LYAPACK: msns_l_i - File Exchange

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Highlights from
LYAPACK

... % Low rank Cholesky factor Newton method (explicit version LRCF-NM and
... % LRCF-ADI for solving the stable Lyapunov equation:
... % Using updated QR factorizations, this routine computes efficiently
as_l(tr,X) % Solves linear systems with the real, symmetric, negative definite matrix A,
as_l_d % Deletes the global data that has been generated by 'as_l_i'.
as_l_i
as_m(tr,X) % Evaluates matrix-matrix products with the real, symmetric matrix A,
as_m_d % Deletes the global data that has been generated by 'as_m_i'.
as_m_i(A)
as_pre(A,B,C) % Preprocessing of the system
as_pst(X,iprm) % Postprocessing. This routine is the counterpart of 'as_pre'. It
as_s(tr,X,i) % Solves shifted linear systems with the real, symmetric, negative definite
as_s_d(p) % Deletes the global data that has been generated by 'as_s_i'.
as_s_i(p)
au_l(tr,X) % Solves linear systems with the real matrix A or its transposed A':
au_l_d % Deletes the global data that has been generated by 'au_l_i'.
au_l_i
au_m(tr,X) % Evaluates matrix-matrix products with the real matrix A or its
au_m_d % Deletes the global data that has been generated by 'au_m_i'.
au_m_i(A)
au_pre(A,B,C) % Preprocessing of the system
au_pst(X,iprm) % Postprocessing. This routine is the counterpart of 'au_pre'. It
au_qmr_ilu_l(tr,X) % Solves linear systems with the real matrix A or its transpose A' using
au_qmr_ilu_l_d % Deletes the global data that has been generated by 'au_qmr_ilu_l_i'.
au_qmr_ilu_l_i % Generates the data used in 'au_qmr_ilu_l'. Data are stored in global
au_qmr_ilu_m(tr,X) % Evaluates matrix-matrix products with the real matrix A or its
au_qmr_ilu_m_d % Deletes the global data that has been generated by 'au_qmr_ilu_m_i'.
au_qmr_ilu_m_i(A,mc,max_it_qm... % Generates the data used in 'au_qmr_ilu_m'. Data are stored in global
au_qmr_ilu_s(tr,X,i) % Solves shifted linear systems with the matrix A or its transpose A' by
au_qmr_ilu_s_d(p) % Deletes the global data that has been generated by 'au_qmr_ilu_s_i'
au_qmr_ilu_s_i(p) % Generates the data used in 'au_qmr_ilu_s'. Data are stored in global
au_s(tr,X,i) % Solves shifted linear systems with the real matrix A or its
au_s_d(p) % Deletes the global data that has been generated by 'au_s_i'.
au_s_i(p)
fdm_2d_matrix(n0,fx_str,fy_st... % Generates the stiffness matrix A for the finite difference
fdm_2d_vector(n0,f_str)
lp_arn_m(name,Bf,Kf,k,r)
lp_arn_p(name,Bf,Kf,k,r)
lp_dspmr(name,B,C,ZB,ZC,max_o... % Model reduction method DSPMR (Dominant Subspace Projection Model
lp_e(i1,i2,i3,i4,i5,i6,i7,i8,... % Auxiliary routine for the execution of strings with MATLAB
lp_gnorm(Gs,m,q) % Given the transfer function sample matrix Gs, which contains
lp_lgfrq(min_freq,max_freq,no... % Delivers a vector of "frequency sampling points" which are
lp_lrsrm(name,B,C,ZB,ZC,max_o... % Model reduction method LRSRM (Low Rank Square Root Method)
lp_mnmx(rw,l0) % Suboptimal solution of the ADI minimax problem. The delivered parameter
lp_nrm( tp, name, Bf, Kf, G, ... % Computes efficiently either of the following norms provided that
lp_para(name,Bf,Kf,l0,kp,km,b... % Estimation of suboptimal ADI shift parameters for the matrix
lp_prm(A,E) % Reordering of SPARSE standard/generalized systems
lp_rcnrm( name, B, C0, R, Z ) % Computes efficiently the Riccati norm when the approximate solution
lp_s(p,set) % Computation of the maximal magnitude of the rational ADI function over
lp_trfia(freq,A,B,C,D,E) % Computes the transfer function for systems
msns_l(tr,X) % Solves linear systems with the symmetric, negative definite matrix A,
msns_l_d % Deletes the global data that has been generated by 'msns_l_i'.
msns_l_i
msns_m(tr,X) % Evaluates matrix-matrix products with the symmetric matrix A,
msns_m_d % Deletes the global data that has been generated by 'msns_m_i'.
msns_m_i(M,MU,N)
msns_pre(M,N,B,C) % Preprocessing of the system
msns_pst(Z,MU,iprm) % Postprocessing. This routine is the counterpart of 'msns_pre'. It
msns_s(tr,X,i) % Solves shifted linear systems with the symmetric, negative definite
msns_s_d(p) % Deletes the global data that has been generated by 'msns_s_i'.
msns_s_i(p)
munu_l(tr,X) % Solves linear systems with the real matrix A or its transposed A':
munu_l_d % Deletes the global data that has been generated by 'munu_l_i'.
munu_l_i
munu_m(tr,X) % Evaluates matrix-matrix products with the real matrix A or its
munu_m_d % Deletes the global data that has been generated by 'munu_m_i'.
munu_m_i(M,ML,MU,N)
munu_pre(M,N,B,C) % Preprocessing of the system
munu_pst(ZB,ZC,ML,MU,iprm) % Postprocessing. This routine is the counterpart of preprocessing
munu_s(tr,X,i) % Solves shifted linear systems with the real matrix A or its
munu_s_d(p) % Deletes the global data that has been generated by 'munu_s_i'.
munu_s_i(p)
demo_l1.m
demo_m1.m
demo_m2.m
demo_r1.m
demo_u1.m
demo_u2.m
demo_u3.m
lstartup.m
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from LYAPACK by Volker Mehrmann
LYAPACK toolbox provides solutions for certain large scale problems related to Lyapunov equations.

msns_l_i

function msns_l_i
%
%  Generates the data used in 'msns_l'. Data are stored in global
%  variables.
%
%  Calling sequence:
%
%    msns_l_i
%
%  Remarks:
% 
%    Call 'msns_m_i' before calling this routine.
%
%
%  LYAPACK 1.0 (Thilo Penzl, October 1999)


global LP_N LP_NU

if ~length(LP_N)
  error('This routine needs global data which must be generated by calling ''msns_m_i'' first.');
end 

[LP_NU,t] = chol(-LP_N);        % Note the minus!

if t~=0
  error('N is not (numerically) negative definite!');
end

Highlights from LYAPACK

Highlights from
LYAPACK