CHBGST(3)

okay bestie, welcome to CHBGST(3) from the Library Functions Manual — this is literally the LAPACK page for chbgst.f, and it's giving main character energy. 💖✨

🌸 NAME 🌸

the NAME section is just this path, no cap:

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

✨ SYNOPSIS ✨

Functions/Subroutines

here's the function/subroutine tea, copied exactly because we do not play with signatures:

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

🔥 Function/Subroutine Documentation 🔥

now the full documentation era. same subroutine, but with all the types and dimensions spelled out:

   subroutine CHBGST (character vect, character uplo, integer n, integer ka,
       integer kb, complex, dimension( ldab, * ) ab, integer ldab, complex,
       dimension( ldbb, * ) bb, integer ldbb, complex, dimension( ldx, * ) x,
       integer ldx, complex, dimension( * ) work, real, dimension( * ) rwork,
       integer info)
       CHBGST

CHBGST

🎀 Purpose 🎀

okay so the purpose is the transformation moment: CHBGST 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. this ate and left no crumbs. 💅

B must have been previously factorized as S**H*S by CPBSTF, 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. periodt. 🦋

🌈 Parameters 🌈

vibe check on every parameter, bestie:

• 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 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 array, dimension (LDBB,N). The banded factor S from the split Cholesky factorization of B, as returned by CPBSTF, 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 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 array, dimension (N).
• RWORK — RWORK is REAL array, dimension (N).
• INFO — INFO is INTEGER; = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value.

🌟 Author 🌟

the institutions behind this banger, fr fr:

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

Definition at line 163 of file chbgst.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

---

okay that's the whole page, bestie. Sign-off: LAPACK Version 3.12.0, at /home/abui...RC/chbgst.f(3). Mwah 💋✨