SGBBRD(3)

💖 SGBBRD(3) — the band-matrix glow-up 💖

okay bestie, this is the LAPACK Library Functions Manual page for SGBBRD, a.k.a. the file sgbbrd.f. we're doing real Fortran band-matrix reduction and making it cute. no cap, it's giving main character energy in a library full of decompositions.

🌸 NAME 🌸

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

✨ SYNOPSIS ✨

💫 Functions/Subroutines 💫

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

🦋 Function/Subroutine Documentation 🦋

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

💖 Purpose 💖

okay so the whole vibe: SGBBRD reduces a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.

The routine computes B, and optionally forms Q or P**T, or computes Q**T*C for a given matrix C. it's giving decomposition with options, and we love that for us.

✨ Parameters ✨

• VECT — CHARACTER*1. Specifies whether or not the matrices Q and P**T are to be formed. the option menu is right here:
  • = 'N': do not form Q or P**T;
  • = 'Q': form Q only;
  • = 'P': form P**T only;
  • = 'B': form both.
• M — INTEGER. The number of rows of the matrix A. M >= 0.
• N — INTEGER. The number of columns of the matrix A. N >= 0.
• NCC — INTEGER. The number of columns of the matrix C. NCC >= 0.
• KL — INTEGER. The number of subdiagonals of the matrix A. KL >= 0.
• KU — INTEGER. The number of superdiagonals of the matrix A. KU >= 0.
• AB — REAL 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 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.
• LDAB — INTEGER. The leading dimension of the array A. LDAB >= KL+KU+1.
• D — REAL array, dimension (min(M,N)). The diagonal elements of the bidiagonal matrix B.
• E — REAL array, dimension (min(M,N)-1). The superdiagonal elements of the bidiagonal matrix B.
• Q — REAL 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.
• LDQ — INTEGER. The leading dimension of the array Q. LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise.
• PT — REAL 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 — INTEGER. The leading dimension of the array PT. LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise.
• C — REAL 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 — INTEGER. The leading dimension of the array C. LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0.
• WORK — REAL array, dimension (2*max(M,N)).
• INFO — INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. so if something smells off, check that INFO tea.

👑 Author 👑

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

Definition at line 185 of file sgbbrd.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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💖 cute sign-off, bestie: the footer says LAPACK, Version 3.12.0, and the file path /home/abui...RC/sgbbrd.f(3). It doesn't show a date on this page — so that's the whole footer tea, periodt. 🎀