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OpenBLAS/lapack-netlib/SRC/clags2.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) {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++ */
#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] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * 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];
zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * 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];
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * 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];
zdotc._Val[1] += Cf(&x[i])._Val[1] * 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];
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * 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];
zdotc._Val[1] += Cd(&x[i])._Val[1] * 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];
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * 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)
*/
/* > \brief \b CLAGS2 */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download CLAGS2 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clags2.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clags2.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clags2.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE CLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, */
/* SNV, CSQ, SNQ ) */
/* LOGICAL UPPER */
/* REAL A1, A3, B1, B3, CSQ, CSU, CSV */
/* COMPLEX A2, B2, SNQ, SNU, SNV */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > CLAGS2 computes 2-by-2 unitary matrices U, V and Q, such */
/* > that if ( UPPER ) then */
/* > */
/* > U**H *A*Q = U**H *( A1 A2 )*Q = ( x 0 ) */
/* > ( 0 A3 ) ( x x ) */
/* > and */
/* > V**H*B*Q = V**H *( B1 B2 )*Q = ( x 0 ) */
/* > ( 0 B3 ) ( x x ) */
/* > */
/* > or if ( .NOT.UPPER ) then */
/* > */
/* > U**H *A*Q = U**H *( A1 0 )*Q = ( x x ) */
/* > ( A2 A3 ) ( 0 x ) */
/* > and */
/* > V**H *B*Q = V**H *( B1 0 )*Q = ( x x ) */
/* > ( B2 B3 ) ( 0 x ) */
/* > where */
/* > */
/* > U = ( CSU SNU ), V = ( CSV SNV ), */
/* > ( -SNU**H CSU ) ( -SNV**H CSV ) */
/* > */
/* > Q = ( CSQ SNQ ) */
/* > ( -SNQ**H CSQ ) */
/* > */
/* > The rows of the transformed A and B are parallel. Moreover, if the */
/* > input 2-by-2 matrix A is not zero, then the transformed (1,1) entry */
/* > of A is not zero. If the input matrices A and B are both not zero, */
/* > then the transformed (2,2) element of B is not zero, except when the */
/* > first rows of input A and B are parallel and the second rows are */
/* > zero. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] UPPER */
/* > \verbatim */
/* > UPPER is LOGICAL */
/* > = .TRUE.: the input matrices A and B are upper triangular. */
/* > = .FALSE.: the input matrices A and B are lower triangular. */
/* > \endverbatim */
/* > */
/* > \param[in] A1 */
/* > \verbatim */
/* > A1 is REAL */
/* > \endverbatim */
/* > */
/* > \param[in] A2 */
/* > \verbatim */
/* > A2 is COMPLEX */
/* > \endverbatim */
/* > */
/* > \param[in] A3 */
/* > \verbatim */
/* > A3 is REAL */
/* > On entry, A1, A2 and A3 are elements of the input 2-by-2 */
/* > upper (lower) triangular matrix A. */
/* > \endverbatim */
/* > */
/* > \param[in] B1 */
/* > \verbatim */
/* > B1 is REAL */
/* > \endverbatim */
/* > */
/* > \param[in] B2 */
/* > \verbatim */
/* > B2 is COMPLEX */
/* > \endverbatim */
/* > */
/* > \param[in] B3 */
/* > \verbatim */
/* > B3 is REAL */
/* > On entry, B1, B2 and B3 are elements of the input 2-by-2 */
/* > upper (lower) triangular matrix B. */
/* > \endverbatim */
/* > */
/* > \param[out] CSU */
/* > \verbatim */
/* > CSU is REAL */
/* > \endverbatim */
/* > */
/* > \param[out] SNU */
/* > \verbatim */
/* > SNU is COMPLEX */
/* > The desired unitary matrix U. */
/* > \endverbatim */
/* > */
/* > \param[out] CSV */
/* > \verbatim */
/* > CSV is REAL */
/* > \endverbatim */
/* > */
/* > \param[out] SNV */
/* > \verbatim */
/* > SNV is COMPLEX */
/* > The desired unitary matrix V. */
/* > \endverbatim */
/* > */
/* > \param[out] CSQ */
/* > \verbatim */
/* > CSQ is REAL */
/* > \endverbatim */
/* > */
/* > \param[out] SNQ */
/* > \verbatim */
/* > SNQ is COMPLEX */
/* > The desired unitary matrix Q. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date December 2016 */
/* > \ingroup complexOTHERauxiliary */
/* ===================================================================== */
/* Subroutine */ void clags2_(logical *upper, real *a1, complex *a2, real *a3,
real *b1, complex *b2, real *b3, real *csu, complex *snu, real *csv,
complex *snv, real *csq, complex *snq)
{
/* System generated locals */
real r__1, r__2, r__3, r__4, r__5, r__6, r__7, r__8;
complex q__1, q__2, q__3, q__4, q__5;
/* Local variables */
real aua11, aua12, aua21, aua22, avb11, avb12, avb21, avb22, ua11r, ua22r,
vb11r, vb22r, a;
complex b, c__;
real d__;
complex r__, d1;
real s1, s2, fb, fc;
extern /* Subroutine */ void slasv2_(real *, real *, real *, real *, real *
, real *, real *, real *, real *), clartg_(complex *, complex *,
real *, complex *, complex *);
complex ua11, ua12, ua21, ua22, vb11, vb12, vb21, vb22;
real csl, csr, snl, snr;
/* -- 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 */
/* ===================================================================== */
if (*upper) {
/* Input matrices A and B are upper triangular matrices */
/* Form matrix C = A*adj(B) = ( a b ) */
/* ( 0 d ) */
a = *a1 * *b3;
d__ = *a3 * *b1;
q__2.r = *b1 * a2->r, q__2.i = *b1 * a2->i;
q__3.r = *a1 * b2->r, q__3.i = *a1 * b2->i;
q__1.r = q__2.r - q__3.r, q__1.i = q__2.i - q__3.i;
b.r = q__1.r, b.i = q__1.i;
fb = c_abs(&b);
/* Transform complex 2-by-2 matrix C to real matrix by unitary */
/* diagonal matrix diag(1,D1). */
d1.r = 1.f, d1.i = 0.f;
if (fb != 0.f) {
q__1.r = b.r / fb, q__1.i = b.i / fb;
d1.r = q__1.r, d1.i = q__1.i;
}
/* The SVD of real 2 by 2 triangular C */
/* ( CSL -SNL )*( A B )*( CSR SNR ) = ( R 0 ) */
/* ( SNL CSL ) ( 0 D ) ( -SNR CSR ) ( 0 T ) */
slasv2_(&a, &fb, &d__, &s1, &s2, &snr, &csr, &snl, &csl);
if (abs(csl) >= abs(snl) || abs(csr) >= abs(snr)) {
/* Compute the (1,1) and (1,2) elements of U**H *A and V**H *B, */
/* and (1,2) element of |U|**H *|A| and |V|**H *|B|. */
ua11r = csl * *a1;
q__2.r = csl * a2->r, q__2.i = csl * a2->i;
q__4.r = snl * d1.r, q__4.i = snl * d1.i;
q__3.r = *a3 * q__4.r, q__3.i = *a3 * q__4.i;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
ua12.r = q__1.r, ua12.i = q__1.i;
vb11r = csr * *b1;
q__2.r = csr * b2->r, q__2.i = csr * b2->i;
q__4.r = snr * d1.r, q__4.i = snr * d1.i;
q__3.r = *b3 * q__4.r, q__3.i = *b3 * q__4.i;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
vb12.r = q__1.r, vb12.i = q__1.i;
aua12 = abs(csl) * ((r__1 = a2->r, abs(r__1)) + (r__2 = r_imag(a2)
, abs(r__2))) + abs(snl) * abs(*a3);
avb12 = abs(csr) * ((r__1 = b2->r, abs(r__1)) + (r__2 = r_imag(b2)
, abs(r__2))) + abs(snr) * abs(*b3);
/* zero (1,2) elements of U**H *A and V**H *B */
if (abs(ua11r) + ((r__1 = ua12.r, abs(r__1)) + (r__2 = r_imag(&
ua12), abs(r__2))) == 0.f) {
q__2.r = vb11r, q__2.i = 0.f;
q__1.r = -q__2.r, q__1.i = -q__2.i;
r_cnjg(&q__3, &vb12);
clartg_(&q__1, &q__3, csq, snq, &r__);
} else if (abs(vb11r) + ((r__1 = vb12.r, abs(r__1)) + (r__2 =
r_imag(&vb12), abs(r__2))) == 0.f) {
q__2.r = ua11r, q__2.i = 0.f;
q__1.r = -q__2.r, q__1.i = -q__2.i;
r_cnjg(&q__3, &ua12);
clartg_(&q__1, &q__3, csq, snq, &r__);
} else if (aua12 / (abs(ua11r) + ((r__1 = ua12.r, abs(r__1)) + (
r__2 = r_imag(&ua12), abs(r__2)))) <= avb12 / (abs(vb11r)
+ ((r__3 = vb12.r, abs(r__3)) + (r__4 = r_imag(&vb12),
abs(r__4))))) {
q__2.r = ua11r, q__2.i = 0.f;
q__1.r = -q__2.r, q__1.i = -q__2.i;
r_cnjg(&q__3, &ua12);
clartg_(&q__1, &q__3, csq, snq, &r__);
} else {
q__2.r = vb11r, q__2.i = 0.f;
q__1.r = -q__2.r, q__1.i = -q__2.i;
r_cnjg(&q__3, &vb12);
clartg_(&q__1, &q__3, csq, snq, &r__);
}
*csu = csl;
q__2.r = -d1.r, q__2.i = -d1.i;
q__1.r = snl * q__2.r, q__1.i = snl * q__2.i;
snu->r = q__1.r, snu->i = q__1.i;
*csv = csr;
q__2.r = -d1.r, q__2.i = -d1.i;
q__1.r = snr * q__2.r, q__1.i = snr * q__2.i;
snv->r = q__1.r, snv->i = q__1.i;
} else {
/* Compute the (2,1) and (2,2) elements of U**H *A and V**H *B, */
/* and (2,2) element of |U|**H *|A| and |V|**H *|B|. */
r_cnjg(&q__4, &d1);
q__3.r = -q__4.r, q__3.i = -q__4.i;
q__2.r = snl * q__3.r, q__2.i = snl * q__3.i;
q__1.r = *a1 * q__2.r, q__1.i = *a1 * q__2.i;
ua21.r = q__1.r, ua21.i = q__1.i;
r_cnjg(&q__5, &d1);
q__4.r = -q__5.r, q__4.i = -q__5.i;
q__3.r = snl * q__4.r, q__3.i = snl * q__4.i;
q__2.r = q__3.r * a2->r - q__3.i * a2->i, q__2.i = q__3.r * a2->i
+ q__3.i * a2->r;
r__1 = csl * *a3;
q__1.r = q__2.r + r__1, q__1.i = q__2.i;
ua22.r = q__1.r, ua22.i = q__1.i;
r_cnjg(&q__4, &d1);
q__3.r = -q__4.r, q__3.i = -q__4.i;
q__2.r = snr * q__3.r, q__2.i = snr * q__3.i;
q__1.r = *b1 * q__2.r, q__1.i = *b1 * q__2.i;
vb21.r = q__1.r, vb21.i = q__1.i;
r_cnjg(&q__5, &d1);
q__4.r = -q__5.r, q__4.i = -q__5.i;
q__3.r = snr * q__4.r, q__3.i = snr * q__4.i;
q__2.r = q__3.r * b2->r - q__3.i * b2->i, q__2.i = q__3.r * b2->i
+ q__3.i * b2->r;
r__1 = csr * *b3;
q__1.r = q__2.r + r__1, q__1.i = q__2.i;
vb22.r = q__1.r, vb22.i = q__1.i;
aua22 = abs(snl) * ((r__1 = a2->r, abs(r__1)) + (r__2 = r_imag(a2)
, abs(r__2))) + abs(csl) * abs(*a3);
avb22 = abs(snr) * ((r__1 = b2->r, abs(r__1)) + (r__2 = r_imag(b2)
, abs(r__2))) + abs(csr) * abs(*b3);
/* zero (2,2) elements of U**H *A and V**H *B, and then swap. */
if ((r__1 = ua21.r, abs(r__1)) + (r__2 = r_imag(&ua21), abs(r__2))
+ ((r__3 = ua22.r, abs(r__3)) + (r__4 = r_imag(&ua22),
abs(r__4))) == 0.f) {
r_cnjg(&q__2, &vb21);
q__1.r = -q__2.r, q__1.i = -q__2.i;
r_cnjg(&q__3, &vb22);
clartg_(&q__1, &q__3, csq, snq, &r__);
} else if ((r__1 = vb21.r, abs(r__1)) + (r__2 = r_imag(&vb21),
abs(r__2)) + c_abs(&vb22) == 0.f) {
r_cnjg(&q__2, &ua21);
q__1.r = -q__2.r, q__1.i = -q__2.i;
r_cnjg(&q__3, &ua22);
clartg_(&q__1, &q__3, csq, snq, &r__);
} else if (aua22 / ((r__1 = ua21.r, abs(r__1)) + (r__2 = r_imag(&
ua21), abs(r__2)) + ((r__3 = ua22.r, abs(r__3)) + (r__4 =
r_imag(&ua22), abs(r__4)))) <= avb22 / ((r__5 = vb21.r,
abs(r__5)) + (r__6 = r_imag(&vb21), abs(r__6)) + ((r__7 =
vb22.r, abs(r__7)) + (r__8 = r_imag(&vb22), abs(r__8)))))
{
r_cnjg(&q__2, &ua21);
q__1.r = -q__2.r, q__1.i = -q__2.i;
r_cnjg(&q__3, &ua22);
clartg_(&q__1, &q__3, csq, snq, &r__);
} else {
r_cnjg(&q__2, &vb21);
q__1.r = -q__2.r, q__1.i = -q__2.i;
r_cnjg(&q__3, &vb22);
clartg_(&q__1, &q__3, csq, snq, &r__);
}
*csu = snl;
q__1.r = csl * d1.r, q__1.i = csl * d1.i;
snu->r = q__1.r, snu->i = q__1.i;
*csv = snr;
q__1.r = csr * d1.r, q__1.i = csr * d1.i;
snv->r = q__1.r, snv->i = q__1.i;
}
} else {
/* Input matrices A and B are lower triangular matrices */
/* Form matrix C = A*adj(B) = ( a 0 ) */
/* ( c d ) */
a = *a1 * *b3;
d__ = *a3 * *b1;
q__2.r = *b3 * a2->r, q__2.i = *b3 * a2->i;
q__3.r = *a3 * b2->r, q__3.i = *a3 * b2->i;
q__1.r = q__2.r - q__3.r, q__1.i = q__2.i - q__3.i;
c__.r = q__1.r, c__.i = q__1.i;
fc = c_abs(&c__);
/* Transform complex 2-by-2 matrix C to real matrix by unitary */
/* diagonal matrix diag(d1,1). */
d1.r = 1.f, d1.i = 0.f;
if (fc != 0.f) {
q__1.r = c__.r / fc, q__1.i = c__.i / fc;
d1.r = q__1.r, d1.i = q__1.i;
}
/* The SVD of real 2 by 2 triangular C */
/* ( CSL -SNL )*( A 0 )*( CSR SNR ) = ( R 0 ) */
/* ( SNL CSL ) ( C D ) ( -SNR CSR ) ( 0 T ) */
slasv2_(&a, &fc, &d__, &s1, &s2, &snr, &csr, &snl, &csl);
if (abs(csr) >= abs(snr) || abs(csl) >= abs(snl)) {
/* Compute the (2,1) and (2,2) elements of U**H *A and V**H *B, */
/* and (2,1) element of |U|**H *|A| and |V|**H *|B|. */
q__4.r = -d1.r, q__4.i = -d1.i;
q__3.r = snr * q__4.r, q__3.i = snr * q__4.i;
q__2.r = *a1 * q__3.r, q__2.i = *a1 * q__3.i;
q__5.r = csr * a2->r, q__5.i = csr * a2->i;
q__1.r = q__2.r + q__5.r, q__1.i = q__2.i + q__5.i;
ua21.r = q__1.r, ua21.i = q__1.i;
ua22r = csr * *a3;
q__4.r = -d1.r, q__4.i = -d1.i;
q__3.r = snl * q__4.r, q__3.i = snl * q__4.i;
q__2.r = *b1 * q__3.r, q__2.i = *b1 * q__3.i;
q__5.r = csl * b2->r, q__5.i = csl * b2->i;
q__1.r = q__2.r + q__5.r, q__1.i = q__2.i + q__5.i;
vb21.r = q__1.r, vb21.i = q__1.i;
vb22r = csl * *b3;
aua21 = abs(snr) * abs(*a1) + abs(csr) * ((r__1 = a2->r, abs(r__1)
) + (r__2 = r_imag(a2), abs(r__2)));
avb21 = abs(snl) * abs(*b1) + abs(csl) * ((r__1 = b2->r, abs(r__1)
) + (r__2 = r_imag(b2), abs(r__2)));
/* zero (2,1) elements of U**H *A and V**H *B. */
if ((r__1 = ua21.r, abs(r__1)) + (r__2 = r_imag(&ua21), abs(r__2))
+ abs(ua22r) == 0.f) {
q__1.r = vb22r, q__1.i = 0.f;
clartg_(&q__1, &vb21, csq, snq, &r__);
} else if ((r__1 = vb21.r, abs(r__1)) + (r__2 = r_imag(&vb21),
abs(r__2)) + abs(vb22r) == 0.f) {
q__1.r = ua22r, q__1.i = 0.f;
clartg_(&q__1, &ua21, csq, snq, &r__);
} else if (aua21 / ((r__1 = ua21.r, abs(r__1)) + (r__2 = r_imag(&
ua21), abs(r__2)) + abs(ua22r)) <= avb21 / ((r__3 =
vb21.r, abs(r__3)) + (r__4 = r_imag(&vb21), abs(r__4)) +
abs(vb22r))) {
q__1.r = ua22r, q__1.i = 0.f;
clartg_(&q__1, &ua21, csq, snq, &r__);
} else {
q__1.r = vb22r, q__1.i = 0.f;
clartg_(&q__1, &vb21, csq, snq, &r__);
}
*csu = csr;
r_cnjg(&q__3, &d1);
q__2.r = -q__3.r, q__2.i = -q__3.i;
q__1.r = snr * q__2.r, q__1.i = snr * q__2.i;
snu->r = q__1.r, snu->i = q__1.i;
*csv = csl;
r_cnjg(&q__3, &d1);
q__2.r = -q__3.r, q__2.i = -q__3.i;
q__1.r = snl * q__2.r, q__1.i = snl * q__2.i;
snv->r = q__1.r, snv->i = q__1.i;
} else {
/* Compute the (1,1) and (1,2) elements of U**H *A and V**H *B, */
/* and (1,1) element of |U|**H *|A| and |V|**H *|B|. */
r__1 = csr * *a1;
r_cnjg(&q__4, &d1);
q__3.r = snr * q__4.r, q__3.i = snr * q__4.i;
q__2.r = q__3.r * a2->r - q__3.i * a2->i, q__2.i = q__3.r * a2->i
+ q__3.i * a2->r;
q__1.r = r__1 + q__2.r, q__1.i = q__2.i;
ua11.r = q__1.r, ua11.i = q__1.i;
r_cnjg(&q__3, &d1);
q__2.r = snr * q__3.r, q__2.i = snr * q__3.i;
q__1.r = *a3 * q__2.r, q__1.i = *a3 * q__2.i;
ua12.r = q__1.r, ua12.i = q__1.i;
r__1 = csl * *b1;
r_cnjg(&q__4, &d1);
q__3.r = snl * q__4.r, q__3.i = snl * q__4.i;
q__2.r = q__3.r * b2->r - q__3.i * b2->i, q__2.i = q__3.r * b2->i
+ q__3.i * b2->r;
q__1.r = r__1 + q__2.r, q__1.i = q__2.i;
vb11.r = q__1.r, vb11.i = q__1.i;
r_cnjg(&q__3, &d1);
q__2.r = snl * q__3.r, q__2.i = snl * q__3.i;
q__1.r = *b3 * q__2.r, q__1.i = *b3 * q__2.i;
vb12.r = q__1.r, vb12.i = q__1.i;
aua11 = abs(csr) * abs(*a1) + abs(snr) * ((r__1 = a2->r, abs(r__1)
) + (r__2 = r_imag(a2), abs(r__2)));
avb11 = abs(csl) * abs(*b1) + abs(snl) * ((r__1 = b2->r, abs(r__1)
) + (r__2 = r_imag(b2), abs(r__2)));
/* zero (1,1) elements of U**H *A and V**H *B, and then swap. */
if ((r__1 = ua11.r, abs(r__1)) + (r__2 = r_imag(&ua11), abs(r__2))
+ ((r__3 = ua12.r, abs(r__3)) + (r__4 = r_imag(&ua12),
abs(r__4))) == 0.f) {
clartg_(&vb12, &vb11, csq, snq, &r__);
} else if ((r__1 = vb11.r, abs(r__1)) + (r__2 = r_imag(&vb11),
abs(r__2)) + ((r__3 = vb12.r, abs(r__3)) + (r__4 = r_imag(
&vb12), abs(r__4))) == 0.f) {
clartg_(&ua12, &ua11, csq, snq, &r__);
} else if (aua11 / ((r__1 = ua11.r, abs(r__1)) + (r__2 = r_imag(&
ua11), abs(r__2)) + ((r__3 = ua12.r, abs(r__3)) + (r__4 =
r_imag(&ua12), abs(r__4)))) <= avb11 / ((r__5 = vb11.r,
abs(r__5)) + (r__6 = r_imag(&vb11), abs(r__6)) + ((r__7 =
vb12.r, abs(r__7)) + (r__8 = r_imag(&vb12), abs(r__8)))))
{
clartg_(&ua12, &ua11, csq, snq, &r__);
} else {
clartg_(&vb12, &vb11, csq, snq, &r__);
}
*csu = snr;
r_cnjg(&q__2, &d1);
q__1.r = csr * q__2.r, q__1.i = csr * q__2.i;
snu->r = q__1.r, snu->i = q__1.i;
*csv = snl;
r_cnjg(&q__2, &d1);
q__1.r = csl * q__2.r, q__1.i = csl * q__2.i;
snv->r = q__1.r, snv->i = q__1.i;
}
}
return;
/* End of CLAGS2 */
} /* clags2_ */
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