| Routine Name | Operation |
|---|---|
| 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 |