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diff --git a/math/llsq/original_f/ldp.f b/math/llsq/original_f/ldp.f
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+      subroutine ldp (g,mdg,m,n,h,x,xnorm,w,index,mode)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1974 mar 1
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c
+c	     **********  least distance programming  **********
+c
+      integer index(m)
+      dimension g(mdg,n), h(m), x(n), w(1)
+      zero=0.
+      one=1.
+      if (n.le.0) go to 120
+	  do 10 j=1,n
+   10	  x(j)=zero
+      xnorm=zero
+      if (m.le.0) go to 110
+c
+c     the declared dimension of w() must be at least (n+1)*(m+2)+2*m.
+c
+c      first (n+1)*m locs of w()   =  matrix e for problem nnls.
+c	next	 n+1 locs of w()   =  vector f for problem nnls.
+c	next	 n+1 locs of w()   =  vector z for problem nnls.
+c	next	   m locs of w()   =  vector y for problem nnls.
+c	next	   m locs of w()   =  vector wdual for problem nnls.
+c     copy g**t into first n rows and m columns of e.
+c     copy h**t into row n+1 of e.
+c
+      iw=0
+	  do 30 j=1,m
+	      do 20 i=1,n
+	      iw=iw+1
+   20	      w(iw)=g(j,i)
+	  iw=iw+1
+   30	  w(iw)=h(j)
+      if=iw+1
+c				 store n zeros followed by a one into f.
+	  do 40 i=1,n
+	  iw=iw+1
+   40	  w(iw)=zero
+      w(iw+1)=one
+c
+      np1=n+1
+      iz=iw+2
+      iy=iz+np1
+      iwdual=iy+m
+c
+      call nnls (w,np1,np1,m,w(if),w(iy),rnorm,w(iwdual),w(iz),index,
+     *		 mode)
+c		       use the following return if unsuccessful in nnls.
+      if (mode.ne.1) return
+      if (rnorm) 130,130,50
+   50 fac=one
+      iw=iy-1
+	  do 60 i=1,m
+	  iw=iw+1
+c				here we are using the solution vector y.
+   60	  fac=fac-h(i)*w(iw)
+c
+      if (diff(one+fac,one)) 130,130,70
+   70 fac=one/fac
+	  do 90 j=1,n
+	  iw=iy-1
+	      do 80 i=1,m
+	      iw=iw+1
+c				here we are using the solution vector y.
+   80	      x(j)=x(j)+g(i,j)*w(iw)
+   90	  x(j)=x(j)*fac
+	  do 100 j=1,n
+  100	  xnorm=xnorm+x(j)**2
+      xnorm=sqrt(xnorm)
+c			      successful return.
+  110 mode=1
+      return
+c			      error return.	  n .le. 0.
+  120 mode=2
+      return
+c			      returning with constraints not compatible.
+  130 mode=4
+      return
+      end