#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 SGETSQRHRT */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SGETSQRHRT + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SGETSQRHRT( M, N, MB1, NB1, NB2, A, LDA, T, LDT, WORK, */ /* $ LWORK, INFO ) */ /* IMPLICIT NONE */ /* INTEGER INFO, LDA, LDT, LWORK, M, N, NB1, NB2, MB1 */ /* REAL A( LDA, * ), T( LDT, * ), WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SGETSQRHRT computes a NB2-sized column blocked QR-factorization */ /* > of a complex M-by-N matrix A with M >= N, */ /* > */ /* > A = Q * R. */ /* > */ /* > The routine uses internally a NB1-sized column blocked and MB1-sized */ /* > row blocked TSQR-factorization and perfors the reconstruction */ /* > of the Householder vectors from the TSQR output. The routine also */ /* > converts the R_tsqr factor from the TSQR-factorization output into */ /* > the R factor that corresponds to the Householder QR-factorization, */ /* > */ /* > A = Q_tsqr * R_tsqr = Q * R. */ /* > */ /* > The output Q and R factors are stored in the same format as in SGEQRT */ /* > (Q is in blocked compact WY-representation). See the documentation */ /* > of SGEQRT for more details on the format. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The number of rows of the matrix A. M >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The number of columns of the matrix A. M >= N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] MB1 */ /* > \verbatim */ /* > MB1 is INTEGER */ /* > The row block size to be used in the blocked TSQR. */ /* > MB1 > N. */ /* > \endverbatim */ /* > */ /* > \param[in] NB1 */ /* > \verbatim */ /* > NB1 is INTEGER */ /* > The column block size to be used in the blocked TSQR. */ /* > N >= NB1 >= 1. */ /* > \endverbatim */ /* > */ /* > \param[in] NB2 */ /* > \verbatim */ /* > NB2 is INTEGER */ /* > The block size to be used in the blocked QR that is */ /* > output. NB2 >= 1. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is REAL array, dimension (LDA,N) */ /* > */ /* > On entry: an M-by-N matrix A. */ /* > */ /* > On exit: */ /* > a) the elements on and above the diagonal */ /* > of the array contain the N-by-N upper-triangular */ /* > matrix R corresponding to the Householder QR; */ /* > b) the elements below the diagonal represent Q by */ /* > the columns of blocked V (compact WY-representation). */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */ /* > \endverbatim */ /* > */ /* > \param[out] T */ /* > \verbatim */ /* > T is REAL array, dimension (LDT,N)) */ /* > The upper triangular block reflectors stored in compact form */ /* > as a sequence of upper triangular blocks. */ /* > \endverbatim */ /* > */ /* > \param[in] LDT */ /* > \verbatim */ /* > LDT is INTEGER */ /* > The leading dimension of the array T. LDT >= NB2. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > (workspace) REAL array, dimension (MAX(1,LWORK)) */ /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ /* > \endverbatim */ /* > */ /* > \param[in] LWORK */ /* > \verbatim */ /* > The dimension of the array WORK. */ /* > LWORK >= MAX( LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ), */ /* > where */ /* > NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)), */ /* > NB1LOCAL = MIN(NB1,N). */ /* > LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL, */ /* > LW1 = NB1LOCAL * N, */ /* > LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ), */ /* > 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. */ /* > \ingroup singleOTHERcomputational */ /* > \par Contributors: */ /* ================== */ /* > */ /* > \verbatim */ /* > */ /* > November 2020, Igor Kozachenko, */ /* > Computer Science Division, */ /* > University of California, Berkeley */ /* > */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int sgetsqrhrt_(integer *m, integer *n, integer *mb1, integer *nb1, integer *nb2, real *a, integer *lda, real *t, integer * ldt, real *work, integer *lwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, t_dim1, t_offset, i__1, i__2, i__3, i__4; real r__1, r__2, r__3; /* Local variables */ integer ldwt, lworkopt, i__, j, iinfo; extern /* Subroutine */ int sorgtsqr_row_(integer *, integer *, integer * , integer *, real *, integer *, real *, integer *, real *, integer *, integer *), scopy_(integer *, real *, integer *, real * , integer *), sorhr_col_(integer *, integer *, integer *, real *, integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *, ftnlen); logical lquery; integer lw1, lw2, num_all_row_blocks__, lwt; extern /* Subroutine */ int slatsqr_(integer *, integer *, integer *, integer *, real *, integer *, real *, integer *, real *, integer * , integer *); integer nb1local, nb2local; /* -- LAPACK computational routine -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* ===================================================================== */ /* Test the input arguments */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; t_dim1 = *ldt; t_offset = 1 + t_dim1 * 1; t -= t_offset; --work; /* Function Body */ *info = 0; lquery = *lwork == -1; if (*m < 0) { *info = -1; } else if (*n < 0 || *m < *n) { *info = -2; } else if (*mb1 <= *n) { *info = -3; } else if (*nb1 < 1) { *info = -4; } else if (*nb2 < 1) { *info = -5; } else if (*lda < f2cmax(1,*m)) { *info = -7; } else /* if(complicated condition) */ { /* Computing MAX */ i__1 = 1, i__2 = f2cmin(*nb2,*n); if (*ldt < f2cmax(i__1,i__2)) { *info = -9; } else { /* Test the input LWORK for the dimension of the array WORK. */ /* This workspace is used to store array: */ /* a) Matrix T and WORK for SLATSQR; */ /* b) N-by-N upper-triangular factor R_tsqr; */ /* c) Matrix T and array WORK for SORGTSQR_ROW; */ /* d) Diagonal D for SORHR_COL. */ if (*lwork < *n * *n + 1 && ! lquery) { *info = -11; } else { /* Set block size for column blocks */ nb1local = f2cmin(*nb1,*n); /* Computing MAX */ r__3 = (real) (*m - *n) / (real) (*mb1 - *n) + .5f; r__1 = 1.f, r__2 = r_int(&r__3); num_all_row_blocks__ = f2cmax(r__1,r__2); /* Length and leading dimension of WORK array to place */ /* T array in TSQR. */ lwt = num_all_row_blocks__ * *n * nb1local; ldwt = nb1local; /* Length of TSQR work array */ lw1 = nb1local * *n; /* Length of SORGTSQR_ROW work array. */ /* Computing MAX */ i__1 = nb1local, i__2 = *n - nb1local; lw2 = nb1local * f2cmax(i__1,i__2); /* Computing MAX */ /* Computing MAX */ i__3 = lwt + *n * *n + lw2, i__4 = lwt + *n * *n + *n; i__1 = lwt + lw1, i__2 = f2cmax(i__3,i__4); lworkopt = f2cmax(i__1,i__2); if (*lwork < f2cmax(1,lworkopt) && ! lquery) { *info = -11; } } } } /* Handle error in the input parameters and return workspace query. */ if (*info != 0) { i__1 = -(*info); xerbla_("SGETSQRHRT", &i__1, (ftnlen)10); return 0; } else if (lquery) { work[1] = (real) lworkopt; return 0; } /* Quick return if possible */ if (f2cmin(*m,*n) == 0) { work[1] = (real) lworkopt; return 0; } nb2local = f2cmin(*nb2,*n); /* (1) Perform TSQR-factorization of the M-by-N matrix A. */ slatsqr_(m, n, mb1, &nb1local, &a[a_offset], lda, &work[1], &ldwt, &work[ lwt + 1], &lw1, &iinfo); /* (2) Copy the factor R_tsqr stored in the upper-triangular part */ /* of A into the square matrix in the work array */ /* WORK(LWT+1:LWT+N*N) column-by-column. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { scopy_(&j, &a[j * a_dim1 + 1], &c__1, &work[lwt + *n * (j - 1) + 1], & c__1); } /* (3) Generate a M-by-N matrix Q with orthonormal columns from */ /* the result stored below the diagonal in the array A in place. */ sorgtsqr_row_(m, n, mb1, &nb1local, &a[a_offset], lda, &work[1], &ldwt, & work[lwt + *n * *n + 1], &lw2, &iinfo); /* (4) Perform the reconstruction of Householder vectors from */ /* the matrix Q (stored in A) in place. */ sorhr_col_(m, n, &nb2local, &a[a_offset], lda, &t[t_offset], ldt, &work[ lwt + *n * *n + 1], &iinfo); /* (5) Copy the factor R_tsqr stored in the square matrix in the */ /* work array WORK(LWT+1:LWT+N*N) into the upper-triangular */ /* part of A. */ /* (6) Compute from R_tsqr the factor R_hr corresponding to */ /* the reconstructed Householder vectors, i.e. R_hr = S * R_tsqr. */ /* This multiplication by the sign matrix S on the left means */ /* changing the sign of I-th row of the matrix R_tsqr according */ /* to sign of the I-th diagonal element DIAG(I) of the matrix S. */ /* DIAG is stored in WORK( LWT+N*N+1 ) from the SORHR_COL output. */ /* (5) and (6) can be combined in a single loop, so the rows in A */ /* are accessed only once. */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (work[lwt + *n * *n + i__] == -1.f) { i__2 = *n; for (j = i__; j <= i__2; ++j) { a[i__ + j * a_dim1] = work[lwt + *n * (j - 1) + i__] * -1.f; } } else { i__2 = *n - i__ + 1; scopy_(&i__2, &work[lwt + *n * (i__ - 1) + i__], n, &a[i__ + i__ * a_dim1], lda); } } work[1] = (real) lworkopt; return 0; /* End of SGETSQRHRT */ } /* sgetsqrhrt_ */