improving the comments

theano/scan_module/scan_op.py

@@ -223,22 +223,23 @@ class Scan(PureOp):
                     'in the inner function of scan %s '
                     'however has dtype %s and %d dimension(s). This '
                     'slice in the inner function of scan should '
-                    'have the same dtype and one fewer dimension in its '
-                    'leading dimension compared to its corresponding '
-                    'slice in the initial state (outputs_info in scan '
-                    'nomenclature). For example, if the inner function '
-                    'of scan returns a vector of dimensionality d and '
-                    'scan uses the values of the previous time-step, then '
-                    'the initial state in scan should be a matrix of '
-                    'dimensionality (1, d). The first dimension of this '
+                    'have the same dtype and one fewer dimension '
+                    'compared to its corresponding slice in the initial '
+                    'state (outputs_info in scan nomenclature). For example, '
+                    'if the inner function of scan returns a vector '
+                    '(dimensionality 1) of size d and scan uses the values of '
+                    'the previous time-step, then the initial state in scan '
+                    'should be a matrix (dimensionality 2) of shape (1, d). '
+                    'The first dimension of this '
                     'matrix corresponds to the number of previous time-steps'
                     'that scan uses in each of its iterations. If for '
                     'example scan uses up to 3 previous time-step values, '
-                    'the initial matrix should have dimensionality of (3, d). '
+                    'the initial matrix should have a shape of (3, d). '
                     'In order to solve this issue if the two slices currently '
-                    'have the same dimensionality, you can increase the first '
-                    'dimension of the initial state in scan by using '
-                    'dimshuffle or shape_padleft. As an exmaple, if you only '
+                    'have the same dimensionality, you can increase the '
+                    'dimensionality of the slice in the initial state of scan '
+                    'by using dimshuffle or shape_padleft. '
+                    'As an exmaple, if you only '
                     'use the values of the previous time-step and the '
                     'corresponding variable in the inner function of scan '
                     'returns a vector, then use v.dimshuffle(\'x\', 0) or '
@@ -260,20 +261,21 @@ class Scan(PureOp):
                     'of variable %s (argument number %d) has %d dimension(s), '
                     'while the corresponding slice in the result of the inner '
                     'function of scan (`fn`) has %d dimension(s) (it should '
-                    'be one less than the initial state). '
-                    'For example, if the inner function '
-                    'of scan returns a vector of dimensionality d and '
-                    'scan uses the values of the previous time-step, then '
-                    'the initial state in scan should be a matrix of '
-                    'dimensionality (1, d). The first dimension of this '
+                    'be one less than the initial state). For example, '
+                    'if the inner function of scan returns a vector '
+                    '(dimensionality 1) of size d and scan uses the values of '
+                    'the previous time-step, then the initial state in scan '
+                    'should be a matrix (dimensionality 2) of shape (1, d). '
+                    'The first dimension of this '
                     'matrix corresponds to the number of previous time-steps'
                     'that scan uses in each of its iterations. If for '
                     'example scan uses up to 3 previous time-step values, '
-                    'the initial matrix should have dimensionality of (3, d). '
+                    'the initial matrix should have a shape of (3, d). '
                     'In order to solve this issue if the two slices currently '
-                    'have the same dimensionality, you can increase the first '
-                    'dimension of the initial state in scan by using '
-                    'dimshuffle or shape_padleft. As an exmaple, if you only '
+                    'have the same dimensionality, you can increase the '
+                    'dimensionality of the slice in the initial state of scan '
+                    'by using dimshuffle or shape_padleft. '
+                    'As an exmaple, if you only '
                     'use the values of the previous time-step and the '
                     'corresponding variable in the inner function of scan '
                     'returns a vector, then use v.dimshuffle(\'x\', 0) or '