Index of Methods

 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.

 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.

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

 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.

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

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

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

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

 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.

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

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

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

 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.

 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.

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

 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.

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

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

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

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

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

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

 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,...

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

 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.

 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.

 -   Difference of two operators.

 \  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.

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

 /  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.

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

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

 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.

 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.

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

 +   Sum of two operators.

 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.

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

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

 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.

 SUBSASGN   Subscribed assignment.

 SUBSREF   Subscripted reference.

 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.

 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.

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

 -   Unary minus.
 
    -A  negates the operator A.

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

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