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---
:name: sgsvj0
:md5sum: 3d2a3ab6cc4e65db034ed891716f6493
:category: :subroutine
:arguments:
- jobv:
:type: char
:intent: input
- m:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: real
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- d:
:type: real
:intent: input/output
:dims:
- n
- sva:
:type: real
:intent: input/output
:dims:
- n
- mv:
:type: integer
:intent: input
- v:
:type: real
:intent: input/output
:dims:
- ldv
- n
- ldv:
:type: integer
:intent: input
- eps:
:type: integer
:intent: input
- sfmin:
:type: integer
:intent: input
- tol:
:type: real
:intent: input
- nsweep:
:type: integer
:intent: input
- work:
:type: real
:intent: workspace
:dims:
- lwork
- lwork:
:type: integer
:intent: input
:option: true
:default: m
- info:
:type: integer
:intent: output
:substitutions:
lwork: m
:fortran_help: " SUBROUTINE SGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SGSVJ0 is called from SGESVJ as a pre-processor and that is its main\n\
* purpose. It applies Jacobi rotations in the same way as SGESVJ does, but\n\
* it does not check convergence (stopping criterion). Few tuning\n\
* parameters (marked by [TP]) are available for the implementer.\n\
*\n\
* Further Details\n\
* ~~~~~~~~~~~~~~~\n\
* SGSVJ0 is used just to enable SGESVJ to call a simplified version of\n\
* itself to work on a submatrix of the original matrix.\n\
*\n\
* Contributors\n\
* ~~~~~~~~~~~~\n\
* Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)\n\
*\n\
* Bugs, Examples and Comments\n\
* ~~~~~~~~~~~~~~~~~~~~~~~~~~~\n\
* Please report all bugs and send interesting test examples and comments to\n\
* drmac@math.hr. Thank you.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* JOBV (input) CHARACTER*1\n\
* Specifies whether the output from this procedure is used\n\
* to compute the matrix V:\n\
* = 'V': the product of the Jacobi rotations is accumulated\n\
* by postmulyiplying the N-by-N array V.\n\
* (See the description of V.)\n\
* = 'A': the product of the Jacobi rotations is accumulated\n\
* by postmulyiplying the MV-by-N array V.\n\
* (See the descriptions of MV and V.)\n\
* = 'N': the Jacobi rotations are not accumulated.\n\
*\n\
* M (input) INTEGER\n\
* The number of rows of the input matrix A. M >= 0.\n\
*\n\
* N (input) INTEGER\n\
* The number of columns of the input matrix A.\n\
* M >= N >= 0.\n\
*\n\
* A (input/output) REAL array, dimension (LDA,N)\n\
* On entry, M-by-N matrix A, such that A*diag(D) represents\n\
* the input matrix.\n\
* On exit,\n\
* A_onexit * D_onexit represents the input matrix A*diag(D)\n\
* post-multiplied by a sequence of Jacobi rotations, where the\n\
* rotation threshold and the total number of sweeps are given in\n\
* TOL and NSWEEP, respectively.\n\
* (See the descriptions of D, TOL and NSWEEP.)\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,M).\n\
*\n\
* D (input/workspace/output) REAL array, dimension (N)\n\
* The array D accumulates the scaling factors from the fast scaled\n\
* Jacobi rotations.\n\
* On entry, A*diag(D) represents the input matrix.\n\
* On exit, A_onexit*diag(D_onexit) represents the input matrix\n\
* post-multiplied by a sequence of Jacobi rotations, where the\n\
* rotation threshold and the total number of sweeps are given in\n\
* TOL and NSWEEP, respectively.\n\
* (See the descriptions of A, TOL and NSWEEP.)\n\
*\n\
* SVA (input/workspace/output) REAL array, dimension (N)\n\
* On entry, SVA contains the Euclidean norms of the columns of\n\
* the matrix A*diag(D).\n\
* On exit, SVA contains the Euclidean norms of the columns of\n\
* the matrix onexit*diag(D_onexit).\n\
*\n\
* MV (input) INTEGER\n\
* If JOBV .EQ. 'A', then MV rows of V are post-multipled by a\n\
* sequence of Jacobi rotations.\n\
* If JOBV = 'N', then MV is not referenced.\n\
*\n\
* V (input/output) REAL array, dimension (LDV,N)\n\
* If JOBV .EQ. 'V' then N rows of V are post-multipled by a\n\
* sequence of Jacobi rotations.\n\
* If JOBV .EQ. 'A' then MV rows of V are post-multipled by a\n\
* sequence of Jacobi rotations.\n\
* If JOBV = 'N', then V is not referenced.\n\
*\n\
* LDV (input) INTEGER\n\
* The leading dimension of the array V, LDV >= 1.\n\
* If JOBV = 'V', LDV .GE. N.\n\
* If JOBV = 'A', LDV .GE. MV.\n\
*\n\
* EPS (input) INTEGER\n\
* EPS = SLAMCH('Epsilon')\n\
*\n\
* SFMIN (input) INTEGER\n\
* SFMIN = SLAMCH('Safe Minimum')\n\
*\n\
* TOL (input) REAL\n\
* TOL is the threshold for Jacobi rotations. For a pair\n\
* A(:,p), A(:,q) of pivot columns, the Jacobi rotation is\n\
* applied only if ABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL.\n\
*\n\
* NSWEEP (input) INTEGER\n\
* NSWEEP is the number of sweeps of Jacobi rotations to be\n\
* performed.\n\
*\n\
* WORK (workspace) REAL array, dimension LWORK.\n\
*\n\
* LWORK (input) INTEGER\n\
* LWORK is the dimension of WORK. LWORK .GE. M.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0 : successful exit.\n\
* < 0 : if INFO = -i, then the i-th argument had an illegal value\n\
*\n\n\
* =====================================================================\n\
*\n\
* .. Local Parameters ..\n REAL ZERO, HALF, ONE, TWO\n PARAMETER ( ZERO = 0.0E0, HALF = 0.5E0, ONE = 1.0E0,\n + TWO = 2.0E0 )\n\
* ..\n\
* .. Local Scalars ..\n REAL AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG,\n + BIGTHETA, CS, MXAAPQ, MXSINJ, ROOTBIG, ROOTEPS,\n + ROOTSFMIN, ROOTTOL, SMALL, SN, T, TEMP1, THETA,\n + THSIGN\n INTEGER BLSKIP, EMPTSW, i, ibr, IERR, igl, IJBLSK, ir1,\n + ISWROT, jbc, jgl, KBL, LKAHEAD, MVL, NBL,\n + NOTROT, p, PSKIPPED, q, ROWSKIP, SWBAND\n LOGICAL APPLV, ROTOK, RSVEC\n\
* ..\n\
* .. Local Arrays ..\n REAL FASTR( 5 )\n\
* ..\n\
* .. Intrinsic Functions ..\n INTRINSIC ABS, AMAX1, AMIN1, FLOAT, MIN0, SIGN, SQRT\n\
* ..\n\
* .. External Functions ..\n REAL SDOT, SNRM2\n INTEGER ISAMAX\n LOGICAL LSAME\n EXTERNAL ISAMAX, LSAME, SDOT, SNRM2\n\
* ..\n\
* .. External Subroutines ..\n EXTERNAL SAXPY, SCOPY, SLASCL, SLASSQ, SROTM, SSWAP\n\
* ..\n"
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