Generalized Nonsymmetric Eigenvalue Problems

?gghrd reduces a pair of matrices to generalized upper Hessenberg form using orthogonal/unitary transformations.
call sgghrd (compq, compz, n, ilo, ihi, a, lda, b, ldb, q, ldq, z, ldz, info)
call dgghrd (compq, compz, n, ilo, ihi, a, lda, b, ldb, q, ldq, z, ldz, info)
call cgghrd (compq, compz, n, ilo, ihi, a, lda, b, ldb, q, ldq, z, ldz, info)
call zgghrd (compq, compz, n, ilo, ihi, a, lda, b, ldb, q, ldq, z, ldz, info)

?ggbal balances a pair of general real or complex matrices.
call sggbal (job, n, a, lda, b, ldb, ilo, ihi, lscale, rscale, work, info)
call dggbal (job, n, a, lda, b, ldb, ilo, ihi, lscale, rscale, work, info)
call cggbal (job, n, a, lda, b, ldb, ilo, ihi, lscale, rscale, work, info)
call zggbal (job, n, a, lda, b, ldb, ilo, ihi, lscale, rscale, work, info)

?ggbak forms the right or left eigenvectors of a generalized eigenvalue problem.
call sggbak (job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)
call dggbak (job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)
call cggbak (job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)
call zggbak (job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)

?hgeqz implements the QZ method for finding the generalized eigenvalues of the matrix pair (H,T).
call shgeqz (job, compq, compz, n, ilo, ihi, h, ldh, t, ldt, alphar, alphai, beta, q, ldq, z, ldz, work, lwork, info)
call dhgeqz (job, compq, compz, n, ilo, ihi, h, ldh, t, ldt, alphar, alphai, beta, q, ldq, z, ldz, work, lwork, info)
call chgeqz (job, compq, compz, n, ilo, ihi, h, ldh, t, ldt, alpha, beta, q, ldq, z, ldz, work, lwork, rwork, info)
call zhgeqz (job, compq, compz, n, ilo, ihi, h, ldh, t, ldt, alpha, beta, q, ldq, z, ldz, work, lwork, rwork, info)

?tgevc computes some or all of the right and/or left generalized eigenvectors of a pair of upper triangular matrices.
call stgevc (side, howmny, select, n, s, lds, p, ldp, vl, ldvl, vr, ldvr, mm, m, work, info)
call dtgevc (side, howmny, select, n, s, lds, p, ldp, vl, ldvl, vr, ldvr, mm, m, work, info)
call ctgevc (side, howmny, select, n, s, lds, p, ldp, vl, ldvl, vr, ldvr, mm, m, work, rwork, info)
call ztgevc (side, howmny, select, n, s, lds, p, ldp, vl, ldvl, vr, ldvr, mm, m, work, rwork, info)

?tgexc reorders the generalized Schur decomposition of a pair of matrices (A,B) so that one diagonal block of (A,B) moves to another row index.
call stgexc (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, ifst, ilst, work, lwork, info)
call dtgexc (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, ifst, ilst, work, lwork, info)
call ctgexc (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, ifst, ilst, info)
call ztgexc (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, ifst, ilst, info)

?tgsen reorders the generalized Schur decomposition of a pair of matrices (A,B) so that a selected cluster of eigenvalues appears in the leading diagonal blocks of (A,B).
call stgsen (ijob, wantq, wantz, select, n, a, lda, b, ldb, alphar, alphai, beta, q, ldq, z, ldz, m, pl, pr, dif, work, lwork, iwork, liwork, info)
call dtgsen (ijob, wantq, wantz, select, n, a, lda, b, ldb, alphar, alphai, beta, q, ldq, z, ldz, m, pl, pr, dif, work, lwork, iwork, liwork, info)
call ctgsen (ijob, wantq, wantz, select, n, a, lda, b, ldb, alpha, beta, q, ldq, z, ldz, m, pl, pr, dif, work, lwork, iwork, liwork, info)
call ztgsen (ijob, wantq, wantz, select, n, a, lda, b, ldb, alpha, beta, q, ldq, z, ldz, m, pl, pr, dif, work, lwork, iwork, liwork, info)

?tgsyl solves the generalized Sylvester equation.
call stgsyl (trans, ijob, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, lde, f, ldf, scale, dif, work, lwork, iwork, info)
call dtgsyl (trans, ijob, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, lde, f, ldf, scale, dif, work, lwork, iwork, info)
call ctgsyl (trans, ijob, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, lde, f, ldf, scale, dif, work, lwork, iwork, info)
call ztgsyl (trans, ijob, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, lde, f, ldf, scale, dif, work, lwork, iwork, info)

?tgsna estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a pair of matrices in generalized real Schur canonical form.
call stgsna (job, howmny, select, n, a, lda, b, ldb, vl, ldvl, vr, ldvr, s, dif, mm, m, work, lwork, iwork, info)
call dtgsna (job, howmny, select, n, a, lda, b, ldb, vl, ldvl, vr, ldvr, s, dif, mm, m, work, lwork, iwork, info)
call ctgsna (job, howmny, select, n, a, lda, b, ldb, vl, ldvl, vr, ldvr, s, dif, mm, m, work, lwork, iwork, info)
call ztgsna (job, howmny, select, n, a, lda, b, ldb, vl, ldvl, vr, ldvr, s, dif, mm, m, work, lwork, iwork, info)

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