diff --git a/libopt/lib/conjgrad.hoon b/libopt/lib/conjgrad.hoon
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+/-  ls=lagoon
+/+  *lagoon
+|^
+~
+::  conjugate gradient descent method
+::    a  is a 2D system of linear equations
+::    b  is the corresponding solutions
+::    x0 is a starting guess at the unknowns
+::
+++  conjgrad
+  |=  [a=ray:ls b=ray:ls x0=ray:ls]
+  ^-  ray:ls
+  =/  r=ray:ls  (sub b (mmul a x0))
+  =/  p=ray:ls  r
+  =/  rsold=ray:ls  (dot r r)
+  ::
+  =/  i=@ud  0
+  =/  x=ray:ls  x0
+  |-  ^-  ray
+  ?:  =(i (&1.shape.meta.b))  x
+  =/  ap=ray  (mmul a p)
+  =/  alpha=ray  (div rsold (dot p ap))
+  =/  x  (add x (mul (fill meta.p alpha) p))
+  =/  r  (sub r (mul (fill meta.ap alpha) ap))
+  =/  rsnew=ray  (dot r r)
+  ?:  (lth rsnew (scalarize meta.rsnew %rs .1e-5))  x
+  %=  $
+    i      +(i)
+    p      (add r (mul (fill meta.p (div rsnew rsold)) p))
+    rsold  rsnew
+  ==
+--
+