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Dot product of two N-dimensional arrays.

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Dot product of two N-dimensional arrays.


Xiaodong (view profile)


DOT3(A, B) returns their scalar product, where A and B are arbitrary arrays with arbitrary sizes.

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%DOT3 Vector dot product.
% This function exploits the MULTIPROD engine (MATLAB Central, file
% #8773), which enables multiple products and array expansion (AX).
% When A and B are vectors (e.g. P×1, 1×P, or 1×1×P arrays):
% C = DOT3(A, B) returns their scalar product. A and B must have the
% same length. If A and B are both column vectors, DOT3(A, B) is the
% same as (A.') * B. Note that: If NDIMS(A) == 2 and NDIMS(B) == 2,
% DOT3(A, B) is not equivalent to DOT(A, B) or DOT2(A,B) (File ID: #8782). DOT(A, B)
% or DOT2(A, B) applies a complex conjugate on the first parameter A,
% but DOT3(A, B) does not apply the complex conjugate on A.
% More generally, when A and B are arrays of any size containing one or
% more vectors:
% C = DOT3(A, B) is equivalent to C = DOT3(A, B, IDA, IDB), where
% IDA and IDB are the first non-singleton dimensions of A and B,
% respectively.
% C = DOT3(A, B, DIM) is equivalent to C = DOT3(A, B, IDA, IDB),
% where IDA = IDB = DIM.
% C = DOT3(A, B, IDA, IDB) returns the scalar products between the
% vectors contained in A along dimension IDA and those contained in B
% along dimension IDB. These vectors must have the same length
% P = SIZE(A,IDA) = SIZE(B,IDB). A and B are viewed as "block
% arrays". IDA and IDB are referred to as their "internal dimensions"
% (IDs). For instance, a 5×6×2 array may be viewed as an array
% containing twelve 5-element blocks. In this case, its size is
% denoted by (5)×6×2, and its ID is 1. Since AX is enabled, A and B
% may have different size, and IDA may not coincide with IDB (see
% C = DOT3(A, B, IDA, IDB) calls C = MULTIPROD(CONJ(A), B, IDA, IDB)
% (MATLAB Central, file #8773), which virtually turns the vectors
% found in CONJ(A) and B into 1×P and P×1 matrices, respectively,
% then returns their products.
% Input and output format (see MULTIPROD, syntax 4b):
% Array Block size Internal dimension
% -------------------------------------------
% A P (1-D) IDA
% B P (1-D) IDB
% C 1 (1-D) MAX(IDA, IDB)
% -------------------------------------------
% Examples:
% If A and B are both (5)×6×2 arrays of vectors,
% C = DOT3(A, B) is a (1)×6×2 array of scalars.
% A single vector B multiplies thirty vectors contained in A:
% If A is .............. a 5×6×(3) array of 30 vectors,
% and B is .............. a (3)×1 vector,
% C = DOT3(A, B, 3, 1) is a 5×6×(1) array of 30 scalars.

% $ Version: 1.0 $
% Code is modified by Xiaodong Qi (i2000s# from DOT2 (dot2 is
% written by Paolo de Leva (IUSM, Rome, IT) 2009 Jan, File ID: #8782) to
% make a good match to another common definition of dot products.
% May 17, 2013.


Multiple Matrix Multiplications, With Array Expansion Enabled and Vector Algebra For Arrays Of Any Size, With Array Expansion Enabled inspired this file.

Required Products MATLAB
MATLAB release MATLAB 8.1 (R2013a)
Other requirements This code uses MULTIPROD function produced by Paolo de Leva with file ID: #8773. Thank Paolo for his contribution.
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