hegvd(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

💖 hegvd(3) — eig, divide and conquer 💖

✨ NAME ✨

hegvd — {he,sy}gvd: eig, divide and conquer 🦋

🦋 SYNOPSIS 🦋

💅 Functions 💅

  • ```fortran subroutine chegvd (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, rwork, lrwork, iwork, liwork, info)
`CHEGVD`

- ```fortran
subroutine dsygvd (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork,
    iwork, liwork, info)

DSYGVD

  • ```fortran subroutine ssygvd (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, iwork, liwork, info)
`SSYGVD`

- ```fortran
subroutine zhegvd (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork,
    rwork, lrwork, iwork, liwork, info)

ZHEGVD

🌸 Detailed Description 🌸

Okay so this part is literally just the vibe check for the functions below — the real tea is in Function Documentation. Keep scrolling, bestie! 💖

👑 Function Documentation 👑

💫 subroutine chegvd (...) 💫

subroutine chegvd (integer itype, character jobz, character uplo, integer n,
    complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, *
    ) b, integer ldb, real, dimension( * ) w, complex, dimension( * ) work,
    integer lwork, real, dimension( * ) rwork, integer lrwork, integer,
    dimension( * ) iwork, integer liwork, integer info)

CHEGVD

🎀 Purpose 🎀

Okay so CHEGVD computes all the eigenvalues, and optionally the eigenvectors, of a complex generalized Hermitian-definite eigenproblem — the kind that looks like A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are assumed to be Hermitian, and B is also positive definite. If you want eigenvectors, it uses a divide and conquer algorithm. Slay. 💅

💅 Parameters 💅

ITYPE

ITYPE is INTEGER and specifies the problem type to be solved:

  • = 1: A*x = (lambda)*B*x
  • = 2: A*B*x = (lambda)*x
  • = 3: B*A*x = (lambda)*x

JOBZ

JOBZ is CHARACTER*1:

  • = 'N': compute eigenvalues only;
  • = 'V': compute eigenvalues and eigenvectors.

UPLO

UPLO is CHARACTER*1:

  • = 'U': upper triangles of A and B are stored;
  • = 'L': lower triangles of A and B are stored.

N

N is INTEGER. The order of the matrices A and B. N >= 0.

A

A is COMPLEX array, dimension (LDA, N). On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A.

On exit, if JOBZ = 'V', then if INFO = 0, A contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows:

  • if ITYPE = 1 or 2, Z**H*B*Z = I;
  • if ITYPE = 3, Z**H*inv(B)*Z = I.
💀 If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') or the lower triangle (if UPLO='L') of A, including the diagonal, is destroyed.

LDA

LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).

B

B is COMPLEX array, dimension (LDB, N). On entry, the Hermitian matrix B. If UPLO = 'U', the leading N-by-N upper triangular part of B contains the upper triangular part of the matrix B. If UPLO = 'L', the leading N-by-N lower triangular part of B contains the lower triangular part of the matrix B.

On exit, if INFO <= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U**H*U or B = L*L**H.

LDB

LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).

W

W is REAL array, dimension (N). If INFO = 0, the eigenvalues in ascending order.

WORK

WORK is COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER. The length of the array WORK.

  • If N <= 1, LWORK >= 1.
  • If JOBZ = 'N' and N > 1, LWORK >= N + 1.
  • If JOBZ = 'V' and N > 1, LWORK >= 2*N + N**2.

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.

RWORK

RWORK is REAL array, dimension (MAX(1,LRWORK)). On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

LRWORK

LRWORK is INTEGER. The dimension of the array RWORK.

  • If N <= 1, LRWORK >= 1.
  • If JOBZ = 'N' and N > 1, LRWORK >= N.
  • If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.

If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.

IWORK

IWORK is INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

LIWORK

LIWORK is INTEGER. The dimension of the array IWORK.

  • If N <= 1, LIWORK >= 1.
  • If JOBZ = 'N' and N > 1, LIWORK >= 1.
  • If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.

If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.

INFO

INFO is INTEGER:

  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value.
  • > 0: CPOTRF or CHEEVD returned an error code:
    • <= N: if INFO = i and JOBZ = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; if INFO = i and JOBZ = 'V', then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1);
    • > N: if INFO = N + i, for 1 <= i <= N, then the leading principal minor of order i of B is not positive. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.

🌟 Author 🌟

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

🔥 Further Details: 🔥

Modified so that no backsubstitution is performed if CHEEVD fails to converge (NEIG in old code could be greater than N causing out of bounds reference to A - reported by Ralf Meyer). Also corrected the description of INFO and the test on ITYPE. Sven, 16 Feb 05.

🫶 Contributors: 🫶

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

📍 Definition 📍

Definition at line 241 of file chegvd.f.

💫 subroutine dsygvd (...) 💫

subroutine dsygvd (integer itype, character jobz, character uplo, integer n,
    double precision, dimension( lda, * ) a, integer lda, double precision,
    dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) w,
    double precision, dimension( * ) work, integer lwork, integer,
    dimension( * ) iwork, integer liwork, integer info)

DSYGVD

🎀 Purpose 🎀

Okay so DSYGVD computes all the eigenvalues, and optionally the eigenvectors, of a real generalized symmetric-definite eigenproblem — of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are assumed to be symmetric, and B is also positive definite. If you want eigenvectors, it uses a divide and conquer algorithm. Periodt. 💅

💅 Parameters 💅

ITYPE

ITYPE is INTEGER and specifies the problem type to be solved:

  • = 1: A*x = (lambda)*B*x
  • = 2: A*B*x = (lambda)*x
  • = 3: B*A*x = (lambda)*x

JOBZ

JOBZ is CHARACTER*1:

  • = 'N': compute eigenvalues only;
  • = 'V': compute eigenvalues and eigenvectors.

UPLO

UPLO is CHARACTER*1:

  • = 'U': upper triangles of A and B are stored;
  • = 'L': lower triangles of A and B are stored.

N

N is INTEGER. The order of the matrices A and B. N >= 0.

A

A is DOUBLE PRECISION array, dimension (LDA, N). On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A.

On exit, if JOBZ = 'V', then if INFO = 0, A contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows:

  • if ITYPE = 1 or 2, Z**T*B*Z = I;
  • if ITYPE = 3, Z**T*inv(B)*Z = I.
💀 If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') or the lower triangle (if UPLO='L') of A, including the diagonal, is destroyed.

LDA

  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N). Keep it big enough bestie 💅
  • B — DOUBLE PRECISION array, dimension (LDB, N). On entry, the symmetric matrix B. If UPLO = 'U', the leading N-by-N upper triangular part of B contains the upper triangular part of the matrix B. If UPLO = 'L', the leading N-by-N lower triangular part of B contains the lower triangular part of the matrix B. On exit, if INFO <= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U**T*U or B = L*L**T. 🦋
  • LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
  • W — DOUBLE PRECISION array, dimension (N). If INFO = 0, the eigenvalues in ascending order. Periodt, sorted and gorgeous ✨
  • WORK — DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. It's giving "I brought receipts" 💅
  • LWORK — INTEGER. The dimension of the array WORK. The tea:
    • If N <= 1, LWORK >= 1.
    • If JOBZ = 'N' and N > 1, LWORK >= 2*N+1.
    • If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. Lowkey the "just tell me what you need" option, iykyk 😌

  • IWORK — INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
  • LIWORK — INTEGER. The dimension of the array IWORK.
    • If N <= 1, LIWORK >= 1.
    • If JOBZ = 'N' and N > 1, LIWORK >= 1.
    • If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.

If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. Same energy as LWORK = -1, but for the integer girlies 💜

  • INFO — INTEGER. Exit status, and it is very specific:
    • = 0: successful exit, we love to see it ✨
    • < 0: if INFO = -i, the i-th argument had an illegal value 🙈
    • > 0: DPOTRF or DSYEVD returned an error code:
      • <= N: if INFO = i and JOBZ = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; if INFO = i and JOBZ = 'V', then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1);
      • > N: if INFO = N + i, for 1 <= i <= N, then the leading principal minor of order i of B is not positive. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed. 💀 That's the "it's not you, it's your matrix" moment.

Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Further Details:

Modified so that no backsubstitution is performed if DSYEVD fails to converge (NEIG in old code could be greater than N causing out of bounds reference to A - reported by Ralf Meyer). Also corrected the description of INFO and the test on ITYPE. Sven, 16 Feb 05.

Contributors:

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 219 of file dsygvd.f.

subroutine ssygvd

subroutine ssygvd (integer itype, character jobz, character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) w, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)

SSYGVD

Purpose:

SSYGVD computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are assumed to be symmetric and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm. Divide and conquer, bestie — it's giving main character energy 🔥

Parameters

  • ITYPE — INTEGER. Specifies the problem type to be solved:
    • = 1: A*x = (lambda)*B*x
    • = 2: A*B*x = (lambda)*x
    • = 3: B*A*x = (lambda)*x
  • JOBZ — CHARACTER*1.
    • = 'N': Compute eigenvalues only;
    • = 'V': Compute eigenvalues and eigenvectors.
  • UPLO — CHARACTER*1.
    • = 'U': Upper triangles of A and B are stored;
    • = 'L': Lower triangles of A and B are stored.
  • N — INTEGER. The order of the matrices A and B. N >= 0.
  • A — REAL array, dimension (LDA, N). On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = 'V', then if INFO = 0, A contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**T*B*Z = I; if ITYPE = 3, Z**T*inv(B)*Z = I. If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') or the lower triangle (if UPLO='L') of A, including the diagonal, is destroyed. RIP to that triangle, it had a good run 😭
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • B — REAL array, dimension (LDB, N). On entry, the symmetric matrix B. If UPLO = 'U', the leading N-by-N upper triangular part of B contains the upper triangular part of the matrix B. If UPLO = 'L', the leading N-by-N lower triangular part of B contains the lower triangular part of the matrix B. On exit, if INFO <= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U**T*U or B = L*L**T. Cholesky ate and left no crumbs 🍓
  • LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
  • W — REAL array, dimension (N). If INFO = 0, the eigenvalues in ascending order. Sorted, slayed, stunning ✨
  • WORK — REAL array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
  • LWORK — INTEGER. The dimension of the array WORK.
    • If N <= 1, LWORK >= 1.
    • If JOBZ = 'N' and N > 1, LWORK >= 2*N+1.
    • If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. The "just ask, don't guess" queen 👑

  • IWORK — INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
  • LIWORK — INTEGER. The dimension of the array IWORK.
    • If N <= 1, LIWORK >= 1.
    • If JOBZ = 'N' and N > 1, LIWORK >= 1.
    • If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.

If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. Same query vibe, integer edition 🙈

  • INFO — INTEGER. Exit status, and it's giving very specific vibes:
    • = 0: successful exit ✨
    • < 0: if INFO = -i, the i-th argument had an illegal value 🙈
    • > 0: SPOTRF or SSYEVD returned an error code:
      • <= N: if INFO = i and JOBZ = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; if INFO = i and JOBZ = 'V', then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1);
      • > N: if INFO = N + i, for 1 <= i <= N, then the leading principal minor of order i of B is not positive. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed. 💀 Same drama, single precision.

Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Further Details:

(no further details in the source — it's giving minimalism ✨)

okay bestie, finishing up the ssygvd notes:

!>
!>  Modified so that no backsubstitution is performed if SSYEVD fails to
!>  converge (NEIG in old code could be greater than N causing out of
!>  bounds reference to A - reported by Ralf Meyer).  Also corrected the
!>  description of INFO and the test on ITYPE. Sven, 16 Feb 05.
!>

Contributors:

  • Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 219 of file ssygvd.f.

💜 subroutine zhegvd

subroutine zhegvd (integer itype, character jobz, character uplo, integer n,
    complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(
    ldb, * ) b, integer ldb, double precision, dimension( * ) w, complex*16,
    dimension( * ) work, integer lwork, double precision, dimension( * )
    rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork,
    integer info)

ZHEGVD — yes bestie, that’s the routine’s name, periodt.

🎀 Purpose:

okay so ZHEGVD computes all the eigenvalues, and optionally the eigenvectors, of a complex generalized Hermitian-definite eigenproblem. The forms are A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are assumed to be Hermitian, and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm. slay.

🌈 Parameters

  • ITYPE — INTEGER. Specifies the problem type to be solved:
    • = 1: A*x = (lambda)*B*x
    • = 2: A*B*x = (lambda)*x
    • = 3: B*A*x = (lambda)*x
  • JOBZ — CHARACTER*1:
    • = 'N': compute eigenvalues only;
    • = 'V': compute eigenvalues and eigenvectors.
  • UPLO — CHARACTER*1:
    • = 'U': upper triangles of A and B are stored;
    • = 'L': lower triangles of A and B are stored.
  • N — INTEGER. The order of the matrices A and B. N >= 0.
  • A — COMPLEX*16 array, dimension (LDA, N).
    • On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A.
    • On exit, if JOBZ = 'V', then if INFO = 0, A contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**H*B*Z = I; if ITYPE = 3, Z**H*inv(B)*Z = I.
    • If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') or the lower triangle (if UPLO='L') of A, including the diagonal, is destroyed. 💀
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • B — COMPLEX*16 array, dimension (LDB, N).
    • On entry, the Hermitian matrix B. If UPLO = 'U', the leading N-by-N upper triangular part of B contains the upper triangular part of the matrix B. If UPLO = 'L', the leading N-by-N lower triangular part of B contains the lower triangular part of the matrix B.
    • On exit, if INFO <= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U**H*U or B = L*L**H.
  • LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
  • W — DOUBLE PRECISION array, dimension (N). If INFO = 0, the eigenvalues in ascending order.
  • WORK — COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
  • LWORK — INTEGER. The length of the array WORK.
    • If N <= 1, LWORK >= 1.
    • If JOBZ = 'N' and N > 1, LWORK >= N + 1.
    • If JOBZ = 'V' and N > 1, LWORK >= 2*N + N**2.
    • If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.
  • RWORK — DOUBLE PRECISION array, dimension (MAX(1,LRWORK)). On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
  • LRWORK — INTEGER. The dimension of the array RWORK.
    • If N <= 1, LRWORK >= 1.
    • If JOBZ = 'N' and N > 1, LRWORK >= N.
    • If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
    • If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.
  • IWORK — INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
  • LIWORK — INTEGER. The dimension of the array IWORK.
    • If N <= 1, LIWORK >= 1.
    • If JOBZ = 'N' and N > 1, LIWORK >= 1.
    • If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
    • If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.
  • INFO — INTEGER.
    • = 0: successful exit.
    • < 0: if INFO = -i, the i-th argument had an illegal value.
    • > 0: ZPOTRF or ZHEEVD returned an error code:
      • <= N: if INFO = i and JOBZ = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; if INFO = i and JOBZ = 'V', then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1).
      • > N: if INFO = N + i, for 1 <= i <= N, then the leading principal minor of order i of B is not positive. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed. 😭

👑 Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

🔥 Further Details:

!>
!>  Modified so that no backsubstitution is performed if ZHEEVD fails to
!>  converge (NEIG in old code could be greater than N causing out of
!>  bounds reference to A - reported by Ralf Meyer).  Also corrected the
!>  description of INFO and the test on ITYPE. Sven, 16 Feb 05.
!>

🫶 Contributors:

  • Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 241 of file zhegvd.f.

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