#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 SLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with d iagonal d and off-diagonal e. Used by sbdsdc. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SLASDA + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, */ /* DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, */ /* PERM, GIVNUM, C, S, WORK, IWORK, INFO ) */ /* INTEGER ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE */ /* INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), */ /* $ K( * ), PERM( LDGCOL, * ) */ /* REAL C( * ), D( * ), DIFL( LDU, * ), DIFR( LDU, * ), */ /* $ E( * ), GIVNUM( LDU, * ), POLES( LDU, * ), */ /* $ S( * ), U( LDU, * ), VT( LDU, * ), WORK( * ), */ /* $ Z( LDU, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > Using a divide and conquer approach, SLASDA computes the singular */ /* > value decomposition (SVD) of a real upper bidiagonal N-by-M matrix */ /* > B with diagonal D and offdiagonal E, where M = N + SQRE. The */ /* > algorithm computes the singular values in the SVD B = U * S * VT. */ /* > The orthogonal matrices U and VT are optionally computed in */ /* > compact form. */ /* > */ /* > A related subroutine, SLASD0, computes the singular values and */ /* > the singular vectors in explicit form. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] ICOMPQ */ /* > \verbatim */ /* > ICOMPQ is INTEGER */ /* > Specifies whether singular vectors are to be computed */ /* > in compact form, as follows */ /* > = 0: Compute singular values only. */ /* > = 1: Compute singular vectors of upper bidiagonal */ /* > matrix in compact form. */ /* > \endverbatim */ /* > */ /* > \param[in] SMLSIZ */ /* > \verbatim */ /* > SMLSIZ is INTEGER */ /* > The maximum size of the subproblems at the bottom of the */ /* > computation tree. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The row dimension of the upper bidiagonal matrix. This is */ /* > also the dimension of the main diagonal array D. */ /* > \endverbatim */ /* > */ /* > \param[in] SQRE */ /* > \verbatim */ /* > SQRE is INTEGER */ /* > Specifies the column dimension of the bidiagonal matrix. */ /* > = 0: The bidiagonal matrix has column dimension M = N; */ /* > = 1: The bidiagonal matrix has column dimension M = N + 1. */ /* > \endverbatim */ /* > */ /* > \param[in,out] D */ /* > \verbatim */ /* > D is REAL array, dimension ( N ) */ /* > On entry D contains the main diagonal of the bidiagonal */ /* > matrix. On exit D, if INFO = 0, contains its singular values. */ /* > \endverbatim */ /* > */ /* > \param[in] E */ /* > \verbatim */ /* > E is REAL array, dimension ( M-1 ) */ /* > Contains the subdiagonal entries of the bidiagonal matrix. */ /* > On exit, E has been destroyed. */ /* > \endverbatim */ /* > */ /* > \param[out] U */ /* > \verbatim */ /* > U is REAL array, */ /* > dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced */ /* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left */ /* > singular vector matrices of all subproblems at the bottom */ /* > level. */ /* > \endverbatim */ /* > */ /* > \param[in] LDU */ /* > \verbatim */ /* > LDU is INTEGER, LDU = > N. */ /* > The leading dimension of arrays U, VT, DIFL, DIFR, POLES, */ /* > GIVNUM, and Z. */ /* > \endverbatim */ /* > */ /* > \param[out] VT */ /* > \verbatim */ /* > VT is REAL array, */ /* > dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced */ /* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right */ /* > singular vector matrices of all subproblems at the bottom */ /* > level. */ /* > \endverbatim */ /* > */ /* > \param[out] K */ /* > \verbatim */ /* > K is INTEGER array, dimension ( N ) */ /* > if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0. */ /* > If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th */ /* > secular equation on the computation tree. */ /* > \endverbatim */ /* > */ /* > \param[out] DIFL */ /* > \verbatim */ /* > DIFL is REAL array, dimension ( LDU, NLVL ), */ /* > where NLVL = floor(log_2 (N/SMLSIZ))). */ /* > \endverbatim */ /* > */ /* > \param[out] DIFR */ /* > \verbatim */ /* > DIFR is REAL array, */ /* > dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and */ /* > dimension ( N ) if ICOMPQ = 0. */ /* > If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1) */ /* > record distances between singular values on the I-th */ /* > level and singular values on the (I -1)-th level, and */ /* > DIFR(1:N, 2 * I ) contains the normalizing factors for */ /* > the right singular vector matrix. See SLASD8 for details. */ /* > \endverbatim */ /* > */ /* > \param[out] Z */ /* > \verbatim */ /* > Z is REAL array, */ /* > dimension ( LDU, NLVL ) if ICOMPQ = 1 and */ /* > dimension ( N ) if ICOMPQ = 0. */ /* > The first K elements of Z(1, I) contain the components of */ /* > the deflation-adjusted updating row vector for subproblems */ /* > on the I-th level. */ /* > \endverbatim */ /* > */ /* > \param[out] POLES */ /* > \verbatim */ /* > POLES is REAL array, */ /* > dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced */ /* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and */ /* > POLES(1, 2*I) contain the new and old singular values */ /* > involved in the secular equations on the I-th level. */ /* > \endverbatim */ /* > */ /* > \param[out] GIVPTR */ /* > \verbatim */ /* > GIVPTR is INTEGER array, */ /* > dimension ( N ) if ICOMPQ = 1, and not referenced if */ /* > ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records */ /* > the number of Givens rotations performed on the I-th */ /* > problem on the computation tree. */ /* > \endverbatim */ /* > */ /* > \param[out] GIVCOL */ /* > \verbatim */ /* > GIVCOL is INTEGER array, */ /* > dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not */ /* > referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */ /* > GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations */ /* > of Givens rotations performed on the I-th level on the */ /* > computation tree. */ /* > \endverbatim */ /* > */ /* > \param[in] LDGCOL */ /* > \verbatim */ /* > LDGCOL is INTEGER, LDGCOL = > N. */ /* > The leading dimension of arrays GIVCOL and PERM. */ /* > \endverbatim */ /* > */ /* > \param[out] PERM */ /* > \verbatim */ /* > PERM is INTEGER array, dimension ( LDGCOL, NLVL ) */ /* > if ICOMPQ = 1, and not referenced */ /* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records */ /* > permutations done on the I-th level of the computation tree. */ /* > \endverbatim */ /* > */ /* > \param[out] GIVNUM */ /* > \verbatim */ /* > GIVNUM is REAL array, */ /* > dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not */ /* > referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */ /* > GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S- */ /* > values of Givens rotations performed on the I-th level on */ /* > the computation tree. */ /* > \endverbatim */ /* > */ /* > \param[out] C */ /* > \verbatim */ /* > C is REAL array, */ /* > dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. */ /* > If ICOMPQ = 1 and the I-th subproblem is not square, on exit, */ /* > C( I ) contains the C-value of a Givens rotation related to */ /* > the right null space of the I-th subproblem. */ /* > \endverbatim */ /* > */ /* > \param[out] S */ /* > \verbatim */ /* > S is REAL array, dimension ( N ) if */ /* > ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 */ /* > and the I-th subproblem is not square, on exit, S( I ) */ /* > contains the S-value of a Givens rotation related to */ /* > the right null space of the I-th subproblem. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is REAL array, dimension */ /* > (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)). */ /* > \endverbatim */ /* > */ /* > \param[out] IWORK */ /* > \verbatim */ /* > IWORK is INTEGER array, dimension (7*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 December 2016 */ /* > \ingroup OTHERauxiliary */ /* > \par Contributors: */ /* ================== */ /* > */ /* > Ming Gu and Huan Ren, Computer Science Division, University of */ /* > California at Berkeley, USA */ /* > */ /* ===================================================================== */ /* Subroutine */ int slasda_(integer *icompq, integer *smlsiz, integer *n, integer *sqre, real *d__, real *e, real *u, integer *ldu, real *vt, integer *k, real *difl, real *difr, real *z__, real *poles, integer * givptr, integer *givcol, integer *ldgcol, integer *perm, real *givnum, real *c__, real *s, real *work, integer *iwork, integer *info) { /* System generated locals */ integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, difl_dim1, difl_offset, difr_dim1, difr_offset, givnum_dim1, givnum_offset, poles_dim1, poles_offset, u_dim1, u_offset, vt_dim1, vt_offset, z_dim1, z_offset, i__1, i__2; /* Local variables */ real beta; integer idxq, nlvl, i__, j, m; real alpha; integer inode, ndiml, ndimr, idxqi, itemp, sqrei, i1; extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, integer *), slasd6_(integer *, integer *, integer *, integer *, real *, real *, real *, real *, real *, integer *, integer *, integer *, integer *, integer *, real *, integer *, real *, real * , real *, real *, integer *, real *, real *, real *, integer *, integer *); integer ic, nwork1, lf, nd, nwork2, ll, nl, vf, nr, vl; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), slasdq_( char *, integer *, integer *, integer *, integer *, integer *, real *, real *, real *, integer *, real *, integer *, real *, integer *, real *, integer *), slasdt_(integer *, integer *, integer *, integer *, integer *, integer *, integer *), slaset_(char *, integer *, integer *, real *, real *, real *, integer *); integer im1, smlszp, ncc, nlf, nrf, vfi, iwk, vli, lvl, nru, ndb1, nlp1, lvl2, nrp1; /* -- 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..-- */ /* December 2016 */ /* ===================================================================== */ /* Test the input parameters. */ /* Parameter adjustments */ --d__; --e; givnum_dim1 = *ldu; givnum_offset = 1 + givnum_dim1 * 1; givnum -= givnum_offset; poles_dim1 = *ldu; poles_offset = 1 + poles_dim1 * 1; poles -= poles_offset; z_dim1 = *ldu; z_offset = 1 + z_dim1 * 1; z__ -= z_offset; difr_dim1 = *ldu; difr_offset = 1 + difr_dim1 * 1; difr -= difr_offset; difl_dim1 = *ldu; difl_offset = 1 + difl_dim1 * 1; difl -= difl_offset; vt_dim1 = *ldu; vt_offset = 1 + vt_dim1 * 1; vt -= vt_offset; u_dim1 = *ldu; u_offset = 1 + u_dim1 * 1; u -= u_offset; --k; --givptr; perm_dim1 = *ldgcol; perm_offset = 1 + perm_dim1 * 1; perm -= perm_offset; givcol_dim1 = *ldgcol; givcol_offset = 1 + givcol_dim1 * 1; givcol -= givcol_offset; --c__; --s; --work; --iwork; /* Function Body */ *info = 0; if (*icompq < 0 || *icompq > 1) { *info = -1; } else if (*smlsiz < 3) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*sqre < 0 || *sqre > 1) { *info = -4; } else if (*ldu < *n + *sqre) { *info = -8; } else if (*ldgcol < *n) { *info = -17; } if (*info != 0) { i__1 = -(*info); xerbla_("SLASDA", &i__1, (ftnlen)6); return 0; } m = *n + *sqre; /* If the input matrix is too small, call SLASDQ to find the SVD. */ if (*n <= *smlsiz) { if (*icompq == 0) { slasdq_("U", sqre, n, &c__0, &c__0, &c__0, &d__[1], &e[1], &vt[ vt_offset], ldu, &u[u_offset], ldu, &u[u_offset], ldu, & work[1], info); } else { slasdq_("U", sqre, n, &m, n, &c__0, &d__[1], &e[1], &vt[vt_offset] , ldu, &u[u_offset], ldu, &u[u_offset], ldu, &work[1], info); } return 0; } /* Book-keeping and set up the computation tree. */ inode = 1; ndiml = inode + *n; ndimr = ndiml + *n; idxq = ndimr + *n; iwk = idxq + *n; ncc = 0; nru = 0; smlszp = *smlsiz + 1; vf = 1; vl = vf + m; nwork1 = vl + m; nwork2 = nwork1 + smlszp * smlszp; slasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr], smlsiz); /* for the nodes on bottom level of the tree, solve */ /* their subproblems by SLASDQ. */ ndb1 = (nd + 1) / 2; i__1 = nd; for (i__ = ndb1; i__ <= i__1; ++i__) { /* IC : center row of each node */ /* NL : number of rows of left subproblem */ /* NR : number of rows of right subproblem */ /* NLF: starting row of the left subproblem */ /* NRF: starting row of the right subproblem */ i1 = i__ - 1; ic = iwork[inode + i1]; nl = iwork[ndiml + i1]; nlp1 = nl + 1; nr = iwork[ndimr + i1]; nlf = ic - nl; nrf = ic + 1; idxqi = idxq + nlf - 2; vfi = vf + nlf - 1; vli = vl + nlf - 1; sqrei = 1; if (*icompq == 0) { slaset_("A", &nlp1, &nlp1, &c_b11, &c_b12, &work[nwork1], &smlszp); slasdq_("U", &sqrei, &nl, &nlp1, &nru, &ncc, &d__[nlf], &e[nlf], & work[nwork1], &smlszp, &work[nwork2], &nl, &work[nwork2], &nl, &work[nwork2], info); itemp = nwork1 + nl * smlszp; scopy_(&nlp1, &work[nwork1], &c__1, &work[vfi], &c__1); scopy_(&nlp1, &work[itemp], &c__1, &work[vli], &c__1); } else { slaset_("A", &nl, &nl, &c_b11, &c_b12, &u[nlf + u_dim1], ldu); slaset_("A", &nlp1, &nlp1, &c_b11, &c_b12, &vt[nlf + vt_dim1], ldu); slasdq_("U", &sqrei, &nl, &nlp1, &nl, &ncc, &d__[nlf], &e[nlf], & vt[nlf + vt_dim1], ldu, &u[nlf + u_dim1], ldu, &u[nlf + u_dim1], ldu, &work[nwork1], info); scopy_(&nlp1, &vt[nlf + vt_dim1], &c__1, &work[vfi], &c__1); scopy_(&nlp1, &vt[nlf + nlp1 * vt_dim1], &c__1, &work[vli], &c__1) ; } if (*info != 0) { return 0; } i__2 = nl; for (j = 1; j <= i__2; ++j) { iwork[idxqi + j] = j; /* L10: */ } if (i__ == nd && *sqre == 0) { sqrei = 0; } else { sqrei = 1; } idxqi += nlp1; vfi += nlp1; vli += nlp1; nrp1 = nr + sqrei; if (*icompq == 0) { slaset_("A", &nrp1, &nrp1, &c_b11, &c_b12, &work[nwork1], &smlszp); slasdq_("U", &sqrei, &nr, &nrp1, &nru, &ncc, &d__[nrf], &e[nrf], & work[nwork1], &smlszp, &work[nwork2], &nr, &work[nwork2], &nr, &work[nwork2], info); itemp = nwork1 + (nrp1 - 1) * smlszp; scopy_(&nrp1, &work[nwork1], &c__1, &work[vfi], &c__1); scopy_(&nrp1, &work[itemp], &c__1, &work[vli], &c__1); } else { slaset_("A", &nr, &nr, &c_b11, &c_b12, &u[nrf + u_dim1], ldu); slaset_("A", &nrp1, &nrp1, &c_b11, &c_b12, &vt[nrf + vt_dim1], ldu); slasdq_("U", &sqrei, &nr, &nrp1, &nr, &ncc, &d__[nrf], &e[nrf], & vt[nrf + vt_dim1], ldu, &u[nrf + u_dim1], ldu, &u[nrf + u_dim1], ldu, &work[nwork1], info); scopy_(&nrp1, &vt[nrf + vt_dim1], &c__1, &work[vfi], &c__1); scopy_(&nrp1, &vt[nrf + nrp1 * vt_dim1], &c__1, &work[vli], &c__1) ; } if (*info != 0) { return 0; } i__2 = nr; for (j = 1; j <= i__2; ++j) { iwork[idxqi + j] = j; /* L20: */ } /* L30: */ } /* Now conquer each subproblem bottom-up. */ j = pow_ii(&c__2, &nlvl); for (lvl = nlvl; lvl >= 1; --lvl) { lvl2 = (lvl << 1) - 1; /* Find the first node LF and last node LL on */ /* the current level LVL. */ if (lvl == 1) { lf = 1; ll = 1; } else { i__1 = lvl - 1; lf = pow_ii(&c__2, &i__1); ll = (lf << 1) - 1; } i__1 = ll; for (i__ = lf; i__ <= i__1; ++i__) { im1 = i__ - 1; ic = iwork[inode + im1]; nl = iwork[ndiml + im1]; nr = iwork[ndimr + im1]; nlf = ic - nl; nrf = ic + 1; if (i__ == ll) { sqrei = *sqre; } else { sqrei = 1; } vfi = vf + nlf - 1; vli = vl + nlf - 1; idxqi = idxq + nlf - 1; alpha = d__[ic]; beta = e[ic]; if (*icompq == 0) { slasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], & work[vli], &alpha, &beta, &iwork[idxqi], &perm[ perm_offset], &givptr[1], &givcol[givcol_offset], ldgcol, &givnum[givnum_offset], ldu, &poles[ poles_offset], &difl[difl_offset], &difr[difr_offset], &z__[z_offset], &k[1], &c__[1], &s[1], &work[nwork1], &iwork[iwk], info); } else { --j; slasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], & work[vli], &alpha, &beta, &iwork[idxqi], &perm[nlf + lvl * perm_dim1], &givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, &givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 * poles_dim1], & difl[nlf + lvl * difl_dim1], &difr[nlf + lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[j], &s[j], &work[nwork1], &iwork[iwk], info); } if (*info != 0) { return 0; } /* L40: */ } /* L50: */ } return 0; /* End of SLASDA */ } /* slasda_ */