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LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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| 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 pre-processor for the routine cgesvj, applies Jacobi rotations targeting only particular pivots.
Download CGSVJ1 + dependencies [TGZ] [ZIP] [TXT]
!> !> 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. !>
| [in] | JOBV | !> 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. !> |
| [in] | M | !> M is INTEGER !> The number of rows of the input matrix A. M >= 0. !> |
| [in] | N | !> N is INTEGER !> The number of columns of the input matrix A. !> M >= N >= 0. !> |
| [in] | N1 | !> 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. !> |
| [in,out] | 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 * 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.) !> |
| [in] | LDA | !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !> |
| [in,out] | D | !> 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.) !> |
| [in,out] | 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 onexit*diag(D_onexit). !> |
| [in] | 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. !> |
| [in,out] | 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. !> |
| [in] | LDV | !> LDV is INTEGER !> The leading dimension of the array V, LDV >= 1. !> If JOBV = 'V', LDV >= N. !> If JOBV = 'A', LDV >= MV. !> |
| [in] | EPS | !> EPS is REAL
!> EPS = SLAMCH('Epsilon')
!> |
| [in] | SFMIN | !> SFMIN is REAL
!> SFMIN = SLAMCH('Safe Minimum')
!> |
| [in] | 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. !> |
| [in] | NSWEEP | !> NSWEEP is INTEGER !> NSWEEP is the number of sweeps of Jacobi rotations to be !> performed. !> |
| [out] | WORK | !> WORK is COMPLEX array, dimension (LWORK) !> |
| [in] | LWORK | !> LWORK is INTEGER !> LWORK is the dimension of WORK. LWORK >= M. !> |
| [out] | INFO | !> INFO is INTEGER !> = 0: successful exit. !> < 0: if INFO = -i, then the i-th argument had an illegal value !> |
Definition at line 232 of file cgsvj1.f.
1.11.0