CGESDD(3)

💖 CGESDD(3) 💖

🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cgesdd.f — that's the file, bestie. The header is giving /home/abui...RC/cgesdd.f(3) + Library Functions Manual + /home/abui...RC/cgesdd.f(3), and it's the CGESDD subroutine page. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

       subroutine CGESDD (jobz, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork,
           rwork, iwork, info)
           CGESDD

💅 Function/Subroutine Documentation 💅

Here's the signature in all its Fortran glory:

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

🦋 Purpose 🦋

okay so CGESDD 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. 💀

🌸 Parameters 🌸

• JOBZ — CHARACTER*1. 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 — INTEGER. The number of rows of the input matrix A. M >= 0.
• N — INTEGER. The number of columns of the input matrix A. N >= 0.
• A — COMPLEX array, dimension (LDA,N). On entry, the M-by-N matrix A. On exit:
  • if JOBZ = 'O' and M >= N, A is overwritten with the first N columns of U (the left singular vectors, stored columnwise);
  • if JOBZ = 'O' and M < N, A is overwritten with the first M rows of V**H (the right singular vectors, stored rowwise);

🚨 if JOBZ .ne. 'O', the contents of A are destroyed.

• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• S — REAL array, dimension (min(M,N)). The singular values of A, sorted so that S(i) >= S(i+1).
• U — COMPLEX 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 — INTEGER. The leading dimension of the array U. LDU >= 1; if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
• VT — COMPLEX 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 — 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 — COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — 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 — REAL 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 — INTEGER array, dimension (8*min(M,N)).
• INFO — 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 SBDSDC 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 219 of file cgesdd.f.

💾 Author 💾

Generated automatically by Doxygen for LAPACK from the source code.

---

and that's the whole page, bestie 🫶 — footer vibe: LAPACK Version 3.12.0, /home/abui...RC/cgesdd.f(3). periodt 💅✨