
====================== INDEX FOR NAPACK =====================

NAPACK contains subroutines to process matrices and equations.
Each subroutine name consists of a stem which describes the
action of the subroutine preceded by a prefix.  If there is no
prefix in front of the stem, then the subroutine usually applies
to a general real matrix.  The prefixes, listed below, describe
the data and the matrix type.

B  -  Band matrix
C  -  Complex matrix
E  -  Upper Hessenberg matrix
H  -  Symmetric band matrix
I  -  Symmetric matrix (symmetric pivoting)
K  -  General matrix (complete pivoting)
O  -  Circulant matrix
P  -  Tridiagonal matrix (partial pivoting)
S  -  Symmetric matrix
T  -  Tridiagonal matrix

The stems which allow one or more prefixes are the following:

Stem     Prefixes            Action
----     --------            ------

BAL      C                   Balance the matrix
CON      B,E,H,I,K,P,S,T     Estimate condition number
DET      B,E,H,I,K,P,S,T     Compute the determinant
DIAG     C,E,H,S,T           Compute the diagonalization
FACT     B,E,H,I,K,P,S,T     Compute the LU factorization
HESS     C,H,S               Reduce to upper Hessenberg form
                             (insert A prefix to also balance)
MULT     B,E,H,O,S,T         Multiply matrix by vector
PACK     C,R                 Rearrange elements of an array so that elements
                             of a square matrix are stored sequentially
                             (use R prefix if matrix is rectangular)
POWER    C,M                 Compute dominant eigenpairs by the power method
                             (use M prefix to compute several eigenpairs)
SIM      C,H,S               Compute the similarity transform used in the
                             reduction to either Hessenberg or tridiagonal form
SOLVE    B,E,H,I,K,O,P,S,T   Solve a factored system of equations
TRANS    B,E,K,P,T           Solve the transpose of a factored system
VALS     C,E,H,O,S,T         Compute eigenvalues
VECT     C,E,H,S,T           Compute eigenvector corresponding to given
                             eigenvalue
VERT     B,C,E,H,I,K,O,P,S,T Invert a matrix

The subroutines in NAPACK that do not have prefixes are

Subroutine     Action
----------     ------

ADDCHG.........Add one vector to another and evaluate 1-norm
               of the increment and 1-norm of the sum
BASIS..........Compute an orthonormal basis for a collection of vectors
BIDAG..........Reduce a matrix to bidiagonal form
BIDAG2.........Reduce a matrix to bidiagonal form and evaluate
               all or part of the orthogonal matrices used in the
               reduction process
CG.............Compute an unconstrained minimum for a multivariate function
               using the (preconditioned) conjugate gradient method
CZERO..........Compute zeros of a (complex) polynomial
FFC............Conjugate fast Fourier transform
FFT............Fast Fourier transform
LANCZ..........Perform an iteration of Lanczos method to reduce
               a matrix to tridiagonal form
NEWTON.........Apply one step of Newton's method to the characteristic
               polynomial for a tridiagonal matrix
NORM1..........Estimate 1-norm of a matrix
NULL...........Compute an orthonormal basis for the space perpendicular to
               a given collection of vectors
OVER...........Compute the least squares solution to an overdetermined
               linear system
PRECG..........Solve a linear system using (preconditioned) conjugate gradients
PSEUDO.........Compute regularized pseudoinverse
QR.............QR factor a matrix
QUASI..........Use a quasi-Newton method to solve a nonlinear system
ROOT...........Solve a scalar equation
RSOLVE.........Compute the regularized solution to a linear system
SDIAG2.........Same as SDIAG except the input matrix is not stored in
               compressed format
SING...........Compute the singular value decomposition of a general matrix
SINGB..........Compute the singular value decomposition of a bidiagonal matrix
SLICE..........Compute the eigenvalues contained on a given interval for a
               tridiagonal matrix whose cross-diagonal products are nonnegative
STOPIT.........Test for convergence
TVAL...........Compute the k-th smallest or the k-th largest eigenvalue of a
               tridiagonal matrix whose cross-diagonal products are nonnegative
UNDER..........Compute the least squares (minimum norm) solution to an
               underdetermined linear system
UPDATE.........Equate one vector to another and evaluate 1-norm
               of the difference and 1-norm of the new vector
WHATIS.........Print iteration number, iteration difference,
               and stopping criterion
