ZUNCSD2BY1(3)

📦 version 3.12.0, in opensuse-leap 16.0

🎀 ZUNCSD2BY1(3) — LAPACK Library Functions Manual 🎀

okay so bestie, this is the <pink>ZUNCSD2BY1(3)</pink> page from the Library Functions Manual, and the header path reads /home/abui...uncsd2by1.f(3). We are keeping every single dimension, flag, and Fortran-typed parameter exactly as the source intended. No cap. 💅

🌸 NAME 🌸

  • /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zuncsd2by1.f — that's the source file, bestie. This whole page is its manual, and it's giving iconic linear-algebra energy. 🦋

✨ SYNOPSIS ✨

💜 Functions/Subroutines 💜

       subroutine ZUNCSD2BY1 (jobu1, jobu2, jobv1t, m, p, q, x11, ldx11, x21,
           ldx21, theta, u1, ldu1, u2, ldu2, v1t, ldv1t, work, lwork, rwork,
           lrwork, iwork, info)
           ZUNCSD2BY1

🦋 Function/Subroutine Documentation 🦋

💜 subroutine ZUNCSD2BY1 💜

   subroutine ZUNCSD2BY1 (character jobu1, character jobu2, character jobv1t,
       integer m, integer p, integer q, complex*16, dimension(ldx11,*) x11,
       integer ldx11, complex*16, dimension(ldx21,*) x21, integer ldx21, 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(*) work,
       integer lwork, double precision, dimension(*) rwork, integer lrwork,
       integer, dimension(*) iwork, integer info)
       ZUNCSD2BY1

🎯 Purpose 🎯

okay so <pink>ZUNCSD2BY1</pink> 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. The layout is literally this iconic:

                               [  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 unitary 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). Periodt. 👑

🔧 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. 🫶
  • 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 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). 🔥
  • 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 X21. LDX21 >= MAX(1,M-P). ⭐
  • THETA — THETA is DOUBLE PRECISION array, dimension (R), in which R = MIN(P,M-P,Q,M-Q). Also: C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ). 😭
  • U1 — U1 is COMPLEX*16 array, dimension (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 (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 (Q). If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary matrix V1**T. 🧚
  • LDV1T — LDV1T is INTEGER. The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >= MAX(1,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 and RWORK arrays, returns this value as the first entry of the WORK and RWORK array, respectively, and no error message related to LWORK or LRWORK 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 WORK and RWORK arrays, returns this value as the first entry of the WORK and RWORK array, respectively, and no error message related to LWORK or 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 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 📌

Definition at line 252 of file zuncsd2by1.f. ✨

📝 Author 📝

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xoxo, LAPACK Version 3.12.0 💖 — footer source: /home/abui...uncsd2by1.f(3) ✨ (no date was printed on the original footer, bestie) 🫶

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