From 00413a56aaddf02b7fec7db8e386e160ddd935e7 Mon Sep 17 00:00:00 2001
From: "Timothy A. Smith" <2timothy18@gmail.com>
Date: Fri, 15 Nov 2019 22:39:20 -0600
Subject: [PATCH 1/7] update test suite to clarify when generalized fluxes are
 being used

---
 test/data_for_test.py        | 12 +++---------
 test/test_eigensystem.py     |  1 +
 test/test_flux_window_ops.py | 10 +++++-----
 3 files changed, 9 insertions(+), 14 deletions(-)

diff --git a/test/data_for_test.py b/test/data_for_test.py
index 9e62317..817fe52 100644
--- a/test/data_for_test.py
+++ b/test/data_for_test.py
@@ -41,13 +41,11 @@ class WindowData:
         self.state_pair = u.transposed_array_from_string(states_str)
         self.states = u.expand_to_n(self.state_pair, 6)
 
-        # FIXME: these should be generalized fluxes
-        # FIXME: make a clear distinction between fluxes in physical and
-        # generalized coordinates
+        self.metrics, self.jacobians = window_metrics
+
         self.fluxes = ref.pointwise_fluxes(
                 self.states)[:,:,self.dir_internal].T.copy(order="F")
-
-        self.metrics, self.jacobians = window_metrics
+        self.generalized_fluxes = self.fluxes # FIXME: wrong
 
 
 @pytest.fixture(scope="session")
@@ -100,10 +98,6 @@ class PairData:
         self.dir_internal = data.dir_internal
 
         self.state_pair = data.states[:,2:4]
-
-        # FIXME: these should be generalized fluxes
-        # FIXME: make a clear distinction between fluxes in physical and
-        # generalized coordinates
         self.flux_pair = data.fluxes[:,2:4]
 
         weighted_metric_slice = data.metrics[2:4]/data.jacobians[2:4,None,None]
diff --git a/test/test_eigensystem.py b/test/test_eigensystem.py
index c077e68..de1e110 100644
--- a/test/test_eigensystem.py
+++ b/test/test_eigensystem.py
@@ -67,6 +67,7 @@ def test_roe_uniform_grid_ideal_gas(queue, pair_data):
     R_inv = R_inv_dev.get()
     lam = lam_dev.get()
 
+    # FIXME: what are Roe identity/property when metric terms are involved?
     check_roe_identity(data.state_pair, R, R_inv)
     check_roe_property(data.state_pair, data.flux_pair, R, R_inv, lam)
 
diff --git a/test/test_flux_window_ops.py b/test/test_flux_window_ops.py
index 0f4742a..a3e163d 100644
--- a/test/test_flux_window_ops.py
+++ b/test/test_flux_window_ops.py
@@ -48,7 +48,7 @@ class WindowResults:
         self.dir_internal = data.dir_internal
 
         self.states = data.states
-        self.fluxes = data.fluxes
+        self.generalized_fluxes = data.generalized_fluxes
         self.state_pair = pair.state_pair
 
         self.metrics = data.metrics
@@ -77,7 +77,7 @@ class WindowResults:
         self.weno_weights_neg = ref.weno_weights(
                 self.oscillation_neg, self.combined_frozen_metric)
 
-        self.consistent = ref.consistent_part(self.fluxes)
+        self.consistent = ref.consistent_part(self.generalized_fluxes)
         self.dissipation_pos = ref.dissipation_part(
                 self.R, self.char_fluxes_pos, self.weno_weights_pos, 1)
         self.dissipation_neg = ref.dissipation_part(
@@ -115,7 +115,7 @@ def test_flux_splitting(queue, window_results):
 
     prg(queue, nvars=data.nvars,
             generalized_states_frozen=data.states,
-            generalized_fluxes_frozen=data.fluxes,
+            generalized_fluxes_frozen=data.generalized_fluxes,
             R_inv=data.R_inv,
             wavespeeds=data.wavespeeds,
             characteristic_fluxes_pos=fluxes_pos_dev,
@@ -133,7 +133,7 @@ def test_weno_flux(queue, window_results):
     flux_dev = u.empty_array_on_device(queue, data.nvars)
 
     prg(queue, nvars=data.nvars,
-            generalized_fluxes=data.fluxes,
+            generalized_fluxes=data.generalized_fluxes,
             characteristic_fluxes_pos=data.char_fluxes_pos,
             characteristic_fluxes_neg=data.char_fluxes_neg,
             combined_frozen_metric=data.combined_frozen_metric,
@@ -152,7 +152,7 @@ def test_consistent_part(queue, window_results):
     consistent_dev = u.empty_array_on_device(queue, data.nvars)
 
     prg(queue, nvars=data.nvars,
-            generalized_fluxes=data.fluxes,
+            generalized_fluxes=data.generalized_fluxes,
             consistent=consistent_dev)
 
     u.compare_arrays(consistent_dev.get(), data.consistent)
-- 
GitLab


From ac0b617a62b3b146d2b94e0dacfec367241820ba Mon Sep 17 00:00:00 2001
From: "Timothy A. Smith" <2timothy18@gmail.com>
Date: Fri, 15 Nov 2019 22:46:57 -0600
Subject: [PATCH 2/7] need to keep track that we compute the generalized fluxes
 in two different ways

---
 test/test_flux_window_ops.py | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/test/test_flux_window_ops.py b/test/test_flux_window_ops.py
index a3e163d..06a000b 100644
--- a/test/test_flux_window_ops.py
+++ b/test/test_flux_window_ops.py
@@ -48,9 +48,11 @@ class WindowResults:
         self.dir_internal = data.dir_internal
 
         self.states = data.states
-        self.generalized_fluxes = data.generalized_fluxes
         self.state_pair = pair.state_pair
 
+        self.generalized_fluxes = data.generalized_fluxes
+        self.generalized_fluxes_frozen = data.generalized_fluxes # FIXME: wrong
+
         self.metrics = data.metrics
         self.jacobians = data.jacobians
 
@@ -115,7 +117,7 @@ def test_flux_splitting(queue, window_results):
 
     prg(queue, nvars=data.nvars,
             generalized_states_frozen=data.states,
-            generalized_fluxes_frozen=data.generalized_fluxes,
+            generalized_fluxes_frozen=data.generalized_fluxes_frozen,
             R_inv=data.R_inv,
             wavespeeds=data.wavespeeds,
             characteristic_fluxes_pos=fluxes_pos_dev,
-- 
GitLab


From feb94554b12399f5232cee7212cdf20796621d44 Mon Sep 17 00:00:00 2001
From: "Timothy A. Smith" <2timothy18@gmail.com>
Date: Sat, 16 Nov 2019 23:55:01 -0600
Subject: [PATCH 3/7] some refactoring to use generalized fluxes for Roe
 property testing

---
 test/data_for_test.py    | 6 +++---
 test/test_eigensystem.py | 3 +--
 2 files changed, 4 insertions(+), 5 deletions(-)

diff --git a/test/data_for_test.py b/test/data_for_test.py
index 817fe52..957fadd 100644
--- a/test/data_for_test.py
+++ b/test/data_for_test.py
@@ -43,9 +43,9 @@ class WindowData:
 
         self.metrics, self.jacobians = window_metrics
 
-        self.fluxes = ref.pointwise_fluxes(
+        # FIXME: wrong
+        self.generalized_fluxes = ref.pointwise_fluxes(
                 self.states)[:,:,self.dir_internal].T.copy(order="F")
-        self.generalized_fluxes = self.fluxes # FIXME: wrong
 
 
 @pytest.fixture(scope="session")
@@ -98,7 +98,7 @@ class PairData:
         self.dir_internal = data.dir_internal
 
         self.state_pair = data.states[:,2:4]
-        self.flux_pair = data.fluxes[:,2:4]
+        self.generalized_flux_pair = data.generalized_fluxes[:,2:4]
 
         weighted_metric_slice = data.metrics[2:4]/data.jacobians[2:4,None,None]
         self.frozen_metrics = np.mean(weighted_metric_slice, axis=0)
diff --git a/test/test_eigensystem.py b/test/test_eigensystem.py
index de1e110..e7b64f1 100644
--- a/test/test_eigensystem.py
+++ b/test/test_eigensystem.py
@@ -67,9 +67,8 @@ def test_roe_uniform_grid_ideal_gas(queue, pair_data):
     R_inv = R_inv_dev.get()
     lam = lam_dev.get()
 
-    # FIXME: what are Roe identity/property when metric terms are involved?
     check_roe_identity(data.state_pair, R, R_inv)
-    check_roe_property(data.state_pair, data.flux_pair, R, R_inv, lam)
+    check_roe_property(data.state_pair, data.generalized_flux_pair, R, R_inv, lam)
 
 
 @pytest.mark.parametrize("lam_pointwise_str,lam_roe_str,lam_expected_str", [
-- 
GitLab


From 0a67b7f41d17da3d6b425f01ea1b3939388601be Mon Sep 17 00:00:00 2001
From: "Timothy A. Smith" <2timothy18@gmail.com>
Date: Sun, 17 Nov 2019 00:09:03 -0600
Subject: [PATCH 4/7] fix incorrect setup for generalized fluxes

---
 test/data_for_test.py        | 8 +++++---
 test/test_flux_window_ops.py | 7 ++++---
 2 files changed, 9 insertions(+), 6 deletions(-)

diff --git a/test/data_for_test.py b/test/data_for_test.py
index 957fadd..28b1a9a 100644
--- a/test/data_for_test.py
+++ b/test/data_for_test.py
@@ -43,9 +43,11 @@ class WindowData:
 
         self.metrics, self.jacobians = window_metrics
 
-        # FIXME: wrong
-        self.generalized_fluxes = ref.pointwise_fluxes(
-                self.states)[:,:,self.dir_internal].T.copy(order="F")
+        self.fluxes = ref.pointwise_fluxes(self.states)
+        self.generalized_fluxes = np.array([np.dot(flux, metrics/jacobian)
+                for flux, metrics, jacobian
+                in zip(self.fluxes, self.metrics, self.jacobians)]
+                )[:,:,self.dir_internal].T.copy(order="F")
 
 
 @pytest.fixture(scope="session")
diff --git a/test/test_flux_window_ops.py b/test/test_flux_window_ops.py
index 06a000b..e6f0667 100644
--- a/test/test_flux_window_ops.py
+++ b/test/test_flux_window_ops.py
@@ -50,9 +50,6 @@ class WindowResults:
         self.states = data.states
         self.state_pair = pair.state_pair
 
-        self.generalized_fluxes = data.generalized_fluxes
-        self.generalized_fluxes_frozen = data.generalized_fluxes # FIXME: wrong
-
         self.metrics = data.metrics
         self.jacobians = data.jacobians
 
@@ -60,6 +57,10 @@ class WindowResults:
         self.frozen_jacobian = pair.frozen_jacobian
         self.combined_frozen_metric = pair.combined_frozen_metrics[self.dir_internal]
 
+        self.generalized_fluxes = data.generalized_fluxes
+        self.generalized_fluxes_frozen = np.array([np.dot(flux, self.frozen_metrics)
+                for flux in data.fluxes])[:,:,self.dir_internal].T.copy(order="F")
+
         self.lam_pointwise = ref.lambda_pointwise(
                 self.states, self.metrics, self.dir_internal)
         self.R, self.R_inv, self.lam_roe = ref.roe_eigensystem(
-- 
GitLab


From 17c02e6279c6e1461220d943afb5947f9151c035 Mon Sep 17 00:00:00 2001
From: "Timothy A. Smith" <2timothy18@gmail.com>
Date: Sun, 17 Nov 2019 00:21:44 -0600
Subject: [PATCH 5/7] refactor out state setup from WindowData

---
 test/data_for_test.py        | 24 +++++++++++++++---------
 test/test_eigensystem.py     |  3 ++-
 test/test_flux_window_ops.py |  3 ++-
 3 files changed, 19 insertions(+), 11 deletions(-)

diff --git a/test/data_for_test.py b/test/data_for_test.py
index 28b1a9a..255932e 100644
--- a/test/data_for_test.py
+++ b/test/data_for_test.py
@@ -31,16 +31,11 @@ class WindowData:
     ndim = ref.gas.ndim
     dirs = ref.gas.dirs
 
-    def __init__(self, states_str, direction, window_metrics):
+    def __init__(self, states, direction, window_metrics):
         self.direction = self.dirs[direction]
         self.dir_internal = self.direction-1
 
-        # FIXME: Move array_from_string stuff outside WindowResults
-        #   -- just pass an array & have external utilities that generate
-        #   Riemann, sine wave, etc. initial conditions
-        self.state_pair = u.transposed_array_from_string(states_str)
-        self.states = u.expand_to_n(self.state_pair, 6)
-
+        self.states = states
         self.metrics, self.jacobians = window_metrics
 
         self.fluxes = ref.pointwise_fluxes(self.states)
@@ -50,6 +45,15 @@ class WindowData:
                 )[:,:,self.dir_internal].T.copy(order="F")
 
 
+@pytest.fixture(scope="session")
+def states_generator():
+    def states(states_str):
+        state_pair = u.transposed_array_from_string(states_str)
+        return u.expand_to_n(state_pair, 6)
+
+    return states
+
+
 @pytest.fixture(scope="session")
 def metrics_generator():
     ndim = ref.gas.ndim
@@ -84,12 +88,14 @@ def metrics_generator():
     ("1 -2 -3 -1 11,2 -8 -12 -4 64", "y", "uniform"),
     ("1 -3 -1 -2 11,2 -12 -4 -8 64", "z", "uniform")
     ])
-def window_data(request, metrics_generator):
+def window_data(request, states_generator, metrics_generator):
     states_str = request.param[0]
     dir_str = request.param[1]
     metric_str = request.param[2]
 
-    return WindowData(states_str, dir_str, metrics_generator(metric_str))
+    return WindowData(states_generator(states_str),
+                      dir_str,
+                      metrics_generator(metric_str))
 
 
 class PairData:
diff --git a/test/test_eigensystem.py b/test/test_eigensystem.py
index e7b64f1..8c1ba93 100644
--- a/test/test_eigensystem.py
+++ b/test/test_eigensystem.py
@@ -35,7 +35,8 @@ import pytest
 
 import utilities as u
 import weno_reference_implementation as ref
-from data_for_test import pair_data, window_data, metrics_generator
+from data_for_test import (
+        pair_data, window_data, states_generator, metrics_generator)
 
 
 def test_roe_uniform_grid_ideal_gas(queue, pair_data):
diff --git a/test/test_flux_window_ops.py b/test/test_flux_window_ops.py
index e6f0667..4bdb27e 100644
--- a/test/test_flux_window_ops.py
+++ b/test/test_flux_window_ops.py
@@ -35,7 +35,8 @@ import pytest
 
 import utilities as u
 import weno_reference_implementation as ref
-from data_for_test import PairData, window_data, metrics_generator
+from data_for_test import (
+        PairData, window_data, states_generator, metrics_generator)
 
 
 class WindowResults:
-- 
GitLab


From 7cd6188141457dc3b1d490bc7e71c9d2846cfaa5 Mon Sep 17 00:00:00 2001
From: "Timothy A. Smith" <2timothy18@gmail.com>
Date: Sun, 17 Nov 2019 00:56:29 -0600
Subject: [PATCH 6/7] refactor ideal_gas and add function to compute conserved
 variables

---
 test/ideal_gas.py | 18 ++++++++++++++----
 1 file changed, 14 insertions(+), 4 deletions(-)

diff --git a/test/ideal_gas.py b/test/ideal_gas.py
index 0be569f..85aa4b7 100644
--- a/test/ideal_gas.py
+++ b/test/ideal_gas.py
@@ -47,13 +47,12 @@ def energy(state):
     return state[ndim+1]
 
 
-def kinetic_energy(state):
-    vel = velocity(state)
-    return 0.5*rho(state)*np.dot(vel, vel)
+def kinetic_energy(rho, vel):
+    return 0.5*rho*np.dot(vel, vel)
 
 
 def internal_energy(state):
-    return energy(state) - kinetic_energy(state)
+    return energy(state) - kinetic_energy(rho(state), velocity(state))
 
 
 def pressure(state):
@@ -75,3 +74,14 @@ def flux(state):
         result[ndim+1,i] += vel[i]*p
 
     return result
+
+
+def conserved(rho, vel, p):
+    def energy(rho, vel, p):
+        return p/(gamma - 1) + kinetic_energy(rho, vel)
+
+    state = np.empty(nvars)
+    state[0] = rho
+    state[1:nvars-1] = rho*vel
+    state[nvars-1] = energy(rho, vel, p)
+    return state
-- 
GitLab


From a5b1d36f1c7a912da01e0fd64aa2e5772b8bd1b5 Mon Sep 17 00:00:00 2001
From: "Timothy A. Smith" <2timothy18@gmail.com>
Date: Sun, 17 Nov 2019 00:56:48 -0600
Subject: [PATCH 7/7] add a sine wave test

---
 test/data_for_test.py | 15 +++++++++++++--
 1 file changed, 13 insertions(+), 2 deletions(-)

diff --git a/test/data_for_test.py b/test/data_for_test.py
index 255932e..483d50b 100644
--- a/test/data_for_test.py
+++ b/test/data_for_test.py
@@ -48,8 +48,16 @@ class WindowData:
 @pytest.fixture(scope="session")
 def states_generator():
     def states(states_str):
-        state_pair = u.transposed_array_from_string(states_str)
-        return u.expand_to_n(state_pair, 6)
+        if states_str == "sine":
+            rho = np.sin(0.01*np.arange(6)+1.55)
+            vel = np.repeat(np.array([1.0, 2.0, 3.0])[None,:], 6, axis=0)
+            pressure = np.repeat(3.2, 6)
+            return u.transposed_array([ref.gas.conserved(r, v, p)
+                for r, v, p
+                in zip(rho, vel, pressure)])
+        else:
+            state_pair = u.transposed_array_from_string(states_str)
+            return u.expand_to_n(state_pair, 6)
 
     return states
 
@@ -72,6 +80,9 @@ def metrics_generator():
 
 
 @pytest.fixture(scope="session", params=[
+    ("sine", "x", "uniform"),
+    ("sine", "y", "uniform"),
+    ("sine", "z", "uniform"),
     ("1 1 1 1 5.5,1 1 1 1 5.5", "x", "uniform"),
     ("1 1 1 1 5.5,1 1 1 1 5.5", "y", "uniform"),
     ("1 1 1 1 5.5,1 1 1 1 5.5", "z", "uniform"),
-- 
GitLab