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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