#include #include #include #include #include #ifdef complex #undef complex #endif #ifdef I #undef I #endif #if defined(_WIN64) typedef long long BLASLONG; typedef unsigned long long BLASULONG; #else typedef long BLASLONG; typedef unsigned long BLASULONG; #endif #ifdef LAPACK_ILP64 typedef BLASLONG blasint; #if defined(_WIN64) #define blasabs(x) llabs(x) #else #define blasabs(x) labs(x) #endif #else typedef int blasint; #define blasabs(x) abs(x) #endif typedef blasint integer; typedef unsigned int uinteger; typedef char *address; typedef short int shortint; typedef float real; typedef double doublereal; typedef struct { real r, i; } complex; typedef struct { doublereal r, i; } doublecomplex; #ifdef _MSC_VER static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;} static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;} static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;} static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;} #else static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;} static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;} static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;} static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;} #endif #define pCf(z) (*_pCf(z)) #define pCd(z) (*_pCd(z)) typedef int logical; typedef short int shortlogical; typedef char logical1; typedef char integer1; #define TRUE_ (1) #define FALSE_ (0) /* Extern is for use with -E */ #ifndef Extern #define Extern extern #endif /* I/O stuff */ typedef int flag; typedef int ftnlen; typedef int ftnint; /*external read, write*/ typedef struct { flag cierr; ftnint ciunit; flag ciend; char *cifmt; ftnint cirec; } cilist; /*internal read, write*/ typedef struct { flag icierr; char *iciunit; flag iciend; char *icifmt; ftnint icirlen; ftnint icirnum; } icilist; /*open*/ typedef struct { flag oerr; ftnint ounit; char *ofnm; ftnlen ofnmlen; char *osta; char *oacc; char *ofm; ftnint orl; char *oblnk; } olist; /*close*/ typedef struct { flag cerr; ftnint cunit; char *csta; } cllist; /*rewind, backspace, endfile*/ typedef struct { flag aerr; ftnint aunit; } alist; /* inquire */ typedef struct { flag inerr; ftnint inunit; char *infile; ftnlen infilen; ftnint *inex; /*parameters in standard's order*/ ftnint *inopen; ftnint *innum; ftnint *innamed; char *inname; ftnlen innamlen; char *inacc; ftnlen inacclen; char *inseq; ftnlen inseqlen; char *indir; ftnlen indirlen; char *infmt; ftnlen infmtlen; char *inform; ftnint informlen; char *inunf; ftnlen inunflen; ftnint *inrecl; ftnint *innrec; char *inblank; ftnlen inblanklen; } inlist; #define VOID void union Multitype { /* for multiple entry points */ integer1 g; shortint h; integer i; /* longint j; */ real r; doublereal d; complex c; doublecomplex z; }; typedef union Multitype Multitype; struct Vardesc { /* for Namelist */ char *name; char *addr; ftnlen *dims; int type; }; typedef struct Vardesc Vardesc; struct Namelist { char *name; Vardesc **vars; int nvars; }; typedef struct Namelist Namelist; #define abs(x) ((x) >= 0 ? (x) : -(x)) #define dabs(x) (fabs(x)) #define f2cmin(a,b) ((a) <= (b) ? (a) : (b)) #define f2cmax(a,b) ((a) >= (b) ? (a) : (b)) #define dmin(a,b) (f2cmin(a,b)) #define dmax(a,b) (f2cmax(a,b)) #define bit_test(a,b) ((a) >> (b) & 1) #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b))) #define bit_set(a,b) ((a) | ((uinteger)1 << (b))) #define abort_() { sig_die("Fortran abort routine called", 1); } #define c_abs(z) (cabsf(Cf(z))) #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); } #ifdef _MSC_VER #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);} #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);} #else #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);} #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);} #endif #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));} #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));} #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));} //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));} #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));} #define d_abs(x) (fabs(*(x))) #define d_acos(x) (acos(*(x))) #define d_asin(x) (asin(*(x))) #define d_atan(x) (atan(*(x))) #define d_atn2(x, y) (atan2(*(x),*(y))) #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); } #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); } #define d_cos(x) (cos(*(x))) #define d_cosh(x) (cosh(*(x))) #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 ) #define d_exp(x) (exp(*(x))) #define d_imag(z) (cimag(Cd(z))) #define r_imag(z) (cimagf(Cf(z))) #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define d_log(x) (log(*(x))) #define d_mod(x, y) (fmod(*(x), *(y))) #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x))) #define d_nint(x) u_nint(*(x)) #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a))) #define d_sign(a,b) u_sign(*(a),*(b)) #define r_sign(a,b) u_sign(*(a),*(b)) #define d_sin(x) (sin(*(x))) #define d_sinh(x) (sinh(*(x))) #define d_sqrt(x) (sqrt(*(x))) #define d_tan(x) (tan(*(x))) #define d_tanh(x) (tanh(*(x))) #define i_abs(x) abs(*(x)) #define i_dnnt(x) ((integer)u_nint(*(x))) #define i_len(s, n) (n) #define i_nint(x) ((integer)u_nint(*(x))) #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b))) #define pow_dd(ap, bp) ( pow(*(ap), *(bp))) #define pow_si(B,E) spow_ui(*(B),*(E)) #define pow_ri(B,E) spow_ui(*(B),*(E)) #define pow_di(B,E) dpow_ui(*(B),*(E)) #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));} #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));} #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));} #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; } #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d)))) #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; } #define sig_die(s, kill) { exit(1); } #define s_stop(s, n) {exit(0);} static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n"; #define z_abs(z) (cabs(Cd(z))) #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));} #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));} #define myexit_() break; #define mycycle() continue; #define myceiling(w) {ceil(w)} #define myhuge(w) {HUGE_VAL} //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);} #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)} /* procedure parameter types for -A and -C++ */ #define F2C_proc_par_types 1 #ifdef __cplusplus typedef logical (*L_fp)(...); #else typedef logical (*L_fp)(); #endif static float spow_ui(float x, integer n) { float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static double dpow_ui(double x, integer n) { double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #ifdef _MSC_VER static _Fcomplex cpow_ui(complex x, integer n) { complex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i; for(u = n; ; ) { if(u & 01) pow.r *= x.r, pow.i *= x.i; if(u >>= 1) x.r *= x.r, x.i *= x.i; else break; } } _Fcomplex p={pow.r, pow.i}; return p; } #else static _Complex float cpow_ui(_Complex float x, integer n) { _Complex float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif #ifdef _MSC_VER static _Dcomplex zpow_ui(_Dcomplex x, integer n) { _Dcomplex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1]; for(u = n; ; ) { if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1]; if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1]; else break; } } _Dcomplex p = {pow._Val[0], pow._Val[1]}; return p; } #else static _Complex double zpow_ui(_Complex double x, integer n) { _Complex double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif static integer pow_ii(integer x, integer n) { integer pow; unsigned long int u; if (n <= 0) { if (n == 0 || x == 1) pow = 1; else if (x != -1) pow = x == 0 ? 1/x : 0; else n = -n; } if ((n > 0) || !(n == 0 || x == 1 || x != -1)) { u = n; for(pow = 1; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static integer dmaxloc_(double *w, integer s, integer e, integer *n) { double m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static integer smaxloc_(float *w, integer s, integer e, integer *n) { float m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) { integer n = *n_, incx = *incx_, incy = *incy_, i; #ifdef _MSC_VER _Fcomplex zdotc = {0.0, 0.0}; if (incx == 1 && incy == 1) { for (i=0;i \brief \b DGSVJ0 pre-processor for the routine dgesvj. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download DGSVJ0 + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE DGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS, */ /* SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) */ /* INTEGER INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP */ /* DOUBLE PRECISION EPS, SFMIN, TOL */ /* CHARACTER*1 JOBV */ /* DOUBLE PRECISION A( LDA, * ), SVA( N ), D( N ), V( LDV, * ), */ /* $ WORK( LWORK ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > 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. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] JOBV */ /* > \verbatim */ /* > 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 N-by-N array V. */ /* > (See the description of V.) */ /* > = 'A': the product of the Jacobi rotations is accumulated */ /* > by postmulyiplying the MV-by-N array V. */ /* > (See the descriptions of MV and V.) */ /* > = 'N': the Jacobi rotations are not accumulated. */ /* > \endverbatim */ /* > */ /* > \param[in] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The number of rows of the input matrix A. M >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The number of columns of the input matrix A. */ /* > M >= N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > 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.) */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */ /* > \endverbatim */ /* > */ /* > \param[in,out] D */ /* > \verbatim */ /* > 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.) */ /* > \endverbatim */ /* > */ /* > \param[in,out] SVA */ /* > \verbatim */ /* > 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). */ /* > \endverbatim */ /* > */ /* > \param[in] MV */ /* > \verbatim */ /* > MV is INTEGER */ /* > If JOBV = 'A', then MV rows of V are post-multipled by a */ /* > sequence of Jacobi rotations. */ /* > If JOBV = 'N', then MV is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in,out] V */ /* > \verbatim */ /* > V is DOUBLE PRECISION array, dimension (LDV,N) */ /* > If JOBV = 'V' then N rows of V are post-multipled by a */ /* > sequence of Jacobi rotations. */ /* > If JOBV = 'A' then MV rows of V are post-multipled by a */ /* > sequence of Jacobi rotations. */ /* > If JOBV = 'N', then V is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDV */ /* > \verbatim */ /* > LDV is INTEGER */ /* > The leading dimension of the array V, LDV >= 1. */ /* > If JOBV = 'V', LDV >= N. */ /* > If JOBV = 'A', LDV >= MV. */ /* > \endverbatim */ /* > */ /* > \param[in] EPS */ /* > \verbatim */ /* > EPS is DOUBLE PRECISION */ /* > EPS = DLAMCH('Epsilon') */ /* > \endverbatim */ /* > */ /* > \param[in] SFMIN */ /* > \verbatim */ /* > SFMIN is DOUBLE PRECISION */ /* > SFMIN = DLAMCH('Safe Minimum') */ /* > \endverbatim */ /* > */ /* > \param[in] TOL */ /* > \verbatim */ /* > 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 DABS(COS(angle(A(:,p),A(:,q)))) > TOL. */ /* > \endverbatim */ /* > */ /* > \param[in] NSWEEP */ /* > \verbatim */ /* > NSWEEP is INTEGER */ /* > NSWEEP is the number of sweeps of Jacobi rotations to be */ /* > performed. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is DOUBLE PRECISION array, dimension (LWORK) */ /* > \endverbatim */ /* > */ /* > \param[in] LWORK */ /* > \verbatim */ /* > LWORK is INTEGER */ /* > LWORK is the dimension of WORK. LWORK >= M. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit. */ /* > < 0: if INFO = -i, then the i-th argument had an illegal value */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date November 2017 */ /* > \ingroup doubleOTHERcomputational */ /* > \par 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. */ /* > */ /* > \par Contributors: */ /* ================== */ /* > */ /* > Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany) */ /* > */ /* > \par Bugs, Examples and Comments: */ /* ================================= */ /* > */ /* > Please report all bugs and send interesting test examples and comments to */ /* > drmac@math.hr. Thank you. */ /* ===================================================================== */ /* Subroutine */ int dgsvj0_(char *jobv, integer *m, integer *n, doublereal * a, integer *lda, doublereal *d__, doublereal *sva, integer *mv, doublereal *v, integer *ldv, doublereal *eps, doublereal *sfmin, doublereal *tol, integer *nsweep, doublereal *work, integer *lwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4, i__5, i__6; doublereal d__1, d__2; /* Local variables */ doublereal aapp, aapq, aaqq; extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, integer *); integer ierr; doublereal bigtheta; integer pskipped; doublereal aapp0; extern doublereal dnrm2_(integer *, doublereal *, integer *); doublereal temp1; integer i__, p, q; doublereal t, apoaq, aqoap; extern logical lsame_(char *, char *); doublereal theta, small; extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); doublereal fastr[5]; extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, doublereal *, integer *); logical applv, rsvec; extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *), drotm_(integer *, doublereal *, integer *, doublereal *, integer *, doublereal *); logical rotok; doublereal rootsfmin, cs, sn; extern /* Subroutine */ int dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *); extern integer idamax_(integer *, doublereal *, integer *); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); integer ijblsk, swband, blskip; doublereal mxaapq; extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *, doublereal *, doublereal *); doublereal thsign, mxsinj; integer ir1, emptsw, notrot, iswrot, jbc; doublereal big; integer kbl, lkahead, igl, ibr, jgl, nbl, mvl; doublereal rootbig, rooteps; integer rowskip; doublereal roottol; /* -- LAPACK computational routine (version 3.8.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* November 2017 */ /* ===================================================================== */ /* Test the input parameters. */ /* Parameter adjustments */ --sva; --d__; a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; v_dim1 = *ldv; v_offset = 1 + v_dim1 * 1; v -= v_offset; --work; /* Function Body */ applv = lsame_(jobv, "A"); rsvec = lsame_(jobv, "V"); if (! (rsvec || applv || lsame_(jobv, "N"))) { *info = -1; } else if (*m < 0) { *info = -2; } else if (*n < 0 || *n > *m) { *info = -3; } else if (*lda < *m) { *info = -5; } else if ((rsvec || applv) && *mv < 0) { *info = -8; } else if (rsvec && *ldv < *n || applv && *ldv < *mv) { *info = -10; } else if (*tol <= *eps) { *info = -13; } else if (*nsweep < 0) { *info = -14; } else if (*lwork < *m) { *info = -16; } else { *info = 0; } /* #:( */ if (*info != 0) { i__1 = -(*info); xerbla_("DGSVJ0", &i__1, (ftnlen)6); return 0; } if (rsvec) { mvl = *n; } else if (applv) { mvl = *mv; } rsvec = rsvec || applv; rooteps = sqrt(*eps); rootsfmin = sqrt(*sfmin); small = *sfmin / *eps; big = 1. / *sfmin; rootbig = 1. / rootsfmin; bigtheta = 1. / rooteps; roottol = sqrt(*tol); /* -#- Row-cyclic Jacobi SVD algorithm with column pivoting -#- */ emptsw = *n * (*n - 1) / 2; notrot = 0; fastr[0] = 0.; /* -#- Row-cyclic pivot strategy with de Rijk's pivoting -#- */ swband = 0; /* [TP] SWBAND is a tuning parameter. It is meaningful and effective */ /* if SGESVJ is used as a computational routine in the preconditioned */ /* Jacobi SVD algorithm SGESVJ. For sweeps i=1:SWBAND the procedure */ /* ...... */ kbl = f2cmin(8,*n); /* [TP] KBL is a tuning parameter that defines the tile size in the */ /* tiling of the p-q loops of pivot pairs. In general, an optimal */ /* value of KBL depends on the matrix dimensions and on the */ /* parameters of the computer's memory. */ nbl = *n / kbl; if (nbl * kbl != *n) { ++nbl; } /* Computing 2nd power */ i__1 = kbl; blskip = i__1 * i__1 + 1; /* [TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. */ rowskip = f2cmin(5,kbl); /* [TP] ROWSKIP is a tuning parameter. */ lkahead = 1; /* [TP] LKAHEAD is a tuning parameter. */ swband = 0; pskipped = 0; i__1 = *nsweep; for (i__ = 1; i__ <= i__1; ++i__) { mxaapq = 0.; mxsinj = 0.; iswrot = 0; notrot = 0; pskipped = 0; i__2 = nbl; for (ibr = 1; ibr <= i__2; ++ibr) { igl = (ibr - 1) * kbl + 1; /* Computing MIN */ i__4 = lkahead, i__5 = nbl - ibr; i__3 = f2cmin(i__4,i__5); for (ir1 = 0; ir1 <= i__3; ++ir1) { igl += ir1 * kbl; /* Computing MIN */ i__5 = igl + kbl - 1, i__6 = *n - 1; i__4 = f2cmin(i__5,i__6); for (p = igl; p <= i__4; ++p) { i__5 = *n - p + 1; q = idamax_(&i__5, &sva[p], &c__1) + p - 1; if (p != q) { dswap_(m, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 + 1], &c__1); if (rsvec) { dswap_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q * v_dim1 + 1], &c__1); } temp1 = sva[p]; sva[p] = sva[q]; sva[q] = temp1; temp1 = d__[p]; d__[p] = d__[q]; d__[q] = temp1; } if (ir1 == 0) { /* Column norms are periodically updated by explicit */ /* norm computation. */ /* Caveat: */ /* Some BLAS implementations compute DNRM2(M,A(1,p),1) */ /* as DSQRT(DDOT(M,A(1,p),1,A(1,p),1)), which may result in */ /* overflow for ||A(:,p)||_2 > DSQRT(overflow_threshold), and */ /* undeflow for ||A(:,p)||_2 < DSQRT(underflow_threshold). */ /* Hence, DNRM2 cannot be trusted, not even in the case when */ /* the true norm is far from the under(over)flow boundaries. */ /* If properly implemented DNRM2 is available, the IF-THEN-ELSE */ /* below should read "AAPP = DNRM2( M, A(1,p), 1 ) * D(p)". */ if (sva[p] < rootbig && sva[p] > rootsfmin) { sva[p] = dnrm2_(m, &a[p * a_dim1 + 1], &c__1) * d__[p]; } else { temp1 = 0.; aapp = 1.; dlassq_(m, &a[p * a_dim1 + 1], &c__1, &temp1, & aapp); sva[p] = temp1 * sqrt(aapp) * d__[p]; } aapp = sva[p]; } else { aapp = sva[p]; } if (aapp > 0.) { pskipped = 0; /* Computing MIN */ i__6 = igl + kbl - 1; i__5 = f2cmin(i__6,*n); for (q = p + 1; q <= i__5; ++q) { aaqq = sva[q]; if (aaqq > 0.) { aapp0 = aapp; if (aaqq >= 1.) { rotok = small * aapp <= aaqq; if (aapp < big / aaqq) { aapq = ddot_(m, &a[p * a_dim1 + 1], & c__1, &a[q * a_dim1 + 1], & c__1) * d__[p] * d__[q] / aaqq / aapp; } else { dcopy_(m, &a[p * a_dim1 + 1], &c__1, & work[1], &c__1); dlascl_("G", &c__0, &c__0, &aapp, & d__[p], m, &c__1, &work[1], lda, &ierr); aapq = ddot_(m, &work[1], &c__1, &a[q * a_dim1 + 1], &c__1) * d__[q] / aaqq; } } else { rotok = aapp <= aaqq / small; if (aapp > small / aaqq) { aapq = ddot_(m, &a[p * a_dim1 + 1], & c__1, &a[q * a_dim1 + 1], & c__1) * d__[p] * d__[q] / aaqq / aapp; } else { dcopy_(m, &a[q * a_dim1 + 1], &c__1, & work[1], &c__1); dlascl_("G", &c__0, &c__0, &aaqq, & d__[q], m, &c__1, &work[1], lda, &ierr); aapq = ddot_(m, &work[1], &c__1, &a[p * a_dim1 + 1], &c__1) * d__[p] / aapp; } } /* Computing MAX */ d__1 = mxaapq, d__2 = abs(aapq); mxaapq = f2cmax(d__1,d__2); /* TO rotate or NOT to rotate, THAT is the question ... */ if (abs(aapq) > *tol) { /* ROTATED = ROTATED + ONE */ if (ir1 == 0) { notrot = 0; pskipped = 0; ++iswrot; } if (rotok) { aqoap = aaqq / aapp; apoaq = aapp / aaqq; theta = (d__1 = aqoap - apoaq, abs( d__1)) * -.5 / aapq; if (abs(theta) > bigtheta) { t = .5 / theta; fastr[2] = t * d__[p] / d__[q]; fastr[3] = -t * d__[q] / d__[p]; drotm_(m, &a[p * a_dim1 + 1], & c__1, &a[q * a_dim1 + 1], &c__1, fastr); if (rsvec) { drotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q * v_dim1 + 1], &c__1, fastr); } /* Computing MAX */ d__1 = 0., d__2 = t * apoaq * aapq + 1.; sva[q] = aaqq * sqrt((f2cmax(d__1, d__2))); /* Computing MAX */ d__1 = 0., d__2 = 1. - t * aqoap * aapq; aapp *= sqrt((f2cmax(d__1,d__2))); /* Computing MAX */ d__1 = mxsinj, d__2 = abs(t); mxsinj = f2cmax(d__1,d__2); } else { thsign = -d_sign(&c_b42, &aapq); t = 1. / (theta + thsign * sqrt( theta * theta + 1.)); cs = sqrt(1. / (t * t + 1.)); sn = t * cs; /* Computing MAX */ d__1 = mxsinj, d__2 = abs(sn); mxsinj = f2cmax(d__1,d__2); /* Computing MAX */ d__1 = 0., d__2 = t * apoaq * aapq + 1.; sva[q] = aaqq * sqrt((f2cmax(d__1, d__2))); /* Computing MAX */ d__1 = 0., d__2 = 1. - t * aqoap * aapq; aapp *= sqrt((f2cmax(d__1,d__2))); apoaq = d__[p] / d__[q]; aqoap = d__[q] / d__[p]; if (d__[p] >= 1.) { if (d__[q] >= 1.) { fastr[2] = t * apoaq; fastr[3] = -t * aqoap; d__[p] *= cs; d__[q] *= cs; drotm_(m, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 + 1], &c__1, fastr); if (rsvec) { drotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[ q * v_dim1 + 1], &c__1, fastr); } } else { d__1 = -t * aqoap; daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[ p * a_dim1 + 1], &c__1); d__1 = cs * sn * apoaq; daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[ q * a_dim1 + 1], &c__1); d__[p] *= cs; d__[q] /= cs; if (rsvec) { d__1 = -t * aqoap; daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], & c__1, &v[p * v_dim1 + 1], &c__1); d__1 = cs * sn * apoaq; daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], & c__1, &v[q * v_dim1 + 1], &c__1); } } } else { if (d__[q] >= 1.) { d__1 = t * apoaq; daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[ q * a_dim1 + 1], &c__1); d__1 = -cs * sn * aqoap; daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[ p * a_dim1 + 1], &c__1); d__[p] /= cs; d__[q] *= cs; if (rsvec) { d__1 = t * apoaq; daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], & c__1, &v[q * v_dim1 + 1], &c__1); d__1 = -cs * sn * aqoap; daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], & c__1, &v[p * v_dim1 + 1], &c__1); } } else { if (d__[p] >= d__[q]) { d__1 = -t * aqoap; daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[p * a_dim1 + 1], &c__1); d__1 = cs * sn * apoaq; daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 + 1], &c__1); d__[p] *= cs; d__[q] /= cs; if (rsvec) { d__1 = -t * aqoap; daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], &c__1, &v[p * v_dim1 + 1], & c__1); d__1 = cs * sn * apoaq; daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], &c__1, &v[q * v_dim1 + 1], & c__1); } } else { d__1 = t * apoaq; daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 + 1], &c__1); d__1 = -cs * sn * aqoap; daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[p * a_dim1 + 1], &c__1); d__[p] /= cs; d__[q] *= cs; if (rsvec) { d__1 = t * apoaq; daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], &c__1, &v[q * v_dim1 + 1], & c__1); d__1 = -cs * sn * aqoap; daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], &c__1, &v[p * v_dim1 + 1], & c__1); } } } } } } else { dcopy_(m, &a[p * a_dim1 + 1], &c__1, & work[1], &c__1); dlascl_("G", &c__0, &c__0, &aapp, & c_b42, m, &c__1, &work[1], lda, &ierr); dlascl_("G", &c__0, &c__0, &aaqq, & c_b42, m, &c__1, &a[q * a_dim1 + 1], lda, &ierr); temp1 = -aapq * d__[p] / d__[q]; daxpy_(m, &temp1, &work[1], &c__1, &a[ q * a_dim1 + 1], &c__1); dlascl_("G", &c__0, &c__0, &c_b42, & aaqq, m, &c__1, &a[q * a_dim1 + 1], lda, &ierr); /* Computing MAX */ d__1 = 0., d__2 = 1. - aapq * aapq; sva[q] = aaqq * sqrt((f2cmax(d__1,d__2))) ; mxsinj = f2cmax(mxsinj,*sfmin); } /* END IF ROTOK THEN ... ELSE */ /* In the case of cancellation in updating SVA(q), SVA(p) */ /* recompute SVA(q), SVA(p). */ /* Computing 2nd power */ d__1 = sva[q] / aaqq; if (d__1 * d__1 <= rooteps) { if (aaqq < rootbig && aaqq > rootsfmin) { sva[q] = dnrm2_(m, &a[q * a_dim1 + 1], &c__1) * d__[q]; } else { t = 0.; aaqq = 1.; dlassq_(m, &a[q * a_dim1 + 1], & c__1, &t, &aaqq); sva[q] = t * sqrt(aaqq) * d__[q]; } } if (aapp / aapp0 <= rooteps) { if (aapp < rootbig && aapp > rootsfmin) { aapp = dnrm2_(m, &a[p * a_dim1 + 1], &c__1) * d__[p]; } else { t = 0.; aapp = 1.; dlassq_(m, &a[p * a_dim1 + 1], & c__1, &t, &aapp); aapp = t * sqrt(aapp) * d__[p]; } sva[p] = aapp; } } else { /* A(:,p) and A(:,q) already numerically orthogonal */ if (ir1 == 0) { ++notrot; } ++pskipped; } } else { /* A(:,q) is zero column */ if (ir1 == 0) { ++notrot; } ++pskipped; } if (i__ <= swband && pskipped > rowskip) { if (ir1 == 0) { aapp = -aapp; } notrot = 0; goto L2103; } /* L2002: */ } /* END q-LOOP */ L2103: /* bailed out of q-loop */ sva[p] = aapp; } else { sva[p] = aapp; if (ir1 == 0 && aapp == 0.) { /* Computing MIN */ i__5 = igl + kbl - 1; notrot = notrot + f2cmin(i__5,*n) - p; } } /* L2001: */ } /* end of the p-loop */ /* end of doing the block ( ibr, ibr ) */ /* L1002: */ } /* end of ir1-loop */ /* ........................................................ */ /* ... go to the off diagonal blocks */ igl = (ibr - 1) * kbl + 1; i__3 = nbl; for (jbc = ibr + 1; jbc <= i__3; ++jbc) { jgl = (jbc - 1) * kbl + 1; /* doing the block at ( ibr, jbc ) */ ijblsk = 0; /* Computing MIN */ i__5 = igl + kbl - 1; i__4 = f2cmin(i__5,*n); for (p = igl; p <= i__4; ++p) { aapp = sva[p]; if (aapp > 0.) { pskipped = 0; /* Computing MIN */ i__6 = jgl + kbl - 1; i__5 = f2cmin(i__6,*n); for (q = jgl; q <= i__5; ++q) { aaqq = sva[q]; if (aaqq > 0.) { aapp0 = aapp; /* -#- M x 2 Jacobi SVD -#- */ /* -#- Safe Gram matrix computation -#- */ if (aaqq >= 1.) { if (aapp >= aaqq) { rotok = small * aapp <= aaqq; } else { rotok = small * aaqq <= aapp; } if (aapp < big / aaqq) { aapq = ddot_(m, &a[p * a_dim1 + 1], & c__1, &a[q * a_dim1 + 1], & c__1) * d__[p] * d__[q] / aaqq / aapp; } else { dcopy_(m, &a[p * a_dim1 + 1], &c__1, & work[1], &c__1); dlascl_("G", &c__0, &c__0, &aapp, & d__[p], m, &c__1, &work[1], lda, &ierr); aapq = ddot_(m, &work[1], &c__1, &a[q * a_dim1 + 1], &c__1) * d__[q] / aaqq; } } else { if (aapp >= aaqq) { rotok = aapp <= aaqq / small; } else { rotok = aaqq <= aapp / small; } if (aapp > small / aaqq) { aapq = ddot_(m, &a[p * a_dim1 + 1], & c__1, &a[q * a_dim1 + 1], & c__1) * d__[p] * d__[q] / aaqq / aapp; } else { dcopy_(m, &a[q * a_dim1 + 1], &c__1, & work[1], &c__1); dlascl_("G", &c__0, &c__0, &aaqq, & d__[q], m, &c__1, &work[1], lda, &ierr); aapq = ddot_(m, &work[1], &c__1, &a[p * a_dim1 + 1], &c__1) * d__[p] / aapp; } } /* Computing MAX */ d__1 = mxaapq, d__2 = abs(aapq); mxaapq = f2cmax(d__1,d__2); /* TO rotate or NOT to rotate, THAT is the question ... */ if (abs(aapq) > *tol) { notrot = 0; /* ROTATED = ROTATED + 1 */ pskipped = 0; ++iswrot; if (rotok) { aqoap = aaqq / aapp; apoaq = aapp / aaqq; theta = (d__1 = aqoap - apoaq, abs( d__1)) * -.5 / aapq; if (aaqq > aapp0) { theta = -theta; } if (abs(theta) > bigtheta) { t = .5 / theta; fastr[2] = t * d__[p] / d__[q]; fastr[3] = -t * d__[q] / d__[p]; drotm_(m, &a[p * a_dim1 + 1], & c__1, &a[q * a_dim1 + 1], &c__1, fastr); if (rsvec) { drotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q * v_dim1 + 1], &c__1, fastr); } /* Computing MAX */ d__1 = 0., d__2 = t * apoaq * aapq + 1.; sva[q] = aaqq * sqrt((f2cmax(d__1, d__2))); /* Computing MAX */ d__1 = 0., d__2 = 1. - t * aqoap * aapq; aapp *= sqrt((f2cmax(d__1,d__2))); /* Computing MAX */ d__1 = mxsinj, d__2 = abs(t); mxsinj = f2cmax(d__1,d__2); } else { thsign = -d_sign(&c_b42, &aapq); if (aaqq > aapp0) { thsign = -thsign; } t = 1. / (theta + thsign * sqrt( theta * theta + 1.)); cs = sqrt(1. / (t * t + 1.)); sn = t * cs; /* Computing MAX */ d__1 = mxsinj, d__2 = abs(sn); mxsinj = f2cmax(d__1,d__2); /* Computing MAX */ d__1 = 0., d__2 = t * apoaq * aapq + 1.; sva[q] = aaqq * sqrt((f2cmax(d__1, d__2))); /* Computing MAX */ d__1 = 0., d__2 = 1. - t * aqoap * aapq; aapp *= sqrt((f2cmax(d__1,d__2))); apoaq = d__[p] / d__[q]; aqoap = d__[q] / d__[p]; if (d__[p] >= 1.) { if (d__[q] >= 1.) { fastr[2] = t * apoaq; fastr[3] = -t * aqoap; d__[p] *= cs; d__[q] *= cs; drotm_(m, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 + 1], &c__1, fastr); if (rsvec) { drotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[ q * v_dim1 + 1], &c__1, fastr); } } else { d__1 = -t * aqoap; daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[ p * a_dim1 + 1], &c__1); d__1 = cs * sn * apoaq; daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[ q * a_dim1 + 1], &c__1); if (rsvec) { d__1 = -t * aqoap; daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], & c__1, &v[p * v_dim1 + 1], &c__1); d__1 = cs * sn * apoaq; daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], & c__1, &v[q * v_dim1 + 1], &c__1); } d__[p] *= cs; d__[q] /= cs; } } else { if (d__[q] >= 1.) { d__1 = t * apoaq; daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[ q * a_dim1 + 1], &c__1); d__1 = -cs * sn * aqoap; daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[ p * a_dim1 + 1], &c__1); if (rsvec) { d__1 = t * apoaq; daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], & c__1, &v[q * v_dim1 + 1], &c__1); d__1 = -cs * sn * aqoap; daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], & c__1, &v[p * v_dim1 + 1], &c__1); } d__[p] /= cs; d__[q] *= cs; } else { if (d__[p] >= d__[q]) { d__1 = -t * aqoap; daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[p * a_dim1 + 1], &c__1); d__1 = cs * sn * apoaq; daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 + 1], &c__1); d__[p] *= cs; d__[q] /= cs; if (rsvec) { d__1 = -t * aqoap; daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], &c__1, &v[p * v_dim1 + 1], & c__1); d__1 = cs * sn * apoaq; daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], &c__1, &v[q * v_dim1 + 1], & c__1); } } else { d__1 = t * apoaq; daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 + 1], &c__1); d__1 = -cs * sn * aqoap; daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[p * a_dim1 + 1], &c__1); d__[p] /= cs; d__[q] *= cs; if (rsvec) { d__1 = t * apoaq; daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], &c__1, &v[q * v_dim1 + 1], & c__1); d__1 = -cs * sn * aqoap; daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], &c__1, &v[p * v_dim1 + 1], & c__1); } } } } } } else { if (aapp > aaqq) { dcopy_(m, &a[p * a_dim1 + 1], & c__1, &work[1], &c__1); dlascl_("G", &c__0, &c__0, &aapp, &c_b42, m, &c__1, &work[1] , lda, &ierr); dlascl_("G", &c__0, &c__0, &aaqq, &c_b42, m, &c__1, &a[q * a_dim1 + 1], lda, &ierr); temp1 = -aapq * d__[p] / d__[q]; daxpy_(m, &temp1, &work[1], &c__1, &a[q * a_dim1 + 1], & c__1); dlascl_("G", &c__0, &c__0, &c_b42, &aaqq, m, &c__1, &a[q * a_dim1 + 1], lda, &ierr); /* Computing MAX */ d__1 = 0., d__2 = 1. - aapq * aapq; sva[q] = aaqq * sqrt((f2cmax(d__1, d__2))); mxsinj = f2cmax(mxsinj,*sfmin); } else { dcopy_(m, &a[q * a_dim1 + 1], & c__1, &work[1], &c__1); dlascl_("G", &c__0, &c__0, &aaqq, &c_b42, m, &c__1, &work[1] , lda, &ierr); dlascl_("G", &c__0, &c__0, &aapp, &c_b42, m, &c__1, &a[p * a_dim1 + 1], lda, &ierr); temp1 = -aapq * d__[q] / d__[p]; daxpy_(m, &temp1, &work[1], &c__1, &a[p * a_dim1 + 1], & c__1); dlascl_("G", &c__0, &c__0, &c_b42, &aapp, m, &c__1, &a[p * a_dim1 + 1], lda, &ierr); /* Computing MAX */ d__1 = 0., d__2 = 1. - aapq * aapq; sva[p] = aapp * sqrt((f2cmax(d__1, d__2))); mxsinj = f2cmax(mxsinj,*sfmin); } } /* END IF ROTOK THEN ... ELSE */ /* In the case of cancellation in updating SVA(q) */ /* Computing 2nd power */ d__1 = sva[q] / aaqq; if (d__1 * d__1 <= rooteps) { if (aaqq < rootbig && aaqq > rootsfmin) { sva[q] = dnrm2_(m, &a[q * a_dim1 + 1], &c__1) * d__[q]; } else { t = 0.; aaqq = 1.; dlassq_(m, &a[q * a_dim1 + 1], & c__1, &t, &aaqq); sva[q] = t * sqrt(aaqq) * d__[q]; } } /* Computing 2nd power */ d__1 = aapp / aapp0; if (d__1 * d__1 <= rooteps) { if (aapp < rootbig && aapp > rootsfmin) { aapp = dnrm2_(m, &a[p * a_dim1 + 1], &c__1) * d__[p]; } else { t = 0.; aapp = 1.; dlassq_(m, &a[p * a_dim1 + 1], & c__1, &t, &aapp); aapp = t * sqrt(aapp) * d__[p]; } sva[p] = aapp; } /* end of OK rotation */ } else { ++notrot; ++pskipped; ++ijblsk; } } else { ++notrot; ++pskipped; ++ijblsk; } if (i__ <= swband && ijblsk >= blskip) { sva[p] = aapp; notrot = 0; goto L2011; } if (i__ <= swband && pskipped > rowskip) { aapp = -aapp; notrot = 0; goto L2203; } /* L2200: */ } /* end of the q-loop */ L2203: sva[p] = aapp; } else { if (aapp == 0.) { /* Computing MIN */ i__5 = jgl + kbl - 1; notrot = notrot + f2cmin(i__5,*n) - jgl + 1; } if (aapp < 0.) { notrot = 0; } } /* L2100: */ } /* end of the p-loop */ /* L2010: */ } /* end of the jbc-loop */ L2011: /* 2011 bailed out of the jbc-loop */ /* Computing MIN */ i__4 = igl + kbl - 1; i__3 = f2cmin(i__4,*n); for (p = igl; p <= i__3; ++p) { sva[p] = (d__1 = sva[p], abs(d__1)); /* L2012: */ } /* L2000: */ } /* 2000 :: end of the ibr-loop */ if (sva[*n] < rootbig && sva[*n] > rootsfmin) { sva[*n] = dnrm2_(m, &a[*n * a_dim1 + 1], &c__1) * d__[*n]; } else { t = 0.; aapp = 1.; dlassq_(m, &a[*n * a_dim1 + 1], &c__1, &t, &aapp); sva[*n] = t * sqrt(aapp) * d__[*n]; } /* Additional steering devices */ if (i__ < swband && (mxaapq <= roottol || iswrot <= *n)) { swband = i__; } if (i__ > swband + 1 && mxaapq < (doublereal) (*n) * *tol && ( doublereal) (*n) * mxaapq * mxsinj < *tol) { goto L1994; } if (notrot >= emptsw) { goto L1994; } /* L1993: */ } /* end i=1:NSWEEP loop */ /* #:) Reaching this point means that the procedure has completed the given */ /* number of iterations. */ *info = *nsweep - 1; goto L1995; L1994: /* #:) Reaching this point means that during the i-th sweep all pivots were */ /* below the given tolerance, causing early exit. */ *info = 0; /* #:) INFO = 0 confirms successful iterations. */ L1995: /* Sort the vector D. */ i__1 = *n - 1; for (p = 1; p <= i__1; ++p) { i__2 = *n - p + 1; q = idamax_(&i__2, &sva[p], &c__1) + p - 1; if (p != q) { temp1 = sva[p]; sva[p] = sva[q]; sva[q] = temp1; temp1 = d__[p]; d__[p] = d__[q]; d__[q] = temp1; dswap_(m, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 + 1], &c__1); if (rsvec) { dswap_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q * v_dim1 + 1], & c__1); } } /* L5991: */ } return 0; } /* dgsvj0_ */