gsvj1(3)

okay bestie, welcome to gsvj1(3) from the Library Functions Manual β€” we are deep in the gesvj step lore and it is lowkey iconic. πŸ’…

πŸŽ€ NAME πŸŽ€

gsvj1 β€” gsvj1: step in gesvj. That's the whole vibe. Slay.


✨ SYNOPSIS ✨

πŸ’… Functions πŸ’…

  • cgsvj1 β€” CGSVJ1 pre-processor for the routine cgesvj, applies Jacobi rotations targeting only particular pivots.
subroutine cgsvj1 (jobv, m, n, n1, a, lda, d, sva, mv, v, ldv, eps,
    sfmin, tol, nsweep, work, lwork, info)
  • dgsvj1 β€” DGSVJ1 pre-processor for the routine dgesvj, applies Jacobi rotations targeting only particular pivots.
subroutine dgsvj1 (jobv, m, n, n1, a, lda, d, sva, mv, v, ldv, eps,
    sfmin, tol, nsweep, work, lwork, info)
  • sgsvj1 β€” SGSVJ1 pre-processor for the routine sgesvj, applies Jacobi rotations targeting only particular pivots.
subroutine sgsvj1 (jobv, m, n, n1, a, lda, d, sva, mv, v, ldv, eps,
    sfmin, tol, nsweep, work, lwork, info)
  • zgsvj1 β€” ZGSVJ1 pre-processor for the routine zgesvj, applies Jacobi rotations targeting only particular pivots.
subroutine zgsvj1 (jobv, m, n, n1, a, lda, d, sva, mv, v, ldv, eps,
    sfmin, tol, nsweep, work, lwork, info)

πŸ¦‹ Detailed Description πŸ¦‹

bestie, the original just drops this heading and then goes straight into the function docs β€” iconic minimalism, honestly. ✨


πŸ”₯ Function Documentation πŸ”₯

πŸ‘‘ subroutine cgsvj1 πŸ‘‘

subroutine cgsvj1 (character*1 jobv, integer m, integer n, integer n1,
    complex, dimension( lda, * ) a, integer lda, complex, dimension( n ) d,
    real, dimension( n ) sva, integer mv, complex, dimension( ldv, * ) v,
    integer ldv, real eps, real sfmin, real tol, integer nsweep, complex,
    dimension( lwork ) work, integer lwork, integer info)

CGSVJ1 is a pre-processor for the routine cgesvj, and it applies Jacobi rotations targeting only particular pivots. no cap, that's the whole job. πŸ’–

🌟 Purpose 🌟

CGSVJ1 is called from CGESVJ as a pre-processor and that is its main purpose. It applies Jacobi rotations in the same way as CGESVJ does, but it targets only particular pivots and it does not check convergence (stopping criterion). Few tuning parameters (marked by [TP]) are available for the implementer.

🧚 Further Details 🧚

CGSVJ1 applies 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 the following 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.

πŸŽ€ Parameters πŸŽ€

  • JOBV β€” JOBV is 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.
  • M β€” M is INTEGER. The number of rows of the input matrix A. M >= 0.
  • N β€” N is INTEGER. The number of columns of the input matrix A. M >= N >= 0.
  • N1 β€” N1 is INTEGER. N1 specifies the 2 x 2 block partition; the first N1 columns are rotated 'against' the remaining N-N1 columns of A.
  • A β€” A is COMPLEX 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 β€” LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • D β€” D is COMPLEX 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 β€” SVA is REAL 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).
  • MV β€” MV is 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 β€” V is COMPLEX 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 β€” LDV is INTEGER. The leading dimension of the array V, LDV >= 1. If JOBV = 'V', LDV >= N. If JOBV = 'A', LDV >= MV.
  • EPS β€” EPS is REAL. EPS = SLAMCH('Epsilon').
  • SFMIN β€” SFMIN is REAL. SFMIN = SLAMCH('Safe Minimum').
  • TOL β€” TOL is REAL. 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.
  • NSWEEP β€” NSWEEP is INTEGER. NSWEEP is the number of sweeps of Jacobi rotations to be performed.
  • WORK β€” WORK is COMPLEX array, dimension (LWORK).
  • LWORK β€” LWORK is INTEGER. LWORK is the dimension of WORK. LWORK >= M.
  • INFO β€” INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, then the i-th argument had an illegal value.

🌈 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 cgsvj1.f.


πŸ‘‘ subroutine dgsvj1 πŸ‘‘

subroutine dgsvj1 (character*1 jobv, integer m, integer n, integer n1,
    double precision, dimension( lda, * ) a, integer lda, double precision,
    dimension( n ) d, double precision, dimension( n ) sva, integer mv,
    double precision, dimension( ldv, * ) v, integer ldv, double precision
    eps, double precision sfmin, double precision tol, integer nsweep,
    double precision, dimension( lwork ) work, integer lwork, integer info)

DGSVJ1 is a pre-processor for the routine dgesvj, and it applies Jacobi rotations targeting only particular pivots. same energy, different precision. πŸ’œ

🌟 Purpose 🌟

DGSVJ1 is called from DGESVJ as a pre-processor and that is its main purpose. It applies Jacobi rotations in the same way as DGESVJ does, but it targets only particular pivots and it does not check convergence (stopping criterion). Few tuning parameters (marked by [TP]) are available for the implementer.

🧚 Further Details 🧚

DGSVJ1 applies 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 the following 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.

πŸŽ€ Parameters πŸŽ€

  • JOBV β€” JOBV is 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.
  • M β€” M is INTEGER. The number of rows of the input matrix A. M >= 0.
  • N β€”

N

N is INTEGER β€” it's the number of columns of the input matrix A. Constraint, no cap: M >= N >= 0. 🫢

N1

N1 is INTEGER β€” bestie, this one sets the 2 x 2 block partition ✨ the first N1 columns get rotated 'against' the remaining N-N1 columns of A. Like, the two teams facing off πŸ’…

A

A is DOUBLE PRECISION array, dimension (LDA,N) β€”

On entry: the 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.) πŸŒ€

LDA

LDA is INTEGER β€” the leading dimension of the array A. LDA >= max(1,M). πŸ“

D

D is DOUBLE PRECISION array, dimension (N) β€”

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.) πŸ’–

SVA

SVA is DOUBLE PRECISION array, dimension (N) β€”

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). ⭐

MV

MV is INTEGER β€”

  • 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. πŸ™ˆ

V

V is DOUBLE PRECISION array, dimension (LDV,N) β€”

  • 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. πŸ’«

LDV

LDV is INTEGER β€” the leading dimension of the array V, LDV >= 1.

  • If JOBV = 'V', LDV >= N.
  • If JOBV = 'A', LDV >= MV. 🌸

EPS

EPS is DOUBLE PRECISION β€” and it's literally just EPS = DLAMCH('Epsilon'). That's the whole assignment, bestie πŸŽ€

SFMIN

SFMIN is DOUBLE PRECISION β€” SFMIN = DLAMCH('Safe Minimum'). Iconic, tiny, safe 🧚

TOL

TOL is DOUBLE PRECISION β€” the threshold for Jacobi rotations, fr fr. For a pair A(:,p), A(:,q) of pivot columns, the Jacobi rotation is applied only if DABS(COS(angle(A(:,p),A(:,q)))) > TOL. πŸ‘‘

NSWEEP

NSWEEP is INTEGER β€” the number of sweeps of Jacobi rotations to be performed. That's how many laps we're doing πŸƒβ€β™€οΈ

WORK

WORK is DOUBLE PRECISION array, dimension (LWORK) β€” the workspace, the vibes buffer ✨

LWORK

LWORK is INTEGER β€” the dimension of WORK. LWORK >= M. πŸ“

INFO

INFO is INTEGER β€”

  • = 0: successful exit. we love a clean win πŸŽ‰
  • < 0: if INFO = -i, then the i-th argument had an illegal value πŸ’€

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany) 🫢

Definition at line 234 of file dgsvj1.f.


subroutine sgsvj1 (character*1 jobv, integer m, integer n, integer n1, real, dimension( lda, * ) a, integer lda, real, dimension( n ) d, real, dimension( n ) sva, integer mv, real, dimension( ldv, * ) v, integer ldv, real eps, real sfmin, real tol, integer nsweep, real, dimension( lwork ) work, integer lwork, integer info)

subroutine sgsvj1 (character*1 jobv, integer m, integer n, integer n1, real,
    dimension( lda, * ) a, integer lda, real, dimension( n ) d, real,
    dimension( n ) sva, integer mv, real, dimension( ldv, * ) v, integer
    ldv, real eps, real sfmin, real tol, integer nsweep, real, dimension(
    lwork ) work, integer lwork, integer info)

SGSVJ1 pre-processor for the routine sgesvj, applies Jacobi rotations targeting only particular pivots. πŸ’…

Purpose:

SGSVJ1 is called from SGESVJ as a pre-processor and that is its main purpose. It applies Jacobi rotations in the same way as SGESVJ does, but it targets only particular pivots and it does not check convergence (stopping criterion). Few tuning parameters (marked by [TP]) are available for the implementer. πŸ”₯

Further Details

SGSVJ1 applies 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 the following 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. πŸ¦‹

Parameters

JOBV

JOBV is CHARACTER*1 β€” 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. 🚫

M

M is INTEGER β€” the number of rows of the input matrix A. M >= 0. πŸ“Š

N

N is INTEGER β€” the number of columns of the input matrix A. M >= N >= 0. 🫢

N1

N1 is INTEGER β€” N1 specifies the 2 x 2 block partition, the first N1 columns are rotated 'against' the remaining N-N1 columns of A. ✨

A

A is REAL array, dimension (LDA,N) β€”

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.) πŸŒ€

LDA

LDA is INTEGER β€” the leading dimension of the array A. LDA >= max(1,M). πŸ“

D

D is REAL array, dimension (N) β€”

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.) πŸ’–

SVA

SVA is REAL array, dimension (N) β€”

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). ⭐

MV

MV is INTEGER β€”

  • 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. πŸ™ˆ

V

V is REAL array, dimension (LDV,N) β€”

  • 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. πŸ’«

LDV

LDV is INTEGER β€” the leading dimension of the array V, LDV >= 1.

  • If JOBV = 'V', LDV >= N.
  • If JOBV = 'A', LDV >= MV. 🌸

EPS

EPS is REAL β€” EPS = SLAMCH('Epsilon'). That's it, that's the parameter πŸŽ€

SFMIN

SFMIN is REAL β€” SFMIN = SLAMCH('Safe Minimum'). Tiny but mighty 🧚

TOL

TOL is REAL β€” 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. πŸ‘‘

NSWEEP

NSWEEP is INTEGER β€” the number of sweeps of Jacobi rotations to be performed. 🌈

WORK

WORK is REAL array, dimension (LWORK) β€” the workspace zone ✨

LWORK

LWORK is INTEGER β€” the dimension of WORK. LWORK >= M. πŸ“

  • INFO β€” INTEGER. The exit-status girlie πŸ’…. = 0: successful exit, we ate and left no crumbs ✨. < 0: if INFO = -i, then the i-th argument had an illegal value β€” so like, go check your inputs bestie, one of them is being messy πŸ™ˆ.

πŸ‘‘ Author

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

🫢 Contributors:

Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany) β€” the icons who made this happen πŸ’–

Definition at line 234 of file sgsvj1.f.


✨ subroutine zgsvj1 ✨

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 the pre-processor for the routine zgesvj, and it applies Jacobi rotations targeting only particular pivots πŸ”₯ no cap.


πŸ’œ Purpose:

ZGSVJ1 is called from ZGESVJ as a pre-processor and that is 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 (stopping criterion). Few tuning parameters (marked by [TP]) are available for the implementer.

🌸 Further Details 🌸

ZGSVJ1 applies 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 the following 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. Literally the whole vibe πŸ¦‹.


πŸŽ€ Parameters

  • JOBV β€” JOBV is CHARACTER*1. It 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.
  • M β€” M is INTEGER. The number of rows of the input matrix A. M >= 0.
  • N β€” N is INTEGER. The number of columns of the input matrix A. M >= N >= 0.
  • N1 β€” N1 is INTEGER. N1 specifies the 2 x 2 block partition, the first N1 columns are rotated 'against' the remaining N-N1 columns of A.
  • A β€” A is 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 β€” LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • D β€” D is 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 β€” SVA is 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).
  • MV β€” MV is 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 β€” V is 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 β€” LDV is INTEGER. The leading dimension of the array V, LDV >= 1.
    • If JOBV = 'V', LDV >= N.
    • If JOBV = 'A', LDV >= MV.
  • EPS β€” EPS is DOUBLE PRECISION. EPS = DLAMCH('Epsilon').
  • SFMIN β€” SFMIN is DOUBLE PRECISION. SFMIN = DLAMCH('Safe Minimum').
  • TOL β€” TOL is 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.
  • NSWEEP β€” NSWEEP is INTEGER. NSWEEP is the number of sweeps of Jacobi rotations to be performed.
  • WORK β€” WORK is COMPLEX*16 array, dimension (LWORK).
  • LWORK β€” LWORK is INTEGER. LWORK is the dimension of WORK. LWORK >= M.
  • INFO β€” INFO is INTEGER. = 0: successful exit, slay πŸ’…. < 0: if INFO = -i, then the i-th argument had an illegal value β€” something in your inputs is not giving, go fix it bestie 😭.

πŸ‘‘ Author

  • Univ. of Tennessee
  • Univ. of Colorado Denver β€” wait, no, correction, the trio is:
  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

🫢 Contributor:

Zlatko Drmac (Zagreb, Croatia) β€” the main character of this whole routine fr fr ✨

Definition at line 234 of file zgsvj1.f.


🌈 Author

Generated automatically by Doxygen for LAPACK from the source code.


And that's the whole page bestie, you made it to the end πŸŽ‰ The footer says this is LAPACK, Version 3.12.0, page gsvj1(3) β€” so like, cite it with pride, it's giving official documentation energy πŸ‘‘πŸ’–βœ¨
πŸ“¦ where this page comes from