SRC/zhpgv.f(3)

🌸 NAME 🌸

SRC/zhpgv.f — okay bestie, this is the LAPACK page for the zhpgv subroutine, straight out of the LAPACK Library Functions Manual. Yes, we're reading the whole thing, and yes, it's gonna be cute but also extremely thorough. 💖

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💖 SYNOPSIS 💖

✨ Functions/Subroutines ✨

subroutine zhpgv (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, rwork,
    info)
    ZHPGV

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🦋 Function/Subroutine Documentation 🦋

subroutine zhpgv (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, double precision, dimension( * )
    rwork, integer info)
    ZHPGV

🎯 Purpose

So ZHPGV 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, stored in packed format, and B is also positive definite. That's the whole vibe. ✨

🎀 Parameters

• ITYPE — ITYPE is INTEGER. It 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.
• AP — AP is COMPLEX*16 array, dimension (N*(N+1)/2). On entry, this is 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. 😭

• BP — BP is COMPLEX*16 array, dimension (N*(N+1)/2). On entry, this is 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, this holds 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 are 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, 2*N-1)).
• RWORK — RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2)).
• INFO — INFO is INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: ZPPTRF or ZHPEV returned an error code:
    • <= N: if INFO = i, ZHPEV failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not convergeto 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.

🌟 Author

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

Definition at line 163 of file zhpgv.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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later bestie 💅 — LAPACK Version 3.12.0, SRC/zhpgv.f(3), mwah 🫶