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check for diagonal matrices in find-diag-in-e-basis #857

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Sep 30, 2022
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check for diagonal matrices in find-diag-in-e-basis #857

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68 changes: 38 additions & 30 deletions src/compilers/approx.lisp
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Original file line number Diff line number Diff line change
Expand Up @@ -199,36 +199,44 @@ This function should be completely deterministic (i.e., produce the same value f
(check-type m magicl:matrix)
(let* ((u (magicl:@ +edag-basis+ m +e-basis+))
(gammag (magicl:@ u (magicl:transpose u))))
(loop :for attempt :from 1 :to num-attempts :do
(let* ((coeff (diagonalizer-number-generator attempt))
(matrix (magicl:map (lambda (z)
(+ (* coeff (realpart z))
(* (- 1 coeff) (imagpart z))))
gammag))
(evecs (ensure-positive-determinant
(orthonormalize-matrix!
(nth-value 1 (magicl:eig matrix)))))
(evals (magicl:diag
(magicl:@ (magicl:transpose evecs)
gammag
evecs)))
(v (magicl:@ evecs
(from-diag evals)
(magicl:transpose evecs))))
(when (and (double= 1.0d0 (magicl:det evecs))
(magicl:every #'double= gammag v))
(when *check-math*
(assert (magicl:every #'double~
(eye 4 :type 'double-float)
(magicl:@ (magicl:transpose evecs)
evecs))
(evecs)
"The calculated eigenvectors were not found to be orthonormal. ~
EE^T =~%~A"
(magicl:@ (magicl:transpose evecs)
evecs)))
(return-from find-diagonalizer-in-e-basis evecs)))))
(error 'diagonalizer-not-found :matrix m :attempts num-attempts))
(cond
;; XXX: It seems that LAPACK distributions on ARM do not work or
;; are not stable when calculating eigenvectors of a diagonal
;; matrix. We have not closely investigated why, but checking
;; for diagonal matrices as a special case seems to work.
((diagonal-matrix-p gammag)
(magicl:eye (magicl:shape m) :type (magicl:element-type m)))
(t
(loop :for attempt :from 1 :to num-attempts :do
(let* ((coeff (diagonalizer-number-generator attempt))
(matrix (magicl:map (lambda (z)
(+ (* coeff (realpart z))
(* (- 1 coeff) (imagpart z))))
gammag))
(evecs (ensure-positive-determinant
(orthonormalize-matrix!
(nth-value 1 (magicl:eig matrix)))))
(evals (magicl:diag
(magicl:@ (magicl:transpose evecs)
gammag
evecs)))
(v (magicl:@ evecs
(from-diag evals)
(magicl:transpose evecs))))
(when (and (double= 1.0d0 (magicl:det evecs))
(magicl:every #'double= gammag v))
(when *check-math*
(assert (magicl:every #'double~
(eye 4 :type 'double-float)
(magicl:@ (magicl:transpose evecs)
evecs))
(evecs)
"The calculated eigenvectors were not found to be orthonormal. ~
EE^T =~%~A"
(magicl:@ (magicl:transpose evecs)
evecs)))
(return-from find-diagonalizer-in-e-basis evecs))))
(error 'diagonalizer-not-found :matrix m :attempts num-attempts)))))

(defun diagonalizer-in-e-basis (m)
"For M in SU(4), compute an SO(4) column matrix of eigenvectors of E^* M E (E^* M E)^T.
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7 changes: 7 additions & 0 deletions src/matrix-operations.lisp
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Original file line number Diff line number Diff line change
Expand Up @@ -8,6 +8,13 @@

(in-package #:cl-quil)

(defun diagonal-matrix-p (m)
"Is M diagonal?"
(dotimes (row (magicl:nrows m) t)
(dotimes (col (magicl:ncols m))
(when (and (/= row col) (not (double~ 0 (magicl:tref m row col))))
(return-from diagonal-matrix-p nil)))))

(defun matrix-first-column-equality (x y)
(check-type x magicl:matrix)
(check-type y magicl:matrix)
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