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OpenBLAS/lapack-netlib/SRC/cgsvj1.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)
*/
/* Table of constant values */
static integer c__1 = 1;
static integer c__0 = 0;
static real c_b18 = 1.f;
/* > \brief \b CGSVJ1 pre-processor for the routine cgesvj, applies Jacobi rotations targeting only particular
pivots. */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download CGSVJ1 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgsvj1.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgsvj1.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgsvj1.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE CGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, */
/* EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) */
/* REAL EPS, SFMIN, TOL */
/* INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP */
/* CHARACTER*1 JOBV */
/* COMPLEX A( LDA, * ), D( N ), V( LDV, * ), WORK( LWORK ) */
/* REAL SVA( N ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > CGSVJ1 is called from CGESVJ as a pre-processor and that is its main */
/* > purpose. It applies Jacobi rotations in the same way as CGESVJ does, but */
/* > it targets only particular pivots and it does not check convergence */
/* > (stopping criterion). Few tunning parameters (marked by [TP]) are */
/* > available for the implementer. */
/* > */
/* > Further Details */
/* > ~~~~~~~~~~~~~~~ */
/* > CGSVJ1 applies few sweeps of Jacobi rotations in the column space of */
/* > the input M-by-N matrix A. The pivot pairs are taken from the (1,2) */
/* > off-diagonal block in the corresponding N-by-N Gram matrix A^T * A. The */
/* > block-entries (tiles) of the (1,2) off-diagonal block are marked by the */
/* > [x]'s in the following scheme: */
/* > */
/* > | * * * [x] [x] [x]| */
/* > | * * * [x] [x] [x]| Row-cycling in the nblr-by-nblc [x] blocks. */
/* > | * * * [x] [x] [x]| Row-cyclic pivoting inside each [x] block. */
/* > |[x] [x] [x] * * * | */
/* > |[x] [x] [x] * * * | */
/* > |[x] [x] [x] * * * | */
/* > */
/* > In terms of the columns of A, the first N1 columns are rotated 'against' */
/* > the remaining N-N1 columns, trying to increase the angle between the */
/* > corresponding subspaces. The off-diagonal block is N1-by(N-N1) and it is */
/* > tiled using quadratic tiles of side KBL. Here, KBL is a tunning parameter. */
/* > The number of sweeps is given in NSWEEP and the orthogonality threshold */
/* > is given in TOL. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] JOBV */
/* > \verbatim */
/* > JOBV is CHARACTER*1 */
/* > Specifies whether the output from this procedure is used */
/* > to compute the matrix V: */
/* > = 'V': the product of the Jacobi rotations is accumulated */
/* > by postmulyiplying the N-by-N array V. */
/* > (See the description of V.) */
/* > = 'A': the product of the Jacobi rotations is accumulated */
/* > by postmulyiplying the MV-by-N array V. */
/* > (See the descriptions of MV and V.) */
/* > = 'N': the Jacobi rotations are not accumulated. */
/* > \endverbatim */
/* > */
/* > \param[in] M */
/* > \verbatim */
/* > M is INTEGER */
/* > The number of rows of the input matrix A. M >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The number of columns of the input matrix A. */
/* > M >= N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] N1 */
/* > \verbatim */
/* > N1 is INTEGER */
/* > N1 specifies the 2 x 2 block partition, the first N1 columns are */
/* > rotated 'against' the remaining N-N1 columns of A. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* > A is COMPLEX array, dimension (LDA,N) */
/* > On entry, M-by-N matrix A, such that A*diag(D) represents */
/* > the input matrix. */
/* > On exit, */
/* > A_onexit * D_onexit represents the input matrix A*diag(D) */
/* > post-multiplied by a sequence of Jacobi rotations, where the */
/* > rotation threshold and the total number of sweeps are given in */
/* > TOL and NSWEEP, respectively. */
/* > (See the descriptions of N1, D, TOL and NSWEEP.) */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
/* > \endverbatim */
/* > */
/* > \param[in,out] D */
/* > \verbatim */
/* > D is COMPLEX array, dimension (N) */
/* > The array D accumulates the scaling factors from the fast scaled */
/* > Jacobi rotations. */
/* > On entry, A*diag(D) represents the input matrix. */
/* > On exit, A_onexit*diag(D_onexit) represents the input matrix */
/* > post-multiplied by a sequence of Jacobi rotations, where the */
/* > rotation threshold and the total number of sweeps are given in */
/* > TOL and NSWEEP, respectively. */
/* > (See the descriptions of N1, A, TOL and NSWEEP.) */
/* > \endverbatim */
/* > */
/* > \param[in,out] SVA */
/* > \verbatim */
/* > SVA is REAL array, dimension (N) */
/* > On entry, SVA contains the Euclidean norms of the columns of */
/* > the matrix A*diag(D). */
/* > On exit, SVA contains the Euclidean norms of the columns of */
/* > the matrix onexit*diag(D_onexit). */
/* > \endverbatim */
/* > */
/* > \param[in] MV */
/* > \verbatim */
/* > MV is INTEGER */
/* > If JOBV = 'A', then MV rows of V are post-multipled by a */
/* > sequence of Jacobi rotations. */
/* > If JOBV = 'N', then MV is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in,out] V */
/* > \verbatim */
/* > V is COMPLEX array, dimension (LDV,N) */
/* > If JOBV = 'V' then N rows of V are post-multipled by a */
/* > sequence of Jacobi rotations. */
/* > If JOBV = 'A' then MV rows of V are post-multipled by a */
/* > sequence of Jacobi rotations. */
/* > If JOBV = 'N', then V is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDV */
/* > \verbatim */
/* > LDV is INTEGER */
/* > The leading dimension of the array V, LDV >= 1. */
/* > If JOBV = 'V', LDV >= N. */
/* > If JOBV = 'A', LDV >= MV. */
/* > \endverbatim */
/* > */
/* > \param[in] EPS */
/* > \verbatim */
/* > EPS is REAL */
/* > EPS = SLAMCH('Epsilon') */
/* > \endverbatim */
/* > */
/* > \param[in] SFMIN */
/* > \verbatim */
/* > SFMIN is REAL */
/* > SFMIN = SLAMCH('Safe Minimum') */
/* > \endverbatim */
/* > */
/* > \param[in] TOL */
/* > \verbatim */
/* > TOL is REAL */
/* > TOL is the threshold for Jacobi rotations. For a pair */
/* > A(:,p), A(:,q) of pivot columns, the Jacobi rotation is */
/* > applied only if ABS(COS(angle(A(:,p),A(:,q)))) > TOL. */
/* > \endverbatim */
/* > */
/* > \param[in] NSWEEP */
/* > \verbatim */
/* > NSWEEP is INTEGER */
/* > NSWEEP is the number of sweeps of Jacobi rotations to be */
/* > performed. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is COMPLEX array, dimension (LWORK) */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* > LWORK is INTEGER */
/* > LWORK is the dimension of WORK. LWORK >= M. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit. */
/* > < 0: if INFO = -i, then the i-th argument had an illegal value */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date June 2016 */
/* > \ingroup complexOTHERcomputational */
/* > \par Contributor: */
/* ================== */
/* > */
/* > Zlatko Drmac (Zagreb, Croatia) */
/* ===================================================================== */
/* Subroutine */ void cgsvj1_(char *jobv, integer *m, integer *n, integer *n1,
complex *a, integer *lda, complex *d__, real *sva, integer *mv,
complex *v, integer *ldv, real *eps, real *sfmin, real *tol, integer *
nsweep, complex *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4, i__5,
i__6, i__7;
real r__1, r__2;
complex q__1, q__2, q__3;
/* Local variables */
integer nblc;
real aapp;
complex aapq;
real aaqq;
integer nblr, ierr;
real bigtheta;
extern /* Subroutine */ void crot_(integer *, complex *, integer *,
complex *, integer *, real *, complex *);
complex ompq;
integer pskipped;
real aapp0, aapq1, temp1;
integer i__, p, q;
real t;
extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer
*, complex *, integer *);
real apoaq, aqoap;
extern logical lsame_(char *, char *);
real theta, small;
extern /* Subroutine */ void ccopy_(integer *, complex *, integer *,
complex *, integer *), cswap_(integer *, complex *, integer *,
complex *, integer *);
logical applv, rsvec;
extern /* Subroutine */ void caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *);
logical rotok;
real rootsfmin;
extern real scnrm2_(integer *, complex *, integer *);
real cs, sn;
extern /* Subroutine */ void clascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, complex *, integer *, integer *);
extern int xerbla_(char *, integer *, ftnlen);
integer ijblsk, swband;
extern integer isamax_(integer *, real *, integer *);
integer blskip;
extern /* Subroutine */ void classq_(integer *, complex *, integer *, real
*, real *);
real mxaapq, thsign, mxsinj;
integer emptsw, notrot, iswrot, jbc;
real big;
integer kbl, igl, ibr, jgl, mvl;
real rootbig, rooteps;
integer rowskip;
real roottol;
/* -- LAPACK computational routine (version 3.8.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* June 2016 */
/* ===================================================================== */
/* Test the input parameters. */
/* Parameter adjustments */
--sva;
--d__;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
v_dim1 = *ldv;
v_offset = 1 + v_dim1 * 1;
v -= v_offset;
--work;
/* Function Body */
applv = lsame_(jobv, "A");
rsvec = lsame_(jobv, "V");
if (! (rsvec || applv || lsame_(jobv, "N"))) {
*info = -1;
} else if (*m < 0) {
*info = -2;
} else if (*n < 0 || *n > *m) {
*info = -3;
} else if (*n1 < 0) {
*info = -4;
} else if (*lda < *m) {
*info = -6;
} else if ((rsvec || applv) && *mv < 0) {
*info = -9;
} else if (rsvec && *ldv < *n || applv && *ldv < *mv) {
*info = -11;
} else if (*tol <= *eps) {
*info = -14;
} else if (*nsweep < 0) {
*info = -15;
} else if (*lwork < *m) {
*info = -17;
} else {
*info = 0;
}
/* #:( */
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGSVJ1", &i__1, (ftnlen)6);
return;
}
if (rsvec) {
mvl = *n;
} else if (applv) {
mvl = *mv;
}
rsvec = rsvec || applv;
rooteps = sqrt(*eps);
rootsfmin = sqrt(*sfmin);
small = *sfmin / *eps;
big = 1.f / *sfmin;
rootbig = 1.f / rootsfmin;
/* LARGE = BIG / SQRT( REAL( M*N ) ) */
bigtheta = 1.f / rooteps;
roottol = sqrt(*tol);
/* RSVEC = LSAME( JOBV, 'Y' ) */
emptsw = *n1 * (*n - *n1);
notrot = 0;
kbl = f2cmin(8,*n);
nblr = *n1 / kbl;
if (nblr * kbl != *n1) {
++nblr;
}
nblc = (*n - *n1) / kbl;
if (nblc * kbl != *n - *n1) {
++nblc;
}
/* Computing 2nd power */
i__1 = kbl;
blskip = i__1 * i__1 + 1;
/* [TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. */
rowskip = f2cmin(5,kbl);
/* [TP] ROWSKIP is a tuning parameter. */
swband = 0;
/* [TP] SWBAND is a tuning parameter. It is meaningful and effective */
/* if CGESVJ is used as a computational routine in the preconditioned */
/* Jacobi SVD algorithm CGEJSV. */
/* | * * * [x] [x] [x]| */
/* | * * * [x] [x] [x]| Row-cycling in the nblr-by-nblc [x] blocks. */
/* | * * * [x] [x] [x]| Row-cyclic pivoting inside each [x] block. */
/* |[x] [x] [x] * * * | */
/* |[x] [x] [x] * * * | */
/* |[x] [x] [x] * * * | */
i__1 = *nsweep;
for (i__ = 1; i__ <= i__1; ++i__) {
mxaapq = 0.f;
mxsinj = 0.f;
iswrot = 0;
notrot = 0;
pskipped = 0;
/* Each sweep is unrolled using KBL-by-KBL tiles over the pivot pairs */
/* 1 <= p < q <= N. This is the first step toward a blocked implementation */
/* of the rotations. New implementation, based on block transformations, */
/* is under development. */
i__2 = nblr;
for (ibr = 1; ibr <= i__2; ++ibr) {
igl = (ibr - 1) * kbl + 1;
/* ... go to the off diagonal blocks */
igl = (ibr - 1) * kbl + 1;
/* DO 2010 jbc = ibr + 1, NBL */
i__3 = nblc;
for (jbc = 1; jbc <= i__3; ++jbc) {
jgl = (jbc - 1) * kbl + *n1 + 1;
/* doing the block at ( ibr, jbc ) */
ijblsk = 0;
/* Computing MIN */
i__5 = igl + kbl - 1;
i__4 = f2cmin(i__5,*n1);
for (p = igl; p <= i__4; ++p) {
aapp = sva[p];
if (aapp > 0.f) {
pskipped = 0;
/* Computing MIN */
i__6 = jgl + kbl - 1;
i__5 = f2cmin(i__6,*n);
for (q = jgl; q <= i__5; ++q) {
aaqq = sva[q];
if (aaqq > 0.f) {
aapp0 = aapp;
/* Safe Gram matrix computation */
if (aaqq >= 1.f) {
if (aapp >= aaqq) {
rotok = small * aapp <= aaqq;
} else {
rotok = small * aaqq <= aapp;
}
if (aapp < big / aaqq) {
cdotc_(&q__3, m, &a[p * a_dim1 + 1], &
c__1, &a[q * a_dim1 + 1], &
c__1);
q__2.r = q__3.r / aaqq, q__2.i =
q__3.i / aaqq;
q__1.r = q__2.r / aapp, q__1.i =
q__2.i / aapp;
aapq.r = q__1.r, aapq.i = q__1.i;
} else {
ccopy_(m, &a[p * a_dim1 + 1], &c__1, &
work[1], &c__1);
clascl_("G", &c__0, &c__0, &aapp, &
c_b18, m, &c__1, &work[1],
lda, &ierr);
cdotc_(&q__2, m, &work[1], &c__1, &a[
q * a_dim1 + 1], &c__1);
q__1.r = q__2.r / aaqq, q__1.i =
q__2.i / aaqq;
aapq.r = q__1.r, aapq.i = q__1.i;
}
} else {
if (aapp >= aaqq) {
rotok = aapp <= aaqq / small;
} else {
rotok = aaqq <= aapp / small;
}
if (aapp > small / aaqq) {
cdotc_(&q__3, m, &a[p * a_dim1 + 1], &
c__1, &a[q * a_dim1 + 1], &
c__1);
r__1 = f2cmax(aaqq,aapp);
q__2.r = q__3.r / r__1, q__2.i =
q__3.i / r__1;
r__2 = f2cmin(aaqq,aapp);
q__1.r = q__2.r / r__2, q__1.i =
q__2.i / r__2;
aapq.r = q__1.r, aapq.i = q__1.i;
} else {
ccopy_(m, &a[q * a_dim1 + 1], &c__1, &
work[1], &c__1);
clascl_("G", &c__0, &c__0, &aaqq, &
c_b18, m, &c__1, &work[1],
lda, &ierr);
cdotc_(&q__2, m, &a[p * a_dim1 + 1], &
c__1, &work[1], &c__1);
q__1.r = q__2.r / aapp, q__1.i =
q__2.i / aapp;
aapq.r = q__1.r, aapq.i = q__1.i;
}
}
/* AAPQ = AAPQ * CONJG(CWORK(p))*CWORK(q) */
aapq1 = -c_abs(&aapq);
/* Computing MAX */
r__1 = mxaapq, r__2 = -aapq1;
mxaapq = f2cmax(r__1,r__2);
/* TO rotate or NOT to rotate, THAT is the question ... */
if (abs(aapq1) > *tol) {
r__1 = c_abs(&aapq);
q__1.r = aapq.r / r__1, q__1.i = aapq.i /
r__1;
ompq.r = q__1.r, ompq.i = q__1.i;
notrot = 0;
/* [RTD] ROTATED = ROTATED + 1 */
pskipped = 0;
++iswrot;
if (rotok) {
aqoap = aaqq / aapp;
apoaq = aapp / aaqq;
theta = (r__1 = aqoap - apoaq, abs(
r__1)) * -.5f / aapq1;
if (aaqq > aapp0) {
theta = -theta;
}
if (abs(theta) > bigtheta) {
t = .5f / theta;
cs = 1.f;
r_cnjg(&q__2, &ompq);
q__1.r = t * q__2.r, q__1.i = t *
q__2.i;
crot_(m, &a[p * a_dim1 + 1], &
c__1, &a[q * a_dim1 + 1],
&c__1, &cs, &q__1);
if (rsvec) {
r_cnjg(&q__2, &ompq);
q__1.r = t * q__2.r, q__1.i = t * q__2.i;
crot_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q *
v_dim1 + 1], &c__1, &cs, &q__1);
}
/* Computing MAX */
r__1 = 0.f, r__2 = t * apoaq *
aapq1 + 1.f;
sva[q] = aaqq * sqrt((f2cmax(r__1,
r__2)));
/* Computing MAX */
r__1 = 0.f, r__2 = 1.f - t *
aqoap * aapq1;
aapp *= sqrt((f2cmax(r__1,r__2)));
/* Computing MAX */
r__1 = mxsinj, r__2 = abs(t);
mxsinj = f2cmax(r__1,r__2);
} else {
thsign = -r_sign(&c_b18, &aapq1);
if (aaqq > aapp0) {
thsign = -thsign;
}
t = 1.f / (theta + thsign * sqrt(
theta * theta + 1.f));
cs = sqrt(1.f / (t * t + 1.f));
sn = t * cs;
/* Computing MAX */
r__1 = mxsinj, r__2 = abs(sn);
mxsinj = f2cmax(r__1,r__2);
/* Computing MAX */
r__1 = 0.f, r__2 = t * apoaq *
aapq1 + 1.f;
sva[q] = aaqq * sqrt((f2cmax(r__1,
r__2)));
/* Computing MAX */
r__1 = 0.f, r__2 = 1.f - t *
aqoap * aapq1;
aapp *= sqrt((f2cmax(r__1,r__2)));
r_cnjg(&q__2, &ompq);
q__1.r = sn * q__2.r, q__1.i = sn
* q__2.i;
crot_(m, &a[p * a_dim1 + 1], &
c__1, &a[q * a_dim1 + 1],
&c__1, &cs, &q__1);
if (rsvec) {
r_cnjg(&q__2, &ompq);
q__1.r = sn * q__2.r, q__1.i = sn * q__2.i;
crot_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q *
v_dim1 + 1], &c__1, &cs, &q__1);
}
}
i__6 = p;
i__7 = q;
q__2.r = -d__[i__7].r, q__2.i = -d__[
i__7].i;
q__1.r = q__2.r * ompq.r - q__2.i *
ompq.i, q__1.i = q__2.r *
ompq.i + q__2.i * ompq.r;
d__[i__6].r = q__1.r, d__[i__6].i =
q__1.i;
} else {
if (aapp > aaqq) {
ccopy_(m, &a[p * a_dim1 + 1], &
c__1, &work[1], &c__1);
clascl_("G", &c__0, &c__0, &aapp,
&c_b18, m, &c__1, &work[1]
, lda, &ierr);
clascl_("G", &c__0, &c__0, &aaqq,
&c_b18, m, &c__1, &a[q *
a_dim1 + 1], lda, &ierr);
q__1.r = -aapq.r, q__1.i =
-aapq.i;
caxpy_(m, &q__1, &work[1], &c__1,
&a[q * a_dim1 + 1], &c__1)
;
clascl_("G", &c__0, &c__0, &c_b18,
&aaqq, m, &c__1, &a[q *
a_dim1 + 1], lda, &ierr);
/* Computing MAX */
r__1 = 0.f, r__2 = 1.f - aapq1 *
aapq1;
sva[q] = aaqq * sqrt((f2cmax(r__1,
r__2)));
mxsinj = f2cmax(mxsinj,*sfmin);
} else {
ccopy_(m, &a[q * a_dim1 + 1], &
c__1, &work[1], &c__1);
clascl_("G", &c__0, &c__0, &aaqq,
&c_b18, m, &c__1, &work[1]
, lda, &ierr);
clascl_("G", &c__0, &c__0, &aapp,
&c_b18, m, &c__1, &a[p *
a_dim1 + 1], lda, &ierr);
r_cnjg(&q__2, &aapq);
q__1.r = -q__2.r, q__1.i =
-q__2.i;
caxpy_(m, &q__1, &work[1], &c__1,
&a[p * a_dim1 + 1], &c__1)
;
clascl_("G", &c__0, &c__0, &c_b18,
&aapp, m, &c__1, &a[p *
a_dim1 + 1], lda, &ierr);
/* Computing MAX */
r__1 = 0.f, r__2 = 1.f - aapq1 *
aapq1;
sva[p] = aapp * sqrt((f2cmax(r__1,
r__2)));
mxsinj = f2cmax(mxsinj,*sfmin);
}
}
/* END IF ROTOK THEN ... ELSE */
/* In the case of cancellation in updating SVA(q), SVA(p) */
/* Computing 2nd power */
r__1 = sva[q] / aaqq;
if (r__1 * r__1 <= rooteps) {
if (aaqq < rootbig && aaqq >
rootsfmin) {
sva[q] = scnrm2_(m, &a[q * a_dim1
+ 1], &c__1);
} else {
t = 0.f;
aaqq = 1.f;
classq_(m, &a[q * a_dim1 + 1], &
c__1, &t, &aaqq);
sva[q] = t * sqrt(aaqq);
}
}
/* Computing 2nd power */
r__1 = aapp / aapp0;
if (r__1 * r__1 <= rooteps) {
if (aapp < rootbig && aapp >
rootsfmin) {
aapp = scnrm2_(m, &a[p * a_dim1 +
1], &c__1);
} else {
t = 0.f;
aapp = 1.f;
classq_(m, &a[p * a_dim1 + 1], &
c__1, &t, &aapp);
aapp = t * sqrt(aapp);
}
sva[p] = aapp;
}
/* end of OK rotation */
} else {
++notrot;
/* [RTD] SKIPPED = SKIPPED + 1 */
++pskipped;
++ijblsk;
}
} else {
++notrot;
++pskipped;
++ijblsk;
}
if (i__ <= swband && ijblsk >= blskip) {
sva[p] = aapp;
notrot = 0;
goto L2011;
}
if (i__ <= swband && pskipped > rowskip) {
aapp = -aapp;
notrot = 0;
goto L2203;
}
/* L2200: */
}
/* end of the q-loop */
L2203:
sva[p] = aapp;
} else {
if (aapp == 0.f) {
/* Computing MIN */
i__5 = jgl + kbl - 1;
notrot = notrot + f2cmin(i__5,*n) - jgl + 1;
}
if (aapp < 0.f) {
notrot = 0;
}
}
/* L2100: */
}
/* end of the p-loop */
/* L2010: */
}
/* end of the jbc-loop */
L2011:
/* 2011 bailed out of the jbc-loop */
/* Computing MIN */
i__4 = igl + kbl - 1;
i__3 = f2cmin(i__4,*n);
for (p = igl; p <= i__3; ++p) {
sva[p] = (r__1 = sva[p], abs(r__1));
/* L2012: */
}
/* ** */
/* L2000: */
}
/* 2000 :: end of the ibr-loop */
if (sva[*n] < rootbig && sva[*n] > rootsfmin) {
sva[*n] = scnrm2_(m, &a[*n * a_dim1 + 1], &c__1);
} else {
t = 0.f;
aapp = 1.f;
classq_(m, &a[*n * a_dim1 + 1], &c__1, &t, &aapp);
sva[*n] = t * sqrt(aapp);
}
/* Additional steering devices */
if (i__ < swband && (mxaapq <= roottol || iswrot <= *n)) {
swband = i__;
}
if (i__ > swband + 1 && mxaapq < sqrt((real) (*n)) * *tol && (real) (*
n) * mxaapq * mxsinj < *tol) {
goto L1994;
}
if (notrot >= emptsw) {
goto L1994;
}
/* L1993: */
}
/* end i=1:NSWEEP loop */
/* #:( Reaching this point means that the procedure has not converged. */
*info = *nsweep - 1;
goto L1995;
L1994:
/* #:) Reaching this point means numerical convergence after the i-th */
/* sweep. */
*info = 0;
/* #:) INFO = 0 confirms successful iterations. */
L1995:
/* Sort the vector SVA() of column norms. */
i__1 = *n - 1;
for (p = 1; p <= i__1; ++p) {
i__2 = *n - p + 1;
q = isamax_(&i__2, &sva[p], &c__1) + p - 1;
if (p != q) {
temp1 = sva[p];
sva[p] = sva[q];
sva[q] = temp1;
i__2 = p;
aapq.r = d__[i__2].r, aapq.i = d__[i__2].i;
i__2 = p;
i__3 = q;
d__[i__2].r = d__[i__3].r, d__[i__2].i = d__[i__3].i;
i__2 = q;
d__[i__2].r = aapq.r, d__[i__2].i = aapq.i;
cswap_(m, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 + 1], &c__1);
if (rsvec) {
cswap_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q * v_dim1 + 1], &
c__1);
}
}
/* L5991: */
}
return;
} /* cgsvj1_ */
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