GSM Solver Technical Notes

Transcription

1 7//5 GM olvr Thl Nots, Pg /7 GM olvr Thl Nots 7 Tkuh Hro (Tokyo Isttut of Thology). Itrouto Ths oumt srs lgorthm, thology mplmtto of GM olvr. Blok N k l l Blok k NPk k l Blok Extto NP Extto 4 Blok Blok 4 Blok Fg. Artrrly-ot sttrg mtrx twork. Tokyo Isttut of Thology 7 Tkuh Hro. All rghts rsrv.

2 7//5 GM olvr Thl Nots, Pg /7. Progrm Ovrvw Th progrm works s follows.. R put fls.. Mk ovrso tls, whh r th stp of mkg mtrx quto.. Bul mtrx quto. (Th mtrx s squr) 4. olv th mtrx quto. (LAPACK rout s us hr) 5. Wrt output fls.. Tls Us ths Co Tl t_gport lk_lport t_lk_lport gport port_ot_fo t_x_vl_ls t_out_ls t_ukow_o Futo Look up lok o. ts lol port o. from glol port o. Look up glol port o. from lok o. ts lol port o. Look up th pr glol port o., whh s th ot glol port o. If th port s th xtto or lo, - r ssg, rsptvly. Lst of glol port umr(s) for xtto. Lst of glol port umr(s) for output. Look up th ukow o. th GM mtrx quto from glol port o. put/output formto. If th posto s kow, - r rtur for xtto lo ( put). Wth ov tls, w frly ovrt th formto whh s to ul th GM systm mtrx. Tokyo Isttut of Thology 7 Tkuh Hro. All rghts rsrv.

3 7//5 GM olvr Thl Nots, Pg /7 4. Bulg th GM ystm Mtrx Equto Lt us look t Port of Blok Fg.. Thr s xtto or mth lo t Port of Blok, wth th xtto offt of (kow offt). f Port of Blok s mth-lo. Norml port Th followg qutos r stsf for ukows of put output. l k (put) NP ( ) l k ( ) + Norml Port l k ( ) Norml Port Extto Extto ( ) ( ) Extto or mth-lo port Iput s kow output s ukow. NP ( ) Norml Port Norml Port (put) (put) (put) (put) ( ) ( ) + Extto Extto ( ) ( ) (put) I th ov prour, qutos wth th sm umr of ukows r ot. Tokyo Isttut of Thology 7 Tkuh Hro. All rghts rsrv.

4 7//5 GM olvr Thl Nots, Pg 4/7 our o s mplmt s follows.! ******** Bul GM Mtrx ******** wrt(*,*) '**** BUILD GM MATRIX ****' wrt(,*) '**** BUILD GM MATRIX ****'! Zro Clr ll mtrx_zro_lr(gsm_mtrx,_gsm_mtrx_ukow,_gsm_mtrx_ukow,_gsm_mtrx_ukow,_gsm_mtrx_ ukow) ll vtor_zro_lr(gsm_rhs_v,_gsm_mtrx_ukow,_gsm_mtrx_ukow) o,_gsm_totl_port! ---- Equto for Iput ---- t_port_ot_fo()! Cot Glol Port No. f( > ) th x_t_ukow_o(,)! Ukow No. of lf Port # x_t_ukow_o(,)! Ukow No. of Cot Port #! Eq. for ##: _{}{}! Eq. for ##: _{}-{} gsm_mtrx(x_,x_)gsm_mtrx(x_,x_)+. gsm_mtrx(x_,x_)gsm_mtrx(x_,x_)-. f! ---- Equto for Output ---- x_t_ukow_o(,)! Ukow No. of lf Port # lok_t_gport lk_lport().lok! Blok No. of Port # s_t_gport lk_lport().lo_port! Lol Port No. of Port #! for ##: _{}um {} _{}! for ##: _{}-um {} _{} gsm_mtrx(x_,x_)gsm_mtrx(x_,x_)+. o k,_port(lok_) t_lk_lport gport(lok_,k)! Glol Port No. #k x_t_ukow_o(,)! Ukow No. of Cot Port # s_k slt s (x_) s ()! No Iput from Port # s (-)! Extto from Port # gsm_rhs_v(x_)gsm_rhs_v(x_)+t_x_vl_ls()*s_mtrx(lok_,s_,s_) s fult! A to GM ystm Mtrx gsm_mtrx(x_,x_)gsm_mtrx(x_,x_)-s_mtrx(lok_,s_,s_) slt o o, Tokyo Isttut of Thology 7 Tkuh Hro. All rghts rsrv.

5 7//5 GM olvr Thl Nots, Pg 5/7 5. olvg th GM ystm Mtrx Equto Trtol mtho, suh s Guss lmto, us for mtrx vrso us th mtrx s squr. But GM olvr, psuo vrs, or grlz vrs, s us for mtrx vrso. By usg psuo vrs, th grl trtmt wthout y moftos th topology wll possl v wh th -mtrs hgs so tht th trmt of th mtrx oms zro. A xmpl wll show ltr. I th lulto of psuo vrs, th sgulr vlu omposto (VD) rout "zgsv.f plus ps" of LAPACK [] s us. I th ostruto of psuo vrs, th mtho th rfr [] or [] (pp.-5) s us. Blok () () () () Blok [ ] ) ( Fg. Exmpl Lt us s o of th xmpls s show Fg.. Th GM mtrx quto ot s follows. () () + + () () () () () () () () () () () () Hr, lt us suppos thr r o trto tw Port of Blok ( ). Tokyo Isttut of Thology 7 Tkuh Hro. All rghts rsrv.

6 7//5 GM olvr Thl Nots, Pg 6/7 Tokyo Isttut of Thology 7 Tkuh Hro. All rghts rsrv. ) ( () Th, th trmt of th ov mtrx s (). Wh (), th mtrx oms sgulr th mtrx quto oms ft. I othr wors, th ov quto ompos s follows., () () Wh (), th so mtrx quto s ft. Th o-trvl soluto of th so mtrx quto s th rsot mo of ths systm. Ths ot y solvg th gvlu prolm λ (), whr λ s gvlu. Th gvtor [ ] T whh orrspos to λ s th rsot soluto. Th rsot soluto s th o-trvl soluto whh xst wthout y xttos. But f you ust wt to kow out (), th psuo vrs us v ths s. Wth psuo vrs, you solv th prolm wthout y mofto topology put fl. omtms ths s vry usful (.g. ullfto of hghr orr mo ouplgs).

7 7//5 GM olvr Thl Nots, Pg 7/7 Rfrs [] LAPACK [] G. trg, Lr Algr ts Appltos, r., Thomso Lrg, 988. [] Numrl Computto oluto of Lr Equtos ( Jps) Tokyo Isttut of Thology 7 Tkuh Hro. All rghts rsrv.