BBTools

bbdbltoeplitz

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bbdbltoeplitz  Create an operator for a doubly Toeplitz matrix
   A matrix, BB, is doubly Toeplitz if it can be written in the form:
     BB=[ U0, U1, U2, ...
          L1, U0, U1, ...
          L2, L1, L2, ...
          ............... ]
   where U0,U1,... and L1,L2,... are Toeplitz matrices.

   In words, a doubly Toeplitz matrix is a block Toeplitz matrix with
   Toeplitz blocks. Is is also known as "Toeplitz-Block Toeplitz".

   Syntax:
     BB=bbdbltoeplitz(RU)
     BB=bbdbltoeplitz(CU,RU)
     BB=bbdbltoeplitz(CU,RU,CL,RL)
     BB=bbdbltoeplitz(CU,RU,[],[])

   RU contains the first rows in U0,U1,..., while CU contain the columns:
     CU=[U0(:,1) , U1(:,1) , U2(:,1) , ...]
     RU=[U0(1,:) ; U1(1,:) ; U2(1,:) ; ...]
   If CU is unspecified, the blocks are assumed to be Hermitian:
     U0=U0', U1=U1', etc.

   CL and RL contain the first columns and rows of L1,L2,...:
     CL=[L1(:,1) , L2(:,1) , ...]
     RL=[L1(1,:) ; L2(1,:) ; ...]
   If CL and RL are unspecified, BB will be block-Hermitian:
     L1=U1', L2=U2', etc.
   If CL and RL are empty matrices, BB consist of a single block row:
     BB=[U0, U1, ... ]

   NOTE: The first element in the column and row in each block must be
   the same.

   See also bbtoeplitz, .

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