#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 SLARZT forms the triangular factor T of a block reflector H = I - vtvH. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SLARZT + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) */ /* CHARACTER DIRECT, STOREV */ /* INTEGER K, LDT, LDV, N */ /* REAL T( LDT, * ), TAU( * ), V( LDV, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SLARZT forms the triangular factor T of a real block reflector */ /* > H of order > n, which is defined as a product of k elementary */ /* > reflectors. */ /* > */ /* > If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; */ /* > */ /* > If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. */ /* > */ /* > If STOREV = 'C', the vector which defines the elementary reflector */ /* > H(i) is stored in the i-th column of the array V, and */ /* > */ /* > H = I - V * T * V**T */ /* > */ /* > If STOREV = 'R', the vector which defines the elementary reflector */ /* > H(i) is stored in the i-th row of the array V, and */ /* > */ /* > H = I - V**T * T * V */ /* > */ /* > Currently, only STOREV = 'R' and DIRECT = 'B' are supported. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] DIRECT */ /* > \verbatim */ /* > DIRECT is CHARACTER*1 */ /* > Specifies the order in which the elementary reflectors are */ /* > multiplied to form the block reflector: */ /* > = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet) */ /* > = 'B': H = H(k) . . . H(2) H(1) (Backward) */ /* > \endverbatim */ /* > */ /* > \param[in] STOREV */ /* > \verbatim */ /* > STOREV is CHARACTER*1 */ /* > Specifies how the vectors which define the elementary */ /* > reflectors are stored (see also Further Details): */ /* > = 'C': columnwise (not supported yet) */ /* > = 'R': rowwise */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the block reflector H. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] K */ /* > \verbatim */ /* > K is INTEGER */ /* > The order of the triangular factor T (= the number of */ /* > elementary reflectors). K >= 1. */ /* > \endverbatim */ /* > */ /* > \param[in,out] V */ /* > \verbatim */ /* > V is REAL array, dimension */ /* > (LDV,K) if STOREV = 'C' */ /* > (LDV,N) if STOREV = 'R' */ /* > The matrix V. See further details. */ /* > \endverbatim */ /* > */ /* > \param[in] LDV */ /* > \verbatim */ /* > LDV is INTEGER */ /* > The leading dimension of the array V. */ /* > If STOREV = 'C', LDV >= f2cmax(1,N); if STOREV = 'R', LDV >= K. */ /* > \endverbatim */ /* > */ /* > \param[in] TAU */ /* > \verbatim */ /* > TAU is REAL array, dimension (K) */ /* > TAU(i) must contain the scalar factor of the elementary */ /* > reflector H(i). */ /* > \endverbatim */ /* > */ /* > \param[out] T */ /* > \verbatim */ /* > T is REAL array, dimension (LDT,K) */ /* > The k by k triangular factor T of the block reflector. */ /* > If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is */ /* > lower triangular. The rest of the array is not used. */ /* > \endverbatim */ /* > */ /* > \param[in] LDT */ /* > \verbatim */ /* > LDT is INTEGER */ /* > The leading dimension of the array T. LDT >= K. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup realOTHERcomputational */ /* > \par Contributors: */ /* ================== */ /* > */ /* > A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > The shape of the matrix V and the storage of the vectors which define */ /* > the H(i) is best illustrated by the following example with n = 5 and */ /* > k = 3. The elements equal to 1 are not stored; the corresponding */ /* > array elements are modified but restored on exit. The rest of the */ /* > array is not used. */ /* > */ /* > DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */ /* > */ /* > ______V_____ */ /* > ( v1 v2 v3 ) / \ */ /* > ( v1 v2 v3 ) ( v1 v1 v1 v1 v1 . . . . 1 ) */ /* > V = ( v1 v2 v3 ) ( v2 v2 v2 v2 v2 . . . 1 ) */ /* > ( v1 v2 v3 ) ( v3 v3 v3 v3 v3 . . 1 ) */ /* > ( v1 v2 v3 ) */ /* > . . . */ /* > . . . */ /* > 1 . . */ /* > 1 . */ /* > 1 */ /* > */ /* > DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */ /* > */ /* > ______V_____ */ /* > 1 / \ */ /* > . 1 ( 1 . . . . v1 v1 v1 v1 v1 ) */ /* > . . 1 ( . 1 . . . v2 v2 v2 v2 v2 ) */ /* > . . . ( . . 1 . . v3 v3 v3 v3 v3 ) */ /* > . . . */ /* > ( v1 v2 v3 ) */ /* > ( v1 v2 v3 ) */ /* > V = ( v1 v2 v3 ) */ /* > ( v1 v2 v3 ) */ /* > ( v1 v2 v3 ) */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int slarzt_(char *direct, char *storev, integer *n, integer * k, real *v, integer *ldv, real *tau, real *t, integer *ldt) { /* System generated locals */ integer t_dim1, t_offset, v_dim1, v_offset, i__1; real r__1; /* Local variables */ integer info, i__, j; extern logical lsame_(char *, char *); extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *), strmv_(char *, char *, char *, integer *, real *, integer *, real *, integer *), xerbla_( char *, integer *, ftnlen); /* -- LAPACK computational 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 */ /* ===================================================================== */ /* Check for currently supported options */ /* Parameter adjustments */ v_dim1 = *ldv; v_offset = 1 + v_dim1 * 1; v -= v_offset; --tau; t_dim1 = *ldt; t_offset = 1 + t_dim1 * 1; t -= t_offset; /* Function Body */ info = 0; if (! lsame_(direct, "B")) { info = -1; } else if (! lsame_(storev, "R")) { info = -2; } if (info != 0) { i__1 = -info; xerbla_("SLARZT", &i__1, (ftnlen)6); return 0; } for (i__ = *k; i__ >= 1; --i__) { if (tau[i__] == 0.f) { /* H(i) = I */ i__1 = *k; for (j = i__; j <= i__1; ++j) { t[j + i__ * t_dim1] = 0.f; /* L10: */ } } else { /* general case */ if (i__ < *k) { /* T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)**T */ i__1 = *k - i__; r__1 = -tau[i__]; sgemv_("No transpose", &i__1, n, &r__1, &v[i__ + 1 + v_dim1], ldv, &v[i__ + v_dim1], ldv, &c_b8, &t[i__ + 1 + i__ * t_dim1], &c__1); /* T(i+1:k,i) = T(i+1:k,i+1:k) * T(i+1:k,i) */ i__1 = *k - i__; strmv_("Lower", "No transpose", "Non-unit", &i__1, &t[i__ + 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ * t_dim1] , &c__1); } t[i__ + i__ * t_dim1] = tau[i__]; } /* L20: */ } return 0; /* End of SLARZT */ } /* slarzt_ */