OpenLibm/slatec/la05as.f
Viral B. Shah c977aa998f Add Makefile.extras to build libopenlibm-extras.
Replace amos with slatec
2012-12-31 16:37:05 -05:00

513 lines
16 KiB
Fortran

*DECK LA05AS
SUBROUTINE LA05AS (A, IND, NZ, IA, N, IP, IW, W, G, U)
C***BEGIN PROLOGUE LA05AS
C***SUBSIDIARY
C***PURPOSE Subsidiary to SPLP
C***LIBRARY SLATEC
C***TYPE SINGLE PRECISION (LA05AS-S, LA05AD-D)
C***AUTHOR (UNKNOWN)
C***DESCRIPTION
C
C THIS SUBPROGRAM IS A SLIGHT MODIFICATION OF A SUBPROGRAM
C FROM THE C. 1979 AERE HARWELL LIBRARY. THE NAME OF THE
C CORRESPONDING HARWELL CODE CAN BE OBTAINED BY DELETING
C THE FINAL LETTER =S= IN THE NAMES USED HERE.
C REVISIONS MADE BY R J HANSON, SNLA, AUGUST, 1979.
C REVISED SEP. 13, 1979.
C
C ROYALTIES HAVE BEEN PAID TO AERE-UK FOR USE OF THEIR CODES
C IN THE PACKAGE GIVEN HERE. ANY PRIMARY USAGE OF THE HARWELL
C SUBROUTINES REQUIRES A ROYALTY AGREEMENT AND PAYMENT BETWEEN
C THE USER AND AERE-UK. ANY USAGE OF THE SANDIA WRITTEN CODES
C SPLP( ) (WHICH USES THE HARWELL SUBROUTINES) IS PERMITTED.
C
C IP(I,1),IP(I,2) POINT TO THE START OF ROW/COL I.
C IW(I,1),IW(I,2) HOLD THE NUMBER OF NON-ZEROS IN ROW/COL I.
C DURING THE MAIN BODY OF THIS SUBROUTINE THE VECTORS IW(.,3),IW(.,5),
C IW(.,7) ARE USED TO HOLD DOUBLY LINKED LISTS OF ROWS THAT HAVE
C NOT BEEN PIVOTAL AND HAVE EQUAL NUMBERS OF NON-ZEROS.
C IW(.,4),IW(.,6),IW(.,8) HOLD SIMILAR LISTS FOR THE COLUMNS.
C IW(I,3),IW(I,4) HOLD FIRST ROW/COLUMN TO HAVE I NON-ZEROS
C OR ZERO IF THERE ARE NONE.
C IW(I,5), IW(I,6) HOLD ROW/COL NUMBER OF ROW/COL PRIOR TO ROW/COL I
C IN ITS LIST, OR ZERO IF NONE.
C IW(I,7), IW(I,8) HOLD ROW/COL NUMBER OF ROW/COL AFTER ROW/COL I
C IN ITS LIST, OR ZERO IF NONE.
C FOR ROWS/COLS THAT HAVE BEEN PIVOTAL IW(I,5),IW(I,6) HOLD NEGATION OF
C POSITION OF ROW/COL I IN THE PIVOTAL ORDERING.
C
C***SEE ALSO SPLP
C***ROUTINES CALLED LA05ES, MC20AS, R1MACH, XERMSG, XSETUN
C***COMMON BLOCKS LA05DS
C***REVISION HISTORY (YYMMDD)
C 811215 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890605 Corrected references to XERRWV. (WRB)
C 890831 Modified array declarations. (WRB)
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
C 900402 Added TYPE section. (WRB)
C 900510 Convert XERRWV calls to XERMSG calls. (RWC)
C***END PROLOGUE LA05AS
INTEGER IP(N,2)
INTEGER IND(IA,2), IW(N,8)
REAL A(*), AMAX, AU, AM, G, U, SMALL, W(*)
LOGICAL FIRST
CHARACTER*8 XERN0, XERN1, XERN2
C
COMMON /LA05DS/ SMALL, LP, LENL, LENU, NCP, LROW, LCOL
C EPS IS THE RELATIVE ACCURACY OF FLOATING-POINT COMPUTATION
SAVE EPS, FIRST
DATA FIRST /.TRUE./
C***FIRST EXECUTABLE STATEMENT LA05AS
IF (FIRST) THEN
EPS = 2.0E0 * R1MACH(4)
ENDIF
FIRST = .FALSE.
C
C SET THE OUTPUT UNIT NUMBER FOR THE ERROR PROCESSOR.
C THE USAGE OF THIS ERROR PROCESSOR IS DOCUMENTED IN THE
C SANDIA LABS. TECH. REPT. SAND78-1189, BY R E JONES.
CALL XSETUN(LP)
IF (U.GT.1.0E0) U = 1.0E0
IF (U.LT.EPS) U = EPS
IF (N.LT.1) GO TO 670
G = 0.
DO 50 I=1,N
W(I) = 0.
DO 40 J=1,5
IW(I,J) = 0
40 CONTINUE
50 CONTINUE
C
C FLUSH OUT SMALL ENTRIES, COUNT ELEMENTS IN ROWS AND COLUMNS
L = 1
LENU = NZ
DO 80 IDUMMY=1,NZ
IF (L.GT.LENU) GO TO 90
DO 60 K=L,LENU
IF (ABS(A(K)).LE.SMALL) GO TO 70
I = IND(K,1)
J = IND(K,2)
G = MAX(ABS(A(K)),G)
IF (I.LT.1 .OR. I.GT.N) GO TO 680
IF (J.LT.1 .OR. J.GT.N) GO TO 680
IW(I,1) = IW(I,1) + 1
IW(J,2) = IW(J,2) + 1
60 CONTINUE
GO TO 90
70 L = K
A(L) = A(LENU)
IND(L,1) = IND(LENU,1)
IND(L,2) = IND(LENU,2)
LENU = LENU - 1
80 CONTINUE
C
90 LENL = 0
LROW = LENU
LCOL = LROW
C MCP IS THE MAXIMUM NUMBER OF COMPRESSES PERMITTED BEFORE AN
C ERROR RETURN RESULTS.
MCP = MAX(N/10,20)
NCP = 0
C CHECK FOR NULL ROW OR COLUMN AND INITIALIZE IP(I,2) TO POINT
C JUST BEYOND WHERE THE LAST COMPONENT OF COLUMN I OF A WILL
C BE STORED.
K = 1
DO 110 IR=1,N
K = K + IW(IR,2)
IP(IR,2) = K
DO 100 L=1,2
IF (IW(IR,L).LE.0) GO TO 700
100 CONTINUE
110 CONTINUE
C REORDER BY ROWS
C CHECK FOR DOUBLE ENTRIES WHILE USING THE NEWLY CONSTRUCTED
C ROW FILE TO CONSTRUCT THE COLUMN FILE. NOTE THAT BY PUTTING
C THE ENTRIES IN BACKWARDS AND DECREASING IP(J,2) EACH TIME IT
C IS USED WE AUTOMATICALLY LEAVE IT POINTING TO THE FIRST ELEMENT.
CALL MC20AS(N, LENU, A, IND(1,2), IP, IND(1,1), 0)
KL = LENU
DO 130 II=1,N
IR = N + 1 - II
KP = IP(IR,1)
DO 120 K=KP,KL
J = IND(K,2)
IF (IW(J,5).EQ.IR) GO TO 660
IW(J,5) = IR
KR = IP(J,2) - 1
IP(J,2) = KR
IND(KR,1) = IR
120 CONTINUE
KL = KP - 1
130 CONTINUE
C
C SET UP LINKED LISTS OF ROWS AND COLS WITH EQUAL NUMBERS OF NON-ZEROS.
DO 150 L=1,2
DO 140 I=1,N
NZ = IW(I,L)
IN = IW(NZ,L+2)
IW(NZ,L+2) = I
IW(I,L+6) = IN
IW(I,L+4) = 0
IF (IN.NE.0) IW(IN,L+4) = I
140 CONTINUE
150 CONTINUE
C
C
C START OF MAIN ELIMINATION LOOP.
DO 590 IPV=1,N
C FIND PIVOT. JCOST IS MARKOWITZ COST OF CHEAPEST PIVOT FOUND SO FAR,
C WHICH IS IN ROW IPP AND COLUMN JP.
JCOST = N*N
C LOOP ON LENGTH OF COLUMN TO BE SEARCHED
DO 240 NZ=1,N
IF (JCOST.LE.(NZ-1)**2) GO TO 250
J = IW(NZ,4)
C SEARCH COLUMNS WITH NZ NON-ZEROS.
DO 190 IDUMMY=1,N
IF (J.LE.0) GO TO 200
KP = IP(J,2)
KL = KP + IW(J,2) - 1
DO 180 K=KP,KL
I = IND(K,1)
KCOST = (NZ-1)*(IW(I,1)-1)
IF (KCOST.GE.JCOST) GO TO 180
IF (NZ.EQ.1) GO TO 170
C FIND LARGEST ELEMENT IN ROW OF POTENTIAL PIVOT.
AMAX = 0.
K1 = IP(I,1)
K2 = IW(I,1) + K1 - 1
DO 160 KK=K1,K2
AMAX = MAX(AMAX,ABS(A(KK)))
IF (IND(KK,2).EQ.J) KJ = KK
160 CONTINUE
C PERFORM STABILITY TEST.
IF (ABS(A(KJ)).LT.AMAX*U) GO TO 180
170 JCOST = KCOST
IPP = I
JP = J
IF (JCOST.LE.(NZ-1)**2) GO TO 250
180 CONTINUE
J = IW(J,8)
190 CONTINUE
C SEARCH ROWS WITH NZ NON-ZEROS.
200 I = IW(NZ,3)
DO 230 IDUMMY=1,N
IF (I.LE.0) GO TO 240
AMAX = 0.
KP = IP(I,1)
KL = KP + IW(I,1) - 1
C FIND LARGEST ELEMENT IN THE ROW
DO 210 K=KP,KL
AMAX = MAX(ABS(A(K)),AMAX)
210 CONTINUE
AU = AMAX*U
DO 220 K=KP,KL
C PERFORM STABILITY TEST.
IF (ABS(A(K)).LT.AU) GO TO 220
J = IND(K,2)
KCOST = (NZ-1)*(IW(J,2)-1)
IF (KCOST.GE.JCOST) GO TO 220
JCOST = KCOST
IPP = I
JP = J
IF (JCOST.LE.(NZ-1)**2) GO TO 250
220 CONTINUE
I = IW(I,7)
230 CONTINUE
240 CONTINUE
C
C PIVOT FOUND.
C REMOVE ROWS AND COLUMNS INVOLVED IN ELIMINATION FROM ORDERING VECTORS.
250 KP = IP(JP,2)
KL = IW(JP,2) + KP - 1
DO 290 L=1,2
DO 280 K=KP,KL
I = IND(K,L)
IL = IW(I,L+4)
IN = IW(I,L+6)
IF (IL.EQ.0) GO TO 260
IW(IL,L+6) = IN
GO TO 270
260 NZ = IW(I,L)
IW(NZ,L+2) = IN
270 IF (IN.GT.0) IW(IN,L+4) = IL
280 CONTINUE
KP = IP(IPP,1)
KL = KP + IW(IPP,1) - 1
290 CONTINUE
C STORE PIVOT
IW(IPP,5) = -IPV
IW(JP,6) = -IPV
C ELIMINATE PIVOTAL ROW FROM COLUMN FILE AND FIND PIVOT IN ROW FILE.
DO 320 K=KP,KL
J = IND(K,2)
KPC = IP(J,2)
IW(J,2) = IW(J,2) - 1
KLC = KPC + IW(J,2)
DO 300 KC=KPC,KLC
IF (IPP.EQ.IND(KC,1)) GO TO 310
300 CONTINUE
310 IND(KC,1) = IND(KLC,1)
IND(KLC,1) = 0
IF (J.EQ.JP) KR = K
320 CONTINUE
C BRING PIVOT TO FRONT OF PIVOTAL ROW.
AU = A(KR)
A(KR) = A(KP)
A(KP) = AU
IND(KR,2) = IND(KP,2)
IND(KP,2) = JP
C
C PERFORM ELIMINATION ITSELF, LOOPING ON NON-ZEROS IN PIVOT COLUMN.
NZC = IW(JP,2)
IF (NZC.EQ.0) GO TO 550
DO 540 NC=1,NZC
KC = IP(JP,2) + NC - 1
IR = IND(KC,1)
C SEARCH NON-PIVOT ROW FOR ELEMENT TO BE ELIMINATED.
KR = IP(IR,1)
KRL = KR + IW(IR,1) - 1
DO 330 KNP=KR,KRL
IF (JP.EQ.IND(KNP,2)) GO TO 340
330 CONTINUE
C BRING ELEMENT TO BE ELIMINATED TO FRONT OF ITS ROW.
340 AM = A(KNP)
A(KNP) = A(KR)
A(KR) = AM
IND(KNP,2) = IND(KR,2)
IND(KR,2) = JP
AM = -A(KR)/A(KP)
C COMPRESS ROW FILE UNLESS IT IS CERTAIN THAT THERE IS ROOM FOR NEW ROW.
IF (LROW+IW(IR,1)+IW(IPP,1)+LENL.LE.IA) GO TO 350
IF (NCP.GE.MCP .OR. LENU+IW(IR,1)+IW(IPP,1)+LENL.GT.IA) GO
* TO 710
CALL LA05ES(A, IND(1,2), IP, N, IW, IA, .TRUE.)
KP = IP(IPP,1)
KR = IP(IR,1)
350 KRL = KR + IW(IR,1) - 1
KQ = KP + 1
KPL = KP + IW(IPP,1) - 1
C PLACE PIVOT ROW (EXCLUDING PIVOT ITSELF) IN W.
IF (KQ.GT.KPL) GO TO 370
DO 360 K=KQ,KPL
J = IND(K,2)
W(J) = A(K)
360 CONTINUE
370 IP(IR,1) = LROW + 1
C
C TRANSFER MODIFIED ELEMENTS.
IND(KR,2) = 0
KR = KR + 1
IF (KR.GT.KRL) GO TO 430
DO 420 KS=KR,KRL
J = IND(KS,2)
AU = A(KS) + AM*W(J)
IND(KS,2) = 0
C IF ELEMENT IS VERY SMALL REMOVE IT FROM U.
IF (ABS(AU).LE.SMALL) GO TO 380
G = MAX(G,ABS(AU))
LROW = LROW + 1
A(LROW) = AU
IND(LROW,2) = J
GO TO 410
380 LENU = LENU - 1
C REMOVE ELEMENT FROM COL FILE.
K = IP(J,2)
KL = K + IW(J,2) - 1
IW(J,2) = KL - K
DO 390 KK=K,KL
IF (IND(KK,1).EQ.IR) GO TO 400
390 CONTINUE
400 IND(KK,1) = IND(KL,1)
IND(KL,1) = 0
410 W(J) = 0.
420 CONTINUE
C
C SCAN PIVOT ROW FOR FILLS.
430 IF (KQ.GT.KPL) GO TO 520
DO 510 KS=KQ,KPL
J = IND(KS,2)
AU = AM*W(J)
IF (ABS(AU).LE.SMALL) GO TO 500
LROW = LROW + 1
A(LROW) = AU
IND(LROW,2) = J
LENU = LENU + 1
C
C CREATE FILL IN COLUMN FILE.
NZ = IW(J,2)
K = IP(J,2)
KL = K + NZ - 1
IF (NZ .EQ. 0) GO TO 460
C IF POSSIBLE PLACE NEW ELEMENT AT END OF PRESENT ENTRY.
IF (KL.NE.LCOL) GO TO 440
IF (LCOL+LENL.GE.IA) GO TO 460
LCOL = LCOL + 1
GO TO 450
440 IF (IND(KL+1,1).NE.0) GO TO 460
450 IND(KL+1,1) = IR
GO TO 490
C NEW ENTRY HAS TO BE CREATED.
460 IF (LCOL+LENL+NZ+1.LT.IA) GO TO 470
C COMPRESS COLUMN FILE IF THERE IS NOT ROOM FOR NEW ENTRY.
IF (NCP.GE.MCP .OR. LENU+LENL+NZ+1.GE.IA) GO TO 710
CALL LA05ES(A, IND, IP(1,2), N, IW(1,2), IA, .FALSE.)
K = IP(J,2)
KL = K + NZ - 1
C TRANSFER OLD ENTRY INTO NEW.
470 IP(J,2) = LCOL + 1
IF (KL .LT. K) GO TO 485
DO 480 KK=K,KL
LCOL = LCOL + 1
IND(LCOL,1) = IND(KK,1)
IND(KK,1) = 0
480 CONTINUE
485 CONTINUE
C ADD NEW ELEMENT.
LCOL = LCOL + 1
IND(LCOL,1) = IR
490 G = MAX(G,ABS(AU))
IW(J,2) = NZ + 1
500 W(J) = 0.
510 CONTINUE
520 IW(IR,1) = LROW + 1 - IP(IR,1)
C
C STORE MULTIPLIER
IF (LENL+LCOL+1.LE.IA) GO TO 530
C COMPRESS COL FILE IF NECESSARY.
IF (NCP.GE.MCP) GO TO 710
CALL LA05ES(A, IND, IP(1,2), N, IW(1,2), IA, .FALSE.)
530 K = IA - LENL
LENL = LENL + 1
A(K) = AM
IND(K,1) = IPP
IND(K,2) = IR
LENU = LENU - 1
540 CONTINUE
C
C INSERT ROWS AND COLUMNS INVOLVED IN ELIMINATION IN LINKED LISTS
C OF EQUAL NUMBERS OF NON-ZEROS.
550 K1 = IP(JP,2)
K2 = IW(JP,2) + K1 - 1
IW(JP,2) = 0
DO 580 L=1,2
IF (K2.LT.K1) GO TO 570
DO 560 K=K1,K2
IR = IND(K,L)
IF (L.EQ.1) IND(K,L) = 0
NZ = IW(IR,L)
IF (NZ.LE.0) GO TO 720
IN = IW(NZ,L+2)
IW(IR,L+6) = IN
IW(IR,L+4) = 0
IW(NZ,L+2) = IR
IF (IN.NE.0) IW(IN,L+4) = IR
560 CONTINUE
570 K1 = IP(IPP,1) + 1
K2 = IW(IPP,1) + K1 - 2
580 CONTINUE
590 CONTINUE
C
C RESET COLUMN FILE TO REFER TO U AND STORE ROW/COL NUMBERS IN
C PIVOTAL ORDER IN IW(.,3),IW(.,4)
DO 600 I=1,N
J = -IW(I,5)
IW(J,3) = I
J = -IW(I,6)
IW(J,4) = I
IW(I,2) = 0
600 CONTINUE
DO 620 I=1,N
KP = IP(I,1)
KL = IW(I,1) + KP - 1
DO 610 K=KP,KL
J = IND(K,2)
IW(J,2) = IW(J,2) + 1
610 CONTINUE
620 CONTINUE
K = 1
DO 630 I=1,N
K = K + IW(I,2)
IP(I,2) = K
630 CONTINUE
LCOL = K - 1
DO 650 II=1,N
I = IW(II,3)
KP = IP(I,1)
KL = IW(I,1) + KP - 1
DO 640 K=KP,KL
J = IND(K,2)
KN = IP(J,2) - 1
IP(J,2) = KN
IND(KN,1) = I
640 CONTINUE
650 CONTINUE
RETURN
C
C THE FOLLOWING INSTRUCTIONS IMPLEMENT THE FAILURE EXITS.
C
660 IF (LP.GT.0) THEN
WRITE (XERN1, '(I8)') IR
WRITE (XERN2, '(I8)') J
CALL XERMSG ('SLATEC', 'LA05AS', 'MORE THAN ONE MATRIX ' //
* 'ENTRY. HERE ROW = ' // XERN1 // ' AND COL = ' // XERN2,
* -4, 1)
ENDIF
G = -4.
RETURN
C
670 IF (LP.GT.0) CALL XERMSG ('SLATEC', 'LA05AS',
* 'THE ORDER OF THE SYSTEM, N, IS NOT POSITIVE.', -1, 1)
G = -1.0E0
RETURN
C
680 IF (LP.GT.0) THEN
WRITE (XERN0, '(I8)') K
WRITE (XERN1, '(I8)') I
WRITE (XERN2, '(I8)') J
CALL XERMSG ('SLATEC', 'LA05AS', 'ELEMENT K = ' // XERN0 //
* ' IS OUT OF BOUNDS.$$HERE ROW = ' // XERN1 //
* ' AND COL = ' // XERN2, -3, 1)
ENDIF
G = -3.
RETURN
C
700 IF (LP.GT.0) THEN
WRITE (XERN1, '(I8)') L
CALL XERMSG ('SLATEC', 'LA05AS', 'ROW OR COLUMN HAS NO ' //
* 'ELEMENTS. HERE INDEX = ' // XERN1, -2, 1)
ENDIF
G = -2.
RETURN
C
710 IF (LP.GT.0) CALL XERMSG ('SLATEC', 'LA05AS',
* 'LENGTHS OF ARRAYS A(*) AND IND(*,2) ARE TOO SMALL.', -7, 1)
G = -7.
RETURN
C
720 IPV = IPV + 1
IW(IPV,1) = IR
DO 730 I=1,N
II = -IW(I,L+4)
IF (II.GT.0) IW(II,1) = I
730 CONTINUE
C
IF (LP.GT.0) THEN
XERN1 = 'ROWS'
IF (L.EQ.2) XERN1 = 'COLUMNS'
CALL XERMSG ('SLATEC', 'LA05AS', 'DEPENDANT ' // XERN1, -5, 1)
C
740 WRITE (XERN1, '(I8)') IW(I,1)
XERN2 = ' '
IF (I+1.LE.IPV) WRITE (XERN2, '(I8)') IW(I+1,1)
CALL XERMSG ('SLATEC', 'LA05AS',
* 'DEPENDENT VECTOR INDICES ARE ' // XERN1 // ' AND ' //
* XERN2, -5, 1)
I = I + 2
IF (I.LE.IPV) GO TO 740
ENDIF
G = -5.
RETURN
END