ZHPGVD(3)

🦋 ZHPGVD(3) — Library Functions Manual realness 🦋

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zhpgvd.f — yep, that's the file, and this page is its Library Functions Manual moment. The star of the show is ZHPGVD(3), bestie. 💅

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✨ SYNOPSIS ✨

🧩 Functions/Subroutines

Ok so the call is exactly this, no cap:

subroutine ZHPGVD (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, lwork,
    rwork, lrwork, iwork, liwork, info)
    ZHPGVD

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🪄 Function/Subroutine Documentation 🪄

Here's the full signature with all the types and dimensions laid out, character for character:

subroutine ZHPGVD (integer itype, character jobz, character uplo, integer n,
    complex*16, dimension( * ) ap, complex*16, dimension( * ) bp, double
    precision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integer
    ldz, complex*16, dimension( * ) work, integer lwork, double precision,
    dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork,
    integer liwork, integer info)
    ZHPGVD

🎯 Purpose

ZHPGVD computes all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem. It's giving three possible forms:

A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.

Here A and B are assumed to be Hermitian, stored in packed format, and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm. Iconic behavior, honestly. ✨

🧾 Parameters

Every single one, periodt:

• ITYPE — ITYPE is 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 — JOBZ is CHARACTER*1; = 'N': compute eigenvalues only; = 'V': compute eigenvalues and eigenvectors. Choose your fighter. 🎀
• 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.
• 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, the contents of AP are destroyed. RIP to that data, fr fr. 💀

• BP — BP is COMPLEX*16 array, dimension (N*(N+1)/2). On entry, the upper or lower triangle of the Hermitian matrix B, packed columnwise in a linear array. The j-th column of B is stored in the array BP as follows:
  • if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
  • if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.

On exit, the triangular factor U or L from the Cholesky factorization B = U**H*U or B = L*L**H, in the same storage format as B.

• W — W is DOUBLE PRECISION array, dimension (N); if INFO = 0, the eigenvalues in ascending order. Slay. ⭐
• Z — Z is COMPLEX*16 array, dimension (LDZ, N); if JOBZ = 'V', then if INFO = 0, Z 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 Z is not referenced.

• 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 (MAX(1,LWORK)); on exit, if INFO = 0, WORK(1) returns the required LWORK.
• LWORK — LWORK is INTEGER; the dimension of the array WORK.
  • If N <= 1, LWORK >= 1.
  • If JOBZ = 'N' and N > 1, LWORK >= N.
  • If JOBZ = 'V' and N > 1, LWORK >= 2*N.
  • If LWORK = -1, then a workspace query is assumed; the routine only calculates the required 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 DOUBLE PRECISION array, dimension (MAX(1,LRWORK)); on exit, if INFO = 0, RWORK(1) returns the required LRWORK.
• LRWORK — LRWORK is INTEGER; the dimension of 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 required 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 required LIWORK.
• LIWORK — LIWORK is INTEGER; the dimension of array IWORK.
  • If JOBZ = 'N' or 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 required 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. We love a clean exit. 🫶
  • < 0: if INFO = -i, the i-th argument had an illegal value.
  • > 0: ZPPTRF or ZHPEVD returned an error code:
    • <= N: if INFO = i, ZHPEVD failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero;
    • > 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. Big yikes. 😭

👑 Author

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

💖 Contributors:

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

🧵 Definition at line

Definition at line 223 of file zhpgvd.f.

🪄 Author 🪄

Generated automatically by Doxygen for LAPACK from the source code.

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Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 · /home/abui...RC/zhpgvd.f(3) — that's the sign-off, bestie. 💅✨