DGBBRD(3)

🦋 DGBBRD(3) — the band-matrix glow-up page 💅

okay so this is from the Library Functions Manual, specifically the file /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgbbrd.f (yes the whole path, she's long but she's slaying). Bestie, buckle in — this is the LAPACK lore on DGBBRD, a real one. ✨

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🌸 SYNOPSIS 🌸

Functions/Subroutines 🎀

subroutine DGBBRD (vect, m, n, ncc, kl, ku, ab, ldab, d, e, q, ldq, pt,
    ldpt, c, ldc, work, info)

literally just DGBBRD. that's the whole vibe. 💖

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👑 Function/Subroutine Documentation 👑

subroutine DGBBRD (character vect, integer m, integer n, integer ncc,
    integer kl, integer ku, double precision, dimension( ldab, * ) ab,
    integer ldab, double precision, dimension( * ) d, double precision,
    dimension( * ) e, double precision, dimension( ldq, * ) q, integer ldq,
    double precision, dimension( ldpt, * ) pt, integer ldpt, double
    precision, dimension( ldc, * ) c, integer ldc, double precision,
    dimension( * ) work, integer info)

DGBBRD — main character energy, no cap. ✨

🎯 Purpose 🎯

okay so what does she even DO:

DGBBRD reduces a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.

that's the whole arc. 🌈

The routine computes B, and optionally forms Q or PT, or computes QT*C for a given matrix C. girl does it all. 💅

🌟 Parameters 🌟

• VECT — VECT is CHARACTER*1. it specifies whether or not the matrices Q and P**T are to be formed, iykyk:
  • = 'N': do not form Q or P**T;
  • = 'Q': form Q only;
  • = 'P': form P**T only;
  • = 'B': form both. 🫶
• M — M is INTEGER. The number of rows of the matrix A. M >= 0. (yes, zero is allowed, she's inclusive like that)
• N — N is INTEGER. The number of columns of the matrix A. N >= 0.
• NCC — NCC is INTEGER. The number of columns of the matrix C. NCC >= 0.
• KL — KL is INTEGER. The number of subdiagonals of the matrix A. KL >= 0.
• KU — KU is INTEGER. The number of superdiagonals of the matrix A. KU >= 0.
• AB — AB is DOUBLE PRECISION array, dimension (LDAB,N). On entry, 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, literally like this: 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 she gets a whole new look, iconic 💖)
• LDAB — LDAB is INTEGER. The leading dimension of the array A. LDAB >= KL+KU+1.
• D — D is DOUBLE PRECISION array, dimension (min(M,N)). The diagonal elements of the bidiagonal matrix B. 🌟
• E — E is DOUBLE PRECISION array, dimension (min(M,N)-1). The superdiagonal elements of the bidiagonal matrix B.
• Q — Q is DOUBLE PRECISION array, dimension (LDQ,M). If VECT = 'Q' or 'B', the m-by-m orthogonal matrix Q. If VECT = 'N' or 'P', the array Q is not referenced. (she's off-duty, don't @ her 🙈)
• LDQ — LDQ is INTEGER. The leading dimension of the array Q. LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise.
• PT — PT is DOUBLE PRECISION array, dimension (LDPT,N). If VECT = 'P' or 'B', the n-by-n orthogonal matrix P'. If VECT = 'N' or 'Q', the array PT is not referenced.
• LDPT — LDPT is INTEGER. The leading dimension of the array PT. LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise.
• C — C is DOUBLE PRECISION array, dimension (LDC,NCC). On entry, an m-by-ncc matrix C. On exit, C is overwritten by Q**T*C. C is not referenced if NCC = 0.
• LDC — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0.
• WORK — WORK is DOUBLE PRECISION array, dimension (2*max(M,N)). that's the workspace, she needs her room to think 🧚
• INFO — INFO is INTEGER:
  • = 0: successful exit. slay! 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value. (so if you see this, something you passed was lowkey not it 💀)

🫶 Author 🫶

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

Definition at line 185 of file dgbbrd.f. 📍

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. (not a human, just vibes ✨)

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aaaand that's the page, bestie! 🎀 this cutie doc came to you from LAPACK, version 3.12.0, and it lives at /home/abui...RC/dgbbrd.f(3) — go forth and reduce some band matrices, you've got this fr fr. 💖🦋🌸