SRC/dorbdb2.f(3)

🎀 NAME 🎀

okay so bestie, welcome to SRC/dorbdb2.f(3) from the Library Functions Manual — this is the page for the DORBDB2 routine, and it's giving linear-algebra main character energy. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

Here's the handshake, no cap:

subroutine dorbdb2 (m, p, q, x11, ldx11, x21, ldx21, theta, phi, taup1,
    taup2, tauq1, work, lwork, info)
    DORBDB2

🦋 Function/Subroutine Documentation 🦋

Full signature, exactly as it appears:

subroutine dorbdb2 (integer m, integer p, integer q, double precision,
    dimension(ldx11,*) x11, integer ldx11, double precision,
    dimension(ldx21,*) x21, integer ldx21, double precision, dimension(*)
    theta, double precision, dimension(*) phi, double precision,
    dimension(*) taup1, double precision, dimension(*) taup2, double
    precision, dimension(*) tauq1, double precision, dimension(*) work,
    integer lwork, integer info)
    DORBDB2

🌸 Purpose 🌸

DORBDB2 simultaneously bidiagonalizes the blocks of a tall and skinny matrix X with orthonormal columns. The vibe is literally this:

                            [ B11 ]
      [ X11 ]   [ P1 |    ] [  0  ]
      [-----] = [---------] [-----] Q1**T .
      [ X21 ]   [    | P2 ] [ B21 ]
                            [  0  ]

X11 is P-by-Q, and X21 is (M-P)-by-Q. P must be no larger than M-P, Q, or M-Q. Routines DORBDB1, DORBDB3, and DORBDB4 handle the cases in which P is not the minimum dimension.

The orthogonal matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P), and (M-Q)-by-(M-Q), respectively. They're represented implicitly by Householder vectors.

B11 and B12 are P-by-P bidiagonal matrices represented implicitly by angles THETA, PHI.

🍓 Parameters 🍓

• M — M is INTEGER. It's literally the number of rows in X11 plus the number of rows in X21.
• P — P is INTEGER — the number of rows in X11. The range is 0 <= P <= min(M-P,Q,M-Q).
• Q — Q is INTEGER — the number of columns in X11 and X21. The range is 0 <= Q <= M.
• X11 — X11 is DOUBLE PRECISION array, dimension (LDX11,Q). On entry, it's the top block of the matrix X to be reduced. On exit, the columns of tril(X11) specify reflectors for P1, and the rows of triu(X11,1) specify reflectors for Q1.
• LDX11 — LDX11 is INTEGER — the leading dimension of X11. It has to satisfy LDX11 >= P.
• X21 — X21 is DOUBLE PRECISION array, dimension (LDX21,Q). On entry, it's the bottom block of the matrix X to be reduced. On exit, the columns of tril(X21) specify reflectors for P2.
• LDX21 — LDX21 is INTEGER — the leading dimension of X21. It has to satisfy LDX21 >= M-P.
• THETA — THETA is DOUBLE PRECISION array, dimension (Q). The entries of the bidiagonal blocks B11, B21 are defined by THETA and PHI. See Further Details.
• PHI — PHI is DOUBLE PRECISION array, dimension (Q-1). The entries of the bidiagonal blocks B11, B21 are defined by THETA and PHI. See Further Details.
• TAUP1 — TAUP1 is DOUBLE PRECISION array, dimension (P-1). The scalar factors of the elementary reflectors that define P1.
• TAUP2 — TAUP2 is DOUBLE PRECISION array, dimension (Q). The scalar factors of the elementary reflectors that define P2.
• TAUQ1 — TAUQ1 is DOUBLE PRECISION array, dimension (Q). The scalar factors of the elementary reflectors that define Q1.
• WORK — WORK is DOUBLE PRECISION array, dimension (LWORK).
• LWORK — LWORK is INTEGER — the dimension of the array WORK. LWORK >= M-Q. 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 👑

The author list is serving:

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

🌈 Further Details 🌈

The upper-bidiagonal blocks B11, B21 are represented implicitly by angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry in each bidiagonal band is a product of a sine or cosine of a THETA with a sine or cosine of a PHI. See [1] or DORCSD for details.

P1, P2, and Q1 are represented as products of elementary reflectors. See DORCSD2BY1 for details on generating P1, P2, and Q1 using DORGQR and DORGLQ.

📚 References 📚

• [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. Algorithms, 50(1):33-65, 2009.

Definition at line 200 of file dorbdb2.f.

💀 Author 💀

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page, bestie — LAPACK Version 3.12.0, SRC/dorbdb2.f(3), mwah 💋💖