SRC/zhbgst.f(3)

hey bestie 💖 welcome to SRC/zhbgst.f(3) — yes, that's the Library Functions Manual page, and we're about to make LAPACK feel like a group chat. No cap, every detail is still here.

💖 NAME

SRC/zhbgst.f — the whole page is literally about the zhbgst subroutine.

✨ SYNOPSIS

🎀 Functions/Subroutines

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

🫶 Function/Subroutine Documentation

Here's the full signature, exactly as it appears, because we do not mess with source code in this house:

   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 tea: 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.

bestie, A gets overwritten — that's not a drill, that's literally what the page says.

🌸 Parameters

• VECT — is CHARACTER*1. = 'N': do not form the transformation matrix X; = 'V': form X.
• UPLO — is CHARACTER*1. = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.
• N — is INTEGER. The order of the matrices A and B. N >= 0.
• 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 — 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 — 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 — is INTEGER. The leading dimension of the array AB. LDAB >= KA+1.
• 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 — is INTEGER. The leading dimension of the array BB. LDBB >= KB+1.
• 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 — is INTEGER. The leading dimension of the array X. LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.
• WORK — is COMPLEX*16 array, dimension (N).
• RWORK — is DOUBLE PRECISION array, dimension (N).
• 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 at line 163 of file zhbgst.f.

💜 Author

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mwah 💋 — shoutout to LAPACK Version 3.12.0 and the page SRC/zhbgst.f(3). Bye bestie! 🦋