SRC/zhpgst.f(3)

🎀 NAME 🎀

SRC/zhpgst.f is the page, bestie — it lives in the Library Functions Manual, and it's all about the ZHPGST subroutine. 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

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

🌸 Function/Subroutine Documentation 🌸

⭐ subroutine zhpgst

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

💖 Purpose 💖

Okay so ZHPGST reduces a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage. Periodt.

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.

B must have been previously factorized as U**H*U or L*L**H by ZPPTRF. No cap, that's required. 🫶

🦋 Parameters 🦋

• 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 — 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 — is INTEGER; the order of the matrices A and B. N >= 0.
• 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)*(2n-j)/2) = A(i,j) for j<=i<=n.

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

• BP — is COMPLEX*16 array, dimension (N*(N+1)/2). This is the triangular factor from the Cholesky factorization of B, stored in the same format as A, as returned by ZPPTRF.
• INFO — is INTEGER:
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

👑 Author 👑

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

📍 Definition

Definition at line 112 of file zhpgst.f.

💌 Author (generated edition) 💌

Generated automatically by Doxygen for LAPACK from the source code. 💖

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That's the whole vibe, bestie: LAPACK Version 3.12.0, page SRC/zhpgst.f(3) — mwah. 🍓💋