#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 CGSVJ1 pre-processor for the routine cgesvj, applies Jacobi rotations targeting only particular pivots. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download CGSVJ1 + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE CGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, */ /* EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) */ /* REAL EPS, SFMIN, TOL */ /* INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP */ /* CHARACTER*1 JOBV */ /* COMPLEX A( LDA, * ), D( N ), V( LDV, * ), WORK( LWORK ) */ /* REAL SVA( N ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > 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 tunning 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 tunning parameter. */ /* > The number of sweeps is given in NSWEEP and the orthogonality threshold */ /* > is given in TOL. */ /* > \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] N1 */ /* > \verbatim */ /* > 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. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > 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.) */ /* > \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 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.) */ /* > \endverbatim */ /* > */ /* > \param[in,out] SVA */ /* > \verbatim */ /* > 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). */ /* > \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 COMPLEX 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 REAL */ /* > EPS = SLAMCH('Epsilon') */ /* > \endverbatim */ /* > */ /* > \param[in] SFMIN */ /* > \verbatim */ /* > SFMIN is REAL */ /* > SFMIN = SLAMCH('Safe Minimum') */ /* > \endverbatim */ /* > */ /* > \param[in] TOL */ /* > \verbatim */ /* > 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. */ /* > \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 COMPLEX 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 June 2016 */ /* > \ingroup complexOTHERcomputational */ /* > \par Contributor: */ /* ================== */ /* > */ /* > Zlatko Drmac (Zagreb, Croatia) */ /* ===================================================================== */ /* Subroutine */ int cgsvj1_(char *jobv, integer *m, integer *n, integer *n1, complex *a, integer *lda, complex *d__, real *sva, integer *mv, complex *v, integer *ldv, real *eps, real *sfmin, real *tol, integer * nsweep, complex *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, i__7; real r__1, r__2; complex q__1, q__2, q__3; /* Local variables */ integer nblc; real aapp; complex aapq; real aaqq; integer nblr, ierr; real bigtheta; extern /* Subroutine */ int crot_(integer *, complex *, integer *, complex *, integer *, real *, complex *); complex ompq; integer pskipped; real aapp0, aapq1, temp1; integer i__, p, q; real t; extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer *, complex *, integer *); real apoaq, aqoap; extern logical lsame_(char *, char *); real theta, small; extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, complex *, integer *), cswap_(integer *, complex *, integer *, complex *, integer *); logical applv, rsvec; extern /* Subroutine */ int caxpy_(integer *, complex *, complex *, integer *, complex *, integer *); logical rotok; real rootsfmin; extern real scnrm2_(integer *, complex *, integer *); real cs, sn; extern /* Subroutine */ int clascl_(char *, integer *, integer *, real *, real *, integer *, integer *, complex *, integer *, integer *), xerbla_(char *, integer *, ftnlen); integer ijblsk, swband; extern integer isamax_(integer *, real *, integer *); integer blskip; extern /* Subroutine */ int classq_(integer *, complex *, integer *, real *, real *); real mxaapq, thsign, mxsinj; integer emptsw, notrot, iswrot, jbc; real big; integer kbl, igl, ibr, jgl, mvl; real rootbig, rooteps; integer rowskip; real 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..-- */ /* June 2016 */ /* ===================================================================== */ /* 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 (*n1 < 0) { *info = -4; } else if (*lda < *m) { *info = -6; } else if ((rsvec || applv) && *mv < 0) { *info = -9; } else if (rsvec && *ldv < *n || applv && *ldv < *mv) { *info = -11; } else if (*tol <= *eps) { *info = -14; } else if (*nsweep < 0) { *info = -15; } else if (*lwork < *m) { *info = -17; } else { *info = 0; } /* #:( */ if (*info != 0) { i__1 = -(*info); xerbla_("CGSVJ1", &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.f / *sfmin; rootbig = 1.f / rootsfmin; /* LARGE = BIG / SQRT( REAL( M*N ) ) */ bigtheta = 1.f / rooteps; roottol = sqrt(*tol); /* RSVEC = LSAME( JOBV, 'Y' ) */ emptsw = *n1 * (*n - *n1); notrot = 0; kbl = f2cmin(8,*n); nblr = *n1 / kbl; if (nblr * kbl != *n1) { ++nblr; } nblc = (*n - *n1) / kbl; if (nblc * kbl != *n - *n1) { ++nblc; } /* 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. */ swband = 0; /* [TP] SWBAND is a tuning parameter. It is meaningful and effective */ /* if CGESVJ is used as a computational routine in the preconditioned */ /* Jacobi SVD algorithm CGEJSV. */ /* | * * * [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] * * * | */ i__1 = *nsweep; for (i__ = 1; i__ <= i__1; ++i__) { mxaapq = 0.f; mxsinj = 0.f; iswrot = 0; notrot = 0; pskipped = 0; /* Each sweep is unrolled using KBL-by-KBL tiles over the pivot pairs */ /* 1 <= p < q <= N. This is the first step toward a blocked implementation */ /* of the rotations. New implementation, based on block transformations, */ /* is under development. */ i__2 = nblr; for (ibr = 1; ibr <= i__2; ++ibr) { igl = (ibr - 1) * kbl + 1; /* ... go to the off diagonal blocks */ igl = (ibr - 1) * kbl + 1; /* DO 2010 jbc = ibr + 1, NBL */ i__3 = nblc; for (jbc = 1; jbc <= i__3; ++jbc) { jgl = (jbc - 1) * kbl + *n1 + 1; /* doing the block at ( ibr, jbc ) */ ijblsk = 0; /* Computing MIN */ i__5 = igl + kbl - 1; i__4 = f2cmin(i__5,*n1); for (p = igl; p <= i__4; ++p) { aapp = sva[p]; if (aapp > 0.f) { 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.f) { aapp0 = aapp; /* Safe Gram matrix computation */ if (aaqq >= 1.f) { if (aapp >= aaqq) { rotok = small * aapp <= aaqq; } else { rotok = small * aaqq <= aapp; } if (aapp < big / aaqq) { cdotc_(&q__3, m, &a[p * a_dim1 + 1], & c__1, &a[q * a_dim1 + 1], & c__1); q__2.r = q__3.r / aaqq, q__2.i = q__3.i / aaqq; q__1.r = q__2.r / aapp, q__1.i = q__2.i / aapp; aapq.r = q__1.r, aapq.i = q__1.i; } else { ccopy_(m, &a[p * a_dim1 + 1], &c__1, & work[1], &c__1); clascl_("G", &c__0, &c__0, &aapp, & c_b18, m, &c__1, &work[1], lda, &ierr); cdotc_(&q__2, m, &work[1], &c__1, &a[ q * a_dim1 + 1], &c__1); q__1.r = q__2.r / aaqq, q__1.i = q__2.i / aaqq; aapq.r = q__1.r, aapq.i = q__1.i; } } else { if (aapp >= aaqq) { rotok = aapp <= aaqq / small; } else { rotok = aaqq <= aapp / small; } if (aapp > small / aaqq) { cdotc_(&q__3, m, &a[p * a_dim1 + 1], & c__1, &a[q * a_dim1 + 1], & c__1); r__1 = f2cmax(aaqq,aapp); q__2.r = q__3.r / r__1, q__2.i = q__3.i / r__1; r__2 = f2cmin(aaqq,aapp); q__1.r = q__2.r / r__2, q__1.i = q__2.i / r__2; aapq.r = q__1.r, aapq.i = q__1.i; } else { ccopy_(m, &a[q * a_dim1 + 1], &c__1, & work[1], &c__1); clascl_("G", &c__0, &c__0, &aaqq, & c_b18, m, &c__1, &work[1], lda, &ierr); cdotc_(&q__2, m, &a[p * a_dim1 + 1], & c__1, &work[1], &c__1); q__1.r = q__2.r / aapp, q__1.i = q__2.i / aapp; aapq.r = q__1.r, aapq.i = q__1.i; } } /* AAPQ = AAPQ * CONJG(CWORK(p))*CWORK(q) */ aapq1 = -c_abs(&aapq); /* Computing MAX */ r__1 = mxaapq, r__2 = -aapq1; mxaapq = f2cmax(r__1,r__2); /* TO rotate or NOT to rotate, THAT is the question ... */ if (abs(aapq1) > *tol) { r__1 = c_abs(&aapq); q__1.r = aapq.r / r__1, q__1.i = aapq.i / r__1; ompq.r = q__1.r, ompq.i = q__1.i; notrot = 0; /* [RTD] ROTATED = ROTATED + 1 */ pskipped = 0; ++iswrot; if (rotok) { aqoap = aaqq / aapp; apoaq = aapp / aaqq; theta = (r__1 = aqoap - apoaq, abs( r__1)) * -.5f / aapq1; if (aaqq > aapp0) { theta = -theta; } if (abs(theta) > bigtheta) { t = .5f / theta; cs = 1.f; r_cnjg(&q__2, &ompq); q__1.r = t * q__2.r, q__1.i = t * q__2.i; crot_(m, &a[p * a_dim1 + 1], & c__1, &a[q * a_dim1 + 1], &c__1, &cs, &q__1); if (rsvec) { r_cnjg(&q__2, &ompq); q__1.r = t * q__2.r, q__1.i = t * q__2.i; crot_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q * v_dim1 + 1], &c__1, &cs, &q__1); } /* Computing MAX */ r__1 = 0.f, r__2 = t * apoaq * aapq1 + 1.f; sva[q] = aaqq * sqrt((f2cmax(r__1, r__2))); /* Computing MAX */ r__1 = 0.f, r__2 = 1.f - t * aqoap * aapq1; aapp *= sqrt((f2cmax(r__1,r__2))); /* Computing MAX */ r__1 = mxsinj, r__2 = abs(t); mxsinj = f2cmax(r__1,r__2); } else { thsign = -r_sign(&c_b18, &aapq1); if (aaqq > aapp0) { thsign = -thsign; } t = 1.f / (theta + thsign * sqrt( theta * theta + 1.f)); cs = sqrt(1.f / (t * t + 1.f)); sn = t * cs; /* Computing MAX */ r__1 = mxsinj, r__2 = abs(sn); mxsinj = f2cmax(r__1,r__2); /* Computing MAX */ r__1 = 0.f, r__2 = t * apoaq * aapq1 + 1.f; sva[q] = aaqq * sqrt((f2cmax(r__1, r__2))); /* Computing MAX */ r__1 = 0.f, r__2 = 1.f - t * aqoap * aapq1; aapp *= sqrt((f2cmax(r__1,r__2))); r_cnjg(&q__2, &ompq); q__1.r = sn * q__2.r, q__1.i = sn * q__2.i; crot_(m, &a[p * a_dim1 + 1], & c__1, &a[q * a_dim1 + 1], &c__1, &cs, &q__1); if (rsvec) { r_cnjg(&q__2, &ompq); q__1.r = sn * q__2.r, q__1.i = sn * q__2.i; crot_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q * v_dim1 + 1], &c__1, &cs, &q__1); } } i__6 = p; i__7 = q; q__2.r = -d__[i__7].r, q__2.i = -d__[ i__7].i; q__1.r = q__2.r * ompq.r - q__2.i * ompq.i, q__1.i = q__2.r * ompq.i + q__2.i * ompq.r; d__[i__6].r = q__1.r, d__[i__6].i = q__1.i; } else { if (aapp > aaqq) { ccopy_(m, &a[p * a_dim1 + 1], & c__1, &work[1], &c__1); clascl_("G", &c__0, &c__0, &aapp, &c_b18, m, &c__1, &work[1] , lda, &ierr); clascl_("G", &c__0, &c__0, &aaqq, &c_b18, m, &c__1, &a[q * a_dim1 + 1], lda, &ierr); q__1.r = -aapq.r, q__1.i = -aapq.i; caxpy_(m, &q__1, &work[1], &c__1, &a[q * a_dim1 + 1], &c__1) ; clascl_("G", &c__0, &c__0, &c_b18, &aaqq, m, &c__1, &a[q * a_dim1 + 1], lda, &ierr); /* Computing MAX */ r__1 = 0.f, r__2 = 1.f - aapq1 * aapq1; sva[q] = aaqq * sqrt((f2cmax(r__1, r__2))); mxsinj = f2cmax(mxsinj,*sfmin); } else { ccopy_(m, &a[q * a_dim1 + 1], & c__1, &work[1], &c__1); clascl_("G", &c__0, &c__0, &aaqq, &c_b18, m, &c__1, &work[1] , lda, &ierr); clascl_("G", &c__0, &c__0, &aapp, &c_b18, m, &c__1, &a[p * a_dim1 + 1], lda, &ierr); r_cnjg(&q__2, &aapq); q__1.r = -q__2.r, q__1.i = -q__2.i; caxpy_(m, &q__1, &work[1], &c__1, &a[p * a_dim1 + 1], &c__1) ; clascl_("G", &c__0, &c__0, &c_b18, &aapp, m, &c__1, &a[p * a_dim1 + 1], lda, &ierr); /* Computing MAX */ r__1 = 0.f, r__2 = 1.f - aapq1 * aapq1; sva[p] = aapp * sqrt((f2cmax(r__1, r__2))); mxsinj = f2cmax(mxsinj,*sfmin); } } /* END IF ROTOK THEN ... ELSE */ /* In the case of cancellation in updating SVA(q), SVA(p) */ /* Computing 2nd power */ r__1 = sva[q] / aaqq; if (r__1 * r__1 <= rooteps) { if (aaqq < rootbig && aaqq > rootsfmin) { sva[q] = scnrm2_(m, &a[q * a_dim1 + 1], &c__1); } else { t = 0.f; aaqq = 1.f; classq_(m, &a[q * a_dim1 + 1], & c__1, &t, &aaqq); sva[q] = t * sqrt(aaqq); } } /* Computing 2nd power */ r__1 = aapp / aapp0; if (r__1 * r__1 <= rooteps) { if (aapp < rootbig && aapp > rootsfmin) { aapp = scnrm2_(m, &a[p * a_dim1 + 1], &c__1); } else { t = 0.f; aapp = 1.f; classq_(m, &a[p * a_dim1 + 1], & c__1, &t, &aapp); aapp = t * sqrt(aapp); } sva[p] = aapp; } /* end of OK rotation */ } else { ++notrot; /* [RTD] SKIPPED = SKIPPED + 1 */ ++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.f) { /* Computing MIN */ i__5 = jgl + kbl - 1; notrot = notrot + f2cmin(i__5,*n) - jgl + 1; } if (aapp < 0.f) { 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] = (r__1 = sva[p], abs(r__1)); /* L2012: */ } /* ** */ /* L2000: */ } /* 2000 :: end of the ibr-loop */ if (sva[*n] < rootbig && sva[*n] > rootsfmin) { sva[*n] = scnrm2_(m, &a[*n * a_dim1 + 1], &c__1); } else { t = 0.f; aapp = 1.f; classq_(m, &a[*n * a_dim1 + 1], &c__1, &t, &aapp); sva[*n] = t * sqrt(aapp); } /* Additional steering devices */ if (i__ < swband && (mxaapq <= roottol || iswrot <= *n)) { swband = i__; } if (i__ > swband + 1 && mxaapq < sqrt((real) (*n)) * *tol && (real) (* 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 not converged. */ *info = *nsweep - 1; goto L1995; L1994: /* #:) Reaching this point means numerical convergence after the i-th */ /* sweep. */ *info = 0; /* #:) INFO = 0 confirms successful iterations. */ L1995: /* Sort the vector SVA() of column norms. */ i__1 = *n - 1; for (p = 1; p <= i__1; ++p) { i__2 = *n - p + 1; q = isamax_(&i__2, &sva[p], &c__1) + p - 1; if (p != q) { temp1 = sva[p]; sva[p] = sva[q]; sva[q] = temp1; i__2 = p; aapq.r = d__[i__2].r, aapq.i = d__[i__2].i; i__2 = p; i__3 = q; d__[i__2].r = d__[i__3].r, d__[i__2].i = d__[i__3].i; i__2 = q; d__[i__2].r = aapq.r, d__[i__2].i = aapq.i; cswap_(m, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 + 1], &c__1); if (rsvec) { cswap_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q * v_dim1 + 1], & c__1); } } /* L5991: */ } return 0; } /* cgsvj1_ */