Computational Routines for Eigenvalue Problems

Routine NameOperation
ssytrd, dsytrd
chetrd, zhetrd
Reduces a symmetric/Hermitian matrix to real symmetric tridiagonal form by an orthogonal/unitary similarity transformation
ssptrd, dsptrd
chptrd, zhptrd
Reduces a symmetric/Hermitian matrix in packed storage to real symmetric tridiagonal form by an orthogonal/unitary similarity transformation
ssbtrd, dsbtrd
chbtrd, zhbtrd
Reduces a symmetric/Hermitian band matrix to real symmetric tridiagonal form by an orthogonal/unitary similarity transformation
sorgtr, dorgtr
cungtr, zungtr
Generates the orthogonal/unitary transformation matrix from a reduction to tridiagonal form determined by SSYTRD/CHETRD
sormtr, dormtr
cunmtr, zunmtr
Multiplies a general matrix by the orthogonal/unitary transformation matrix from a reduction to tridiagonal form determined by SSYTRD/CHETRD
sopgtr, dopgtr
cupgtr, zupgtr
Generates the orthogonal/unitary transformation matrix from a reduction to tridiagonal form determined by SSPTRD/CHPTRD
sopmtr, dopmtr
cupmtr, zupmtr
Multiplies a general matrix by the orthogonal/unitary transformation matrix from a reduction to tridiagonal form determined by SSPTRD/CHPTRD
ssteqr, dsteqr
csteqr, zsteqr
Computes all eigenvalues and eigenvectors of a real symmetric tridiagonal matrix, using the implicit QL or QR algorithm
ssterf, dsterf Computes all eigenvalues of a real symmetric tridiagonal matrix, using a root-free variant of the QL or QR algorithm
sstebz, dstebz Computes selected eigenvalues of a real symmetric tridiagonal matrix by bisection
sstein, dstein
cstein, zstein
Computes selected eigenvectors of a real symmetric tridiagonal matrix by inverse iteration
spteqr, dpteqr
cpteqr, zpteqr
Computes all eigenvalues and eigenvectors of a real symmetric positive definite tridiagonal matrix, by computing the SVD of its bidiagonal Cholesky factor
sgehrd, dgehrd
cgehrd, zgehrd
Reduces a general matrix to upper Hessenberg form by an orthogonal/unitary similarity transformation
sgebal, dgebal
cgebal, zgebal
Balances a general matrix in order to improve the accuracy of computed eigenvalues
sgebak, dgebak
cgebak, zgebak
Transforms eigenvectors of a balanced matrix to those of the original matrix supplied to SGEBAL/CGEBAL
sorghr, dorghr
cunghr, zunghr
Generates the orthogonal/unitary transformation matrix from a reduction to Hessenberg form determined by SGEHRD/CGEHRD
sormhr, dormhr
cunmhr, zunmhr
Multiplies a general matrix by the orthogonal/unitary transformation matrix from a reduction to Hessenberg form determined by SGEHRD/CGEHRD
shseqr, dhseqr
chseqr, zhseqr
Computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the multishift QR algorithm
shsein, dhsein
chsein, zhsein
Computes specified right and/or left eigenvectors of an upper Hessenberg matrix by inverse iteration
strevc, dtrevc
ctrevc, ztrevc
Computes left and right eigenvectors of an upper quasi-triangular/triangular matrix
strexc, dtrexc
ctrexc, ztrexc
Reorders the Schur factorization of a matrix by a unitary similarity transformation
strsyl, dtrsyl
ctrsyl, ztrsyl
Solves the Sylvester matrix equation A X +/- X B=C where A and B are upper quasi-triangular/triangular and may be transposed
strsna, dtrsna
ctrsna, ztrsna
Estimates the reciprocal condition numbers (sensitivities) of selected eigenvalues and eigenvectors of an upper quasi-triangular/triangular matrix
strsen, dtrsen
ctrsen, ztrsen
Reorders the Schur factorization of a matrix in order to find an orthonormal basis of a right invariant subspace corresponding to selected eigenvalues, and returns reciprocal condition numbers (sensitivities) of the average of the cluster of eigenvalues and of the invariant subspace
ssygst, dsygst
chegst, zhegst
Reduces a symmetric/Hermitian-definite generalized eigenproblem Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard form, where B has been factorized by SPOTRF/CPOTRF
sspgst, dspgst
chpgst, zhpgst
Reduces a symmetric/Hermitian-definite generalized eigenproblem Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard form, where A and B are held in packed storage, and B has been factorized by SPPTRF/CPPTRF
sgghrd, dgghrd
cgghrd, zgghrd
Reduces a pair of real/complex matrices to generalized upper Hessenberg form using orthogonal/unitary similarity transformations
sggbal, dggbal
cggbal, zggbal
Balances a pair of general real/complex matrices for the generalized eigenvalue problem A x = lambda B x
sggbak, dggbak
cggbak, zggbak
Forms the right or left eigenvectors of the generalized eigenvalue problem by backward transformation on the computed eigenvectors of the balanced matrix output by xGGBAL
shgeqz, dhgeqz
chgeqz, zhgeqz
Implements a single-/double-shift version of the QZ method for finding the generalized eigenvalues of the equation det(A - w(i) B) = 0
stgevc, dtgevc
ctgevc, ztgevc
Computes selected left and/or right generalized eigenvectors of a pair of real/complex upper triangular matrices

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