version 1.0.0.0 (2.51 KB) by
Xiaodong

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

%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

% MULTIPROD).

%

% 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.

%

% See also DOT, DOT2, CROSS2, CROSSDIV, OUTER, MAGN, UNIT, PROJECTION,

% REJECTION, MULTIPROD, TESTDOT2.

% $ Version: 1.0 $

% Code is modified by Xiaodong Qi (i2000s# hotmail.com) 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.

Created with
R2013a

Compatible with any release

**Inspired by:**
Multiple matrix multiplications, with array expansion enabled, Vector algebra for arrays of any size, with array expansion enabled

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