lit
    JINRLIB

EISPACK - .

F220

: J.M.Boyle, B.S.Garbow, B.T.Smith :

aco apa aa cop aop opopa, pa po acc aopo, ca c c coc a coc opo poo c oc ap.
co a c:

  1. acapoa ap oo a, oo oc ooc c coc a;
  2. p o ap apa caoo a;
  3. c coc a ap caoo a;
  4. c coc opo ap caoo a;
  5. occao coc opo coo ap o cooc opa popaoao ap.

aopa ooca aa ooc MACHEP, - INIT_CONST (JINRLINPACK, F499). REAL*8 1.0E-17.

p cco opopa, o a, c aa , ao pao oca. opoo oca aoo aopa, oa ooc poa o cooa opopa a pao [1].

BALANC acapoa co ap
oo a
. 1
BALBAK occao coc opo
coo co ap oo
a
.17
BISECT c coc a
cpco paoao ap
aao pa
.12
CBABK2 occao coc opo
coo oco ap oo a
.18
CBAL acapoa oco ap
oo a
. 2
COMHES p oco ap oo a
oco p op ccpa
ap popaoa oo
. 5
COMLR c coc a
oco ap p op
ccpa
.10
COMLR2 c coc a
coc opo oco ap
p op ccpa
.14
ELMHES p co ap oo
a p op ccpa
ap popaoa oo
. 3
ELTRAN op pp ap
popaoa
. 4
HQR c coc a
co ap p op
ccpa
. 9
HQR2 c coc a
coc opo co
ap p op ccpa
.13
HTRIBK occao coc opo
coo oco poo ap
.20
HTRIDI p oco poo ap
co cpco
paoao ap
popaoa
. 8
IMTQL1 c coc a
cpco paoao ap
.11
IMTQL2 c coc a
coc opo cpco
paoao ap
.15
TINVIT c coc opo
cpco paoao ap
aao pa
.16
TQL1 c coc a
cpco paoao ap
.11
TQL2 c coc a
coc opo cpco
paoao ap
.15
TRBAK1 occao coc opo
coo cpco ap
.19
TRED1 p co cpco
ap cpco paoao
opooa popaoa
. 6
TRED2 p co cpco
ap cpco paoao
opooa popaoa c
ao
. 7

:

: - SUBROUTINE
: - BALANC BALBAK BISECT CBABK2 CBAL COMHES COMLR COMLR2 ELMHES ELTRAN HQR HQR2 HTRIBK HTRIDI IMTQL1 IMTQL2 TINVIT TQL1 TQL2 TRBAK1 TRED1 TRED2
: - INIT_CONST(F499)
COMMON BLOCK: - /F499_RCONST/

:

  1. J.M. Bol, B.S.Garow, B.T.Smit et.al.
    Matrix Eigensystem Routines - EISPACK Guide. Scond dition.
    Lcture Notes in Computer Science. Vol.6.
    Springr-Vrlag, Nw Yor. 1976.
  2. ..co, .a. Cpao aopo a .
    a apa, Moca, "Maocpo", 1976.
  3. ..co. paca poa coc a.
    Moca, "Haa" 1970.
  4. http://www.netlib.org/eispack

1. acapoa co ap oo a ( BALANC ).

:

popaa acap c ap oo a (c. [1], cp.200 [2], cp.277). p o c o cooc cpoa coa ac po pa ooo popaoa oo, .. apa caoc paoco.
acapoa oa op coo ap, o cao p oca coc a .
oo cco oc ooc c coc a / coc opo.
po oo, BALANC o oooc "opoa" coc a c oo pcaoo cpo coo.

:

CALL BALANC (NM,N,A,LOW,IGH,SCALE), :

NM - oco cpo poo acca A opaop DIMENSION a popa.
N - opo aao ap, N ≤ NM.
A - c p acc A(NM,N), copa a o co ap opa N, a o - paoc ap.
LOW,IGH - p, aa a o pa co paoco ap.
SCALE - c oop acc papoc N, copa a o opa o popaoa oo (c.[1], cp.202).

:

  1. BALANC ooo p c pa, oa apa c paoco, .. cpo co cco paac o a op.
    p pao popa BALANC ao o cpa c p pao popa, c coc a / coc op. o p p papo acapoa oac ooc c coc a / coc opo.
    oo BALANC poc p ca oo ca.
  2. oc op coc opo popaoao ap p popa BALBAK (. .17) ao coc opo coo ap.
2. acapoa oco ap oo a ( CBAL ).

popaa acap oc ap oo a (c.[1], cp.224). p o c o cooc cpoa coa ac po pa ooo popaoa oo, .. apa caoc paoco. acapoa oa op coo ap, o p oca coc a . o oo cc oc ooc c coc a / coc opo. po oo CBAL o oooc "opoa" coc a c oo pcaoo cpo coo.

:

CALL CBAL (NM,N,AR,AI,LOW,IGH,SCALE), :

NM - oco cpo p acco AR AI opaop DIMENSION a popa.
N - opo aao ap, N ≤ NM.
AR,AI - c p acc AR(NM,N) AI(NM,N), copa a o cooco c ac oco ap opa N, a o - c ac paoco ap.
LOW,IGH - p, aa a o pa co paoco ap.
SCALE - c oop acc papoc N, copa a o opa popaoa oo (c.[1], cp.226).

:

  1. CBAL ooo p c pa, oa apa c paoco, .. cpo co cco paac o a op.
    pao popa CBAL ao o cpa c p pao popa, c coc a / coc op. o p p papo acapoa oac ooc c coc a / coc opo. oo CBAL poc p ca oo ca.
  2. oc op coc opo popaoao ap p popa CBABK2 (. .18) ao coc opo coo ap.
3. p co ap oo a p op ccpa
ap popaoa ( ELMHES )
.

:

popaa po c ap oo a p op ccpa, p co ap popaoa oo (c.[1], cp.310; [2], cp.298). aa pa opa coc p popaa ao coc a / coc opo coo ap.

:

CALL ELMHES (NM,N,LOW,IJH,A,INT), :

NM - oco cpo poo acca A opaop DIMENSION a popa.
N - opo aao ap, N ≤ NM.
LOW,IGH - p, aa a o pa co paoco ap. c o apapa poa BALANC, c oa a pa.
acapoa poooc, o LOW=1, IGH=N.
A - c p acc A(NM,N), copa a o o c ap opa N, a o - o ap p op ccpa, a a oop o, co p (c.[1], cp.311).
INT - oo oop acc c papoc IGH ooa cpo coo, oop opac pcaoa. popa ELMHES ac coc oo oo o LOW+1 o IGH-1 o.

:

  1. c c coc a coo ap poc a cooa popa HQR (. .9)
  2. c c coc a coc opo - ELTRAN (. .4), HQR2 (. .13) BALBAK (. .17)
4. p pp ap popaoa ( ELTRAN ).

:

popaa op pp ap popaoa (c.[1], cp.316;
[2], cp.329), oopa pac p p paoco co ap oo a p op ccpa o popa ELMHES.

:

CALL ELTRAN (NM,N,LOW,IGH,A,INT,Z), :

NM - oco cpo poo acca A opaop DIMENSION a popa.
N - opo aao ap, N ≤ NM.
LOW,IGH - p, aa a o pa co paoco ap. c o apapa popa BALANC, c oa a pa.
c acapoa poooc, o LOW=1, IGH=N.
A - c p acc A(NM,IGH).
po oaoa cop a o o, oop cooa o ap ccpa popa ELMHES (c.[1], cp. 311). caac p ac A pooa.
INT - oo oop acc p papoc IGH ooa cpo coo, oop opac pcaoa o p pao popa ELMHES (c.[1], cp.311).
Z - c p acc Z(NM,N), copa a o ap popaoa.

:

c c coc a coc opo coo ap a popaa oa coa a ELMHES (. .3), a a - HQR2 (. .13).


5. p oco ap oo a oco p op ccpa
ap popaoa oo ( COMHES )
.

:

popaa po oc ap oo a oco p op ccpa, p co ap popaoa oo (c.[1], cp.253; [2], cp.301). a pa opa coc p popaa ao coc a / coc opo coo ap.

:

CALL COMHES (NM,N,LOW,IGH,AR,AI,INT), :

NM - oco cpo p acco AR, AI opaop DIMENSION a popa.
N - opo aao oco ap, N ≤ NM.
LOW,IGH - p, aa a o pa co paoco ap. c o apapa popa CBAL, c oa a pa.
acapoa poooc, o LOW=1,IGH=N.
AR,AI - c p acc AR(NM,N), AI(NM,N), copa a o cooco c ac oco ap opa N, a o - c ac co ap p op ccpa, a a oop o, co popaoa (c.[1] cp. 255).
INT - oop acc c papoc IGH ooa cpo coo, oop opac pcaoa. COMHES ac co oo oo o LOW+1 o IGH-1 o.

:

  1. c c coc a coo ap poc a cooa popa OMLR (. .10).
  2. c c coc a coc opo - COMLR2 (. .14).

6. p co cpco ap cpco paoao
, pooa popaoa ( TRED1 )
.

:

popaa po c cpc ap cpco paoao, p opooa popaoa oo (c.[1], cp.483;
[2], cp.190). a pa opa coc p popaa ao coc a / coc opo coo ap.

:

CALL TRED1 (NM,N,A,D,E,E2), :

NM - oco cpo poo acca A opaop DIMENSION a popa.
N - opo aao ap, N ≤ NM.
A - c p acc A(NM,N), copa a o cpc ap opa N. a o oaoa copa opa o opooao popaoa (c.[1], cp.485).
popa cooa o poa.
po poa op co ap.
D - c oop acc papoc N, copa a o aoa paoao ap.
E - c oop acc papoc N, oc N-1 o oopoo a o copa aoa paoao ap, a E(1)=0.
E2 - c oop acc papoc N, oc N-1 o oopoo a o copa apa aoa o paoao ap, oo popa BISECT (. .12), a E2(1)=0.

:

  1. c c coc a coo ap poc a cooa TQL1 (. .11).
  2. c coc a aao pa - BISECT (. .12).
  3. c coc a aao pa cooc coc opo - BISECT (. .12), TINVIT (. .16) TRBAK1 (. .19).
  4. c c coc a coc opo coo ap c cooa TRED2 (. .7) co TRED1 (. .6 ), a TQL2
    (. .15).
  5. c apa po aao o, o a o aoc o p (c.[2], cp.198).
7. p co cpco ap cpco paoao
opooa popaoa c ao ( TRED2)
.

:

popaa po c cpc ap cpco paoao, p opooa popaoa oo c ao
(c.[1], cp.489; [2], cp.190). a pa opa coc p popaa ao coc a / coc opo coo ap.

:

CALL TRED2 (NM,N,A,D,E,Z), :

NM - oco cpo p acco A Z opaop DIMENSION a popa.
N - opo aao ap, N ≤ NM.
A - c p acc A(NM,N), copa a o cpc ap opa N.
popa cooa o poa ap.
D - c oop acc papoc N, copa o aoa paoao ap.
E - c oop acc papoc N, oc N-1 o oopoo a o copa aoa paoao ap, a E(1)=0.
Z - c p acc Z(NM,N) copa opooa ap popaoa. a apa po co ap paoao op.

:

  1. c c coc a coc opo poc a cooa TQL2 (. .15).
  2. p ca c coc a coc opo (oo coc a, coc a aao pa cooc
    coc opo ..) p TRED1 (. .6) co TRED2 (. .7).
  3. c apa po aao o, o a o aoc o p (c.[2], cp.198).
  4. apap A Z o pa.
8. p oco poo ap co pco
paoao ap popaoa ( HTRIDI )
.

:

popaa po oc po ap co cpco paoao, p ap popaoa oo (c.[1], cp.357).
pa opa coc p popaa ao coc a / coc opo coo ap.

:

CALL HTRIDI (NM,N,AR,AI,D,E,E2,TAU), :

NM - oco cpo p acco AR AI opaop DIMENSION a popa.
N - opo aao ap, N ≤ NM.
AR,AI - c p acc AR(NM,N), AI(NM,N), copa a o cooco c ac poo ap.
popa cooa o poa ap.
o oaoa AR po AI cop oop opa o ap popaoa.
p po AR aaoa AI ocac p (c.[1], cp.359).
D - c oop acc papoc N, copa a o aoa co cpco paoao ap.
E - c oop acc papoc N, oc N-1 o oopoo a o copa aoa paoao ap, a E(1)=0.
E2 - c oop acc papoc N, oc N-1 o oopoo a o copa apa aoa o paoao ap, oo popa BISECT (. .12), a E2(1)=0.
TAU - c p acc TAU(2,N), copa a o oop opa o ap popaoa (c.[1], cp.359).

:

  1. c c coc a coo ap poc a cooa TQL1 IMTQL1 (. .11).
  2. c c coc a coc opo - TQL2 IMTQL2 (. .15), a a HTRIBK (. .20).
  3. c coc a aao pa - BISECT (. .12).
  4. c coc a aao pa cooc coc opo - BISECT (. .12), TINVIT (. .16), HTRIBK (. .20).
9. c coc a co ap p op
ccpa ( HQR )
.

:

popaa c coc a co ap p op ccpa, co QR-aop (c.[1], cp.330; [2], cp.316).

:

CALL HQR (NM,N,LOW,IGH,H,WR,WI,IERR), :

NM - oco cpo poo acca H opaop DIMENSION a popa.
N - opo aao ap, N ≤ NM.
LOW,IGH - p, aa a o pa co paoco ap. c o apapa popa BALANC (. .1), c oa a pa.
c acapoa poooc, o LOW=1, IGH=N.
H - c p acc H(NM,N), copa a o ap opa N p op ccpa. a o apa copac.
WR,WI - c oop acc papoc N, copa a o cooco c ac coc a ap ccpa. oc a opo, o oco-cop ap co ocoao, p caaa coc a c ooo o ac.
IERR - a pa, apapa pa pao popa. c p c coc a pc o 30 pa, o paoa popa aaac IERR oaa pao c cooco cocoo a. oc a acca WR WI o p IERR+1, IERR+2,..., N. c c coc a oca pa 30 pa, o IERR=0.

:

op coc a co ap oo a popa HQR oa pcoa ELMHES (. .3).


10. c coc a oco ap p op
ccpa ( COMLR )
.

:

popaa c coc a oco ap p op ccpa, p opoa LR-aop (c.[1], cp.259; [2], cp.327).

:

CALL COMLR (NM,N,LOW,IGH,HR,HI,WR,WI,IERR), :

NM - oco cpo p acco HR, HI opaop DIMENSION a popa.
N - opo aao ap, N ≤ NM.
LOW,IGH - p, aa a o pa co paoco ap. c o apapa popa CBAL, c oa a pa.
acapoa poooc, o LOW=1, IGH=N.
HR,HI - c p acc HR(NM,N) HI(NM,N), copa a o cooco c ac oco ap ccpa.
WR,WI - c oop acc papoc N, copa a o cooco c ac coc a ap ccpa.
IERR - a pa, apapa pa pao popa. c p c oopoo cocoo a pc o 30 pa, o paoa popa aaac IERR oaa pao c cooco cocoo a.
oc a WR WI pa IERR+1, IERR+2,..., N. c c coc a op pa 30 pa, o IERR=0.

:

  1. op coc a oco ap oo a popa COMLR oa pcoa COMHES (. .5).
  2. paa aopa cooaa ca apa, a c c apaoo op ocoo ca oc c.
11. c coc a cpco paoao ap
( TQL1, IMTQL1 )
.

:

popa c c coc a cpco paoao ap, p QL-aop c co (c.[1], cp.378,463; [2], cp.203,216).
TQL1 oo paoa ap, oop c o o cpoa c po pa cpoo opaca o po o oc cpo.
op IMTQL1 c ao papoc a, oo poc cpco paoao ap, oa cppa ca.

:

CALL TQL1 (N,D,E,IERR)
CALL IMTQL1 (N,D,E,IERR), :

N - opo aao ap.
D - c oop acc papoc N, copa a o aoa cpco paoao ap,
a o - coc a o ap opaca op.
E - c oop acc papoc N, oc N-1 o oopoo a o copa aoa cpco paoao ap, a a E(1) pooa. a o acc copac.
IERR - a pa, apapa pa pao popa. c p c oopoo cocoo a pc o 30 pa, o paoa popa aaac IERR oaa pao c cooco cocoo a.
oc a acc D p opo co 1,2,...,IERR-1. c c coc a op pa 30 pa, o IERR=0.

:

  1. op coc a oo cpco ap popaa TQL1 IMTQL1 oa pcoa TRED1 (. .6).
  2. op coc a oco poo ap popaa TQL1 IMTQL1 oa pcoa HTRIDI (. .8).
  3. o IMTQL1 o opoo paoa c apa, oop c o o cpoa c po pa, o TRED1 HTRIDI o aa oo pa o ca. oo pco IMTQL1 p TQL1 ca ca ooo popaoa TRED1 HTRIDI.
12. c coc a cpco paoao ap
aao pa ( BISECT )
.

:

popaa c coc a cpco paoao ap aao pa, co ocoaoc pa (c.[1], cp.211; [2], cp.223).

:

CALL BISECT (N,EPS1,D,E,E2,LB,UB,MM,M,W,IND,IERR,RV4,RV5), :

N - opo aao ap.
EPS1 - ca pa, oca acoa oa p c coc a.
c a EPS1 cao oaaac ooo, o popaa caa aa EPS1 (c.[2], cp.227).
D - acc papoc N, copa a o aoa cpco paoao ap.
E - acc papoc N, oc N-1 o oopoo a o copa aoa cpco paoao ap,
a E(1)=0.
E2 - acc papoc N, oc N-1 o oopoo a o copa apa aoa o cpco paoao ap, a E2(1) - pooa a. a o E2(1)=0.
c oop acca cac a, o cooc E2 oaa pa , a opao, apa paac a c oap.
LB,UB - c o p, op cooco p pa paa coc a, LB ≤ UB.
MM - o co, aa a o poaao oco coc a pa (LB,UB).
M - o co, op a o oco c coc a pa (LB,UB)
W - acc papoc MM, copa a o M coc a cpco paoao pa (LB,UB), pacoo op opaca.
IND - acc c papoc MM, copa a o c coc a acca W, cooc oapa. oc a, oocc po oap, c 1, o opo - 2 ...
IERR - a pa, apapa pa pao popa. c M pa MM, o popaa c coc a oaa IRR=3*N+1. p o M pao oc coc a, a pa (LB,UB). c M ≤ MM, o IERR=0.
RV4,RV5 - pao acc papoc N.

:

  1. op coc a aao pa oo cpco ap popa BISECT oa pcoa popaa TRED1 (. .6).
  2. op coc a aao pa oco poo ap popa BISECT oa pcoa popaa HTRIDI (. .8).
  3. op coc opo, cooc c coc a, a c cooa TINVIT (. .16) TRBAK1 (. .19), c pac TRED1 (. .6), TINVIT (. .16) HTRIBK (. .20), c pac HTRIDI (. .8).
  4. popa TQL1 IMTQL1 op c coc a cpco paoao ap paoa cp BISECT, c aao pa o 25 poo c coc a. oao, c ooo c o 25 poo coc a, o poc cooa TQL1 IMTL1.
13. coc a coc opo co ap
p op ccpa ( HQR2 )
.

:

popaa c coc a coc op co ap p op ccpa QR - aop (c.[1], cp.338; [2], cp.330).
oc op co ap oo a oo c, c c oo popa ELMHES pc ap op ccpa , ELTRAN, ap popaoa.

:

CALL HQR2 (NM,N,LOW,IGH,H,WR,WI,Z,IERR), :

NM - oco cpo p acco H Z opaop DIMENSION a popa
N - opo aao ap, N ≤ NM.
LOW,IGH - p, aa a o pa co paoco ap. c o apapa popa BALANC, c oa a pa.
c acapoa poooc, o LOW=1,IGH=N.
H - p acc H(NM,N), copa a o ap (N*N) p op ccpa.
o apa copac.
WR,WI - c acc papoc N, copa a o cooco c ac a ap ccpa.
oc a opo, o oco-cop ap co ocoao, p caaa - coc a c ooo o ac.
Z - c p acc Z(NM,N).
pc c coc op ap ccpa, o a o Z cop ap opa N, a o - coa coc op ap ccpa.
c pc c coc op co ap oo a, o a o Z cop ap popaoa, o popao ELTRAN, a a o - coa coc op ap oo a. c J-o coco a oco, o (J+1)-o - oco-copo. oc coc op, cooc o oco-copo ap, o a a a J-o coa + i*(J+1)-o coa cooco J-o coa - i*(J+1)-o coa acca Z. oc op opaoa.
IERR - a pa, apapa pa pao popa. c p c oopoo cocoo a pc o 30 pa, o paoa popa ppaac IERR oaa pao c cooco cocoo a.
oc a acca WR WI p co IERR+1, IERR+2,..., N, a coc op cc.
c c coc a op pa 30 pa, o IERR=0.

:

  1. c coc a coc opo co ap oo a popa HQR2 oa pcoa ELMHES (. .3) ELTRAN (. .4).
  2. oc o ca poo acapoa o popa BALANC (. .1) p cooa ELMHES, a a oc HQR2 (. .13) p popa BALBAK (. .17).
14. c coc a coc opo oco ap
p op ccpa ( COMLR2 )
.

:

popaa c coc a coc op oco ap p op ccpa, co opoa LR-aop op coc a aoa LR-popoa op coc opo (c.[1], cp.266; [2], cp.328).
oc op oco ap oo a a oo c c oo COMLR2, c papo pc ap p op ccpa, p popa COMHES.

:

CALL COMLR2 (NM,N,LOW,IGH,INT,HR,HI,WR,WI,ZR,IERR), :

NM - oco cpo p acco HR,HI,ZR,ZI opaop DIMENSION a popa.
N - opo aao ap, N ≤ NM.
LOW,IGH - p, aa a o pa co paoco ap. c o apapa popa CBAL, c oa a pa.
acapoa poooc, o LOW=1, IGH=N.
INT - acc p papoc IGH.
popa coc oo o LOW o IGH. c cc coc op oco ap ccpa, o a o oaa INT(J)=J J=LOW, LOW+1,...,IGH.
c oco ap oo a, o INT cop opa o cpoa coa, oop opac pcaoa popa COMHES.
HR,HI - c p acc HR(NM,N), HI(NM,N), copa a o cooco c ac oco ap ccpa. c cc coc op ap ccpa, o po HR HI, a oaoa, oaa pa . c oco ap oo a, o po HR HI copa o, o popao COMHES.
oc pao popa acc copac, a HR(1,1) copc opa poo ap, opo a ca aco a c oo c o poo ap.
WR,WI - c acc papoc N, copa a o cooco c ac coc a ap ccpa.
ZR,ZI - c p acc ZR(NM,N), ZI(NM,N), copa a o cooco c ac coc opo. oc op opaoa.
IERR - a pa, apapa pa pao popa. c p c oopoo cocoo a pc o 30 pa, o paoa popa ppaac IERR oaa pao c cooco cocoo a.
oc a WR WI p co IERR+1,IERR+2,...,N, a coc op cc. c c coc a opc pa 30 pa, o IERR=0.

:

  1. c coc a coc opo oco ap oo a popa COMLR2 oa pcoa COMHES (. .5).
  2. o ca poc p popao COMHES poo acapoa o CBAL (. .2), a a COMLR2 p popa CBABK2 (. .18).
  3. popaa o oop ca aa oo pa (ocoo coc opa), oco po pa poco ap o. o o co o p LR-pa. pp oo o o cpa op ap ( a aoc HR(1,1) c cooc opo opa coc a (c. [2], cp.268).
  4. paa aopa cooaa apa c c, a c apaoo op oc c oc c.
15. c coc a coc opo cpco
paoao ap ( TQL2, IMTQL2 )
.

:

popa op coc a coc op cpco paoao ap (c.[1], cp.384,468; [2], cp.203,216). c coc a pc QL-aop, p o aoac apa popaoa c oc coc opo. oc op oo cpco ap a oo c, c papo popaoa paoa, p TRED2 .
popaa TQL2 oo paoa ap, oop c o o cpoa c po pa cpoo opaca o po o oc cpo. op IMTQL2 c ao papoc a, oo poc cpco paoao ap, oa cppa ca.

:

CALL TQL2 (NM,N,D,E,Z,IERR)
CALL IMTQL2 (NM,N,D,E,Z,IERR), :

NM - oco cpo poo acca Z opaop DIMENSION a popa.
N - opo aao ap, N ≤ NM.
D - acc papoc N, copa a o aoa cpco paoao ap. a o cop coc a o ap opaca op.
- acc papoc N, oc N-1 o oopoo a o copa aoa cpco paoao ap, a (1) pooa.
o acca copac.
Z - p acc Z(NM,N).
c pc c coc op cpco paoao ap, o a o Z cop ap opa N, a a o cop opooppoa coc op o paoao ap.
c pc c coc op oo cpco ap, o a o Z cop ap popaoa, o popao TRED2, a a o cop pooppoa coc op o oo cpco ap.
IERR - a pa, apapa pa pao popa.
c p c oopoo cocoo a pc o 30 pa, o paoa popa paac IERR oaa pao c cooco cocoo a.
oc a coc op acca D Z cooco p co 1,2,...,IERR-1, o coc a opo.
c c coc a op pa 30 pa, o IERR=0.

:

  1. c coc a coc opo oo cpco ap popaa TQL2 IMTQL2 oa pcoa TRED2 (. .7).
  2. c coc a coc opo oco poo ap popaa TQL2 IMTQL2 oa pcoa HTRIDI (. .8), a oo acc Z TQL2 IMTQL2 o copa ap. a popaa TQL2 IMTQL2 oa coa HTRIBK (. .20) popaoa coc opo, o o TQL2 IMTQL2, coc op coo ap.
  3. o IMTQL2 o opoo paoa c apa, oop c o o cpoa c po pa, o TRED2 HTRIDI o aa oo pa o ca. oo pco IMTQL2 p TQL2 ca ca ooo popaoa TRED2 HTRIDI.
16. c coc opo aao pa cpco
paoao ap ( TINVIT )
.

:

popaa c coc op cpco paoao ap, cooc ocoaoc opo p coc a. coc aop opao pa (c.[1], cp.448).

:

CALL TINVIT (NM,N,D,E,E2,M,W,IND,Z,IERR,RV1,RV2,RV3,RV4,RV6), :

NM - oco cpo po acc Z opaop DIMENSION a popa.
N - opo aao ap, N ≤ NM.
D - acc papoc N, copa a o aoa cpco paoao ap.
- acc papoc N, oc N-1 o oopoo a o copa aoa cpco paoao ap,
a (1) - pooa a.
2 - acc papoc N, oc N-1 o oopoo a o copa apa cooc o (opa a
cooc 2);
(I) ppo a 2(I) oaa pa , c oo o po MACHEP a c
D(I) D(I-1)).     (*)
c coc a a opaca op, o 2(1)= 0.0, c a op, o 2(1)=2.0.
c cooaac popaa BISECT coc a, o oo acc 2 popa BISECT c o TINVIT.
- oco aa coc a, oop pc op cooc coc op.
W - c acc papoc , copa a o aa coc a cpco paoao ap.
oc a o opo opaca a op.
opoa ooo op ac opooa coc opo, cooc coc a.
IND - acc p papoc ,
copa a o c oap, oop oca cooc coc a acc W. oc a, paa po oap, c 1, o opo oap - c 2 ...
cooaac popaa BISECT op coc a, o oo acc IND popa BISECT o TINVIT.
Z - c p acc Z(NM,N),
copa a o opooa coc opo cpco paoao ap, cooc M coc a acc W.
IERR - a pa, apapa pa pao popa. c op oopoo cocoo opa pc o 5 pa, o c aaac oaa IERR=-R, R - c cocoo opa. c o poco o ooo cocoo opa, o IERR acac oc ca, a cooc co Z oca .
c c coc op op pa 5 pa, o IERR=0.
RV1,RV2,
RV3,RV4,
RV6
- pao acc papoc N (c.[1], cp.450).

:

  1. c coc a aao pa cooc coc opo oo cpco ap popa TINVIT oa pcoa TRED1 (. .6), BISECT (. .12), a a TINVIT - TRBAK1 (. .19).
  2. c coc a aao pa cooc coc opo oco poo ap popa TINVIT o pcoa HTRIDI (. .8), BISECT (. .12), a a TINVIT - HTRIBK (. .20).
  3. c coc opo oo opao pa p, o ooc coc a a copa c a ooc o opa MACHEP ap a.     (*)
    oca cpc paoa ap ocaoo, o acoa oa coc a, oop opc coc op, a po paa op ap, oo a MACHEP. o oop ap pc a acoa oa: a coco a, oo a MACHEP.
---------------
(*) MACHEP - , ,
1.0 + MACHEP > 1.0;
REAL*8 1.0E-17.

17. occao coc opo coo co ap oo
a ( BALBAK )
.

:

popaa op coc op coo co ap oo a o cooc coc opa paoco ap (c.[1], cp.207;
[2], cp.277). aoca apa cc popao BALANC.

:

CALL BALBAK (NM,N,LOW,IGH,SCALE,M,Z), :

NM - oco cpo poo acca Z opaop DIMENSION a popa.
N - oco oo opa acc Z, N ≤ NM.
LOW,IGH - p, aa a o pa co paoco ap.
SCALE - acc papoc N, copa a o opa o popaoa oo (c. BALANC, .1).
M - oco coo acc Z, .. oco coc opo paoco ap, oop oa popaoa.
Z - c p acc Z(NM,N),
copa a o p coa c ac coc opo, oop oa popaoa.
o coo copa c ac popaoa coc opo (c. HQR2, .13).

18. occao coc opo coo oco ap oo a
( CBABK2 )
.

:

popaa op coc op coo oco ap oo a o cooc coc opa paoco ap (c.[1], cp.220).
aoca apa cc popao CBAL (c. .2).

:

CALL CBABK2 (NM,N,LOW,IGH,SCALE,,ZR,ZI), :

NM - oco cpo p acco ZR ZI opaop DIMENSION a popa.
N - oco oo opa acc Z=(ZR,ZI), N ≤ NM.
LOW,IGH - p, aa a o pa co paoco ap.
SCALE - acc papoc N, copa a o opa o popaoa oo (c. CBAL, .2).
- oco coo Z=(ZR,ZI), .. oco coc opo paoco ap, oop oa popaoa.
ZR,ZI - a c p acca ZR(NM,) ZI(NM,), copa a o p coa ZR ZI cooco c ac coc opo, oa popaoa. a o coo ZR ZI copa c ac popaoa coc opo (c. COMLR2, .14).

19. occao coc opo coo co cpco
ap ( TRBAK1 )

:

popaa op coc op coo co cpco ap o coc opa cpco paoao ap
(c.[1], cp.475; [2], cp.190). ca cpca apa poc cpco paoao popao TRED1 (c. .6).

:

CALL TRBAK1 (NM,N,A,E,M,Z), :

NM - oco cpo p acco A Z opaop DIMENSION a popa.
N - opo aao ap, N ≤ NM.
A - p acc A(NM,N), oaoa oopoo a o copa oop opa o opooa popaoa
(c. TRED1, .6). caac p ac ap pooa.
E - acc papoc N, oc N-1 o oopoo a o copa aoa paoao ap. a E(1) pooa. ca copa ocac opa o opooa popaoa.
M - oco coo Z, .. oco coc opo, oop oa popaoa.
Z - p acc Z(NM,N), copa a o p M coa coc op, oop oa popaoa. a o co copa popaoa coc op.
oppoa, c o coc op ooppoa.

20. occao coc opo coo oco poo ap
( HTRIBK )

:

popaa op coc op coo oco poo ap o cooc coc opa co cpco paoao (c.[1], .349).
popa HTRIDI (c. .8).

:

CALL HTRIBK (NM,N,AR,AI,TAU,M,ZR,ZI), :

NM - oco cpo p acco AR,AI,ZR,ZI opaop DIMENSION a popa.
N - opo aao ap, N ≤ NM.
AR,AI - p acc AR(NM,N), AI(NM,N).
oaoa po AR po AI copa a o oop opa o ap popaoa (c. HTRIDI, .8).
TAU - p acc TAU(2,N), copa a o oop opa o ap popaoa (c. HTRIDI, .8).
M - oco coo Z=(ZR,ZI), ..
oco coc opo, oop oa popaoa.
ZR,ZI - c p acc ZR=(NM,M), ZI(NM,M),
copa a o p M coa ZR coc op, oa popaoa, a copo ZI pooo.
a o M o ZR ZI copa cooco c ac popaoa coc opo.
ooppoa, c o coc
op ooppoa.


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