gsvj0(3)

📦
version 3.12.1 · 9 versions
, in arch rolling
💅 ok bestie, this is part 1 of a chonky one — a Library Functions Manual page for gsvj0(3). Buckle up, we're doing linear algebra and we're doing it cutely. ✨

🌸 NAME 🌸

gsvj0 — gsvj0: step in gesvj

✨ SYNOPSIS ✨

🎀 Functions 🎀

  • subroutine cgsvj0 — CGSVJ0 pre-processor for the routine cgesvj.
subroutine cgsvj0 (jobv, m, n, a, lda, d, sva, mv, v, ldv, eps, sfmin,
    tol, nsweep, work, lwork, info)
  • subroutine dgsvj0 — DGSVJ0 pre-processor for the routine dgesvj.
subroutine dgsvj0 (jobv, m, n, a, lda, d, sva, mv, v, ldv, eps, sfmin,
    tol, nsweep, work, lwork, info)
  • subroutine sgsvj0 — SGSVJ0 pre-processor for the routine sgesvj.
subroutine sgsvj0 (jobv, m, n, a, lda, d, sva, mv, v, ldv, eps, sfmin,
    tol, nsweep, work, lwork, info)
  • subroutine zgsvj0 — ZGSVJ0 pre-processor for the routine zgesvj.
subroutine zgsvj0 (jobv, m, n, a, lda, d, sva, mv, v, ldv, eps, sfmin,
    tol, nsweep, work, lwork, info)

🦋 Detailed Description 🦋

💫 Function Documentation 💫

🌈 subroutine cgsvj0

subroutine cgsvj0 (character*1 jobv, integer m, integer n, 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)

CGSVJ0 pre-processor for the routine cgesvj.

🌟 Purpose:

CGSVJ0 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 does not check convergence (stopping criterion). Few tuning parameters (marked by [TP]) are available for the implementer.

🧚 Parameters 🧚

  • JOBV — 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 — 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. M >= N >= 0.
  • A — 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 * diag(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 D, TOL and NSWEEP.)
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • D — D is COMPLEX array, dimension (N). The array D accumulates the scaling factors from the complex 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 A, TOL and NSWEEP.)
  • SVA — 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 A_onexit*diag(D_onexit).
  • MV — 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 — 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 — LDV is INTEGER. The leading dimension of the array V, LDV >= 1.
    • If JOBV = 'V', LDV >= N.
    • If JOBV = 'A', LDV >= MV.
  • EPS — EPS is REAL. EPS = SLAMCH('Epsilon').
  • SFMIN — SFMIN is REAL. SFMIN = SLAMCH('Safe Minimum').
  • TOL — 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 — NSWEEP is INTEGER. NSWEEP is the number of sweeps of Jacobi rotations to be performed.
  • WORK — WORK is COMPLEX array, dimension (LWORK).
  • LWORK — LWORK is INTEGER. LWORK is the dimension of WORK. LWORK >= M.
  • INFO — 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.

🔥 Further Details:

CGSVJ0 is used just to enable CGESVJ to call a simplified version of itself to work on a submatrix of the original matrix.

🫶 Contributor:

Zlatko Drmac (Zagreb, Croatia)

💀 Bugs, Examples and Comments:

Please report all bugs and send interesting test examples and comments to drmac@math.hr. Thank you.

⭐ Definition at line 216 of file cgsvj0.f.

🌈 subroutine dgsvj0

subroutine dgsvj0 (character*1 jobv, integer m, integer n, 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)

DGSVJ0 pre-processor for the routine dgesvj.

🌟 Purpose:

DGSVJ0 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 does not check convergence (stopping criterion). Few tuning parameters (marked by [TP]) are available for the implementer.

🧚 Parameters 🧚

  • JOBV — 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 — 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. M >= N >= 0.
  • A — A is DOUBLE PRECISION 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 D, TOL and NSWEEP.)
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • D — D is DOUBLE PRECISION 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 A, TOL and NSWEEP.)
  • SVA — 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 — 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 — V is DOUBLE PRECISION 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 — LDV is INTEGER. The leading dimension of the array V, LDV >= 1.
    • If JOBV = 'V', LDV >= N.
    • If JOBV = 'A', LDV >= MV.
  • EPS
  • EPS — it's a DOUBLE PRECISION, bestie, and you set it like this:
EPS = DLAMCH('Epsilon')
  • SFMIN — also DOUBLE PRECISION, also a one-liner:
SFMIN = DLAMCH('Safe Minimum')
  • TOL — DOUBLE PRECISION, and this one's the threshold for Jacobi rotations ✨. Here's the vibe: for a pair A(:,p), A(:,q) of pivot columns, the Jacobi rotation gets applied only if DABS(COS(angle(A(:,p),A(:,q)))) > TOL. That's it. That's the whole gate. 💅
  • NSWEEP — INTEGER, and it's literally the number of sweeps of Jacobi rotations that are gonna be performed. No cap, just sweeps. 🌈
  • WORK — DOUBLE PRECISION array, dimension (LWORK). It's the workspace, it works. 🫶
  • LWORK — INTEGER, the dimension of WORK. And LWORK >= M. Respect the constraint or perish. 💀
  • INFO — INTEGER, the receipts:
    • = 0: successful exit. 🎉
    • < 0: if INFO = -i, then the i-th argument had an illegal value. Not me finding out argument number i was bad… 😭

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🔍 Further Details:

DGSVJ0 is used just to enable DGESVJ to call a simplified version of itself to work on a submatrix of the original matrix. Lowkey recursive main character energy. 🌀

🌟 Contributors:

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

🐛 Bugs, Examples and Comments:

Please report all bugs and send interesting test examples and comments to drmac@math.hr. Thank you. Fr fr, they want your weird little test cases. 🍓

Definition at line 216 of file dgsvj0.f.

💖 subroutine sgsvj0

subroutine sgsvj0 (character*1 jobv, integer m, integer n, 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)

SGSVJ0 pre-processor for the routine sgesvj. Bestie, it's the opening act. 🎬

🎯 Purpose:

SGSVJ0 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 does not check convergence (stopping criterion). Few tuning parameters (marked by [TP]) are available for the implementer. So iconic of it — does the rotations, skips the vibe check. ✨

🎀 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. 🙈
  • 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.
  • A — REAL 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 D, TOL and NSWEEP.) 🦋
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • D — REAL 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 A, TOL and NSWEEP.) 💫
  • SVA — 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). (Yes, exactly as written — no cap.) 🌸
  • 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. Ghosted. 👻
  • V — REAL 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 — REAL:
EPS = SLAMCH('Epsilon')
  • SFMIN — REAL:
SFMIN = SLAMCH('Safe Minimum')
  • TOL — 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. Same rule, single precision edition. 🔥
  • NSWEEP — INTEGER. NSWEEP is the number of sweeps of Jacobi rotations to be performed.
  • WORK — REAL 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. 💀

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🔍 Further Details:

SGSVJ0 is used just to enable SGESVJ to call a simplified version of itself to work on a submatrix of the original matrix. It's giving "I contain multitudes, but make it a submatrix." 🧚

🌟 Contributors:

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

🐛 Bugs, Examples and Comments:

Please report all bugs and send interesting test examples and comments to drmac@math.hr. Thank you. 🍓

Definition at line 216 of file sgsvj0.f.

🦋 subroutine zgsvj0

subroutine zgsvj0 (character*1 jobv, integer m, integer n, 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)

ZGSVJ0 pre-processor for the routine zgesvj. The complex icon has entered the chat. 💜

🎯 Purpose:

ZGSVJ0 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 does not check convergence (stopping criterion). Few tuning parameters (marked by [TP]) are available for the implementer. ✨

🎀 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. 🙈
  • 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.
  • 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 * diag(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 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 complex 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 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 A_onexit*diag(D_onexit). 🎀
  • 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. Ghosted again. 👻

Picking up the argument list right where we left off — every flag and condition stays exactly as it was, fr fr:

  • MV — 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 — 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 — LDV is INTEGER. The leading dimension of the array V, LDV >= 1. If JOBV = 'V', LDV >= N. If JOBV = 'A', LDV >= MV.
  • EPS — EPS is DOUBLE PRECISION. EPS = DLAMCH('Epsilon').
  • SFMIN — SFMIN is DOUBLE PRECISION. SFMIN = DLAMCH('Safe Minimum').
  • TOL — 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 — NSWEEP is INTEGER. NSWEEP is the number of sweeps of Jacobi rotations to be performed.
  • WORK — WORK is COMPLEX*16 array, dimension (LWORK).
  • LWORK — LWORK is INTEGER. LWORK is the dimension of WORK. LWORK >= M.
  • INFO — 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.

🔍 Further Details:

ZGSVJ0 is used just to enable ZGESVJ to call a simplified version of itself to work on a submatrix of the original matrix.

🌟 Contributor:

Zlatko Drmac (Zagreb, Croatia)

🐞 Bugs, Examples and Comments:

Please report all bugs and send interesting test examples and comments to drmac@math.hr. Thank you.

Definition at line 216 of file zgsvj0.f.

🤖 Author

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