double precision function dasum(n,dx,incx) c c takes the sum of the absolute values. c jack dongarra, linpack, 3/11/78. c double precision dx(1),dtemp integer i,incx,m,mp1,n,nincx c dasum = 0.0d0 dtemp = 0.0d0 if(n.le.0)return if(incx.eq.1)go to 20 c c code for increment not equal to 1 c nincx = n*incx do 10 i = 1,nincx,incx dtemp = dtemp + dabs(dx(i)) 10 continue dasum = dtemp return c c code for increment equal to 1 c c c clean-up loop c 20 m = mod(n,6) if( m .eq. 0 ) go to 40 do 30 i = 1,m dtemp = dtemp + dabs(dx(i)) 30 continue if( n .lt. 6 ) go to 60 40 mp1 = m + 1 do 50 i = mp1,n,6 dtemp = dtemp + dabs(dx(i)) + dabs(dx(i + 1)) + dabs(dx(i + 2)) * + dabs(dx(i + 3)) + dabs(dx(i + 4)) + dabs(dx(i + 5)) 50 continue 60 dasum = dtemp return end subroutine daxpy(n,da,dx,incx,dy,incy) c c constant times a vector plus a vector. c uses unrolled loops for increments equal to one. c jack dongarra, linpack, 3/11/78. c double precision dx(1),dy(1),da integer i,incx,incy,ix,iy,m,mp1,n c if(n.le.0)return if (da .eq. 0.0d0) return if(incx.eq.1.and.incy.eq.1)go to 20 c c code for unequal increments or equal increments c not equal to 1 c ix = 1 iy = 1 if(incx.lt.0)ix = (-n+1)*incx + 1 if(incy.lt.0)iy = (-n+1)*incy + 1 do 10 i = 1,n dy(iy) = dy(iy) + da*dx(ix) ix = ix + incx iy = iy + incy 10 continue return c c code for both increments equal to 1 c c c clean-up loop c 20 m = mod(n,4) if( m .eq. 0 ) go to 40 do 30 i = 1,m dy(i) = dy(i) + da*dx(i) 30 continue if( n .lt. 4 ) return 40 mp1 = m + 1 do 50 i = mp1,n,4 dy(i) = dy(i) + da*dx(i) dy(i + 1) = dy(i + 1) + da*dx(i + 1) dy(i + 2) = dy(i + 2) + da*dx(i + 2) dy(i + 3) = dy(i + 3) + da*dx(i + 3) 50 continue return end subroutine dcopy(n,dx,incx,dy,incy) c c copies a vector, x, to a vector, y. c uses unrolled loops for increments equal to one. c jack dongarra, linpack, 3/11/78. c double precision dx(1),dy(1) integer i,incx,incy,ix,iy,m,mp1,n c if(n.le.0)return if(incx.eq.1.and.incy.eq.1)go to 20 c c code for unequal increments or equal increments c not equal to 1 c ix = 1 iy = 1 if(incx.lt.0)ix = (-n+1)*incx + 1 if(incy.lt.0)iy = (-n+1)*incy + 1 do 10 i = 1,n dy(iy) = dx(ix) ix = ix + incx iy = iy + incy 10 continue return c c code for both increments equal to 1 c c c clean-up loop c 20 m = mod(n,7) if( m .eq. 0 ) go to 40 do 30 i = 1,m dy(i) = dx(i) 30 continue if( n .lt. 7 ) return 40 mp1 = m + 1 do 50 i = mp1,n,7 dy(i) = dx(i) dy(i + 1) = dx(i + 1) dy(i + 2) = dx(i + 2) dy(i + 3) = dx(i + 3) dy(i + 4) = dx(i + 4) dy(i + 5) = dx(i + 5) dy(i + 6) = dx(i + 6) 50 continue return end double precision function ddot(n,dx,incx,dy,incy) c c forms the dot product of two vectors. c uses unrolled loops for increments equal to one. c jack dongarra, linpack, 3/11/78. c double precision dx(1),dy(1),dtemp integer i,incx,incy,ix,iy,m,mp1,n c ddot = 0.0d0 dtemp = 0.0d0 if(n.le.0)return if(incx.eq.1.and.incy.eq.1)go to 20 c c code for unequal increments or equal increments c not equal to 1 c ix = 1 iy = 1 if(incx.lt.0)ix = (-n+1)*incx + 1 if(incy.lt.0)iy = (-n+1)*incy + 1 do 10 i = 1,n dtemp = dtemp + dx(ix)*dy(iy) ix = ix + incx iy = iy + incy 10 continue ddot = dtemp return c c code for both increments equal to 1 c c c clean-up loop c 20 m = mod(n,5) if( m .eq. 0 ) go to 40 do 30 i = 1,m dtemp = dtemp + dx(i)*dy(i) 30 continue if( n .lt. 5 ) go to 60 40 mp1 = m + 1 do 50 i = mp1,n,5 dtemp = dtemp + dx(i)*dy(i) + dx(i + 1)*dy(i + 1) + * dx(i + 2)*dy(i + 2) + dx(i + 3)*dy(i + 3) + dx(i + 4)*dy(i + 4) 50 continue 60 ddot = dtemp return end double precision function dmach(job) integer job c c smach computes machine parameters of floating point c arithmetic for use in testing only. not required by c linpack proper. c c if trouble with automatic computation of these quantities, c they can be set by direct assignment statements. c assume the computer has c c b = base of arithmetic c t = number of base b digits c l = smallest possible exponent c u = largest possible exponent c c then c c eps = b**(1-t) c tiny = 100.0*b**(-l+t) c huge = 0.01*b**(u-t) c c dmach same as smach except t, l, u apply to c double precision. c c cmach same as smach except if complex division c is done by c c 1/(x+i*y) = (x-i*y)/(x**2+y**2) c c then c c tiny = sqrt(tiny) c huge = sqrt(huge) c c c job is 1, 2 or 3 for epsilon, tiny and huge, respectively. c double precision eps,tiny,huge,s c eps = 1.0d0 10 eps = eps/2.0d0 s = 1.0d0 + eps if (s .gt. 1.0d0) go to 10 eps = 2.0d0*eps c s = 1.0d0 20 tiny = s s = s/16.0d0 if (s*1.0 .ne. 0.0d0) go to 20 tiny = (tiny/eps)*100.0 huge = 1.0d0/tiny c if (job .eq. 1) dmach = eps if (job .eq. 2) dmach = tiny if (job .eq. 3) dmach = huge return end double precision function dnrm2 ( n, dx, incx) integer next double precision dx(1), cutlo, cuthi, hitest, sum, xmax,zero,one data zero, one /0.0d0, 1.0d0/ c c euclidean norm of the n-vector stored in dx() with storage c increment incx . c if n .le. 0 return with result = 0. c if n .ge. 1 then incx must be .ge. 1 c c c.l.lawson, 1978 jan 08 c c four phase method using two built-in constants that are c hopefully applicable to all machines. c cutlo = maximum of dsqrt(u/eps) over all known machines. c cuthi = minimum of dsqrt(v) over all known machines. c where c eps = smallest no. such that eps + 1. .gt. 1. c u = smallest positive no. (underflow limit) c v = largest no. (overflow limit) c c brief outline of algorithm.. c c phase 1 scans zero components. c move to phase 2 when a component is nonzero and .le. cutlo c move to phase 3 when a component is .gt. cutlo c move to phase 4 when a component is .ge. cuthi/m c where m = n for x() real and m = 2*n for complex. c c values for cutlo and cuthi.. c from the environmental parameters listed in the imsl converter c document the limiting values are as follows.. c cutlo, s.p. u/eps = 2**(-102) for honeywell. close seconds are c univac and dec at 2**(-103) c thus cutlo = 2**(-51) = 4.44089e-16 c cuthi, s.p. v = 2**127 for univac, honeywell, and dec. c thus cuthi = 2**(63.5) = 1.30438e19 c cutlo, d.p. u/eps = 2**(-67) for honeywell and dec. c thus cutlo = 2**(-33.5) = 8.23181d-11 c cuthi, d.p. same as s.p. cuthi = 1.30438d19 c data cutlo, cuthi / 8.232d-11, 1.304d19 / c data cutlo, cuthi / 4.441e-16, 1.304e19 / data cutlo, cuthi / 8.232d-11, 1.304d19 / c if(n .gt. 0) go to 10 dnrm2 = zero go to 300 c 10 assign 30 to next sum = zero nn = n * incx c begin main loop i = 1 20 go to next,(30, 50, 70, 110) 30 if( dabs(dx(i)) .gt. cutlo) go to 85 assign 50 to next xmax = zero c c phase 1. sum is zero c 50 if( dx(i) .eq. zero) go to 200 if( dabs(dx(i)) .gt. cutlo) go to 85 c c prepare for phase 2. assign 70 to next go to 105 c c prepare for phase 4. c 100 i = j assign 110 to next sum = (sum / dx(i)) / dx(i) 105 xmax = dabs(dx(i)) go to 115 c c phase 2. sum is small. c scale to avoid destructive underflow. c 70 if( dabs(dx(i)) .gt. cutlo ) go to 75 c c common code for phases 2 and 4. c in phase 4 sum is large. scale to avoid overflow. c 110 if( dabs(dx(i)) .le. xmax ) go to 115 sum = one + sum * (xmax / dx(i))**2 xmax = dabs(dx(i)) go to 200 c 115 sum = sum + (dx(i)/xmax)**2 go to 200 c c c prepare for phase 3. c 75 sum = (sum * xmax) * xmax c c c for real or d.p. set hitest = cuthi/n c for complex set hitest = cuthi/(2*n) c 85 hitest = cuthi/float( n ) c c phase 3. sum is mid-range. no scaling. c do 95 j =i,nn,incx if(dabs(dx(j)) .ge. hitest) go to 100 95 sum = sum + dx(j)**2 dnrm2 = dsqrt( sum ) go to 300 c 200 continue i = i + incx if ( i .le. nn ) go to 20 c c end of main loop. c c compute square root and adjust for scaling. c dnrm2 = xmax * dsqrt(sum) 300 continue return end subroutine drot (n,dx,incx,dy,incy,c,s) c c applies a plane rotation. c jack dongarra, linpack, 3/11/78. c double precision dx(1),dy(1),dtemp,c,s integer i,incx,incy,ix,iy,n c if(n.le.0)return if(incx.eq.1.and.incy.eq.1)go to 20 c c code for unequal increments or equal increments not equal c to 1 c ix = 1 iy = 1 if(incx.lt.0)ix = (-n+1)*incx + 1 if(incy.lt.0)iy = (-n+1)*incy + 1 do 10 i = 1,n dtemp = c*dx(ix) + s*dy(iy) dy(iy) = c*dy(iy) - s*dx(ix) dx(ix) = dtemp ix = ix + incx iy = iy + incy 10 continue return c c code for both increments equal to 1 c 20 do 30 i = 1,n dtemp = c*dx(i) + s*dy(i) dy(i) = c*dy(i) - s*dx(i) dx(i) = dtemp 30 continue return end subroutine drotg(da,db,c,s) c c construct givens plane rotation. c jack dongarra, linpack, 3/11/78. c double precision da,db,c,s,roe,scale,r,z c roe = db if( dabs(da) .gt. dabs(db) ) roe = da scale = dabs(da) + dabs(db) if( scale .ne. 0.0d0 ) go to 10 c = 1.0d0 s = 0.0d0 r = 0.0d0 go to 20 10 r = scale*dsqrt((da/scale)**2 + (db/scale)**2) r = dsign(1.0d0,roe)*r c = da/r s = db/r 20 z = 1.0d0 if( dabs(da) .gt. dabs(db) ) z = s if( dabs(db) .ge. dabs(da) .and. c .ne. 0.0d0 ) z = 1.0d0/c da = r db = z return end subroutine dscal(n,da,dx,incx) c c scales a vector by a constant. c uses unrolled loops for increment equal to one. c jack dongarra, linpack, 3/11/78. c double precision da,dx(1) integer i,incx,m,mp1,n,nincx c if(n.le.0)return if(incx.eq.1)go to 20 c c code for increment not equal to 1 c nincx = n*incx do 10 i = 1,nincx,incx dx(i) = da*dx(i) 10 continue return c c code for increment equal to 1 c c c clean-up loop c 20 m = mod(n,5) if( m .eq. 0 ) go to 40 do 30 i = 1,m dx(i) = da*dx(i) 30 continue if( n .lt. 5 ) return 40 mp1 = m + 1 do 50 i = mp1,n,5 dx(i) = da*dx(i) dx(i + 1) = da*dx(i + 1) dx(i + 2) = da*dx(i + 2) dx(i + 3) = da*dx(i + 3) dx(i + 4) = da*dx(i + 4) 50 continue return end subroutine dswap (n,dx,incx,dy,incy) c c interchanges two vectors. c uses unrolled loops for increments equal one. c jack dongarra, linpack, 3/11/78. c double precision dx(1),dy(1),dtemp integer i,incx,incy,ix,iy,m,mp1,n c if(n.le.0)return if(incx.eq.1.and.incy.eq.1)go to 20 c c code for unequal increments or equal increments not equal c to 1 c ix = 1 iy = 1 if(incx.lt.0)ix = (-n+1)*incx + 1 if(incy.lt.0)iy = (-n+1)*incy + 1 do 10 i = 1,n dtemp = dx(ix) dx(ix) = dy(iy) dy(iy) = dtemp ix = ix + incx iy = iy + incy 10 continue return c c code for both increments equal to 1 c c c clean-up loop c 20 m = mod(n,3) if( m .eq. 0 ) go to 40 do 30 i = 1,m dtemp = dx(i) dx(i) = dy(i) dy(i) = dtemp 30 continue if( n .lt. 3 ) return 40 mp1 = m + 1 do 50 i = mp1,n,3 dtemp = dx(i) dx(i) = dy(i) dy(i) = dtemp dtemp = dx(i + 1) dx(i + 1) = dy(i + 1) dy(i + 1) = dtemp dtemp = dx(i + 2) dx(i + 2) = dy(i + 2) dy(i + 2) = dtemp 50 continue return end integer function idamax(n,dx,incx) c c finds the index of element having max. absolute value. c jack dongarra, linpack, 3/11/78. c double precision dx(1),dmax integer i,incx,ix,n c idamax = 0 if( n .lt. 1 ) return idamax = 1 if(n.eq.1)return if(incx.eq.1)go to 20 c c code for increment not equal to 1 c ix = 1 dmax = dabs(dx(1)) ix = ix + incx do 10 i = 2,n if(dabs(dx(ix)).le.dmax) go to 5 idamax = i dmax = dabs(dx(ix)) 5 ix = ix + incx 10 continue return c c code for increment equal to 1 c 20 dmax = dabs(dx(1)) do 30 i = 2,n if(dabs(dx(i)).le.dmax) go to 30 idamax = i dmax = dabs(dx(i)) 30 continue return end