SRC/ssbevx.f(3)

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💖 SRC/ssbevx.f(3) 💖

okay so this is from the Library Functions Manual, and it’s the page for SRC/ssbevx.f. Buckle up bestie, we’re getting into selected eigenvalues and eigenvectors of a real symmetric band matrix A ✨

🌸 NAME 🌸

SRC/ssbevx.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

  • subroutine ssbevx (jobz, range, uplo, n, kd, ab, ldab, q, ldq, vl, vu, il, iu, abstol, m, w, z, ldz, work, iwork, ifail, info) — SSBEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine ssbevx (jobz, range, uplo, n, kd, ab, ldab, q, ldq, vl, vu,
           il, iu, abstol, m, w, z, ldz, work, iwork, ifail, info)

🫶 Function/Subroutine Documentation 🫶

🌟 subroutine ssbevx 🌟

subroutine ssbevx (character jobz, character range, character uplo, integer
     n, integer kd, real, dimension( ldab, * ) ab, integer ldab, real,
     dimension( ldq, * ) q, integer ldq, real vl, real vu, integer il,
     integer iu, real abstol, integer m, real, dimension( * ) w, real,
     dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer,
     dimension( * ) iwork, integer, dimension( * ) ifail, integer info)

SSBEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

🎯 Purpose 🎯

!> SSBEVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues. !>

🎀 Parameters 🎀

  • JOBZ — is CHARACTER*1. = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors.
  • RANGE — is CHARACTER*1. = 'A': all eigenvalues will be found; = 'V': all eigenvalues in the half-open interval (VL,VU] will be found; = 'I': the IL-th through IU-th eigenvalues will be found.
  • UPLO — is CHARACTER*1. = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.
  • N — is INTEGER. The order of the matrix A. N >= 0.
  • KD — is INTEGER. The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.
  • AB — is REAL array, dimension (LDAB, N). On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, AB is overwritten by values generated during the reduction to tridiagonal form. If UPLO = 'U', the first superdiagonal and the diagonal of the tridiagonal matrix T are returned in rows KD and KD+1 of AB, and if UPLO = 'L', the diagonal and first subdiagonal of T are returned in the first two rows of AB.

  • LDAB — is INTEGER. The leading dimension of the array AB. LDAB >= KD + 1.
  • Q — is REAL array, dimension (LDQ, N). If JOBZ = 'V', the N-by-N orthogonal matrix used in the reduction to tridiagonal form. If JOBZ = 'N', the array Q is not referenced.
  • LDQ — is INTEGER. The leading dimension of the array Q. If JOBZ = 'V', then LDQ >= max(1,N).
  • VL — is REAL. If RANGE='V', the lower bound of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'.
  • VU — is REAL. If RANGE='V', the upper bound of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'.
  • IL — is INTEGER. If RANGE='I', the index of the smallest eigenvalue to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'.
  • IU — is INTEGER. If RANGE='I', the index of the largest eigenvalue to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'.
  • ABSTOL — is REAL. The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to
ABSTOL + EPS *   max( |a|,|b| ) ,

where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing AB to tridiagonal form.

Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*SLAMCH('S'), not zero. If this routine returns with INFO>0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*SLAMCH('S').

See See by Demmel and Kahan, LAPACK Working Note #3.

  • M — is INTEGER. The total number of eigenvalues found. 0 <= M <= N. If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
  • W — is REAL array, dimension (N). The first M elements contain the selected eigenvalues in ascending order.
  • Z — is REAL array, dimension (LDZ, max(1,M)). If JOBZ = 'V', then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). If an eigenvector fails to converge, then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL. If JOBZ = 'N', then Z is not referenced. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = 'V', the exact value of M is not known in advance and an upper bound must be used.
  • LDZ — is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
  • WORK — is REAL array, dimension (7*N).
  • IWORK — is INTEGER array, dimension (5*N).
  • IFAIL — is INTEGER array, dimension (N). If JOBZ = 'V', then if INFO = 0, the first M elements of IFAIL are zero. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge. If JOBZ = 'N', then IFAIL is not referenced.
  • INFO — is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = i, then i eigenvectors failed to converge. Their indices are stored in array IFAIL.

👑 Author 👑

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

Definition at line 262 of file ssbevx.f.

👑 Author 👑

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