/home/abui...RC/zhpgv.f(3)

✨ NAME ✨

Okay bestie, welcome to the zhpgv.f(3) page from the Library Functions Manual — the header is giving truncated-path main-character energy (/home/abui...RC/zhpgv.f(3)), and the full NAME is:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zhpgv.f

This is the ZHPGV routine, and she is here to handle a complex generalized Hermitian-definite eigenproblem. Iconic. 💅

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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 💖

Here’s the whole signature, copied exactly because we do not play with function definitions:

   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 🌸

Bestie, ZHPGV computes all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form:

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. Very demure, very mindful. 🎀

🎀 Parameters 🎀

💫 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.

💫 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. 😭 So don’t come crying to AP later, she’s gone.

💫 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, BP 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. She ate and left no crumbs. ✨

💫 W 💫

W is DOUBLE PRECISION array, dimension (N)

If INFO = 0, the eigenvalues in ascending order. Periodt.

💫 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. She’s not even invited to the function. 💀

💫 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 (typo and all 😭);
  • > 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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✨ That’s the whole page, bestie! This one was generated automatically by Doxygen for LAPACK from the source code, and the footer is serving LAPACK Version 3.12.0 with /home/abui...RC/zhpgv.f(3). Periodt. 💖