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doctorondemand
doctorondemand / Pygments python
Repository URL to install this package:
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Version:
2.5.0 ▾
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ræ rç hX rè ré j£ X &rê rë j X rì rí hX SCR1rî rï j© jÈ rð hX SCR2rñ rò j© jÈ ró hX IPVTrô rõ j© jÈ rö hX JPVTr÷ rø j© jÈ rù hX CONrú rû j© jÈ rü hX WORKrý rþ j© jÈ rÿ hX ISEEDr r j© jÈ r hX IERRr r j© X )r r j j» r jL X !Testr r jL X inline commentr
r j jæ r jL X C
r
r jL X C FUNCTION:
r r jL X CF
r r jL XD CF Determines whether the pair (A,B) is controllable and flags
r r jL X? CF the eigenvalues corresponding to uncontrollable modes.
r r jL XG CF this ad-hoc controllability calculation uses a random matrix F
r r jL XG CF and computes whether eigenvalues move from A to the controlled
r r jL X CF system A+B*F.
r r jL X CF
r r jL X C USAGE:
r r jL X CU
r! r" jL XI CU CALL AHCON (SIZE,N,M,A,B,OLEVR,OLEVI,CLEVR,CLEVI,SCR1,SCR2,IPVT,
r# r$ jL X. CU JPVT,CON,WORK,ISEED,IERR)
r% r& jL X CU
r' r( jL XC CU since AHCON generates different random F matrices for each
r) r* jL XA CU call, as long as iseed is not re-initialized by the main
r+ r, jL XD CU program, and since this code has the potential to be fooled
r- r. jL XA CU by extremely ill-conditioned problems, the cautious user
r/ r0 jL XA CU may wish to call it multiple times and rely, perhaps, on
r1 r2 jL XB CU a 2-of-3 vote. We believe, but have not proved, that any
r3 r4 jL XE CU errors this routine may produce are conservative--i.e., that
r5 r6 jL X? CU it may flag a controllable mode as uncontrollable, but
r7 r8 jL X CU not vice-versa.
r9 r: jL X CU
r; r< jL X C INPUTS:
r= r> jL X CI
r? r@ jL X= CI SIZE integer - first dimension of all 2-d arrays.
rA rB jL X CI
rC rD jL X, CI N integer - number of states.
rE rF jL X CI
rG rH jL X, CI M integer - number of inputs.
rI rJ jL X CI
rK rL jL XB CI A double precision - SIZE by N array containing the
rM rN jL X1 CI N by N system dynamics matrix A.
rO rP jL X CI
rQ rR jL XB CI B double precision - SIZE by M array containing the
rS rT jL X. CI N by M system input matrix B.
rU rV jL X CI
rW rX jL XF CI ISEED initial seed for random number generator; if ISEED=0,
rY rZ jL X< CI then AHCON will set ISEED to a legal value.
r[ r\ jL X CI
r] r^ jL X C OUTPUTS:
r_ r` jL X CO
ra rb jL XG CO OLEVR double precision - N dimensional vector containing the
rc rd jL X4 CO real parts of the eigenvalues of A.
re rf jL X CO
rg rh jL XG CO OLEVI double precision - N dimensional vector containing the
ri rj jL X9 CO imaginary parts of the eigenvalues of A.
rk rl jL X CO
rm rn jL XC CO CLEVR double precision - N dimensional vector work space
ro rp jL XG CO containing the real parts of the eigenvalues of A+B*F,
rq rr jL X. CO where F is the random matrix.
rs rt jL X CO
ru rv jL XC CO CLEVI double precision - N dimensional vector work space
rw rx jL XE CO containing the imaginary parts of the eigenvalues of
ry rz jL X5 CO A+B*F, where F is the random matrix.
r{ r| jL X CO
r} r~ jL XG CO SCR1 double precision - N dimensional vector containing the
r r jL XB CO magnitudes of the corresponding eigenvalues of A.
r r jL X CO
r r jL XG CO SCR2 double precision - N dimensional vector containing the
r
r jL XG CO damping factors of the corresponding eigenvalues of A.
r r jL X CO
r r jL XH CO IPVT integer - N dimensional vector; contains the row pivots
r r jL XI CO used in finding the nearest neighbor eigenvalues between
r r jL XF CO those of A and of A+B*F. The IPVT(1)th eigenvalue of
r r jL XH CO A and the JPVT(1)th eigenvalue of A+B*F are the closest
r r jL X CO pair.
r r jL X CO
r r jL XD CO JPVT integer - N dimensional vector; contains the column
r r jL XI CO pivots used in finding the nearest neighbor eigenvalues;
r r jL X CO see IPVT.
r r jL X CO
r r jL XL CO CON logical - N dimensional vector; flagging the uncontrollable
r r jL X@ CO modes of the system. CON(I)=.TRUE. implies the
r¡ r¢ jL XO CO eigenvalue of A given by DCMPLX(OLEVR(IPVT(I)),OLEVI(IPVT(i)))
r£ r¤ jL XC CO corresponds to a controllable mode; CON(I)=.FALSE.
r¥ r¦ jL XD CO implies an uncontrollable mode for that eigenvalue.
r§ r¨ jL X CO
r© rª jL XJ CO WORK double precision - SIZE by N dimensional array containing
r« r¬ jL XE CO an N by N matrix. WORK(I,J) is the distance between
r r® jL XL CO the open loop eigenvalue given by DCMPLX(OLEVR(I),OLEVI(I))
r¯ r° jL XA CO and the closed loop eigenvalue of A+B*F given by
r± r² jL X+ CO DCMPLX(CLEVR(J),CLEVI(J)).
r³ r´ jL X CO
rµ r¶ jL XE CO IERR integer - IERR=0 indicates normal return; a non-zero
r· r¸ jL XG CO value indicates trouble in the eigenvalue calculation.
r¹ rº jL XE CO see the EISPACK and EIGEN documentation for details.
r» r¼ jL X CO
r½ r¾ jL X C ALGORITHM:
r¿ rÀ jL X CA
rÁ r jL X? CA Calculate eigenvalues of A and of A+B*F for a randomly
rà rÄ jL XB CA generated F, and see which ones change. Use a full pivot
rÅ rÆ jL X? CA search through a matrix of euclidean distance measures
rÇ rÈ jL X: CA between each pair of eigenvalues from (A,A+BF) to
rÉ rÊ jL X% CA determine the closest pairs.
rË rÌ jL X CA
rÍ rÎ jL X C MACHINE DEPENDENCIES:
rÏ rÐ jL X CM
rÑ rÒ jL X CM NONE
rÓ rÔ jL X CM
rÕ rÖ jL X C HISTORY:
r× rØ jL X CH
rÙ rÚ jL X0 CH written by: Birdwell & Laub
rÛ rÜ jL X- CH date: May 18, 1985
rÝ rÞ jL X$ CH current version: 1.0
rß rà jL XJ CH modifications: made machine independent and modified for
rá râ jL X- CH f77:bb:8-86.
rã rä jL XE CH changed cmplx -> dcmplx: 7/27/88 jdb
rå ræ jL X CH
rç rè jL X C ROUTINES CALLED:
ré rê jL X CC
rë rì jL X CC EIGEN,RAND
rí rî jL X CC
rï rð jL X C COMMON MEMORY USED:
rñ rò jL X CM
ró rô jL X
CM none
rõ rö jL X CM
r÷ rø jL XH C----------------------------------------------------------------------
rù rú jL X, C written for: The CASCADE Project
rû rü jL X6 C Oak Ridge National Laboratory
rý rþ jL X2 C U.S. Department of Energy
rÿ r jL X: C contract number DE-AC05-840R21400
r r jL X8 C subcontract number 37B-7685 S13
r r jL XD C organization: The University of Tennessee
r r jL XH C----------------------------------------------------------------------
r r jL X. C THIS SOFTWARE IS IN THE PUBLIC DOMAIN
r r
jL X/ C NO RESTRICTIONS ON ITS USE ARE IMPLIED
r r jL XH C----------------------------------------------------------------------
r
r jL X C
r r jL X C--global variables:
r r jL X C
r r hX r r j j» r j X r r jÏ X INTEGER r r hX SIZEr r j jæ r hX r r j j» r! j X r" r# jÏ X INTEGER r$ r% hjÊ r& j jæ r' hX r( r) j j» r* j X r+ r, jÏ X INTEGER r- r. hjÍ r/ j jæ r0 hX r1 r2 j j» r3 j X r4 r5 jÏ X INTEGER r6 r7 hX IPVTr8 r9 j© jÄ r: jA X 1r; r< j© j r= j jæ r> hX r? r@ j j» rA j X rB rC jÏ X INTEGER rD rE hX JPVTrF rG j© jÄ rH jA j; rI j© j rJ j jæ rK hX rL rM j j» rN j X rO rP jÏ X INTEGER rQ rR hX IERRrS rT j jæ rU jL X C
rV rW hX rX rY j j» rZ j X r[ r\ jÏ X DOUBLE PRECISION r] r^ hjÐ r_ j© jÄ r` hX SIZEra rb j© jÈ rc hjÊ rd j© j re j jæ rf hX rg rh j j» ri j X rj rk jÏ X DOUBLE PRECISION rl rm hjÓ rn j© jÄ ro hX SIZErp rq j© jÈ rr hjÍ rs j© j rt j jæ ru hX rv rw j j» rx j X ry rz jÏ X DOUBLE PRECISION r{ r| hX WORKr} r~ j© jÄ r hX SIZEr r j© jÈ r hjÊ r j© j r j jæ r
hX r r j j» r j X r r jÏ X DOUBLE PRECISION r r hX CLEVRr r j© jÄ r hjÊ r j© j r j jæ r hX r r j j» r j X r r jÏ X DOUBLE PRECISION r r hX CLEVIr r j© jÄ r hjÊ r j© j r j jæ r hX r r¡ j j» r¢ j X r£ r¤ jÏ X DOUBLE PRECISION r¥ r¦ hX OLEVRr§ r¨ j© jÄ r© hjÊ rª j© j r« j jæ r¬ hX r r® j j» r¯ j X r° r± jÏ X DOUBLE PRECISION r² r³ hX OLEVIr´ rµ j© jÄ r¶ hjÊ r· j© j r¸ j jæ r¹ hX rº r» j j» r¼ j X r½ r¾ jÏ X DOUBLE PRECISION r¿ rÀ hX SCR1rÁ r j© jÄ rà hjÊ rÄ j© j rÅ j jæ rÆ hX rÇ rÈ j j» rÉ j X rÊ rË jÏ X DOUBLE PRECISION rÌ rÍ hX SCR2rÎ rÏ j© jÄ rÐ hjÊ rÑ j© j rÒ j jæ rÓ jL X C
rÔ rÕ hX rÖ r× j j» rØ j X rÙ rÚ jÏ X LOGICAL rÛ rÜ hX CONrÝ rÞ j© jÄ rß hjÊ rà j© j rá j jæ râ jL X C
rã rä jL X C--local variables:
rå ræ jL X C
rç rè hX ré rê j j» rë j X rì rí jÏ X INTEGER rî rï hX ISEEDrð rñ j jæ rò hX ró rô j j» rõ j X rö r÷ jÏ X INTEGER rø rù hX ITEMPrú rû j jæ rü hX rý rþ j j» rÿ j X r r jÏ X INTEGER r r hX K1r r j jæ r hX r r j j» r j X r
r jÏ X INTEGER r r
hX K2r r j jæ r hX r r j j» r j X r r jÏ X INTEGER r r hX Ir r j jæ r hX r r j j» r j X r r jÏ X INTEGER r r! hX Jr" r# j jæ r$ hX r% r& j j» r' j X r( r) jÏ X INTEGER r* r+ hX Kr, r- j jæ r. hX r/ r0 j j» r1 j X r2 r3 jÏ X INTEGER r4 r5 hX IMAXr6 r7 j jæ r8 hX r9 r: j j» r; j X r< r= jÏ X INTEGER r> r? hX JMAXr@ rA j jæ rB jL X C
rC rD hX rE rF j j» rG j X rH rI jÏ X DOUBLE PRECISION rJ rK j¼ X VALUErL rM j jæ rN hX rO rP j j» rQ j X rR rS jÏ X DOUBLE PRECISION rT rU hX EPSrV rW j jæ rX hX rY rZ j j» r[ j X r\ r] jÏ X DOUBLE PRECISION r^ r_ hX EPS1r` ra j jæ rb hX rc rd j j» re j X rf rg jÏ X DOUBLE PRECISION rh ri hX TEMPrj rk j jæ rl hX rm rn j j» ro j X rp rq jÏ X DOUBLE PRECISION rr rs hX CURRrt ru j jæ rv hX rw rx j j» ry j X rz r{ jÏ X DOUBLE PRECISION r| r} hX ANORMr~ r j jæ r hX r r j j» r j X r r
jÏ X DOUBLE PRECISION r r hX BNORMr r j jæ r hX r r j j» r j X r r jÏ X DOUBLE PRECISION r r hX COLNRMr r j jæ r hX r r j j» r j X r r jÏ X DOUBLE PRECISION r r hX RNDMNOr r j jæ r jL X C
r r hX r¡ r¢ j j» r£ j X r¤ r¥ jÏ X DOUBLE COMPLEX r¦ r§ hX DCMPLXr¨ r© j jæ rª jL X C
r« r¬ jL X C--compute machine epsilon
r r® jL X C
r¯ r° hX r± r² j j» r³ j X r´ rµ hX EPSr¶ r· j j» r¸ j X =r¹ rº j j» r» j
X 1.D0r¼ r½ j jæ r¾ hX 100 r¿ rÀ j j» rÁ j X r rà j¼ X CONTINUErÄ rÅ j jæ rÆ hX rÇ rÈ j j» rÉ j X rÊ rË hX EPSrÌ rÍ j j» rÎ j j¹ rÏ j j» rÐ hX EPSrÑ rÒ j j» rÓ j X /rÔ rÕ j j» rÖ j
X 2.D0r× rØ j jæ rÙ hX rÚ rÛ j j» rÜ j X rÝ rÞ hX EPS1rß rà j j» rá j j¹ râ j j» rã j
X 1.D0rä rå j j» ræ j X +rç rè j j» ré hX EPSrê rë j jæ rì hX rí rî j j» rï j X rð rñ j¼ X IFrò ró j j» rô j© jÄ rõ hX EPS1rö r÷ j j» rø j© X .rù rú hX NErû rü j© jù rý j j» rþ j
X 1.D0rÿ r j© j r j j» r hX GOr r j j» r hX TOr r j j» r jA X 100r r
j jæ r hX r r
j j» r j X r r hX EPSr r j j» r j j¹ r j j» r hX EPSr r j j» r j X *r r j j» r j
X 2.D0r r j jæ r jL X C
r r jL X C--compute the l-1 norm of a
r! r" jL X C
r# r$ hX r% r& j j» r' j X r( r) hX ANORMr* r+ j j» r, j j¹ r- j j» r. j
X 0.0D0r/ r0 j jæ r1 hX r2 r3 j j» r4 j X r5 r6 j¼ X DO r7 r8 jA X 120r9 r: j j» r; hj" r< j j» r= j j¹ r> j j» r? jA j; r@ j© jÈ rA j j» rB hjÊ rC j jæ rD hX rE rF j j» rG j X rH rI hX COLNRMrJ rK j j» rL j j¹ rM j j» rN j
X 0.D0rO rP j jæ rQ hX rR rS j j» rT j X rU rV j¼ X DO rW rX jA X 110rY rZ j j» r[ hj r\ j j» r] j j¹ r^ j j» r_ jA j; r` j© jÈ ra j j» rb hjÊ rc j jæ rd hX re rf j j» rg j X rh ri hX COLNRMrj rk j j» rl j j¹ rm j j» rn hX COLNRMro rp j j» rq j jç rr j j» rs hÃX ABSrt ru j© jÄ rv hjÐ rw j© jÄ rx hj ry j© jÈ rz hj" r{ j© j r| j© j r} j jæ r~ hX 110 r r j j» r j X r r j¼ X CONTINUEr r
j jæ r hX r r j j» r j X r r j¼ X IFr r j j» r j© jÄ r hX COLNRMr r j j» r j© jù r hX GTr r j© jù r j j» r hX ANORMr r j© j r j j» r hX ANORMr r j j» r j j¹ r j j» r hX COLNRMr¡ r¢ j jæ r£ hX 120 r¤ r¥ j j» r¦ j X r§ r¨ j¼ X CONTINUEr© rª j jæ r« jL X C
r¬ r jL X C--compute the l-1 norm of b
r® r¯ jL X C
r° r± hX r² r³ j j» r´ j X rµ r¶ hX BNORMr· r¸ j j» r¹ j j¹ rº j j» r» j
X 0.0D0r¼ r½ j jæ r¾ hX r¿ rÀ j j» rÁ j X r rà j¼ X DO rÄ rÅ jA X 140rÆ rÇ j j» rÈ hj" rÉ j j» rÊ j j¹ rË j j» rÌ jA j; rÍ j© jÈ rÎ j j» rÏ hjÍ rÐ j jæ rÑ hX rÒ rÓ j j» rÔ j X rÕ rÖ hX COLNRMr× rØ j j» rÙ j j¹ rÚ j j» rÛ j
X 0.D0rÜ rÝ j jæ rÞ hX rß rà j j» rá j X râ rã j¼ X DO rä rå jA X 130ræ rç j j» rè hj ré j j» rê j j¹ rë j j» rì jA j; rí j© jÈ rî j j» rï hjÊ rð j jæ rñ hX rò ró j j» rô j X rõ rö hX COLNRMr÷ rø j j» rù j j¹ rú j j» rû hX COLNRMrü rý j j» rþ j jç rÿ j j» r hÃX ABSr r j© jÄ r hjÓ r j© jÄ r hj r j© jÈ r hj" r j© j r j© j r
j jæ r hX 130 r r
j j» r j X r r j¼ X CONTINUEr r j jæ r hX r r j j» r j X r r j¼ X IFr r j j» r j© jÄ r hX COLNRMr r j j» r j© jù r hX GTr! r" j© jù r# j j» r$ hX BNORMr% r& j© j r' j j» r( hX BNORMr) r* j j» r+ j j¹ r, j j» r- hX COLNRMr. r/ j jæ r0 hX 140 r1 r2 j j» r3 j X r4 r5 j¼ X CONTINUEr6 r7 j jæ r8 jL X C
r9 r: jL X C--compute a + b * f
r; r< jL X C
r= r> hX r? r@ j j» rA j X rB rC j¼ X DO rD rE jA X 160rF rG j j» rH hj" rI j j» rJ j j¹ rK j j» rL jA j; rM j© jÈ rN j j» rO hjÊ rP j jæ rQ hX rR rS j j» rT j X rU rV j¼ X DO rW rX jA X 150rY rZ j j» r[ hj r\ j j» r] j j¹ r^ j j» r_ jA j; r` j© jÈ ra j j» rb hjÊ rc j jæ rd hX re rf j j» rg j X rh ri hX WORKrj rk j© jÄ rl hj rm j© jÈ rn hj" ro j© j rp j j» rq j j¹ rr j j» rs hjÐ rt j© jÄ ru hj rv j© jÈ rw hj" rx j© j ry j jæ rz hX 150 r{ r| j j» r} j X r~ r j¼ X CONTINUEr r j jæ r hX 160 r r j j» r
j X r r j¼ X CONTINUEr r j jæ r jL X C
r r jL X: C--the elements of f are random with uniform distribution
r r jL X% C--from -anorm/bnorm to +anorm/bnorm
r r jL X4 C--note that f is not explicitly stored as a matrix
r r jL X@ C--pathalogical floating point notes: the if (bnorm .gt. 0.d0)
r r jL X@ C--test should actually be if (bnorm .gt. dsmall), where dsmall
r r jL X> C--is the smallest representable number whose reciprocal does
r r jL X2 C--not generate an overflow or loss of precision.
r r jL X C
r r hX r r j j» r j X r r¡ j¼ X IFr¢ r£ j j» r¤ j© jÄ r¥ hX ISEEDr¦ r§ j j» r¨ j© jù r© hX EQrª r« j© jù r¬ j j» r jA X 0r® r¯ j© j r° j j» r± hX ISEEDr² r³ j j» r´ j j¹ rµ j j» r¶ jA X 86345823r· r¸ j jæ r¹ hX rº r» j j» r¼ j X r½ r¾ j¼ X IFr¿ rÀ j j» rÁ j© jÄ r hX ANORMrà rÄ j j» rÅ j© jù rÆ hX EQrÇ rÈ j© jù rÉ j j» rÊ j
X 0.D0rË rÌ j© j rÍ j j» rÎ hX ANORMrÏ rÐ j j» rÑ j j¹ rÒ j j» rÓ j
X 1.D0rÔ rÕ j jæ rÖ hX r× rØ j j» rÙ j X rÚ rÛ j¼ X IFrÜ rÝ j j» rÞ j© jÄ rß hX BNORMrà rá j j» râ j© jù rã hX GTrä rå j© jù ræ j j» rç j
X 0.D0rè ré j© j rê j j» rë j¼ X THENrì rí j jæ rî hX rï rð j j» rñ j X rò ró hX TEMPrô rõ j j» rö j j¹ r÷ j j» rø j
X 2.D0rù rú j j» rû j j rü j j» rý hX ANORMrþ rÿ j j» r j jÔ r j j» r hX BNORMr r j jæ r hX r r j j» r j X r r
j¼ X ELSEr r j jæ r
hX r r j j» r j X r r hX TEMPr r j j» r j j¹ r j j» r j
X 2.D0r r j jæ r hX r r j j» r j X r r j¼ X END r r! j¼ X IFr" r# j jæ r$ hX r% r& j j» r' j X r( r) j¼ X DO r* r+ jA X 190r, r- j j» r. hj, r/ j j» r0 j j¹ r1 j j» r2 jA j; r3 j© jÈ r4 j j» r5 hjÍ r6 j jæ r7 hX r8 r9 j j» r: j X r; r< j¼ X DO r= r> jA X 180r? r@ j j» rA hj" rB j j» rC j j¹ rD j j» rE jA j; rF j© jÈ rG j j» rH hjÊ rI j jæ rJ hX rK rL j j» rM j X rN rO j¼ X CALL rP rQ hÃX RANDrR rS j© jÄ rT hX ISEEDrU rV j© jÈ rW hX ISEEDrX rY j© jÈ rZ hX RNDMNOr[ r\ j© j r] j jæ r^ hX r_ r` j j» ra j X rb rc j¼ X VALUErd re j j» rf j j¹ rg j j» rh j© jÄ ri hX RNDMNOrj rk j j» rl j X -rm rn j j» ro j
X 0.5D0rp rq j© j rr j j» rs j j rt j j» ru hX TEMPrv rw j jæ rx hX ry rz j j» r{ j X r| r} j¼ X DO r~ r jA X 170r r j j» r hj r j j» r j j¹ r
j j» r jA j; r j© jÈ r j j» r hjÊ r j jæ r hX r r j j» r j X r r hX WORKr r j© jÄ r hj r j© jÈ r hj" r j© j r j j» r j j¹ r j j» r hX WORKr r j© jÄ r hj r j© jÈ r hj" r j© j r¡ j j» r¢ j jç r£ j j» r¤ hjÓ r¥ j© jÄ r¦ hj r§ j© jÈ r¨ hj, r© j© j rª j j r« j¼ X VALUEr¬ r j jæ r® hX 170 r¯ r° e(j j» r± j X r² r³ j¼ X CONTINUEr´ rµ j jæ r¶ hX 180 r· r¸ j j» r¹ j X rº r» j¼ X CONTINUEr¼ r½ j jæ r¾ hX 190 r¿ rÀ j j» rÁ j X r rà j¼ X CONTINUErÄ rÅ j jæ rÆ jL X C
rÇ rÈ jL X@ C--compute the eigenvalues of a + b*f, and several other things
rÉ rÊ jL X C
rË rÌ hX rÍ rÎ j j» rÏ j X rÐ rÑ j¼ X CALL rÒ rÓ hX EIGENrÔ rÕ j j» rÖ j© jÄ r× jA j® rØ j© jÈ rÙ hX SIZErÚ rÛ j© jÈ rÜ hjÊ rÝ j© jÈ rÞ hX WORKrß rà j© jÈ rá hX CLEVRrâ rã j© jÈ rä hX CLEVIrå ræ j© jÈ rç hX WORKrè ré j© jÈ rê hX SCR1rë rì j© jÈ rí hX SCR2rî rï j© jÈ rð hX IERRrñ rò j© j ró j jæ rô hX rõ rö j j» r÷ j X rø rù j¼ X IFrú rû j j» rü j© jÄ rý hX IERRrþ rÿ j j» r
j© jù r
hX NEr
r
j© jù r
j j» r
jA j® r
j© j r
j j» r
j¼ X RETURNr
r
j jæ r
jL X C
r
r
jL X! C--copy a so it is not destroyed
r
r
jL X C
r
r
hX r
r
j j» r
j X r
r
j¼ X DO r
r
jA X 210r
r
j j» r
hj" r
j j» r
j j¹ r
j j» r
jA j; r
j© jÈ r!
j j» r"
hjÊ r#
j jæ r$
hX r%
r&
j j» r'
j X r(
r)
j¼ X DO r*
r+
jA X 200r,
r-
j j» r.
hj r/
j j» r0
j j¹ r1
j j» r2
jA j; r3
j© jÈ r4
j j» r5
hjÊ r6
j jæ r7
hX r8
r9
j j» r:
j X r;
r<
hX WORKr=
r>
j© jÄ r?
hj r@
j© jÈ rA
hj" rB
j© j rC
j j» rD
j j¹ rE
j j» rF
hjÐ rG
j© jÄ rH
hj rI
j© jÈ rJ
hj" rK
j© j rL
j jæ rM
hX 200 rN
rO
j j» rP
j X rQ
rR
j¼ X CONTINUErS
rT
j jæ rU
hX 210 rV
rW
j j» rX
j X rY
rZ
j¼ X CONTINUEr[
r\
j jæ r]
jL X C
r^
r_
jL X: C--compute the eigenvalues of a, and several other things
r`
ra
jL X C
rb
rc
hX rd
re
j j» rf
j X rg
rh
j¼ X CALL ri
rj
hX EIGENrk
rl
j j» rm
j© jÄ rn
jA j® ro
j© jÈ rp
hX SIZErq
rr
j© jÈ rs
hjÊ rt
j© jÈ ru
hX WORKrv
rw
j© jÈ rx
hX OLEVRry
rz
j© jÈ r{
hX OLEVIr|
r}
j© jÈ r~
hX WORKr
r
j© jÈ r
hX SCR1r
r
j© jÈ r
hX SCR2r
r
j© jÈ r
hX IERRr
r
j© j r
j jæ r
hX r
r
j j» r
j X r
r
j¼ X IFr
r
j j» r
j© jÄ r
hX IERRr
r
j j» r
j© jù r
hX NEr
r
j© jù r
j j» r
jA j® r
j© j r
j j» r
j¼ X RETURNr
r¡
j jæ r¢
jL X C
r£
r¤
jL X= C--form the matrix of distances between eigenvalues of a and
r¥
r¦
jL X C--EIGENVALUES OF A+B*F
r§
r¨
jL X C
r©
rª
hX r«
r¬
j j» r
j X r®
r¯
j¼ X DO r°
r±
jA X 230r²
r³
j j» r´
hj" rµ
j j» r¶
j j¹ r·
j j» r¸
jA j; r¹
j© jÈ rº
j j» r»
hjÊ r¼
j jæ r½
hX r¾
r¿
j j» rÀ
j X rÁ
rÂ
j¼ X DO rÃ
rÄ
jA X 220rÅ
rÆ
j j» rÇ
hj rÈ
j j» rÉ
j j¹ rÊ
j j» rË
jA j; rÌ
j© jÈ rÍ
j j» rÎ
hjÊ rÏ
j jæ rÐ
hX rÑ
rÒ
j j» rÓ
j X rÔ
rÕ
hX WORKrÖ
r×
j© jÄ rØ
hj rÙ
j© jÈ rÚ
hj" rÛ
j© j rÜ
j j» rÝ
j j¹ rÞ
j jæ rß
hX rà
rá
j£ jê râ
j X rã
rä
hÃX ABSrå
ræ
j© jÄ rç
hX DCMPLXrè
ré
j© jÄ rê
hX OLEVRrë
rì
j© jÄ rí
hj rî
j© j rï
j© jÈ rð
hX OLEVIrñ
rò
j© jÄ ró
hj rô
j© j rõ
j© j rö
j jm r÷
hX DCMPLXrø
rù
j© jÄ rú
hX CLEVRrû
rü
j© jÄ rý
hj" rþ
j© j rÿ
j© jÈ r hX CLEVIr r j© jÄ r hj" r j© j r j© j r j© j r j jæ r hX 220 r r
j j» r j X r r
j¼ X CONTINUEr r j jæ r hX 230 r r j j» r j X r r j¼ X CONTINUEr r j jæ r jL X C
r r jL X$ C--initialize row and column pivots
r r jL X C
r r hX r r j j» r! j X r" r# j¼ X DO r$ r% jA X 240r& r' j j» r( hj r) j j» r* j j¹ r+ j j» r, jA j; r- j© jÈ r. j j» r/ hjÊ r0 j jæ r1 hX r2 r3 j j» r4 j X r5 r6 hX IPVTr7 r8 j© jÄ r9 hj r: j© j r; j j» r< j j¹ r= j j» r> hj r? j jæ r@ hX rA rB j j» rC j X rD rE hX JPVTrF rG j© jÄ rH hj rI j© j rJ j j» rK j j¹ rL j j» rM hj rN j jæ rO hX 240 rP rQ j j» rR j X rS rT j¼ X CONTINUErU rV j jæ rW jL X C
rX rY jL X4 C--a little bit messy to avoid swapping columns and
rZ r[ jL X C--rows of work
r\ r] jL X C
r^ r_ hX r` ra j j» rb j X rc rd j¼ X DO re rf jA X 270rg rh j j» ri hj rj j j» rk j j¹ rl j j» rm jA j; rn j© jÈ ro j j» rp hjÊ rq j jm rr jA j; rs j jæ rt jL X C
ru rv jL X7 C--find the minimum element of each lower right square
rw rx jL X4 C--submatrix of work, for submatrices of size n x n
ry rz jL X C--through 2 x 2
r{ r| jL X C
r} r~ hX r r j j» r j X r r hX CURRr r
j j» r j j¹ r j j» r hX WORKr r j© jÄ r hX IPVTr r j© jÄ r hj r j© j r j© jÈ r hX JPVTr r j© jÄ r hj r j© j r j© j r j jæ r hX r r j j» r j X r r hX IMAXr r j j» r j j¹ r¡ j j» r¢ hj r£ j jæ r¤ hX r¥ r¦ j j» r§ j X r¨ r© hX JMAXrª r« j j» r¬ j j¹ r j j» r® hj r¯ j jæ r° hX r± r² j j» r³ j X r´ rµ hX TEMPr¶ r· j j» r¸ j j¹ r¹ j j» rº hX CURRr» r¼ j jæ r½ jL X C
r¾ r¿ jL X C--find the minimum element
rÀ rÁ jL X C
r rà hX rÄ rÅ j j» rÆ j X rÇ rÈ j¼ X DO rÉ rÊ jA X 260rË rÌ j j» rÍ hX K1rÎ rÏ j j» rÐ j j¹ rÑ j j» rÒ hj rÓ j© jÈ rÔ j j» rÕ hjÊ rÖ j jæ r× hX rØ rÙ j j» rÚ j X rÛ rÜ j¼ X DO rÝ rÞ jA X 250rß rà j j» rá hX K2râ rã j j» rä j j¹ rå j j» ræ hj rç j© jÈ rè j j» ré hjÊ rê j jæ rë hX rì rí j j» rî j X rï rð j¼ X IFrñ rò j j» ró j© jÄ rô hX WORKrõ rö j© jÄ r÷ hX IPVTrø rù j© jÄ rú hX K1rû rü j© j rý j© jÈ rþ hX JPVTrÿ r j© jÄ r hX K2r r j© j r j© j r j j» r j© jù r hX LTr r j© jù r
j j» r hX TEMPr r
j© j r j j» r j¼ X THENr r j jæ r hX r r j j» r j X
r r hX TEMPr r j j» r j j¹ r j j» r hX WORKr r j© jÄ r hX IPVTr r! j© jÄ r" hX K1r# r$ j© j r% j© jÈ r& hX JPVTr' r( j© jÄ r) hX K2r* r+ j© j r, j© j r- j jæ r. hX r/ r0 j j» r1 j X
r2 r3 hX IMAXr4 r5 j j» r6 j j¹ r7 j j» r8 hX K1r9 r: j jæ r; hX r< r= j j» r> j X
r? r@ hX JMAXrA rB j j» rC j j¹ rD j j» rE hX K2rF rG j jæ rH hX rI rJ j j» rK j X rL rM j¼ X END rN rO j¼ X IFrP rQ j jæ rR hX 250 rS rT j j» rU j X rV rW j¼ X CONTINUErX rY j jæ rZ hX 260 r[ r\ j j» r] j X r^ r_ j¼ X CONTINUEr` ra j jæ rb jL X C
rc rd jL X@ C--update row and column pivots for indirect addressing of work
re rf jL X C
rg rh hX ri rj j j» rk j X rl rm hX ITEMPrn ro j j» rp j j¹ rq j j» rr hX IPVTrs rt j© jÄ ru hj rv j© j rw j jæ rx hX ry rz j j» r{ j X r| r} hX IPVTr~ r j© jÄ r hj r j© j r j j» r j j¹ r j j» r
hX IPVTr r j© jÄ r hX IMAXr r j© j r j jæ r hX r r j j» r j X r r hX IPVTr r j© jÄ r hX IMAXr r j© j r j j» r j j¹ r j j» r hX ITEMPr r j jæ r jL X C
r r hX r r¡ j j» r¢ j X r£ r¤ hX ITEMPr¥ r¦ j j» r§ j j¹ r¨ j j» r© hX JPVTrª r« j© jÄ r¬ hj r j© j r® j jæ r¯ hX r° r± j j» r² j X r³ r´ hX JPVTrµ r¶ j© jÄ r· hj r¸ j© j r¹ j j» rº j j¹ r» j j» r¼ hX JPVTr½ r¾ j© jÄ r¿ hX JMAXrÀ rÁ j© j r j jæ rà hX rÄ rÅ j j» rÆ j X rÇ rÈ hX JPVTrÉ rÊ j© jÄ rË hX JMAXrÌ rÍ j© j rÎ j j» rÏ j j¹ rÐ j j» rÑ hX ITEMPrÒ rÓ j jæ rÔ jL X C
rÕ rÖ jL X C--do next submatrix
r× rØ jL X C
rÙ rÚ hX 270 rÛ rÜ j j» rÝ j X rÞ rß j¼ X CONTINUErà rá j jæ râ jL X C
rã rä jL X9 C--this threshold for determining when an eigenvalue has
rå ræ jL X< C--not moved, and is therefore uncontrollable, is critical,
rç rè jL X8 C--and may require future changes with more experience.
ré rê jL X C
rë rì hX rí rî j j» rï j X rð rñ hX EPS1rò ró j j» rô j j¹ rõ j j» rö hÃX SQRTr÷ rø j© jÄ rù hX EPSrú rû j© j rü j jæ rý jL X C
rþ rÿ jL X: C--for each eigenvalue pair, decide if it is controllable
r
r
jL X C
r
r
hX r
r
j j» r
j X r
r
j¼ X DO r
r
jA X 280r
r
j j» r
hj r
j j» r
j j¹ r
j j» r
jA j; r
j© jÈ r
j j» r
hjÊ r
j jæ r
jL X C
r
r
jL X; C--note that we are working with the "pivoted" work matrix
r
r
jL X, C--and are looking at its diagonal elements
r
r
jL X C
r
r
hX r
r
j j» r!
j X r"
r#
j¼ X IFr$
r%
j j» r&
j© jÄ r'
hX WORKr(
r)
j© jÄ r*
hX IPVTr+
r,
j© jÄ r-
hj r.
j© j r/
j© jÈ r0
hX JPVTr1
r2
j© jÄ r3
hj r4
j© j r5
j© j r6
j jÔ r7
hX ANORMr8
r9
j j» r:
j© jù r;
hX LEr<
r=
j© jù r>
j j» r?
hX EPS1r@
rA
j© j rB
j j» rC
j¼ X THENrD
rE
j jæ rF
hX rG
rH
j j» rI
j X rJ
rK
hX CONrL
rM
j© jÄ rN
hj rO
j© j rP
j j» rQ
j j¹ rR
j j» rS
j© jù rT
hX FALSErU
rV
j© jù rW
j jæ rX
hX rY
rZ
j j» r[
j X r\
r]
j¼ X ELSEr^
r_
j jæ r`
hX ra
rb
j j» rc
j X rd
re
hX CONrf
rg
j© jÄ rh
hj ri
j© j rj
j j» rk
j j¹ rl
j j» rm
j© jù rn
hX TRUEro
rp
j© jù rq
j jæ rr
hX rs
rt
j j» ru
j X rv
rw
j¼ X END rx
ry
j¼ X IFrz
r{
j jæ r|
hX 280 r}
r~
j j» r
j X r
r
j¼ X CONTINUEr
r
j jæ r
jL X C
r
r
jL X C--finally!
r
r
jL X C
r
r
hX r
r
j j» r
j X r
r
j¼ X RETURNr
r
j jæ r
hX r
r
j j» r
j X r
r
j¼ X ENDr
r
j jæ r
e.