#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 SBDSDC */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SBDSDC + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SBDSDC( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ, */ /* WORK, IWORK, INFO ) */ /* CHARACTER COMPQ, UPLO */ /* INTEGER INFO, LDU, LDVT, N */ /* INTEGER IQ( * ), IWORK( * ) */ /* REAL D( * ), E( * ), Q( * ), U( LDU, * ), */ /* $ VT( LDVT, * ), WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SBDSDC computes the singular value decomposition (SVD) of a real */ /* > N-by-N (upper or lower) bidiagonal matrix B: B = U * S * VT, */ /* > using a divide and conquer method, where S is a diagonal matrix */ /* > with non-negative diagonal elements (the singular values of B), and */ /* > U and VT are orthogonal matrices of left and right singular vectors, */ /* > respectively. SBDSDC can be used to compute all singular values, */ /* > and optionally, singular vectors or singular vectors in compact form. */ /* > */ /* > This code makes very mild assumptions about floating point */ /* > arithmetic. It will work on machines with a guard digit in */ /* > add/subtract, or on those binary machines without guard digits */ /* > which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. */ /* > It could conceivably fail on hexadecimal or decimal machines */ /* > without guard digits, but we know of none. See SLASD3 for details. */ /* > */ /* > The code currently calls SLASDQ if singular values only are desired. */ /* > However, it can be slightly modified to compute singular values */ /* > using the divide and conquer method. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] UPLO */ /* > \verbatim */ /* > UPLO is CHARACTER*1 */ /* > = 'U': B is upper bidiagonal. */ /* > = 'L': B is lower bidiagonal. */ /* > \endverbatim */ /* > */ /* > \param[in] COMPQ */ /* > \verbatim */ /* > COMPQ is CHARACTER*1 */ /* > Specifies whether singular vectors are to be computed */ /* > as follows: */ /* > = 'N': Compute singular values only; */ /* > = 'P': Compute singular values and compute singular */ /* > vectors in compact form; */ /* > = 'I': Compute singular values and singular vectors. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix B. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] D */ /* > \verbatim */ /* > D is REAL array, dimension (N) */ /* > On entry, the n diagonal elements of the bidiagonal matrix B. */ /* > On exit, if INFO=0, the singular values of B. */ /* > \endverbatim */ /* > */ /* > \param[in,out] E */ /* > \verbatim */ /* > E is REAL array, dimension (N-1) */ /* > On entry, the elements of E contain the offdiagonal */ /* > elements of the bidiagonal matrix whose SVD is desired. */ /* > On exit, E has been destroyed. */ /* > \endverbatim */ /* > */ /* > \param[out] U */ /* > \verbatim */ /* > U is REAL array, dimension (LDU,N) */ /* > If COMPQ = 'I', then: */ /* > On exit, if INFO = 0, U contains the left singular vectors */ /* > of the bidiagonal matrix. */ /* > For other values of COMPQ, U is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDU */ /* > \verbatim */ /* > LDU is INTEGER */ /* > The leading dimension of the array U. LDU >= 1. */ /* > If singular vectors are desired, then LDU >= f2cmax( 1, N ). */ /* > \endverbatim */ /* > */ /* > \param[out] VT */ /* > \verbatim */ /* > VT is REAL array, dimension (LDVT,N) */ /* > If COMPQ = 'I', then: */ /* > On exit, if INFO = 0, VT**T contains the right singular */ /* > vectors of the bidiagonal matrix. */ /* > For other values of COMPQ, VT is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVT */ /* > \verbatim */ /* > LDVT is INTEGER */ /* > The leading dimension of the array VT. LDVT >= 1. */ /* > If singular vectors are desired, then LDVT >= f2cmax( 1, N ). */ /* > \endverbatim */ /* > */ /* > \param[out] Q */ /* > \verbatim */ /* > Q is REAL array, dimension (LDQ) */ /* > If COMPQ = 'P', then: */ /* > On exit, if INFO = 0, Q and IQ contain the left */ /* > and right singular vectors in a compact form, */ /* > requiring O(N log N) space instead of 2*N**2. */ /* > In particular, Q contains all the REAL data in */ /* > LDQ >= N*(11 + 2*SMLSIZ + 8*INT(LOG_2(N/(SMLSIZ+1)))) */ /* > words of memory, where SMLSIZ is returned by ILAENV and */ /* > is equal to the maximum size of the subproblems at the */ /* > bottom of the computation tree (usually about 25). */ /* > For other values of COMPQ, Q is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[out] IQ */ /* > \verbatim */ /* > IQ is INTEGER array, dimension (LDIQ) */ /* > If COMPQ = 'P', then: */ /* > On exit, if INFO = 0, Q and IQ contain the left */ /* > and right singular vectors in a compact form, */ /* > requiring O(N log N) space instead of 2*N**2. */ /* > In particular, IQ contains all INTEGER data in */ /* > LDIQ >= N*(3 + 3*INT(LOG_2(N/(SMLSIZ+1)))) */ /* > words of memory, where SMLSIZ is returned by ILAENV and */ /* > is equal to the maximum size of the subproblems at the */ /* > bottom of the computation tree (usually about 25). */ /* > For other values of COMPQ, IQ is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is REAL array, dimension (MAX(1,LWORK)) */ /* > If COMPQ = 'N' then LWORK >= (4 * N). */ /* > If COMPQ = 'P' then LWORK >= (6 * N). */ /* > If COMPQ = 'I' then LWORK >= (3 * N**2 + 4 * N). */ /* > \endverbatim */ /* > */ /* > \param[out] IWORK */ /* > \verbatim */ /* > IWORK is INTEGER array, dimension (8*N) */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit. */ /* > < 0: if INFO = -i, the i-th argument had an illegal value. */ /* > > 0: The algorithm failed to compute a singular value. */ /* > The update process of divide and conquer failed. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date June 2016 */ /* > \ingroup auxOTHERcomputational */ /* > \par Contributors: */ /* ================== */ /* > */ /* > Ming Gu and Huan Ren, Computer Science Division, University of */ /* > California at Berkeley, USA */ /* > */ /* ===================================================================== */ /* Subroutine */ int sbdsdc_(char *uplo, char *compq, integer *n, real *d__, real *e, real *u, integer *ldu, real *vt, integer *ldvt, real *q, integer *iq, real *work, integer *iwork, integer *info) { /* System generated locals */ integer u_dim1, u_offset, vt_dim1, vt_offset, i__1, i__2; real r__1; /* Local variables */ integer difl, difr, ierr, perm, mlvl, sqre, i__, j, k; real p, r__; integer z__; extern logical lsame_(char *, char *); integer poles; extern /* Subroutine */ int slasr_(char *, char *, char *, integer *, integer *, real *, real *, real *, integer *); integer iuplo, nsize, start; extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, integer *), sswap_(integer *, real *, integer *, real *, integer * ), slasd0_(integer *, integer *, real *, real *, real *, integer * , real *, integer *, integer *, integer *, real *, integer *); integer ic, ii, kk; real cs; integer is, iu; real sn; extern real slamch_(char *); extern /* Subroutine */ int slasda_(integer *, integer *, integer *, integer *, real *, real *, real *, integer *, real *, integer *, real *, real *, real *, real *, integer *, integer *, integer *, integer *, real *, real *, real *, real *, integer *, integer *), xerbla_(char *, integer *, ftnlen); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *); integer givcol; extern /* Subroutine */ int slasdq_(char *, integer *, integer *, integer *, integer *, integer *, real *, real *, real *, integer *, real * , integer *, real *, integer *, real *, integer *); integer icompq; extern /* Subroutine */ int slaset_(char *, integer *, integer *, real *, real *, real *, integer *), slartg_(real *, real *, real * , real *, real *); real orgnrm; integer givnum; extern real slanst_(char *, integer *, real *, real *); integer givptr, nm1, qstart, smlsiz, wstart, smlszp; real eps; integer ivt; /* -- LAPACK computational routine (version 3.7.1) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* June 2016 */ /* ===================================================================== */ /* Changed dimension statement in comment describing E from (N) to */ /* (N-1). Sven, 17 Feb 05. */ /* ===================================================================== */ /* Test the input parameters. */ /* Parameter adjustments */ --d__; --e; u_dim1 = *ldu; u_offset = 1 + u_dim1 * 1; u -= u_offset; vt_dim1 = *ldvt; vt_offset = 1 + vt_dim1 * 1; vt -= vt_offset; --q; --iq; --work; --iwork; /* Function Body */ *info = 0; iuplo = 0; if (lsame_(uplo, "U")) { iuplo = 1; } if (lsame_(uplo, "L")) { iuplo = 2; } if (lsame_(compq, "N")) { icompq = 0; } else if (lsame_(compq, "P")) { icompq = 1; } else if (lsame_(compq, "I")) { icompq = 2; } else { icompq = -1; } if (iuplo == 0) { *info = -1; } else if (icompq < 0) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*ldu < 1 || icompq == 2 && *ldu < *n) { *info = -7; } else if (*ldvt < 1 || icompq == 2 && *ldvt < *n) { *info = -9; } if (*info != 0) { i__1 = -(*info); xerbla_("SBDSDC", &i__1, (ftnlen)6); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } smlsiz = ilaenv_(&c__9, "SBDSDC", " ", &c__0, &c__0, &c__0, &c__0, ( ftnlen)6, (ftnlen)1); if (*n == 1) { if (icompq == 1) { q[1] = r_sign(&c_b15, &d__[1]); q[smlsiz * *n + 1] = 1.f; } else if (icompq == 2) { u[u_dim1 + 1] = r_sign(&c_b15, &d__[1]); vt[vt_dim1 + 1] = 1.f; } d__[1] = abs(d__[1]); return 0; } nm1 = *n - 1; /* If matrix lower bidiagonal, rotate to be upper bidiagonal */ /* by applying Givens rotations on the left */ wstart = 1; qstart = 3; if (icompq == 1) { scopy_(n, &d__[1], &c__1, &q[1], &c__1); i__1 = *n - 1; scopy_(&i__1, &e[1], &c__1, &q[*n + 1], &c__1); } if (iuplo == 2) { qstart = 5; if (icompq == 2) { wstart = (*n << 1) - 1; } i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { slartg_(&d__[i__], &e[i__], &cs, &sn, &r__); d__[i__] = r__; e[i__] = sn * d__[i__ + 1]; d__[i__ + 1] = cs * d__[i__ + 1]; if (icompq == 1) { q[i__ + (*n << 1)] = cs; q[i__ + *n * 3] = sn; } else if (icompq == 2) { work[i__] = cs; work[nm1 + i__] = -sn; } /* L10: */ } } /* If ICOMPQ = 0, use SLASDQ to compute the singular values. */ if (icompq == 0) { /* Ignore WSTART, instead using WORK( 1 ), since the two vectors */ /* for CS and -SN above are added only if ICOMPQ == 2, */ /* and adding them exceeds documented WORK size of 4*n. */ slasdq_("U", &c__0, n, &c__0, &c__0, &c__0, &d__[1], &e[1], &vt[ vt_offset], ldvt, &u[u_offset], ldu, &u[u_offset], ldu, &work[ 1], info); goto L40; } /* If N is smaller than the minimum divide size SMLSIZ, then solve */ /* the problem with another solver. */ if (*n <= smlsiz) { if (icompq == 2) { slaset_("A", n, n, &c_b29, &c_b15, &u[u_offset], ldu); slaset_("A", n, n, &c_b29, &c_b15, &vt[vt_offset], ldvt); slasdq_("U", &c__0, n, n, n, &c__0, &d__[1], &e[1], &vt[vt_offset] , ldvt, &u[u_offset], ldu, &u[u_offset], ldu, &work[ wstart], info); } else if (icompq == 1) { iu = 1; ivt = iu + *n; slaset_("A", n, n, &c_b29, &c_b15, &q[iu + (qstart - 1) * *n], n); slaset_("A", n, n, &c_b29, &c_b15, &q[ivt + (qstart - 1) * *n], n); slasdq_("U", &c__0, n, n, n, &c__0, &d__[1], &e[1], &q[ivt + ( qstart - 1) * *n], n, &q[iu + (qstart - 1) * *n], n, &q[ iu + (qstart - 1) * *n], n, &work[wstart], info); } goto L40; } if (icompq == 2) { slaset_("A", n, n, &c_b29, &c_b15, &u[u_offset], ldu); slaset_("A", n, n, &c_b29, &c_b15, &vt[vt_offset], ldvt); } /* Scale. */ orgnrm = slanst_("M", n, &d__[1], &e[1]); if (orgnrm == 0.f) { return 0; } slascl_("G", &c__0, &c__0, &orgnrm, &c_b15, n, &c__1, &d__[1], n, &ierr); slascl_("G", &c__0, &c__0, &orgnrm, &c_b15, &nm1, &c__1, &e[1], &nm1, & ierr); eps = slamch_("Epsilon"); mlvl = (integer) (log((real) (*n) / (real) (smlsiz + 1)) / log(2.f)) + 1; smlszp = smlsiz + 1; if (icompq == 1) { iu = 1; ivt = smlsiz + 1; difl = ivt + smlszp; difr = difl + mlvl; z__ = difr + (mlvl << 1); ic = z__ + mlvl; is = ic + 1; poles = is + 1; givnum = poles + (mlvl << 1); k = 1; givptr = 2; perm = 3; givcol = perm + mlvl; } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if ((r__1 = d__[i__], abs(r__1)) < eps) { d__[i__] = r_sign(&eps, &d__[i__]); } /* L20: */ } start = 1; sqre = 0; i__1 = nm1; for (i__ = 1; i__ <= i__1; ++i__) { if ((r__1 = e[i__], abs(r__1)) < eps || i__ == nm1) { /* Subproblem found. First determine its size and then */ /* apply divide and conquer on it. */ if (i__ < nm1) { /* A subproblem with E(I) small for I < NM1. */ nsize = i__ - start + 1; } else if ((r__1 = e[i__], abs(r__1)) >= eps) { /* A subproblem with E(NM1) not too small but I = NM1. */ nsize = *n - start + 1; } else { /* A subproblem with E(NM1) small. This implies an */ /* 1-by-1 subproblem at D(N). Solve this 1-by-1 problem */ /* first. */ nsize = i__ - start + 1; if (icompq == 2) { u[*n + *n * u_dim1] = r_sign(&c_b15, &d__[*n]); vt[*n + *n * vt_dim1] = 1.f; } else if (icompq == 1) { q[*n + (qstart - 1) * *n] = r_sign(&c_b15, &d__[*n]); q[*n + (smlsiz + qstart - 1) * *n] = 1.f; } d__[*n] = (r__1 = d__[*n], abs(r__1)); } if (icompq == 2) { slasd0_(&nsize, &sqre, &d__[start], &e[start], &u[start + start * u_dim1], ldu, &vt[start + start * vt_dim1], ldvt, &smlsiz, &iwork[1], &work[wstart], info); } else { slasda_(&icompq, &smlsiz, &nsize, &sqre, &d__[start], &e[ start], &q[start + (iu + qstart - 2) * *n], n, &q[ start + (ivt + qstart - 2) * *n], &iq[start + k * *n], &q[start + (difl + qstart - 2) * *n], &q[start + ( difr + qstart - 2) * *n], &q[start + (z__ + qstart - 2) * *n], &q[start + (poles + qstart - 2) * *n], &iq[ start + givptr * *n], &iq[start + givcol * *n], n, & iq[start + perm * *n], &q[start + (givnum + qstart - 2) * *n], &q[start + (ic + qstart - 2) * *n], &q[ start + (is + qstart - 2) * *n], &work[wstart], & iwork[1], info); } if (*info != 0) { return 0; } start = i__ + 1; } /* L30: */ } /* Unscale */ slascl_("G", &c__0, &c__0, &c_b15, &orgnrm, n, &c__1, &d__[1], n, &ierr); L40: /* Use Selection Sort to minimize swaps of singular vectors */ i__1 = *n; for (ii = 2; ii <= i__1; ++ii) { i__ = ii - 1; kk = i__; p = d__[i__]; i__2 = *n; for (j = ii; j <= i__2; ++j) { if (d__[j] > p) { kk = j; p = d__[j]; } /* L50: */ } if (kk != i__) { d__[kk] = d__[i__]; d__[i__] = p; if (icompq == 1) { iq[i__] = kk; } else if (icompq == 2) { sswap_(n, &u[i__ * u_dim1 + 1], &c__1, &u[kk * u_dim1 + 1], & c__1); sswap_(n, &vt[i__ + vt_dim1], ldvt, &vt[kk + vt_dim1], ldvt); } } else if (icompq == 1) { iq[i__] = i__; } /* L60: */ } /* If ICOMPQ = 1, use IQ(N,1) as the indicator for UPLO */ if (icompq == 1) { if (iuplo == 1) { iq[*n] = 1; } else { iq[*n] = 0; } } /* If B is lower bidiagonal, update U by those Givens rotations */ /* which rotated B to be upper bidiagonal */ if (iuplo == 2 && icompq == 2) { slasr_("L", "V", "B", n, n, &work[1], &work[*n], &u[u_offset], ldu); } return 0; /* End of SBDSDC */ } /* sbdsdc_ */