Nonsymmetric Eigenvalue Problems

?gehrd reduces a general matrix to upper Hessenberg form.
call sgehrd (n, ilo, ihi, a, lda, tau, work, lwork, info)
call dgehrd (n, ilo, ihi, a, lda, tau, work, lwork, info)
call cgehrd (n, ilo, ihi, a, lda, tau, work, lwork, info)
call zgehrd (n, ilo, ihi, a, lda, tau, work, lwork, info)

?orghr generates the real orthogonal matrix Q determined by ?gehrd.
call sorghr (n, ilo, ihi, a, lda, tau, work, lwork, info)
call dorghr (n, ilo, ihi, a, lda, tau, work, lwork, info)

?ormhr multiplies an arbitrary real matrix C by the real orthogonal matrix Q determined by ?gehrd.
call sormhr (side, trans, m, n, ilo, ihi, a, lda, tau, c, ldc, work, lwork, info)
call dormhr (side, trans, m, n, ilo, ihi, a, lda, tau, c, ldc, work, lwork, info)

?unghr generates the complex unitary matrix Q determined by ?gehrd.
call cunghr (n, ilo, ihi, a, lda, tau, work, lwork, info)
call zunghr (n, ilo, ihi, a, lda, tau, work, lwork, info)

?unmhr multiplies an arbitrary complex matrix C by the complex unitary matrix Q determined by ?gehrd.
call cunmhr (side, trans, m, n, ilo, ihi, a, lda, tau, c, ldc, work, lwork, info)
call zunmhr (side, trans, m, n, ilo, ihi, a, lda, tau, c, ldc, work, lwork, info)

?gebal balances a general matrix to improve the accuracy of computed eigenvalues and eigenvectors.
call sgebal (job, n, a, lda, ilo, ihi, scale, info)
call dgebal (job, n, a, lda, ilo, ihi, scale, info)
call cgebal (job, n, a, lda, ilo, ihi, scale, info)
call zgebal (job, n, a, lda, ilo, ihi, scale, info)

?gebak transforms eigenvectors of a balanced matrix to those of the original nonsymmetric matrix.
call sgebak (job, side, n, ilo, ihi, scale, m, v, ldv, info)
call dgebak (job, side, n, ilo, ihi, scale, m, v, ldv, info)
call cgebak (job, side, n, ilo, ihi, scale, m, v, ldv, info)
call zgebak (job, side, n, ilo, ihi, scale, m, v, ldv, info)

?hseqr computes all eigenvalues and (optionally) the Schur factorization of a matrix reduced to Hessenberg form.
call shseqr (job, compz, n, ilo, ihi, h, ldh, wr, wi, z, ldz, work, lwork, info)
call dhseqr (job, compz, n, ilo, ihi, h, ldh, wr, wi, z, ldz, work, lwork, info)
call chseqr (job, compz, n, ilo, ihi, h, ldh, w, z, ldz, work, lwork, info)
call zhseqr (job, compz, n, ilo, ihi, h, ldh, w, z, ldz, work, lwork, info)

?hsein computes selected eigenvectors of an upper Hessenberg matrix that correspond to specified eigenvalues.
call shsein (job, eigsrc, initv, select, n, h, ldh, wr, wi, vl, ldvl, vr, ldvr, mm, m, work, ifaill, ifailr, info)
call dhsein (job, eigsrc, initv, select, n, h, ldh, wr, wi, vl, ldvl, vr, ldvr, mm, m, work, ifaill, ifailr, info)
call chsein (job, eigsrc, initv, select, n, h, ldh, w, vl, ldvl, vr, ldvr, mm, m, work, rwork, ifaill, ifailr, info)
call zhsein (job, eigsrc, initv, select, n, h, ldh, w, vl, ldvl, vr, ldvr, mm, m, work, rwork, ifaill, ifailr, info)

?trevc computes selected eigenvectors of an upper (quasi-)triangular matrix computed by ?hseqr.
call strevc (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, info)
call dtrevc (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, info)
call ctrevc (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, rwork, info)
call ztrevc (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, rwork, info)

?trsna estimates condition numbers for specified eigenvalues and right eigenvectors of an upper (quasi-)triangular matrix.
call strsna (job, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, s, sep, mm, m, work, ldwork, iwork, info)
call dtrsna (job, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, s, sep, mm, m, work, ldwork, iwork, info)
call ctrsna (job, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, s, sep, mm, m, work, ldwork, rwork, info)
call ztrsna (job, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, s, sep, mm, m, work, ldwork, rwork, info)

?trexc reorders the Schur factorization of a general matrix.
call strexc (compq, n, t, ldt, q, ldq, ifst, ilst, work, info)
call dtrexc (compq, n, t, ldt, q, ldq, ifst, ilst, work, info)
call ctrexc (compq, n, t, ldt, q, ldq, ifst, ilst, info)
call ztrexc (compq, n, t, ldt, q, ldq, ifst, ilst, info)

?trsen reorders the Schur factorization of a matrix and (optionally) computes the reciprocal condition numbers and invariant subspace for the selected cluster of eigenvalues.
call strsen (job, compq, select, n, t, ldt, q, ldq, wr, wi, m, s, sep, work, lwork, iwork, liwork, info)
call dtrsen (job, compq, select, n, t, ldt, q, ldq, wr, wi, m, s, sep, work, lwork, iwork, liwork, info)
call ctrsen (job, compq, select, n, t, ldt, q, ldq, w, m, s, sep, work, lwork, info)
call ztrsen (job, compq, select, n, t, ldt, q, ldq, w, m, s, sep, work, lwork, info)

?trsyl solves Sylvester’s equation for real quasi-triangular or complex triangular matrices.
call strsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info)
call dtrsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info)
call ctrsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info)
call ztrsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info)

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