#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 DORBDB3 */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download DORBDB3 + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE DORBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, */ /* TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO ) */ /* INTEGER INFO, LWORK, M, P, Q, LDX11, LDX21 */ /* DOUBLE PRECISION PHI(*), THETA(*) */ /* DOUBLE PRECISION TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*), */ /* $ X11(LDX11,*), X21(LDX21,*) */ /* > \par Purpose: */ /* ============= */ /* > */ /* >\verbatim */ /* > */ /* > DORBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny */ /* > matrix X with orthonomal columns: */ /* > */ /* > [ B11 ] */ /* > [ X11 ] [ P1 | ] [ 0 ] */ /* > [-----] = [---------] [-----] Q1**T . */ /* > [ X21 ] [ | P2 ] [ B21 ] */ /* > [ 0 ] */ /* > */ /* > X11 is P-by-Q, and X21 is (M-P)-by-Q. M-P must be no larger than P, */ /* > Q, or M-Q. Routines DORBDB1, DORBDB2, and DORBDB4 handle cases in */ /* > which M-P is not the minimum dimension. */ /* > */ /* > The orthogonal matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P), */ /* > and (M-Q)-by-(M-Q), respectively. They are represented implicitly by */ /* > Householder vectors. */ /* > */ /* > B11 and B12 are (M-P)-by-(M-P) bidiagonal matrices represented */ /* > implicitly by angles THETA, PHI. */ /* > */ /* >\endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The number of rows X11 plus the number of rows in X21. */ /* > \endverbatim */ /* > */ /* > \param[in] P */ /* > \verbatim */ /* > P is INTEGER */ /* > The number of rows in X11. 0 <= P <= M. M-P <= f2cmin(P,Q,M-Q). */ /* > \endverbatim */ /* > */ /* > \param[in] Q */ /* > \verbatim */ /* > Q is INTEGER */ /* > The number of columns in X11 and X21. 0 <= Q <= M. */ /* > \endverbatim */ /* > */ /* > \param[in,out] X11 */ /* > \verbatim */ /* > X11 is DOUBLE PRECISION array, dimension (LDX11,Q) */ /* > On entry, the top block of the matrix X to be reduced. On */ /* > exit, the columns of tril(X11) specify reflectors for P1 and */ /* > the rows of triu(X11,1) specify reflectors for Q1. */ /* > \endverbatim */ /* > */ /* > \param[in] LDX11 */ /* > \verbatim */ /* > LDX11 is INTEGER */ /* > The leading dimension of X11. LDX11 >= P. */ /* > \endverbatim */ /* > */ /* > \param[in,out] X21 */ /* > \verbatim */ /* > X21 is DOUBLE PRECISION array, dimension (LDX21,Q) */ /* > On entry, the bottom block of the matrix X to be reduced. On */ /* > exit, the columns of tril(X21) specify reflectors for P2. */ /* > \endverbatim */ /* > */ /* > \param[in] LDX21 */ /* > \verbatim */ /* > LDX21 is INTEGER */ /* > The leading dimension of X21. LDX21 >= M-P. */ /* > \endverbatim */ /* > */ /* > \param[out] THETA */ /* > \verbatim */ /* > THETA is DOUBLE PRECISION array, dimension (Q) */ /* > The entries of the bidiagonal blocks B11, B21 are defined by */ /* > THETA and PHI. See Further Details. */ /* > \endverbatim */ /* > */ /* > \param[out] PHI */ /* > \verbatim */ /* > PHI is DOUBLE PRECISION array, dimension (Q-1) */ /* > The entries of the bidiagonal blocks B11, B21 are defined by */ /* > THETA and PHI. See Further Details. */ /* > \endverbatim */ /* > */ /* > \param[out] TAUP1 */ /* > \verbatim */ /* > TAUP1 is DOUBLE PRECISION array, dimension (P) */ /* > The scalar factors of the elementary reflectors that define */ /* > P1. */ /* > \endverbatim */ /* > */ /* > \param[out] TAUP2 */ /* > \verbatim */ /* > TAUP2 is DOUBLE PRECISION array, dimension (M-P) */ /* > The scalar factors of the elementary reflectors that define */ /* > P2. */ /* > \endverbatim */ /* > */ /* > \param[out] TAUQ1 */ /* > \verbatim */ /* > TAUQ1 is DOUBLE PRECISION array, dimension (Q) */ /* > The scalar factors of the elementary reflectors that define */ /* > Q1. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is DOUBLE PRECISION array, dimension (LWORK) */ /* > \endverbatim */ /* > */ /* > \param[in] LWORK */ /* > \verbatim */ /* > LWORK is INTEGER */ /* > The dimension of the array WORK. LWORK >= M-Q. */ /* > */ /* > If LWORK = -1, then a workspace query is assumed; the routine */ /* > only calculates the optimal size of the WORK array, returns */ /* > this value as the first entry of the WORK array, and no error */ /* > message related to LWORK is issued by XERBLA. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit. */ /* > < 0: if INFO = -i, 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 July 2012 */ /* > \ingroup doubleOTHERcomputational */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > The upper-bidiagonal blocks B11, B21 are represented implicitly by */ /* > angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry */ /* > in each bidiagonal band is a product of a sine or cosine of a THETA */ /* > with a sine or cosine of a PHI. See [1] or DORCSD for details. */ /* > */ /* > P1, P2, and Q1 are represented as products of elementary reflectors. */ /* > See DORCSD2BY1 for details on generating P1, P2, and Q1 using DORGQR */ /* > and DORGLQ. */ /* > \endverbatim */ /* > \par References: */ /* ================ */ /* > */ /* > [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. */ /* > Algorithms, 50(1):33-65, 2009. */ /* > */ /* ===================================================================== */ /* Subroutine */ int dorbdb3_(integer *m, integer *p, integer *q, doublereal * x11, integer *ldx11, doublereal *x21, integer *ldx21, doublereal * theta, doublereal *phi, doublereal *taup1, doublereal *taup2, doublereal *tauq1, doublereal *work, integer *lwork, integer *info) { /* System generated locals */ integer x11_dim1, x11_offset, x21_dim1, x21_offset, i__1, i__2, i__3, i__4; doublereal d__1, d__2; /* Local variables */ extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *); integer lworkmin; extern doublereal dnrm2_(integer *, doublereal *, integer *); integer lworkopt; doublereal c__; integer i__; doublereal s; extern /* Subroutine */ int dlarf_(char *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *); integer ilarf, llarf, childinfo; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); logical lquery; extern /* Subroutine */ int dorbdb5_(integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, integer *); integer iorbdb5, lorbdb5; extern /* Subroutine */ int dlarfgp_(integer *, doublereal *, doublereal * , integer *, doublereal *); /* -- 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..-- */ /* July 2012 */ /* ==================================================================== */ /* Test input arguments */ /* Parameter adjustments */ x11_dim1 = *ldx11; x11_offset = 1 + x11_dim1 * 1; x11 -= x11_offset; x21_dim1 = *ldx21; x21_offset = 1 + x21_dim1 * 1; x21 -= x21_offset; --theta; --phi; --taup1; --taup2; --tauq1; --work; /* Function Body */ *info = 0; lquery = *lwork == -1; if (*m < 0) { *info = -1; } else if (*p << 1 < *m || *p > *m) { *info = -2; } else if (*q < *m - *p || *m - *q < *m - *p) { *info = -3; } else if (*ldx11 < f2cmax(1,*p)) { *info = -5; } else /* if(complicated condition) */ { /* Computing MAX */ i__1 = 1, i__2 = *m - *p; if (*ldx21 < f2cmax(i__1,i__2)) { *info = -7; } } /* Compute workspace */ if (*info == 0) { ilarf = 2; /* Computing MAX */ i__1 = *p, i__2 = *m - *p - 1, i__1 = f2cmax(i__1,i__2), i__2 = *q - 1; llarf = f2cmax(i__1,i__2); iorbdb5 = 2; lorbdb5 = *q - 1; /* Computing MAX */ i__1 = ilarf + llarf - 1, i__2 = iorbdb5 + lorbdb5 - 1; lworkopt = f2cmax(i__1,i__2); lworkmin = lworkopt; work[1] = (doublereal) lworkopt; if (*lwork < lworkmin && ! lquery) { *info = -14; } } if (*info != 0) { i__1 = -(*info); xerbla_("DORBDB3", &i__1, (ftnlen)7); return 0; } else if (lquery) { return 0; } /* Reduce rows 1, ..., M-P of X11 and X21 */ i__1 = *m - *p; for (i__ = 1; i__ <= i__1; ++i__) { if (i__ > 1) { i__2 = *q - i__ + 1; drot_(&i__2, &x11[i__ - 1 + i__ * x11_dim1], ldx11, &x21[i__ + i__ * x21_dim1], ldx11, &c__, &s); } i__2 = *q - i__ + 1; dlarfgp_(&i__2, &x21[i__ + i__ * x21_dim1], &x21[i__ + (i__ + 1) * x21_dim1], ldx21, &tauq1[i__]); s = x21[i__ + i__ * x21_dim1]; x21[i__ + i__ * x21_dim1] = 1.; i__2 = *p - i__ + 1; i__3 = *q - i__ + 1; dlarf_("R", &i__2, &i__3, &x21[i__ + i__ * x21_dim1], ldx21, &tauq1[ i__], &x11[i__ + i__ * x11_dim1], ldx11, &work[ilarf]); i__2 = *m - *p - i__; i__3 = *q - i__ + 1; dlarf_("R", &i__2, &i__3, &x21[i__ + i__ * x21_dim1], ldx21, &tauq1[ i__], &x21[i__ + 1 + i__ * x21_dim1], ldx21, &work[ilarf]); i__2 = *p - i__ + 1; /* Computing 2nd power */ d__1 = dnrm2_(&i__2, &x11[i__ + i__ * x11_dim1], &c__1); i__3 = *m - *p - i__; /* Computing 2nd power */ d__2 = dnrm2_(&i__3, &x21[i__ + 1 + i__ * x21_dim1], &c__1); c__ = sqrt(d__1 * d__1 + d__2 * d__2); theta[i__] = atan2(s, c__); i__2 = *p - i__ + 1; i__3 = *m - *p - i__; i__4 = *q - i__; dorbdb5_(&i__2, &i__3, &i__4, &x11[i__ + i__ * x11_dim1], &c__1, &x21[ i__ + 1 + i__ * x21_dim1], &c__1, &x11[i__ + (i__ + 1) * x11_dim1], ldx11, &x21[i__ + 1 + (i__ + 1) * x21_dim1], ldx21, &work[iorbdb5], &lorbdb5, &childinfo); i__2 = *p - i__ + 1; dlarfgp_(&i__2, &x11[i__ + i__ * x11_dim1], &x11[i__ + 1 + i__ * x11_dim1], &c__1, &taup1[i__]); if (i__ < *m - *p) { i__2 = *m - *p - i__; dlarfgp_(&i__2, &x21[i__ + 1 + i__ * x21_dim1], &x21[i__ + 2 + i__ * x21_dim1], &c__1, &taup2[i__]); phi[i__] = atan2(x21[i__ + 1 + i__ * x21_dim1], x11[i__ + i__ * x11_dim1]); c__ = cos(phi[i__]); s = sin(phi[i__]); x21[i__ + 1 + i__ * x21_dim1] = 1.; i__2 = *m - *p - i__; i__3 = *q - i__; dlarf_("L", &i__2, &i__3, &x21[i__ + 1 + i__ * x21_dim1], &c__1, & taup2[i__], &x21[i__ + 1 + (i__ + 1) * x21_dim1], ldx21, & work[ilarf]); } x11[i__ + i__ * x11_dim1] = 1.; i__2 = *p - i__ + 1; i__3 = *q - i__; dlarf_("L", &i__2, &i__3, &x11[i__ + i__ * x11_dim1], &c__1, &taup1[ i__], &x11[i__ + (i__ + 1) * x11_dim1], ldx11, &work[ilarf]); } /* Reduce the bottom-right portion of X11 to the identity matrix */ i__1 = *q; for (i__ = *m - *p + 1; i__ <= i__1; ++i__) { i__2 = *p - i__ + 1; dlarfgp_(&i__2, &x11[i__ + i__ * x11_dim1], &x11[i__ + 1 + i__ * x11_dim1], &c__1, &taup1[i__]); x11[i__ + i__ * x11_dim1] = 1.; i__2 = *p - i__ + 1; i__3 = *q - i__; dlarf_("L", &i__2, &i__3, &x11[i__ + i__ * x11_dim1], &c__1, &taup1[ i__], &x11[i__ + (i__ + 1) * x11_dim1], ldx11, &work[ilarf]); } return 0; /* End of DORBDB3 */ } /* dorbdb3_ */