subroutine dpodi(a,lda,n,det,job) integer lda,n,job double precision a(lda,1) double precision det(2) 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 linpack. this version dated 08/14/78 . c cleve moler, university of new mexico, argonne national lab. c c subroutines and functions c c blas daxpy,dscal c fortran mod c c internal variables c double precision t double precision s integer i,j,jm1,k,kp1 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) c ...exit 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