Fix bug in heat equation example

Only write grdecl file for iteration 0,
otherwise the updated field will be overwritten.
Change seed to create prior that makes the problem easier to solve.

test-data/heat_equation/config.ert

@@ -23,4 +23,4 @@ FIELD COND PARAMETER cond.grdecl INIT_FILES:cond.grdecl FORWARD_INIT:True
 GEN_DATA MY_RESPONSE RESULT_FILE:gen_data_%d.out REPORT_STEPS:10,71,132,193,255,316,377,438 INPUT_FORMAT:ASCII
 
 INSTALL_JOB heat_equation HEAT_EQUATION
-SIMULATION_JOB heat_equation <IENS>
+SIMULATION_JOB heat_equation <IENS> <ITER>

test-data/heat_equation/generate_files.py

@@ -12,7 +12,9 @@
 from definition import Coordinate, obs_coordinates, obs_times
 from heat_equation import heat_equation, sample_prior_conductivity
 
-rng = np.random.default_rng(11223344)
+# Some seeds produce priors that yield poor results.
+# Worth playing around with.
+rng = np.random.default_rng(1234)
 
 
 def create_egrid_file():

test-data/heat_equation/heat_equation.py

@@ -9,6 +9,8 @@
 import numpy.typing as npt
 from definition import dx, k_end, k_start, nx, obs_coordinates, obs_times, u_init
 
+from ert.field_utils.grdecl_io import export_grdecl, import_grdecl
+
 
 def heat_equation(
     u: npt.NDArray[np.float64],
@@ -58,21 +60,18 @@ def sample_prior_conductivity(ensemble_size, nx, rng):
 
 if __name__ == "__main__":
     iens = int(sys.argv[1])
+    iteration = int(sys.argv[2])
     rng = np.random.default_rng(iens)
     cond = sample_prior_conductivity(ensemble_size=1, nx=nx, rng=rng).reshape(nx, nx)
 
-    # Write the array to a GRDECL formatted file
-    with open("cond.grdecl", "w", encoding="utf-8") as f:
-        f.write("COND\n")  # Write the property name
-        f.write("-- Conductivity data\n")  # Optional comment line
-
-        # Write the data
-        for row in cond:
-            for value in row:
-                f.write(f"{value:.6f} ")
-            f.write("\n")
+    if iteration == 0:
+        export_grdecl(cond, "cond.grdecl", "COND", binary=False)
+    else:
+        cond = import_grdecl("cond.grdecl", "COND", dimensions=(nx, nx))
 
-        f.write("/\n")  # End the data section with a slash
+    # The update may give non-physical parameter values, which here means negative heat conductivity.
+    # Setting negative values to a small positive value but not zero because we want to be able to divide by them.
+    cond = cond.clip(min=1e-8)
 
     # Calculate maximum `dt`.
     # If higher values are used, the numerical solution will become unstable.

test-data/heat_equation/obs_10.txt

@@ -1,6 +1,6 @@
-0.12768275433672183 0.006488917943407967
-3.0368036238666027 0.14544770793104408
-8.775028931053242 0.4498048818705942
-13.059948516348125 0.6600383581024866
-0.6246961500720613 0.0325455421675484
-12.831585565944733 0.6849812341743811
+5.644282891424409e-06 3.0797309738845924e-07
+0.4141034913970046 0.020194884393806192
+3.6679650461183813 0.16482328265801968
+16.248260775729047 0.7711986689272523
+1.7635921856785681 0.08703349479288272
+22.164467870340125 1.172137832164079

test-data/heat_equation/obs_132.txt

@@ -1,6 +1,6 @@
-1.5716360848486481 0.07841198652325546
-5.70904881169535 0.27805884604045616
-4.6359274211650465 0.23688032310841162
-7.690562477594383 0.37684849400298187
-2.446579063931665 0.11968462852792194
-6.966783167860096 0.36510800657023174
+0.44779702579071645 0.02217893764751358
+3.24857545175091 0.15681634617125523
+2.760504470567121 0.13250138130254852
+3.3842521445536913 0.16395530223818405
+0.9695985099612162 0.04802326866530623
+2.0614711879846066 0.09892536429937095

test-data/heat_equation/obs_193.txt

@@ -1,6 +1,6 @@
-1.0502697408535813 0.050249877727283246
-3.629866441977895 0.18327680822627104
-2.960774288633309 0.13955259374461457
-4.481886461832233 0.23409425850515386
-1.2993697929710817 0.0686953030021008
-4.036911990951465 0.21331180461247895
+0.5958134294947841 0.03025694175903222
+2.4593591604433196 0.12647358190342392
+1.5710086333003375 0.08528870630118744
+1.6568063803163675 0.09129362898991836
+0.5932408395176263 0.029074626755391172
+1.2126053149741356 0.05481999368425038

test-data/heat_equation/obs_255.txt

@@ -1,6 +1,6 @@
-0.6310622418009374 0.032488575019987025
-2.521390080041612 0.12059552143095845
-1.6503563354895465 0.08558627403540048
-2.924686653695442 0.14697797215599903
-0.7653506764858619 0.041125619497665494
-2.426252682276415 0.12838898993061534
+0.6227307374702258 0.03097070678698683
+1.9783727463142318 0.0986479450282891
+1.2544246608567926 0.05970441297989272
+1.1879846428445189 0.057891275403232016
+0.35755049482970386 0.019673050795920986
+0.7009343241465649 0.03513379961138451

test-data/heat_equation/obs_316.txt

@@ -1,6 +1,6 @@
-0.41917915231764985 0.02138290844488322
-1.4914525747093 0.08018501607364692
-1.0928690326051034 0.05428245248478661
-1.9832718843085502 0.09390177155175192
-0.46698555594867486 0.025630460596029542
-1.5797253869062449 0.07975283486740689
+0.5524614350856832 0.028125076406103185
+1.412412637815958 0.07717531221040153
+0.9199307278481795 0.04439419911256866
+0.7604110043935532 0.040243854530727374
+0.2833847824680585 0.014347799635988293
+0.5029466084851733 0.02474437100264124

test-data/heat_equation/obs_377.txt

@@ -1,6 +1,6 @@
-0.2931205763589738 0.014140217358236368
-1.078094078363641 0.053365783886943366
-0.7192203876910312 0.034901828394380906
-1.2109229760377362 0.060403462021153945
-0.33739602727437984 0.01626283811285199
-1.0303481357741326 0.05027127570950877
+0.5145913371974361 0.024116728328300304
+1.2130120795386947 0.06058558661585877
+0.6612465555505336 0.03405614051381544
+0.6018131783406871 0.029445994400563853
+0.23849281866670452 0.01088287872549113
+0.35652866446374504 0.01832894260196113

test-data/heat_equation/obs_438.txt

@@ -1,6 +1,6 @@
-0.1664581863654361 0.009364965672609851
-0.7300976951071562 0.035495489261655876
-0.46912528290095123 0.02261674411907338
-0.7072805644338298 0.03906096830312989
-0.21631992781141549 0.010430508490340842
-0.6447669420574793 0.032010045332414874
+0.39953767757628283 0.020053305021488894
+0.9295898697400751 0.04770972792415899
+0.5497094384908743 0.02657803741684105
+0.4480479415467605 0.022226512076016683
+0.17204797615905992 0.008437608752461214
+0.2758280704559395 0.013980361434629683

test-data/heat_equation/obs_71.txt

@@ -1,6 +1,6 @@
-2.2438672355992333 0.11671718386773551
-7.892807449865204 0.40982953403161915
-8.92516752247771 0.43228873919471245
-12.500888303994804 0.628865108680274
-4.1069538345763466 0.20842320133194528
-12.762539072098512 0.651852316119926
+0.12972441046117011 0.006459468053345893
+3.4099513667440347 0.1623673652866253
+4.751474206590012 0.235669334834115
+7.793057950541453 0.36514142638442393
+2.0595838023223245 0.09825818825978899
+4.514816590427751 0.24168886166817694