SRC/zhpevx.f(3)

🦋 SRC/zhpevx.f(3) — Library Functions Manual

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💖 NAME

SRC/zhpevx.f — the ZHPEVX page, periodt.

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✨ SYNOPSIS

🧚 Functions/Subroutines

subroutine zhpevx (jobz, range, uplo, n, ap, vl, vu, il, iu, abstol, m,
    w, z, ldz, work, rwork, iwork, ifail, info)

ZHPEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. 💅

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🫶 Function/Subroutine Documentation

subroutine zhpevx (character jobz, character range, character uplo, integer
    n, complex*16, dimension( * ) ap, double precision vl, double precision
    vu, integer il, integer iu, double precision abstol, integer m, double
    precision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integer
    ldz, complex*16, dimension( * ) work, double precision, dimension( * )
    rwork, integer, dimension( * ) iwork, integer, dimension( * ) ifail,
    integer info)

ZHPEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. 🫶

🌸 Purpose

ZHPEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage. Eigenvalues/vectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues. Iconic behavior, honestly. 👑

🎀 Parameters

• JOBZ — JOBZ is CHARACTER*1
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors.
• RANGE — 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 — UPLO is CHARACTER*1
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — N is INTEGER The order of the matrix A. N >= 0.
• AP — AP is COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, AP is overwritten by values generated during the reduction to tridiagonal form. If UPLO = 'U', the diagonal and first superdiagonal of the tridiagonal matrix T overwrite the corresponding elements of A, and if UPLO = 'L', the diagonal and first subdiagonal of T overwrite the corresponding elements of A.
• VL — VL is DOUBLE PRECISION If RANGE='V', the lower bound of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'.
• VU — VU is DOUBLE PRECISION If RANGE='V', the upper bound of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'.
• IL — 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 — 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 — ABSTOL is DOUBLE PRECISION 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 AP to tridiagonal form. Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*DLAMCH('S'), not zero. If this routine returns with INFO>0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*DLAMCH('S'). See by Demmel and Kahan, LAPACK Working Note #3.
• M — 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 — W is DOUBLE PRECISION array, dimension (N) If INFO = 0, the selected eigenvalues in ascending order.
• Z — Z is COMPLEX*16 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 — LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
• WORK — WORK is COMPLEX*16 array, dimension (2*N)
• RWORK — RWORK is DOUBLE PRECISION array, dimension (7*N)
• IWORK — IWORK is INTEGER array, dimension (5*N)
• IFAIL — 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 — 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 237 of file zhpevx.f

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👑 Author

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