SRC/chpevx.f(3)

💖 NAME 💖

okay bestie, this is the SRC/chpevx.f(3) page from the Library Functions Manual ✨

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

one iconic little workhorse:

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

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

🫶 Function/Subroutine Documentation 🫶

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

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

🎯 Purpose 🎯

okay so the whole vibe is: CHPEVX 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 ✨

🌸 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 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 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 — 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 — 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 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 AP 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'). There's a cite to 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 REAL array, dimension (N) 🌸 If INFO = 0, the selected eigenvalues in ascending order.
• Z — Z is COMPLEX 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 array, dimension (2*N) 💻
• RWORK — RWORK is REAL 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 chpevx.f. 🎀

💜 Author 💜

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