SUBROUTINE SSPDI(AP,N,KPVT,DET,INERT,WORK,JOB) INTEGER N,JOB REAL AP(1),WORK(1) REAL DET(2) INTEGER KPVT(1),INERT(3) C C SSPDI COMPUTES THE DETERMINANT, INERTIA AND INVERSE C OF A REAL SYMMETRIC MATRIX USING THE FACTORS FROM SSPFA, C WHERE THE MATRIX IS STORED IN PACKED FORM. C C ON ENTRY C C AP REAL (N*(N+1)/2) C THE OUTPUT FROM SSPFA. C C N INTEGER C THE ORDER OF THE MATRIX A. C C KPVT INTEGER(N) C THE PIVOT VECTOR FROM SSPFA. C C WORK REAL(N) C WORK VECTOR. CONTENTS IGNORED. C C JOB INTEGER C JOB HAS THE DECIMAL EXPANSION ABC WHERE C IF C .NE. 0, THE INVERSE IS COMPUTED, C IF B .NE. 0, THE DETERMINANT IS COMPUTED, C IF A .NE. 0, THE INERTIA IS COMPUTED. C C FOR EXAMPLE, JOB = 111 GIVES ALL THREE. C C ON RETURN C C VARIABLES NOT REQUESTED BY JOB ARE NOT USED. C C AP CONTAINS THE UPPER TRIANGLE OF THE INVERSE OF C THE ORIGINAL MATRIX, STORED IN PACKED FORM. C THE COLUMNS OF THE UPPER TRIANGLE ARE STORED C SEQUENTIALLY IN A ONE-DIMENSIONAL ARRAY. C C DET REAL(2) C DETERMINANT OF ORIGINAL MATRIX. C DETERMINANT = DET(1) * 10.0**DET(2) C WITH 1.0 .LE. ABS(DET(1)) .LT. 10.0 C OR DET(1) = 0.0. C C INERT INTEGER(3) C THE INERTIA OF THE ORIGINAL MATRIX. C INERT(1) = NUMBER OF POSITIVE EIGENVALUES. C INERT(2) = NUMBER OF NEGATIVE EIGENVALUES. C INERT(3) = NUMBER OF ZERO EIGENVALUES. C C ERROR CONDITION C C A DIVISION BY ZERO WILL OCCUR IF THE INVERSE IS REQUESTED C AND SSPCO HAS SET RCOND .EQ. 0.0 C OR SSPFA HAS SET INFO .NE. 0 . C C LINPACK. THIS VERSION DATED 08/14/78 . C JAMES BUNCH, UNIV. CALIF. SAN DIEGO, ARGONNE NAT. LAB. C C SUBROUTINES AND FUNCTIONS C C BLAS SAXPY,SCOPY,SDOT,SSWAP C FORTRAN ABS,IABS,MOD C C INTERNAL VARIABLES. C REAL AKKP1,SDOT,TEMP REAL TEN,D,T,AK,AKP1 INTEGER IJ,IK,IKP1,IKS,J,JB,JK,JKP1 INTEGER K,KK,KKP1,KM1,KS,KSJ,KSKP1,KSTEP LOGICAL NOINV,NODET,NOERT C NOINV = MOD(JOB,10) .EQ. 0 NODET = MOD(JOB,100)/10 .EQ. 0 NOERT = MOD(JOB,1000)/100 .EQ. 0 C IF (NODET .AND. NOERT) GO TO 140 IF (NOERT) GO TO 10 INERT(1) = 0 INERT(2) = 0 INERT(3) = 0 10 CONTINUE IF (NODET) GO TO 20 DET(1) = 1.0E0 DET(2) = 0.0E0 TEN = 10.0E0 20 CONTINUE T = 0.0E0 IK = 0 DO 130 K = 1, N KK = IK + K D = AP(KK) C C CHECK IF 1 BY 1 C IF (KPVT(K) .GT. 0) GO TO 50 C C 2 BY 2 BLOCK C USE DET (D S) = (D/T * C - T) * T , T = ABS(S) C (S C) C TO AVOID UNDERFLOW/OVERFLOW TROUBLES. C TAKE TWO PASSES THROUGH SCALING. USE T FOR FLAG. C IF (T .NE. 0.0E0) GO TO 30 IKP1 = IK + K KKP1 = IKP1 + K T = ABS(AP(KKP1)) D = (D/T)*AP(KKP1+1) - T GO TO 40 30 CONTINUE D = T T = 0.0E0 40 CONTINUE 50 CONTINUE C IF (NOERT) GO TO 60 IF (D .GT. 0.0E0) INERT(1) = INERT(1) + 1 IF (D .LT. 0.0E0) INERT(2) = INERT(2) + 1 IF (D .EQ. 0.0E0) INERT(3) = INERT(3) + 1 60 CONTINUE C IF (NODET) GO TO 120 DET(1) = D*DET(1) IF (DET(1) .EQ. 0.0E0) GO TO 110 70 IF (ABS(DET(1)) .GE. 1.0E0) GO TO 80 DET(1) = TEN*DET(1) DET(2) = DET(2) - 1.0E0 GO TO 70 80 CONTINUE 90 IF (ABS(DET(1)) .LT. TEN) GO TO 100 DET(1) = DET(1)/TEN DET(2) = DET(2) + 1.0E0 GO TO 90 100 CONTINUE 110 CONTINUE 120 CONTINUE IK = IK + K 130 CONTINUE 140 CONTINUE C C COMPUTE INVERSE(A) C IF (NOINV) GO TO 270 K = 1 IK = 0 150 IF (K .GT. N) GO TO 260 KM1 = K - 1 KK = IK + K IKP1 = IK + K KKP1 = IKP1 + K IF (KPVT(K) .LT. 0) GO TO 180 C C 1 BY 1 C AP(KK) = 1.0E0/AP(KK) IF (KM1 .LT. 1) GO TO 170 CALL SCOPY(KM1,AP(IK+1),1,WORK,1) IJ = 0 DO 160 J = 1, KM1 JK = IK + J AP(JK) = SDOT(J,AP(IJ+1),1,WORK,1) CALL SAXPY(J-1,WORK(J),AP(IJ+1),1,AP(IK+1),1) IJ = IJ + J 160 CONTINUE AP(KK) = AP(KK) + SDOT(KM1,WORK,1,AP(IK+1),1) 170 CONTINUE KSTEP = 1 GO TO 220 180 CONTINUE C C 2 BY 2 C T = ABS(AP(KKP1)) AK = AP(KK)/T AKP1 = AP(KKP1+1)/T AKKP1 = AP(KKP1)/T D = T*(AK*AKP1 - 1.0E0) AP(KK) = AKP1/D AP(KKP1+1) = AK/D AP(KKP1) = -AKKP1/D IF (KM1 .LT. 1) GO TO 210 CALL SCOPY(KM1,AP(IKP1+1),1,WORK,1) IJ = 0 DO 190 J = 1, KM1 JKP1 = IKP1 + J AP(JKP1) = SDOT(J,AP(IJ+1),1,WORK,1) CALL SAXPY(J-1,WORK(J),AP(IJ+1),1,AP(IKP1+1),1) IJ = IJ + J 190 CONTINUE AP(KKP1+1) = AP(KKP1+1) * + SDOT(KM1,WORK,1,AP(IKP1+1),1) AP(KKP1) = AP(KKP1) * + SDOT(KM1,AP(IK+1),1,AP(IKP1+1),1) CALL SCOPY(KM1,AP(IK+1),1,WORK,1) IJ = 0 DO 200 J = 1, KM1 JK = IK + J AP(JK) = SDOT(J,AP(IJ+1),1,WORK,1) CALL SAXPY(J-1,WORK(J),AP(IJ+1),1,AP(IK+1),1) IJ = IJ + J 200 CONTINUE AP(KK) = AP(KK) + SDOT(KM1,WORK,1,AP(IK+1),1) 210 CONTINUE KSTEP = 2 220 CONTINUE C C SWAP C KS = IABS(KPVT(K)) IF (KS .EQ. K) GO TO 250 IKS = (KS*(KS - 1))/2 CALL SSWAP(KS,AP(IKS+1),1,AP(IK+1),1) KSJ = IK + KS DO 230 JB = KS, K J = K + KS - JB JK = IK + J TEMP = AP(JK) AP(JK) = AP(KSJ) AP(KSJ) = TEMP KSJ = KSJ - (J - 1) 230 CONTINUE IF (KSTEP .EQ. 1) GO TO 240 KSKP1 = IKP1 + KS TEMP = AP(KSKP1) AP(KSKP1) = AP(KKP1) AP(KKP1) = TEMP 240 CONTINUE 250 CONTINUE IK = IK + K IF (KSTEP .EQ. 2) IK = IK + K + 1 K = K + KSTEP GO TO 150 260 CONTINUE 270 CONTINUE RETURN END