subroutine zsidi(a,lda,n,kpvt,det,work,job) integer lda,n,job complex*16 a(lda,1),det(2),work(1) integer kpvt(1) c c zsidi computes the determinant and inverse c of a complex*16 symmetric matrix using the factors from zsifa. c c on entry c c a complex*16(lda,n) c the output from zsifa. 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 zsifa. c c work complex*16(n) c work vector. contents destroyed. c c job integer c job has the decimal expansion ab where c if b .ne. 0, the inverse is computed, c if a .ne. 0, the determinant is computed, c c for example, job = 11 gives both. 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 complex*16(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 error condition c c a division by zero may occur if the inverse is requested c and zsico has set rcond .eq. 0.0 c or zsifa 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 zaxpy,zcopy,zdotu,zswap c fortran dabs,dcmplx,iabs,mod c c internal variables. c complex*16 ak,akp1,akkp1,zdotu,d,t,temp double precision ten integer j,jb,k,km1,ks,kstep logical noinv,nodet c complex*16 zdum double precision cabs1 double precision dreal,dimag complex*16 zdumr,zdumi dreal(zdumr) = zdumr dimag(zdumi) = (0.0d0,-1.0d0)*zdumi cabs1(zdum) = dabs(dreal(zdum)) + dabs(dimag(zdum)) c noinv = mod(job,10) .eq. 0 nodet = mod(job,100)/10 .eq. 0 c if (nodet) go to 100 det(1) = (1.0d0,0.0d0) det(2) = (0.0d0,0.0d0) ten = 10.0d0 t = (0.0d0,0.0d0) do 90 k = 1, n d = a(k,k) c c check if 1 by 1 c if (kpvt(k) .gt. 0) go to 30 c c 2 by 2 block c use det (d t) = (d/t * c - t) * t c (t c) c to avoid underflow/overflow troubles. c take two passes through scaling. use t for flag. c if (cabs1(t) .ne. 0.0d0) go to 10 t = a(k,k+1) d = (d/t)*a(k+1,k+1) - t go to 20 10 continue d = t t = (0.0d0,0.0d0) 20 continue 30 continue c det(1) = d*det(1) if (cabs1(det(1)) .eq. 0.0d0) go to 80 40 if (cabs1(det(1)) .ge. 1.0d0) go to 50 det(1) = dcmplx(ten,0.0d0)*det(1) det(2) = det(2) - (1.0d0,0.0d0) go to 40 50 continue 60 if (cabs1(det(1)) .lt. ten) go to 70 det(1) = det(1)/dcmplx(ten,0.0d0) det(2) = det(2) + (1.0d0,0.0d0) go to 60 70 continue 80 continue 90 continue 100 continue c c compute inverse(a) c if (noinv) go to 230 k = 1 110 if (k .gt. n) go to 220 km1 = k - 1 if (kpvt(k) .lt. 0) go to 140 c c 1 by 1 c a(k,k) = (1.0d0,0.0d0)/a(k,k) if (km1 .lt. 1) go to 130 call zcopy(km1,a(1,k),1,work,1) do 120 j = 1, km1 a(j,k) = zdotu(j,a(1,j),1,work,1) call zaxpy(j-1,work(j),a(1,j),1,a(1,k),1) 120 continue a(k,k) = a(k,k) + zdotu(km1,work,1,a(1,k),1) 130 continue kstep = 1 go to 180 140 continue c c 2 by 2 c t = 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 - (1.0d0,0.0d0)) a(k,k) = akp1/d a(k+1,k+1) = ak/d a(k,k+1) = -akkp1/d if (km1 .lt. 1) go to 170 call zcopy(km1,a(1,k+1),1,work,1) do 150 j = 1, km1 a(j,k+1) = zdotu(j,a(1,j),1,work,1) call zaxpy(j-1,work(j),a(1,j),1,a(1,k+1),1) 150 continue a(k+1,k+1) = a(k+1,k+1) * + zdotu(km1,work,1,a(1,k+1),1) a(k,k+1) = a(k,k+1) + zdotu(km1,a(1,k),1,a(1,k+1),1) call zcopy(km1,a(1,k),1,work,1) do 160 j = 1, km1 a(j,k) = zdotu(j,a(1,j),1,work,1) call zaxpy(j-1,work(j),a(1,j),1,a(1,k),1) 160 continue a(k,k) = a(k,k) + zdotu(km1,work,1,a(1,k),1) 170 continue kstep = 2 180 continue c c swap c ks = iabs(kpvt(k)) if (ks .eq. k) go to 210 call zswap(ks,a(1,ks),1,a(1,k),1) do 190 jb = ks, k j = k + ks - jb temp = a(j,k) a(j,k) = a(ks,j) a(ks,j) = temp 190 continue if (kstep .eq. 1) go to 200 temp = a(ks,k+1) a(ks,k+1) = a(k,k+1) a(k,k+1) = temp 200 continue 210 continue k = k + kstep go to 110 220 continue 230 continue return end