SRC/zgsvj1.f(3)

💖 NAME

SRC/zgsvj1.f — and okurrr, this page is SRC/zgsvj1.f(3) from the Library Functions Manual 💅✨

---

🛰️ SYNOPSIS

🧚 Functions/Subroutines

subroutine zgsvj1 (jobv, m, n, n1, a, lda, d, sva, mv, v, ldv, eps,
    sfmin, tol, nsweep, work, lwork, info)

okay so ZGSVJ1 is a pre-processor for the routine zgesvj, and it applies Jacobi rotations targeting only particular pivots. periodt. 💫

---

🧚 Function/Subroutine Documentation

   subroutine zgsvj1 (character*1 jobv, integer m, integer n, integer n1,
       complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( n
       ) d, double precision, dimension( n ) sva, integer mv, complex*16,
       dimension( ldv, * ) v, integer ldv, double precision eps, double
       precision sfmin, double precision tol, integer nsweep, complex*16,
       dimension( lwork ) work, integer lwork, integer info)

ZGSVJ1 is a pre-processor for the routine zgesvj, and it applies Jacobi rotations targeting only particular pivots. iykyk 🫶

🎯 Purpose

okay so ZGSVJ1 gets called from ZGESVJ as a pre-processor, and that is literally its main purpose. It applies Jacobi rotations in the same way as ZGESVJ does, but it targets only particular pivots and it does not check convergence (the stopping criterion). A few tuning parameters — marked by [TP] — are available for the implementer. 💅

Further Details

~~~~~~~~~~~~~~~

ZGSVJ1 applies a few sweeps of Jacobi rotations in the column space of the input M-by-N matrix A. The pivot pairs are taken from the (1,2) off-diagonal block in the corresponding N-by-N Gram matrix A^T * A. The block-entries (tiles) of the (1,2) off-diagonal block are marked by the [x]'s in this scheme:

   | *  *  * [x] [x] [x]|
   | *  *  * [x] [x] [x]|    Row-cycling in the nblr-by-nblc [x] blocks.
   | *  *  * [x] [x] [x]|    Row-cyclic pivoting inside each [x] block.
   |[x] [x] [x] *  *  * |
   |[x] [x] [x] *  *  * |
   |[x] [x] [x] *  *  * |

In terms of the columns of A, the first N1 columns are rotated 'against' the remaining N-N1 columns, trying to increase the angle between the corresponding subspaces. The off-diagonal block is N1-by-(N-N1) and it is tiled using quadratic tiles of side KBL. Here, KBL is a tuning parameter. The number of sweeps is given in NSWEEP and the orthogonality threshold is given in TOL. 🌈

🎛️ Parameters

• JOBV — CHARACTER*1. Specifies whether the output from this procedure is used to compute the matrix V:
  • = 'V': the product of the Jacobi rotations is accumulated by postmultiplying the N-by-N array V. (See the description of V.)
  • = 'A': the product of the Jacobi rotations is accumulated by postmultiplying the MV-by-N array V. (See the descriptions of MV and V.)
  • = 'N': the Jacobi rotations are not accumulated. no accumulation, no problem.
• M — INTEGER. The number of rows of the input matrix A. M >= 0.
• N — INTEGER. The number of columns of the input matrix A. M >= N >= 0.
• N1 — INTEGER. N1 specifies the 2 x 2 block partition, the first N1 columns are rotated 'against' the remaining N-N1 columns of A.
• A — COMPLEX*16 array, dimension (LDA,N). On entry, M-by-N matrix A, such that A*diag(D) represents the input matrix. On exit, A_onexit * D_onexit represents the input matrix A*diag(D) post-multiplied by a sequence of Jacobi rotations, where the rotation threshold and the total number of sweeps are given in TOL and NSWEEP, respectively. (See the descriptions of N1, D, TOL and NSWEEP.)
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• D — COMPLEX*16 array, dimension (N). The array D accumulates the scaling factors from the fast scaled Jacobi rotations. On entry, A*diag(D) represents the input matrix. On exit, A_onexit*diag(D_onexit) represents the input matrix post-multiplied by a sequence of Jacobi rotations, where the rotation threshold and the total number of sweeps are given in TOL and NSWEEP, respectively. (See the descriptions of N1, A, TOL and NSWEEP.)
• SVA — DOUBLE PRECISION array, dimension (N). On entry, SVA contains the Euclidean norms of the columns of the matrix A*diag(D). On exit, SVA contains the Euclidean norms of the columns of the matrix onexit*diag(D_onexit). (yes, that's onexit exactly as written — I'm not fixing it, bestie)
• MV — INTEGER. If JOBV = 'A', then MV rows of V are post-multiplied by a sequence of Jacobi rotations. If JOBV = 'N', then MV is not referenced.
• V — COMPLEX*16 array, dimension (LDV,N). If JOBV = 'V' then N rows of V are post-multiplied by a sequence of Jacobi rotations. If JOBV = 'A' then MV rows of V are post-multiplied by a sequence of Jacobi rotations. If JOBV = 'N', then V is not referenced.
• LDV — INTEGER. The leading dimension of the array V, LDV >= 1. If JOBV = 'V', LDV >= N. If JOBV = 'A', LDV >= MV.
• EPS — DOUBLE PRECISION. EPS = DLAMCH('Epsilon').
• SFMIN — DOUBLE PRECISION. SFMIN = DLAMCH('Safe Minimum').
• TOL — DOUBLE PRECISION. TOL is the threshold for Jacobi rotations. For a pair A(:,p), A(:,q) of pivot columns, the Jacobi rotation is applied only if ABS(COS(angle(A(:,p),A(:,q)))) > TOL. threshold slay.
• NSWEEP — INTEGER. NSWEEP is the number of sweeps of Jacobi rotations to be performed.
• WORK — COMPLEX*16 array, dimension (LWORK).
• LWORK — INTEGER. LWORK is the dimension of WORK. LWORK >= M.
• INFO — INTEGER. = 0: successful exit. < 0: if INFO = -i, then the i-th argument had an illegal value. rude, but informative.

👑 Author

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

🌟 Contributor:

Zlatko Drmac (Zagreb, Croatia)

Definition at line 234 of file zgsvj1.f.

---

🧾 Author

Generated automatically by Doxygen for LAPACK from the source code.

---

Later, bestie 💖 This lil' page is from LAPACK Version 3.12.0, source SRC/zgsvj1.f(3) — the footer energy is literally LAPACK Version 3.12.0 + SRC/zgsvj1.f(3), and there's no separate date on this one. 🎀🦋✨