SRC/zungbr.f(3)

💖 NAME 💖

okay so this is SRC/zungbr.f(3) from the Library Functions Manual — and the actual main character is ZUNGBR, no cap 🫶

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine zungbr (vect, m, n, k, a, lda, tau, work, lwork, info)

ZUNGBR

🦋 Function/Subroutine Documentation 🦋

subroutine zungbr (character vect, integer m, integer n, integer k,
     complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( *
     ) tau, complex*16, dimension( * ) work, integer lwork, integer info)

ZUNGBR

💅 Purpose 💅

okay bestie, ZUNGBR generates one of the complex unitary matrices Q or P**H determined by ZGEBRD 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. iconic behavior, honestly ✨

• 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 ZUNGBR returns the first n columns of Q, where m >= n >= k;
  • if m < k, Q = H(1) H(2) . . . H(m-1) and ZUNGBR 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 ZUNGBR 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 ZUNGBR returns P**H as an N-by-N matrix.

🌸 Parameters 🌸

• VECT — VECT is CHARACTER*1. Specifies whether the matrix Q or the matrix P**H is required, as defined in the transformation applied by ZGEBRD: = '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 ZGEBRD. If VECT = 'P', the number of rows in the original K-by-N matrix reduced by ZGEBRD. K >= 0.
• A — A is COMPLEX*16 array, dimension (LDA,N). On entry, the vectors which define the elementary reflectors, as returned by ZGEBRD. 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*16 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 ZGEBRD in its array argument TAUQ or TAUP.
• WORK — WORK is COMPLEX*16 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 ⭐

Definition at line 156 of file zungbr.f.

🙈 Author 🙈

Generated automatically by Doxygen for LAPACK from the source code.

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