diff --git a/regtest/sizeshape/Makefile b/regtest/sizeshape/Makefile
new file mode 100644
index 0000000000..42480767ae
--- /dev/null
+++ b/regtest/sizeshape/Makefile
@@ -0,0 +1,2 @@
+include ../scripts/module.make
+
diff --git a/regtest/sizeshape/rt-mahadist/Makefile b/regtest/sizeshape/rt-mahadist/Makefile
new file mode 100644
index 0000000000..3703b27cea
--- /dev/null
+++ b/regtest/sizeshape/rt-mahadist/Makefile
@@ -0,0 +1 @@
+include ../../scripts/test.make
diff --git a/regtest/sizeshape/rt-mahadist/config b/regtest/sizeshape/rt-mahadist/config
new file mode 100644
index 0000000000..f2c2f7b285
--- /dev/null
+++ b/regtest/sizeshape/rt-mahadist/config
@@ -0,0 +1,3 @@
+type=driver
+plumed_modules=sizeshape
+arg="--plumed plumed.dat --itrr test_traj.trr"
diff --git a/regtest/sizeshape/rt-mahadist/deriv.reference b/regtest/sizeshape/rt-mahadist/deriv.reference
new file mode 100644
index 0000000000..ed340f8946
--- /dev/null
+++ b/regtest/sizeshape/rt-mahadist/deriv.reference
@@ -0,0 +1,391 @@
+#! FIELDS time parameter d
+ 0.000000 0    0.073
+ 0.000000 1    0.152
+ 0.000000 2   -0.299
+ 0.000000 3    0.128
+ 0.000000 4   -0.403
+ 0.000000 5    0.630
+ 0.000000 6   -1.717
+ 0.000000 7    2.577
+ 0.000000 8   -0.466
+ 0.000000 9    1.793
+ 0.000000 10   -2.024
+ 0.000000 11    0.019
+ 0.000000 12    0.672
+ 0.000000 13   -3.252
+ 0.000000 14    0.580
+ 0.000000 15   -1.216
+ 0.000000 16    2.568
+ 0.000000 17   -0.813
+ 0.000000 18   -0.865
+ 0.000000 19   -1.512
+ 0.000000 20   -0.051
+ 0.000000 21    2.083
+ 0.000000 22    3.175
+ 0.000000 23    1.265
+ 0.000000 24   -2.147
+ 0.000000 25   -0.827
+ 0.000000 26    0.672
+ 0.000000 27    1.087
+ 0.000000 28   -0.619
+ 0.000000 29   -0.977
+ 0.000000 30    0.887
+ 0.000000 31   -0.591
+ 0.000000 32   -1.649
+ 0.000000 33   -2.266
+ 0.000000 34   -2.066
+ 0.000000 35    0.291
+ 0.000000 36    1.479
+ 0.000000 37    2.678
+ 0.000000 38   -1.886
+ 0.000000 39    0.924
+ 0.000000 40    0.730
+ 0.000000 41    3.040
+ 0.000000 42   -2.052
+ 0.000000 43    0.043
+ 0.000000 44    1.569
+ 0.000000 45    2.054
+ 0.000000 46   -1.377
+ 0.000000 47   -4.637
+ 0.000000 48   -2.290
+ 0.000000 49    1.402
+ 0.000000 50    1.496
+ 0.000000 51    0.425
+ 0.000000 52   -0.488
+ 0.000000 53    5.286
+ 0.000000 54    2.387
+ 0.000000 55    1.137
+ 0.000000 56   -2.983
+ 0.000000 57   -2.033
+ 0.000000 58   -5.916
+ 0.000000 59    2.411
+ 0.000000 60    1.649
+ 0.000000 61    4.954
+ 0.000000 62   -3.420
+ 0.000000 63   -1.986
+ 0.000000 64   -0.851
+ 0.000000 65    0.515
+ 0.000000 66    0.930
+ 0.000000 67    0.512
+ 0.000000 68   -0.595
+ 0.000000 69    2.692
+ 0.000000 70    0.575
+ 0.000000 71    3.468
+ 0.000000 72    0.575
+ 0.000000 73   -4.199
+ 0.000000 74    4.022
+ 0.000000 75    3.468
+ 0.000000 76    4.022
+ 0.000000 77  -18.669
+ 1.000000 0    0.484
+ 1.000000 1    0.093
+ 1.000000 2   -0.455
+ 1.000000 3   -1.082
+ 1.000000 4   -0.345
+ 1.000000 5    1.037
+ 1.000000 6    0.900
+ 1.000000 7    1.688
+ 1.000000 8   -0.555
+ 1.000000 9   -0.976
+ 1.000000 10   -1.503
+ 1.000000 11   -0.367
+ 1.000000 12    1.359
+ 1.000000 13   -1.997
+ 1.000000 14    0.144
+ 1.000000 15   -0.158
+ 1.000000 16    4.747
+ 1.000000 17   -1.600
+ 1.000000 18    0.011
+ 1.000000 19   -2.663
+ 1.000000 20    0.513
+ 1.000000 21   -1.477
+ 1.000000 22   -2.846
+ 1.000000 23    3.938
+ 1.000000 24    2.165
+ 1.000000 25    1.594
+ 1.000000 26   -4.052
+ 1.000000 27   -0.637
+ 1.000000 28    1.258
+ 1.000000 29    0.686
+ 1.000000 30   -2.156
+ 1.000000 31    0.128
+ 1.000000 32    1.837
+ 1.000000 33    2.777
+ 1.000000 34   -0.183
+ 1.000000 35   -2.703
+ 1.000000 36   -4.607
+ 1.000000 37   -2.879
+ 1.000000 38    1.985
+ 1.000000 39    4.088
+ 1.000000 40    4.293
+ 1.000000 41    1.664
+ 1.000000 42   -1.597
+ 1.000000 43   -1.907
+ 1.000000 44    0.133
+ 1.000000 45    1.347
+ 1.000000 46    0.062
+ 1.000000 47   -1.966
+ 1.000000 48   -1.623
+ 1.000000 49    1.593
+ 1.000000 50   -0.433
+ 1.000000 51    1.843
+ 1.000000 52   -0.277
+ 1.000000 53   -0.251
+ 1.000000 54    0.647
+ 1.000000 55    1.340
+ 1.000000 56   -2.888
+ 1.000000 57   -0.229
+ 1.000000 58   -4.507
+ 1.000000 59    4.897
+ 1.000000 60    0.495
+ 1.000000 61    2.792
+ 1.000000 62   -1.925
+ 1.000000 63   -2.629
+ 1.000000 64   -0.631
+ 1.000000 65    0.410
+ 1.000000 66    1.053
+ 1.000000 67    0.149
+ 1.000000 68   -0.051
+ 1.000000 69    2.078
+ 1.000000 70    1.930
+ 1.000000 71   -6.979
+ 1.000000 72    1.930
+ 1.000000 73   -1.450
+ 1.000000 74   -1.751
+ 1.000000 75   -6.979
+ 1.000000 76   -1.751
+ 1.000000 77   -1.923
+ 2.000000 0   -0.259
+ 2.000000 1    0.217
+ 2.000000 2   -0.027
+ 2.000000 3    0.413
+ 2.000000 4   -0.461
+ 2.000000 5   -0.096
+ 2.000000 6    0.302
+ 2.000000 7    0.629
+ 2.000000 8   -1.096
+ 2.000000 9   -1.509
+ 2.000000 10    0.249
+ 2.000000 11    1.141
+ 2.000000 12    1.119
+ 2.000000 13   -0.211
+ 2.000000 14    1.538
+ 2.000000 15   -2.266
+ 2.000000 16   -0.915
+ 2.000000 17   -0.134
+ 2.000000 18    1.495
+ 2.000000 19    0.585
+ 2.000000 20   -0.715
+ 2.000000 21    1.914
+ 2.000000 22    0.404
+ 2.000000 23   -0.638
+ 2.000000 24   -2.092
+ 2.000000 25    0.939
+ 2.000000 26    1.288
+ 2.000000 27   -1.100
+ 2.000000 28   -0.123
+ 2.000000 29    0.958
+ 2.000000 30    3.093
+ 2.000000 31   -2.066
+ 2.000000 32   -3.391
+ 2.000000 33   -3.433
+ 2.000000 34   -0.783
+ 2.000000 35    2.963
+ 2.000000 36    6.051
+ 2.000000 37    2.725
+ 2.000000 38   -6.009
+ 2.000000 39   -3.825
+ 2.000000 40   -2.038
+ 2.000000 41    5.326
+ 2.000000 42    1.159
+ 2.000000 43    0.994
+ 2.000000 44   -2.187
+ 2.000000 45   -0.322
+ 2.000000 46   -0.138
+ 2.000000 47   -1.123
+ 2.000000 48   -1.114
+ 2.000000 49    1.470
+ 2.000000 50    2.194
+ 2.000000 51   -0.371
+ 2.000000 52   -2.130
+ 2.000000 53    6.053
+ 2.000000 54   -0.849
+ 2.000000 55   -1.105
+ 2.000000 56   -1.620
+ 2.000000 57    1.027
+ 2.000000 58   -2.146
+ 2.000000 59   -0.858
+ 2.000000 60    0.206
+ 2.000000 61    3.559
+ 2.000000 62   -2.421
+ 2.000000 63    0.784
+ 2.000000 64   -0.097
+ 2.000000 65   -1.587
+ 2.000000 66   -0.425
+ 2.000000 67    0.442
+ 2.000000 68    0.441
+ 2.000000 69   -5.569
+ 2.000000 70   -2.247
+ 2.000000 71    8.952
+ 2.000000 72   -2.247
+ 2.000000 73   -4.776
+ 2.000000 74    7.667
+ 2.000000 75    8.952
+ 2.000000 76    7.667
+ 2.000000 77  -26.507
+ 3.000000 0    0.068
+ 3.000000 1    0.700
+ 3.000000 2   -0.427
+ 3.000000 3   -0.091
+ 3.000000 4   -1.269
+ 3.000000 5    0.587
+ 3.000000 6    0.911
+ 3.000000 7    0.334
+ 3.000000 8   -2.507
+ 3.000000 9   -1.199
+ 3.000000 10   -0.323
+ 3.000000 11    1.455
+ 3.000000 12    0.112
+ 3.000000 13    1.878
+ 3.000000 14    3.936
+ 3.000000 15   -1.360
+ 3.000000 16   -2.231
+ 3.000000 17   -4.126
+ 3.000000 18    2.599
+ 3.000000 19    3.163
+ 3.000000 20    0.524
+ 3.000000 21   -1.154
+ 3.000000 22   -2.645
+ 3.000000 23    2.368
+ 3.000000 24   -0.228
+ 3.000000 25    2.462
+ 3.000000 26   -1.045
+ 3.000000 27   -1.090
+ 3.000000 28   -1.703
+ 3.000000 29   -0.717
+ 3.000000 30    2.890
+ 3.000000 31   -1.979
+ 3.000000 32   -1.998
+ 3.000000 33   -2.846
+ 3.000000 34    0.814
+ 3.000000 35    2.418
+ 3.000000 36    2.685
+ 3.000000 37    2.818
+ 3.000000 38   -0.797
+ 3.000000 39   -1.149
+ 3.000000 40   -1.608
+ 3.000000 41   -0.757
+ 3.000000 42   -1.048
+ 3.000000 43    0.879
+ 3.000000 44    1.609
+ 3.000000 45    0.994
+ 3.000000 46   -2.378
+ 3.000000 47   -1.511
+ 3.000000 48   -0.332
+ 3.000000 49    1.778
+ 3.000000 50   -1.192
+ 3.000000 51    0.477
+ 3.000000 52   -1.921
+ 3.000000 53    3.006
+ 3.000000 54   -0.187
+ 3.000000 55    2.121
+ 3.000000 56   -0.063
+ 3.000000 57    1.103
+ 3.000000 58    0.664
+ 3.000000 59   -0.606
+ 3.000000 60   -2.488
+ 3.000000 61   -2.232
+ 3.000000 62    0.087
+ 3.000000 63    3.094
+ 3.000000 64    0.971
+ 3.000000 65   -0.556
+ 3.000000 66   -1.759
+ 3.000000 67   -0.292
+ 3.000000 68    0.313
+ 3.000000 69    1.322
+ 3.000000 70   -0.060
+ 3.000000 71    3.191
+ 3.000000 72   -0.060
+ 3.000000 73   -2.330
+ 3.000000 74    0.666
+ 3.000000 75    3.191
+ 3.000000 76    0.666
+ 3.000000 77   -3.863
+ 4.000000 0    0.172
+ 4.000000 1   -0.097
+ 4.000000 2   -0.027
+ 4.000000 3   -0.339
+ 4.000000 4    0.132
+ 4.000000 5    0.133
+ 4.000000 6    1.060
+ 4.000000 7   -0.226
+ 4.000000 8   -0.224
+ 4.000000 9   -0.158
+ 4.000000 10   -0.046
+ 4.000000 11   -0.069
+ 4.000000 12   -1.393
+ 4.000000 13   -0.455
+ 4.000000 14   -0.335
+ 4.000000 15    2.032
+ 4.000000 16    2.215
+ 4.000000 17    0.346
+ 4.000000 18   -1.129
+ 4.000000 19   -0.408
+ 4.000000 20    0.120
+ 4.000000 21    1.362
+ 4.000000 22   -2.677
+ 4.000000 23    0.978
+ 4.000000 24   -1.485
+ 4.000000 25    2.101
+ 4.000000 26   -0.197
+ 4.000000 27    2.096
+ 4.000000 28   -0.645
+ 4.000000 29   -1.466
+ 4.000000 30   -3.881
+ 4.000000 31   -1.356
+ 4.000000 32   -0.126
+ 4.000000 33    2.639
+ 4.000000 34    0.931
+ 4.000000 35    2.695
+ 4.000000 36   -1.438
+ 4.000000 37   -1.618
+ 4.000000 38   -1.701
+ 4.000000 39    1.900
+ 4.000000 40    6.712
+ 4.000000 41    0.583
+ 4.000000 42   -0.214
+ 4.000000 43   -6.084
+ 4.000000 44    1.579
+ 4.000000 45   -2.135
+ 4.000000 46    2.667
+ 4.000000 47   -2.042
+ 4.000000 48    0.728
+ 4.000000 49    0.167
+ 4.000000 50    0.479
+ 4.000000 51    1.249
+ 4.000000 52    0.120
+ 4.000000 53    0.647
+ 4.000000 54   -3.243
+ 4.000000 55   -0.523
+ 4.000000 56   -5.153
+ 4.000000 57    4.809
+ 4.000000 58   -1.885
+ 4.000000 59    4.914
+ 4.000000 60   -1.390
+ 4.000000 61    1.190
+ 4.000000 62   -0.789
+ 4.000000 63   -2.277
+ 4.000000 64   -0.160
+ 4.000000 65   -0.867
+ 4.000000 66    1.034
+ 4.000000 67   -0.054
+ 4.000000 68    0.520
+ 4.000000 69   -6.832
+ 4.000000 70   -0.198
+ 4.000000 71  -10.388
+ 4.000000 72   -0.198
+ 4.000000 73   -2.674
+ 4.000000 74   -3.229
+ 4.000000 75  -10.388
+ 4.000000 76   -3.229
+ 4.000000 77   -7.698
diff --git a/regtest/sizeshape/rt-mahadist/global_avg.txt b/regtest/sizeshape/rt-mahadist/global_avg.txt
new file mode 100644
index 0000000000..3fe06fc8dd
--- /dev/null
+++ b/regtest/sizeshape/rt-mahadist/global_avg.txt
@@ -0,0 +1,23 @@
+4.265825962982551012e+00 2.336690414907679203e-01 3.662809312682036023e+00
+4.214057267340745483e+00 1.072049513718947578e-01 4.314804999781733486e+00
+3.671228981308725103e+00 1.274792340073149510e-01 3.977231205572313577e+00
+2.343698812761148886e+00 -2.841411661146072132e-01 3.478414401687389024e+00
+1.686436487941495699e+00 -8.665088225218358087e-01 4.100811861077803044e+00
+4.360230108844224128e-01 -1.347015411672896512e+00 3.844097514796287030e+00
+3.117457174800847969e-02 -1.024227536411313366e+00 2.585940217022081988e+00
+6.808808862178362675e-01 -5.870202775664047357e-01 2.290245252111865248e+00
+4.586351396567848737e-01 -2.433497671270518359e-01 1.192357902655695634e+00
+4.931328549364416558e-01 2.515992483355074527e-01 2.956934483804412803e-02
+1.406321673638208702e+00 6.682431861735423917e-01 7.908513055476143472e-02
+1.646908036369386430e+00 1.186975749838515615e+00 -8.956858825186609918e-01
+5.912530303131902087e-01 8.617407774506029572e-01 -1.344660953846545715e+00
+8.530666038486142688e-02 2.536604398394486926e-01 -4.506541385680229994e-01
+-8.727821507437001358e-01 -1.296438909175296195e-01 -6.398328611456164383e-01
+-2.067478377458112249e+00 -3.906550201962756819e-01 -1.401863559473397691e+00
+-2.408455843196946056e+00 -6.754022773093291132e-01 -1.106090740276666429e+00
+-3.499742687863982127e+00 -9.747491888605476218e-01 -1.653484266030961436e+00
+-3.548593077032900389e+00 -4.204563480815317056e-01 -3.070014906890367268e+00
+-2.499045339091049645e+00 2.342840846507300567e-01 -3.442979964675248805e+00
+-2.331926055743990922e+00 8.142912721692037170e-01 -4.695739761431558357e+00
+-2.568879301577981611e+00 1.091951813009595762e+00 -5.625053366993444826e+00
+-2.213980543775061705e+00 1.112069908442180788e+00 -5.229306740929514419e+00
diff --git a/regtest/sizeshape/rt-mahadist/global_precision.txt b/regtest/sizeshape/rt-mahadist/global_precision.txt
new file mode 100644
index 0000000000..6cd0c4b4ec
--- /dev/null
+++ b/regtest/sizeshape/rt-mahadist/global_precision.txt
@@ -0,0 +1,23 @@
+1.341060592612849689e+01 -2.432209892648744542e+01 1.533381940780554942e+01 -7.657303908462504083e+00 1.776037152155568455e+00 4.338540983771763671e+00 -3.609963145053606937e+00 2.810411955027056319e+00 -1.043671268084174208e+00 -1.475196332213428052e+00 5.759621172324607130e-01 -8.527089597052168735e-01 9.644241803601940610e-01 -7.723571031369950157e-01 -9.902209008702838045e-01 1.137035356431496114e+00 -7.992059372693161023e-01 -2.078782440990323555e-01 3.883776323509380735e+00 -3.312986073939271581e+00 3.260580287172311076e-01 -2.407079734553001227e-01 7.276273416339069655e-01
+-2.432209892648744542e+01 5.224657127170035409e+01 -4.184495643299391787e+01 2.691929890881726450e+01 -1.133485157950145350e+01 -4.581368136551017045e+00 5.418668441607914055e+00 -4.721462749988712737e+00 7.612938084579194686e-02 3.416864986007456029e+00 -1.915387904627712246e+00 1.300900115134859814e+00 -9.304157403410605598e-01 6.940752221505136488e-01 1.446934261540284483e+00 -1.833895730955714232e+00 1.069137481710279447e+00 7.471315977387903429e-01 -5.206532972119772396e+00 4.646086172638097977e+00 -9.512588298321154046e-01 4.764495021104730443e-01 -8.160183386215708046e-01
+1.533381940780554942e+01 -4.184495643299391787e+01 1.006909570680676609e+02 -9.001875555992035061e+01 -3.451475916336282523e+01 4.163490105870881308e+01 1.599032505888508560e+01 -1.109541021072212708e+01 5.753834304617886808e+00 -5.207568591756271958e-01 -4.504124622286217239e+00 4.467889138659089987e+00 -1.979451375310257388e+00 1.428207880391368700e+00 2.455983409910902082e-01 -3.661844077828322330e-01 1.301366752271428284e+00 1.865718345450012861e-01 -5.661336629183209013e+00 4.110320821833330029e+00 -4.436445385268852210e-02 -9.273163347354730357e-01 3.336243824700811378e-01
+-7.657303908462504083e+00 2.691929890881726450e+01 -9.001875555992035061e+01 1.219943530037234609e+02 -1.755683353726008988e+01 -1.486034955695616766e+01 -3.364530734833785885e+01 1.815403977068739394e+01 5.330083239917091653e+00 -5.787673063672293949e+00 8.949916505352897289e+00 -1.337407792820569874e+01 5.626279540052188999e+00 -3.353587794831017099e+00 -1.939256656091284045e-02 2.049939558614113921e-02 1.365089261756972094e+00 -8.149336646290846531e+00 -1.593034705295243825e+00 2.922427496009236236e+00 2.418471544653607364e+00 1.735086438573440581e+00 5.801075102971581243e-01
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diff --git a/regtest/sizeshape/rt-mahadist/output.reference b/regtest/sizeshape/rt-mahadist/output.reference
new file mode 100644
index 0000000000..4458c2b895
--- /dev/null
+++ b/regtest/sizeshape/rt-mahadist/output.reference
@@ -0,0 +1,6 @@
+#! FIELDS time d
+ 0.000000 6.59472498
+ 1.000000 5.04830502
+ 2.000000 6.38109182
+ 3.000000 5.63516600
+ 4.000000 6.20313896
diff --git a/regtest/sizeshape/rt-mahadist/plumed.dat b/regtest/sizeshape/rt-mahadist/plumed.dat
new file mode 100644
index 0000000000..fdfb926223
--- /dev/null
+++ b/regtest/sizeshape/rt-mahadist/plumed.dat
@@ -0,0 +1,15 @@
+# units
+UNITS LENGTH=A TIME=ps ENERGY=kcal/mol
+
+# make a group of atoms
+GROUP ATOMS=18,20,22,31,33,35,44,46,48,57,59,61,70,72,74,83,85,87,96,98,100,109,111 LABEL=ga_list
+
+# mahadist
+d: SIZESHAPE_POSITION_MAHA_DIST REFERENCE=global_avg.txt PRECISION=global_precision.txt GROUP=ga_list
+
+#print
+PRINT ARG=d STRIDE=1 FILE=output FMT=%8.8f
+
+# dump derivatives
+DUMPDERIVATIVES ARG=d STRIDE=1 FILE=deriv FMT=%8.3f
+
diff --git a/regtest/sizeshape/rt-mahadist/test_traj.trr b/regtest/sizeshape/rt-mahadist/test_traj.trr
new file mode 100644
index 0000000000..6698336cbe
Binary files /dev/null and b/regtest/sizeshape/rt-mahadist/test_traj.trr differ
diff --git a/regtest/sizeshape/rt-sizeshape-mpi/COLVAR.reference b/regtest/sizeshape/rt-sizeshape-mpi/COLVAR.reference
new file mode 100644
index 0000000000..d8dc94d277
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape-mpi/COLVAR.reference
@@ -0,0 +1,6 @@
+#! FIELDS time ld1
+ 0.000000 -53.42214977
+ 1.000000 -53.56701954
+ 2.000000 -51.75886201
+ 3.000000 -53.01109644
+ 4.000000 -52.57399786
diff --git a/regtest/sizeshape/rt-sizeshape-mpi/Makefile b/regtest/sizeshape/rt-sizeshape-mpi/Makefile
new file mode 100644
index 0000000000..3703b27cea
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape-mpi/Makefile
@@ -0,0 +1 @@
+include ../../scripts/test.make
diff --git a/regtest/sizeshape/rt-sizeshape-mpi/config b/regtest/sizeshape/rt-sizeshape-mpi/config
new file mode 100644
index 0000000000..ae37970300
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape-mpi/config
@@ -0,0 +1,4 @@
+type=driver
+mpiprocs=4
+plumed_modules=sizeshape
+arg="--plumed plumed.dat --itrr test_traj.trr"
diff --git a/regtest/sizeshape/rt-sizeshape-mpi/deriv.reference b/regtest/sizeshape/rt-sizeshape-mpi/deriv.reference
new file mode 100644
index 0000000000..b6e896896b
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape-mpi/deriv.reference
@@ -0,0 +1,391 @@
+#! FIELDS time parameter ld1
+ 0.000000 0   -0.747
+ 0.000000 1    1.806
+ 0.000000 2    0.181
+ 0.000000 3   -0.521
+ 0.000000 4    0.961
+ 0.000000 5    0.216
+ 0.000000 6    0.976
+ 0.000000 7   -3.388
+ 0.000000 8   -0.749
+ 0.000000 9   -0.276
+ 0.000000 10   -0.621
+ 0.000000 11   -0.502
+ 0.000000 12   -0.191
+ 0.000000 13    1.000
+ 0.000000 14    0.094
+ 0.000000 15   -0.061
+ 0.000000 16   -0.675
+ 0.000000 17   -0.042
+ 0.000000 18    0.213
+ 0.000000 19   -1.567
+ 0.000000 20   -0.747
+ 0.000000 21   -0.166
+ 0.000000 22   -0.023
+ 0.000000 23   -0.045
+ 0.000000 24   -1.457
+ 0.000000 25    4.729
+ 0.000000 26    0.969
+ 0.000000 27   -0.074
+ 0.000000 28    0.093
+ 0.000000 29   -0.142
+ 0.000000 30   -0.143
+ 0.000000 31   -0.891
+ 0.000000 32   -0.319
+ 0.000000 33   -0.299
+ 0.000000 34    0.502
+ 0.000000 35    0.094
+ 0.000000 36   -0.463
+ 0.000000 37    0.642
+ 0.000000 38    0.019
+ 0.000000 39   -0.248
+ 0.000000 40    0.298
+ 0.000000 41    0.036
+ 0.000000 42    1.153
+ 0.000000 43   -4.986
+ 0.000000 44   -1.449
+ 0.000000 45    1.493
+ 0.000000 46   -5.907
+ 0.000000 47   -1.102
+ 0.000000 48   -1.910
+ 0.000000 49    6.659
+ 0.000000 50    1.163
+ 0.000000 51    0.044
+ 0.000000 52   -0.831
+ 0.000000 53   -0.406
+ 0.000000 54   -0.373
+ 0.000000 55    0.760
+ 0.000000 56    0.136
+ 0.000000 57    0.263
+ 0.000000 58   -1.311
+ 0.000000 59   -0.510
+ 0.000000 60   -2.336
+ 0.000000 61    7.304
+ 0.000000 62    1.589
+ 0.000000 63   -0.525
+ 0.000000 64    1.138
+ 0.000000 65    0.051
+ 0.000000 66    1.655
+ 0.000000 67   -6.270
+ 0.000000 68   -1.306
+ 0.000000 69   50.236
+ 0.000000 70   -6.694
+ 0.000000 71   28.810
+ 0.000000 72  111.741
+ 0.000000 73   66.389
+ 0.000000 74   96.952
+ 0.000000 75  101.422
+ 0.000000 76   25.227
+ 0.000000 77   75.637
+ 1.000000 0   -0.775
+ 1.000000 1    1.792
+ 1.000000 2    0.036
+ 1.000000 3   -0.547
+ 1.000000 4    0.974
+ 1.000000 5    0.134
+ 1.000000 6    1.054
+ 1.000000 7   -3.398
+ 1.000000 8   -0.497
+ 1.000000 9   -0.240
+ 1.000000 10   -0.660
+ 1.000000 11   -0.479
+ 1.000000 12   -0.210
+ 1.000000 13    1.006
+ 1.000000 14    0.026
+ 1.000000 15   -0.069
+ 1.000000 16   -0.612
+ 1.000000 17    0.004
+ 1.000000 18    0.278
+ 1.000000 19   -1.623
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diff --git a/regtest/sizeshape/rt-sizeshape-mpi/global_avg.txt b/regtest/sizeshape/rt-sizeshape-mpi/global_avg.txt
new file mode 100644
index 0000000000..3fe06fc8dd
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape-mpi/global_avg.txt
@@ -0,0 +1,23 @@
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diff --git a/regtest/sizeshape/rt-sizeshape-mpi/global_precision.txt b/regtest/sizeshape/rt-sizeshape-mpi/global_precision.txt
new file mode 100644
index 0000000000..6cd0c4b4ec
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape-mpi/global_precision.txt
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diff --git a/regtest/sizeshape/rt-sizeshape-mpi/ld1_scalings.txt b/regtest/sizeshape/rt-sizeshape-mpi/ld1_scalings.txt
new file mode 100644
index 0000000000..0d6d305798
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape-mpi/ld1_scalings.txt
@@ -0,0 +1,69 @@
+-1.008123761803866980e+00
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diff --git a/regtest/sizeshape/rt-sizeshape-mpi/plumed.dat b/regtest/sizeshape/rt-sizeshape-mpi/plumed.dat
new file mode 100644
index 0000000000..635da1dcf8
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape-mpi/plumed.dat
@@ -0,0 +1,14 @@
+# units
+UNITS LENGTH=A TIME=ps ENERGY=kcal/mol
+
+# make a group of atoms
+GROUP ATOMS=18,20,22,31,33,35,44,46,48,57,59,61,70,72,74,83,85,87,96,98,100,109,111 LABEL=ga_list
+
+# ld1
+ld1: SIZESHAPE_POSITION_LINEAR_PROJ REFERENCE=global_avg.txt PRECISION=global_precision.txt COEFFS=ld1_scalings.txt GROUP=ga_list 
+
+#print
+PRINT ARG=ld1 STRIDE=1 FILE=COLVAR FMT=%8.8f
+
+# dump derivatives
+DUMPDERIVATIVES ARG=ld1 STRIDE=1 FILE=deriv FMT=%8.3f
diff --git a/regtest/sizeshape/rt-sizeshape-mpi/report.txt b/regtest/sizeshape/rt-sizeshape-mpi/report.txt
new file mode 100644
index 0000000000..4eba530597
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape-mpi/report.txt
@@ -0,0 +1,7 @@
+Tue May  7 17:13:00 EDT 2024
+Running regtest in /home/subarna/plumed2-sizeshape/regtest/sizeshape/rt-sizeshape-mpi
+++ Test type: driver
+++ Arguments: --plumed plumed.dat --itrr test_traj.trr
+++ Processors: 4
+/home/subarna/plumed2-sizeshape/regtest/sizeshape/rt-sizeshape-mpi/tmp
+NOT_APPLICABLE (MPI NOT INSTALLED)
diff --git a/regtest/sizeshape/rt-sizeshape-mpi/test_traj.trr b/regtest/sizeshape/rt-sizeshape-mpi/test_traj.trr
new file mode 100644
index 0000000000..6698336cbe
Binary files /dev/null and b/regtest/sizeshape/rt-sizeshape-mpi/test_traj.trr differ
diff --git a/regtest/sizeshape/rt-sizeshape-mpi/tmp/COLVAR.reference b/regtest/sizeshape/rt-sizeshape-mpi/tmp/COLVAR.reference
new file mode 100644
index 0000000000..d8dc94d277
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape-mpi/tmp/COLVAR.reference
@@ -0,0 +1,6 @@
+#! FIELDS time ld1
+ 0.000000 -53.42214977
+ 1.000000 -53.56701954
+ 2.000000 -51.75886201
+ 3.000000 -53.01109644
+ 4.000000 -52.57399786
diff --git a/regtest/sizeshape/rt-sizeshape-mpi/tmp/Makefile b/regtest/sizeshape/rt-sizeshape-mpi/tmp/Makefile
new file mode 100644
index 0000000000..3703b27cea
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape-mpi/tmp/Makefile
@@ -0,0 +1 @@
+include ../../scripts/test.make
diff --git a/regtest/sizeshape/rt-sizeshape-mpi/tmp/config b/regtest/sizeshape/rt-sizeshape-mpi/tmp/config
new file mode 100644
index 0000000000..ae37970300
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape-mpi/tmp/config
@@ -0,0 +1,4 @@
+type=driver
+mpiprocs=4
+plumed_modules=sizeshape
+arg="--plumed plumed.dat --itrr test_traj.trr"
diff --git a/regtest/sizeshape/rt-sizeshape-mpi/tmp/deriv.reference b/regtest/sizeshape/rt-sizeshape-mpi/tmp/deriv.reference
new file mode 100644
index 0000000000..5ac798a64a
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape-mpi/tmp/deriv.reference
@@ -0,0 +1,391 @@
+#! FIELDS time parameter ld1
+ 0.000000 0   -0.7465037939
+ 0.000000 1    1.8058080784
+ 0.000000 2    0.1806327248
+ 0.000000 3   -0.5209154224
+ 0.000000 4    0.9607693215
+ 0.000000 5    0.2164921646
+ 0.000000 6    0.9760679639
+ 0.000000 7   -3.3880242995
+ 0.000000 8   -0.7494042038
+ 0.000000 9   -0.2757943278
+ 0.000000 10   -0.6212341177
+ 0.000000 11   -0.5016006632
+ 0.000000 12   -0.1907059719
+ 0.000000 13    1.0000372605
+ 0.000000 14    0.0937873381
+ 0.000000 15   -0.0614433191
+ 0.000000 16   -0.6754772826
+ 0.000000 17   -0.0422200053
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+ 0.000000 20   -0.7468818026
+ 0.000000 21   -0.1656536320
+ 0.000000 22   -0.0234855690
+ 0.000000 23   -0.0453223542
+ 0.000000 24   -1.4568328943
+ 0.000000 25    4.7293672466
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+ 0.000000 28    0.0928309674
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+ 0.000000 31   -0.8905229315
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+ 0.000000 44   -1.4489906796
+ 0.000000 45    1.4925953053
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+ 0.000000 47   -1.1018027344
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+ 1.000000 10   -0.6598967992
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diff --git a/regtest/sizeshape/rt-sizeshape-mpi/tmp/global_avg.txt b/regtest/sizeshape/rt-sizeshape-mpi/tmp/global_avg.txt
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index 0000000000..3fe06fc8dd
--- /dev/null
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diff --git a/regtest/sizeshape/rt-sizeshape-mpi/tmp/global_precision.txt b/regtest/sizeshape/rt-sizeshape-mpi/tmp/global_precision.txt
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index 0000000000..6cd0c4b4ec
--- /dev/null
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diff --git a/regtest/sizeshape/rt-sizeshape-mpi/tmp/ld1_scalings.txt b/regtest/sizeshape/rt-sizeshape-mpi/tmp/ld1_scalings.txt
new file mode 100644
index 0000000000..0d6d305798
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape-mpi/tmp/ld1_scalings.txt
@@ -0,0 +1,69 @@
+-1.008123761803866980e+00
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diff --git a/regtest/sizeshape/rt-sizeshape-mpi/tmp/plumed.dat b/regtest/sizeshape/rt-sizeshape-mpi/tmp/plumed.dat
new file mode 100644
index 0000000000..d2da872af6
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape-mpi/tmp/plumed.dat
@@ -0,0 +1,14 @@
+# units
+UNITS LENGTH=A TIME=ps ENERGY=kcal/mol
+
+# make a group of atoms
+GROUP ATOMS=18,20,22,31,33,35,44,46,48,57,59,61,70,72,74,83,85,87,96,98,100,109,111 LABEL=ga_list
+
+# ld1
+ld1: SIZESHAPE_POSITION_LINEAR_PROJ REFERENCE=global_avg.txt PRECISION=global_precision.txt COEFFS=ld1_scalings.txt GROUP=ga_list 
+
+#print
+PRINT ARG=ld1 STRIDE=1 FILE=COLVAR FMT=%8.8f
+
+# dump derivatives
+DUMPDERIVATIVES ARG=ld1 STRIDE=1 FILE=deriv
diff --git a/regtest/sizeshape/rt-sizeshape-mpi/tmp/report.txt b/regtest/sizeshape/rt-sizeshape-mpi/tmp/report.txt
new file mode 100644
index 0000000000..3c2ecd79bf
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape-mpi/tmp/report.txt
@@ -0,0 +1,2 @@
+Tue May  7 17:13:00 EDT 2024
+Running regtest in /home/subarna/plumed2-sizeshape/regtest/sizeshape/rt-sizeshape-mpi
diff --git a/regtest/sizeshape/rt-sizeshape-mpi/tmp/test_traj.trr b/regtest/sizeshape/rt-sizeshape-mpi/tmp/test_traj.trr
new file mode 100644
index 0000000000..6698336cbe
Binary files /dev/null and b/regtest/sizeshape/rt-sizeshape-mpi/tmp/test_traj.trr differ
diff --git a/regtest/sizeshape/rt-sizeshape/COLVAR.reference b/regtest/sizeshape/rt-sizeshape/COLVAR.reference
new file mode 100644
index 0000000000..d8dc94d277
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape/COLVAR.reference
@@ -0,0 +1,6 @@
+#! FIELDS time ld1
+ 0.000000 -53.42214977
+ 1.000000 -53.56701954
+ 2.000000 -51.75886201
+ 3.000000 -53.01109644
+ 4.000000 -52.57399786
diff --git a/regtest/sizeshape/rt-sizeshape/Makefile b/regtest/sizeshape/rt-sizeshape/Makefile
new file mode 100644
index 0000000000..3703b27cea
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape/Makefile
@@ -0,0 +1 @@
+include ../../scripts/test.make
diff --git a/regtest/sizeshape/rt-sizeshape/config b/regtest/sizeshape/rt-sizeshape/config
new file mode 100644
index 0000000000..f2c2f7b285
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape/config
@@ -0,0 +1,3 @@
+type=driver
+plumed_modules=sizeshape
+arg="--plumed plumed.dat --itrr test_traj.trr"
diff --git a/regtest/sizeshape/rt-sizeshape/deriv.reference b/regtest/sizeshape/rt-sizeshape/deriv.reference
new file mode 100644
index 0000000000..b6e896896b
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape/deriv.reference
@@ -0,0 +1,391 @@
+#! FIELDS time parameter ld1
+ 0.000000 0   -0.747
+ 0.000000 1    1.806
+ 0.000000 2    0.181
+ 0.000000 3   -0.521
+ 0.000000 4    0.961
+ 0.000000 5    0.216
+ 0.000000 6    0.976
+ 0.000000 7   -3.388
+ 0.000000 8   -0.749
+ 0.000000 9   -0.276
+ 0.000000 10   -0.621
+ 0.000000 11   -0.502
+ 0.000000 12   -0.191
+ 0.000000 13    1.000
+ 0.000000 14    0.094
+ 0.000000 15   -0.061
+ 0.000000 16   -0.675
+ 0.000000 17   -0.042
+ 0.000000 18    0.213
+ 0.000000 19   -1.567
+ 0.000000 20   -0.747
+ 0.000000 21   -0.166
+ 0.000000 22   -0.023
+ 0.000000 23   -0.045
+ 0.000000 24   -1.457
+ 0.000000 25    4.729
+ 0.000000 26    0.969
+ 0.000000 27   -0.074
+ 0.000000 28    0.093
+ 0.000000 29   -0.142
+ 0.000000 30   -0.143
+ 0.000000 31   -0.891
+ 0.000000 32   -0.319
+ 0.000000 33   -0.299
+ 0.000000 34    0.502
+ 0.000000 35    0.094
+ 0.000000 36   -0.463
+ 0.000000 37    0.642
+ 0.000000 38    0.019
+ 0.000000 39   -0.248
+ 0.000000 40    0.298
+ 0.000000 41    0.036
+ 0.000000 42    1.153
+ 0.000000 43   -4.986
+ 0.000000 44   -1.449
+ 0.000000 45    1.493
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diff --git a/regtest/sizeshape/rt-sizeshape/global_avg.txt b/regtest/sizeshape/rt-sizeshape/global_avg.txt
new file mode 100644
index 0000000000..3fe06fc8dd
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape/global_avg.txt
@@ -0,0 +1,23 @@
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diff --git a/regtest/sizeshape/rt-sizeshape/global_precision.txt b/regtest/sizeshape/rt-sizeshape/global_precision.txt
new file mode 100644
index 0000000000..6cd0c4b4ec
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape/global_precision.txt
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diff --git a/regtest/sizeshape/rt-sizeshape/ld1_scalings.txt b/regtest/sizeshape/rt-sizeshape/ld1_scalings.txt
new file mode 100644
index 0000000000..0d6d305798
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape/ld1_scalings.txt
@@ -0,0 +1,69 @@
+-1.008123761803866980e+00
+1.626510375189665680e+00
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diff --git a/regtest/sizeshape/rt-sizeshape/plumed.dat b/regtest/sizeshape/rt-sizeshape/plumed.dat
new file mode 100644
index 0000000000..635da1dcf8
--- /dev/null
+++ b/regtest/sizeshape/rt-sizeshape/plumed.dat
@@ -0,0 +1,14 @@
+# units
+UNITS LENGTH=A TIME=ps ENERGY=kcal/mol
+
+# make a group of atoms
+GROUP ATOMS=18,20,22,31,33,35,44,46,48,57,59,61,70,72,74,83,85,87,96,98,100,109,111 LABEL=ga_list
+
+# ld1
+ld1: SIZESHAPE_POSITION_LINEAR_PROJ REFERENCE=global_avg.txt PRECISION=global_precision.txt COEFFS=ld1_scalings.txt GROUP=ga_list 
+
+#print
+PRINT ARG=ld1 STRIDE=1 FILE=COLVAR FMT=%8.8f
+
+# dump derivatives
+DUMPDERIVATIVES ARG=ld1 STRIDE=1 FILE=deriv FMT=%8.3f
diff --git a/regtest/sizeshape/rt-sizeshape/test_traj.trr b/regtest/sizeshape/rt-sizeshape/test_traj.trr
new file mode 100644
index 0000000000..6698336cbe
Binary files /dev/null and b/regtest/sizeshape/rt-sizeshape/test_traj.trr differ
diff --git a/src/sizeshape/COPYRIGHT b/src/sizeshape/COPYRIGHT
new file mode 100644
index 0000000000..c748bf6906
--- /dev/null
+++ b/src/sizeshape/COPYRIGHT
@@ -0,0 +1,14 @@
+Copyright (c) 2024 by Glen Hocky, New York University on behalf of authors
+
+The sizeshape module 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.
+
+The sizeshape module 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/>.
diff --git a/src/sizeshape/Makefile b/src/sizeshape/Makefile
new file mode 100644
index 0000000000..d9e15607a6
--- /dev/null
+++ b/src/sizeshape/Makefile
@@ -0,0 +1,3 @@
+USE=core tools colvar
+# generic makefile
+include ../maketools/make.module
diff --git a/src/sizeshape/mahadist.cpp b/src/sizeshape/mahadist.cpp
new file mode 100644
index 0000000000..550fcf1474
--- /dev/null
+++ b/src/sizeshape/mahadist.cpp
@@ -0,0 +1,448 @@
+/* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+Copyright (c) 2024 by Glen Hocky, New York University on behalf of authors
+
+The sizeshape module 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.
+
+The sizeshape module 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 "colvar/Colvar.h"
+#include "core/ActionRegister.h"
+#include "tools/Pbc.h"
+#include "tools/File.h"           // Input and output from files 
+#include "tools/Matrix.h"         // Linear Algebra operations
+#include <sstream>
+#include <cmath>
+
+namespace PLMD {
+namespace sizeshape {
+
+//+PLUMEDOC sizeshapeMOD_COLVAR SIZESHAPE_POSITION_MAHA_DIST
+/*
+Calculates Mahalanobis distance of a current configuration from a  given reference configurational distribution in size-and-shape space.
+
+The Mahalanobis distance is given as:
+
+\f[
+d(\mathbf{x}, \mathbf{\mu}, \mathbf{\Sigma}) = \sqrt{(\mathbf{x}-\mathbf{\mu})^T \mathbf{\Sigma}^{-1} (\mathbf{x}-\mathbf{\mu})}
+\f]
+
+Here \f$\mathbf{x}\f$ is the configuration at time t, \f$\mathbf{\mu}\f$ is the reference and \f$\mathbf{\Sigma}^{-1}\f$ is the \f$N \times N\f$ precision matrix.
+
+Size-and-shape Gaussian Mixture Model (shapeGMM) \cite Heidi-shapeGMM-2022 is a probabilistic clustering technique that is used to perform structural clusteing on ensemble of molecular configurations and to obtain reference \f$(\mathbf{\mu})\f$ and precision \f$(\mathbf{\Sigma}^{-1})\f$ corresponding to each of the cluster centers. Please chcek out <a href="https://github.com/mccullaghlab/shapeGMMTorch">shapeGMMTorch-GitHub</a> and <a href="https://pypi.org/project/shapeGMMTorch/"> shapeGMMTorch-PyPI</a> for examples and informations on preforming shapeGMM clustering.
+
+\par Examples
+In the following example, a group is defined with atom indices of selected atoms and then Mahalanobis distance is calculated with respect to the given reference and precision. Each file is a space separated list of 3N floating point numbers.
+
+\plumedfile
+UNITS LENGTH=A TIME=ps ENERGY=kcal/mol
+GROUP ATOMS=18,20,22,31,33,35,44,46,48,57,59,61,70,72,74,83,85,87,96,98,100,109,111 LABEL=ga_list
+#SETTINGS AUXFILE=regtest/sizeshape/rt-mahadist/global_avg.txt
+#SETTINGS AUXFILE=regtest/sizeshape/rt-mahadist/global_precision.txt
+d: SIZESHAPE_POSITION_MAHA_DIST REFERENCE=global_avg.txt PRECISION=global_precision.txt GROUP=ga_list
+PRINT ARG=d STRIDE=1 FILE=output FMT=%8.8f
+\endplumedfile
+
+*/
+//+ENDPLUMEDOC
+
+class position_maha_dist : public Colvar {
+
+private:
+  bool pbc, squared;
+  std::string prec_f_name;      		// precision file name
+  std::string ref_f_name;       		// reference file name
+  IFile in_;             			// create an object of class IFile
+  //Log out_;
+  Matrix<double> ref_str;       	        // coords of reference
+  Matrix<double> mobile_str;    		// coords of mobile
+  Matrix<double> prec;        			// precision data
+  Matrix<double> rotation;
+  Matrix<double> derv_;
+  Matrix<double> derv_numeric;
+  void readinputs();                            // reads the input data
+  double dist;
+  std::vector<AtomNumber> atom_list;            // list of atoms
+  const double SMALL = 1.0E-30;
+  const double delta = 0.00001;
+public:
+  static void registerKeywords( Keywords& keys );
+  explicit position_maha_dist(const ActionOptions&);
+  double determinant(int n, const std::vector<std::vector<double>>* B);
+  void kabsch_rot_mat();   		// gives rotation matrix
+  double cal_maha_dist();    		// calculates the mahalanobis distance
+  void grad_maha(double);        	// calculates the gradient
+  void numeric_maha();        		// calculates the numeric gradient
+  // active methods:
+  void calculate() override;
+};
+
+PLUMED_REGISTER_ACTION(position_maha_dist,"SIZESHAPE_POSITION_MAHA_DIST")
+
+void position_maha_dist::registerKeywords( Keywords& keys ) {
+  Colvar::registerKeywords( keys );
+  keys.add("compulsory", "PRECISION", "Precision Matrix (inverse of covariance)" );
+  keys.add("compulsory", "REFERENCE", "Reference structure.");
+  keys.add("atoms","GROUP","The group of atoms being used");
+  keys.addFlag("SQUARED",false,"Returns the square of distance.");
+}
+
+// constructor function
+position_maha_dist::position_maha_dist(const ActionOptions&ao):
+  PLUMED_COLVAR_INIT(ao),
+  pbc(true),
+  squared(false),
+  dist(0),
+  prec_f_name(""),
+  ref_f_name("")    // Note! no comma here in the last line.
+{
+  parseAtomList("GROUP",atom_list);
+  parse("REFERENCE", ref_f_name);
+  parse("PRECISION", prec_f_name);
+
+  bool nopbc=!pbc;
+  parseFlag("NOPBC",nopbc);
+  parseFlag("SQUARED",squared);
+  pbc=!nopbc;
+
+  checkRead();
+
+  log.printf("  of %u atoms\n",static_cast<unsigned>(atom_list.size()));
+  for(unsigned int i=0; i<atom_list.size(); ++i) {
+    log.printf("  %d", atom_list[i].serial());
+  }
+
+  if(squared)log.printf("\n chosen to use SQUARED option for SIZESHAPE_POSITION_MAHA_DIST\n");
+
+  if(pbc) log.printf("\n using periodic boundary conditions\n");
+  else log.printf("\n without periodic boundary conditions\n");
+
+  addValueWithDerivatives(); setNotPeriodic();
+
+  requestAtoms(atom_list);
+
+  // call the readinputs() function here
+  readinputs();
+
+}
+
+// read inputs function
+void position_maha_dist::readinputs()
+{
+  unsigned N=getNumberOfAtoms();
+  // read ref coords
+  in_.open(ref_f_name);
+
+  ref_str.resize(N,3); prec.resize(N,N);
+
+  std::string line_, val_;
+  unsigned c_=0;
+
+  while (c_ < N)
+  {
+    in_.getline(line_);
+    std::vector<std::string> items_;
+    std::stringstream check_(line_);
+
+    while(std::getline(check_, val_, ' ')) { items_.push_back(val_); }
+    for(int i=0; i<3; ++i) { ref_str(c_,i) = std::stold(items_[i]); }
+    c_ += 1;
+  }
+  in_.close();
+
+  //read precision
+  in_.open(prec_f_name);
+
+  std::string line, val;
+  unsigned int c = 0;
+
+  while(c < N)
+  {
+    in_.getline(line);
+
+    // vector for storing the objects
+    std::vector<std::string> items;
+
+    // stringstream helps to treat a string like an ifstream!
+    std::stringstream check(line);
+
+    while (std::getline(check, val, ' '))
+    {
+      items.push_back(val);
+    }
+
+    for(unsigned int i=0; i<N; ++i)
+    {
+      prec(c, i) = std::stold(items[i]);
+    }
+
+    c += 1;
+
+  }
+  in_.close();
+}
+
+
+double position_maha_dist::determinant(int n, const std::vector<std::vector<double>>* B)
+{
+
+  std::vector<std::vector<double>> A(n, std::vector<double>(n, 0));
+  // make a copy first!
+  for(int i=0; i<n; ++i) {
+    for(int j=0; j<n; ++j) {A[i][j] = (*B)[i][j];}
+  }
+
+
+  //  It calculates determinant of a matrix using partial pivoting.
+
+  double det = 1;
+
+  // Row operations for i = 0, ,,,, n - 2 (n-1 not needed)
+  for ( int i = 0; i < n - 1; i++ )
+  {
+    // Partial pivot: find row r below with largest element in column i
+    int r = i;
+    double maxA = std::abs( A[i][i] );
+    for ( int k = i + 1; k < n; k++ )
+    {
+      double val = std::abs( A[k][i] );
+      if ( val > maxA )
+      {
+        r = k;
+        maxA = val;
+      }
+    }
+    if ( r != i )
+    {
+      for ( int j = i; j < n; j++ ) std::swap( A[i][j], A[r][j] );
+      det = -det;
+    }
+
+    // Row operations to make upper-triangular
+    double pivot = A[i][i];
+    if (std::abs( pivot ) < SMALL ) return 0.0;              // Singular matrix
+
+    for ( int r = i + 1; r < n; r++ )                    // On lower rows
+    {
+      double multiple = A[r][i] / pivot;                // Multiple of row i to clear element in ith column
+      for ( int j = i; j < n; j++ ) A[r][j] -= multiple * A[i][j];
+    }
+    det *= pivot;                                        // Determinant is product of diagonal
+  }
+
+  det *= A[n-1][n-1];
+
+  return det;
+}
+
+// kabsch rotation
+void position_maha_dist::kabsch_rot_mat() {
+
+  unsigned N=getNumberOfAtoms();
+
+  Matrix<double> mobile_str_T(3,N);
+  Matrix<double> prec_dot_ref_str(N,3);
+  Matrix<double> correlation(3,3);
+
+
+  transpose(mobile_str, mobile_str_T);
+  mult(prec, ref_str, prec_dot_ref_str);
+  mult(mobile_str_T, prec_dot_ref_str, correlation);
+
+
+  int rw = correlation.nrows();
+  int cl = correlation.ncols();
+  int sz = rw*cl;
+
+  // SVD part (taking from plu2/src/tools/Matrix.h: pseudoInvert function)
+
+  std::vector<double> da(sz);
+  unsigned k=0;
+
+  // Transfer the matrix to the local array
+  for (int i=0; i<cl; ++i) for (int j=0; j<rw; ++j) da[k++]=static_cast<double>( correlation(j,i) ); // note! its [j][i] not [i][j]
+
+  int nsv, info, nrows=rw, ncols=cl;
+  if(rw>cl) {nsv=cl;} else {nsv=rw;}
+
+  // Create some containers for stuff from single value decomposition
+  std::vector<double> S(nsv);
+  std::vector<double> U(nrows*nrows);
+  std::vector<double> VT(ncols*ncols);
+  std::vector<int> iwork(8*nsv);
+
+  // This optimizes the size of the work array used in lapack singular value decomposition
+  int lwork=-1;
+  std::vector<double> work(1);
+  plumed_lapack_dgesdd( "A", &nrows, &ncols, da.data(), &nrows, S.data(), U.data(), &nrows, VT.data(), &ncols, work.data(), &lwork, iwork.data(), &info );
+  //if(info!=0) return info;
+  if(info!=0) log.printf("info:", info);
+
+  // Retrieve correct sizes for work and rellocate
+  lwork=(int) work[0]; work.resize(lwork);
+
+  // This does the singular value decomposition
+  plumed_lapack_dgesdd( "A", &nrows, &ncols, da.data(), &nrows, S.data(), U.data(), &nrows, VT.data(), &ncols, work.data(), &lwork, iwork.data(), &info );
+  //if(info!=0) return info;
+  if(info!=0) log.printf("info:", info);
+
+
+  // get U and VT in form of 2D vector (U_, VT_)
+  std::vector<std::vector<double>> U_(nrows, std::vector<double>(nrows,0));
+  std::vector<std::vector<double>> VT_(ncols, std::vector<double>(ncols,0));
+
+  int  c=0;
+
+  for(int i=0; i<nrows; ++i) { for(int j=0; j<nrows; ++j) { U_[j][i] = U[c]; c += 1;} } c = 0; // note! its [j][i] not [i][j]
+  for(int i=0; i<ncols; ++i) { for(int j=0; j<ncols; ++j) { VT_[j][i] = VT[c]; c += 1;} } c=0; // note! its [j][i] not [i][j]
+
+
+  // calculate determinants
+  double det_u = determinant(nrows, &U_);
+  double det_vt = determinant(ncols, &VT_);
+
+  // check!
+  if (det_u * det_vt < 0.0) { for(int i=0; i<nrows; ++i) {U_[i][nrows-1] *= -1;} }
+
+
+  //Matrix<double> rotation(3,3);
+  rotation.resize(3,3);
+  Matrix<double> u(3,3), vt(3,3);
+  for(int i=0; i<3; ++i) { for(int j=0; j<3; ++j) { u(i,j)=U_[i][j]; vt(i,j)=VT_[i][j]; } }
+
+  // get rotation matrix
+  mult(u, vt, rotation);
+
+}
+
+
+// calculates maha dist
+double position_maha_dist::cal_maha_dist() {
+
+  unsigned N=getNumberOfAtoms();
+
+  Matrix<double> rotated_obj(N,3);
+  // rotate the object
+  mult(mobile_str, rotation, rotated_obj);
+
+  // compute the displacement
+  Matrix<double> disp(N,3);
+  for(unsigned int i=0; i<N; ++i) { for(unsigned int j=0; j<3; ++j) { disp(i,j) = (rotated_obj(i,j)-ref_str(i,j)); } }
+
+  Matrix<double> prec_dot_disp(N,3);
+  Matrix<double> disp_T(3,N);
+  Matrix<double> out(3,3);
+
+  mult(prec, disp, prec_dot_disp);
+  transpose(disp, disp_T);
+  mult(disp_T, prec_dot_disp, out);
+
+
+
+  double maha_d=0.0;
+  for(int i=0; i<3; ++i) { maha_d += out(i,i);}
+
+  if (!squared) maha_d = std::sqrt(maha_d);
+
+  return maha_d;
+}
+
+// gradient function
+void position_maha_dist::grad_maha(double d) {
+
+  unsigned N=getNumberOfAtoms();
+
+  derv_.resize(N,3);
+
+  Matrix<double> ref_str_rot_T(N,3);
+  Matrix<double> rot_T(3,3);
+  Matrix<double> diff_(N,3);
+
+  transpose(rotation, rot_T);
+  mult(ref_str, rot_T, ref_str_rot_T);
+
+  for(unsigned i=0; i<N; ++i) { for(unsigned j=0; j<3; ++j) { diff_(i,j) = mobile_str(i,j) - ref_str_rot_T(i,j); } }
+
+  mult(prec, diff_, derv_);
+
+  //for(unsigned i=0; i<N; ++i){ for(unsigned j=0; j<3; ++j) {derv_(i,j) /= (N*d);} }  // dividing by N here!
+  for(unsigned i=0; i<N; ++i) { for(unsigned j=0; j<3; ++j) { if (!squared) {derv_(i,j) /= d;} else {derv_(i,j) *= 2.0;}}}
+
+
+}
+
+
+// numeric gradient
+void position_maha_dist::numeric_maha() {
+  // This function performs numerical derivative.
+  unsigned N=getNumberOfAtoms();
+  derv_numeric.resize(N,3);
+
+  for(unsigned int atom=0; atom<N; ++atom) {
+    for(unsigned int j=0; j<3; ++j) {
+      mobile_str(atom,j) += delta;
+      kabsch_rot_mat();
+      derv_numeric(atom,j) = (cal_maha_dist() - dist)/delta;
+      mobile_str(atom,j) -= delta;
+    }
+  }
+
+}
+
+
+// calculator
+void position_maha_dist::calculate() {
+
+  if(pbc) makeWhole();
+  unsigned N=getNumberOfAtoms();
+
+  mobile_str.resize(N,3);
+
+  // load the mobile str
+  for(unsigned int i=0; i<N; ++i) {
+    Vector pos=getPosition(i);  // const PLMD::Vector
+    for(unsigned j=0; j<3; ++j) {
+      mobile_str(i,j) = pos[j];
+    }
+  }
+
+  // translating the structure to center of geometry
+  double center_of_geometry[3]= {0.0, 0.0, 0.0};
+
+  for(unsigned int i=0; i<N; ++i)
+  {
+    center_of_geometry[0] += mobile_str(i,0); center_of_geometry[1] += mobile_str(i,1); center_of_geometry[2] += mobile_str(i,2);
+  }
+
+  for(unsigned int i=0; i<N; ++i)
+  {
+    for(unsigned int j=0; j<3; ++j) { mobile_str(i,j) -= (center_of_geometry[j]/N); }
+  }
+
+  kabsch_rot_mat();
+  dist = cal_maha_dist();
+
+  grad_maha(dist);
+  // set derivatives
+  for(unsigned i=0; i<N; ++i) {
+    Vector vi(derv_(i,0), derv_(i,1), derv_(i,2) );
+    setAtomsDerivatives(i, vi);
+  }
+  setBoxDerivativesNoPbc();
+  setValue(dist);
+
+}
+
+}
+}
+
+
+
diff --git a/src/sizeshape/module.type b/src/sizeshape/module.type
new file mode 100644
index 0000000000..de83273033
--- /dev/null
+++ b/src/sizeshape/module.type
@@ -0,0 +1 @@
+default-off
diff --git a/src/sizeshape/pos_proj.cpp b/src/sizeshape/pos_proj.cpp
new file mode 100644
index 0000000000..dec0af2953
--- /dev/null
+++ b/src/sizeshape/pos_proj.cpp
@@ -0,0 +1,458 @@
+/* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+Copyright (c) 2024 by Glen Hocky, New York University on behalf of authors
+
+The sizeshape module 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.
+
+The sizeshape module 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 "colvar/Colvar.h"
+#include "core/ActionRegister.h"
+#include "tools/Pbc.h"
+#include "tools/File.h"           // Input and output from files 
+#include "tools/Matrix.h"         // Linear Algebra operations
+#include <sstream>
+#include <cmath>
+#include "tools/Communicator.h"   // All the MPI related stuffs
+
+namespace PLMD {
+namespace sizeshape {
+
+//+PLUMEDOC sizeshapeMOD_COLVAR SIZESHAPE_POSITION_LINEAR_PROJ
+/*
+Calculates a linear projection in the space of a given reference configurational distribution in size-and-shape space.
+
+This method is described in \cite Sasmal-poslda-2023.
+
+The linear projection is given by:
+\f[
+    l(\mathbf{x}) = \mathbf{v}\cdot(\mathbf{R}\cdot(\mathbf{x}(t) - \vec{{\zeta}}(t)) - \mathbf{\mu}),
+\f]
+Where \f$\mathbf{v}\f$ is a vector of linear coefficients, \f$\mathbf{x}(t)\f$ is the configuration at time t, \f$\vec{\zeta}(t)\f$ is the difference in the geometric mean of the current configuration and that of the reference configuration \f$\mathbf{\mu}\f$. \f$\vec{\zeta}(t) = \frac{1}{N} \sum_{i=1}^N \vec{x_{i}}(t) - \frac{1}{N} \sum_{i=1}^N \vec{\mu_{i}}(t)\f$, for N atoms.
+
+\f$\mathbf{R}\f$ is an optimal rotation matrix that minimizes the Mahalanobis distance between the current configuration and reference. \f$\mathbf{R}\f$ is obtained by using Kabsch algorithm within the code. The Mahalanobis distance is given as:
+
+\f[
+d(\mathbf{x}, \mathbf{\mu}, \mathbf{\Sigma}) = \sqrt{(\mathbf{x}-\mathbf{\mu})^T \mathbf{\Sigma}^{-1} (\mathbf{x}-\mathbf{\mu})}
+\f]
+
+where, \f$\mathbf{\Sigma}^{-1}\f$ is the \f$N\times N\f$ precision matrix. See also \ref POSITION_MAHA_DIST for information about calculating Mahalanobis distance in size-and-shape space.
+
+Size-and-shape Gaussian Mixture Model (shapeGMM) \cite Heidi-shapeGMM-2022 is a probabilistic clustering technique that is used to perform structural clusteing on ensemble of molecular configurations and to obtain reference \f$(\mathbf{\mu})\f$ and precision \f$(\mathbf{\Sigma}^{-1})\f$ corresponding to each of the cluster centers. Please chcek out <a href="https://github.com/mccullaghlab/shapeGMMTorch">shapeGMMTorch-GitHub</a> and <a href="https://pypi.org/project/shapeGMMTorch/"> shapeGMMTorch-PyPI</a> for examples and informations on preforming shapeGMM clustering.
+
+\par Examples
+In the following example, a group is defined with atom indices of selected atoms and then linear projection is calculated for the given reference, precision and coefficients. Each file is a space separated list of 3N floating point numbers.
+
+\plumedfile
+UNITS LENGTH=A TIME=ps ENERGY=kcal/mol
+GROUP ATOMS=18,20,22,31,33,35,44,46,48,57,59,61,70,72,74,83,85,87,96,98,100,109,111 LABEL=ga_list
+#SETTINGS AUXFILE=regtest/sizeshape/rt-sizeshape/global_avg.txt
+#SETTINGS AUXFILE=regtest/sizeshape/rt-sizeshape/global_precision.txt
+#SETTINGS AUXFILE=regtest/sizeshape/rt-sizeshape/ld1_scalings.txt
+proj: SIZESHAPE_POSITION_LINEAR_PROJ REFERENCE=global_avg.txt PRECISION=global_precision.txt COEFFS=ld1_scalings.txt GROUP=ga_list
+PRINT ARG=proj STRIDE=1 FILE=COLVAR FMT=%8.8f
+\endplumedfile
+
+*/
+//+ENDPLUMEDOC
+
+
+class position_linear_proj : public Colvar {
+
+private:
+  bool pbc, serial;
+  std::string prec_f_name;      		// precision file name
+  std::string ref_f_name;       		// reference file name
+  std::string coeffs_f_name; 			// file containing linear coeffs
+  IFile in_;             			// create an object of class IFile
+  Log out_;
+  Matrix<double> ref_str;       	        // coords of reference
+  Matrix<double> mobile_str;    		// coords of mobile
+  Matrix<double> prec;        			// precision data
+  Matrix<double> rotation;
+  std::vector<double> linear_coeffs;            // Linear Coefficients
+  Matrix<double> derv_numeric;
+  void readinputs();            		// reads the input data
+  double proj;					// projection value
+  std::vector<AtomNumber> atom_list;            // list of atoms
+  const double SMALL = 1.0E-30;
+  const double delta = 0.00001;
+public:
+  static void registerKeywords( Keywords& keys );
+  explicit position_linear_proj(const ActionOptions&);
+  double determinant(int n, const std::vector<std::vector<double>>* B);
+  void kabsch_rot_mat();   		// gives rotation matrix
+  double cal_position_linear_proj();    // calculates the linear projection
+  void numeric_grad();        		// calculates the numeric gradient
+  // active methods:
+  void calculate() override;
+};
+
+PLUMED_REGISTER_ACTION(position_linear_proj, "SIZESHAPE_POSITION_LINEAR_PROJ")
+
+// register keywords function
+void position_linear_proj::registerKeywords( Keywords& keys ) {
+  Colvar::registerKeywords( keys );
+  keys.add("compulsory", "PRECISION", "Precision Matrix (inverse of covariance)." );
+  keys.add("compulsory", "REFERENCE", "Coordinates of the reference structure.");
+  keys.add("atoms","GROUP","Group of atoms being used");
+  keys.add("compulsory", "COEFFS", "Vector of linear coefficients.");
+  keys.addFlag("SERIAL",false,"Perform the calculation in serial, for debug purposes only.");
+}
+
+// constructor function
+position_linear_proj::position_linear_proj(const ActionOptions&ao):
+  PLUMED_COLVAR_INIT(ao),
+  pbc(true),
+  serial(false),
+  proj(0),
+  prec_f_name(""),
+  ref_f_name(""),
+  coeffs_f_name("")   // Note! no comma here in the last line.
+{
+  parseFlag("SERIAL",serial);
+  parseAtomList("GROUP",atom_list);
+  parse("REFERENCE", ref_f_name);
+  parse("PRECISION", prec_f_name);
+  parse("COEFFS", coeffs_f_name);
+  bool nopbc=!pbc;
+  parseFlag("NOPBC",nopbc);
+  pbc=!nopbc;
+
+  checkRead();
+
+  log.printf("  of %u atoms\n",static_cast<unsigned>(atom_list.size()));
+  for(unsigned int i=0; i<atom_list.size(); ++i) {
+    log.printf("  %d", atom_list[i].serial());
+  }
+
+  if(pbc) log.printf("\n using periodic boundary conditions\n");
+  else log.printf("\n without periodic boundary conditions\n");
+
+  addValueWithDerivatives(); setNotPeriodic();
+
+  requestAtoms(atom_list);
+
+  // call the readinputs() function here
+  readinputs();
+
+}
+
+// read inputs function
+void position_linear_proj::readinputs()
+{
+  unsigned N=getNumberOfAtoms();
+  // read ref coords
+  in_.open(ref_f_name);
+
+  ref_str.resize(N,3); prec.resize(N,N);
+  derv_numeric.resize(N,3);
+
+  std::string line_, val_;
+  unsigned c_=0;
+
+  while (c_ < N)
+  {
+    in_.getline(line_);
+    std::vector<std::string> items_;
+    std::stringstream check_(line_);
+
+    while(std::getline(check_, val_, ' ')) { items_.push_back(val_); }
+    for(int i=0; i<3; ++i) { ref_str(c_,i) = std::stold(items_[i]); }
+    c_ += 1;
+  }
+  in_.close();
+
+  //read precision
+  in_.open(prec_f_name);
+
+  std::string line, val;
+  unsigned int c = 0;
+
+  while(c < N)
+  {
+    in_.getline(line);
+
+    // vector for storing the objects
+    std::vector<std::string> items;
+
+    // stringstream helps to treat a string like an ifstream!
+    std::stringstream check(line);
+
+    while (std::getline(check, val, ' '))
+    {
+      items.push_back(val);
+    }
+
+    for(unsigned int i=0; i<N; ++i)
+    {
+      prec(c, i) = std::stold(items[i]);
+    }
+
+    c += 1;
+
+  }
+  in_.close();
+
+  // read in the linear coeffs
+  in_.open(coeffs_f_name);
+  unsigned n_=0;
+  std::string l_;
+  while (n_ < N*3) { in_.getline(l_); linear_coeffs.push_back(std::stod(l_)); n_ += 1; }
+  linear_coeffs.resize(N*3);
+
+  in_.close();
+
+}
+
+
+
+double position_linear_proj::determinant(int n, const std::vector<std::vector<double>>* B)
+{
+
+  std::vector<std::vector<double>> A(n, std::vector<double>(n, 0));
+  // make a copy first!
+  for(int i=0; i<n; ++i) {
+    for(int j=0; j<n; ++j) {A[i][j] = (*B)[i][j];}
+  }
+
+
+  //  It calculates determinant of a matrix using partial pivoting.
+
+  double det = 1;
+
+  // Row operations for i = 0, ,,,, n - 2 (n-1 not needed)
+  for ( int i = 0; i < n - 1; i++ )
+  {
+    // Partial pivot: find row r below with largest element in column i
+    int r = i;
+    double maxA = std::abs( A[i][i] );
+    for ( int k = i + 1; k < n; k++ )
+    {
+      double val = std::abs( A[k][i] );
+      if ( val > maxA )
+      {
+        r = k;
+        maxA = val;
+      }
+    }
+    if ( r != i )
+    {
+      for ( int j = i; j < n; j++ ) std::swap( A[i][j], A[r][j] );
+      det = -det;
+    }
+
+    // Row operations to make upper-triangular
+    double pivot = A[i][i];
+    if (std::abs( pivot ) < SMALL ) return 0.0;              // Singular matrix
+
+    for ( int r = i + 1; r < n; r++ )                    // On lower rows
+    {
+      double multiple = A[r][i] / pivot;                // Multiple of row i to clear element in ith column
+      for ( int j = i; j < n; j++ ) A[r][j] -= multiple * A[i][j];
+    }
+    det *= pivot;                                        // Determinant is product of diagonal
+  }
+
+  det *= A[n-1][n-1];
+
+  return det;
+}
+
+// kabsch rotation
+void position_linear_proj::kabsch_rot_mat() {
+
+  unsigned N=getNumberOfAtoms();
+
+  Matrix<double> mobile_str_T(3,N);
+  Matrix<double> prec_dot_ref_str(N,3);
+  Matrix<double> correlation(3,3);
+
+
+  transpose(mobile_str, mobile_str_T);
+  mult(prec, ref_str, prec_dot_ref_str);
+  mult(mobile_str_T, prec_dot_ref_str, correlation);
+
+
+  int rw = correlation.nrows();
+  int cl = correlation.ncols();
+  int sz = rw*cl;
+
+  // SVD part (taking from plu2/src/tools/Matrix.h: pseudoInvert function)
+
+  std::vector<double> da(sz);
+  unsigned k=0;
+
+  // Transfer the matrix to the local array
+  for (int i=0; i<cl; ++i) for (int j=0; j<rw; ++j) da[k++]=static_cast<double>( correlation(j,i) ); // note! its [j][i] not [i][j]
+
+  int nsv, info, nrows=rw, ncols=cl;
+  if(rw>cl) {nsv=cl;} else {nsv=rw;}
+
+  // Create some containers for stuff from single value decomposition
+  std::vector<double> S(nsv);
+  std::vector<double> U(nrows*nrows);
+  std::vector<double> VT(ncols*ncols);
+  std::vector<int> iwork(8*nsv);
+
+  // This optimizes the size of the work array used in lapack singular value decomposition
+  int lwork=-1;
+  std::vector<double> work(1);
+  plumed_lapack_dgesdd( "A", &nrows, &ncols, da.data(), &nrows, S.data(), U.data(), &nrows, VT.data(), &ncols, work.data(), &lwork, iwork.data(), &info );
+  //if(info!=0) return info;
+  if(info!=0) log.printf("info:", info);
+
+  // Retrieve correct sizes for work and rellocate
+  lwork=(int) work[0]; work.resize(lwork);
+
+  // This does the singular value decomposition
+  plumed_lapack_dgesdd( "A", &nrows, &ncols, da.data(), &nrows, S.data(), U.data(), &nrows, VT.data(), &ncols, work.data(), &lwork, iwork.data(), &info );
+  //if(info!=0) return info;
+  if(info!=0) log.printf("info:", info);
+
+
+  // get U and VT in form of 2D vector (U_, VT_)
+  std::vector<std::vector<double>> U_(nrows, std::vector<double>(nrows,0));
+  std::vector<std::vector<double>> VT_(ncols, std::vector<double>(ncols,0));
+
+  int  c=0;
+
+  for(int i=0; i<nrows; ++i) { for(int j=0; j<nrows; ++j) { U_[j][i] = U[c]; c += 1;} } c = 0; // note! its [j][i] not [i][j]
+  for(int i=0; i<ncols; ++i) { for(int j=0; j<ncols; ++j) { VT_[j][i] = VT[c]; c += 1;} } c=0; // note! its [j][i] not [i][j]
+
+
+  // calculate determinants
+  double det_u = determinant(nrows, &U_);
+  double det_vt = determinant(ncols, &VT_);
+
+  // check!
+  if (det_u * det_vt < 0.0) { for(int i=0; i<nrows; ++i) {U_[i][nrows-1] *= -1;} }
+
+
+  //Matrix<double> rotation(3,3);
+  rotation.resize(3,3);
+  Matrix<double> u(3,3), vt(3,3);
+  for(int i=0; i<3; ++i) { for(int j=0; j<3; ++j) { u(i,j)=U_[i][j]; vt(i,j)=VT_[i][j]; } }
+
+  // get rotation matrix
+  mult(u, vt, rotation);
+
+}
+
+
+// calculates linear projection
+double position_linear_proj::cal_position_linear_proj() {
+
+  unsigned N=getNumberOfAtoms();
+
+  Matrix<double> rotated_obj(N,3);
+  // rotate the object
+  mult(mobile_str, rotation, rotated_obj);
+
+  // compute the displacement
+  std::vector<double> disp(N*3);
+  unsigned c=0;
+  for(unsigned int i=0; i<N; ++i) { for(int j=0; j<3; ++j) { disp[c] = (rotated_obj(i,j)-ref_str(i,j)); c+=1;} }
+
+  //double proj_val = dotProduct(disp, linear_coeffs);
+  double proj_val = 0.0;
+  for(unsigned int i=0; i<N*3; ++i) { proj_val += (linear_coeffs[i]*disp[i]);}
+
+  return proj_val;
+}
+
+// numeric gradient
+void position_linear_proj::numeric_grad() {
+  // This function performs numerical derivative.
+  unsigned N=getNumberOfAtoms();
+
+  unsigned stride;
+  unsigned rank;
+  if(serial) {
+    // when using components the parallelisation do not work
+    stride=1;
+    rank=0;
+  } else {
+    stride=comm.Get_size();
+    rank=comm.Get_rank();
+  }
+
+  for(unsigned i=rank; i<N; i+=stride) {
+    for (unsigned j=0; j<3; ++j) {
+
+      mobile_str(i,j) += delta;
+      kabsch_rot_mat();
+      derv_numeric(i,j) = ((cal_position_linear_proj() - proj)/delta);
+
+      mobile_str(i,j) -= delta;
+    }
+
+  }
+
+  if(!serial) {
+    if(!derv_numeric.getVector().empty()) comm.Sum(&derv_numeric(0,0), derv_numeric.getVector().size());
+  }
+
+
+  for(unsigned i=0; i<N; ++i) {
+    Vector vi(derv_numeric(i,0), derv_numeric(i,1), derv_numeric(i,2) );
+    setAtomsDerivatives(i, vi);
+  }
+
+  // clear the matrix (very important step!!)
+  derv_numeric *= 0;
+}
+
+
+// calculator
+void position_linear_proj::calculate() {
+
+  if(pbc) makeWhole();
+  unsigned N=getNumberOfAtoms();
+
+  mobile_str.resize(N,3);
+
+  // load the mobile str
+  for(unsigned int i=0; i<N; ++i) {
+    Vector pos=getPosition(i);  // const PLMD::Vector
+    for(unsigned j=0; j<3; ++j) {
+      mobile_str(i,j) = pos[j];
+    }
+  }
+
+  // translating the structure to center of geometry
+  double center_of_geometry[3]= {0.0, 0.0, 0.0};
+
+  for(unsigned int i=0; i<N; ++i)
+  {
+    center_of_geometry[0] += mobile_str(i,0); center_of_geometry[1] += mobile_str(i,1); center_of_geometry[2] += mobile_str(i,2);
+  }
+
+  for(unsigned int i=0; i<N; ++i)
+  {
+    for(int j=0; j<3; ++j) { mobile_str(i,j) -= (center_of_geometry[j]/N); }
+  }
+
+  kabsch_rot_mat();
+  proj = cal_position_linear_proj();
+
+  numeric_grad();
+  setBoxDerivativesNoPbc();
+  setValue(proj);
+
+
+}
+
+}
+}
+
+
+
diff --git a/user-doc/sizeshapeMOD.md b/user-doc/sizeshapeMOD.md
new file mode 100644
index 0000000000..8a53bfe434
--- /dev/null
+++ b/user-doc/sizeshapeMOD.md
@@ -0,0 +1,26 @@
+\page sizeshapeMOD sizeshape collective variable
+
+<!-- 
+description: Linear projection in size and shape space
+authors: Subarna Sasmal, Glen M Hocky
+reference: \cite Sasmal-poslda-2023
+-->
+
+\section Overview
+
+This sizeshape module contains method for calculating a 1D linear projection and the Mahalanobis distance in size and shape space for a given reference configurational distribution, as described in \cite Sasmal-poslda-2023.
+
+\section Installation 
+This module is not installed by default. Add '\-\-enable-modules=sizeshape' to your './configure' command when building PLUMED to enable these features.
+
+\section Usage
+Currently, all features of the sizeshape module are included in a single sizeshape collective variable: \ref POSITION_LINEAR_PROJ \ref POSITION_MAHA_DIST
+
+\section Module Contents
+- \subpage sizeshapeMODColvar
+
+\page sizeshapeMODColvar CVs Documentation
+
+The following list contains descriptions of collective variable developed for the PLUMED-sizeshape module. They can be used in combination with other actions outside of the sizeshape module.
+
+@sizeshapeMOD_COLVAR@