SRC/zuncsd.f(3)

📦

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💜 SRC/zuncsd.f — from the Library Functions Manual (section 3) 💜

ok so bestie. this is the manual page for SRC/zuncsd.f, and it's a whole mood. it's the docs for the recursive subroutine zuncsd, and no cap, it's a lot — but we're gonna get through it together, i promise 🫶

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

recursive subroutine zuncsd (jobu1, jobu2, jobv1t, jobv2t, trans, signs,
    m, p, q, x11, ldx11, x12, ldx12, x21, ldx21, x22, ldx22, theta, u1,
    ldu1, u2, ldu2, v1t, ldv1t, v2t, ldv2t, work, lwork, rwork, lrwork,
    iwork, info)

ZUNCSD

🦋 Function/Subroutine Documentation 🦋

👑 the full signature, bestie

recursive subroutine zuncsd (character jobu1, character jobu2, character
    jobv1t, character jobv2t, character trans, character signs, integer m,
    integer p, integer q, complex*16, dimension( ldx11, * ) x11, integer
    ldx11, complex*16, dimension( ldx12, * ) x12, integer ldx12, complex*16,
    dimension( ldx21, * ) x21, integer ldx21, complex*16, dimension( ldx22,
    * ) x22, integer ldx22, double precision, dimension( * ) theta,
    complex*16, dimension( ldu1, * ) u1, integer ldu1, complex*16,
    dimension( ldu2, * ) u2, integer ldu2, complex*16, dimension( ldv1t, * )
    v1t, integer ldv1t, complex*16, dimension( ldv2t, * ) v2t, integer
    ldv2t, complex*16, dimension( * ) work, integer lwork, double precision,
    dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork,
    integer info)

ZUNCSD

🎀 Purpose 🎀

ok so what does this icon actually do. ZUNCSD computes the CS decomposition of an M-by-M partitioned unitary matrix X. that's it. that's the whole vibe. 💅

here's the picture, and honestly, it's giving art:

                                [  I  0  0 |  0  0  0 ]
                                [  0  C  0 |  0 -S  0 ]
    [ X11 | X12 ]   [ U1 |    ] [  0  0  0 |  0  0 -I ] [ V1 |    ]**H
X = [-----------] = [---------] [---------------------] [---------]   .
    [ X21 | X22 ]   [    | U2 ] [  0  0  0 |  I  0  0 ] [    | V2 ]
                                [  0  S  0 |  0  C  0 ]
                                [  0  0  I |  0  0  0 ]

X11 is P-by-Q. the unitary matrices U1, U2, V1, and V2 are P-by-P, (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-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).

literally the whole thing. slay. ⭐

🌸 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.

💖 JOBV2T

JOBV2T is CHARACTER.

= 'Y': V2T is computed;
otherwise: V2T is not computed.

💖 TRANS

TRANS is CHARACTER.

= 'T': X, U1, U2, V1T, and V2T are stored in row-major order;
otherwise: X, U1, U2, V1T, and V2T are stored in column-major order.

💖 SIGNS

SIGNS is CHARACTER.

= 'O': the lower-left block is made nonpositive (the convention);
otherwise: the upper-right block is made nonpositive (the convention).

iykyk, both of those are "the convention" — that's exactly what the page says, so i'm not gonna pretend otherwise 🙈

💖 M

M is INTEGER. the number of rows and columns in X.

💖 P

P is INTEGER. the number of rows in X11 and X12. 0 <= P <= M.

💖 Q

Q is INTEGER. the number of columns in X11 and X21. 0 <= Q <= M.

💖 X11

X11 is COMPLEX*16 array, dimension (LDX11,Q). on entry, part of the unitary matrix whose CSD is desired.

💖 LDX11

LDX11 is INTEGER. the leading dimension of X11. LDX11 >= MAX(1,P).

💖 X12

X12 is COMPLEX*16 array, dimension (LDX12,M-Q). on entry, part of the unitary matrix whose CSD is desired.

💖 LDX12

LDX12 is INTEGER. the leading dimension of X12. LDX12 >= MAX(1,P).

💖 X21

X21 is COMPLEX*16 array, dimension (LDX21,Q). on entry, part of the unitary matrix whose CSD is desired.

💖 LDX21

LDX21 is INTEGER. the leading dimension of X11. LDX21 >= MAX(1,M-P).

💖 X22

X22 is COMPLEX*16 array, dimension (LDX22,M-Q). on entry, part of the unitary matrix whose CSD is desired.

💖 LDX22

LDX22 is INTEGER. the leading dimension of X11. LDX22 >= MAX(1,M-P).

not me reading LDX21 and LDX22 saying "leading dimension of X11" — that's genuinely what the page says, so i'm keeping it verbatim. no cap, don't come for me 💀

💖 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 COMPLEX*16 array, dimension (LDU1,P). if JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1.

💖 LDU1

LDU1 is INTEGER. the leading dimension of U1. if JOBU1 = 'Y', LDU1 >= MAX(1,P).

💖 U2

U2 is COMPLEX*16 array, dimension (LDU2,M-P). if JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary matrix U2.

💖 LDU2

LDU2 is INTEGER. the leading dimension of U2. if JOBU2 = 'Y', LDU2 >= MAX(1,M-P).

💖 V1T

V1T is COMPLEX*16 array, dimension (LDV1T,Q). if JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary matrix V1**H.

💖 LDV1T

LDV1T is INTEGER. the leading dimension of V1T. if JOBV1T = 'Y', LDV1T >= MAX(1,Q).

💖 V2T

V2T is COMPLEX*16 array, dimension (LDV2T,M-Q). if JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) unitary matrix V2**H.

💖 LDV2T

LDV2T is INTEGER. the leading dimension of V2T. if JOBV2T = 'Y', LDV2T >= MAX(1,M-Q).

💖 WORK

WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)). on exit, if INFO = 0, WORK(1) returns the optimal LWORK.

💖 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.

💖 RWORK

RWORK is DOUBLE PRECISION array, dimension MAX(1,LRWORK). on exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. if INFO > 0 on exit, RWORK(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.

💖 LRWORK

LRWORK is INTEGER. the dimension of the array RWORK.

if LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the RWORK array, returns this value as the first entry of the work array, and no error message related to LRWORK 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: ZBBCSD did not converge. see the description of RWORK 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 314 of file zuncsd.f.

🍓 Author (the meta one) 🍓

generated automatically by Doxygen for LAPACK from the source code.

and that's the whole page bestie, we ate and left no crumbs 👑✨ this lil masterpiece was brought to you by LAPACK, Version 3.12.0, and the file formerly known as SRC/zuncsd.f(3) — mwah, go compute something iconic 💅💖

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms