From b9b07ca1af77445cb3ec7c74cd92a77e5a56b136 Mon Sep 17 00:00:00 2001
From: Gareth Tribello <gt@eider.phy.qub.ac.uk>
Date: Tue, 4 Oct 2016 16:50:16 +0100
Subject: [PATCH] Add functionality to calculate the integral of a grid and to
 use this as a cv

---
 regtest/analysis/rt-integral/Makefile         |    1 +
 regtest/analysis/rt-integral/colvar.reference |    6 +
 regtest/analysis/rt-integral/config           |    3 +
 regtest/analysis/rt-integral/forces.reference | 1015 +++++++++++++++++
 regtest/analysis/rt-integral/plumed.dat       |    6 +
 regtest/analysis/rt-integral/trajectory.xyz   | 1015 +++++++++++++++++
 .../analysis/rt-uweights-integral/Makefile    |    1 +
 .../rt-uweights-integral/colvar.reference     |    6 +
 regtest/analysis/rt-uweights-integral/config  |    3 +
 .../rt-uweights-integral/forces.reference     | 1015 +++++++++++++++++
 .../analysis/rt-uweights-integral/plumed.dat  |    8 +
 .../rt-uweights-integral/trajectory.xyz       | 1015 +++++++++++++++++
 regtest/analysis/rt-weights-integral/Makefile |    1 +
 .../rt-weights-integral/colvar.reference      |    6 +
 regtest/analysis/rt-weights-integral/config   |    3 +
 .../rt-weights-integral/forces.reference      | 1015 +++++++++++++++++
 .../analysis/rt-weights-integral/plumed.dat   |    8 +
 .../rt-weights-integral/trajectory.xyz        | 1015 +++++++++++++++++
 src/analysis/Analysis.h                       |    2 +
 src/analysis/Average.cpp                      |    2 +
 src/analysis/Histogram.cpp                    |   98 +-
 src/analysis/Makefile                         |    2 +-
 src/core/ActionPilot.cpp                      |    4 +
 src/core/ActionPilot.h                        |    2 +
 src/gridtools/ActionWithGrid.cpp              |   29 +
 src/gridtools/ActionWithGrid.h                |    2 +
 src/gridtools/ActionWithInputGrid.h           |    1 +
 src/gridtools/ActionWithIntegral.cpp          |   62 +
 src/gridtools/ActionWithIntegral.h            |   60 +
 src/gridtools/AverageOnGrid.h                 |    2 +
 src/gridtools/GridVessel.cpp                  |   27 +-
 src/gridtools/GridVessel.h                    |   16 +
 src/gridtools/HistogramOnGrid.cpp             |   56 +-
 src/gridtools/HistogramOnGrid.h               |    2 +
 src/gridtools/IntegrateGrid.cpp               |   53 +
 src/multicolvar/MultiColvarDensity.cpp        |    1 +
 src/vesselbase/ActionWithAveraging.cpp        |    6 +-
 src/vesselbase/ActionWithAveraging.h          |   17 +-
 src/vesselbase/AveragingVessel.h              |    2 +-
 src/vesselbase/StoreDataVessel.h              |    7 +
 src/vesselbase/Vessel.h                       |    7 +
 41 files changed, 6579 insertions(+), 23 deletions(-)
 create mode 100644 regtest/analysis/rt-integral/Makefile
 create mode 100644 regtest/analysis/rt-integral/colvar.reference
 create mode 100644 regtest/analysis/rt-integral/config
 create mode 100644 regtest/analysis/rt-integral/forces.reference
 create mode 100644 regtest/analysis/rt-integral/plumed.dat
 create mode 100644 regtest/analysis/rt-integral/trajectory.xyz
 create mode 100644 regtest/analysis/rt-uweights-integral/Makefile
 create mode 100644 regtest/analysis/rt-uweights-integral/colvar.reference
 create mode 100644 regtest/analysis/rt-uweights-integral/config
 create mode 100644 regtest/analysis/rt-uweights-integral/forces.reference
 create mode 100644 regtest/analysis/rt-uweights-integral/plumed.dat
 create mode 100644 regtest/analysis/rt-uweights-integral/trajectory.xyz
 create mode 100644 regtest/analysis/rt-weights-integral/Makefile
 create mode 100644 regtest/analysis/rt-weights-integral/colvar.reference
 create mode 100644 regtest/analysis/rt-weights-integral/config
 create mode 100644 regtest/analysis/rt-weights-integral/forces.reference
 create mode 100644 regtest/analysis/rt-weights-integral/plumed.dat
 create mode 100644 regtest/analysis/rt-weights-integral/trajectory.xyz
 create mode 100644 src/gridtools/ActionWithIntegral.cpp
 create mode 100644 src/gridtools/ActionWithIntegral.h
 create mode 100644 src/gridtools/IntegrateGrid.cpp

diff --git a/regtest/analysis/rt-integral/Makefile b/regtest/analysis/rt-integral/Makefile
new file mode 100644
index 000000000..3703b27ce
--- /dev/null
+++ b/regtest/analysis/rt-integral/Makefile
@@ -0,0 +1 @@
+include ../../scripts/test.make
diff --git a/regtest/analysis/rt-integral/colvar.reference b/regtest/analysis/rt-integral/colvar.reference
new file mode 100644
index 000000000..b5545e66d
--- /dev/null
+++ b/regtest/analysis/rt-integral/colvar.reference
@@ -0,0 +1,6 @@
+#! FIELDS time iv b.bias b.force2
+ 0.000000   0.9994   0.3110   6.2200
+ 1.000000   0.9998   0.3121   6.2421
+ 2.000000   0.9959   0.3023   6.0462
+ 3.000000   0.9997   0.3116   6.2327
+ 4.000000   0.9993   0.3108   6.2161
diff --git a/regtest/analysis/rt-integral/config b/regtest/analysis/rt-integral/config
new file mode 100644
index 000000000..b007fddeb
--- /dev/null
+++ b/regtest/analysis/rt-integral/config
@@ -0,0 +1,3 @@
+type=driver
+# this is to test a different name
+arg="--plumed plumed.dat --ixyz trajectory.xyz --dump-forces forces --dump-forces-fmt %8.4f"
diff --git a/regtest/analysis/rt-integral/forces.reference b/regtest/analysis/rt-integral/forces.reference
new file mode 100644
index 000000000..892e706e1
--- /dev/null
+++ b/regtest/analysis/rt-integral/forces.reference
@@ -0,0 +1,1015 @@
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diff --git a/regtest/analysis/rt-integral/plumed.dat b/regtest/analysis/rt-integral/plumed.dat
new file mode 100644
index 000000000..42ef5e8c4
--- /dev/null
+++ b/regtest/analysis/rt-integral/plumed.dat
@@ -0,0 +1,6 @@
+c1: COORDINATIONNUMBER SPECIESA=1-10 SPECIESB=1-200 SWITCH={RATIONAL R_0=1.0} LOWMEM
+h: HISTOGRAM DATA=c1 GRID_BIN=200 GRID_MIN=0 GRID_MAX=10 BANDWIDTH=0.1 
+iv: INTEGRATE_GRID GRID=h 
+
+b: RESTRAINT ARG=iv AT=0.75 KAPPA=10.0 
+PRINT ARG=iv,b.* FILE=colvar FMT=%8.4f
diff --git a/regtest/analysis/rt-integral/trajectory.xyz b/regtest/analysis/rt-integral/trajectory.xyz
new file mode 100644
index 000000000..13fdd1145
--- /dev/null
+++ b/regtest/analysis/rt-integral/trajectory.xyz
@@ -0,0 +1,1015 @@
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diff --git a/regtest/analysis/rt-uweights-integral/Makefile b/regtest/analysis/rt-uweights-integral/Makefile
new file mode 100644
index 000000000..3703b27ce
--- /dev/null
+++ b/regtest/analysis/rt-uweights-integral/Makefile
@@ -0,0 +1 @@
+include ../../scripts/test.make
diff --git a/regtest/analysis/rt-uweights-integral/colvar.reference b/regtest/analysis/rt-uweights-integral/colvar.reference
new file mode 100644
index 000000000..57c2dcbc9
--- /dev/null
+++ b/regtest/analysis/rt-uweights-integral/colvar.reference
@@ -0,0 +1,6 @@
+#! FIELDS time iv b.bias b.force2
+ 0.000000   0.3598   0.7614  15.2271
+ 1.000000   0.5437   0.2128   4.2565
+ 2.000000   0.0000   2.8124  56.2470
+ 3.000000   0.0000   2.8122  56.2440
+ 4.000000   2.0008   7.8226 156.4529
diff --git a/regtest/analysis/rt-uweights-integral/config b/regtest/analysis/rt-uweights-integral/config
new file mode 100644
index 000000000..b007fddeb
--- /dev/null
+++ b/regtest/analysis/rt-uweights-integral/config
@@ -0,0 +1,3 @@
+type=driver
+# this is to test a different name
+arg="--plumed plumed.dat --ixyz trajectory.xyz --dump-forces forces --dump-forces-fmt %8.4f"
diff --git a/regtest/analysis/rt-uweights-integral/forces.reference b/regtest/analysis/rt-uweights-integral/forces.reference
new file mode 100644
index 000000000..7fad8efe2
--- /dev/null
+++ b/regtest/analysis/rt-uweights-integral/forces.reference
@@ -0,0 +1,1015 @@
+201
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diff --git a/regtest/analysis/rt-uweights-integral/plumed.dat b/regtest/analysis/rt-uweights-integral/plumed.dat
new file mode 100644
index 000000000..4dbd98516
--- /dev/null
+++ b/regtest/analysis/rt-uweights-integral/plumed.dat
@@ -0,0 +1,8 @@
+z1: ZANGLES GROUP=1-5 SWITCH={RATIONAL D_0=2.0 R_0=0.5 D_MAX=5.0}
+z2: ZXTORSIONS GROUP=1-5 SWITCH={RATIONAL D_0=2.0 R_0=0.5 D_MAX=5.0}
+ 
+h: HISTOGRAM DATA=z1,z2 GRID_BIN=20,20 GRID_MIN=0,-pi GRID_MAX=pi,pi BANDWIDTH=0.2,0.2 UNORMALIZED
+iv: INTEGRATE_GRID GRID=h 
+
+b: RESTRAINT ARG=iv AT=0.75 KAPPA=10.0 
+PRINT ARG=iv,b.* FILE=colvar FMT=%8.4f
diff --git a/regtest/analysis/rt-uweights-integral/trajectory.xyz b/regtest/analysis/rt-uweights-integral/trajectory.xyz
new file mode 100644
index 000000000..13fdd1145
--- /dev/null
+++ b/regtest/analysis/rt-uweights-integral/trajectory.xyz
@@ -0,0 +1,1015 @@
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diff --git a/regtest/analysis/rt-weights-integral/Makefile b/regtest/analysis/rt-weights-integral/Makefile
new file mode 100644
index 000000000..3703b27ce
--- /dev/null
+++ b/regtest/analysis/rt-weights-integral/Makefile
@@ -0,0 +1 @@
+include ../../scripts/test.make
diff --git a/regtest/analysis/rt-weights-integral/colvar.reference b/regtest/analysis/rt-weights-integral/colvar.reference
new file mode 100644
index 000000000..bf707a0bf
--- /dev/null
+++ b/regtest/analysis/rt-weights-integral/colvar.reference
@@ -0,0 +1,6 @@
+#! FIELDS time iv b.bias b.force2
+ 0.000000   1.0002   0.3129   6.2579
+ 1.000000   0.9993   0.3108   6.2163
+ 2.000000   1.0002   0.3130   6.2595
+ 3.000000   0.9888   0.2852   5.7033
+ 4.000000   1.0004   0.3135   6.2703
diff --git a/regtest/analysis/rt-weights-integral/config b/regtest/analysis/rt-weights-integral/config
new file mode 100644
index 000000000..b007fddeb
--- /dev/null
+++ b/regtest/analysis/rt-weights-integral/config
@@ -0,0 +1,3 @@
+type=driver
+# this is to test a different name
+arg="--plumed plumed.dat --ixyz trajectory.xyz --dump-forces forces --dump-forces-fmt %8.4f"
diff --git a/regtest/analysis/rt-weights-integral/forces.reference b/regtest/analysis/rt-weights-integral/forces.reference
new file mode 100644
index 000000000..532a9a71f
--- /dev/null
+++ b/regtest/analysis/rt-weights-integral/forces.reference
@@ -0,0 +1,1015 @@
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diff --git a/regtest/analysis/rt-weights-integral/plumed.dat b/regtest/analysis/rt-weights-integral/plumed.dat
new file mode 100644
index 000000000..1a4e74554
--- /dev/null
+++ b/regtest/analysis/rt-weights-integral/plumed.dat
@@ -0,0 +1,8 @@
+z1: ZANGLES GROUP=1-5 SWITCH={RATIONAL D_0=2.0 R_0=0.5 D_MAX=5.0}
+z2: ZXTORSIONS GROUP=1-5 SWITCH={RATIONAL D_0=2.0 R_0=0.5 D_MAX=5.0}
+ 
+h: HISTOGRAM DATA=z1,z2 GRID_BIN=20,20 GRID_MIN=0,-pi GRID_MAX=pi,pi BANDWIDTH=0.2,0.2 
+iv: INTEGRATE_GRID GRID=h 
+
+b: RESTRAINT ARG=iv AT=0.75 KAPPA=10.0 
+PRINT ARG=iv,b.* FILE=colvar FMT=%8.4f
diff --git a/regtest/analysis/rt-weights-integral/trajectory.xyz b/regtest/analysis/rt-weights-integral/trajectory.xyz
new file mode 100644
index 000000000..13fdd1145
--- /dev/null
+++ b/regtest/analysis/rt-weights-integral/trajectory.xyz
@@ -0,0 +1,1015 @@
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+Ar 7.75146 8.72537 7.31582
+Ar 8.2173 8.13283 8.42835
+Ar 5.87103 4.41705 7.36285
+Ar 9.59406 7.41339 6.86644
+Ar 8.44531 0.363607 1.13458
+Ar 4.12048 2.8767 8.66202
+Ar 6.61595 4.21433 0.190167
+Ar 3.24932 1.25038 5.15464
+Ar 4.82227 7.90702 3.33424
+Ar 0.0198728 4.00283 5.56947
+Ar 4.28414 3.61125 4.26834
+Ar 4.84291 4.7602 4.7442
+Ar 0.814141 3.27089 3.80451
+Ar 9.43368 1.93755 4.33632
+Ar 5.91948 8.66953 8.8569
+Ar 0.522875 7.95447 0.860441
+Ar 2.1557 0.774862 3.10631
+Ar 2.31509 9.70521 5.54465
+Ar 7.60733 6.35225 2.21052
+Ar 4.99441 1.03751 7.4424
+Ar 7.81586 1.18925 7.74786
+Ar 9.58102 8.1604 1.76983
+Ar 0.757743 5.39434 2.67695
+Ar 9.78321 6.40155 0.794262
+Ar 7.62175 8.69311 5.09753
+Ar 1.36002 7.79604 7.98831
+Ar 5.54308 2.62802 9.10738
+Ar 0.933215 4.54895 4.257
+Ar 7.91614 6.64819 6.21247
+Ar 9.85106 6.84372 2.36851
+Ar 5.97392 3.70014 8.24905
+Ar 6.64836 9.00852 6.14584
+Ar 3.26696 7.72741 4.6529
+Ar 2.08414 8.20126 8.5472
+Ar 8.71225 6.83691 7.88704
+Ar 7.78519 5.69214 7.71757
+Ar 9.78456 9.12228 8.14702
+Ar 4.18868 9.10694 0.322859
+Ar 8.30622 2.6772 5.65806
+Ar 0.0157827 5.25929 2.88429
+Ar 0.632955 8.0814 4.11825
+Ar 5.01598 3.58241 9.48683
+Ar 6.2658 9.24671 9.49752
+Ar 5.29306 0.482018 1.27549
+Ar 1.34334 7.5973 7.88174
+Ar 6.84132 2.1142 3.40302
+Ar 8.03589 9.19091 1.63418
+Ar 0.873677 3.89043 6.50166
+Ar 2.08449 4.0845 8.1333
+Ar 0.499961 2.83645 2.26594
+Ar 5.12893 1.87383 3.39278
+Ar 7.96486 5.35161 4.56202
+Ar 0.835465 1.66366 1.1062
+Ar 8.88116 5.57788 7.50574
+Ar 9.00944 1.63399 2.39468
+Ar 8.10724 8.31387 1.1825
+Ar 7.40154 7.65349 2.18798
+Ar 5.80881 8.67864 1.94781
+Ar 4.47492 9.93644 1.79788
+Ar 8.01359 4.39 2.7289
+Ar 4.25763 7.93677 3.35346
+Ar 6.64434 1.34455 7.78315
+Ar 9.5285 5.42773 3.83717
+Ar 3.79528 7.30003 1.58419
+Ar 8.66185 9.6574 1.92608
+Ar 3.86281 2.25192 8.08468
+Ar 5.4693 2.60563 2.80889
+Ar 2.73772 2.92202 0.463033
+Ar 9.32158 7.7224 0.34999
+Ar 3.39061 5.98839 6.82779
+Ar 5.58232 2.10435 7.73404
+Ar 9.11083 5.67101 2.63003
+Ar 0.590107 7.93451 5.35025
+Ar 7.92024 5.52079 7.95577
+Ar 8.834 3.01055 8.28432
+Ar 8.8867 8.8272 8.6824
+Ar 2.77907 7.78888 7.70617
+Ar 9.63608 3.52666 2.59576
+Ar 9.9523 8.32903 6.02341
+Ar 5.02671 3.86767 3.99013
+Ar 9.89527 9.85848 1.39968
+Ar 5.66065 8.60828 9.44422
+Ar 3.25281 9.9649 0.0565812
+Ar 9.22475 0.377142 8.63133
+Ar 6.98223 0.27845 9.91102
+Ar 0.954877 8.61968 0.9086
+Ar 4.66669 2.98862 9.7805
+Ar 3.2901 6.73037 7.29006
+Ar 9.43989 6.2528 0.73777
+Ar 5.2691 7.78675 1.9626
+Ar 2.37807 8.25969 0.664659
+Ar 5.7161 0.444766 5.19037
+Ar 1.77788 0.838111 6.12816
+Ar 3.77918 6.68077 3.73031
+Ar 7.05868 5.18765 8.83197
+Ar 5.07012 3.43673 1.10128
+Ar 5.46813 2.88451 9.94419
+Ar 9.86988 2.99554 6.02776
+Ar 2.1216 7.68248 9.39316
+Ar 9.15878 1.55022 4.47531
+Ar 4.50696 8.42133 7.25026
+Ar 2.39512 4.72938 6.73935
+Ar 9.49451 4.19622 5.86391
+Ar 6.70501 1.07076 6.31325
+Ar 7.49134 7.01545 8.59661
+Ar 2.83648 2.75877 6.57069
+Ar 0.226766 1.25274 4.87276
+Ar 2.96327 3.68784 1.49853
+Ar 8.14282 6.32737 4.09754
+Ar 4.63358 6.59755 5.0765
+Ar 4.76308 3.09981 8.49083
+Ar 2.2856 4.0852 9.92717
+Ar 8.72976 1.0972 0.622184
+Ar 4.05474 7.98644 8.01343
+Ar 6.0611 8.82793 0.971363
+Ar 5.21621 8.90506 7.42054
+Ar 0.85252 8.31187 7.55784
+Ar 5.08025 3.78838 1.26698
+Ar 4.28152 9.54903 0.467227
+Ar 1.27929 1.10995 4.96625
+Ar 7.85078 8.07968 5.21226
+Ar 2.03223 5.74007 3.43845
+Ar 6.12752 5.15792 9.0895
+Ar 6.31432 4.74453 1.28442
+Ar 0.14469 1.80883 1.00882
+Ar 3.38733 0.859129 9.3866
+Ar 1.8513 4.83748 3.57565
+Ar 4.9641 1.69709 2.92853
+Ar 4.69439 8.58465 2.24284
+Ar 8.52547 7.61727 3.499
+Ar 5.41058 5.62408 3.91523
+Ar 4.29181 2.48439 5.20293
+Ar 2.54077 2.77065 6.32843
+Ar 9.42594 1.73494 9.07766
+Ar 7.05099 6.06211 5.80371
+Ar 5.62884 3.99252 2.32817
+Ar 3.01044 6.47846 3.49305
+Ar 8.11484 6.03974 9.99273
+Ar 6.75007 8.43681 7.50192
+Ar 7.78899 9.57315 5.97498
+Ar 5.15115 5.30966 9.47706
+Ar 9.31936 0.443993 2.18826
+Ar 7.14071 3.97125 4.85273
+Ar 5.07424 2.67889 4.05894
+Ar 1.72002 8.30412 7.30678
+Ar 8.9812 7.09069 3.30219
+Ar 2.71071 8.90597 2.62741
+Ar 1.81835 1.03718 1.82565
+Ar 8.37568 0.125978 7.30861
+Ar 8.92944 7.10977 3.83388
+Ar 9.39118 7.58272 2.7392
+201
+10 10 10
+Ar 5 5 5
+Ar 3.87313 5.73295 3.63497
+Ar 1.26258 0.100799 4.12172
+Ar 1.10159 4.34212 8.03789
+Ar 1.68553 8.74191 5.25031
+Ar 3.13274 1.94513 1.85997
+Ar 7.03405 1.31265 1.73485
+Ar 4.08922 7.47022 2.06127
+Ar 3.58184 0.00244104 1.02653
+Ar 5.27005 3.80757 3.76106
+Ar 2.89607 4.28288 2.40539
+Ar 0.114875 0.702451 6.08648
+Ar 9.34867 3.02487 9.05185
+Ar 1.84465 2.99507 8.0757
+Ar 6.06855 4.20323 3.7223
+Ar 3.25266 7.48637 3.35445
+Ar 7.16833 8.19242 0.0718171
+Ar 9.08901 9.00553 5.94015
+Ar 0.189675 7.86545 4.61016
+Ar 6.39849 9.35537 5.73023
+Ar 0.697546 3.65579 2.9288
+Ar 9.39054 6.74899 0.240582
+Ar 5.49707 9.28968 1.65453
+Ar 3.27444 3.51501 6.81452
+Ar 6.29866 1.5525 2.79149
+Ar 4.64982 9.60691 3.2555
+Ar 8.15288 5.51547 8.54029
+Ar 6.94179 0.599838 1.47644
+Ar 5.37966 5.96036 5.79728
+Ar 9.8735 3.95466 5.96734
+Ar 4.16777 7.64724 7.08618
+Ar 6.04369 6.22166 7.43236
+Ar 3.97462 1.4452 9.53387
+Ar 2.57261 7.93528 8.18957
+Ar 2.63467 0.829112 4.88013
+Ar 8.1737 5.4002 1.11248
+Ar 5.12547 3.70872 2.44357
+Ar 3.82244 3.81637 1.79699
+Ar 9.31441 7.23388 9.79397
+Ar 5.2172 5.52303 5.55224
+Ar 1.51073 0.920974 8.80278
+Ar 6.54699 5.25457 3.63229
+Ar 0.975062 7.86054 2.08892
+Ar 9.40749 1.6041 0.0695826
+Ar 9.3944 1.76099 7.02375
+Ar 1.05714 7.26908 1.40206
+Ar 0.875512 4.73728 9.53985
+Ar 0.87403 9.82149 9.78365
+Ar 9.08002 7.92467 9.95481
+Ar 8.81729 2.21584 1.57518
+Ar 9.95981 4.57134 0.530516
+Ar 3.01772 8.74764 1.52663
+Ar 1.4901 4.09918 4.85936
+Ar 2.14934 4.01285 4.04616
+Ar 3.94403 7.37757 4.88059
+Ar 2.71207 1.79254 7.2659
+Ar 7.72304 1.19616 3.9264
+Ar 1.46436 1.41616 1.41128
+Ar 6.25419 4.08813 9.26625
+Ar 5.47793 7.64297 5.31423
+Ar 1.24938 8.28795 5.64537
+Ar 5.906 2.20219 2.22719
+Ar 7.99586 6.40725 6.67558
+Ar 7.90695 2.08468 7.22678
+Ar 2.38571 6.54578 4.94976
+Ar 0.543483 4.32665 7.95794
+Ar 9.07555 2.81133 9.97924
+Ar 1.23925 7.99383 2.2824
+Ar 2.93181 4.88769 7.48209
+Ar 6.57922 7.03311 5.44743
+Ar 5.12078 4.9839 4.35566
+Ar 0.802694 0.877835 3.76606
+Ar 8.24957 0.516574 2.06065
+Ar 8.90722 3.65429 7.58976
+Ar 0.790915 2.90278 7.03097
+Ar 1.48872 0.835137 6.15335
+Ar 0.880791 3.45231 2.98357
+Ar 0.616992 9.78219 9.32629
+Ar 6.93267 7.37385 2.29875
+Ar 7.83518 5.78737 8.30345
+Ar 3.45898 5.08621 3.93421
+Ar 3.18839 7.21309 0.34932
+Ar 7.35437 4.84111 4.51841
+Ar 4.74387 0.259729 5.26859
+Ar 3.91218 1.96141 5.39494
+Ar 6.36433 5.35012 9.44947
+Ar 5.57066 6.1013 4.57543
+Ar 3.71078 7.13575 0.554679
+Ar 7.13267 8.751 8.08733
+Ar 8.4745 0.95792 9.7614
+Ar 6.51654 3.49025 0.550051
+Ar 4.51249 1.40634 6.39581
+Ar 4.61514 6.63256 3.35415
+Ar 6.44425 8.54386 6.58629
+Ar 3.85636 3.77078 5.43398
+Ar 9.44688 3.70312 8.32443
+Ar 3.20095 8.29598 0.518127
+Ar 8.66746 3.93658 2.16028
+Ar 4.47321 1.24615 3.99721
+Ar 3.23632 2.8568 4.22255
+Ar 0.305042 6.84601 0.845912
+Ar 4.30951 9.89081 4.81353
+Ar 5.91209 4.46826 8.08957
+Ar 2.89971 5.44071 2.08941
+Ar 9.1212 0.0409497 8.2423
+Ar 8.0862 4.81407 9.99059
+Ar 8.70323 5.10685 0.842173
+Ar 3.37046 7.37802 2.33168
+Ar 0.57017 2.84092 7.35925
+Ar 1.86622 5.56774 7.07927
+Ar 5.84218 9.5658 2.48035
+Ar 7.12449 1.24036 6.78823
+Ar 7.54274 0.831074 7.85693
+Ar 3.43707 6.7934 6.59203
+Ar 4.49628 8.96041 7.62218
+Ar 5.13876 7.08872 0.0466171
+Ar 0.329645 0.343775 7.82165
+Ar 5.90956 2.02453 6.30304
+Ar 5.60079 2.5502 1.13809
+Ar 0.648723 3.07937 4.9558
+Ar 6.55088 0.616576 2.78534
+Ar 1.88598 7.69475 5.67168
+Ar 6.47486 3.03928 1.09507
+Ar 4.7741 8.22263 7.81637
+Ar 4.67219 5.55962 0.577062
+Ar 2.12326 5.69258 5.24466
+Ar 1.13544 3.34053 4.33406
+Ar 4.29996 9.34654 7.28091
+Ar 8.37924 9.93932 0.116003
+Ar 3.85205 1.44965 4.19509
+Ar 7.23612 7.55002 3.13938
+Ar 6.55743 0.648518 9.64876
+Ar 5.7365 3.36003 2.04684
+Ar 5.40897 8.60198 3.3941
+Ar 8.8512 2.10176 4.25653
+Ar 8.37896 5.1477 7.42059
+Ar 2.43862 5.87741 1.59926
+Ar 0.857514 2.23809 5.65975
+Ar 5.20599 7.00215 5.14985
+Ar 2.245 1.74703 2.32142
+Ar 8.19193 1.72719 8.80939
+Ar 1.92166 7.2765 6.12871
+Ar 9.60594 7.0251 0.783787
+Ar 7.49085 8.79009 5.01202
+Ar 5.12531 1.03312 3.61994
+Ar 6.68699 8.23934 8.65404
+Ar 5.85407 9.37865 6.91885
+Ar 8.28803 6.91793 9.71231
+Ar 0.154994 4.99089 1.81561
+Ar 7.47213 4.11338 3.59508
+Ar 4.94654 6.47822 9.44509
+Ar 5.0936 8.16921 9.92238
+Ar 1.06304 6.57717 2.5574
+Ar 6.40198 8.14627 4.44098
+Ar 4.90826 3.16757 7.38135
+Ar 8.95555 6.00488 4.08592
+Ar 3.95336 4.17199 8.71278
+Ar 5.47846 6.40654 4.7525
+Ar 7.36347 7.83685 3.85437
+Ar 8.27623 8.65346 8.70981
+Ar 1.6617 8.19874 6.1984
+Ar 4.50241 2.00458 0.971449
+Ar 7.76135 5.04448 2.63619
+Ar 8.71161 6.07659 9.21288
+Ar 6.76582 3.08604 7.01563
+Ar 9.21579 9.78598 2.96539
+Ar 0.855888 4.90513 0.457679
+Ar 8.2507 9.56063 5.59129
+Ar 2.08136 1.42156 2.19529
+Ar 7.70847 6.17798 3.27745
+Ar 0.754502 0.909584 7.37261
+Ar 9.43419 0.423678 0.760008
+Ar 5.435 6.11527 9.33427
+Ar 8.02994 9.2571 4.03267
+Ar 0.606574 4.6945 0.383465
+Ar 9.35323 9.74732 3.19666
+Ar 6.36671 5.22578 9.74157
+Ar 5.95597 1.91401 8.77683
+Ar 1.40332 5.56064 7.74702
+Ar 6.30169 2.42405 1.04518
+Ar 2.34835 8.69722 4.20179
+Ar 0.670357 6.6892 5.34706
+Ar 8.63881 2.45052 5.89593
+Ar 1.26038 3.14406 2.16308
+Ar 1.58515 1.54755 9.59656
+Ar 7.05547 1.25183 9.5881
+Ar 3.01513 5.25619 0.776404
+Ar 2.64111 9.14238 6.04527
+Ar 6.33888 7.62816 6.48992
+Ar 5.49963 2.2152 0.907294
+Ar 7.72449 5.53304 3.83241
+Ar 4.46581 6.90197 1.34986
+Ar 7.2834 2.1483 6.41683
+Ar 9.77827 3.36416 1.43895
+Ar 3.87117 2.67413 4.07172
+Ar 6.46873 9.92897 6.25149
+Ar 0.268344 0.0617421 7.69979
+Ar 8.13526 9.23425 0.117487
+Ar 9.51619 8.66444 3.31978
+Ar 2.70354 8.34826 9.27735
+Ar 3.98257 4.97261 4.6757
diff --git a/src/analysis/Analysis.h b/src/analysis/Analysis.h
index 49456224f..2a6c371af 100644
--- a/src/analysis/Analysis.h
+++ b/src/analysis/Analysis.h
@@ -110,6 +110,8 @@ public:
   static void registerKeywords( Keywords& keys );
   explicit Analysis(const ActionOptions&);
   ~Analysis();
+  void calculate(){}
+  void apply(){}
   void accumulate();
   void performOperations( const bool& from_update );
   virtual void performAnalysis()=0;
diff --git a/src/analysis/Average.cpp b/src/analysis/Average.cpp
index 93778b59e..ec2da2ad2 100644
--- a/src/analysis/Average.cpp
+++ b/src/analysis/Average.cpp
@@ -95,6 +95,8 @@ private:
 public:
   static void registerKeywords( Keywords& keys );
   explicit Average( const ActionOptions& );
+  void calculate(){}
+  void apply(){}
   void performOperations( const bool& from_update );
   void finishAveraging();
   bool isPeriodic(){ return false; } 
diff --git a/src/analysis/Histogram.cpp b/src/analysis/Histogram.cpp
index cb34a285e..2f3fdf08d 100644
--- a/src/analysis/Histogram.cpp
+++ b/src/analysis/Histogram.cpp
@@ -24,6 +24,7 @@
 #include "gridtools/ActionWithGrid.h"
 #include "vesselbase/ActionWithVessel.h"
 #include "vesselbase/StoreDataVessel.h"
+#include "multicolvar/MultiColvarBase.h"
 #include "core/PlumedMain.h"
 #include "core/ActionSet.h"
 
@@ -160,7 +161,9 @@ DUMPGRID GRID=hh FILE=histo STRIDE=100000
 class Histogram : public gridtools::ActionWithGrid { 
 private:
   double ww;
+  bool in_apply;
   KernelFunctions* kernel;
+  std::vector<double> forcesToApply, finalForces;
   std::vector<vesselbase::ActionWithVessel*> myvessels;
   std::vector<vesselbase::StoreDataVessel*> stashes;
   gridtools::HistogramOnGrid* myhist; 
@@ -173,7 +176,9 @@ public:
   void finishAveraging();
   bool isPeriodic(){ return false; }
   unsigned getNumberOfDerivatives(); 
+  void turnOnDerivatives();
   void compute( const unsigned& , MultiValue& ) const ;
+  void apply();
 };
 
 PLUMED_REGISTER_ACTION(Histogram,"HISTOGRAM")
@@ -192,6 +197,7 @@ Histogram::Histogram(const ActionOptions&ao):
 Action(ao),
 ActionWithGrid(ao),
 ww(0.0),
+in_apply(false),
 kernel(NULL)
 {
   // Read in arguments 
@@ -277,9 +283,31 @@ kernel(NULL)
   checkRead(); 
 }
 
+void Histogram::turnOnDerivatives(){
+  ActionWithGrid::turnOnDerivatives();
+  std::vector<AtomNumber> all_atoms, tmp_atoms;
+  for(unsigned i=0;i<myvessels.size();++i){
+      multicolvar::MultiColvarBase* mbase=dynamic_cast<multicolvar::MultiColvarBase*>( myvessels[i] );
+      if( !mbase ) error("do not know how to get histogram derivatives for actions of type " + myvessels[i]->getName() );
+      tmp_atoms = mbase->getAbsoluteIndexes();
+      for(unsigned j=0;j<tmp_atoms.size();++j) all_atoms.push_back( tmp_atoms[j] );
+  }
+  ActionAtomistic::requestAtoms( all_atoms ); 
+  finalForces.resize( 3*all_atoms.size() + 9 ); 
+  forcesToApply.resize( 3*all_atoms.size() + 9*myvessels.size() );
+  // And make sure we still have the dependencies which are cleared by requestAtoms
+  for(unsigned i=0;i<myvessels.size();++i) addDependency( myvessels[i] );
+  // And resize the histogram so that we have a place to store the forces
+  in_apply=true; mygrid->resize(); in_apply=false;
+}
+
 unsigned Histogram::getNumberOfDerivatives(){ 
-  if( myvessels.size()>0 ) return myvessels.size(); 
-  return getNumberOfArguments(); 
+  if( in_apply ){
+     unsigned nder=0;
+     for(unsigned i=0;i<myvessels.size();++i) nder += myvessels[i]->getNumberOfDerivatives();
+     return nder;
+  }
+  return getNumberOfArguments();
 }
 
 unsigned Histogram::getNumberOfQuantities() const {
@@ -301,7 +329,10 @@ void Histogram::prepareForAveraging(){
           }
           norm += tnorm; taskFlags[i]=1;
       }
-      lockContributors(); ww = cweight / norm;
+      lockContributors(); 
+      // Sort out normalization of histogram
+      if( !noNormalization() ) ww = cweight / norm;
+      else ww = cweight;  
   } else {
       // Now fetch the kernel and the active points
       std::vector<double> point( getNumberOfArguments() );  
@@ -331,14 +362,44 @@ void Histogram::compute( const unsigned& current, MultiValue& myvals ) const {
   if( myvessels.size()>0 ){
       std::vector<double> cvals( myvessels[0]->getNumberOfQuantities() );
       stashes[0]->retrieveSequentialValue( current, false, cvals );
-      double tnorm = cvals[0]; myvals.setValue( 1, cvals[1] ); 
+      unsigned derbase; double totweight=cvals[0], tnorm = cvals[0]; myvals.setValue( 1, cvals[1] ); 
+      // Get the derivatives as well if we are in apply
+      if( in_apply ){
+           // This bit gets the total weight
+           double weight0 = cvals[0];  // Store the current weight
+           for(unsigned j=1;j<myvessels.size();++j){
+               stashes[j]->retrieveSequentialValue( current, false, cvals ); totweight *= cvals[0]; 
+           }
+           // And this bit the derivatives
+           MultiValue tmpval( myvessels[0]->getNumberOfQuantities(), myvessels[0]->getNumberOfDerivatives() ); 
+           stashes[0]->retrieveDerivatives( stashes[0]->getTrueIndex(current), false, tmpval );
+           for(unsigned j=0;j<tmpval.getNumberActive();++j){
+               unsigned jder=tmpval.getActiveIndex(j); 
+               myvals.addDerivative( 1, jder, tmpval.getDerivative(1,jder) );
+               myvals.addDerivative( 0, jder, (totweight/weight0)*tmpval.getDerivative(0,jder) );
+           }
+           derbase = myvessels[0]->getNumberOfDerivatives();
+      }
       for(unsigned i=1;i<myvessels.size();++i){
           if( cvals.size()!=myvessels[i]->getNumberOfQuantities() ) cvals.resize( myvessels[i]->getNumberOfQuantities() );
           stashes[i]->retrieveSequentialValue( current, false, cvals );
           tnorm *= cvals[0]; myvals.setValue( 1+i, cvals[1] ); 
+          // Get the derivatives as well if we are in apply
+          if( in_apply ){
+               MultiValue tmpval( myvessels[i]->getNumberOfQuantities(), myvessels[i]->getNumberOfDerivatives() );
+               stashes[i]->retrieveDerivatives( stashes[i]->getTrueIndex(current), false, tmpval );
+               for(unsigned j=0;j<tmpval.getNumberActive();++j){
+                   unsigned jder=tmpval.getActiveIndex(j); 
+                   myvals.addDerivative( 1+i, derbase+jder, tmpval.getDerivative(1,jder) );
+                   myvals.addDerivative( 0, derbase+jder, (totweight/cvals[0])*tmpval.getDerivative(0,jder) );
+               }
+               derbase += myvessels[i]->getNumberOfDerivatives();
+          }
       }
-      myvals.setValue( 0, tnorm ); myvals.setValue( 1+myvessels.size(), ww );
+      myvals.setValue( 0, tnorm ); myvals.setValue( 1+myvessels.size(), ww ); 
+      if( in_apply ) myvals.updateDynamicList();
   } else {
+      plumed_assert( !in_apply );
       std::vector<Value*> vv( myhist->getVectorOfValues() );
       std::vector<double> val( getNumberOfArguments() ), der( getNumberOfArguments() ); 
       // Retrieve the location of the grid point at which we are evaluating the kernel
@@ -351,5 +412,32 @@ void Histogram::compute( const unsigned& current, MultiValue& myvals ) const {
   }
 }
 
+void Histogram::apply(){
+  if( !myhist->wasForced() ) return ;
+  in_apply=true; 
+  // Run the loop to calculate the forces
+  runAllTasks(); finishAveraging(); 
+  // We now need to retrieve the buffer and set the forces on the atoms
+  myhist->applyForce( forcesToApply ); 
+  // Now make the forces make sense for the virial
+  unsigned fbase=0, tbase=0, vbase = getNumberOfDerivatives() - myvessels.size()*9;
+  for(unsigned i=vbase;i<vbase+9;++i) finalForces[i]=0.0;
+  for(unsigned i=0;i<myvessels.size();++i){
+      for(unsigned j=0;j<myvessels[i]->getNumberOfDerivatives()-9;++j){
+          finalForces[fbase + j] = forcesToApply[tbase + j];
+      }
+      unsigned k=0;
+      for(unsigned j=myvessels[i]->getNumberOfDerivatives()-9;j<myvessels[i]->getNumberOfDerivatives();++j){
+          finalForces[vbase + k] += forcesToApply[tbase + j]; k++;
+      }
+      fbase += myvessels[i]->getNumberOfDerivatives() - 9;
+      tbase += myvessels[i]->getNumberOfDerivatives();
+  }
+  // And set the final forces on the atoms
+  setForcesOnAtoms( finalForces );
+  // Reset everything for next regular loop
+  in_apply=false; 
+}
+
 }
 }
diff --git a/src/analysis/Makefile b/src/analysis/Makefile
index bdf98d20a..02080ce4b 100644
--- a/src/analysis/Makefile
+++ b/src/analysis/Makefile
@@ -1,4 +1,4 @@
-USE=core tools reference vesselbase gridtools
+USE=core tools reference vesselbase gridtools multicolvar
 
 #generic makefile
 include ../maketools/make.module
diff --git a/src/core/ActionPilot.cpp b/src/core/ActionPilot.cpp
index 5e24138bc..10007dedc 100644
--- a/src/core/ActionPilot.cpp
+++ b/src/core/ActionPilot.cpp
@@ -48,6 +48,10 @@ int ActionPilot::getStride()const{
   return stride;
 }
 
+void ActionPilot::setStride( const int& n ){
+  stride=n;
+}
+
 }
 
 
diff --git a/src/core/ActionPilot.h b/src/core/ActionPilot.h
index 45acc9386..007508ca6 100644
--- a/src/core/ActionPilot.h
+++ b/src/core/ActionPilot.h
@@ -46,6 +46,8 @@ public:
   static void registerKeywords(Keywords& keys);
 /// Check if the action is active on this step
   virtual bool onStep()const;
+/// Set the value of the stride
+  void setStride( const int& n );
 /// Get the stride
   int getStride()const;
 };
diff --git a/src/gridtools/ActionWithGrid.cpp b/src/gridtools/ActionWithGrid.cpp
index d95d6cc69..601534842 100644
--- a/src/gridtools/ActionWithGrid.cpp
+++ b/src/gridtools/ActionWithGrid.cpp
@@ -63,6 +63,35 @@ void ActionWithGrid::createGrid( const std::string& type, const std::string& inp
   } 
 }
 
+void ActionWithGrid::turnOnDerivatives(){
+  needsDerivatives(); ActionWithValue::turnOnDerivatives(); 
+  if( getStride()==1 ) setStride(0);
+  else if( getStride()!=0 ) error("conflicting instructions for grid - stride was set but must be evaluated on every step for derivatives - remove STRIDE keyword");
+  if( clearstride>1 ) error("conflicting instructions for grid - CLEAR was set but grid must be reset on every step for derivatives - remove CLEAR keyword" ); 
+  if( weights.size()>0 ) error("conflicting instructions for grid - LOGWEIGHTS was set but weights are not considered when derivatives of grid are evaluated - remove LOGWEIGHTS keyword"); 
+}
+
+void ActionWithGrid::calculate(){
+  // Do nothing if derivatives are not required
+  if( doNotCalculateDerivatives() ) return;
+  // Clear on every step
+  if( mygrid ) clearAverage();
+  // Should not be any reweighting so just set these accordingly
+  lweight=0; cweight=1.0;
+  // Prepare to do the averaging
+  prepareForAveraging();
+  // Run all the tasks (if required
+  if( useRunAllTasks ) runAllTasks();
+  // This the averaging if it is not done using task list
+  else performOperations( true );
+  // Update the norm
+  if( mygrid ) mygrid->setNorm( cweight );
+  // Finish the averaging
+  finishAveraging();
+  // And reset for next step
+  if( mygrid ) mygrid->reset();
+}
+
 void ActionWithGrid::performTask( const unsigned& task_index, const unsigned& current, MultiValue& myvals ) const {
   // Set the weight of this point
   myvals.setValue( 0, cweight ); compute( current, myvals );
diff --git a/src/gridtools/ActionWithGrid.h b/src/gridtools/ActionWithGrid.h
index b8ba6d294..f87c5e6e6 100644
--- a/src/gridtools/ActionWithGrid.h
+++ b/src/gridtools/ActionWithGrid.h
@@ -44,6 +44,8 @@ protected:
 public:
   static void registerKeywords( Keywords& keys );
   explicit ActionWithGrid( const ActionOptions& ); 
+  virtual void turnOnDerivatives();
+  void calculate();
   void performTask( const unsigned& task_index, const unsigned& current, MultiValue& myvals ) const ;
   virtual void compute( const unsigned& current, MultiValue& myvals ) const = 0;
 };
diff --git a/src/gridtools/ActionWithInputGrid.h b/src/gridtools/ActionWithInputGrid.h
index ea5ae67b6..0799f4de6 100644
--- a/src/gridtools/ActionWithInputGrid.h
+++ b/src/gridtools/ActionWithInputGrid.h
@@ -44,6 +44,7 @@ public:
   virtual void prepareForAveraging();
   virtual bool checkAllActive() const { return true; }
   virtual void performOperations( const bool& from_update );
+  virtual void apply(){};
 };
 
 inline
diff --git a/src/gridtools/ActionWithIntegral.cpp b/src/gridtools/ActionWithIntegral.cpp
new file mode 100644
index 000000000..addfb46db
--- /dev/null
+++ b/src/gridtools/ActionWithIntegral.cpp
@@ -0,0 +1,62 @@
+/* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+   Copyright (c) 2016 The plumed team
+   (see the PEOPLE file at the root of the distribution for a list of names)
+
+   See http://www.plumed.org for more information.
+
+   This file is part of plumed, version 2.
+
+   plumed is free software: you can redistribute it and/or modify
+   it under the terms of the GNU Lesser General Public License as published by
+   the Free Software Foundation, either version 3 of the License, or
+   (at your option) any later version.
+
+   plumed is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+   GNU Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public License
+   along with plumed.  If not, see <http://www.gnu.org/licenses/>.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ */
+#include "ActionWithIntegral.h"
+
+namespace PLMD {
+namespace gridtools {
+
+void ActionWithIntegral::registerKeywords( Keywords& keys ){
+  ActionWithInputGrid::registerKeywords( keys );
+  keys.remove("KERNEL"); keys.remove("BANDWIDTH"); 
+  keys.remove("CLEAR"); keys.add("compulsory","CLEAR","1","the frequency with which to clear all the accumulated data.");
+}
+
+ActionWithIntegral::ActionWithIntegral(const ActionOptions&ao):
+Action(ao),
+ActionWithInputGrid(ao)
+{
+  plumed_assert( ingrid->getNumberOfComponents()==1 ); 
+  // Retrieve the volume of the grid (for integration)
+  volume = ingrid->getCellVolume();
+  // Create something that is going to calculate the sum of all the values 
+  // at the various grid points - this is going to be the integral
+  std::string fake_input; addVessel( "SUM", fake_input, -1 ); readVesselKeywords();
+  // Now create task list - number of tasks is equal to the number of grid points
+  // as we have to evaluate the function at each grid points
+  for(unsigned i=0;i<ingrid->getNumberOfPoints();++i) addTaskToList(i);
+  // And activate all tasks
+  deactivateAllTasks(); 
+  for(unsigned i=0;i<ingrid->getNumberOfPoints();++i) taskFlags[i]=1;
+  lockContributors();
+}
+
+void ActionWithIntegral::turnOnDerivatives(){
+  ActionWithGrid::turnOnDerivatives();
+  forcesToApply.resize( ingrid->getNumberOfPoints() );
+}
+
+void ActionWithIntegral::apply(){
+  if( getForcesFromVessels( forcesToApply ) ) ingrid->setForce( forcesToApply );
+}
+
+}
+}
diff --git a/src/gridtools/ActionWithIntegral.h b/src/gridtools/ActionWithIntegral.h
new file mode 100644
index 000000000..aa7309163
--- /dev/null
+++ b/src/gridtools/ActionWithIntegral.h
@@ -0,0 +1,60 @@
+/* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+   Copyright (c) 2016 The plumed team
+   (see the PEOPLE file at the root of the distribution for a list of names)
+  
+   See http://www.plumed.org for more information.
+  
+   This file is part of plumed, version 2.
+
+   plumed is free software: you can redistribute it and/or modify
+   it under the terms of the GNU Lesser General Public License as published by
+   the Free Software Foundation, either version 3 of the License, or
+   (at your option) any later version.
+  
+   plumed is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+   GNU Lesser General Public License for more details.
+  
+   You should have received a copy of the GNU Lesser General Public License
+   along with plumed.  If not, see <http://www.gnu.org/licenses/>.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ */
+#ifndef __PLUMED_gridtools_ActionWithIntegral_h
+#define __PLUMED_gridtools_ActionWithIntegral_h
+
+#include "ActionWithInputGrid.h"
+
+namespace PLMD {
+namespace gridtools {
+
+class ActionWithIntegral : public ActionWithInputGrid {
+private:
+  double volume;
+  std::vector<double> forcesToApply;
+protected:
+/// Get the volume of a grid box
+  double getVolume() const ;
+public:
+  static void registerKeywords( Keywords& keys );
+  explicit ActionWithIntegral(const ActionOptions&ao);
+  unsigned getNumberOfDerivatives();
+  void turnOnDerivatives();
+/// Unless I am mistaken an integral should never be a periodic function
+  bool isPeriodic(){ return false; }
+  void apply();
+};
+
+inline
+double ActionWithIntegral::getVolume() const {
+  return volume;
+}
+
+inline
+unsigned ActionWithIntegral::getNumberOfDerivatives(){
+  return ingrid->getNumberOfPoints();
+}
+
+}
+}
+#endif
+
diff --git a/src/gridtools/AverageOnGrid.h b/src/gridtools/AverageOnGrid.h
index 77638f5a7..8b224bf05 100644
--- a/src/gridtools/AverageOnGrid.h
+++ b/src/gridtools/AverageOnGrid.h
@@ -32,8 +32,10 @@ public:
   static void registerKeywords( Keywords& keys );
   explicit AverageOnGrid( const vesselbase::VesselOptions& da );
   void accumulate( const unsigned& ipoint, const double& weight, const double& dens, const std::vector<double>& der, std::vector<double>& buffer ) const ;
+  void accumulateForce( const unsigned& ipoint, const double& weight, const std::vector<double>& der, std::vector<double>& intforce ) const { plumed_error(); }
   double getGridElement( const unsigned& ipoint, const unsigned& jelement ) const ;
   unsigned getNumberOfComponents() const ;
+  void getFinalForces( const std::vector<double>& buffer, std::vector<double>& finalForces ){ plumed_error(); }
 };
 
 inline
diff --git a/src/gridtools/GridVessel.cpp b/src/gridtools/GridVessel.cpp
index 750b06c8e..08b9bb19d 100644
--- a/src/gridtools/GridVessel.cpp
+++ b/src/gridtools/GridVessel.cpp
@@ -38,7 +38,8 @@ AveragingVessel(da),
 bounds_set(false),
 cube_units(1.0),
 noderiv(false),
-npoints(0)
+npoints(0),
+wasforced(false)
 {
   std::vector<std::string> compnames; parseVector("COMPONENTS",compnames);
   std::vector<std::string> coordnames; parseVector("COORDINATES",coordnames);
@@ -120,7 +121,8 @@ std::string GridVessel::description(){
 
 void GridVessel::resize(){
   plumed_massert( nper>0, "Number of datapoints at each grid point has not been set");
-  resizeBuffer( getNumberOfBufferPoints()*nper ); setDataSize( npoints*nper ); 
+  resizeBuffer( getNumberOfBufferPoints()*nper + 1 + 2*getAction()->getNumberOfDerivatives() ); 
+  setDataSize( npoints*nper ); forces.resize( npoints );
   if( active.size()!=npoints) active.resize( npoints, true );
 }
 
@@ -205,6 +207,11 @@ void GridVessel::calculate( const unsigned& current, MultiValue& myvals, std::ve
   for(unsigned i=0;i<nper;++i) buffer[bufstart + nper*current + i] += myvals.get(i+1);
 }
 
+void GridVessel::finish( const std::vector<double>& buffer ){
+  if( wasforced ) getFinalForces( buffer, finalForces );
+  else AveragingVessel::finish( buffer );
+}
+
 double GridVessel::getGridElement( const std::vector<unsigned>& indices, const unsigned& jelement ) const {
   return getGridElement( getIndex( indices ), jelement );
 }
@@ -344,6 +351,22 @@ void GridVessel::activateThesePoints( const std::vector<bool>& to_activate ){
   for(unsigned i=0;i<npoints;++i) active[i]=to_activate[i];
 }
 
+void GridVessel::setForce( const std::vector<double>& inforces ){
+  plumed_dbg_assert( inforces.size()==npoints );
+  wasforced=true; for(unsigned i=0;i<npoints;++i) forces[i]=inforces[i];
+}
+
+bool GridVessel::wasForced() const {
+  return wasforced;
+}
+
+bool GridVessel::applyForce( std::vector<double>& fforces ){
+  plumed_dbg_assert( fforces.size()==finalForces.size() ); 
+  if( !wasforced ) return false;
+  for(unsigned i=0;i<finalForces.size();++i) fforces[i]=finalForces[i]; 
+  wasforced=false; return true;
+}
+
 }
 }
 
diff --git a/src/gridtools/GridVessel.h b/src/gridtools/GridVessel.h
index a0aacf47c..2683ddbc6 100644
--- a/src/gridtools/GridVessel.h
+++ b/src/gridtools/GridVessel.h
@@ -50,7 +50,13 @@ private:
  std::vector<unsigned> nbin;
 /// The grid point that was requested last by getGridPointCoordinates
  unsigned currentGridPoint;
+/// Is forced
+ bool wasforced;
+/// The forces that will be output at the end of the calculation
+ std::vector<double> finalForces;
 protected:
+/// Forces acting on grid elements
+ std::vector<double> forces;
 /// Do we have derivatives
  bool noderiv;
 /// The names of the various columns in the grid file
@@ -140,6 +146,8 @@ public:
  double getGridExtent( const unsigned& i ) const ;
 /// Copy data from the action into the grid
  virtual void calculate( const unsigned& current, MultiValue& myvals, std::vector<double>& buffer, std::vector<unsigned>& der_list ) const ;
+/// Finish the calculation
+ virtual void finish( const std::vector<double>& buffer );
 /// This ensures that Gaussian cube fies are in correct units
  void setCubeUnits( const double& units );
 /// This ensures that Gaussian cube files are in correct units
@@ -154,6 +162,14 @@ public:
  void activateThesePoints( const std::vector<bool>& to_activate );
 /// Is this point active
  bool inactive( const unsigned& ip ) const ;
+/// This retrieves the final force
+ virtual void getFinalForces( const std::vector<double>& buffer, std::vector<double>& finalForces ){ plumed_error(); }
+/// Apply the forces
+ void setForce( const std::vector<double>& inforces ); 
+/// Was a force added to the grid
+ bool wasForced() const ;
+/// And retrieve the forces
+ bool applyForce( std::vector<double>& fforces );
 };
 
 inline
diff --git a/src/gridtools/HistogramOnGrid.cpp b/src/gridtools/HistogramOnGrid.cpp
index b227ef693..ff026231f 100644
--- a/src/gridtools/HistogramOnGrid.cpp
+++ b/src/gridtools/HistogramOnGrid.cpp
@@ -87,7 +87,7 @@ std::vector<Value*> HistogramOnGrid::getVectorOfValues() const {
 
 void HistogramOnGrid::calculate( const unsigned& current, MultiValue& myvals, std::vector<double>& buffer, std::vector<unsigned>& der_list ) const {
   if( addOneKernelAtATime ){
-     plumed_dbg_assert( myvals.getNumberOfValues()==2 );
+     plumed_dbg_assert( myvals.getNumberOfValues()==2 && !wasforced );
      std::vector<double> der( dimension ); 
      for(unsigned i=0;i<dimension;++i) der[i]=myvals.getDerivative( 1, i );
      accumulate( getAction()->getPositionInCurrentTaskList(current), myvals.get(0), myvals.get(1), der, buffer );
@@ -105,7 +105,9 @@ void HistogramOnGrid::calculate( const unsigned& current, MultiValue& myvals, st
          plumed_dbg_assert( num_neigh==1 );
          accumulate( neighbors[0], weight, 1.0, der, buffer );
      } else {
-         std::vector<Value*> vv( getVectorOfValues() );
+         double totwforce=0.0;
+         std::vector<double> intforce( 2*dimension, 0.0 ); 
+         std::vector<Value*> vv( getVectorOfValues() ); 
 
          double newval; std::vector<double> xx( dimension );
          for(unsigned i=0;i<num_neigh;++i){
@@ -113,11 +115,34 @@ void HistogramOnGrid::calculate( const unsigned& current, MultiValue& myvals, st
              if( inactive( ineigh ) ) continue ;
              getGridPointCoordinates( ineigh, xx );
              for(unsigned j=0;j<dimension;++j) vv[j]->set(xx[j]);
-             newval = kernel->evaluate( vv, der, true );
+             newval = kernel->evaluate( vv, der, true ); 
              accumulate( ineigh, weight, newval, der, buffer );
+             if( wasForced() ){  
+                 accumulateForce( ineigh, weight, der, intforce ); 
+                 totwforce += myvals.get( 1+dimension )*newval*forces[ineigh];
+             } 
          }
-         delete kernel;
-         for(unsigned i=0;i<dimension;++i) delete vv[i];
+         if( wasForced() ){
+             unsigned nder = getAction()->getNumberOfDerivatives();
+             unsigned gridbuf = getNumberOfBufferPoints()*getNumberOfQuantities(); 
+             for(unsigned j=0;j<dimension;++j){
+                 for(unsigned k=0;k<myvals.getNumberActive();++k){
+                     // Minus sign here as we are taking derivative with respect to position of center of kernel NOT derivative wrt to
+                     // grid point
+                     unsigned kder=myvals.getActiveIndex(k); 
+                     buffer[ bufstart + gridbuf + kder ] -= intforce[j]*myvals.getDerivative( j+1, kder ); 
+                 }
+             }
+             // Accumulate the sum of all the weights
+             buffer[ bufstart + gridbuf + nder ] += myvals.get(0);   
+             // Add the derivatives of the weights into the force -- this is separate loop as weights of all parts are considered together
+             for(unsigned k=0;k<myvals.getNumberActive();++k){
+                 unsigned kder=myvals.getActiveIndex(k); 
+                 buffer[ bufstart + gridbuf + kder ] += totwforce*myvals.getDerivative( 0, kder );
+                 buffer[ bufstart + gridbuf + nder + 1 + kder ] += myvals.getDerivative( 0, kder );
+             }
+         }
+         delete kernel; for(unsigned i=0;i<dimension;++i) delete vv[i];
      }
   }
 }
@@ -127,6 +152,27 @@ void HistogramOnGrid::accumulate( const unsigned& ipoint, const double& weight,
   if( der.size()>0 ) for(unsigned j=0;j<dimension;++j) buffer[bufstart+nper*ipoint + 1 + j] += weight*der[j]; 
 }
 
+void HistogramOnGrid::accumulateForce( const unsigned& ipoint, const double& weight, const std::vector<double>& der, std::vector<double>& intforce ) const {
+  for(unsigned j=0;j<der.size();++j) intforce[j] += forces[ipoint]*weight*der[j];
+}
+
+void HistogramOnGrid::getFinalForces( const std::vector<double>& buffer, std::vector<double>& finalForces ){
+  if( finalForces.size()!=getAction()->getNumberOfDerivatives() ) finalForces.resize( getAction()->getNumberOfDerivatives() );
+  // And the final force
+  unsigned nder = getAction()->getNumberOfDerivatives(); 
+  // Derivatives due to normalization
+  unsigned gridbuf = getNumberOfBufferPoints()*getNumberOfQuantities();
+  for(unsigned i=0;i<finalForces.size();++i) finalForces[i] = buffer[ bufstart + gridbuf + i ]; 
+  // Derivatives due to normalization
+  if( !noAverage() ){
+      unsigned wderstart = bufstart + gridbuf + nder;
+      for(unsigned ipoint=0;ipoint<getNumberOfPoints();++ipoint){
+           double pref = forces[ipoint]*buffer[ bufstart + ipoint*nper ] / buffer[wderstart];
+           for(unsigned j=0;j<finalForces.size();++j) finalForces[j] -= pref*buffer[ wderstart + 1 + j ];
+      }
+  }
+}
+
 void HistogramOnGrid::finish( const std::vector<double>& buffer ){
   if( addOneKernelAtATime ){
      for(unsigned i=0;i<getAction()->getCurrentNumberOfActiveTasks();++i){ 
diff --git a/src/gridtools/HistogramOnGrid.h b/src/gridtools/HistogramOnGrid.h
index 18bcf19eb..91fd5db11 100644
--- a/src/gridtools/HistogramOnGrid.h
+++ b/src/gridtools/HistogramOnGrid.h
@@ -47,10 +47,12 @@ public:
   void calculate( const unsigned& current, MultiValue& myvals, std::vector<double>& buffer, std::vector<unsigned>& der_list ) const ;
   void finish( const std::vector<double>& buffer );
   virtual void accumulate( const unsigned& ipoint, const double& weight, const double& dens, const std::vector<double>& der, std::vector<double>& buffer ) const ;
+  virtual void accumulateForce( const unsigned& ipoint, const double& weight, const std::vector<double>& der, std::vector<double>& intforce ) const ;
   unsigned getNumberOfBufferPoints() const ;
   KernelFunctions* getKernelAndNeighbors( std::vector<double>& point, unsigned& num_neigh, std::vector<unsigned>& neighbors ) const;
   std::vector<Value*> getVectorOfValues() const ;
   void addOneKernelEachTimeOnly(){ addOneKernelAtATime=true; }
+  virtual void getFinalForces( const std::vector<double>& buffer, std::vector<double>& finalForces );
   bool noDiscreteKernels() const ;
 };
 
diff --git a/src/gridtools/IntegrateGrid.cpp b/src/gridtools/IntegrateGrid.cpp
new file mode 100644
index 000000000..11538cc3a
--- /dev/null
+++ b/src/gridtools/IntegrateGrid.cpp
@@ -0,0 +1,53 @@
+/* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+   Copyright (c) 2016 The plumed team
+   (see the PEOPLE file at the root of the distribution for a list of names)
+
+   See http://www.plumed.org for more information.
+
+   This file is part of plumed, version 2.
+
+   plumed is free software: you can redistribute it and/or modify
+   it under the terms of the GNU Lesser General Public License as published by
+   the Free Software Foundation, either version 3 of the License, or
+   (at your option) any later version.
+
+   plumed is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+   GNU Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public License
+   along with plumed.  If not, see <http://www.gnu.org/licenses/>.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ */
+#include "core/ActionRegister.h"
+#include "ActionWithIntegral.h"
+
+namespace PLMD {
+namespace gridtools {
+
+class IntegrateGrid : public ActionWithIntegral {
+public:
+  static void registerKeywords( Keywords& keys );
+  explicit IntegrateGrid(const ActionOptions&ao);
+  void compute( const unsigned& current, MultiValue& myvals ) const ;
+};
+
+PLUMED_REGISTER_ACTION(IntegrateGrid,"INTEGRATE_GRID")
+
+void IntegrateGrid::registerKeywords( Keywords& keys ){
+  ActionWithIntegral::registerKeywords( keys );
+}
+
+IntegrateGrid::IntegrateGrid(const ActionOptions&ao):
+Action(ao),
+ActionWithIntegral(ao)
+{
+}
+
+void IntegrateGrid::compute( const unsigned& current, MultiValue& myvals ) const {
+  myvals.setValue( 0, 1.0 ); myvals.setValue( 1, getVolume()*getFunctionValue( current ) );
+  if( !doNotCalculateDerivatives() ) myvals.addDerivative( 1, current, getVolume() );
+}
+
+}
+}
diff --git a/src/multicolvar/MultiColvarDensity.cpp b/src/multicolvar/MultiColvarDensity.cpp
index 9fffc355e..20c3f0354 100644
--- a/src/multicolvar/MultiColvarDensity.cpp
+++ b/src/multicolvar/MultiColvarDensity.cpp
@@ -104,6 +104,7 @@ public:
   void clearAverage();
   void prepareForAveraging();
   void compute( const unsigned& , MultiValue& ) const ;
+  void apply(){}
 };
 
 PLUMED_REGISTER_ACTION(MultiColvarDensity,"MULTICOLVARDENS")
diff --git a/src/vesselbase/ActionWithAveraging.cpp b/src/vesselbase/ActionWithAveraging.cpp
index b295bdbc2..e6111a769 100644
--- a/src/vesselbase/ActionWithAveraging.cpp
+++ b/src/vesselbase/ActionWithAveraging.cpp
@@ -43,10 +43,10 @@ ActionAtomistic(ao),
 ActionWithArguments(ao),
 ActionWithValue(ao),
 ActionWithVessel(ao),
-lweight(0),cweight(0),
 myaverage(NULL),
 useRunAllTasks(false),
-clearstride(0)
+clearstride(0),
+lweight(0),cweight(0)
 {
   if( keywords.exists("CLEAR") ){
       parse("CLEAR",clearstride);
@@ -93,7 +93,7 @@ void ActionWithAveraging::calculateNumericalDerivatives(PLMD::ActionWithValue*){
 }
 
 void ActionWithAveraging::update(){
-  if( getStep()==0 || !onStep() ) return;
+  if( (clearstride!=1 && getStep()==0) || !onStep() ) return;
   // Clear if it is time to reset
   if( myaverage ){
       if( myaverage->wasreset() ) clearAverage();
diff --git a/src/vesselbase/ActionWithAveraging.h b/src/vesselbase/ActionWithAveraging.h
index 4d90431ad..fe33827e7 100644
--- a/src/vesselbase/ActionWithAveraging.h
+++ b/src/vesselbase/ActionWithAveraging.h
@@ -53,19 +53,21 @@ friend class AveragingVessel;
 private:
 /// The vessel which is used to compute averages
   AveragingVessel* myaverage;
-/// This ensures runAllTasks is used
-  bool useRunAllTasks;
-/// The frequency with which to clear the grid
-  unsigned clearstride;
 /// The weights we are going to use for reweighting
   std::vector<Value*> weights;
 /// Are we accumulated the unormalized quantity
   bool unormalised;
 protected:
+/// This ensures runAllTasks is used
+  bool useRunAllTasks;
+/// The frequency with which to clear the grid
+  unsigned clearstride;
 /// The current weight and its logarithm
   double lweight, cweight;
 /// Set the averaging action
   void setAveragingAction( AveragingVessel* av_vessel, const bool& usetasks );
+/// Check if we are using the normalization condition when calculating this quantity
+  bool noNormalization() const ;
 public:
   static void registerKeywords( Keywords& keys );
   explicit ActionWithAveraging( const ActionOptions& );
@@ -76,8 +78,6 @@ public:
   unsigned getNumberOfArguments() const ;
 /// Overwrite ActionWithArguments getArguments() so that we don't return the bias
   std::vector<Value*> getArguments();  
-  void calculate(){}
-  void apply(){}
   void update();
 /// This does the clearing of the action
   virtual void clearAverage();
@@ -101,6 +101,11 @@ std::vector<Value*> ActionWithAveraging::getArguments(){
   return arg_vals;
 }
 
+inline
+bool ActionWithAveraging::noNormalization() const {
+  return unormalised;
+}
+
 }
 }
 #endif
diff --git a/src/vesselbase/AveragingVessel.h b/src/vesselbase/AveragingVessel.h
index cbf679221..0d5ad0cfb 100644
--- a/src/vesselbase/AveragingVessel.h
+++ b/src/vesselbase/AveragingVessel.h
@@ -62,7 +62,7 @@ public:
 /// Functions for dealing with normalisation constant
  void setNorm( const double& snorm );
  double getNorm() const ;
- bool applyForce(  std::vector<double>& forces ){ return false; } 
+ virtual bool applyForce(  std::vector<double>& forces ){ return false; } 
 };
 
 inline
diff --git a/src/vesselbase/StoreDataVessel.h b/src/vesselbase/StoreDataVessel.h
index 210387637..ae75aa6ee 100644
--- a/src/vesselbase/StoreDataVessel.h
+++ b/src/vesselbase/StoreDataVessel.h
@@ -87,6 +87,8 @@ public:
   virtual unsigned getNumberOfStoredValues() const ;
 /// Get the index to store a particular index inside
   unsigned getStoreIndex( const unsigned& ) const ;
+/// Get the true index of a quantity from the index it is stored in
+  unsigned getTrueIndex( const unsigned& ) const ;
 /// Recalculate one of the base quantities
   void recalculateStoredQuantity( const unsigned& myelm, MultiValue& myvals );
 /// Set a hard cutoff on the weight of an element
@@ -180,6 +182,11 @@ unsigned StoreDataVessel::getStoreIndex( const unsigned& ind ) const {
   plumed_merror("requested task is not active");
 }
 
+inline
+unsigned StoreDataVessel::getTrueIndex( const unsigned& ind ) const {
+  return getAction()->indexOfTaskInFullList[ind];
+}
+
 inline
 void StoreDataVessel::recalculateStoredQuantity( const unsigned& myelem, MultiValue& myvals ){
   getAction()->performTask( myelem, getAction()->getTaskCode(myelem), myvals );
diff --git a/src/vesselbase/Vessel.h b/src/vesselbase/Vessel.h
index c67b0dad7..f193e264c 100644
--- a/src/vesselbase/Vessel.h
+++ b/src/vesselbase/Vessel.h
@@ -118,6 +118,8 @@ protected:
   double getTolerance() const ;
 /// Return the value of the neighbor list tolerance
   double getNLTolerance() const ;
+/// Return the size of the buffer
+  unsigned getSizeOfBuffer() const ;
 /// Set the size of the data buffer
   void resizeBuffer( const unsigned& n );
 public:
@@ -237,6 +239,11 @@ ActionWithVessel* Vessel::getAction() const {
   return action;
 }
 
+inline
+unsigned Vessel::getSizeOfBuffer() const {
+  return bufsize;
+}
+
 }
 }
 #endif
-- 
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