SRC/chpgst.f(3)

💅 NAME

SRC/chpgst.f — bestie, this is the CHPGST situation, and it's about to reduce a complex Hermitian-definite generalized eigenproblem to standard form using packed storage. Iconic behavior, honestly.

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✨ SYNOPSIS

🎀 Functions/Subroutines

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

CHPGST 💖

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🫶 Function/Subroutine Documentation

🌸 subroutine chpgst

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

CHPGST — okay so this is the whole vibe:

🔥 Purpose

CHPGST reduces a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage.

So like, here's how it goes down, depending on ITYPE:

• 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, no cap: B must have been previously factorized as U**H*U or L*L**H by CPPTRF. Like, that's a prerequisite, bestie. Not optional.

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👑 Parameters

• ITYPE — ITYPE is INTEGER. The selector, the moment, the main character:
  • = 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. Which triangle are we serving today?
  • = '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. And N >= 0, periodt. Negative N is not the vibe.
• AP — AP is 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)*(2n-j)/2) = A(i,j) for j<=i<=n.

On exit, if INFO = 0, you get the transformed matrix, stored in the same format as A. She glows up in place 💖

• BP — BP is COMPLEX array, dimension (N*(N+1)/2). This one holds the triangular factor from the Cholesky factorization of B, stored in the same format as A, exactly as returned by CPPTRF. (iykyk 🫶)
• INFO — INFO is INTEGER. The receipts:
  • = 0: successful exit ✨ slay;
  • < 0: if INFO = -i, the i-th argument had an illegal value 😭 not slay.

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🧚 Author

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

⭐ Definition at line 112 of file chpgst.f.

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🌈 Author

Generated automatically by Doxygen for LAPACK from the source code. (Not a human, just a little automaton doing its thing 🎀)

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And that's the whole page, bestie — LAPACK, Version 3.12.0, SRC/chpgst.f(3). Go forth and factorize responsibly 💜