C dgbfa.f C is freely available from netlib. It is not subject to any GNU License C set by the authors of the ASCEND math programming system. C \$Date: 1996/04/30 18:17:11 \$ \$Revision: 1.1.1.1 \$ C subroutine dgbfa(abd,lda,n,ml,mu,ipvt,info) integer lda,n,ml,mu,ipvt(1),info double precision abd(lda,1) c c dgbfa factors a double precision band matrix by elimination. c c dgbfa is usually called by dgbco, but it can be called c directly with a saving in time if rcond is not needed. c c on entry c c abd double precision(lda, n) c contains the matrix in band storage. the columns c of the matrix are stored in the columns of abd and c the diagonals of the matrix are stored in rows c ml+1 through 2*ml+mu+1 of abd . c see the comments below for details. c c lda integer c the leading dimension of the array abd . c lda must be .ge. 2*ml + mu + 1 . c c n integer c the order of the original matrix. c c ml integer c number of diagonals below the main diagonal. c 0 .le. ml .lt. n . c c mu integer c number of diagonals above the main diagonal. c 0 .le. mu .lt. n . c more efficient if ml .le. mu . c on return c c abd an upper triangular matrix in band storage and c the multipliers which were used to obtain it. c the factorization can be written a = l*u where c l is a product of permutation and unit lower c triangular matrices and u is upper triangular. c c ipvt integer(n) c an integer vector of pivot indices. c c info integer c = 0 normal value. c = k if u(k,k) .eq. 0.0 . this is not an error c condition for this subroutine, but it does c indicate that dgbsl will divide by zero if c called. use rcond in dgbco for a reliable c indication of singularity. c c band storage c c if a is a band matrix, the following program segment c will set up the input. c c ml = (band width below the diagonal) c mu = (band width above the diagonal) c m = ml + mu + 1 c do 20 j = 1, n c i1 = max0(1, j-mu) c i2 = min0(n, j+ml) c do 10 i = i1, i2 c k = i - j + m c abd(k,j) = a(i,j) c 10 continue c 20 continue c c this uses rows ml+1 through 2*ml+mu+1 of abd . c in addition, the first ml rows in abd are used for c elements generated during the triangularization. c the total number of rows needed in abd is 2*ml+mu+1 . c the ml+mu by ml+mu upper left triangle and the c ml by ml lower right triangle are not referenced. 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,idamax c fortran max0,min0 c c internal variables c double precision t integer i,idamax,i0,j,ju,jz,j0,j1,k,kp1,l,lm,m,mm,nm1 c c m = ml + mu + 1 info = 0 c c zero initial fill-in columns c j0 = mu + 2 j1 = min0(n,m) - 1 if (j1 .lt. j0) go to 30 do 20 jz = j0, j1 i0 = m + 1 - jz do 10 i = i0, ml abd(i,jz) = 0.0d0 10 continue 20 continue 30 continue jz = j1 ju = 0 c c gaussian elimination with partial pivoting c nm1 = n - 1 if (nm1 .lt. 1) go to 130 do 120 k = 1, nm1 kp1 = k + 1 c c zero next fill-in column c jz = jz + 1 if (jz .gt. n) go to 50 if (ml .lt. 1) go to 50 do 40 i = 1, ml abd(i,jz) = 0.0d0 40 continue 50 continue c c find l = pivot index c lm = min0(ml,n-k) l = idamax(lm+1,abd(m,k),1) + m - 1 ipvt(k) = l + k - m c c zero pivot implies this column already triangularized c if (abd(l,k) .eq. 0.0d0) go to 100 c c interchange if necessary c if (l .eq. m) go to 60 t = abd(l,k) abd(l,k) = abd(m,k) abd(m,k) = t 60 continue c c compute multipliers c t = -1.0d0/abd(m,k) call dscal(lm,t,abd(m+1,k),1) c c row elimination with column indexing c ju = min0(max0(ju,mu+ipvt(k)),n) mm = m if (ju .lt. kp1) go to 90 do 80 j = kp1, ju l = l - 1 mm = mm - 1 t = abd(l,j) if (l .eq. mm) go to 70 abd(l,j) = abd(mm,j) abd(mm,j) = t 70 continue call daxpy(lm,t,abd(m+1,k),1,abd(mm+1,j),1) 80 continue 90 continue go to 110 100 continue info = k 110 continue 120 continue 130 continue ipvt(n) = n if (abd(m,n) .eq. 0.0d0) info = n return end