SRC/chpgv.f(3)

💅 SRC/chpgv.f — like, the chpgv era 🫶

okay bestie, welcome to the chpgv page from the LAPACK Library Functions Manual ✨ this is a Fortran subroutine page and honestly it's giving main character energy for anyone doing generalized Hermitian-definite eigenproblems. sit down, grab a strawberry 🍓, we're doing this.

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🌸 SYNOPSIS 🌸

Functions/Subroutines

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

it's CHPGV, no cap 🔥

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✨ Function/Subroutine Documentation ✨

subroutine chpgv (integer itype, character jobz, character uplo, integer n, complex, dimension( * ) ap, complex, dimension( * ) bp, real, dimension( * ) w, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

so that's CHPGV — same name, now with the whole squad of arguments 💜

🎀 Purpose 🎀

!>
!> CHPGV 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.
!>

so like, CHPGV gives you all the eigenvalues and, if you want them, the eigenvectors too — for a complex generalized Hermitian-definite eigenproblem. the three flavors are A*x=(lambda)*B*x, A*Bx=(lambda)*x, and B*A*x=(lambda)*x. A and B are assumed Hermitian and packed, and B also has to be positive definite. periodt 💅

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🌈 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
!>

ITYPE is an INTEGER and it picks which problem type you're solving, iykyk:

• = 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.
!>

JOBZ is CHARACTER*1 — do you want just the eigenvalues or the whole package?

• = 'N': eigenvalues only, minimal effort, respect
• = 'V': eigenvalues and eigenvectors, go off 👑

UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangles of A and B are stored;
!>          = 'L':  Lower triangles of A and B are stored.
!>

UPLO is CHARACTER*1 and it tells us which triangle you actually stored:

• = 'U': the upper triangles of A and B are stored
• = 'L': the lower triangles of A and B are stored

N

!>          N is INTEGER
!>          The order of the matrices A and B.  N >= 0.
!>

N is an INTEGER — the order of the matrices A and B. and N >= 0, fr fr.

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, the contents of AP are destroyed.
!>

AP is a COMPLEX array, dimension (N*(N+1)/2). on entry it's the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. the j-th column of A lives in AP like this:

• 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. not me warning you twice — bestie, save your data before you call this 😭

BP

!>          BP is COMPLEX 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.
!>

BP is a COMPLEX array, dimension (N*(N+1)/2). on entry it holds the upper or lower triangle of the Hermitian matrix B, packed columnwise in a linear array. the j-th column of B sits in BP like so:

• 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 it gets rewritten as 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. glow-up tbh 🦋

W

!>          W is REAL array, dimension (N)
!>          If INFO = 0, the eigenvalues in ascending order.
!>

W is a REAL array, dimension (N). if INFO = 0, these are the eigenvalues, in ascending order ✨ (organized queen behavior)

Z

!>          Z is COMPLEX 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.
!>

Z is a COMPLEX array, dimension (LDZ, N). if JOBZ = 'V' and INFO = 0, Z contains the matrix Z of eigenvectors, normalized like this:

• 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 at all. she's literally not invited to the function call 🙈

LDZ

!>          LDZ is INTEGER
!>          The leading dimension of the array Z.  LDZ >= 1, and if
!>          JOBZ = 'V', LDZ >= max(1,N).
!>

LDZ is an INTEGER — the leading dimension of the array Z. constraints: LDZ >= 1, and if JOBZ = 'V', then LDZ >= max(1,N). respect the bounds or the compiler will come for you 💀

WORK

!>          WORK is COMPLEX array, dimension (max(1, 2*N-1))
!>

WORK is a COMPLEX array, dimension (max(1, 2*N-1)). it's the workspace, it's doing its thing 🧚

RWORK

!>          RWORK is REAL array, dimension (max(1, 3*N-2))
!>

RWORK is a REAL array, dimension (max(1, 3*N-2)). the real-valued workspace counterpart, she's matching vibes with WORK 💖

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          > 0:  CPPTRF or CHPEV returned an error code:
!>             <= N:  if INFO = i, CHPEV 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.
!>

INFO is an INTEGER and it's the vibe check at the end:

• = 0: successful exit, we ate 🎀
• < 0: if INFO = -i, the i-th argument had an illegal value — somebody passed something cursed
• > 0: CPPTRF or CHPEV returned an error code:
  • <= N: if INFO = i, CHPEV failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero (yes, the original says "convergeto" — we keep it exactly, character for character 💅)
  • > 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. worst case scenario, honestly 😭

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👑 Author 👑

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

legendary lineup, no notes 🌟

Definition at line 163 of file chpgv.f.

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🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code. (the robots wrote this one, and honestly they slayed)

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okay bestie that's the whole page 🫶 this was LAPACK, Version 3.12.0, SRC/chpgv.f(3) — go forth and compute those eigenvalues, and remember: back up AP before you do 🌸✨💜