SRC/cgbbrd.f(3)

📦
version 3.12.1 · 4 versions
, in arch rolling

🌸 NAME 🌸

SRC/cgbbrd.f — bestie, this is the Library Functions Manual page for the CGBBRD routine 💅 It’s a LAPACK subroutine, and it’s giving very serious “I do linear algebra and I do it fabulously” energy.

✨ SYNOPSIS ✨

Functions/Subroutines

  • subroutine cgbbrd — the whole call is right here:
subroutine cgbbrd (vect, m, n, ncc, kl, ku, ab, ldab, d, e, q, ldq, pt,
    ldpt, c, ldc, work, rwork, info)
  • CGBBRD — iconic routine name, no notes.

💖 Function/Subroutine Documentation 💖

CGBBRD

subroutine cgbbrd (character vect, integer m, integer n, integer ncc,
    integer kl, integer ku, complex, dimension( ldab, * ) ab, integer ldab,
    real, dimension( * ) d, real, dimension( * ) e, complex, dimension( ldq,
    * ) q, integer ldq, complex, dimension( ldpt, * ) pt, integer ldpt,
    complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * )
    work, real, dimension( * ) rwork, integer info)

CGBBRD — okay bestie, here’s the whole vibe 😭💖

Purpose

So CGBBRD reduces a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation:

Q**H * A * P = B

It computes B, and optionally forms Q or P**H, or computes Q**H*C for a given matrix C. That’s the whole mission, and it ate 💅

Parameters

VECT

VECT is CHARACTER*1 and tells us whether or not the matrices Q and P**H are to be formed:

  • = 'N': do not form Q or P**H;
  • = 'Q': form Q only;
  • = 'P': form P**H only;
  • = 'B': form both.

M

M is INTEGER. It’s the number of rows of the matrix A. M >= 0.

N

N is INTEGER. It’s the number of columns of the matrix A. N >= 0.

NCC

NCC is INTEGER. It’s the number of columns of the matrix C. NCC >= 0.

KL

KL is INTEGER. It’s the number of subdiagonals of the matrix A. KL >= 0.

KU

KU is INTEGER. It’s the number of superdiagonals of the matrix A. KU >= 0.

AB

AB is COMPLEX array, dimension (LDAB,N).

On entry, it’s the m-by-n band matrix A, stored in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows:

AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).

On exit, A is overwritten by values generated during the reduction. So yeah, it gets transformed — track the lore 🫶

LDAB

LDAB is INTEGER. It’s the leading dimension of the array A. LDAB >= KL+KU+1.

D

D is REAL array, dimension (min(M,N)). These are the diagonal elements of the bidiagonal matrix B. Main-character entries only 👑

E

E is REAL array, dimension (min(M,N)-1). These are the superdiagonal elements of the bidiagonal matrix B.

Q

Q is COMPLEX array, dimension (LDQ,M).

If VECT = 'Q' or 'B', it’s the m-by-m unitary matrix Q. If VECT = 'N' or 'P', the array Q is not referenced. She’s only invited when she’s needed 💅

LDQ

LDQ is INTEGER. It’s the leading dimension of the array Q.

LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise.

PT

PT is COMPLEX array, dimension (LDPT,N).

If VECT = 'P' or 'B', it’s the n-by-n unitary matrix P'. If VECT = 'N' or 'Q', the array PT is not referenced. Lowkey shy until called upon.

LDPT

LDPT is INTEGER. It’s the leading dimension of the array PT.

LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise.

C

C is COMPLEX array, dimension (LDC,NCC).

On entry, it’s an m-by-ncc matrix C. On exit, C is overwritten by Q**H*C. C is not referenced if NCC = 0. Gatekept only when NCC = 0, periodt.

LDC

LDC is INTEGER. It’s the leading dimension of the array C.

LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0.

WORK

WORK is COMPLEX array, dimension (max(M,N)). It’s the workspace bestie — just vibing and holding things down.

RWORK

RWORK is REAL array, dimension (max(M,N)). Real-valued workspace, also holding it down.

INFO

INFO is INTEGER.

  • = 0: successful exit. Slay.
  • < 0: if INFO = -i, the i-th argument had an illegal value. Read the room, bestie 💀

Author

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

Definition at line 191 of file cgbbrd.f.

👑 Author 👑

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k bye bestie 💖 this page came from LAPACK Version 3.12.0 and lives at SRC/cgbbrd.f(3) ✨🫶

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