SRC/cungbr.f(3)

🦋 SRC/cungbr.f(3) — Library Functions Manual, bestie edition 💖

okay so we're looking at SRC/cungbr.f from the Library Functions Manual, and this page is all about the routine CUNGBR. It's giving Fortran linear-algebra royalty, no cap. Let's get into it.

💅 NAME

SRC/cungbr.f

Yes bestie, the NAME section is literally just that file path. The subroutine living here is CUNGBR.

✨ SYNOPSIS

Functions/Subroutines

• subroutine cungbr (vect, m, n, k, a, lda, tau, work, lwork, info) — CUNGBR.

🫶 Function/Subroutine Documentation

🌸 subroutine cungbr

subroutine cungbr (character vect, integer m, integer n, integer k, complex,
     dimension( lda, * ) a, integer lda, complex, dimension( * ) tau,
     complex, dimension( * ) work, integer lwork, integer info)

👑 CUNGBR

🎀 Purpose

okay so CUNGBR generates one of the complex unitary matrices Q or P**H determined by CGEBRD when reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q and P**H are defined as products of elementary reflectors H(i) or G(i) respectively. slay.

• If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q is of order M:
  • if m >= k, Q = H(1) H(2) . . . H(k) and CUNGBR returns the first n columns of Q, where m >= n >= k;
  • if m < k, Q = H(1) H(2) . . . H(m-1) and CUNGBR returns Q as an M-by-M matrix.
• If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H is of order N:
  • if k < n, P**H = G(k) . . . G(2) G(1) and CUNGBR returns the first m rows of P**H, where n >= m >= k;
  • if k >= n, P**H = G(n-1) . . . G(2) G(1) and CUNGBR returns P**H as an N-by-N matrix.

💅 Parameters

• VECT — VECT is CHARACTER*1. It specifies whether the matrix Q or the matrix P**H is required, as defined in the transformation applied by CGEBRD:
  • = 'Q': generate Q;
  • = 'P': generate P**H.
• M — M is INTEGER. The number of rows of the matrix Q or P**H to be returned. M >= 0.
• N — N is INTEGER. The number of columns of the matrix Q or P**H to be returned. N >= 0. If VECT = 'Q', M >= N >= min(M,K); if VECT = 'P', N >= M >= min(N,K).
• K — K is INTEGER. If VECT = 'Q', the number of columns in the original M-by-K matrix reduced by CGEBRD. If VECT = 'P', the number of rows in the original K-by-N matrix reduced by CGEBRD. K >= 0.
• A — A is COMPLEX array, dimension (LDA,N). On entry, the vectors which define the elementary reflectors, as returned by CGEBRD. On exit, the M-by-N matrix Q or P**H.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= M.
• TAU — TAU is COMPLEX array, dimension (min(M,K)) if VECT = 'Q' (min(N,K)) if VECT = 'P'. TAU(i) must contain the scalar factor of the elementary reflector H(i) or G(i), which determines Q or P**H, as returned by CGEBRD in its array argument TAUQ or TAUP.
• WORK — WORK is COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= max(1,min(M,N)). For optimum performance LWORK >= min(M,N)*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
• INFO — 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 156 of file cungbr.f.

💜 Author

Generated automatically by Doxygen for LAPACK from the source code.

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byeee bestie 🫶💖 source/version vibe: LAPACK Version 3.12.0 · file: SRC/cungbr.f(3) · date: not shown on the page, so I'm not inventing one 💀✨ periodt.