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c
c L-BFGS-B is released under the “New BSD License” (aka “Modified BSD License”
c or “3-clause license”)
c Please read attached file License.txt
c
subroutine dpofa(a,lda,n,info)
integer lda,n,info
double precision a(lda,*)
c
c dpofa factors a double precision symmetric positive definite
c matrix.
c
c dpofa is usually called by dpoco, but it can be called
c directly with a saving in time if rcond is not needed.
c (time for dpoco) = (1 + 18/n)*(time for dpofa) .
c
c on entry
c
c a double precision(lda, n)
c the symmetric matrix to be factored. only the
c diagonal and upper triangle are used.
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 on return
c
c a an upper triangular matrix r so that a = trans(r)*r
c where trans(r) is the transpose.
c the strict lower triangle is unaltered.
c if info .ne. 0 , the factorization is not complete.
c
c info integer
c = 0 for normal return.
c = k signals an error condition. the leading minor
c of order k is not positive definite.
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 ddot
c fortran sqrt
c
c internal variables
c
double precision ddot,t
double precision s
integer j,jm1,k
c begin block with ...exits to 40
c
c
do 30 j = 1, n
info = j
s = 0.0d0
jm1 = j - 1
if (jm1 .lt. 1) go to 20
do 10 k = 1, jm1
t = a(k,j) - ddot(k-1,a(1,k),1,a(1,j),1)
t = t/a(k,k)
a(k,j) = t
s = s + t*t
10 continue
20 continue
s = a(j,j) - s
c ......exit
if (s .le. 0.0d0) go to 40
a(j,j) = sqrt(s)
30 continue
info = 0
40 continue
return
end
c====================== The end of dpofa ===============================
subroutine dtrsl(t,ldt,n,b,job,info)
integer ldt,n,job,info
double precision t(ldt,*),b(*)
c
c
c dtrsl solves systems of the form
c
c t * x = b
c or
c trans(t) * x = b
c
c where t is a triangular matrix of order n. here trans(t)
c denotes the transpose of the matrix t.
c
c on entry
c
c t double precision(ldt,n)
c t contains the matrix of the system. the zero
c elements of the matrix are not referenced, and
c the corresponding elements of the array can be
c used to store other information.
c
c ldt integer
c ldt is the leading dimension of the array t.
c
c n integer
c n is the order of the system.
c
c b double precision(n).
c b contains the right hand side of the system.
c
c job integer
c job specifies what kind of system is to be solved.
c if job is
c
c 00 solve t*x=b, t lower triangular,
c 01 solve t*x=b, t upper triangular,
c 10 solve trans(t)*x=b, t lower triangular,
c 11 solve trans(t)*x=b, t upper triangular.
c
c on return
c
c b b contains the solution, if info .eq. 0.
c otherwise b is unaltered.
c
c info integer
c info contains zero if the system is nonsingular.
c otherwise info contains the index of
c the first zero diagonal element of t.
c
c linpack. this version dated 08/14/78 .
c g. w. stewart, university of maryland, argonne national lab.
c
c subroutines and functions
c
c blas daxpy,ddot
c fortran mod
c
c internal variables
c
double precision ddot,temp
integer case,j,jj
c
c begin block permitting ...exits to 150
c
c check for zero diagonal elements.
c
do 10 info = 1, n
c ......exit
if (t(info,info) .eq. 0.0d0) go to 150
10 continue
info = 0
c
c determine the task and go to it.
c
case = 1
if (mod(job,10) .ne. 0) case = 2
if (mod(job,100)/10 .ne. 0) case = case + 2
go to (20,50,80,110), case
c
c solve t*x=b for t lower triangular
c
20 continue
b(1) = b(1)/t(1,1)
if (n .lt. 2) go to 40
do 30 j = 2, n
temp = -b(j-1)
call daxpy(n-j+1,temp,t(j,j-1),1,b(j),1)
b(j) = b(j)/t(j,j)
30 continue
40 continue
go to 140
c
c solve t*x=b for t upper triangular.
c
50 continue
b(n) = b(n)/t(n,n)
if (n .lt. 2) go to 70
do 60 jj = 2, n
j = n - jj + 1
temp = -b(j+1)
call daxpy(j,temp,t(1,j+1),1,b(1),1)
b(j) = b(j)/t(j,j)
60 continue
70 continue
go to 140
c
c solve trans(t)*x=b for t lower triangular.
c
80 continue
b(n) = b(n)/t(n,n)
if (n .lt. 2) go to 100
do 90 jj = 2, n
j = n - jj + 1
b(j) = b(j) - ddot(jj-1,t(j+1,j),1,b(j+1),1)
b(j) = b(j)/t(j,j)
90 continue
100 continue
go to 140
c
c solve trans(t)*x=b for t upper triangular.
c
110 continue
b(1) = b(1)/t(1,1)
if (n .lt. 2) go to 130
do 120 j = 2, n
b(j) = b(j) - ddot(j-1,t(1,j),1,b(1),1)
b(j) = b(j)/t(j,j)
120 continue
130 continue
140 continue
150 continue
return
end
c====================== The end of dtrsl ===============================
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