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*DECK DPODI
SUBROUTINE DPODI (A, LDA, N, DET, JOB)
C***BEGIN PROLOGUE DPODI
C***PURPOSE Compute the determinant and inverse of a certain real
C symmetric positive definite matrix using the factors
C computed by DPOCO, DPOFA or DQRDC.
C***LIBRARY SLATEC (LINPACK)
C***CATEGORY D2B1B, D3B1B
C***TYPE DOUBLE PRECISION (SPODI-S, DPODI-D, CPODI-C)
C***KEYWORDS DETERMINANT, INVERSE, LINEAR ALGEBRA, LINPACK, MATRIX,
C POSITIVE DEFINITE
C***AUTHOR Moler, C. B., (U. of New Mexico)
C***DESCRIPTION
C
C DPODI computes the determinant and inverse of a certain
C double precision symmetric positive definite matrix (see below)
C using the factors computed by DPOCO, DPOFA or DQRDC.
C
C On Entry
C
C A DOUBLE PRECISION(LDA, N)
C the output A from DPOCO or DPOFA
C or the output X from DQRDC.
C
C LDA INTEGER
C the leading dimension of the array A .
C
C N INTEGER
C the order of the matrix A .
C
C JOB INTEGER
C = 11 both determinant and inverse.
C = 01 inverse only.
C = 10 determinant only.
C
C On Return
C
C A If DPOCO or DPOFA was used to factor A , then
C DPODI produces the upper half of INVERSE(A) .
C If DQRDC was used to decompose X , then
C DPODI produces the upper half of inverse(TRANS(X)*X)
C where TRANS(X) is the transpose.
C Elements of A below the diagonal are unchanged.
C If the units digit of JOB is zero, A is unchanged.
C
C DET DOUBLE PRECISION(2)
C determinant of A or of TRANS(X)*X if requested.
C Otherwise not referenced.
C Determinant = DET(1) * 10.0**DET(2)
C with 1.0 .LE. DET(1) .LT. 10.0
C or DET(1) .EQ. 0.0 .
C
C Error Condition
C
C A division by zero will occur if the input factor contains
C a zero on the diagonal and the inverse is requested.
C It will not occur if the subroutines are called correctly
C and if DPOCO or DPOFA has set INFO .EQ. 0 .
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 DAXPY, DSCAL
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 DPODI
INTEGER LDA,N,JOB
DOUBLE PRECISION A(LDA,*)
DOUBLE PRECISION DET(2)
C
DOUBLE PRECISION T
DOUBLE PRECISION S
INTEGER I,J,JM1,K,KP1
C***FIRST EXECUTABLE STATEMENT DPODI
C
C COMPUTE DETERMINANT
C
IF (JOB/10 .EQ. 0) GO TO 70
DET(1) = 1.0D0
DET(2) = 0.0D0
S = 10.0D0
DO 50 I = 1, N
DET(1) = A(I,I)**2*DET(1)
IF (DET(1) .EQ. 0.0D0) GO TO 60
10 IF (DET(1) .GE. 1.0D0) GO TO 20
DET(1) = S*DET(1)
DET(2) = DET(2) - 1.0D0
GO TO 10
20 CONTINUE
30 IF (DET(1) .LT. S) GO TO 40
DET(1) = DET(1)/S
DET(2) = DET(2) + 1.0D0
GO TO 30
40 CONTINUE
50 CONTINUE
60 CONTINUE
70 CONTINUE
C
C COMPUTE INVERSE(R)
C
IF (MOD(JOB,10) .EQ. 0) GO TO 140
DO 100 K = 1, N
A(K,K) = 1.0D0/A(K,K)
T = -A(K,K)
CALL DSCAL(K-1,T,A(1,K),1)
KP1 = K + 1
IF (N .LT. KP1) GO TO 90
DO 80 J = KP1, N
T = A(K,J)
A(K,J) = 0.0D0
CALL DAXPY(K,T,A(1,K),1,A(1,J),1)
80 CONTINUE
90 CONTINUE
100 CONTINUE
C
C FORM INVERSE(R) * TRANS(INVERSE(R))
C
DO 130 J = 1, N
JM1 = J - 1
IF (JM1 .LT. 1) GO TO 120
DO 110 K = 1, JM1
T = A(K,J)
CALL DAXPY(K,T,A(1,J),1,A(1,K),1)
110 CONTINUE
120 CONTINUE
T = A(J,J)
CALL DSCAL(J,T,A(1,J),1)
130 CONTINUE
140 CONTINUE
RETURN
END
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