_tp * F)
+    return
+
+
 class TestGprinter(unittest.TestCase):
+    def setUp(self):
+        os.makedirs(DIR_GENERATED, exist_ok=True)
+        os.makedirs(DIR_DIFF, exist_ok=True)
+        os.chdir(DIR_GENERATED)
+
+    def gen_pdf(self, name, documentclass):
+        gxpdf('%s.tex' % name, pdfprog='tectonic', rm=False, null=False, evince=False, documentclass=documentclass)
+
+    def check_pdf(self, name, expected_retcode=0):
+        retcode = subprocess.call([
+            'diff-pdf',
+            '--output-diff=%s' % (DIR_DIFF / ('%s-diff.pdf' % name)),
+            DIR_FIXTURES / ('%s.pdf' % name),
+            DIR_GENERATED / ('%s.pdf' % name)
+        ])
+        assert retcode == expected_retcode
+
     @pytest.mark.skipif("TEST_GXPDF" not in os.environ, reason="Only run if TEST_GXPDF is set")
     def test_gxpdf(self):
         gFormat()
@@ -54,20 +177,12 @@ def test_gxpdf(self):
 
         gprint(r'{\nabla} = ', grad)
 
-        # mkdir -p
-        os.makedirs(DIR_GENERATED, exist_ok=True)
-        os.makedirs(DIR_DIFF, exist_ok=True)
-        os.chdir(DIR_GENERATED)
-
-        gxpdf('test_gprinter.tex', pdfprog='tectonic', rm=False, null=False, evince=False)
-
-        os.chdir(ROOT)
-        retcode = subprocess.call([
-            'diff-pdf',
-            '--output-diff=%s' % (DIR_DIFF / 'test_gprinter-diff.pdf'),
-            DIR_FIXTURES / 'test_gprinter.pdf',
-            DIR_GENERATED / 'test_gprinter.pdf'
-        ])
-        assert retcode == 0
+        self.gen_pdf('test_gprinter', documentclass='book')
+        self.check_pdf('test_gprinter')
 
-        # os.system('pdf2svg test_gprinter.pdf test_gprinter.svg')
+    # This test is a POC, and should skip for now
+    @pytest.mark.skip
+    def test_lt_pdf(self):
+        lin_tran()
+        self.gen_pdf('test_lt_pdf', documentclass='report')
+        self.check_pdf('test_lt_pdf', expected_retcode=1)