ZGESDD(3)

🌸 NAME 🌸

Bestie, this page is literally for the file /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zgesdd.f — that’s the ZGESDD source file. 💅

---

✨ SYNOPSIS ✨

Here’s the exact synopsis energy, no cap:

   Functions/Subroutines
       subroutine ZGESDD (jobz, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork,
           rwork, iwork, info)
           ZGESDD

---

🦋 Function/Subroutine Documentation 🦋

Signature, verbatim, because we do not play with exact code:

   subroutine ZGESDD (character jobz, integer m, integer n, complex*16,
       dimension( lda, * ) a, integer lda, double precision, dimension( * ) s,
       complex*16, dimension( ldu, * ) u, integer ldu, complex*16, dimension(
       ldvt, * ) vt, integer ldvt, complex*16, dimension( * ) work, integer
       lwork, double precision, dimension( * ) rwork, integer, dimension( * )
       iwork, integer info)
       ZGESDD

🌈 Purpose 🌈

okay so ZGESDD computes the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method. The SVD is written

     A = U * SIGMA * conjugate-transpose(V)

where SIGMA is an M-by-N matrix which is zero except for its min(m,n) diagonal elements, U is an M-by-M unitary matrix, and V is an N-by-N unitary matrix. The diagonal elements of SIGMA are the singular values of A; they are real and non-negative, and are returned in descending order. The first min(m,n) columns of U and V are the left and right singular vectors of A.

Note that the routine returns VT = V**H, not V. That’s the little plot twist, bestie. 🫶

---

🎀 Parameters 🎀

• JOBZ — JOBZ is CHARACTER*1. It specifies options for computing all or part of the matrix U:
  • 'A' — all M columns of U and all N rows of V**H are returned in the arrays U and VT;
  • 'S' — the first min(M,N) columns of U and the first min(M,N) rows of V**H are returned in the arrays U and VT;
  • 'O' — If M >= N, the first N columns of U are overwritten in the array A and all rows of V**H are returned in the array VT; otherwise, all columns of U are returned in the array U and the first M rows of V**H are overwritten in the array A;
  • 'N' — no columns of U or rows of V**H are computed.
• M — M is INTEGER. The number of rows of the input matrix A. M >= 0. 👑
• N — N is INTEGER. The number of columns of the input matrix A. N >= 0. ✨
• A — A is COMPLEX*16 array, dimension (LDA,N).
  • On entry, the M-by-N matrix A.
  • On exit,
    • if JOBZ = 'O', A is overwritten with the first N columns of U (the left singular vectors, stored columnwise) if M >= N; A is overwritten with the first M rows of V**H (the right singular vectors, stored rowwise) otherwise.
    • if JOBZ .ne. 'O', the contents of A are destroyed. 💀
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• S — S is DOUBLE PRECISION array, dimension (min(M,N)). The singular values of A, sorted so that S(i) >= S(i+1). 🍓
• U — U is COMPLEX*16 array, dimension (LDU,UCOL).
  • UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
  • UCOL = min(M,N) if JOBZ = 'S'.
  • If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M unitary matrix U;
  • if JOBZ = 'S', U contains the first min(M,N) columns of U (the left singular vectors, stored columnwise);
  • if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced. 🙈
• LDU — LDU is INTEGER. The leading dimension of the array U. LDU >= 1; if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
• VT — VT is COMPLEX*16 array, dimension (LDVT,N).
  • If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the N-by-N unitary matrix V**H;
  • if JOBZ = 'S', VT contains the first min(M,N) rows of V**H (the right singular vectors, stored rowwise);
  • if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced. 🦋
• LDVT — LDVT is INTEGER. The leading dimension of the array VT. LDVT >= 1; if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; if JOBZ = 'S', LDVT >= min(M,N).
• 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. LWORK >= 1.
  • If LWORK = -1, a workspace query is assumed. The optimal size for the WORK array is calculated and stored in WORK(1), and no other work except argument checking is performed.
  • Let mx = max(M,N) and mn = min(M,N).
  • If JOBZ = 'N', LWORK >= 2*mn + mx.
  • If JOBZ = 'O', LWORK >= 2*mn*mn + 2*mn + mx.
  • If JOBZ = 'S', LWORK >= mn*mn + 3*mn.
  • If JOBZ = 'A', LWORK >= mn*mn + 2*mn + mx.
  • These are not tight minimums in all cases; see comments inside code. For good performance, LWORK should generally be larger; a query is recommended. 🔥
• RWORK — RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)).
  • Let mx = max(M,N) and mn = min(M,N).
  • If JOBZ = 'N', LRWORK >= 5*mn (LAPACK <= 3.6 needs 7*mn);
  • else if mx >> mn, LRWORK >= 5*mn*mn + 5*mn;
  • else LRWORK >= max( 5*mn*mn + 5*mn, 2*mx*mn + 2*mn*mn + mn ). 🌸
• IWORK — IWORK is INTEGER array, dimension (8*min(M,N)). 🧚
• INFO — INFO is INTEGER.
  • < 0: if INFO = -i, the i-th argument had an illegal value.
  • = -4: if A had a NAN entry.
  • > 0: The updating process of DBDSDC did not converge.
  • = 0: successful exit. ⭐

---

👑 Author 👑

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

🌟 Contributors 🌟

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA. 🫶

📌 Definition at line 📌

Definition at line 219 of file zgesdd.f.

---

💅 Author 💅

Generated automatically by Doxygen for LAPACK from the source code.

---

LAPACK, Version 3.12.0, and the footer path /home/abui...RC/zgesdd.f(3) — that’s the cute little source/version sign-off, bestie. Bye! 💖✨