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Up-> ckbs utility ckbs_blkbidiag_symm_mul

ckbs-> license ckbs_t_general ckbs_nonlinear ckbs_L1_nonlinear ckbs_affine ckbs_affine_singular ckbs_L1_affine utility all_ok.m whatsnew wishlist bib

utility-> ckbs_t_obj ckbs_t_grad ckbs_t_hess ckbs_diag_solve ckbs_bidiag_solve ckbs_bidiag_solve_t ckbs_blkbidiag_symm_mul ckbs_blkdiag_mul ckbs_blkdiag_mul_t ckbs_blkbidiag_mul_t ckbs_blkbidiag_mul ckbs_blktridiag_mul ckbs_sumsq_obj ckbs_L2L1_obj ckbs_sumsq_grad ckbs_process_grad ckbs_sumsq_hes ckbs_process_hes ckbs_tridiag_solve ckbs_tridiag_solve_b ckbs_tridiag_solve_pcg ckbs_newton_step ckbs_newton_step_L1 ckbs_kuhn_tucker ckbs_kuhn_tucker_L1

ckbs_blkbidiag_symm_mul-> blkbidiag_symm_mul_ok.m

Headings-> Syntax Purpose Bdia Boffdia Ddia B D r s Example

Packed Block Bidiagonal Matrix Symmetric Multiply
Syntax
[r, s] = ckbs_blkbidiag_symm_mul(Bdia, Boffdia, Ddia)

Purpose
This routine takes a packed block bidiagonal matrix and a packed block diagonal matrix (optional), and returns the symmetric product matrix (as packed tridiagonal matrix):  \[
      W = B * D * B^T
\]  The actual output consists of a packed representation of the diagonal and off-diagonal blocks of the matrix  W .

Bdia
The argument Bdia is an  m \times n \times N array. For  k = 1 , \ldots , N we define  B_k \in \B{R}^{m \times n} by  \[
      B_k = Bdia(:, :, k)
\] 

Boffdia
The argument Boffdia is an  m \times n \times N array. For  k = 2 , \ldots , N we define  C_k \in \B{R}^{m \times n} by  \[
      C_k = Boffdia(:, :, k)
\] 

Ddia
The argument Ddia is an  n \times n \times N array. For  k = 1 , \ldots , N we define  D_k \in \B{R}^{n \times n} by  \[
      D_k = Ddia(:, :, k)
\] 

B
The matrix  B is defined by  \[
B
=
\left( \begin{array}{cccc}
      B_1 & 0      & 0      &           \\
      C_2^T   & B_2    & \ddots      & 0         \\
      0   & \ddots      & \ddots & 0         \\
          & 0      & C_N^T      & B_N
\end{array} \right)
\] 

D
The matrix  D is defined by  \[
D
=
\left( \begin{array}{cccc}
      D_1 & 0      & 0      &           \\
      0   & D_2    & \ddots      & 0         \\
      0   & \ddots      & \ddots & 0         \\
          & 0      & 0      & D_N
\end{array} \right)
\] 

r
The result r is an  n \times n \times N array. For  k = 1 , \ldots , N we define  r_k \in \B{R}^{n \times n} by  \[
      r_k = r(:, :, k)
\]  %

s
The result s is an  m \times n \times N array. For  k = 2 , \ldots , N we define  r_k \in \B{R}^{m \times n} by  \[
      s_k = s(:, :, k)
\] 

Example
The file blkbidiag_symm_mul_ok.m contains an example and test of ckbs_blkbidiag_symm_mul. It returns true if ckbs_blkbidiag_symm_mul passes the test and false otherwise.

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Input File: src/ckbs_blkbidiag_symm_mul.m