subroutine tgslz1(a1,a2,b,x,c1,c2,r1,r2,r3,r5,r6,r,m,l,lda)
      integer m,l,lda
      double complex a1(lda,l),a2(lda,1),b(m,l),x(m,l),c1(m,m,1),
     *     c2(m,m,1),r1(m,m),r2(m,m),r3(m,m),r5(m,m),r6(m,m),r(m)
c
c     tgslz1 solves the double complex linear system
c     a * x = b
c     with the tg - matrix a .
c
c     on entry
c
c        a1      double complex(m**2,l)
c                the first row of blocks of the tg - matrix a .
c                each block is represented by columns .
c                on return a1 is unaltered .
c
c        a2      double complex(m**2,l - 1)
c                the first column of blocks of the tg - matrix a
c                beginning with the second block. each block is
c                represented by columns. on return a2 is unaltered .
c
c        b       double complex(m*l)
c                the right hand side vector .
c                on return b is unaltered .
c
c        c1      double complex(m,m,l - 1)
c                a work array .
c
c        c2      double complex(m,m,l - 1)
c                a work array .
c
c        r1      double complex(m,m)
c                a work array .
c
c        r2      double complex(m,m)
c                a work array .
c
c        r3      double complex(m,m)
c                a work array .
c
c        r5      double complex(m,m)
c                a work array .
c
c        r6      double complex(m,m)
c                a work array .
c
c        r       double complex(m)
c                a work vector .
c
c        m       integer
c                the order of the blocks of the matrix a .
c
c        l       integer
c                the number of blocks in a row or column
c                of the matrix a .
c
c        lda     integer
c                the leading dimension of the array a .
c
c     on return
c
c        x       double complex(m*l)
c                the solution vector. x may coincide with b .
c
c     toeplitz package. this version dated 07/23/82 .
c
c     subroutines and functions
c
c        linpack ... zaxpy,zgefa,zgesl
c                ... (for in-line zaxpy, see directions in comments)
c
c     internal variables
c
      integer i,i1,i2,i3,ii,j,n,n1,n2
c
c     solve the system with the principal minor of order m .
c
      i3 = 1
      do 20 j = 1, m
         do 10 i = 1, m
            c1(i,j,1) = a1(i3,1)
            r1(i,j) = a1(i3,1)
            r3(i,j) = r1(i,j)
            i3 = i3 + 1
   10    continue
         x(j,1) = b(j,1)
   20 continue
      call zgefa(r3,m,m,r,ii)
      call zgesl(r3,m,m,r,x(1,1),0)
      if (l .eq. 1) go to 420
c
c     recurrent process for solving the system
c     with the tg - matrix for n = 2, l .
c
      do 410 n = 2, l
c
c        compute multiples of the first and last block columns of
c        the inverse of the principal minor of order m*n .
c
         n1 = n - 1
         n2 = n - 2
         i3 = 1
         do 40 j = 1, m
            do 30 i = 1, m
               r5(i,j) = a2(i3,n1)
               r6(i,j) = a1(i3,n)
               i3 = i3 + 1
   30       continue
   40    continue
         if (n .eq. 2) go to 100
            do 60 j = 1, m
               do 50 i = 1, m
                  c1(i,j,n1) = r2(i,j)
   50          continue
   60       continue
            do 90 i1 = 1, n2
               i2 = n - i1
               do 80 j = 1, m
                  i3 = 1
                  do 70 i = 1, m
c for in-line zaxpy, activate next 5 lines and deactivate following 3 .
c                    do 65 ii = 1, m
c                       r5(ii,j) = r5(ii,j) + c1(i,j,i2)*a2(i3,i1)
c                       r6(ii,j) = r6(ii,j) + c2(i,j,i1)*a1(i3,i1+1)
c                       i3 = i3 + 1
c  65                continue
                     call zaxpy(m,c1(i,j,i2),a2(i3,i1),1,r5(1,j),1)
                     call zaxpy(m,c2(i,j,i1),a1(i3,i1+1),1,r6(1,j),1)
                     i3 = i3 + m
   70             continue
   80          continue
   90       continue
  100    continue
         do 120 j = 1, m
            do 110 i = 1, m
               r2(i,j) = -r5(i,j)
  110       continue
            call zgesl(r3,m,m,r,r2(1,j),0)
  120    continue
         do 140 j = 1, m
            do 130 i = 1, m
               r3(i,j) = r6(i,j)
               r6(i,j) = -c1(i,j,1)
  130       continue
  140    continue
         do 160 j = 1, m
            do 150 i = 1, m
c for in-line zaxpy, activate next 3 lines and deactivate following 1 .
c              do 145 ii = 1, m
c                 c1(ii,j,1) = c1(ii,j,1) + r2(i,j)*r3(ii,i)
c 145          continue
               call zaxpy(m,r2(i,j),r3(1,i),1,c1(1,j,1),1)
  150       continue
  160    continue
         call zgefa(r6,m,m,r,ii)
         do 180 j = 1, m
            call zgesl(r6,m,m,r,r3(1,j),0)
            do 170 i = 1, m
c for in-line zaxpy, activate next 3 lines and deactivate following 1 .
c              do 165 ii = 1, m
c                 r1(ii,j) = r1(ii,j) + r3(i,j)*r5(ii,i)
c 165          continue
               call zaxpy(m,r3(i,j),r5(1,i),1,r1(1,j),1)
  170       continue
  180    continue
         if (n .eq. 2) go to 320
            do 200 j = 1, m
               do 190 i = 1, m
                  r6(i,j) = c2(i,j,1)
  190          continue
  200       continue
            do 310 i1 = 2, n1
               if (i1 .eq. n1) go to 230
                  do 220 j = 1, m
                     do 210 i = 1, m
                        r5(i,j) = c2(i,j,i1)
  210                continue
  220             continue
  230          continue
               do 260 j = 1, m
                  do 240 i = 1, m
                     c2(i,j,i1) = r6(i,j)
  240             continue
                  do 250 i = 1, m
c for in-line zaxpy, activate next 3 lines and deactivate following 1 .
c                    do 245 ii = 1, m
c                       c2(ii,j,i1) = c2(ii,j,i1) + r3(i,j)*c1(ii,i,i1)
c 245                continue
                     call zaxpy(m,r3(i,j),c1(1,i,i1),1,c2(1,j,i1),1)
  250             continue
  260          continue
               do 280 j = 1, m
                  do 270 i = 1, m
c for in-line zaxpy, activate next 3 lines and deactivate following 1 .
c                    do 265 ii = 1, m
c                       c1(ii,j,i1) = c1(ii,j,i1) + r2(i,j)*r6(ii,i)
c 265                continue
                     call zaxpy(m,r2(i,j),r6(1,i),1,c1(1,j,i1),1)
  270             continue
  280          continue
               do 300 j = 1, m
                  do 290 i = 1, m
                     r6(i,j) = r5(i,j)
  290             continue
  300          continue
  310       continue
  320    continue
         do 340 j = 1, m
            do 330 i = 1, m
               c2(i,j,1) = r3(i,j)
  330       continue
  340    continue
c
c        compute the solution of the system with the
c        principal minor of order m*n .
c
         do 360 j = 1, m
            do 350 i = 1, m
               r3(i,j) = r1(i,j)
  350       continue
            x(j,n) = b(j,n)
  360    continue
         do 380 i1 = 1, n1
            i2 = n - i1
            i3 = 1
            do 370 i = 1, m
c for in-line zaxpy, activate next 4 lines and deactivate following 2 .
c              do 365 ii = 1, m
c                 x(ii,n) = x(ii,n) - x(i,i2)*a2(i3,i1)
c                 i3 = i3 + 1
c 365          continue
               call zaxpy(m,-x(i,i2),a2(i3,i1),1,x(1,n),1)
               i3 = i3 + m
  370       continue
  380    continue
         call zgefa(r3,m,m,r,ii)
         call zgesl(r3,m,m,r,x(1,n),0)
         do 400 i1 = 1, n1
            do 390 i = 1, m
c for in-line zaxpy, activate next 3 lines and deactivate following 1 .
c              do 385 ii = 1, m
c                 x(ii,i1) = x(ii,i1) + x(i,n)*c2(ii,i,i1)
c 385          continue
               call zaxpy(m,x(i,n),c2(1,i,i1),1,x(1,i1),1)
  390       continue
  400    continue
  410 continue
  420 continue
      return
      end