EISPACK
Eigenvalue Calculations
EISPACK,
a FORTRAN90 library which
calculates the eigenvalues and eigenvectors of a matrix.
A variety of options are available for special matrix formats.
Note that EISPACK "simulates" complex arithmetic. That is,
complex data is stored as pairs of real numbers, and complex
arithmetic is done by carefully manipulating the real numbers.
EISPACK is old, and its functionality has been replaced by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.
EISPACK includes a function to compute the singular value decomposition (SVD)
of a rectangular matrix.
The pristine correct original source code for EISPACK is available
through
the NETLIB web site.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the MIT license
Languages:
EISPACK is available in
a C version and
a C++ version and
a FORTRAN90 version.
Related Data and Programs:
ARPACK,
a FORTRAN90 library which
uses Arnoldi iteration to compute
some of the eigenvalues and eigenvectors of a large sparse matrix.
eispack_test
JACOBI_EIGENVALUE,
a FORTRAN90 library which
implements the Jacobi iteration for the iterative determination
of the eigenvalues and eigenvectors of a real symmetric matrix.
TEST_EIGEN,
a FORTRAN90 library which
defines various eigenvalue test cases.
TEST_MAT,
a FORTRAN90 library which
defines test matrices, some of
which have known eigenvalues and eigenvectors.
Reference:

Hilary Bowdler, Roger Martin, Christian Reinsch, James Wilkinson,
The QR and QL algorithms for Symmetric Matrices: TQL1 and TQL2,
Numerische Mathematik,
Volume 11, Number 4, May 1968, pages 293306.

Gene Golub, Christian Reinsch,
Singular Value Decomposition and Least Squares Solutions,
Numerische Mathematik,
Volume 14, Number 5, April 1970, pages 403420.

Roger Martin, G Peters, James Wilkinson,
HQR, The QR Algorithm for Real Hessenberg Matrices,
Numerische Mathematik,
Volume 14, Number 3, February 1970, pages 219231.

Roger Martin, Christian Reinsch, James Wilkinson,
Householder's Tridiagonalization of a Symmetric Matrix:
TRED1, TRED2 and TRED3,
Numerische Mathematik,
Volume 11, Number 3, March 1968, pages 181195.

Roger Martin, James Wilkinson,
Similarity Reduction of a General Matrix to Hessenberg Form:
ELMHES,
Numerische Mathematik,
Volume 12, Number 5, December 1968, pages 349368.

Beresford Parlett, Christian Reinsch,
Balancing a Matrix for Calculation of Eigenvalues and
Eigenvectors,
Numerische Mathematik,
Volume 13, Number 4, August 1969, pages 293304.

Christian Reinsch,
Algorithm 464:
Eigenvalues of a real symmetric tridiagonal matrix,
Communications of the ACM,
Volume 16, Number 11, November 1973, page 689.

Brian Smith, James Boyle, Jack Dongarra, Burton Garbow,
Yasuhiko Ikebe, Virginia Klema, Cleve Moler,
Matrix Eigensystem Routines, EISPACK Guide,
Lecture Notes in Computer Science, Volume 6,
Springer, 1976,
ISBN13: 9783540075462,
LC: QA193.M37.

James Wilkinson, Christian Reinsch,
Handbook for Automatic Computation,
Volume II, Linear Algebra, Part 2,
Springer, 1971,
ISBN: 0387054146,
LC: QA251.W67.
Source Code:
Last revised on 02 May 2019.