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# ### Julia Tutorial: Array Slicing
# Array slicing in Julia differs a bit from Matlab.  
# In Matlab, everything is an array; even a scalar is a 1x1 array.  
# In Julia, there are distinct data types for scalars, vectors, AdjointVectors and Arrays.  
# This notebook illustrates how those differences affect array slicing.  
# For rationale, see the "Dimension sum slices" section under this blog:  
# https://julialang.org/blog/2016/10/julia-0.5-highlights  
# Jeff Fessler, University of Michigan  
# 2017-07-24, original  
# 2020-08-05, Julia 1.5.0  
# 2021-08-23, Julia 1.6.2

A = [10*m+n for m=1:3, n=1:4] # start with a simple "self documenting" 2D array

A[1:2,:] # slicing multiple rows or columns works the same as in Matlab

A[2,:] # however, slicing a single row returns a 1D vector, not a 1×4 array!

A[[2],:] # this unusual version of slicing a single row returns a 1×4 array!

A[:,3] # slicing a single column yields a vector, NOT a 3×1 array

A[[2],:] * A[[3],:]' # 1×4 array times a 4×1 array yields a 1×1 array!

A[:,[3]] # this way gives a 3×1 array, not a vector

A[:,3]' * A[:,2] # dot product between Adjoint Vector and vector yields a scalar

A[:,[3]]' * A[:,[2]] # 1×3 array times a 3×1 array yields a 1×1 array!

A[2,:] * A[3,:]' # this would be a dot product in Matlab
                 # but it is an outer product in Julia.