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OpenBLAS/lapack-netlib/SRC/clarft.c

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#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <complex.h>
#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 blasint logical;
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) {float nenn=crealf(_FCmulcc(Cf(b),conjf(Cf(b)))); _Fcomplex zaehl=_FCmulcc(Cf(a),conjf(Cf(b))); pCf(c)=_FCbuild(crealf(zaehl)/nenn,cimagf(zaehl)/nenn);}
#define z_div(c, a, b) {double nenn=creal(_Cmulcc(Cd(b),conj(Cd(b)))); _Dcomplex zaehl=_Cmulcc(Cd(a),conj(Cd(b))); pCd(c)=_Cbuild(creal(zaehl)/nenn,cimag(zaehl)/nenn);}
#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);}
#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++ */
#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<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0]
+ Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
zdotc._Val[1] -= Cf(&x[i])._Val[1] * Cf(&y[i])._Val[0]
- Cf(&x[i])._Val[0] * Cf(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0]
+ Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
zdotc._Val[1] -= Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1]
- Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[1];
}
}
pCf(z) = zdotc;
}
#else
_Complex float zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
}
}
pCf(z) = zdotc;
}
#endif
static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Dcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0]
+ Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1]
- Cd(&x[i])._Val[0] * Cd(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0]
+ Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1]
- Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[1];
}
}
pCd(z) = zdotc;
}
#else
_Complex double zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
}
}
pCd(z) = zdotc;
}
#endif
static inline void cdotu_(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<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0]
- Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1]
+ Cf(&x[i])._Val[0] * Cf(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0]
- Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1]
+ Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[1];
}
}
pCf(z) = zdotc;
}
#else
_Complex float zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cf(&x[i]) * Cf(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
}
}
pCf(z) = zdotc;
}
#endif
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Dcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0]
- Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1]
+ Cd(&x[i])._Val[0] * Cd(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0]
- Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1]
+ Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[1];
}
}
pCd(z) = zdotc;
}
#else
_Complex double zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cd(&x[i]) * Cd(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
}
}
pCd(z) = zdotc;
}
#endif
/* -- translated by f2c (version 20000121).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
/* Table of constant values */
static complex c_b1 = {1.f,0.f};
static complex c_b3 = {-1.f,0.f};
static integer c__3 = 3;
static integer c_n1 = -1;
static integer c__2 = 2;
/* > \brief \b CLARFT 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/ */
/* > Download CLARFT + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clarft.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clarft.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clarft.
f"> */
/* > [TXT]</a> */
/* Definition: */
/* =========== */
/* SUBROUTINE CLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) */
/* CHARACTER DIRECT, STOREV */
/* INTEGER K, LDT, LDV, N */
/* COMPLEX T( LDT, * ), TAU( * ), V( LDV, * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > CLARFT forms the triangular factor T of a complex 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**H */
/* > */
/* > 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**H * T * V */
/* > \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) */
/* > = '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 */
/* > = '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] V */
/* > \verbatim */
/* > V is COMPLEX 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 COMPLEX array, dimension (K) */
/* > TAU(i) must contain the scalar factor of the elementary */
/* > reflector H(i). */
/* > \endverbatim */
/* > */
/* > \param[out] T */
/* > \verbatim */
/* > T is COMPLEX 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. */
/* > \ingroup larft */
/* > \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. */
/* > */
/* > DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */
/* > */
/* > V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) */
/* > ( v1 1 ) ( 1 v2 v2 v2 ) */
/* > ( v1 v2 1 ) ( 1 v3 v3 ) */
/* > ( v1 v2 v3 ) */
/* > ( v1 v2 v3 ) */
/* > */
/* > DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */
/* > */
/* > V = ( v1 v2 v3 ) V = ( v1 v1 1 ) */
/* > ( v1 v2 v3 ) ( v2 v2 v2 1 ) */
/* > ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) */
/* > ( 1 v3 ) */
/* > ( 1 ) */
/* > \endverbatim */
/* > */
/* ===================================================================== */
/* Subroutine */ int clarft_(char *direct, char *storev, integer *n, integer *
k, complex *v, integer *ldv, complex *tau, complex *t, integer *ldt)
{
/* System generated locals */
address a__1[2];
integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2[2], i__3, i__4;
complex q__1;
char ch__1[2];
/* Local variables */
integer i__, j, l;
logical lq, ql, qr;
integer nx;
extern /* Subroutine */ int clarft_lvl2__(char *, char *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *);
logical dirf, colv;
extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *,
integer *, complex *, complex *, integer *, complex *, integer *,
complex *, complex *, integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ int ctrmm_(char *, char *, char *, char *,
integer *, integer *, complex *, complex *, integer *, complex *,
integer *), clacpy_(char *,
integer *, integer *, complex *, integer *, complex *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
/* -- LAPACK auxiliary routine -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* The general scheme used is inspired by the approach inside DGEQRT3 */
/* which was (at the time of writing this code): */
/* Based on the algorithm of Elmroth and Gustavson, */
/* IBM J. Res. Develop. Vol 44 No. 4 July 2000. */
/* Quick return if possible */
/* Parameter adjustments */
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
--tau;
t_dim1 = *ldt;
t_offset = 1 + t_dim1;
t -= t_offset;
/* Function Body */
if (*n == 0 || *k == 0) {
return 0;
}
/* Base case */
if (*n == 1 || *k == 1) {
i__1 = t_dim1 + 1;
t[i__1].r = tau[1].r, t[i__1].i = tau[1].i;
return 0;
}
/* Determine when to cross over into the level 2 based implementation */
/* Writing concatenation */
i__2[0] = 1, a__1[0] = direct;
i__2[1] = 1, a__1[1] = storev;
s_cat(ch__1, a__1, i__2, &c__2, (ftnlen)2);
nx = ilaenv_(&c__3, "CLARFT", ch__1, n, k, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)2);
if (*k < nx) {
clarft_lvl2__(direct, storev, n, k, &v[v_offset], ldv, &tau[1], &t[
t_offset], ldt);
return 0;
}
/* Beginning of executable statements */
l = *k / 2;
/* Determine what kind of Q we need to compute */
/* We assume that if the user doesn't provide 'F' for DIRECT, */
/* then they meant to provide 'B' and if they don't provide */
/* 'C' for STOREV, then they meant to provide 'R' */
dirf = lsame_(direct, "F");
colv = lsame_(storev, "C");
/* QR happens when we have forward direction in column storage */
qr = dirf && colv;
/* LQ happens when we have forward direction in row storage */
lq = dirf && ! colv;
/* QL happens when we have backward direction in column storage */
ql = ! dirf && colv;
/* The last case is RQ. Due to how we structured this, if the */
/* above 3 are false, then RQ must be true, so we never store */
/* this */
/* RQ happens when we have backward direction in row storage */
/* RQ = (.NOT.DIRF).AND.(.NOT.COLV) */
if (qr) {
/* Break V apart into 6 components */
/* V = |---------------| */
/* |V_{1,1} 0 | */
/* |V_{2,1} V_{2,2}| */
/* |V_{3,1} V_{3,2}| */
/* |---------------| */
/* V_{1,1}\in\C^{l,l} unit lower triangular */
/* V_{2,1}\in\C^{k-l,l} rectangular */
/* V_{3,1}\in\C^{n-k,l} rectangular */
/* V_{2,2}\in\C^{k-l,k-l} unit lower triangular */
/* V_{3,2}\in\C^{n-k,k-l} rectangular */
/* We will construct the T matrix */
/* T = |---------------| */
/* |T_{1,1} T_{1,2}| */
/* |0 T_{2,2}| */
/* |---------------| */
/* T is the triangular factor obtained from block reflectors. */
/* To motivate the structure, assume we have already computed T_{1,1} */
/* and T_{2,2}. Then collect the associated reflectors in V_1 and V_2 */
/* T_{1,1}\in\C^{l, l} upper triangular */
/* T_{2,2}\in\C^{k-l, k-l} upper triangular */
/* T_{1,2}\in\C^{l, k-l} rectangular */
/* Where l = floor(k/2) */
/* Then, consider the product: */
/* (I - V_1*T_{1,1}*V_1')*(I - V_2*T_{2,2}*V_2') */
/* = I - V_1*T_{1,1}*V_1' - V_2*T_{2,2}*V_2' + V_1*T_{1,1}*V_1'*V_2*T_{2,2}*V_2' */
/* Define T{1,2} = -T_{1,1}*V_1'*V_2*T_{2,2} */
/* Then, we can define the matrix V as */
/* V = |-------| */
/* |V_1 V_2| */
/* |-------| */
/* So, our product is equivalent to the matrix product */
/* I - V*T*V' */
/* This means, we can compute T_{1,1} and T_{2,2}, then use this information */
/* to compute T_{1,2} */
/* Compute T_{1,1} recursively */
clarft_(direct, storev, n, &l, &v[v_offset], ldv, &tau[1], &t[
t_offset], ldt);
/* Compute T_{2,2} recursively */
i__1 = *n - l;
i__3 = *k - l;
clarft_(direct, storev, &i__1, &i__3, &v[l + 1 + (l + 1) * v_dim1],
ldv, &tau[l + 1], &t[l + 1 + (l + 1) * t_dim1], ldt);
/* Compute T_{1,2} */
/* T_{1,2} = V_{2,1}' */
i__1 = l;
for (j = 1; j <= i__1; ++j) {
i__3 = *k - l;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = j + (l + i__) * t_dim1;
r_cnjg(&q__1, &v[l + i__ + j * v_dim1]);
t[i__4].r = q__1.r, t[i__4].i = q__1.i;
}
}
/* T_{1,2} = T_{1,2}*V_{2,2} */
i__1 = *k - l;
ctrmm_("Right", "Lower", "No transpose", "Unit", &l, &i__1, &c_b1, &v[
l + 1 + (l + 1) * v_dim1], ldv, &t[(l + 1) * t_dim1 + 1], ldt);
/* T_{1,2} = V_{3,1}'*V_{3,2} + T_{1,2} */
/* Note: We assume K <= N, and GEMM will do nothing if N=K */
i__1 = *k - l;
i__3 = *n - *k;
cgemm_("Conjugate", "No transpose", &l, &i__1, &i__3, &c_b1, &v[*k +
1 + v_dim1], ldv, &v[*k + 1 + (l + 1) * v_dim1], ldv, &c_b1, &
t[(l + 1) * t_dim1 + 1], ldt);
/* At this point, we have that T_{1,2} = V_1'*V_2 */
/* All that is left is to pre and post multiply by -T_{1,1} and T_{2,2} */
/* respectively. */
/* T_{1,2} = -T_{1,1}*T_{1,2} */
i__1 = *k - l;
ctrmm_("Left", "Upper", "No transpose", "Non-unit", &l, &i__1, &c_b3,
&t[t_offset], ldt, &t[(l + 1) * t_dim1 + 1], ldt);
/* T_{1,2} = T_{1,2}*T_{2,2} */
i__1 = *k - l;
ctrmm_("Right", "Upper", "No transpose", "Non-unit", &l, &i__1, &c_b1,
&t[l + 1 + (l + 1) * t_dim1], ldt, &t[(l + 1) * t_dim1 + 1],
ldt);
} else if (lq) {
/* Break V apart into 6 components */
/* V = |----------------------| */
/* |V_{1,1} V_{1,2} V{1,3}| */
/* |0 V_{2,2} V{2,3}| */
/* |----------------------| */
/* V_{1,1}\in\C^{l,l} unit upper triangular */
/* V_{1,2}\in\C^{l,k-l} rectangular */
/* V_{1,3}\in\C^{l,n-k} rectangular */
/* V_{2,2}\in\C^{k-l,k-l} unit upper triangular */
/* V_{2,3}\in\C^{k-l,n-k} rectangular */
/* Where l = floor(k/2) */
/* We will construct the T matrix */
/* T = |---------------| */
/* |T_{1,1} T_{1,2}| */
/* |0 T_{2,2}| */
/* |---------------| */
/* T is the triangular factor obtained from block reflectors. */
/* To motivate the structure, assume we have already computed T_{1,1} */
/* and T_{2,2}. Then collect the associated reflectors in V_1 and V_2 */
/* T_{1,1}\in\C^{l, l} upper triangular */
/* T_{2,2}\in\C^{k-l, k-l} upper triangular */
/* T_{1,2}\in\C^{l, k-l} rectangular */
/* Then, consider the product: */
/* (I - V_1'*T_{1,1}*V_1)*(I - V_2'*T_{2,2}*V_2) */
/* = I - V_1'*T_{1,1}*V_1 - V_2'*T_{2,2}*V_2 + V_1'*T_{1,1}*V_1*V_2'*T_{2,2}*V_2 */
/* Define T_{1,2} = -T_{1,1}*V_1*V_2'*T_{2,2} */
/* Then, we can define the matrix V as */
/* V = |---| */
/* |V_1| */
/* |V_2| */
/* |---| */
/* So, our product is equivalent to the matrix product */
/* I - V'*T*V */
/* This means, we can compute T_{1,1} and T_{2,2}, then use this information */
/* to compute T_{1,2} */
/* Compute T_{1,1} recursively */
clarft_(direct, storev, n, &l, &v[v_offset], ldv, &tau[1], &t[
t_offset], ldt);
/* Compute T_{2,2} recursively */
i__1 = *n - l;
i__3 = *k - l;
clarft_(direct, storev, &i__1, &i__3, &v[l + 1 + (l + 1) * v_dim1],
ldv, &tau[l + 1], &t[l + 1 + (l + 1) * t_dim1], ldt);
/* Compute T_{1,2} */
/* T_{1,2} = V_{1,2} */
i__1 = *k - l;
clacpy_("All", &l, &i__1, &v[(l + 1) * v_dim1 + 1], ldv, &t[(l + 1) *
t_dim1 + 1], ldt);
/* T_{1,2} = T_{1,2}*V_{2,2}' */
i__1 = *k - l;
ctrmm_("Right", "Upper", "Conjugate", "Unit", &l, &i__1, &c_b1, &v[l
+ 1 + (l + 1) * v_dim1], ldv, &t[(l + 1) * t_dim1 + 1], ldt);
/* T_{1,2} = V_{1,3}*V_{2,3}' + T_{1,2} */
/* Note: We assume K <= N, and GEMM will do nothing if N=K */
i__1 = *k - l;
i__3 = *n - *k;
cgemm_("No transpose", "Conjugate", &l, &i__1, &i__3, &c_b1, &v[(*k +
1) * v_dim1 + 1], ldv, &v[l + 1 + (*k + 1) * v_dim1], ldv, &
c_b1, &t[(l + 1) * t_dim1 + 1], ldt);
/* At this point, we have that T_{1,2} = V_1*V_2' */
/* All that is left is to pre and post multiply by -T_{1,1} and T_{2,2} */
/* respectively. */
/* T_{1,2} = -T_{1,1}*T_{1,2} */
i__1 = *k - l;
ctrmm_("Left", "Upper", "No transpose", "Non-unit", &l, &i__1, &c_b3,
&t[t_offset], ldt, &t[(l + 1) * t_dim1 + 1], ldt);
/* T_{1,2} = T_{1,2}*T_{2,2} */
i__1 = *k - l;
ctrmm_("Right", "Upper", "No transpose", "Non-unit", &l, &i__1, &c_b1,
&t[l + 1 + (l + 1) * t_dim1], ldt, &t[(l + 1) * t_dim1 + 1],
ldt);
} else if (ql) {
/* Break V apart into 6 components */
/* V = |---------------| */
/* |V_{1,1} V_{1,2}| */
/* |V_{2,1} V_{2,2}| */
/* |0 V_{3,2}| */
/* |---------------| */
/* V_{1,1}\in\C^{n-k,k-l} rectangular */
/* V_{2,1}\in\C^{k-l,k-l} unit upper triangular */
/* V_{1,2}\in\C^{n-k,l} rectangular */
/* V_{2,2}\in\C^{k-l,l} rectangular */
/* V_{3,2}\in\C^{l,l} unit upper triangular */
/* We will construct the T matrix */
/* T = |---------------| */
/* |T_{1,1} 0 | */
/* |T_{2,1} T_{2,2}| */
/* |---------------| */
/* T is the triangular factor obtained from block reflectors. */
/* To motivate the structure, assume we have already computed T_{1,1} */
/* and T_{2,2}. Then collect the associated reflectors in V_1 and V_2 */
/* T_{1,1}\in\C^{k-l, k-l} non-unit lower triangular */
/* T_{2,2}\in\C^{l, l} non-unit lower triangular */
/* T_{2,1}\in\C^{k-l, l} rectangular */
/* Where l = floor(k/2) */
/* Then, consider the product: */
/* (I - V_2*T_{2,2}*V_2')*(I - V_1*T_{1,1}*V_1') */
/* = I - V_2*T_{2,2}*V_2' - V_1*T_{1,1}*V_1' + V_2*T_{2,2}*V_2'*V_1*T_{1,1}*V_1' */
/* Define T_{2,1} = -T_{2,2}*V_2'*V_1*T_{1,1} */
/* Then, we can define the matrix V as */
/* V = |-------| */
/* |V_1 V_2| */
/* |-------| */
/* So, our product is equivalent to the matrix product */
/* I - V*T*V' */
/* This means, we can compute T_{1,1} and T_{2,2}, then use this information */
/* to compute T_{2,1} */
/* Compute T_{1,1} recursively */
i__1 = *n - l;
i__3 = *k - l;
clarft_(direct, storev, &i__1, &i__3, &v[v_offset], ldv, &tau[1], &t[
t_offset], ldt);
/* Compute T_{2,2} recursively */
clarft_(direct, storev, n, &l, &v[(*k - l + 1) * v_dim1 + 1], ldv, &
tau[*k - l + 1], &t[*k - l + 1 + (*k - l + 1) * t_dim1], ldt);
/* Compute T_{2,1} */
/* T_{2,1} = V_{2,2}' */
i__1 = *k - l;
for (j = 1; j <= i__1; ++j) {
i__3 = l;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = *k - l + i__ + j * t_dim1;
r_cnjg(&q__1, &v[*n - *k + j + (*k - l + i__) * v_dim1]);
t[i__4].r = q__1.r, t[i__4].i = q__1.i;
}
}
/* T_{2,1} = T_{2,1}*V_{2,1} */
i__1 = *k - l;
ctrmm_("Right", "Upper", "No transpose", "Unit", &l, &i__1, &c_b1, &v[
*n - *k + 1 + v_dim1], ldv, &t[*k - l + 1 + t_dim1], ldt);
/* T_{2,1} = V_{2,2}'*V_{2,1} + T_{2,1} */
/* Note: We assume K <= N, and GEMM will do nothing if N=K */
i__1 = *k - l;
i__3 = *n - *k;
cgemm_("Conjugate", "No transpose", &l, &i__1, &i__3, &c_b1, &v[(*k -
l + 1) * v_dim1 + 1], ldv, &v[v_offset], ldv, &c_b1, &t[*k -
l + 1 + t_dim1], ldt);
/* At this point, we have that T_{2,1} = V_2'*V_1 */
/* All that is left is to pre and post multiply by -T_{2,2} and T_{1,1} */
/* respectively. */
/* T_{2,1} = -T_{2,2}*T_{2,1} */
i__1 = *k - l;
ctrmm_("Left", "Lower", "No transpose", "Non-unit", &l, &i__1, &c_b3,
&t[*k - l + 1 + (*k - l + 1) * t_dim1], ldt, &t[*k - l + 1 +
t_dim1], ldt);
/* T_{2,1} = T_{2,1}*T_{1,1} */
i__1 = *k - l;
ctrmm_("Right", "Lower", "No transpose", "Non-unit", &l, &i__1, &c_b1,
&t[t_offset], ldt, &t[*k - l + 1 + t_dim1], ldt);
} else {
/* Else means RQ case */
/* Break V apart into 6 components */
/* V = |-----------------------| */
/* |V_{1,1} V_{1,2} 0 | */
/* |V_{2,1} V_{2,2} V_{2,3}| */
/* |-----------------------| */
/* V_{1,1}\in\C^{k-l,n-k} rectangular */
/* V_{1,2}\in\C^{k-l,k-l} unit lower triangular */
/* V_{2,1}\in\C^{l,n-k} rectangular */
/* V_{2,2}\in\C^{l,k-l} rectangular */
/* V_{2,3}\in\C^{l,l} unit lower triangular */
/* We will construct the T matrix */
/* T = |---------------| */
/* |T_{1,1} 0 | */
/* |T_{2,1} T_{2,2}| */
/* |---------------| */
/* T is the triangular factor obtained from block reflectors. */
/* To motivate the structure, assume we have already computed T_{1,1} */
/* and T_{2,2}. Then collect the associated reflectors in V_1 and V_2 */
/* T_{1,1}\in\C^{k-l, k-l} non-unit lower triangular */
/* T_{2,2}\in\C^{l, l} non-unit lower triangular */
/* T_{2,1}\in\C^{k-l, l} rectangular */
/* Where l = floor(k/2) */
/* Then, consider the product: */
/* (I - V_2'*T_{2,2}*V_2)*(I - V_1'*T_{1,1}*V_1) */
/* = I - V_2'*T_{2,2}*V_2 - V_1'*T_{1,1}*V_1 + V_2'*T_{2,2}*V_2*V_1'*T_{1,1}*V_1 */
/* Define T_{2,1} = -T_{2,2}*V_2*V_1'*T_{1,1} */
/* Then, we can define the matrix V as */
/* V = |---| */
/* |V_1| */
/* |V_2| */
/* |---| */
/* So, our product is equivalent to the matrix product */
/* I - V'*T*V */
/* This means, we can compute T_{1,1} and T_{2,2}, then use this information */
/* to compute T_{2,1} */
/* Compute T_{1,1} recursively */
i__1 = *n - l;
i__3 = *k - l;
clarft_(direct, storev, &i__1, &i__3, &v[v_offset], ldv, &tau[1], &t[
t_offset], ldt);
/* Compute T_{2,2} recursively */
clarft_(direct, storev, n, &l, &v[*k - l + 1 + v_dim1], ldv, &tau[*k
- l + 1], &t[*k - l + 1 + (*k - l + 1) * t_dim1], ldt);
/* Compute T_{2,1} */
/* T_{2,1} = V_{2,2} */
i__1 = *k - l;
clacpy_("All", &l, &i__1, &v[*k - l + 1 + (*n - *k + 1) * v_dim1],
ldv, &t[*k - l + 1 + t_dim1], ldt);
/* T_{2,1} = T_{2,1}*V_{1,2}' */
i__1 = *k - l;
ctrmm_("Right", "Lower", "Conjugate", "Unit", &l, &i__1, &c_b1, &v[(*
n - *k + 1) * v_dim1 + 1], ldv, &t[*k - l + 1 + t_dim1], ldt);
/* T_{2,1} = V_{2,1}*V_{1,1}' + T_{2,1} */
/* Note: We assume K <= N, and GEMM will do nothing if N=K */
i__1 = *k - l;
i__3 = *n - *k;
cgemm_("No transpose", "Conjugate", &l, &i__1, &i__3, &c_b1, &v[*k -
l + 1 + v_dim1], ldv, &v[v_offset], ldv, &c_b1, &t[*k - l + 1
+ t_dim1], ldt);
/* At this point, we have that T_{2,1} = V_2*V_1' */
/* All that is left is to pre and post multiply by -T_{2,2} and T_{1,1} */
/* respectively. */
/* T_{2,1} = -T_{2,2}*T_{2,1} */
i__1 = *k - l;
ctrmm_("Left", "Lower", "No tranpose", "Non-unit", &l, &i__1, &c_b3, &
t[*k - l + 1 + (*k - l + 1) * t_dim1], ldt, &t[*k - l + 1 +
t_dim1], ldt);
/* T_{2,1} = T_{2,1}*T_{1,1} */
i__1 = *k - l;
ctrmm_("Right", "Lower", "No tranpose", "Non-unit", &l, &i__1, &c_b1,
&t[t_offset], ldt, &t[*k - l + 1 + t_dim1], ldt);
}
return 0;
} /* clarft_ */
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