ZHPGST(3)

🎀 NAME 🎀

okay bestie, welcome to the Library Functions Manual page for ZHPGST(3) — yes, the packed-storage Hermitian-definite generalized eigenproblem girlies are thriving 💅. The source file is literally:

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

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✨ SYNOPSIS ✨

Under Functions/Subroutines, the main character is:

subroutine ZHPGST (itype, uplo, n, ap, bp, info)

and the full signature is giving:

subroutine ZHPGST (integer itype, character uplo, integer n, complex*16,
     dimension( * ) ap, complex*16, dimension( * ) bp, integer info)

ZHPGST — that’s the routine. Iconic. 🫶

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💖 Function/Subroutine Documentation 💖

🦋 Purpose 🦋

okay so real talk: ZHPGST reduces a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage. That’s the whole assignment, no cap.

• If ITYPE = 1, the problem is A*x = lambda*B*x, and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H).
• If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L.

Important, bestie: B must have been previously factorized as U**H*U or L*L**H by ZPPTRF.

💅 Parameters 💅

🌸 ITYPE 🌸

• ITYPE — is INTEGER
  • = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H);
  • = 2 or 3: compute U*A*U**H or L**H*A*L.

🌸 UPLO 🌸

• UPLO — is CHARACTER*1
  • = 'U': Upper triangle of A is stored and B is factored as U**H*U;
  • = 'L': Lower triangle of A is stored and B is factored as L*L**H.

🌸 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)*(2n-j)/2) = A(i,j) for j<=i<=n.

On exit, if INFO = 0, the transformed matrix, stored in the same format as A.

🌸 BP 🌸

• BP — is COMPLEX*16 array, dimension (N*(N+1)/2). The triangular factor from the Cholesky factorization of B, stored in the same format as A, as returned by ZPPTRF.

🌸 INFO 🌸

• INFO — is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

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👑 Author 👑

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

Definition at line 112 of file zhpgst.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie 🫶. Footer vibes: LAPACK Version 3.12.0, and the file path shown as /home/abui...RC/zhpgst.f(3). No date is shown on this page, so I’m not gonna invent one — periodt 💅✨