EISPACK: Eigenvalue Calculations

EISPACK is a library of routines for calculating the eigenvalues and eigenvectors of a matrix. A variety of options are available for special matrix formats.

EISPACK is old, and its functionality has been replaced by the more modern and efficient LAPACK. There are some advantages, not all sentimental, to keeping a copy of EISPACK around. For one thing, the implementation of the LAPACK routines makes it a trying task to try to comprehend the algorithm by reading the source code. A single user level routine may refer indirectly to thirty or forty others.

The pristine correct original source code for EISPACK is available through the NETLIB web site.

Files you may copy include:

• EISPACK.F90, the source code;
• EISPACK_PRB.F90, the calling program;
• EISPACK_PRB.OUT, the sample output.

The list of routines includes:

• BAKVEC determines eigenvectors by reversing the FIGI transformation.
• BALANC balances a real matrix before eigenvalue calculations.
• BALBAK determines eigenvectors by undoing the BALANC transformation.
• BANDR reduces a symmetric band matrix to tridiagonal form.
• BANDV finds eigenvectors from eigenvalues, for a real symmetric band matrix.
• BISECT computes some eigenvalues of a real symmetric band matrix.
• BQR finds the eigenvalue of smallest magnitude, for a real symmetric band matrix.
• CBABK2 finds eigenvectors by undoing the CBAL transformation.
• CBAL balances a complex matrix before eigenvalue calculations.
• CDIV emulates complex division, using real arithmetic.
• CG gets eigenvalues and eigenvectors of a complex general matrix.
• CH gets eigenvalues and eigenvectors of a complex Hermitian matrix. .
• CINVIT gets eigenvectors from eigenvalues, for a complex Hessenberg matrix.
• COMBAK determines eigenvectors by undoing the COMHES transformation.
• COMHES transforms a complex general matrix to upper Hessenberg form.
• COMLR gets all eigenvalues of a complex upper Hessenberg matrix.
• COMLR2 gets eigenvalues/vectors of a complex upper Hessenberg matrix.
• COMQR gets eigenvalues of a complex upper Hessenberg matrix.
• COMQR2 gets eigenvalues/vectors of a complex upper Hessenberg matrix.
• CORTB determines eigenvectors by undoing the CORTH transformation.
• CORTH transforms a complex general matrix to upper Hessenberg form.
• CSROOT computes the complex square root of a complex quantity.
• ELMBAK determines eigenvectors by undoing the ELMHES transformation.
• ELMHES transforms a real general matrix to upper Hessenberg form.
• ELTRAN accumulates similarity transformations used by ELMHES.
• FIGI transforms a real nonsymmetric tridiagonal matrix to symmetric form.
• FIGI2 transforms a real nonsymmetric tridiagonal matrix to symmetric form.
• HQR computes all eigenvalues of a real upper Hessenberg matrix.
• HQR2 computes eigenvalues and eigenvectors of a real upper Hessenberg matrix.
• HTRIB3 determines eigenvectors by undoing the HTRID3 transformation.
• HTRIBK determines eigenvectors by undoing the HTRIDI transformation.
• HTRID3 tridiagonalizes a complex hermitian packed matrix.
• HTRIDI tridiagonalizes a complex hermitian matrix.
• IMTQL1 computes all eigenvalues of a symmetric tridiagonal matrix.
• IMTQL2 computes all eigenvalues/vectors of a symmetric tridiagonal matrix.
• IMTQLV computes all eigenvalues of a real symmetric tridiagonal matrix.
• INVIT computes eigenvectors given eigenvalues, for a real upper Hessenberg matrix.
• MINFIT solves the least squares problem, for a real overdetermined linear system.
• ORTBAK determines eigenvectors by undoing the ORTHES transformation.
• ORTHES transforms a real general matrix to upper Hessenberg form.
• ORTRAN accumulates similarity transformations generated by ORTHES.
• PYTHAG computes SQRT ( A**2 + B**2 ) carefully.
• QZHES carries out transformations for a generalized eigenvalue problem.
• QZIT carries out iterations to solve a generalized eigenvalue problem.
• QZVAL computes eigenvalues for a generalized eigenvalue problem.
• QZVEC computes eigenvectors for a generalized eigenvalue problem.
• R_SWAP switches two real values.
• RATQR computes selected eigenvalues of a real symmetric tridiagonal matrix.
• REBAK determines eigenvectors by undoing the REDUC transformation.
• REBAKB determines eigenvectors by undoing the REDUC2 transformation.
• REDUC reduces the eigenvalue problem A*x=lambda*B*x to A*x=lambda*x.
• REDUC2 reduces the eigenvalue problem A*B*x=lamdba*x to A*x=lambda*x.
• RG computes igenvalues and eigenvectors of a real general matrix.
• RGG computes eigenvalues/vectors for the generalized problem A*x = lambda*B*x.
• RMAT_IDENT sets the square matrix A to the identity.
• RMAT_PRINT prints a real matrix, with an optional title.
• RS computes eigenvalues and eigenvectors of real symmetric matrix.
• RSB computes eigenvalues and eigenvectors of a real symmetric band matrix.
• RSG computes eigenvalues/vectors, A*x=lambda*B*x, A symmetric, B pos-def.
• RSGAB computes eigenvalues/vectors, A*B*x=lambda*x, A symmetric, B pos-def.
• RSGBA computes eigenvalues/vectors, B*A*x=lambda*x, A symmetric, B pos-def.
• RSM computes eigenvalues, some eigenvectors, real symmetric matrix.
• RSP computes eigenvalues and eigenvectors of real symmetric packed matrix.
• RSPP computes some eigenvalues/vectors, real symmetric packed matrix.
• RST computes eigenvalues/vectors, real symmetric tridiagonal matrix.
• RT computes eigenvalues/vectors, real sign-symmetric tridiagonal matrix.
• RVEC_PRINT prints a real vector, with an optional title.
• SVD computes the singular value decomposition for a real matrix.
• TINVIT computes eigenvectors from eigenvalues, real tridiagonal symmetric.
• TQL1 computes all eigenvalues of a real symmetric tridiagonal matrix.
• TQL2 computes all eigenvalues/vectors, real symmetric tridiagonal matrix.
• TQLRAT compute all eigenvalues of a real symmetric tridiagonal matrix.
• TRBAK1 determines eigenvectors by undoing the TRED1 transformation.
• TRBAK3 determines eigenvectors by undoing the TRED3 transformation.
• TRED1 transforms a real symmetric matrix to tridiagonal form.
• TRED2 transforms a real symmetric matrix to tridiagonal form.
• TRED3 transforms a real symmetric packed matrix to tridiagonal form.
• TRIDIB computes some eigenvalues of a real symmetric tridiagonal matrix.
• TSTURM computes some eigenvalues/vectors, real symmetric tridiagonal matrix.

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