*DECK STRDI SUBROUTINE STRDI (T, LDT, N, DET, JOB, INFO) C***BEGIN PROLOGUE STRDI C***PURPOSE Compute the determinant and inverse of a triangular matrix. C***LIBRARY SLATEC (LINPACK) C***CATEGORY D2A3, D3A3 C***TYPE SINGLE PRECISION (STRDI-S, DTRDI-D, CTRDI-C) C***KEYWORDS DETERMINANT, INVERSE, LINEAR ALGEBRA, LINPACK, MATRIX, C TRIANGULAR C***AUTHOR Moler, C. B., (U. of New Mexico) C***DESCRIPTION C C STRDI computes the determinant and inverse of a real C triangular matrix. C C On Entry C C T REAL(LDT,N) C T contains the triangular matrix. The zero C elements of the matrix are not referenced, and C the corresponding elements of the array can be C used to store other information. C C LDT INTEGER C LDT is the leading dimension of the array T. C C N INTEGER C N is the order of the system. C C JOB INTEGER C = 010 no det, inverse of lower triangular. C = 011 no det, inverse of upper triangular. C = 100 det, no inverse. C = 110 det, inverse of lower triangular. C = 111 det, inverse of upper triangular. C C On Return C C T inverse of original matrix if requested. C Otherwise unchanged. C C DET REAL(2) C determinant of original matrix if requested. C Otherwise not referenced. C Determinant = DET(1) * 10.0**DET(2) C with 1.0 .LE. ABS(DET(1)) .LT. 10.0 C or DET(1) .EQ. 0.0 . C C INFO INTEGER C INFO contains zero if the system is nonsingular C and the inverse is requested. C Otherwise INFO contains the index of C a zero diagonal element of T. C C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. C Stewart, LINPACK Users' Guide, SIAM, 1979. C***ROUTINES CALLED SAXPY, SSCAL C***REVISION HISTORY (YYMMDD) C 780814 DATE WRITTEN C 890831 Modified array declarations. (WRB) C 890831 REVISION DATE from Version 3.2 C 891214 Prologue converted to Version 4.0 format. (BAB) C 900326 Removed duplicate information from DESCRIPTION section. C (WRB) C 920501 Reformatted the REFERENCES section. (WRB) C***END PROLOGUE STRDI INTEGER LDT,N,JOB,INFO REAL T(LDT,*),DET(2) C REAL TEMP REAL TEN INTEGER I,J,K,KB,KM1,KP1 C***FIRST EXECUTABLE STATEMENT STRDI C C COMPUTE DETERMINANT C IF (JOB/100 .EQ. 0) GO TO 70 DET(1) = 1.0E0 DET(2) = 0.0E0 TEN = 10.0E0 DO 50 I = 1, N DET(1) = T(I,I)*DET(1) IF (DET(1) .EQ. 0.0E0) GO TO 60 10 IF (ABS(DET(1)) .GE. 1.0E0) GO TO 20 DET(1) = TEN*DET(1) DET(2) = DET(2) - 1.0E0 GO TO 10 20 CONTINUE 30 IF (ABS(DET(1)) .LT. TEN) GO TO 40 DET(1) = DET(1)/TEN DET(2) = DET(2) + 1.0E0 GO TO 30 40 CONTINUE 50 CONTINUE 60 CONTINUE 70 CONTINUE C C COMPUTE INVERSE OF UPPER TRIANGULAR C IF (MOD(JOB/10,10) .EQ. 0) GO TO 170 IF (MOD(JOB,10) .EQ. 0) GO TO 120 DO 100 K = 1, N INFO = K IF (T(K,K) .EQ. 0.0E0) GO TO 110 T(K,K) = 1.0E0/T(K,K) TEMP = -T(K,K) CALL SSCAL(K-1,TEMP,T(1,K),1) KP1 = K + 1 IF (N .LT. KP1) GO TO 90 DO 80 J = KP1, N TEMP = T(K,J) T(K,J) = 0.0E0 CALL SAXPY(K,TEMP,T(1,K),1,T(1,J),1) 80 CONTINUE 90 CONTINUE 100 CONTINUE INFO = 0 110 CONTINUE GO TO 160 120 CONTINUE C C COMPUTE INVERSE OF LOWER TRIANGULAR C DO 150 KB = 1, N K = N + 1 - KB INFO = K IF (T(K,K) .EQ. 0.0E0) GO TO 180 T(K,K) = 1.0E0/T(K,K) TEMP = -T(K,K) IF (K .NE. N) CALL SSCAL(N-K,TEMP,T(K+1,K),1) KM1 = K - 1 IF (KM1 .LT. 1) GO TO 140 DO 130 J = 1, KM1 TEMP = T(K,J) T(K,J) = 0.0E0 CALL SAXPY(N-K+1,TEMP,T(K,K),1,T(K,J),1) 130 CONTINUE 140 CONTINUE 150 CONTINUE INFO = 0 160 CONTINUE 170 CONTINUE 180 CONTINUE RETURN END