CUNGBR(3)

💅 CUNGBR(3) — Library Functions Manual, but make it cute 💅

Hiii bestie! Welcome to the Library Functions Manual page for CUNGBR(3) 💖. The source file is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cungbr.f, and yes, we're keeping that whole path because details are sacred. No cap, this whole page is lowkey about one subroutine: CUNGBR.

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cungbr.f — that's the file. The manual name is CUNGBR(3), and the main character is the CUNGBR subroutine. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

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

📚 Function/Subroutine Documentation 📚

Here's the full signature, bestie — exact vibes, exact args:

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. Periodt.

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. It's the number of rows of the matrix Q or P**H to be returned. M >= 0.

N

N is INTEGER. It's 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', it's the number of columns in the original M-by-K matrix reduced by CGEBRD. If VECT = 'P', it's 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, it's the vectors which define the elementary reflectors, as returned by CGEBRD. On exit, it's the M-by-N matrix Q or P**H.

LDA

LDA is INTEGER. It's 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. It's 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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