SRC/dorcsd2by1.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

✨ NAME ✨

okay so bestie, this is SRC/dorcsd2by1.f(3), page from the Library Functions Manual 💖. The file in the spotlight is SRC/dorcsd2by1.f, and it's literally here to explain DORCSD2BY1 — yes, the CS-decomposition bestie of your dreams 🫶.

🌸 SYNOPSIS 🌸

Functions/Subroutines

Here's the signature, copied exactly so no cap:

       subroutine dorcsd2by1 (jobu1, jobu2, jobv1t, m, p, q, x11, ldx11, x21,
           ldx21, theta, u1, ldu1, u2, ldu2, v1t, ldv1t, work, lwork, iwork,
           info)

And the routine's name is DORCSD2BY1 ✨.

🦋 Function/Subroutine Documentation 🦋

🌟 subroutine dorcsd2by1 — DORCSD2BY1 🌟

okay, full signature tea, exactly as written:

   subroutine dorcsd2by1 (character jobu1, character jobu2, character jobv1t,
       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(ldu1,*) u1, integer ldu1, double precision, dimension(ldu2,*)
       u2, integer ldu2, double precision, dimension(ldv1t,*) v1t, integer
       ldv1t, double precision, dimension(*) work, integer lwork, integer,
       dimension(*) iwork, integer info)

DORCSD2BY1 is the main character here 👑.

🎀 Purpose 🎀

So DORCSD2BY1 computes the CS decomposition of an M-by-Q matrix X with orthonormal columns that has been partitioned into a 2-by-1 block structure:

                               [  I1 0  0 ]
                               [  0  C  0 ]
         [ X11 ]   [ U1 |    ] [  0  0  0 ]
     X = [-----] = [---------] [----------] V1**T .
         [ X21 ]   [    | U2 ] [  0  0  0 ]
                               [  0  S  0 ]
                               [  0  0  I2]

X11 is P-by-Q. The orthogonal matrices U1, U2, and V1 are P-by-P, (M-P)-by-(M-P), and Q-by-Q, respectively. C and S are R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in which R = MIN(P,M-P,Q,M-Q). I1 is a K1-by-K1 identity matrix and I2 is a K2-by-K2 identity matrix, where K1 = MAX(Q+P-M,0), K2 = MAX(Q-P,0). That's the whole vibe check 💅.

🌈 Parameters 🌈

  • JOBU1 — JOBU1 is CHARACTER. = 'Y': U1 is computed; otherwise: U1 is not computed. no pressure bestie ✨
  • JOBU2 — JOBU2 is CHARACTER. = 'Y': U2 is computed; otherwise: U2 is not computed.
  • JOBV1T — JOBV1T is CHARACTER. = 'Y': V1T is computed; otherwise: V1T is not computed.
  • M — M is INTEGER. The number of rows in X.
  • P — P is INTEGER. The number of rows in X11. 0 <= P <= M.
  • Q — Q is INTEGER. The number of columns in X11 and X21. 0 <= Q <= M.
  • X11 — X11 is DOUBLE PRECISION array, dimension (LDX11,Q). On entry, part of the orthogonal matrix whose CSD is desired.
  • LDX11 — LDX11 is INTEGER. The leading dimension of X11. LDX11 >= MAX(1,P).
  • X21 — X21 is DOUBLE PRECISION array, dimension (LDX21,Q). On entry, part of the orthogonal matrix whose CSD is desired.
  • LDX21 — LDX21 is INTEGER. The leading dimension of X21. LDX21 >= MAX(1,M-P).
  • THETA — THETA is DOUBLE PRECISION array, dimension (R), in which R = MIN(P,M-P,Q,M-Q). C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ).
  • U1 — U1 is DOUBLE PRECISION array, dimension (P). If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1.
  • LDU1 — LDU1 is INTEGER. The leading dimension of U1. If JOBU1 = 'Y', LDU1 >= MAX(1,P).
  • U2 — U2 is DOUBLE PRECISION array, dimension (M-P). If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal matrix U2.
  • LDU2 — LDU2 is INTEGER. The leading dimension of U2. If JOBU2 = 'Y', LDU2 >= MAX(1,M-P).
  • V1T — V1T is DOUBLE PRECISION array, dimension (Q). If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal matrix V1**T.
  • LDV1T — LDV1T is INTEGER. The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >= MAX(1,Q).
  • WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. If INFO > 0 on exit, WORK(2:R) contains the values PHI(1), ..., PHI(R-1) that, together with THETA(1), ..., THETA(R), define the matrix in intermediate bidiagonal-block form remaining after nonconvergence. INFO specifies the number of nonzero PHI's.
  • LWORK — LWORK is INTEGER. The dimension of the array WORK. 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.
  • IWORK — IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q)).
  • INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: DBBCSD did not converge. See the description of WORK above for details.
bestie, the INFO > 0 case is not a slay — DBBCSD did not converge, and the WORK description above has the details 😭.

📚 References 📚

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

👑 Author 👑

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

📍 Definition 📍

Definition at line 230 of file dorcsd2by1.f.

Generated automatically by Doxygen for LAPACK from the source code.

okay bestie, final cute sign-off: this was SRC/dorcsd2by1.f(3) from the Library Functions Manual, source file SRC/dorcsd2by1.f, and LAPACK Version 3.12.0 — periodt, bye bestie 💖🦋✨

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