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| pure subroutine, public | la_lapack_eigv_gen2::la_slaein (rightv, noinit, n, h, ldh, wr, wi, vr, vi, b, ldb, work, eps3, smlnum, bignum, info) |
| | SLAEIN: uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H.
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| pure subroutine, public | la_lapack_eigv_gen2::la_dlaein (rightv, noinit, n, h, ldh, wr, wi, vr, vi, b, ldb, work, eps3, smlnum, bignum, info) |
| | DLAEIN: uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H.
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| pure subroutine, public | la_lapack_eigv_gen2::la_qlaein (rightv, noinit, n, h, ldh, wr, wi, vr, vi, b, ldb, work, eps3, smlnum, bignum, info) |
| | QLAEIN: uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H.
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| pure subroutine, public | la_lapack_eigv_gen2::la_strevc (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, info) |
| | STREVC: computes some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T. Matrices of this type are produced by the Schur factorization of a real general matrix: A = Q*T*Q**T, as computed by SHSEQR. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by: T*x = w*x, (y**H)*T = w*(y**H) where y**H denotes the conjugate transpose of y. The eigenvalues are not input to this routine, but are read directly from the diagonal blocks of T. This routine returns the matrices X and/or Y of right and left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input matrix. If Q is the orthogonal factor that reduces a matrix A to Schur form T, then Q*X and Q*Y are the matrices of right and left eigenvectors of A.
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| pure subroutine, public | la_lapack_eigv_gen2::la_dtrevc (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, info) |
| | DTREVC: computes some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T. Matrices of this type are produced by the Schur factorization of a real general matrix: A = Q*T*Q**T, as computed by DHSEQR. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by: T*x = w*x, (y**H)*T = w*(y**H) where y**H denotes the conjugate transpose of y. The eigenvalues are not input to this routine, but are read directly from the diagonal blocks of T. This routine returns the matrices X and/or Y of right and left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input matrix. If Q is the orthogonal factor that reduces a matrix A to Schur form T, then Q*X and Q*Y are the matrices of right and left eigenvectors of A.
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| pure subroutine, public | la_lapack_eigv_gen2::la_qtrevc (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, info) |
| | QTREVC: computes some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T. Matrices of this type are produced by the Schur factorization of a real general matrix: A = Q*T*Q**T, as computed by QHSEQR. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by: T*x = w*x, (y**H)*T = w*(y**H) where y**H denotes the conjugate transpose of y. The eigenvalues are not input to this routine, but are read directly from the diagonal blocks of T. This routine returns the matrices X and/or Y of right and left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input matrix. If Q is the orthogonal factor that reduces a matrix A to Schur form T, then Q*X and Q*Y are the matrices of right and left eigenvectors of A.
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| pure subroutine, public | la_lapack_eigv_gen2::la_strevc3 (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, lwork, info) |
| | STREVC3: computes some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T. Matrices of this type are produced by the Schur factorization of a real general matrix: A = Q*T*Q**T, as computed by SHSEQR. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by: T*x = w*x, (y**T)*T = w*(y**T) where y**T denotes the transpose of the vector y. The eigenvalues are not input to this routine, but are read directly from the diagonal blocks of T. This routine returns the matrices X and/or Y of right and left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input matrix. If Q is the orthogonal factor that reduces a matrix A to Schur form T, then Q*X and Q*Y are the matrices of right and left eigenvectors of A. This uses a Level 3 BLAS version of the back transformation.
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| pure subroutine, public | la_lapack_eigv_gen2::la_dtrevc3 (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, lwork, info) |
| | DTREVC3: computes some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T. Matrices of this type are produced by the Schur factorization of a real general matrix: A = Q*T*Q**T, as computed by DHSEQR. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by: T*x = w*x, (y**T)*T = w*(y**T) where y**T denotes the transpose of the vector y. The eigenvalues are not input to this routine, but are read directly from the diagonal blocks of T. This routine returns the matrices X and/or Y of right and left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input matrix. If Q is the orthogonal factor that reduces a matrix A to Schur form T, then Q*X and Q*Y are the matrices of right and left eigenvectors of A. This uses a Level 3 BLAS version of the back transformation.
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| pure subroutine, public | la_lapack_eigv_gen2::la_qtrevc3 (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, lwork, info) |
| | QTREVC3: computes some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T. Matrices of this type are produced by the Schur factorization of a real general matrix: A = Q*T*Q**T, as computed by QHSEQR. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by: T*x = w*x, (y**T)*T = w*(y**T) where y**T denotes the transpose of the vector y. The eigenvalues are not input to this routine, but are read directly from the diagonal blocks of T. This routine returns the matrices X and/or Y of right and left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input matrix. If Q is the orthogonal factor that reduces a matrix A to Schur form T, then Q*X and Q*Y are the matrices of right and left eigenvectors of A. This uses a Level 3 BLAS version of the back transformation.
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| subroutine, public | la_lapack_eigv_gen2::la_strsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info) |
| | STRSYL: solves the real Sylvester matrix equation: op(A)*X + X*op(B) = scale*C or op(A)*X - X*op(B) = scale*C, where op(A) = A or A**T, and A and B are both upper quasi- triangular. A is M-by-M and B is N-by-N; the right hand side C and the solution X are M-by-N; and scale is an output scale factor, set <= 1 to avoid overflow in X. A and B must be in Schur canonical form (as returned by SHSEQR), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign.
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| subroutine, public | la_lapack_eigv_gen2::la_dtrsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info) |
| | DTRSYL: solves the real Sylvester matrix equation: op(A)*X + X*op(B) = scale*C or op(A)*X - X*op(B) = scale*C, where op(A) = A or A**T, and A and B are both upper quasi- triangular. A is M-by-M and B is N-by-N; the right hand side C and the solution X are M-by-N; and scale is an output scale factor, set <= 1 to avoid overflow in X. A and B must be in Schur canonical form (as returned by DHSEQR), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign.
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| subroutine, public | la_lapack_eigv_gen2::la_qtrsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info) |
| | QTRSYL: solves the real Sylvester matrix equation: op(A)*X + X*op(B) = scale*C or op(A)*X - X*op(B) = scale*C, where op(A) = A or A**T, and A and B are both upper quasi- triangular. A is M-by-M and B is N-by-N; the right hand side C and the solution X are M-by-N; and scale is an output scale factor, set <= 1 to avoid overflow in X. A and B must be in Schur canonical form (as returned by QHSEQR), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign.
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| subroutine, public | la_lapack_eigv_gen2::la_shsein (side, eigsrc, initv, select, n, h, ldh, wr, wi, vl, ldvl, vr, ldvr, mm, m, work, ifaill, ifailr, info) |
| | SHSEIN: uses inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H. The right eigenvector x and the left eigenvector y of the matrix H corresponding to an eigenvalue w are defined by: H * x = w * x, y**h * H = w * y**h where y**h denotes the conjugate transpose of the vector y.
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| subroutine, public | la_lapack_eigv_gen2::la_dhsein (side, eigsrc, initv, select, n, h, ldh, wr, wi, vl, ldvl, vr, ldvr, mm, m, work, ifaill, ifailr, info) |
| | DHSEIN: uses inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H. The right eigenvector x and the left eigenvector y of the matrix H corresponding to an eigenvalue w are defined by: H * x = w * x, y**h * H = w * y**h where y**h denotes the conjugate transpose of the vector y.
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| subroutine, public | la_lapack_eigv_gen2::la_qhsein (side, eigsrc, initv, select, n, h, ldh, wr, wi, vl, ldvl, vr, ldvr, mm, m, work, ifaill, ifailr, info) |
| | QHSEIN: uses inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H. The right eigenvector x and the left eigenvector y of the matrix H corresponding to an eigenvalue w are defined by: H * x = w * x, y**h * H = w * y**h where y**h denotes the conjugate transpose of the vector y.
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| subroutine, public | la_lapack_eigv_gen2::la_strsen (job, compq, select, n, t, ldt, q, ldq, wr, wi, m, s, sep, work, lwork, iwork, liwork, info) |
| | STRSEN: reorders the real Schur factorization of a real matrix A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace. Optionally the routine computes the reciprocal condition numbers of the cluster of eigenvalues and/or the invariant subspace. T must be in Schur canonical form (as returned by SHSEQR), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign.
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| subroutine, public | la_lapack_eigv_gen2::la_dtrsen (job, compq, select, n, t, ldt, q, ldq, wr, wi, m, s, sep, work, lwork, iwork, liwork, info) |
| | DTRSEN: reorders the real Schur factorization of a real matrix A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace. Optionally the routine computes the reciprocal condition numbers of the cluster of eigenvalues and/or the invariant subspace. T must be in Schur canonical form (as returned by DHSEQR), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign.
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| subroutine, public | la_lapack_eigv_gen2::la_qtrsen (job, compq, select, n, t, ldt, q, ldq, wr, wi, m, s, sep, work, lwork, iwork, liwork, info) |
| | QTRSEN: reorders the real Schur factorization of a real matrix A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace. Optionally the routine computes the reciprocal condition numbers of the cluster of eigenvalues and/or the invariant subspace. T must be in Schur canonical form (as returned by QHSEQR), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign.
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| subroutine, public | la_lapack_eigv_gen2::la_strsna (job, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, s, sep, mm, m, work, ldwork, iwork, info) |
| | STRSNA: estimates reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q orthogonal). T must be in Schur canonical form (as returned by SHSEQR), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign.
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| subroutine, public | la_lapack_eigv_gen2::la_dtrsna (job, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, s, sep, mm, m, work, ldwork, iwork, info) |
| | DTRSNA: estimates reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q orthogonal). T must be in Schur canonical form (as returned by DHSEQR), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign.
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| subroutine, public | la_lapack_eigv_gen2::la_qtrsna (job, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, s, sep, mm, m, work, ldwork, iwork, info) |
| | QTRSNA: estimates reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q orthogonal). T must be in Schur canonical form (as returned by QHSEQR), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign.
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| subroutine, public | la_lapack_eigv_gen2::la_shseqr (job, compz, n, ilo, ihi, h, ldh, wr, wi, z, ldz, work, lwork, info) |
| | SHSEQR: computes the eigenvalues of a Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**T, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors. Optionally Z may be postmultiplied into an input orthogonal matrix Q so that this routine can give the Schur factorization of a matrix A which has been reduced to the Hessenberg form H by the orthogonal matrix Q: A = Q*H*Q**T = (QZ)*T*(QZ)**T.
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| subroutine, public | la_lapack_eigv_gen2::la_dhseqr (job, compz, n, ilo, ihi, h, ldh, wr, wi, z, ldz, work, lwork, info) |
| | DHSEQR: computes the eigenvalues of a Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**T, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors. Optionally Z may be postmultiplied into an input orthogonal matrix Q so that this routine can give the Schur factorization of a matrix A which has been reduced to the Hessenberg form H by the orthogonal matrix Q: A = Q*H*Q**T = (QZ)*T*(QZ)**T.
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| subroutine, public | la_lapack_eigv_gen2::la_qhseqr (job, compz, n, ilo, ihi, h, ldh, wr, wi, z, ldz, work, lwork, info) |
| | QHSEQR: computes the eigenvalues of a Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**T, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors. Optionally Z may be postmultiplied into an input orthogonal matrix Q so that this routine can give the Schur factorization of a matrix A which has been reduced to the Hessenberg form H by the orthogonal matrix Q: A = Q*H*Q**T = (QZ)*T*(QZ)**T.
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| pure subroutine, public | la_lapack_eigv_gen2::la_ctrevc (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, rwork, info) |
| | CTREVC: computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix T. Matrices of this type are produced by the Schur factorization of a complex general matrix: A = Q*T*Q**H, as computed by CHSEQR. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by: T*x = w*x, (y**H)*T = w*(y**H) where y**H denotes the conjugate transpose of the vector y. The eigenvalues are not input to this routine, but are read directly from the diagonal of T. This routine returns the matrices X and/or Y of right and left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input matrix. If Q is the unitary factor that reduces a matrix A to Schur form T, then Q*X and Q*Y are the matrices of right and left eigenvectors of A.
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| pure subroutine, public | la_lapack_eigv_gen2::la_ztrevc (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, rwork, info) |
| | ZTREVC: computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix T. Matrices of this type are produced by the Schur factorization of a complex general matrix: A = Q*T*Q**H, as computed by ZHSEQR. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by: T*x = w*x, (y**H)*T = w*(y**H) where y**H denotes the conjugate transpose of the vector y. The eigenvalues are not input to this routine, but are read directly from the diagonal of T. This routine returns the matrices X and/or Y of right and left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input matrix. If Q is the unitary factor that reduces a matrix A to Schur form T, then Q*X and Q*Y are the matrices of right and left eigenvectors of A.
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| pure subroutine, public | la_lapack_eigv_gen2::la_wtrevc (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, rwork, info) |
| | WTREVC: computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix T. Matrices of this type are produced by the Schur factorization of a complex general matrix: A = Q*T*Q**H, as computed by WHSEQR. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by: T*x = w*x, (y**H)*T = w*(y**H) where y**H denotes the conjugate transpose of the vector y. The eigenvalues are not input to this routine, but are read directly from the diagonal of T. This routine returns the matrices X and/or Y of right and left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input matrix. If Q is the unitary factor that reduces a matrix A to Schur form T, then Q*X and Q*Y are the matrices of right and left eigenvectors of A.
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| pure subroutine, public | la_lapack_eigv_gen2::la_ctrevc3 (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, lwork, rwork, lrwork, info) |
| | CTREVC3: computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix T. Matrices of this type are produced by the Schur factorization of a complex general matrix: A = Q*T*Q**H, as computed by CHSEQR. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by: T*x = w*x, (y**H)*T = w*(y**H) where y**H denotes the conjugate transpose of the vector y. The eigenvalues are not input to this routine, but are read directly from the diagonal of T. This routine returns the matrices X and/or Y of right and left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input matrix. If Q is the unitary factor that reduces a matrix A to Schur form T, then Q*X and Q*Y are the matrices of right and left eigenvectors of A. This uses a Level 3 BLAS version of the back transformation.
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| pure subroutine, public | la_lapack_eigv_gen2::la_ztrevc3 (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, lwork, rwork, lrwork, info) |
| | ZTREVC3: computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix T. Matrices of this type are produced by the Schur factorization of a complex general matrix: A = Q*T*Q**H, as computed by ZHSEQR. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by: T*x = w*x, (y**H)*T = w*(y**H) where y**H denotes the conjugate transpose of the vector y. The eigenvalues are not input to this routine, but are read directly from the diagonal of T. This routine returns the matrices X and/or Y of right and left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input matrix. If Q is the unitary factor that reduces a matrix A to Schur form T, then Q*X and Q*Y are the matrices of right and left eigenvectors of A. This uses a Level 3 BLAS version of the back transformation.
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| pure subroutine, public | la_lapack_eigv_gen2::la_wtrevc3 (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, lwork, rwork, lrwork, info) |
| | WTREVC3: computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix T. Matrices of this type are produced by the Schur factorization of a complex general matrix: A = Q*T*Q**H, as computed by WHSEQR. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by: T*x = w*x, (y**H)*T = w*(y**H) where y**H denotes the conjugate transpose of the vector y. The eigenvalues are not input to this routine, but are read directly from the diagonal of T. This routine returns the matrices X and/or Y of right and left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input matrix. If Q is the unitary factor that reduces a matrix A to Schur form T, then Q*X and Q*Y are the matrices of right and left eigenvectors of A. This uses a Level 3 BLAS version of the back transformation.
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| pure subroutine, public | la_lapack_eigv_gen2::la_ctrsna (job, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, s, sep, mm, m, work, ldwork, rwork, info) |
| | CTRSNA: estimates reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q*T*Q**H with Q unitary).
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| pure subroutine, public | la_lapack_eigv_gen2::la_ztrsna (job, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, s, sep, mm, m, work, ldwork, rwork, info) |
| | ZTRSNA: estimates reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q*T*Q**H with Q unitary).
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| pure subroutine, public | la_lapack_eigv_gen2::la_wtrsna (job, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, s, sep, mm, m, work, ldwork, rwork, info) |
| | WTRSNA: estimates reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q*T*Q**H with Q unitary).
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| pure subroutine, public | la_lapack_eigv_gen2::la_claein (rightv, noinit, n, h, ldh, w, v, b, ldb, rwork, eps3, smlnum, info) |
| | CLAEIN: uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H.
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| pure subroutine, public | la_lapack_eigv_gen2::la_zlaein (rightv, noinit, n, h, ldh, w, v, b, ldb, rwork, eps3, smlnum, info) |
| | ZLAEIN: uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H.
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| pure subroutine, public | la_lapack_eigv_gen2::la_wlaein (rightv, noinit, n, h, ldh, w, v, b, ldb, rwork, eps3, smlnum, info) |
| | WLAEIN: uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H.
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| subroutine, public | la_lapack_eigv_gen2::la_ctrsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info) |
| | CTRSYL: solves the complex Sylvester matrix equation: op(A)*X + X*op(B) = scale*C or op(A)*X - X*op(B) = scale*C, where op(A) = A or A**H, and A and B are both upper triangular. A is M-by-M and B is N-by-N; the right hand side C and the solution X are M-by-N; and scale is an output scale factor, set <= 1 to avoid overflow in X.
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| subroutine, public | la_lapack_eigv_gen2::la_ztrsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info) |
| | ZTRSYL: solves the complex Sylvester matrix equation: op(A)*X + X*op(B) = scale*C or op(A)*X - X*op(B) = scale*C, where op(A) = A or A**H, and A and B are both upper triangular. A is M-by-M and B is N-by-N; the right hand side C and the solution X are M-by-N; and scale is an output scale factor, set <= 1 to avoid overflow in X.
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| subroutine, public | la_lapack_eigv_gen2::la_wtrsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info) |
| | WTRSYL: solves the complex Sylvester matrix equation: op(A)*X + X*op(B) = scale*C or op(A)*X - X*op(B) = scale*C, where op(A) = A or A**H, and A and B are both upper triangular. A is M-by-M and B is N-by-N; the right hand side C and the solution X are M-by-N; and scale is an output scale factor, set <= 1 to avoid overflow in X.
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| subroutine, public | la_lapack_eigv_gen2::la_chsein (side, eigsrc, initv, select, n, h, ldh, w, vl, ldvl, vr, ldvr, mm, m, work, rwork, ifaill, ifailr, info) |
| | CHSEIN: uses inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H. The right eigenvector x and the left eigenvector y of the matrix H corresponding to an eigenvalue w are defined by: H * x = w * x, y**h * H = w * y**h where y**h denotes the conjugate transpose of the vector y.
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| subroutine, public | la_lapack_eigv_gen2::la_zhsein (side, eigsrc, initv, select, n, h, ldh, w, vl, ldvl, vr, ldvr, mm, m, work, rwork, ifaill, ifailr, info) |
| | ZHSEIN: uses inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H. The right eigenvector x and the left eigenvector y of the matrix H corresponding to an eigenvalue w are defined by: H * x = w * x, y**h * H = w * y**h where y**h denotes the conjugate transpose of the vector y.
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| subroutine, public | la_lapack_eigv_gen2::la_whsein (side, eigsrc, initv, select, n, h, ldh, w, vl, ldvl, vr, ldvr, mm, m, work, rwork, ifaill, ifailr, info) |
| | WHSEIN: uses inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H. The right eigenvector x and the left eigenvector y of the matrix H corresponding to an eigenvalue w are defined by: H * x = w * x, y**h * H = w * y**h where y**h denotes the conjugate transpose of the vector y.
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| subroutine, public | la_lapack_eigv_gen2::la_ctrsen (job, compq, select, n, t, ldt, q, ldq, w, m, s, sep, work, lwork, info) |
| | CTRSEN: reorders the Schur factorization of a complex matrix A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace. Optionally the routine computes the reciprocal condition numbers of the cluster of eigenvalues and/or the invariant subspace.
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| subroutine, public | la_lapack_eigv_gen2::la_ztrsen (job, compq, select, n, t, ldt, q, ldq, w, m, s, sep, work, lwork, info) |
| | ZTRSEN: reorders the Schur factorization of a complex matrix A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace. Optionally the routine computes the reciprocal condition numbers of the cluster of eigenvalues and/or the invariant subspace.
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| subroutine, public | la_lapack_eigv_gen2::la_wtrsen (job, compq, select, n, t, ldt, q, ldq, w, m, s, sep, work, lwork, info) |
| | WTRSEN: reorders the Schur factorization of a complex matrix A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace. Optionally the routine computes the reciprocal condition numbers of the cluster of eigenvalues and/or the invariant subspace.
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| pure subroutine, public | la_lapack_eigv_gen2::la_chseqr (job, compz, n, ilo, ihi, h, ldh, w, z, ldz, work, lwork, info) |
| | CHSEQR: computes the eigenvalues of a Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors. Optionally Z may be postmultiplied into an input unitary matrix Q so that this routine can give the Schur factorization of a matrix A which has been reduced to the Hessenberg form H by the unitary matrix Q: A = Q*H*Q**H = (QZ)*T*(QZ)**H.
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| pure subroutine, public | la_lapack_eigv_gen2::la_zhseqr (job, compz, n, ilo, ihi, h, ldh, w, z, ldz, work, lwork, info) |
| | ZHSEQR: computes the eigenvalues of a Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors. Optionally Z may be postmultiplied into an input unitary matrix Q so that this routine can give the Schur factorization of a matrix A which has been reduced to the Hessenberg form H by the unitary matrix Q: A = Q*H*Q**H = (QZ)*T*(QZ)**H.
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| pure subroutine, public | la_lapack_eigv_gen2::la_whseqr (job, compz, n, ilo, ihi, h, ldh, w, z, ldz, work, lwork, info) |
| | WHSEQR: computes the eigenvalues of a Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors. Optionally Z may be postmultiplied into an input unitary matrix Q so that this routine can give the Schur factorization of a matrix A which has been reduced to the Hessenberg form H by the unitary matrix Q: A = Q*H*Q**H = (QZ)*T*(QZ)**H.
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1.13.2