| fe4da5cc |
1 | * |
| 2 | * $Id$ |
| 3 | * |
| 4 | * $Log$ |
| 5 | * Revision 1.1.1.1 1996/04/01 15:02:19 mclareni |
| 6 | * Mathlib gen |
| 7 | * |
| 8 | * |
| 9 | #include "gen/pilot.h" |
| 10 | SUBROUTINE D501N2(K,N,M,A,AL,AU,X,NX,WORK,B,DPHI,DSCAL,LAMU, |
| 11 | 1 AM,COV,IAFR,MFR,SUB,EPS0,EPS,MODE,NERROR) |
| 12 | |
| 13 | #include "gen/imp64.inc" |
| 14 | #include "gen/def64.inc" |
| 15 | + LAMU |
| 16 | DIMENSION A(*),AL(*),AU(*),X(*),WORK(*),B(*),DPHI(*),DSCAL(*) |
| 17 | DIMENSION LAMU(*),AM(M,*),COV(M,*),IAFR(*) |
| 18 | PARAMETER (Z0 = 0) |
| 19 | |
| 20 | ************************************************************************* |
| 21 | * LEAMAX, VERSION: 15.03.1993 |
| 22 | ************************************************************************* |
| 23 | * |
| 24 | * THIS ROUTINE COMPUTES THE GRADIENT, THE JACOBIAN, AND IT SETS UP |
| 25 | * THE MATRIX FOR THE NORMAL EQUATIONS. IT ALSO DETERMINES THE ACTIVE |
| 26 | * SET OF CONSTRAINTS AND THE LAGRANGE-MULTIPLIER. |
| 27 | * |
| 28 | ************************************************************************ |
| 29 | |
| 30 | ************************************************************************ |
| 31 | * SET INITIAL VALUES |
| 32 | ************************************************************************ |
| 33 | |
| 34 | HREL=SQRT(EPS0) |
| 35 | HABS=10*EPS0 |
| 36 | |
| 37 | ************************************************************************ |
| 38 | * COMPUTE THE GRADIENT B OF THE OBJECTIVE FUNCTION |
| 39 | * COMPUTE AN APPROXIMATION AM OF THE SECOND DERIVATIVE (THE HESSIAN) |
| 40 | * OF THE OBJECTIVE FUNCTION |
| 41 | ************************************************************************ |
| 42 | |
| 43 | NERROR=0 |
| 44 | CALL DVSET(M,Z0,B(1),B(2)) |
| 45 | CALL DMSET(M,M,Z0,AM(1,1),AM(1,2),AM(2,1)) |
| 46 | IX=1 |
| 47 | |
| 48 | DO 30 I=1,N |
| 49 | |
| 50 | CALL SUB(K,X(IX),M,A,F0,WORK,MODE,NERROR) |
| 51 | IF(NERROR .NE. 0 .OR. F0 .LE. 0) THEN |
| 52 | NERROR=3 |
| 53 | RETURN |
| 54 | ENDIF |
| 55 | |
| 56 | IF(MODE .EQ. 0) THEN |
| 57 | |
| 58 | ************************************************************************ |
| 59 | * APPROXIMATE DERIVATIVES |
| 60 | ************************************************************************ |
| 61 | |
| 62 | DO 10 J=1,M |
| 63 | H =ABS(A(J))*HREL+HABS |
| 64 | IF (A(J)+H .GT. AU(J)) H =-H |
| 65 | A(J)=A(J)+H |
| 66 | CALL SUB(K,X(IX),M,A,FH,WORK,MODE,NERROR) |
| 67 | IF(NERROR .NE. 0) THEN |
| 68 | NERROR=3 |
| 69 | RETURN |
| 70 | ENDIF |
| 71 | A(J)=A(J)-H |
| 72 | 10 WORK(J)=(FH-F0)/H |
| 73 | ENDIF |
| 74 | |
| 75 | CALL DVSCL(M,1/F0,WORK(1),WORK(2),WORK(1),WORK(2)) |
| 76 | CALL DVSUB(M,B(1),B(2),WORK(1),WORK(2),B(1),B(2)) |
| 77 | |
| 78 | DO 20 L=1,M |
| 79 | DO 20 J=L,M |
| 80 | 20 AM(L,J)=AM(L,J)+WORK(L)*WORK(J) |
| 81 | |
| 82 | 30 IX=IX+NX |
| 83 | |
| 84 | CALL DMUTL(M,AM(1,1),AM(1,2),AM(2,1)) |
| 85 | |
| 86 | ************************************************************************ |
| 87 | * COPY THE GRADIENT OF THE OBJECTIVE FUNCTION TO DPHI |
| 88 | ************************************************************************ |
| 89 | |
| 90 | CALL DVCPY(M,B(1),B(2),DPHI(1),DPHI(2)) |
| 91 | |
| 92 | ************************************************************************ |
| 93 | * DETERMINE THE DIAGONAL MATRIX DSCAL FOR SCALING THE PROBLEM |
| 94 | ************************************************************************ |
| 95 | |
| 96 | DO 40 I=1,M |
| 97 | 40 DSCAL(I)=MAX(DSCAL(I),SQRT(AM(I,I))) |
| 98 | |
| 99 | ************************************************************************ |
| 100 | * DETERMINE FREE VARIABLES AND STORE THEIR INDICES IN IAFR |
| 101 | * DETERMINE LAGRANGE MULTIPLIER LAMU |
| 102 | ************************************************************************ |
| 103 | |
| 104 | GR=0 |
| 105 | DO 50 I=1,MFR |
| 106 | 50 GR=GR+(DSCAL(I)*A(IAFR(I)))**2 |
| 107 | GR=HREL*SQRT(GR) |
| 108 | CALL DVSET(M,Z0,LAMU(1),LAMU(2)) |
| 109 | |
| 110 | MFR=0 |
| 111 | |
| 112 | DO 60 I=1,M |
| 113 | IF(AU(I)-AL(I) .LT. EPS*(ABS(AU(I))+ABS(AL(I)))+2*HABS) THEN |
| 114 | A(I)=AU(I) |
| 115 | LAMU(I)=DPHI(I) |
| 116 | ELSE |
| 117 | IF(A(I) .GE. AU(I)-(EPS * ABS(AU(I)) + HABS)) THEN |
| 118 | A(I)=AU(I) |
| 119 | IF(DPHI(I) .GT. -GR) THEN |
| 120 | MFR=MFR+1 |
| 121 | IAFR(MFR)=I |
| 122 | ELSE |
| 123 | LAMU(I)=DPHI(I) |
| 124 | ENDIF |
| 125 | ELSE IF(A(I) .LE. AL(I)+(EPS * ABS(AL(I)) + HABS)) THEN |
| 126 | A(I)=AL(I) |
| 127 | IF(DPHI(I) .LT. GR) THEN |
| 128 | MFR=MFR+1 |
| 129 | IAFR(MFR)=I |
| 130 | ELSE |
| 131 | LAMU(I)=DPHI(I) |
| 132 | ENDIF |
| 133 | ELSE |
| 134 | MFR=MFR+1 |
| 135 | IAFR(MFR)=I |
| 136 | ENDIF |
| 137 | ENDIF |
| 138 | |
| 139 | 60 CONTINUE |
| 140 | |
| 141 | *********************************************************************** |
| 142 | * DELETE ROWS AND COLUMNS OF AM AND B WHICH BELONG TO NON-FREE |
| 143 | * VARIABLES |
| 144 | ************************************************************************ |
| 145 | |
| 146 | IF(MFR .EQ. 0 .OR. MFR .EQ. M) THEN |
| 147 | MFC=M |
| 148 | ELSE |
| 149 | MFC=MFR |
| 150 | DO 70 I =1,MFR |
| 151 | B(I)=B(IAFR(I)) |
| 152 | DSCAL(I)=DSCAL(IAFR(I)) |
| 153 | DO 70 L = 1,M |
| 154 | 70 AM(L,I)=AM(L,IAFR(I)) |
| 155 | DO 80 I=1,MFR |
| 156 | DO 80 L=1,M |
| 157 | 80 AM(I,L)=AM(IAFR(I),L) |
| 158 | ENDIF |
| 159 | |
| 160 | CALL DMCPY(MFC,MFC,AM(1,1),AM(1,2),AM(2,1), |
| 161 | + COV(1,1),COV(1,2),COV(2,1)) |
| 162 | RETURN |
| 163 | |
| 164 | END |
| 165 | |
| 166 | |
| 167 | |
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