onenormest.m File Reference

Functions
	if (ismatrix(varargin{1})) n
if	error ("onenormest: matrix must be square")
	if (size(varargin) > 1) t
else	if (size(varargin, 2)< 3) print_usage()
	if (size(varargin) > 3) t
	if (issing) myeps
	if (est > est_old||iter==2) w
	if (iter > itmax)
	if (all(partest)) break
endif	if (any(partest)) numpar
	S (:, partest)
	if (iter >=2 &&mhi==ind_best) break
	if (t > 1) firstind
	if (all(been_there(firstind))) break
endfor	been_there (ind(1:t))
	v (ind_best)
	!norm (inv(A), 1)%!test%!N
	!assert (nm1, N,-2 *eps)
	!assert (nminf, N,-2 *eps)
	!assert (norm(w1, 1), nm1 *norm(v1, 1),-2 *eps)%!assert(norm(winf
nminf *	norm (vinf, 1)
id	N ()
	!assert (nm1, norm(A, 1),-2 *eps)
	!assert (nminf, norm(A, inf),-2 *eps)
	!assert (nm1, norm(A, 1),-.1)
	!assert (nminf, norm(A, inf),-.1)
Variables
	function [est, v, w, iter]
endif	default_t = 5
	itmax = 10
if	n = size (varargin{1}, 2)
endif	apply = @(x) varargin{1} * x
	apply_t = @(x) varargin{1}' * x
else	t = min (n, default_t)
endif	issing = isa (varargin {1}, "single")
endif	X = rand (n, t)
	been_there = zeros (n, 1)
	est_old = 0
	S = zeros (n, t)
else	myeps = eps
endif for	iter
	break
	S_old = S
	partest = any (abs (S_old' * S - n) < 4*eps*n)
	replacements = 2*(rand (n,numpar) < 0.5) - 1
endif	Z = feval (apply_t, S)
	h = max (abs (Z),2)
	endif [h, ind] = sort (h, 'descend')
endif	ind = ind (!been_there (ind))
for	zz
endfor	v = zeros (n, 1)
endfunction!demo	!N = 100
	!A = randn(N) + eye(N)
	!nm1inv = lu(A) onenormest(@(x) U\(L\(P*x)), @(x) P'*(L'\(U'\x))
	N

---

Function Documentation

!assert	(	nminf	,
		norm(A, inf)	,
		-.	1
	)

!assert	(	nm1	,
		norm(A, 1)	,
		-.	1
	)

!assert	(	nminf	,
		norm(A, inf)	,
		-2 *	eps
	)

!assert	(	nm1	,
		norm(A, 1)	,
		-2 *	eps
	)

!assert	(	norm(w1, 1)	,
		nm1 *	normv1, 1,
		-2 *	eps
	)

!assert	(	nminf	,
		N	,
		-2 *	eps
	)

!assert	(	nm1	,
		N	,
		-2 *	eps
	)

!norm	(	inv(A)	,
		1
	)

Type Constraints

endfor been_there

(

ind(1:t)

)

if error

(

"onenormest: matrix must be square"

)

Type Constraints

if

(

all(been_there(firstind))

)

if	(	t	,
		1
	)

if

(

iter >=2 &&

mhi = =ind_best

)

endif if

(

any(partest)

)

if

(

all(partest)

)

if	(	iter	,
		itmax
	)

if	(	est	,
		est_old||	iter = =2
	)

if

(

issing

)

if	(	size(varargin)	,
		3
	)

else if

(

)

if	(	size(varargin)	,
		1
	)

if

(

ismatrix(varargin{1})

)

id N

(

)

[virtual]

nminf * norm	(	vinf	,
		1
	)

S	(	:	,
		partest
	)

v

(

ind_best

)

---

Variable Documentation

!A = randn(N) + eye(N)

endfunction !demo !N = 100

!nm1inv = lu(A) onenormest(@(x) U\(L\(P*x)), @(x) P'*(L'\(U'\x))

apply = @(x) varargin{1} * x

apply_t = @(x) varargin{1}' * x

been_there = zeros (n, 1)

break

endif default_t = 5

endif[h, ind] = sort (h, 'descend')

endif est_old = 0

function[est, v, w, iter]

Initial value:

 onenormest (varargin)

  if (size (varargin, 2) < 1 || size (varargin, 2) > 4)
    print_usage ()

h = max (abs (Z),2)

endif ind = ind (!been_there (ind))

endif issing = isa (varargin {1}, "single")

endif for iter

Initial value:

 1 : itmax + 1
    Y = feval (apply, X)

itmax = 10

else myeps = eps

N

endif n = size (varargin{1}, 2)

endif partest = any (abs (S_old' * S - n) < 4*eps*n)

replacements = 2*(rand (n,numpar) < 0.5) - 1

endif S = zeros (n, t)

S_old = S

else t = min (n, default_t)

endfor v = zeros (n, 1)

endif endif X = rand (n, t)

endif Z = feval (apply_t, S)

endif zz

Initial value:

 1 : t
      X(ind(zz),zz) = 1