ZHBGST(3)

💖 NAME 💖

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

Okay bestie, welcome to the zhbgst.f(3) page — Library Functions Manual energy, LAPACK edition. This is the source-file page for the one and only ZHBGST, and yes, the path is long enough to need its own emotional support water bottle. 💅

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✨ SYNOPSIS ✨

Functions/Subroutines — here's the callable vibe:

subroutine ZHBGST (vect, uplo, n, ka, kb, ab, ldab, bb, ldbb, x, ldx,
           work, rwork, info)

ZHBGST

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🦋 Function/Subroutine Documentation 🦋

Here's the full signature, copied exactly because we do not mess with code:

subroutine ZHBGST (character vect, character uplo, integer n, integer ka,
     integer kb, complex*16, dimension( ldab, * ) ab, integer ldab,
     complex*16, dimension( ldbb, * ) bb, integer ldbb, complex*16,
     dimension( ldx, * ) x, integer ldx, complex*16, dimension( * ) work,
     double precision, dimension( * ) rwork, integer info)

ZHBGST

🎀 Purpose 🎀

Okay so here's the glow-up: ZHBGST reduces a complex Hermitian-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, such that C has the same bandwidth as A.

B must have been previously factorized as S**H*S by ZPBSTF, using a split Cholesky factorization. A is overwritten by C = X**H*A*X, where X = S**(-1)*Q and Q is a unitary matrix chosen to preserve the bandwidth of A.

That's the whole arc, no cap. ✨

🌸 Parameters 🌸

💅 VECT 💅

VECT is CHARACTER*1

• = 'N': do not form the transformation matrix X;
• = 'V': form X.

🎀 UPLO 🎀

UPLO is CHARACTER*1

• = 'U': Upper triangle of A is stored;
• = 'L': Lower triangle of A is stored.

🦋 N 🦋

N is INTEGER

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

🌈 KA 🌈

KA is INTEGER

The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0.

🍓 KB 🍓

KB is INTEGER

The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= KB >= 0.

💜 AB 💜

AB is COMPLEX*16 array, dimension (LDAB,N)

On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first ka+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:

if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).

On exit, the transformed matrix X**H*A*X, stored in the same format as A.

🧚 LDAB 🧚

LDAB is INTEGER

The leading dimension of the array AB. LDAB >= KA+1.

🔥 BB 🔥

BB is COMPLEX*16 array, dimension (LDBB,N)

The banded factor S from the split Cholesky factorization of B, as returned by ZPBSTF, stored in the first kb+1 rows of the array.

👑 LDBB 👑

LDBB is INTEGER

The leading dimension of the array BB. LDBB >= KB+1.

🫶 X 🫶

X is COMPLEX*16 array, dimension (LDX,N)

If VECT = 'V', the n-by-n matrix X. If VECT = 'N', the array X is not referenced.

⭐ LDX ⭐

LDX is INTEGER

The leading dimension of the array X. LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.

💀 WORK 💀

WORK is COMPLEX*16 array, dimension (N)

🙈 RWORK 🙈

RWORK is DOUBLE PRECISION array, dimension (N)

🎯 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 📌

Definition at line 163 of file zhbgst.f.

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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Okay that's the whole page, bestie. 🫶 Source/version sign-off: LAPACK Version 3.12.0, footer path /home/abui...RC/zhbgst.f(3). That's the version-and-path combo we got, and it ate. Stay iconic, and may your arguments never be illegal. 💅✨