BICG BiConjugate Gradients Method.
X = bicg(A,B) attempts to solve the linear system A*X=B via the
BICG method.
This routine is simply a wrapper to Matlab's own BICGS routine,
and the argument list variations described in Matlab's BICG
documentation are also allowed here. The usage is identical to
Matlab's default version, except that the first argument must be a
Spot operator.

M-File Help: opSpot/bicgstab

opSpot/bicgstab

BICGSTAB BiConjugate Gradients Stabilized Method.
X = bicgstab(A,B) attempts to solve the linear system A*X=B via
the BICGSTAB method.
This routine is simply a wrapper to Matlab's own BICGSTAB routine,
and the argument list variations described in Matlab's BICGSTAB
documentation are also allowed here. The usage is identical to
Matlab's default version, except that the first argument must be a
Spot operator.

M-File Help: opSpot/blkdiag

opSpot/blkdiag

BLKDIAG Block-diagonal concatenation of operator input arguments.
B = blkdiag(OP1,OP2,...) produces the block-diagonal operator
[ OP1 ]
B = [ OP2 ]
[ ... ]
[ OPN ]

M-File Help: opSpot/cgs

opSpot/cgs

CGS Conjugate Gradients Squared Method.
X = cgs(A,B) attempts to solve the square linear system A*X=B via
the CGS method.
This routine is simply a wrapper to Matlab's own CGS routine,
and the argument list variations described in Matlab's CGS
documentation are also allowed here. The usage is identical to
Matlab's default version, except that the first argument must be a
Spot operator.

M-File Help: opSpot/char

opSpot/char

CHAR Create a string representation of a Spot operator.
char(A) converts the Spot operator into a string representation.

M-File Help: opSpot/conj

opSpot/conj

CONJ Elementwise conjugate of operator.
conj(OP) is the elementwise conjugate of the Spot operator OP.

M-File Help: opSpot/ctranspose

opSpot/ctranspose

' Complex conjugate tranpose.
A' is the complex conjugate transpose of A.
ctranspose(A) is called for the syntax A' when A is an operator.

M-File Help: opSpot/diag

opSpot/diag

DIAG Diagonal operator and diagonals of an operator.
diag(OP) is the main diagonal of the Spot operator OP.

M-File Help: opSpot/disp

opSpot/disp

DISP Display a Spot operator.
disp(A) displays a Spot operator, excluding its name.
disp(A,NAME) displays a Spot operator along with its name.

M-File Help: opSpot/display

opSpot/display

DISPLAY Display an operator.
display(A) displays an operator.

M-File Help: opSpot/double

opSpot/double

double Converts a Spot operator to matrix.
double(A) converts a Spot operator to an explicit matrix.

M-File Help: opSpot/drandn

opSpot/drandn

DRANDN Normally distributed pseudorandom vector in the operator domain.
drandn(A) returns a pseudorandom vector in the domain of A.

M-File Help: opSpot/eigs

opSpot/eigs

EIGS Find a few eigenvalues and eigenvectors of an operator using ARPACK.
eigs(A) returns six of the largest eigenvalues of an operator.
This routine is simply a wrapper to Matlab's own EIGS routine, and
most of the argument-list variations described in Matlab's EIGS
documentation are also allowed here. The usage is identical to
Matlab's default version, except that the first argument must be a
Spot operator, and only the largest eigenvalues are considered.
Supported usage includes
D = EIGS(A)
[V,D] = EIGS(A)
[V,D,FLAG] = EIGS(A)
[V,D,FLAG] = EIGS(A,K)
[V,D,FLAG] = EIGS(A,K,SIGMA)
[V,D,FLAG] = EIGS(A,K,SIGMA,OPTS)
Again, see Matlab's built-in EIGS for details on these calls.

M-File Help: opSpot/end

opSpot/end

END returns maximum index
end(OP,K,IDXCOUNT) returns the maximum index of operator
OP in dimension K. When IDXCOUNT equals one argument K is
ignored and the product of number of rows and columns of OP is
returned.

M-File Help: opSpot/full

opSpot/full

FULL Convert a Spot operator into a (dense) matrix.
X = full(A) converts the Spot operator A into a dense matrix X.

M-File Help: opSpot/gmres

opSpot/gmres

GMRES Generalized Minimum Residual Method.
X = gmres(A,B) attempts to solve the square linear system A*X=B via
the GMRES method.
This routine is simply a wrapper to Matlab's own GMRES routine,
and the argument list variations described in Matlab's GMRES
documentation are also allowed here. The usage is identical to
Matlab's default version, except that the first argument must be a
Spot operator.

M-File Help: opSpot/horzcat

opSpot/horzcat

HORZCAT Horizontal concatenation.
[A B] is the horizonal concatenation of operators A and B.

M-File Help: opSpot/imag

opSpot/imag

IMAG Complex imaginary part.
imag(A) returns a new operator comprised of imaginary part of A.

M-File Help: opSpot/inv

opSpot/inv

INV Inverse of a linear operator.
inv(A) returns the operator inverse of A. This routine is
a simple front-end to opInverse.

M-File Help: opSpot/isempty

opSpot/isempty

ISEMPTY True for empty operator.
isempty(A) returns true if A is an empty operator.

M-File Help: opSpot/isreal

opSpot/isreal

ISREAL True for real operator.
isreal(A) returns true if A is a real operator.

M-File Help: opSpot/isscalar

opSpot/isscalar

ISSCALAR True if operator is a scalar.
isscalar(A) returns true if A is a 1-by-1 operator.

M-File Help: opSpot/kron

opSpot/kron

KRON Kronecker tensor product of operators.
kron(A,B) is the Kroneker tensor product of A and B.
kron(A,B,C,...) is the Kroneker product of A,B,C,...

M-File Help: opSpot/length

opSpot/length

LENGTH Maximum dimension of operator.
length(A) returns the maximum dimension of the operator A.

M-File Help: opSpot/lsqr

opSpot/lsqr

LSQR LSQR Method.
X = lsqr(A,B) attempts to solve the least-squares problem
minimize || A*X - B ||_2
This routine is simply a wrapper to Matlab's own LSQR routine,
and the argument list variations described in Matlab's LSQR
documentation are also allowed here. The usage is identical to
Matlab's default version, except that the first argument must be a
Spot operator.

M-File Help: opSpot/minres

opSpot/minres

MINRES Minimum Residual Method.
X = minres(A,B) attempts to find a minimum-norm residual solution
X to the symmetric linear system A*X=B via the MINRES method.
This routine is simply a wrapper to Matlab's own MINRES routine,
and the argument list variations described in Matlab's MINRES
documentation are also allowed here. The usage is identical to
Matlab's default version, except that the first argument must be a
Spot operator.

M-File Help: opSpot/minus

opSpot/minus

- Difference of two operators.

M-File Help: opSpot/mldivide

opSpot/mldivide

\ Backslash or left matrix divide.
X = A\B is similar to Matlab's backslash operator. If A is a Spot
operator and B is a vector, then in general X is computed as the solution to the
least-squares problem
(*) minimize ||Ax - b||_2.
However, some Spot operators implement their own mldivide routines
that determine exactly how a solution to (*) is obtained. For
example, the orthogonal operators (e.g., opWavlet) obtain X via
A'*b.
If A is a scalar and B is a spot operator, then X = opFoG(1/A,B).
The least-squares problem (*) is solved using LSQR with default
parameters specified by spotparams.

M-File Help: opSpot/mpower

opSpot/mpower

^ Matrix power.
A^y is A to the y power.

M-File Help: opSpot/mrdivide

opSpot/mrdivide

/ Slash or right matrix divide.
X = A/B is similar to Matlab's slash operator. If B is a Spot
operator and A is a matrix then X is computed as the transpose
of the solution to the least-squares problem
(*) minimize ||B'x - A'||_F;
when A is a vector, this is a standard least-squares problem.
If B is a scalar and A is a spot operator, then X = opFoG(1/B,A).
The least-squares problem (*) is solved using LSQR with default
parameters specified by spotparams.

M-File Help: opSpot/mtimes

opSpot/mtimes

* Product of two operators.
A*B returns an operator that is the product of two operators.

M-File Help: opSpot/ndims

opSpot/ndims

NDIMS Number of dimensions.
ndims(OP) always returns 2, i.e., all Spot operators are
representable as matrices.

M-File Help: opSpot/normest

opSpot/normest

NORMEST Estimate the matrix 2-norm.
normest(S) is an estimate of the 2-norm of the matrix S.
normest(S,tol) uses relative error tol instead of 1e-6.
[nrm,cnt] = normest(..) also gives the number of iterations used.
This function is a minor adaptation of Matlab's built-in NORMEST.

M-File Help: opSpot/pcg

opSpot/pcg

PCG Preconditioned Conjugate Gradients Method.
X = pcg(A,B) attempts to solve the symmetric positive-definite
linear system A*X=B via the PCG method.
This routine is simply a wrapper to Matlab's own PCG routine,
and the argument list variations described in Matlab's PCG
documentation are also allowed here. The usage is identical to
Matlab's default version, except that the first argument must be a
Spot operator.

M-File Help: opSpot/pinv

opSpot/pinv

PINV Pseudo-inverse of an operator
pinv(A) returns the operator pseudo-inverse of A.

M-File Help: opSpot/plus

opSpot/plus

+ Sum of two operators.

M-File Help: opSpot/qmr

opSpot/qmr

QMR Quasi-Minimal Residual Method.
X = qmr(A,B) attempts to solve the square linear system A*X=B via
the QMR method.
This routine is simply a wrapper to Matlab's own QMR routine,
and the argument list variations described in Matlab's QMR
documentation are also allowed here. The usage is identical to
Matlab's default version, except that the first argument must be a
Spot operator.

M-File Help: opSpot/real

opSpot/real

REAL Complex real part.
opReal(A) returns an operator comprised of the real part of A.

M-File Help: opSpot/rrandn

opSpot/rrandn

RRANDN Normally distributed pseudorandom vector in the operator range.
rrandn(A) returns a pseudorandom vector in the range of A.

M-File Help: opSpot/size

opSpot/size

size Dimensions of a Spot operator.
D = size(A), for an M-by-N Spot operator A, returns the
two-element row vectors D = [M,N].
[M,N] = size(A) returns M and N as separate arguments.
M = size(A,DIM) retuns the length of the dimension specified by
the scalar DIM. Note that DIM must be 1 or 2.

M-File Help: opSpot/subsasgn

opSpot/subsasgn

SUBSASGN Subscribed assignment.

M-File Help: opSpot/subsref

opSpot/subsref

SUBSREF Subscripted reference.

M-File Help: opSpot/sum

opSpot/sum

SUM Sums rows or columns of a Spot operator.
S = sum(A), for an M-by-N Spot operator A, S is a row vector with the
sum of elements of each column.
S = SUM(A,DIM) sums along the dimension DIM.
Note that DIM must be 1 or 2.

M-File Help: opSpot/symmlq

opSpot/symmlq

SYMMLQ Symetric LQ Method.
X = symmlq(A,B) attempts to solve the system of linear equations A*X=B
for X, where A is symmetric.
This routine is simply a wrapper to Matlab's own MINRES routine,
and the argument list variations described in Matlab's MINRES
documentation are also allowed here. The usage is identical to
Matlab's default version, except that the first argument must be a
Spot operator.

M-File Help: opSpot/transpose

opSpot/transpose

.' Operator tranpose.
A.' is the (non-conjugate) transpose of A.
transpose(A) is called for the syntax A.' when A is an operator.

M-File Help: opSpot/uminus

opSpot/uminus

- Unary minus.
-A negates the operator A.

M-File Help: opSpot/uplus

opSpot/uplus

+ Unary plus.
B = uplus(A), or B = +A, simply returns the operator A.

M-File Help: opSpot/vertcat

opSpot/vertcat

VERTCAT Vertical concatenation.
[A; B] is the vertical concatenation of the operators A and B.