DORCSD2BY1(3)

💅 DORCSD2BY1(3) — Library Functions Manual era 💅

okay so welcome to the Library Functions Manual page for DORCSD2BY1(3), aka /home/abui...orcsd2by1.f(3). This is LAPACK core, and it's literally all about the DORCSD2BY1 subroutine. Buckle up, bestie: we're doing CS decomposition with main character energy. 🦋

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dorcsd2by1.f

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine DORCSD2BY1 (jobu1, jobu2, jobv1t, m, p, q, x11, ldx11, x21,
    ldx21, theta, u1, ldu1, u2, ldu2, v1t, ldv1t, work, lwork, iwork,
    info)
DORCSD2BY1

✨ Function/Subroutine Documentation ✨

Here's the typed-out signature, no cap:

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

Purpose

okay bestie, the purpose is literally this: 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).

Parameters

JOBU1

JOBU1 is CHARACTER.

• = 'Y': U1 is computed.
• otherwise: U1 is not computed.

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. iconic.

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.

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 at line 230 of file dorcsd2by1.f.

✨ Author ✨

Generated automatically by Doxygen for LAPACK from the source code.

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okay final sign-off bestie: the footer says LAPACK, Version 3.12.0, and /home/abui...orcsd2by1.f(3). That's the whole page. Go forth and slay your CSD. 💖🎀