SORMBR(3)

💅 SORMBR(3) — Library Functions Manual 💅

okay bestie, welcome to the Library Functions Manual page for SORMBR(3). This is the LAPACK subroutine that applies Q, Q**T, P, or P**T to a real matrix C from the left or right — and we are keeping every single flag, dimension, and tiny detail. no skipping, we're eating the whole thing 🍓

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✨ NAME ✨

the NAME section is just this path (the page wraps it after lapack-; here it is stitched back together so it's copy-pasteable):

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

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine SORMBR (vect, side, trans, m, n, k, a, lda, tau, c, ldc,
    work, lwork, info)
    SORMBR

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🦋 Function/Subroutine Documentation 🦋

the full signature, exactly as it appears:

subroutine SORMBR (character vect, character side, character trans, integer
    m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real,
    dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real,
    dimension( * ) work, integer lwork, integer info)
    SORMBR

✨ Purpose ✨

okay so here's the whole deal, bestie: if VECT = 'Q', SORMBR overwrites the general real M-by-N matrix C with:

                SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'T':      Q**T * C       C * Q**T

if VECT = 'P', SORMBR overwrites the general real M-by-N matrix C with:

                SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      P * C          C * P
TRANS = 'T':      P**T * C       C * P**T

here Q and P**T are the orthogonal matrices determined by SGEBRD when reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and P**T are defined as products of elementary reflectors H(i) and G(i) respectively.

let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. thus nq is the order of the orthogonal matrix Q or P**T that is applied.

if VECT = 'Q', A is assumed to have been an NQ-by-K matrix:

• if nq >= k, Q = H(1) H(2) . . . H(k);
• if nq < k, Q = H(1) H(2) . . . H(nq-1).

if VECT = 'P', A is assumed to have been a K-by-NQ matrix:

• if k < nq, P = G(1) G(2) . . . G(k);
• if k >= nq, P = G(1) G(2) . . . G(nq-1).

🎀 Parameters 🎀

• VECT — is CHARACTER*1. = 'Q': apply Q or Q**T; = 'P': apply P or P**T. pick your icon 💅
• SIDE — is CHARACTER*1. = 'L': apply Q, Q**T, P or P**T from the Left; = 'R': apply Q, Q**T, P or P**T from the Right.
• TRANS — is CHARACTER*1. = 'N': No transpose, apply Q or P; = 'T': Transpose, apply Q**T or P**T.
• M — is INTEGER. The number of rows of the matrix C. M >= 0.
• N — is INTEGER. The number of columns of the matrix C. N >= 0.
• K — is INTEGER. If VECT = 'Q', the number of columns in the original matrix reduced by SGEBRD. If VECT = 'P', the number of rows in the original matrix reduced by SGEBRD. K >= 0.
• A — is REAL array, dimension (LDA,min(nq,K)) if VECT = 'Q', or (LDA,nq) if VECT = 'P'. The vectors which define the elementary reflectors H(i) and G(i), whose products determine the matrices Q and P, as returned by SGEBRD.
• LDA — is INTEGER. The leading dimension of the array A. If VECT = 'Q', LDA >= max(1,nq); if VECT = 'P', LDA >= max(1,min(nq,K)).
• TAU — is REAL array, dimension (min(nq,K)). TAU(i) must contain the scalar factor of the elementary reflector H(i) or G(i) which determines Q or P, as returned by SGEBRD in the array argument TAUQ or TAUP.
• C — is REAL array, dimension (LDC,N). On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q or P*C or P**T*C or C*P or C*P**T.
• LDC — is INTEGER. The leading dimension of the array C. LDC >= max(1,M).
• WORK — is REAL array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — is INTEGER. The dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE = 'R', 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 — is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.

Author

the author glow-up is:

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

Definition at line

Definition at line 194 of file sormbr.f.

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🫶 Author (the Doxygen-generated one) 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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kisses bestie 💖 — this page's footer says LAPACK Version 3.12.0, and the footer path is /home/abui...RC/sormbr.f(3). there's no date printed in the footer, so I'm not inventing one — periodt. 🌈