LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  sgsvj1 (JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO) 
SGSVJ1 preprocessor for the routine sgesvj, applies Jacobi rotations targeting only particular pivots. 
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 preprocessor for the routine sgesvj, applies Jacobi rotations targeting only particular pivots.
Download SGSVJ1 + dependencies [TGZ] [ZIP] [TXT]SGSVJ1 is called from SGESVJ as a preprocessor 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 tunning parameters (marked by [TP]) are available for the implementer. Further Details ~~~~~~~~~~~~~~~ SGSVJ1 applies few sweeps of Jacobi rotations in the column space of the input MbyN matrix A. The pivot pairs are taken from the (1,2) offdiagonal block in the corresponding NbyN Gram matrix A^T * A. The blockentries (tiles) of the (1,2) offdiagonal block are marked by the [x]'s in the following scheme:  * * * [x] [x] [x]  * * * [x] [x] [x] Rowcycling in the nblrbynblc [x] blocks.  * * * [x] [x] [x] Rowcyclic 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 NN1 columns, trying to increase the angle between the corresponding subspaces. The offdiagonal block is N1by(NN1) and it is tiled using quadratic tiles of side KBL. Here, KBL is a tunning parmeter. 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 postmulyiplying the NbyN array V. (See the description of V.) = 'A': the product of the Jacobi rotations is accumulated by postmulyiplying the MVbyN 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 NN1 columns of A. 
[in,out]  A  A is REAL array, dimension (LDA,N) On entry, MbyN matrix A, such that A*diag(D) represents the input matrix. On exit, A_onexit * D_onexit represents the input matrix A*diag(D) postmultiplied 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 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 postmultiplied 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 .EQ. 'A', then MV rows of V are postmultipled by a sequence of Jacobi rotations. If JOBV = 'N', then MV is not referenced. 
[in,out]  V  V is REAL array, dimension (LDV,N) If JOBV .EQ. 'V' then N rows of V are postmultipled by a sequence of Jacobi rotations. If JOBV .EQ. 'A' then MV rows of V are postmultipled 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 .GE. N. If JOBV = 'A', LDV .GE. 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)))) .GT. TOL. 
[in]  NSWEEP  NSWEEP is INTEGER NSWEEP is the number of sweeps of Jacobi rotations to be performed. 
[out]  WORK  WORK is REAL array, dimension LWORK. 
[in]  LWORK  LWORK is INTEGER LWORK is the dimension of WORK. LWORK .GE. M. 
[out]  INFO  INFO is INTEGER = 0 : successful exit. < 0 : if INFO = i, then the ith argument had an illegal value 
Definition at line 236 of file sgsvj1.f.