SRC/cgesdd.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

💖 NAME 💖

SRC/cgesdd.f — bestie, welcome to the Library Functions Manual page for this iconic LAPACK routine. It’s giving “complex SVD, divide-and-conquer, main character energy.” 💅

✨ SYNOPSIS ✨

Functions/Subroutines

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

🎀 Function/Subroutine Documentation 🎀

   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 like:

     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 vibe. Don’t get it twisted, bestie.

🌸 Parameters 🌸

🌟 JOBZ

JOBZ is 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

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 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.
🫶 heads up, bestie: that “contents of A are destroyed” line is not a drill. It’s literally in the spec.

🌟 LDA

LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).

🌟 S

S is REAL array, dimension (min(M,N)). The singular values of A, sorted so that S(i) >= S(i+1).

🌟 U

U is 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

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 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 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 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

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 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.

💖 that’s the whole page, bestie — this was SRC/cgesdd.f(3), from the Library Functions Manual, LAPACK Version 3.12.0. mwah 💅✨

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