I am trying to solve the Procrustes problem
min |Y - K* X|
I have implemented SVD and the Procrustes problem in a code that I inherited. I have written 2 versions,
First version:
I am projecting X (e.g. self.__psiNNx) and Y (e.g. self.__psiNNy) onto the leading POD modes to reduce the requirements of the computation
self.__psiNNx and self.__psiNNy have dimensions (54, 1)
Sx, Ux , Vx =tf.linalg.svd(self.__psiNNx, full_matrices=False, compute_uv=True)
# # Project X and Y onto Principal components
Yproj=tf.matmul(tf.transpose(Ux), self.__psiNNy)
Xproj=tf.matmul(tf.transpose(Ux), self.__psiNNx)
Syx, Uyx, Vyx =tf.linalg.svd(tf.matmul(Yproj, tf.transpose(Xproj)),full_matrices=False, compute_uv=True)
This version works fine!
Second version:
I do not do the projections onto POD modes
Syx , Uyx, Vyx =tf.linalg.svd(tf.matmul(self.__psiNNy, tf.transpose(self.__psiNNx)),full_matrices=True, compute_uv=True)
This version gives me an error:
---------------------------------------------------------------------------
InvalidArgumentError Traceback (most recent call last)
~/opt/anaconda3/envs/edmd_DL_new/lib/python3.6/site-packages/tensorflow/python/client/session.py in _do_call(self, fn, *args)
1333 try:
-> 1334 return fn(*args)
1335 except errors.OpError as e:
~/opt/anaconda3/envs/edmd_DL_new/lib/python3.6/site-packages/tensorflow/python/client/session.py in _run_fn(feed_dict, fetch_list, target_list, options, run_metadata)
1318 return self._call_tf_sessionrun(
-> 1319 options, feed_dict, fetch_list, target_list, run_metadata)
1320
~/opt/anaconda3/envs/edmd_DL_new/lib/python3.6/site-packages/tensorflow/python/client/session.py in _call_tf_sessionrun(self, options, feed_dict, fetch_list, target_list, run_metadata)
1406 self._session, options, feed_dict, fetch_list, target_list,
-> 1407 run_metadata)
1408
InvalidArgumentError: ConcatOp : Dimensions of inputs should match: shape[0] = [54,1] vs. shape[1] = [100000,3]
[[{{node Model/concat}} = ConcatV2[N=3, T=DT_DOUBLE, Tidx=DT_INT32, _device="/job:localhost/replica:0/task:0/device:CPU:0"](Model/ones_like, _arg_Placeholder_0_0, Model/Output_projection/add, Model_1/concat/axis)]]
During handling of the above exception, another exception occurred:
InvalidArgumentError Traceback (most recent call last)
<ipython-input-217-4dbea9e9e52a> in <module>
15 # Train model
16 # Can use bigger batch sizes (e.g. 1000 to 5000) if training on GPU
---> 17 losses = model.train(num_epochs=500, batch_size=5000, log_interval=50, verbose=True, x_data=x_data, y_data=y_data)
I am not sure why the second version is not valid, as I am computing the SVD while the first one works fine
