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OpenBLAS/lapack-netlib/SRC/zlaic1.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 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]/Cd(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<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)
*/
/* Table of constant values */
static integer c__1 = 1;
/* > \brief \b ZLAIC1 applies one step of incremental condition estimation. */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download ZLAIC1 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaic1.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaic1.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaic1.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE ZLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C ) */
/* INTEGER J, JOB */
/* DOUBLE PRECISION SEST, SESTPR */
/* COMPLEX*16 C, GAMMA, S */
/* COMPLEX*16 W( J ), X( J ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > ZLAIC1 applies one step of incremental condition estimation in */
/* > its simplest version: */
/* > */
/* > Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j */
/* > lower triangular matrix L, such that */
/* > twonorm(L*x) = sest */
/* > Then ZLAIC1 computes sestpr, s, c such that */
/* > the vector */
/* > [ s*x ] */
/* > xhat = [ c ] */
/* > is an approximate singular vector of */
/* > [ L 0 ] */
/* > Lhat = [ w**H gamma ] */
/* > in the sense that */
/* > twonorm(Lhat*xhat) = sestpr. */
/* > */
/* > Depending on JOB, an estimate for the largest or smallest singular */
/* > value is computed. */
/* > */
/* > Note that [s c]**H and sestpr**2 is an eigenpair of the system */
/* > */
/* > diag(sest*sest, 0) + [alpha gamma] * [ conjg(alpha) ] */
/* > [ conjg(gamma) ] */
/* > */
/* > where alpha = x**H * w. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] JOB */
/* > \verbatim */
/* > JOB is INTEGER */
/* > = 1: an estimate for the largest singular value is computed. */
/* > = 2: an estimate for the smallest singular value is computed. */
/* > \endverbatim */
/* > */
/* > \param[in] J */
/* > \verbatim */
/* > J is INTEGER */
/* > Length of X and W */
/* > \endverbatim */
/* > */
/* > \param[in] X */
/* > \verbatim */
/* > X is COMPLEX*16 array, dimension (J) */
/* > The j-vector x. */
/* > \endverbatim */
/* > */
/* > \param[in] SEST */
/* > \verbatim */
/* > SEST is DOUBLE PRECISION */
/* > Estimated singular value of j by j matrix L */
/* > \endverbatim */
/* > */
/* > \param[in] W */
/* > \verbatim */
/* > W is COMPLEX*16 array, dimension (J) */
/* > The j-vector w. */
/* > \endverbatim */
/* > */
/* > \param[in] GAMMA */
/* > \verbatim */
/* > GAMMA is COMPLEX*16 */
/* > The diagonal element gamma. */
/* > \endverbatim */
/* > */
/* > \param[out] SESTPR */
/* > \verbatim */
/* > SESTPR is DOUBLE PRECISION */
/* > Estimated singular value of (j+1) by (j+1) matrix Lhat. */
/* > \endverbatim */
/* > */
/* > \param[out] S */
/* > \verbatim */
/* > S is COMPLEX*16 */
/* > Sine needed in forming xhat. */
/* > \endverbatim */
/* > */
/* > \param[out] C */
/* > \verbatim */
/* > C is COMPLEX*16 */
/* > Cosine needed in forming xhat. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date December 2016 */
/* > \ingroup complex16OTHERauxiliary */
/* ===================================================================== */
/* Subroutine */ int zlaic1_(integer *job, integer *j, doublecomplex *x,
doublereal *sest, doublecomplex *w, doublecomplex *gamma, doublereal *
sestpr, doublecomplex *s, doublecomplex *c__)
{
/* System generated locals */
doublereal d__1, d__2;
doublecomplex z__1, z__2, z__3, z__4, z__5, z__6;
/* Local variables */
doublecomplex sine;
doublereal test, zeta1, zeta2, b, t;
doublecomplex alpha;
doublereal norma;
extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
doublereal s1, s2;
extern doublereal dlamch_(char *);
doublereal absgam, absalp;
doublecomplex cosine;
doublereal absest, scl, eps, tmp;
/* -- 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 */
/* ===================================================================== */
/* Parameter adjustments */
--w;
--x;
/* Function Body */
eps = dlamch_("Epsilon");
zdotc_(&z__1, j, &x[1], &c__1, &w[1], &c__1);
alpha.r = z__1.r, alpha.i = z__1.i;
absalp = z_abs(&alpha);
absgam = z_abs(gamma);
absest = abs(*sest);
if (*job == 1) {
/* Estimating largest singular value */
/* special cases */
if (*sest == 0.) {
s1 = f2cmax(absgam,absalp);
if (s1 == 0.) {
s->r = 0., s->i = 0.;
c__->r = 1., c__->i = 0.;
*sestpr = 0.;
} else {
z__1.r = alpha.r / s1, z__1.i = alpha.i / s1;
s->r = z__1.r, s->i = z__1.i;
z__1.r = gamma->r / s1, z__1.i = gamma->i / s1;
c__->r = z__1.r, c__->i = z__1.i;
d_cnjg(&z__4, s);
z__3.r = s->r * z__4.r - s->i * z__4.i, z__3.i = s->r *
z__4.i + s->i * z__4.r;
d_cnjg(&z__6, c__);
z__5.r = c__->r * z__6.r - c__->i * z__6.i, z__5.i = c__->r *
z__6.i + c__->i * z__6.r;
z__2.r = z__3.r + z__5.r, z__2.i = z__3.i + z__5.i;
z_sqrt(&z__1, &z__2);
tmp = z__1.r;
z__1.r = s->r / tmp, z__1.i = s->i / tmp;
s->r = z__1.r, s->i = z__1.i;
z__1.r = c__->r / tmp, z__1.i = c__->i / tmp;
c__->r = z__1.r, c__->i = z__1.i;
*sestpr = s1 * tmp;
}
return 0;
} else if (absgam <= eps * absest) {
s->r = 1., s->i = 0.;
c__->r = 0., c__->i = 0.;
tmp = f2cmax(absest,absalp);
s1 = absest / tmp;
s2 = absalp / tmp;
*sestpr = tmp * sqrt(s1 * s1 + s2 * s2);
return 0;
} else if (absalp <= eps * absest) {
s1 = absgam;
s2 = absest;
if (s1 <= s2) {
s->r = 1., s->i = 0.;
c__->r = 0., c__->i = 0.;
*sestpr = s2;
} else {
s->r = 0., s->i = 0.;
c__->r = 1., c__->i = 0.;
*sestpr = s1;
}
return 0;
} else if (absest <= eps * absalp || absest <= eps * absgam) {
s1 = absgam;
s2 = absalp;
if (s1 <= s2) {
tmp = s1 / s2;
scl = sqrt(tmp * tmp + 1.);
*sestpr = s2 * scl;
z__2.r = alpha.r / s2, z__2.i = alpha.i / s2;
z__1.r = z__2.r / scl, z__1.i = z__2.i / scl;
s->r = z__1.r, s->i = z__1.i;
z__2.r = gamma->r / s2, z__2.i = gamma->i / s2;
z__1.r = z__2.r / scl, z__1.i = z__2.i / scl;
c__->r = z__1.r, c__->i = z__1.i;
} else {
tmp = s2 / s1;
scl = sqrt(tmp * tmp + 1.);
*sestpr = s1 * scl;
z__2.r = alpha.r / s1, z__2.i = alpha.i / s1;
z__1.r = z__2.r / scl, z__1.i = z__2.i / scl;
s->r = z__1.r, s->i = z__1.i;
z__2.r = gamma->r / s1, z__2.i = gamma->i / s1;
z__1.r = z__2.r / scl, z__1.i = z__2.i / scl;
c__->r = z__1.r, c__->i = z__1.i;
}
return 0;
} else {
/* normal case */
zeta1 = absalp / absest;
zeta2 = absgam / absest;
b = (1. - zeta1 * zeta1 - zeta2 * zeta2) * .5;
d__1 = zeta1 * zeta1;
c__->r = d__1, c__->i = 0.;
if (b > 0.) {
d__1 = b * b;
z__4.r = d__1 + c__->r, z__4.i = c__->i;
z_sqrt(&z__3, &z__4);
z__2.r = b + z__3.r, z__2.i = z__3.i;
z_div(&z__1, c__, &z__2);
t = z__1.r;
} else {
d__1 = b * b;
z__3.r = d__1 + c__->r, z__3.i = c__->i;
z_sqrt(&z__2, &z__3);
z__1.r = z__2.r - b, z__1.i = z__2.i;
t = z__1.r;
}
z__3.r = alpha.r / absest, z__3.i = alpha.i / absest;
z__2.r = -z__3.r, z__2.i = -z__3.i;
z__1.r = z__2.r / t, z__1.i = z__2.i / t;
sine.r = z__1.r, sine.i = z__1.i;
z__3.r = gamma->r / absest, z__3.i = gamma->i / absest;
z__2.r = -z__3.r, z__2.i = -z__3.i;
d__1 = t + 1.;
z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1;
cosine.r = z__1.r, cosine.i = z__1.i;
d_cnjg(&z__4, &sine);
z__3.r = sine.r * z__4.r - sine.i * z__4.i, z__3.i = sine.r *
z__4.i + sine.i * z__4.r;
d_cnjg(&z__6, &cosine);
z__5.r = cosine.r * z__6.r - cosine.i * z__6.i, z__5.i = cosine.r
* z__6.i + cosine.i * z__6.r;
z__2.r = z__3.r + z__5.r, z__2.i = z__3.i + z__5.i;
z_sqrt(&z__1, &z__2);
tmp = z__1.r;
z__1.r = sine.r / tmp, z__1.i = sine.i / tmp;
s->r = z__1.r, s->i = z__1.i;
z__1.r = cosine.r / tmp, z__1.i = cosine.i / tmp;
c__->r = z__1.r, c__->i = z__1.i;
*sestpr = sqrt(t + 1.) * absest;
return 0;
}
} else if (*job == 2) {
/* Estimating smallest singular value */
/* special cases */
if (*sest == 0.) {
*sestpr = 0.;
if (f2cmax(absgam,absalp) == 0.) {
sine.r = 1., sine.i = 0.;
cosine.r = 0., cosine.i = 0.;
} else {
d_cnjg(&z__2, gamma);
z__1.r = -z__2.r, z__1.i = -z__2.i;
sine.r = z__1.r, sine.i = z__1.i;
d_cnjg(&z__1, &alpha);
cosine.r = z__1.r, cosine.i = z__1.i;
}
/* Computing MAX */
d__1 = z_abs(&sine), d__2 = z_abs(&cosine);
s1 = f2cmax(d__1,d__2);
z__1.r = sine.r / s1, z__1.i = sine.i / s1;
s->r = z__1.r, s->i = z__1.i;
z__1.r = cosine.r / s1, z__1.i = cosine.i / s1;
c__->r = z__1.r, c__->i = z__1.i;
d_cnjg(&z__4, s);
z__3.r = s->r * z__4.r - s->i * z__4.i, z__3.i = s->r * z__4.i +
s->i * z__4.r;
d_cnjg(&z__6, c__);
z__5.r = c__->r * z__6.r - c__->i * z__6.i, z__5.i = c__->r *
z__6.i + c__->i * z__6.r;
z__2.r = z__3.r + z__5.r, z__2.i = z__3.i + z__5.i;
z_sqrt(&z__1, &z__2);
tmp = z__1.r;
z__1.r = s->r / tmp, z__1.i = s->i / tmp;
s->r = z__1.r, s->i = z__1.i;
z__1.r = c__->r / tmp, z__1.i = c__->i / tmp;
c__->r = z__1.r, c__->i = z__1.i;
return 0;
} else if (absgam <= eps * absest) {
s->r = 0., s->i = 0.;
c__->r = 1., c__->i = 0.;
*sestpr = absgam;
return 0;
} else if (absalp <= eps * absest) {
s1 = absgam;
s2 = absest;
if (s1 <= s2) {
s->r = 0., s->i = 0.;
c__->r = 1., c__->i = 0.;
*sestpr = s1;
} else {
s->r = 1., s->i = 0.;
c__->r = 0., c__->i = 0.;
*sestpr = s2;
}
return 0;
} else if (absest <= eps * absalp || absest <= eps * absgam) {
s1 = absgam;
s2 = absalp;
if (s1 <= s2) {
tmp = s1 / s2;
scl = sqrt(tmp * tmp + 1.);
*sestpr = absest * (tmp / scl);
d_cnjg(&z__4, gamma);
z__3.r = z__4.r / s2, z__3.i = z__4.i / s2;
z__2.r = -z__3.r, z__2.i = -z__3.i;
z__1.r = z__2.r / scl, z__1.i = z__2.i / scl;
s->r = z__1.r, s->i = z__1.i;
d_cnjg(&z__3, &alpha);
z__2.r = z__3.r / s2, z__2.i = z__3.i / s2;
z__1.r = z__2.r / scl, z__1.i = z__2.i / scl;
c__->r = z__1.r, c__->i = z__1.i;
} else {
tmp = s2 / s1;
scl = sqrt(tmp * tmp + 1.);
*sestpr = absest / scl;
d_cnjg(&z__4, gamma);
z__3.r = z__4.r / s1, z__3.i = z__4.i / s1;
z__2.r = -z__3.r, z__2.i = -z__3.i;
z__1.r = z__2.r / scl, z__1.i = z__2.i / scl;
s->r = z__1.r, s->i = z__1.i;
d_cnjg(&z__3, &alpha);
z__2.r = z__3.r / s1, z__2.i = z__3.i / s1;
z__1.r = z__2.r / scl, z__1.i = z__2.i / scl;
c__->r = z__1.r, c__->i = z__1.i;
}
return 0;
} else {
/* normal case */
zeta1 = absalp / absest;
zeta2 = absgam / absest;
/* Computing MAX */
d__1 = zeta1 * zeta1 + 1. + zeta1 * zeta2, d__2 = zeta1 * zeta2 +
zeta2 * zeta2;
norma = f2cmax(d__1,d__2);
/* See if root is closer to zero or to ONE */
test = (zeta1 - zeta2) * 2. * (zeta1 + zeta2) + 1.;
if (test >= 0.) {
/* root is close to zero, compute directly */
b = (zeta1 * zeta1 + zeta2 * zeta2 + 1.) * .5;
d__1 = zeta2 * zeta2;
c__->r = d__1, c__->i = 0.;
d__2 = b * b;
z__2.r = d__2 - c__->r, z__2.i = -c__->i;
d__1 = b + sqrt(z_abs(&z__2));
z__1.r = c__->r / d__1, z__1.i = c__->i / d__1;
t = z__1.r;
z__2.r = alpha.r / absest, z__2.i = alpha.i / absest;
d__1 = 1. - t;
z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1;
sine.r = z__1.r, sine.i = z__1.i;
z__3.r = gamma->r / absest, z__3.i = gamma->i / absest;
z__2.r = -z__3.r, z__2.i = -z__3.i;
z__1.r = z__2.r / t, z__1.i = z__2.i / t;
cosine.r = z__1.r, cosine.i = z__1.i;
*sestpr = sqrt(t + eps * 4. * eps * norma) * absest;
} else {
/* root is closer to ONE, shift by that amount */
b = (zeta2 * zeta2 + zeta1 * zeta1 - 1.) * .5;
d__1 = zeta1 * zeta1;
c__->r = d__1, c__->i = 0.;
if (b >= 0.) {
z__2.r = -c__->r, z__2.i = -c__->i;
d__1 = b * b;
z__5.r = d__1 + c__->r, z__5.i = c__->i;
z_sqrt(&z__4, &z__5);
z__3.r = b + z__4.r, z__3.i = z__4.i;
z_div(&z__1, &z__2, &z__3);
t = z__1.r;
} else {
d__1 = b * b;
z__3.r = d__1 + c__->r, z__3.i = c__->i;
z_sqrt(&z__2, &z__3);
z__1.r = b - z__2.r, z__1.i = -z__2.i;
t = z__1.r;
}
z__3.r = alpha.r / absest, z__3.i = alpha.i / absest;
z__2.r = -z__3.r, z__2.i = -z__3.i;
z__1.r = z__2.r / t, z__1.i = z__2.i / t;
sine.r = z__1.r, sine.i = z__1.i;
z__3.r = gamma->r / absest, z__3.i = gamma->i / absest;
z__2.r = -z__3.r, z__2.i = -z__3.i;
d__1 = t + 1.;
z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1;
cosine.r = z__1.r, cosine.i = z__1.i;
*sestpr = sqrt(t + 1. + eps * 4. * eps * norma) * absest;
}
d_cnjg(&z__4, &sine);
z__3.r = sine.r * z__4.r - sine.i * z__4.i, z__3.i = sine.r *
z__4.i + sine.i * z__4.r;
d_cnjg(&z__6, &cosine);
z__5.r = cosine.r * z__6.r - cosine.i * z__6.i, z__5.i = cosine.r
* z__6.i + cosine.i * z__6.r;
z__2.r = z__3.r + z__5.r, z__2.i = z__3.i + z__5.i;
z_sqrt(&z__1, &z__2);
tmp = z__1.r;
z__1.r = sine.r / tmp, z__1.i = sine.i / tmp;
s->r = z__1.r, s->i = z__1.i;
z__1.r = cosine.r / tmp, z__1.i = cosine.i / tmp;
c__->r = z__1.r, c__->i = z__1.i;
return 0;
}
}
return 0;
/* End of ZLAIC1 */
} /* zlaic1_ */
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