NAPACK

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NAPACK is a collection of Fortran subroutines for doing numerical linear algebra and optimization. It may be used to solve linear systems, to estimate the condition number or the norm of a matrix, to compute determinants, to multiply a matrix by a vector, to invert a matrix, to solve least squares problems, to perform unconstrained minimization, to compute eigenvalues, eigenvectors, the singular value decomposition, or the QR decomposition. The package has special routines for general, band, symmetric, indefinite, tridiagonal, upper Hessenberg, and circulant matrices.


file	addchg.f
for	Add one vector to another and evaluate 1-norm of the increment and 1-norm of the sum

file	basis.f  basis.f plus dependencies
for	Compute an orthonormal basis for a collection of vectors

file	bidag.f
for	Reduce a matrix to bidiagonal form

file	bidag2.f  bidag2.f plus dependencies
for	Reduce a matrix to bidiagonal form and evaluate all or part of the orthogonal matrices used in the reduction process

file	cg.f  cg.f plus dependencies
for	Compute an unconstrained minimum for a multivariate function using the (preconditioned) conjugate gradient method

file	czero.f  czero.f plus dependencies
for	Compute zeros of a (complex) polynomial

file	ffc.f  ffc.f plus dependencies
for	Conjugate fast Fourier transform

file	fft.f  fft.f plus dependencies
for	Fast Fourier transform

file	lancz.f
for	Perform an iteration of Lanczos method to reduce a matrix to tridiagonal form

file	newton.f  newton.f plus dependencies
for	Apply one step of Newton's method to the characteristic polynomial for a tridiagonal matrix

file	norm1.f
for	Estimate 1-norm of a matrix

file	null.f  null.f plus dependencies
for	Compute an orthonormal basis for the space perpendicular to a given collection of vectors

file	over.f  over.f plus dependencies
for	Compute the least squares solution to an overdetermined linear system

file	precg.f  precg.f plus dependencies
for	Solve a linear system using (preconditioned) conjugate gradients

file	pseudo.f
for	Compute regularized pseudoinverse

file	qr.f  qr.f plus dependencies
for	QR factor a matrix

file	quasi.f  quasi.f plus dependencies
for	Use a quasi-Newton method to solve a nonlinear system

file	root.f  root.f plus dependencies
for	Solve a scalar equation

file	rsolve.f
for	Compute the regularized solution to a linear system

file	sdiag2.f  sdiag2.f plus dependencies
for	Same as SDIAG except the input matrix is not stored in compressed format

file	sing.f  sing.f plus dependencies
for	Compute the singular value decomposition of a general matrix

file	singb.f  singb.f plus dependencies
for	Compute the singular value decomposition of a bidiagonal matrix

file	slice.f  slice.f plus dependencies
for	Compute the eigenvalues contained on a given interval for a tridiagonal matrix whose cross-diagonal products are nonnegative

file	stopit.f
for	Test for convergence

file	tval.f  tval.f plus dependencies
for	Compute the k-th smallest or the k-th largest eigenvalue of a tridiagonal matrix whose cross-diagonal products are nonnegative

file	under.f  under.f plus dependencies
for	Compute the least squares (minimum norm) solution to an underdetermined linear system

file	update.f
for	Equate one vector to another and evaluate 1-norm of the difference and 1-norm of the new vector

file	whatis.f  whatis.f plus dependencies
for	Print iteration number, iteration difference, and stopping criterion

#	Most of the other files in napack obey the following naming scheme
#	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,C,E,H,I,K,P,S,T   Estimate condition number
#	DET      B,C,E,H,I,K,P,S,T   Compute the determinant
#	DIAG     C,E,H,S,T           Compute the diagonalization
#	FACT     B,C,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,C,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,C,E,H,I,K,O,P,S,T Solve a factored system of equations
#	TRANS    B,C,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
file	ahess.f  ahess.f plus dependencies

file	bal.f

file	bcon.f  bcon.f plus dependencies

file	bdet.f  bdet.f plus dependencies

file	bfact.f  bfact.f plus dependencies

file	bmult.f

file	bsolve.f  bsolve.f plus dependencies

file	btrans.f  btrans.f plus dependencies

file	bvert.f  bvert.f plus dependencies

file	cahess.f  cahess.f plus dependencies

file	cbal.f  cbal.f plus dependencies

file	ccon.f  ccon.f plus dependencies

file	cdet.f  cdet.f plus dependencies

file	cdiag.f  cdiag.f plus dependencies

file	cediag.f  cediag.f plus dependencies

file	ceig.f  ceig.f plus dependencies

file	cemult.f

file	cevals.f  cevals.f plus dependencies

file	cevect.f  cevect.f plus dependencies

file	cfact.f  cfact.f plus dependencies

file	changes

file	chess.f  chess.f plus dependencies

file	cmult.f

file	con.f  con.f plus dependencies

file	cpack.f  cpack.f plus dependencies

file	cpower.f  cpower.f plus dependencies

file	csim.f  csim.f plus dependencies

file	csolve.f  csolve.f plus dependencies

file	ctrans.f  ctrans.f plus dependencies

file	cvals.f  cvals.f plus dependencies

file	cvect.f  cvect.f plus dependencies

file	cvert.f  cvert.f plus dependencies

file	dag.f  dag.f plus dependencies

file	det.f  det.f plus dependencies

file	diag.f  diag.f plus dependencies

file	dmag.f

file	econ.f  econ.f plus dependencies

file	edet.f  edet.f plus dependencies

file	ediag.f  ediag.f plus dependencies

file	efact.f

file	eig2.f  eig2.f plus dependencies

file	eig3.f

file	emult.f

file	esolve.f  esolve.f plus dependencies

file	etrans.f  etrans.f plus dependencies

file	evals.f  evals.f plus dependencies

file	evect.f

file	evert.f  evert.f plus dependencies

file	fact.f  fact.f plus dependencies

file	fasem.f  fasem.f plus dependencies

file	ffc0.f  ffc0.f plus dependencies

file	fft0.f  fft0.f plus dependencies

file	fix.Sep88

file	hcon.f  hcon.f plus dependencies

file	hdet.f  hdet.f plus dependencies

file	hdiag.f  hdiag.f plus dependencies

file	hess.f  hess.f plus dependencies

file	hfact.f  hfact.f plus dependencies

file	hhess.f  hhess.f plus dependencies

file	hmult.f

file	hsim.f  hsim.f plus dependencies

file	hsolve.f  hsolve.f plus dependencies

file	hsr1.f

file	hsr2.f

file	hsr3.f  hsr3.f plus dependencies

file	hsr4.f  hsr4.f plus dependencies

file	hsr5.f  hsr5.f plus dependencies

file	hvals.f  hvals.f plus dependencies

file	hvect.f

file	hvert.f  hvert.f plus dependencies

file	icon.f  icon.f plus dependencies

file	idet.f  idet.f plus dependencies

file	ifact.f  ifact.f plus dependencies

file	isolve.f  isolve.f plus dependencies

file	ivert.f  ivert.f plus dependencies

file	kcon.f  kcon.f plus dependencies

file	kdet.f  kdet.f plus dependencies

file	kfact.f  kfact.f plus dependencies

file	ksolve.f  ksolve.f plus dependencies

file	ktrans.f  ktrans.f plus dependencies

file	kvert.f  kvert.f plus dependencies

file	mag.f

file	mgrid.f  mgrid.f plus dependencies

file	mpower.f  mpower.f plus dependencies

file	mult.f

file	omult.f  omult.f plus dependencies

file	osolve.f  osolve.f plus dependencies

file	ovals.f  ovals.f plus dependencies

file	overt.f  overt.f plus dependencies

file	pack.f  pack.f plus dependencies

file	pcon.f  pcon.f plus dependencies

file	pdet.f  pdet.f plus dependencies

file	pfact.f  pfact.f plus dependencies

file	power.f  power.f plus dependencies

file	psolve.f  psolve.f plus dependencies

file	ptrans.f  ptrans.f plus dependencies

file	pvect.f

file	pvert.f  pvert.f plus dependencies

file	rpack.f  rpack.f plus dependencies

file	scon.f  scon.f plus dependencies

file	sdet.f  sdet.f plus dependencies

file	sdiag.f  sdiag.f plus dependencies

file	semcon.f  semcon.f plus dependencies

file	sfact.f

file	shess.f

file	sim.f  sim.f plus dependencies

file	smult.f

file	solve.f  solve.f plus dependencies

file	sort.f

file	sort2.f

file	sqr.f

file	ssim.f  ssim.f plus dependencies

file	ssolve.f  ssolve.f plus dependencies

file	svals.f  svals.f plus dependencies

file	svect.f  svect.f plus dependencies

file	svert.f  svert.f plus dependencies

file	tcon.f  tcon.f plus dependencies

file	tdet.f  tdet.f plus dependencies

file	tdg.f  tdg.f plus dependencies

file	tdiag.f  tdiag.f plus dependencies

file	tfact.f

file	tmult.f

file	trans.f  trans.f plus dependencies

file	tsolve.f  tsolve.f plus dependencies

file	ttrans.f  ttrans.f plus dependencies

file	tvals.f  tvals.f plus dependencies

file	tvect.f

file	tvert.f  tvert.f plus dependencies

file	vals.f  vals.f plus dependencies

file	vect.f  vect.f plus dependencies

file	vert.f  vert.f plus dependencies

file	vls.f  vls.f plus dependencies