subroutine dsidi(a,lda,n,kpvt,det,inert,work,job) integer lda,n,job double precision a(lda,1),work(1) double precision det(2) integer kpvt(1),inert(3) c c dsidi computes the determinant, inertia and inverse c of a double precision symmetric matrix using the factors from c dsifa. c c on entry c c a double precision(lda,n) c the output from dsifa. 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 kpvt integer(n) c the pivot vector from dsifa. c c work double precision(n) c work vector. contents destroyed. 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 a contains the upper triangle of the inverse of c the original matrix. the strict lower triangle c is never referenced. c c det double precision(2) c determinant of original matrix. c determinant = det(1) * 10.0**det(2) c with 1.0 .le. dabs(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 may occur if the inverse is requested c and dsico has set rcond .eq. 0.0 c or dsifa 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 daxpy,dcopy,ddot,dswap c fortran dabs,iabs,mod c c internal variables. c double precision akkp1,ddot,temp double precision ten,d,t,ak,akp1 integer j,jb,k,km1,ks,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) = 1.0d0 det(2) = 0.0d0 ten = 10.0d0 20 continue t = 0.0d0 do 130 k = 1, n d = a(k,k) 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 = dabs(s) c (s c) c to avoid underflow/overflow troubles. c take two passes through scaling. use t for flag. c if (t .ne. 0.0d0) go to 30 t = dabs(a(k,k+1)) d = (d/t)*a(k+1,k+1) - t go to 40 30 continue d = t t = 0.0d0 40 continue 50 continue c if (noert) go to 60 if (d .gt. 0.0d0) inert(1) = inert(1) + 1 if (d .lt. 0.0d0) inert(2) = inert(2) + 1 if (d .eq. 0.0d0) inert(3) = inert(3) + 1 60 continue c if (nodet) go to 120 det(1) = d*det(1) if (det(1) .eq. 0.0d0) go to 110 70 if (dabs(det(1)) .ge. 1.0d0) go to 80 det(1) = ten*det(1) det(2) = det(2) - 1.0d0 go to 70 80 continue 90 if (dabs(det(1)) .lt. ten) go to 100 det(1) = det(1)/ten det(2) = det(2) + 1.0d0 go to 90 100 continue 110 continue 120 continue 130 continue 140 continue c c compute inverse(a) c if (noinv) go to 270 k = 1 150 if (k .gt. n) go to 260 km1 = k - 1 if (kpvt(k) .lt. 0) go to 180 c c 1 by 1 c a(k,k) = 1.0d0/a(k,k) if (km1 .lt. 1) go to 170 call dcopy(km1,a(1,k),1,work,1) do 160 j = 1, km1 a(j,k) = ddot(j,a(1,j),1,work,1) call daxpy(j-1,work(j),a(1,j),1,a(1,k),1) 160 continue a(k,k) = a(k,k) + ddot(km1,work,1,a(1,k),1) 170 continue kstep = 1 go to 220 180 continue c c 2 by 2 c t = dabs(a(k,k+1)) ak = a(k,k)/t akp1 = a(k+1,k+1)/t akkp1 = a(k,k+1)/t d = t*(ak*akp1 - 1.0d0) a(k,k) = akp1/d a(k+1,k+1) = ak/d a(k,k+1) = -akkp1/d if (km1 .lt. 1) go to 210 call dcopy(km1,a(1,k+1),1,work,1) do 190 j = 1, km1 a(j,k+1) = ddot(j,a(1,j),1,work,1) call daxpy(j-1,work(j),a(1,j),1,a(1,k+1),1) 190 continue a(k+1,k+1) = a(k+1,k+1) + ddot(km1,work,1,a(1,k+1),1) a(k,k+1) = a(k,k+1) + ddot(km1,a(1,k),1,a(1,k+1),1) call dcopy(km1,a(1,k),1,work,1) do 200 j = 1, km1 a(j,k) = ddot(j,a(1,j),1,work,1) call daxpy(j-1,work(j),a(1,j),1,a(1,k),1) 200 continue a(k,k) = a(k,k) + ddot(km1,work,1,a(1,k),1) 210 continue kstep = 2 220 continue c c swap c ks = iabs(kpvt(k)) if (ks .eq. k) go to 250 call dswap(ks,a(1,ks),1,a(1,k),1) do 230 jb = ks, k j = k + ks - jb temp = a(j,k) a(j,k) = a(ks,j) a(ks,j) = temp 230 continue if (kstep .eq. 1) go to 240 temp = a(ks,k+1) a(ks,k+1) = a(k,k+1) a(k,k+1) = temp 240 continue 250 continue k = k + kstep go to 150 260 continue 270 continue return end