#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 SLASD6 computes the SVD of an updated upper bidiagonal matrix obtained by merging two smaller o nes by appending a row. Used by sbdsdc. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SLASD6 + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SLASD6( ICOMPQ, NL, NR, SQRE, D, VF, VL, ALPHA, BETA, */ /* IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, */ /* LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK, */ /* IWORK, INFO ) */ /* INTEGER GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL, */ /* $ NR, SQRE */ /* REAL ALPHA, BETA, C, S */ /* INTEGER GIVCOL( LDGCOL, * ), IDXQ( * ), IWORK( * ), */ /* $ PERM( * ) */ /* REAL D( * ), DIFL( * ), DIFR( * ), */ /* $ GIVNUM( LDGNUM, * ), POLES( LDGNUM, * ), */ /* $ VF( * ), VL( * ), WORK( * ), Z( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SLASD6 computes the SVD of an updated upper bidiagonal matrix B */ /* > obtained by merging two smaller ones by appending a row. This */ /* > routine is used only for the problem which requires all singular */ /* > values and optionally singular vector matrices in factored form. */ /* > B is an N-by-M matrix with N = NL + NR + 1 and M = N + SQRE. */ /* > A related subroutine, SLASD1, handles the case in which all singular */ /* > values and singular vectors of the bidiagonal matrix are desired. */ /* > */ /* > SLASD6 computes the SVD as follows: */ /* > */ /* > ( D1(in) 0 0 0 ) */ /* > B = U(in) * ( Z1**T a Z2**T b ) * VT(in) */ /* > ( 0 0 D2(in) 0 ) */ /* > */ /* > = U(out) * ( D(out) 0) * VT(out) */ /* > */ /* > where Z**T = (Z1**T a Z2**T b) = u**T VT**T, and u is a vector of dimension M */ /* > with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros */ /* > elsewhere; and the entry b is empty if SQRE = 0. */ /* > */ /* > The singular values of B can be computed using D1, D2, the first */ /* > components of all the right singular vectors of the lower block, and */ /* > the last components of all the right singular vectors of the upper */ /* > block. These components are stored and updated in VF and VL, */ /* > respectively, in SLASD6. Hence U and VT are not explicitly */ /* > referenced. */ /* > */ /* > The singular values are stored in D. The algorithm consists of two */ /* > stages: */ /* > */ /* > The first stage consists of deflating the size of the problem */ /* > when there are multiple singular values or if there is a zero */ /* > in the Z vector. For each such occurrence the dimension of the */ /* > secular equation problem is reduced by one. This stage is */ /* > performed by the routine SLASD7. */ /* > */ /* > The second stage consists of calculating the updated */ /* > singular values. This is done by finding the roots of the */ /* > secular equation via the routine SLASD4 (as called by SLASD8). */ /* > This routine also updates VF and VL and computes the distances */ /* > between the updated singular values and the old singular */ /* > values. */ /* > */ /* > SLASD6 is called from SLASDA. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] ICOMPQ */ /* > \verbatim */ /* > ICOMPQ is INTEGER */ /* > Specifies whether singular vectors are to be computed in */ /* > factored form: */ /* > = 0: Compute singular values only. */ /* > = 1: Compute singular vectors in factored form as well. */ /* > \endverbatim */ /* > */ /* > \param[in] NL */ /* > \verbatim */ /* > NL is INTEGER */ /* > The row dimension of the upper block. NL >= 1. */ /* > \endverbatim */ /* > */ /* > \param[in] NR */ /* > \verbatim */ /* > NR is INTEGER */ /* > The row dimension of the lower block. NR >= 1. */ /* > \endverbatim */ /* > */ /* > \param[in] SQRE */ /* > \verbatim */ /* > SQRE is INTEGER */ /* > = 0: the lower block is an NR-by-NR square matrix. */ /* > = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */ /* > */ /* > The bidiagonal matrix has row dimension N = NL + NR + 1, */ /* > and column dimension M = N + SQRE. */ /* > \endverbatim */ /* > */ /* > \param[in,out] D */ /* > \verbatim */ /* > D is REAL array, dimension (NL+NR+1). */ /* > On entry D(1:NL,1:NL) contains the singular values of the */ /* > upper block, and D(NL+2:N) contains the singular values */ /* > of the lower block. On exit D(1:N) contains the singular */ /* > values of the modified matrix. */ /* > \endverbatim */ /* > */ /* > \param[in,out] VF */ /* > \verbatim */ /* > VF is REAL array, dimension (M) */ /* > On entry, VF(1:NL+1) contains the first components of all */ /* > right singular vectors of the upper block; and VF(NL+2:M) */ /* > contains the first components of all right singular vectors */ /* > of the lower block. On exit, VF contains the first components */ /* > of all right singular vectors of the bidiagonal matrix. */ /* > \endverbatim */ /* > */ /* > \param[in,out] VL */ /* > \verbatim */ /* > VL is REAL array, dimension (M) */ /* > On entry, VL(1:NL+1) contains the last components of all */ /* > right singular vectors of the upper block; and VL(NL+2:M) */ /* > contains the last components of all right singular vectors of */ /* > the lower block. On exit, VL contains the last components of */ /* > all right singular vectors of the bidiagonal matrix. */ /* > \endverbatim */ /* > */ /* > \param[in,out] ALPHA */ /* > \verbatim */ /* > ALPHA is REAL */ /* > Contains the diagonal element associated with the added row. */ /* > \endverbatim */ /* > */ /* > \param[in,out] BETA */ /* > \verbatim */ /* > BETA is REAL */ /* > Contains the off-diagonal element associated with the added */ /* > row. */ /* > \endverbatim */ /* > */ /* > \param[in,out] IDXQ */ /* > \verbatim */ /* > IDXQ is INTEGER array, dimension (N) */ /* > This contains the permutation which will reintegrate the */ /* > subproblem just solved back into sorted order, i.e. */ /* > D( IDXQ( I = 1, N ) ) will be in ascending order. */ /* > \endverbatim */ /* > */ /* > \param[out] PERM */ /* > \verbatim */ /* > PERM is INTEGER array, dimension ( N ) */ /* > The permutations (from deflation and sorting) to be applied */ /* > to each block. Not referenced if ICOMPQ = 0. */ /* > \endverbatim */ /* > */ /* > \param[out] GIVPTR */ /* > \verbatim */ /* > GIVPTR is INTEGER */ /* > The number of Givens rotations which took place in this */ /* > subproblem. Not referenced if ICOMPQ = 0. */ /* > \endverbatim */ /* > */ /* > \param[out] GIVCOL */ /* > \verbatim */ /* > GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) */ /* > Each pair of numbers indicates a pair of columns to take place */ /* > in a Givens rotation. Not referenced if ICOMPQ = 0. */ /* > \endverbatim */ /* > */ /* > \param[in] LDGCOL */ /* > \verbatim */ /* > LDGCOL is INTEGER */ /* > leading dimension of GIVCOL, must be at least N. */ /* > \endverbatim */ /* > */ /* > \param[out] GIVNUM */ /* > \verbatim */ /* > GIVNUM is REAL array, dimension ( LDGNUM, 2 ) */ /* > Each number indicates the C or S value to be used in the */ /* > corresponding Givens rotation. Not referenced if ICOMPQ = 0. */ /* > \endverbatim */ /* > */ /* > \param[in] LDGNUM */ /* > \verbatim */ /* > LDGNUM is INTEGER */ /* > The leading dimension of GIVNUM and POLES, must be at least N. */ /* > \endverbatim */ /* > */ /* > \param[out] POLES */ /* > \verbatim */ /* > POLES is REAL array, dimension ( LDGNUM, 2 ) */ /* > On exit, POLES(1,*) is an array containing the new singular */ /* > values obtained from solving the secular equation, and */ /* > POLES(2,*) is an array containing the poles in the secular */ /* > equation. Not referenced if ICOMPQ = 0. */ /* > \endverbatim */ /* > */ /* > \param[out] DIFL */ /* > \verbatim */ /* > DIFL is REAL array, dimension ( N ) */ /* > On exit, DIFL(I) is the distance between I-th updated */ /* > (undeflated) singular value and the I-th (undeflated) old */ /* > singular value. */ /* > \endverbatim */ /* > */ /* > \param[out] DIFR */ /* > \verbatim */ /* > DIFR is REAL array, */ /* > dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and */ /* > dimension ( K ) if ICOMPQ = 0. */ /* > On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not */ /* > defined and will not be referenced. */ /* > */ /* > If ICOMPQ = 1, DIFR(1:K,2) is an array containing the */ /* > normalizing factors for the right singular vector matrix. */ /* > */ /* > See SLASD8 for details on DIFL and DIFR. */ /* > \endverbatim */ /* > */ /* > \param[out] Z */ /* > \verbatim */ /* > Z is REAL array, dimension ( M ) */ /* > The first elements of this array contain the components */ /* > of the deflation-adjusted updating row vector. */ /* > \endverbatim */ /* > */ /* > \param[out] K */ /* > \verbatim */ /* > K is INTEGER */ /* > Contains the dimension of the non-deflated matrix, */ /* > This is the order of the related secular equation. 1 <= K <=N. */ /* > \endverbatim */ /* > */ /* > \param[out] C */ /* > \verbatim */ /* > C is REAL */ /* > C contains garbage if SQRE =0 and the C-value of a Givens */ /* > rotation related to the right null space if SQRE = 1. */ /* > \endverbatim */ /* > */ /* > \param[out] S */ /* > \verbatim */ /* > S is REAL */ /* > S contains garbage if SQRE =0 and the S-value of a Givens */ /* > rotation related to the right null space if SQRE = 1. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is REAL array, dimension ( 4 * M ) */ /* > \endverbatim */ /* > */ /* > \param[out] IWORK */ /* > \verbatim */ /* > IWORK is INTEGER array, dimension ( 3 * 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: if INFO = 1, a singular value did not converge */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date June 2016 */ /* > \ingroup OTHERauxiliary */ /* > \par Contributors: */ /* ================== */ /* > */ /* > Ming Gu and Huan Ren, Computer Science Division, University of */ /* > California at Berkeley, USA */ /* > */ /* ===================================================================== */ /* Subroutine */ int slasd6_(integer *icompq, integer *nl, integer *nr, integer *sqre, real *d__, real *vf, real *vl, real *alpha, real *beta, integer *idxq, integer *perm, integer *givptr, integer *givcol, integer *ldgcol, real *givnum, integer *ldgnum, real *poles, real * difl, real *difr, real *z__, integer *k, real *c__, real *s, real * work, integer *iwork, integer *info) { /* System generated locals */ integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset, poles_dim1, poles_offset, i__1; real r__1, r__2; /* Local variables */ integer idxc, idxp, ivfw, ivlw, i__, m, n; extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, integer *); integer n1, n2; extern /* Subroutine */ int slasd7_(integer *, integer *, integer *, integer *, integer *, real *, real *, real *, real *, real *, real *, real *, real *, real *, real *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, real *, integer *, real *, real *, integer *), slasd8_(integer *, integer *, real *, real *, real *, real *, real *, real *, integer *, real *, real *, integer *); integer iw, isigma; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), slascl_( char *, integer *, integer *, real *, real *, integer *, integer * , real *, integer *, integer *), slamrg_(integer *, integer *, real *, integer *, integer *, integer *); real orgnrm; integer idx; /* -- LAPACK auxiliary routine (version 3.7.0) -- */ /* -- 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 */ --d__; --vf; --vl; --idxq; --perm; givcol_dim1 = *ldgcol; givcol_offset = 1 + givcol_dim1 * 1; givcol -= givcol_offset; poles_dim1 = *ldgnum; poles_offset = 1 + poles_dim1 * 1; poles -= poles_offset; givnum_dim1 = *ldgnum; givnum_offset = 1 + givnum_dim1 * 1; givnum -= givnum_offset; --difl; --difr; --z__; --work; --iwork; /* Function Body */ *info = 0; n = *nl + *nr + 1; m = n + *sqre; if (*icompq < 0 || *icompq > 1) { *info = -1; } else if (*nl < 1) { *info = -2; } else if (*nr < 1) { *info = -3; } else if (*sqre < 0 || *sqre > 1) { *info = -4; } else if (*ldgcol < n) { *info = -14; } else if (*ldgnum < n) { *info = -16; } if (*info != 0) { i__1 = -(*info); xerbla_("SLASD6", &i__1, (ftnlen)6); return 0; } /* The following values are for bookkeeping purposes only. They are */ /* integer pointers which indicate the portion of the workspace */ /* used by a particular array in SLASD7 and SLASD8. */ isigma = 1; iw = isigma + n; ivfw = iw + m; ivlw = ivfw + m; idx = 1; idxc = idx + n; idxp = idxc + n; /* Scale. */ /* Computing MAX */ r__1 = abs(*alpha), r__2 = abs(*beta); orgnrm = f2cmax(r__1,r__2); d__[*nl + 1] = 0.f; i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { if ((r__1 = d__[i__], abs(r__1)) > orgnrm) { orgnrm = (r__1 = d__[i__], abs(r__1)); } /* L10: */ } slascl_("G", &c__0, &c__0, &orgnrm, &c_b7, &n, &c__1, &d__[1], &n, info); *alpha /= orgnrm; *beta /= orgnrm; /* Sort and Deflate singular values. */ slasd7_(icompq, nl, nr, sqre, k, &d__[1], &z__[1], &work[iw], &vf[1], & work[ivfw], &vl[1], &work[ivlw], alpha, beta, &work[isigma], & iwork[idx], &iwork[idxp], &idxq[1], &perm[1], givptr, &givcol[ givcol_offset], ldgcol, &givnum[givnum_offset], ldgnum, c__, s, info); /* Solve Secular Equation, compute DIFL, DIFR, and update VF, VL. */ slasd8_(icompq, k, &d__[1], &z__[1], &vf[1], &vl[1], &difl[1], &difr[1], ldgnum, &work[isigma], &work[iw], info); /* Report the possible convergence failure. */ if (*info != 0) { return 0; } /* Save the poles if ICOMPQ = 1. */ if (*icompq == 1) { scopy_(k, &d__[1], &c__1, &poles[poles_dim1 + 1], &c__1); scopy_(k, &work[isigma], &c__1, &poles[(poles_dim1 << 1) + 1], &c__1); } /* Unscale. */ slascl_("G", &c__0, &c__0, &c_b7, &orgnrm, &n, &c__1, &d__[1], &n, info); /* Prepare the IDXQ sorting permutation. */ n1 = *k; n2 = n - *k; slamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &idxq[1]); return 0; /* End of SLASD6 */ } /* slasd6_ */