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