OpenBLAS/lapack-netlib/SRC/clals0.c

1165 lines
33 KiB
C

#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 real c_b5 = -1.f;
static integer c__1 = 1;
static real c_b13 = 1.f;
static real c_b15 = 0.f;
static integer c__0 = 0;
/* > \brief \b CLALS0 applies back multiplying factors in solving the least squares problem using divide and c
onquer SVD approach. Used by sgelsd. */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download CLALS0 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clals0.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clals0.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clals0.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE CLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, */
/* PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, */
/* POLES, DIFL, DIFR, Z, K, C, S, RWORK, INFO ) */
/* INTEGER GIVPTR, ICOMPQ, INFO, K, LDB, LDBX, LDGCOL, */
/* $ LDGNUM, NL, NR, NRHS, SQRE */
/* REAL C, S */
/* INTEGER GIVCOL( LDGCOL, * ), PERM( * ) */
/* REAL DIFL( * ), DIFR( LDGNUM, * ), */
/* $ GIVNUM( LDGNUM, * ), POLES( LDGNUM, * ), */
/* $ RWORK( * ), Z( * ) */
/* COMPLEX B( LDB, * ), BX( LDBX, * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > CLALS0 applies back the multiplying factors of either the left or the */
/* > right singular vector matrix of a diagonal matrix appended by a row */
/* > to the right hand side matrix B in solving the least squares problem */
/* > using the divide-and-conquer SVD approach. */
/* > */
/* > For the left singular vector matrix, three types of orthogonal */
/* > matrices are involved: */
/* > */
/* > (1L) Givens rotations: the number of such rotations is GIVPTR; the */
/* > pairs of columns/rows they were applied to are stored in GIVCOL; */
/* > and the C- and S-values of these rotations are stored in GIVNUM. */
/* > */
/* > (2L) Permutation. The (NL+1)-st row of B is to be moved to the first */
/* > row, and for J=2:N, PERM(J)-th row of B is to be moved to the */
/* > J-th row. */
/* > */
/* > (3L) The left singular vector matrix of the remaining matrix. */
/* > */
/* > For the right singular vector matrix, four types of orthogonal */
/* > matrices are involved: */
/* > */
/* > (1R) The right singular vector matrix of the remaining matrix. */
/* > */
/* > (2R) If SQRE = 1, one extra Givens rotation to generate the right */
/* > null space. */
/* > */
/* > (3R) The inverse transformation of (2L). */
/* > */
/* > (4R) The inverse transformation of (1L). */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] ICOMPQ */
/* > \verbatim */
/* > ICOMPQ is INTEGER */
/* > Specifies whether singular vectors are to be computed in */
/* > factored form: */
/* > = 0: Left singular vector matrix. */
/* > = 1: Right singular vector matrix. */
/* > \endverbatim */
/* > */
/* > \param[in] NL */
/* > \verbatim */
/* > NL is INTEGER */
/* > The row dimension of the upper block. NL >= 1. */
/* > \endverbatim */
/* > */
/* > \param[in] NR */
/* > \verbatim */
/* > NR is INTEGER */
/* > The row dimension of the lower block. NR >= 1. */
/* > \endverbatim */
/* > */
/* > \param[in] SQRE */
/* > \verbatim */
/* > SQRE is INTEGER */
/* > = 0: the lower block is an NR-by-NR square matrix. */
/* > = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */
/* > */
/* > The bidiagonal matrix has row dimension N = NL + NR + 1, */
/* > and column dimension M = N + SQRE. */
/* > \endverbatim */
/* > */
/* > \param[in] NRHS */
/* > \verbatim */
/* > NRHS is INTEGER */
/* > The number of columns of B and BX. NRHS must be at least 1. */
/* > \endverbatim */
/* > */
/* > \param[in,out] B */
/* > \verbatim */
/* > B is COMPLEX array, dimension ( LDB, NRHS ) */
/* > On input, B contains the right hand sides of the least */
/* > squares problem in rows 1 through M. On output, B contains */
/* > the solution X in rows 1 through N. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* > LDB is INTEGER */
/* > The leading dimension of B. LDB must be at least */
/* > f2cmax(1,MAX( M, N ) ). */
/* > \endverbatim */
/* > */
/* > \param[out] BX */
/* > \verbatim */
/* > BX is COMPLEX array, dimension ( LDBX, NRHS ) */
/* > \endverbatim */
/* > */
/* > \param[in] LDBX */
/* > \verbatim */
/* > LDBX is INTEGER */
/* > The leading dimension of BX. */
/* > \endverbatim */
/* > */
/* > \param[in] PERM */
/* > \verbatim */
/* > PERM is INTEGER array, dimension ( N ) */
/* > The permutations (from deflation and sorting) applied */
/* > to the two blocks. */
/* > \endverbatim */
/* > */
/* > \param[in] GIVPTR */
/* > \verbatim */
/* > GIVPTR is INTEGER */
/* > The number of Givens rotations which took place in this */
/* > subproblem. */
/* > \endverbatim */
/* > */
/* > \param[in] GIVCOL */
/* > \verbatim */
/* > GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) */
/* > Each pair of numbers indicates a pair of rows/columns */
/* > involved in a Givens rotation. */
/* > \endverbatim */
/* > */
/* > \param[in] LDGCOL */
/* > \verbatim */
/* > LDGCOL is INTEGER */
/* > The leading dimension of GIVCOL, must be at least N. */
/* > \endverbatim */
/* > */
/* > \param[in] GIVNUM */
/* > \verbatim */
/* > GIVNUM is REAL array, dimension ( LDGNUM, 2 ) */
/* > Each number indicates the C or S value used in the */
/* > corresponding Givens rotation. */
/* > \endverbatim */
/* > */
/* > \param[in] LDGNUM */
/* > \verbatim */
/* > LDGNUM is INTEGER */
/* > The leading dimension of arrays DIFR, POLES and */
/* > GIVNUM, must be at least K. */
/* > \endverbatim */
/* > */
/* > \param[in] POLES */
/* > \verbatim */
/* > POLES is REAL array, dimension ( LDGNUM, 2 ) */
/* > On entry, POLES(1:K, 1) contains the new singular */
/* > values obtained from solving the secular equation, and */
/* > POLES(1:K, 2) is an array containing the poles in the secular */
/* > equation. */
/* > \endverbatim */
/* > */
/* > \param[in] DIFL */
/* > \verbatim */
/* > DIFL is REAL array, dimension ( K ). */
/* > On entry, DIFL(I) is the distance between I-th updated */
/* > (undeflated) singular value and the I-th (undeflated) old */
/* > singular value. */
/* > \endverbatim */
/* > */
/* > \param[in] DIFR */
/* > \verbatim */
/* > DIFR is REAL array, dimension ( LDGNUM, 2 ). */
/* > On entry, DIFR(I, 1) contains the distances between I-th */
/* > updated (undeflated) singular value and the I+1-th */
/* > (undeflated) old singular value. And DIFR(I, 2) is the */
/* > normalizing factor for the I-th right singular vector. */
/* > \endverbatim */
/* > */
/* > \param[in] Z */
/* > \verbatim */
/* > Z is REAL array, dimension ( K ) */
/* > Contain the components of the deflation-adjusted updating row */
/* > vector. */
/* > \endverbatim */
/* > */
/* > \param[in] K */
/* > \verbatim */
/* > K is INTEGER */
/* > Contains the dimension of the non-deflated matrix, */
/* > This is the order of the related secular equation. 1 <= K <=N. */
/* > \endverbatim */
/* > */
/* > \param[in] C */
/* > \verbatim */
/* > C is REAL */
/* > C contains garbage if SQRE =0 and the C-value of a Givens */
/* > rotation related to the right null space if SQRE = 1. */
/* > \endverbatim */
/* > */
/* > \param[in] S */
/* > \verbatim */
/* > S is REAL */
/* > S contains garbage if SQRE =0 and the S-value of a Givens */
/* > rotation related to the right null space if SQRE = 1. */
/* > \endverbatim */
/* > */
/* > \param[out] RWORK */
/* > \verbatim */
/* > RWORK is REAL array, dimension */
/* > ( K*(1+NRHS) + 2*NRHS ) */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit. */
/* > < 0: if INFO = -i, 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 December 2016 */
/* > \ingroup complexOTHERcomputational */
/* > \par Contributors: */
/* ================== */
/* > */
/* > Ming Gu and Ren-Cang Li, Computer Science Division, University of */
/* > California at Berkeley, USA \n */
/* > Osni Marques, LBNL/NERSC, USA \n */
/* ===================================================================== */
/* Subroutine */ void clals0_(integer *icompq, integer *nl, integer *nr,
integer *sqre, integer *nrhs, complex *b, integer *ldb, complex *bx,
integer *ldbx, integer *perm, integer *givptr, integer *givcol,
integer *ldgcol, real *givnum, integer *ldgnum, real *poles, real *
difl, real *difr, real *z__, integer *k, real *c__, real *s, real *
rwork, integer *info)
{
/* System generated locals */
integer givcol_dim1, givcol_offset, difr_dim1, difr_offset, givnum_dim1,
givnum_offset, poles_dim1, poles_offset, b_dim1, b_offset,
bx_dim1, bx_offset, i__1, i__2, i__3, i__4, i__5;
real r__1;
complex q__1;
/* Local variables */
integer jcol;
real temp;
integer jrow;
extern real snrm2_(integer *, real *, integer *);
integer i__, j, m, n;
real diflj, difrj, dsigj;
extern /* Subroutine */ void ccopy_(integer *, complex *, integer *,
complex *, integer *), sgemv_(char *, integer *, integer *, real *
, real *, integer *, real *, integer *, real *, real *, integer *), csrot_(integer *, complex *, integer *, complex *,
integer *, real *, real *);
extern real slamc3_(real *, real *);
real dj;
extern /* Subroutine */ void clascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, complex *, integer *, integer *), csscal_(integer *, real *, complex *, integer *),
clacpy_(char *, integer *, integer *, complex *, integer *,
complex *, integer *);
extern int xerbla_(char *, integer *, ftnlen);
real dsigjp;
integer nlp1;
/* -- LAPACK computational routine (version 3.7.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* December 2016 */
/* ===================================================================== */
/* Test the input parameters. */
/* Parameter adjustments */
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
bx_dim1 = *ldbx;
bx_offset = 1 + bx_dim1 * 1;
bx -= bx_offset;
--perm;
givcol_dim1 = *ldgcol;
givcol_offset = 1 + givcol_dim1 * 1;
givcol -= givcol_offset;
difr_dim1 = *ldgnum;
difr_offset = 1 + difr_dim1 * 1;
difr -= difr_offset;
poles_dim1 = *ldgnum;
poles_offset = 1 + poles_dim1 * 1;
poles -= poles_offset;
givnum_dim1 = *ldgnum;
givnum_offset = 1 + givnum_dim1 * 1;
givnum -= givnum_offset;
--difl;
--z__;
--rwork;
/* Function Body */
*info = 0;
n = *nl + *nr + 1;
if (*icompq < 0 || *icompq > 1) {
*info = -1;
} else if (*nl < 1) {
*info = -2;
} else if (*nr < 1) {
*info = -3;
} else if (*sqre < 0 || *sqre > 1) {
*info = -4;
} else if (*nrhs < 1) {
*info = -5;
} else if (*ldb < n) {
*info = -7;
} else if (*ldbx < n) {
*info = -9;
} else if (*givptr < 0) {
*info = -11;
} else if (*ldgcol < n) {
*info = -13;
} else if (*ldgnum < n) {
*info = -15;
// } else if (*k < 1) {
} else if (*k < 0) {
*info = -20;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CLALS0", &i__1, (ftnlen)6);
return;
}
m = n + *sqre;
nlp1 = *nl + 1;
if (*icompq == 0) {
/* Apply back orthogonal transformations from the left. */
/* Step (1L): apply back the Givens rotations performed. */
i__1 = *givptr;
for (i__ = 1; i__ <= i__1; ++i__) {
csrot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, &
b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ +
(givnum_dim1 << 1)], &givnum[i__ + givnum_dim1]);
/* L10: */
}
/* Step (2L): permute rows of B. */
ccopy_(nrhs, &b[nlp1 + b_dim1], ldb, &bx[bx_dim1 + 1], ldbx);
i__1 = n;
for (i__ = 2; i__ <= i__1; ++i__) {
ccopy_(nrhs, &b[perm[i__] + b_dim1], ldb, &bx[i__ + bx_dim1],
ldbx);
/* L20: */
}
/* Step (3L): apply the inverse of the left singular vector */
/* matrix to BX. */
if (*k == 1) {
ccopy_(nrhs, &bx[bx_offset], ldbx, &b[b_offset], ldb);
if (z__[1] < 0.f) {
csscal_(nrhs, &c_b5, &b[b_offset], ldb);
}
} else {
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
diflj = difl[j];
dj = poles[j + poles_dim1];
dsigj = -poles[j + (poles_dim1 << 1)];
if (j < *k) {
difrj = -difr[j + difr_dim1];
dsigjp = -poles[j + 1 + (poles_dim1 << 1)];
}
if (z__[j] == 0.f || poles[j + (poles_dim1 << 1)] == 0.f) {
rwork[j] = 0.f;
} else {
rwork[j] = -poles[j + (poles_dim1 << 1)] * z__[j] / diflj
/ (poles[j + (poles_dim1 << 1)] + dj);
}
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
if (z__[i__] == 0.f || poles[i__ + (poles_dim1 << 1)] ==
0.f) {
rwork[i__] = 0.f;
} else {
rwork[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__]
/ (slamc3_(&poles[i__ + (poles_dim1 << 1)], &
dsigj) - diflj) / (poles[i__ + (poles_dim1 <<
1)] + dj);
}
/* L30: */
}
i__2 = *k;
for (i__ = j + 1; i__ <= i__2; ++i__) {
if (z__[i__] == 0.f || poles[i__ + (poles_dim1 << 1)] ==
0.f) {
rwork[i__] = 0.f;
} else {
rwork[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__]
/ (slamc3_(&poles[i__ + (poles_dim1 << 1)], &
dsigjp) + difrj) / (poles[i__ + (poles_dim1 <<
1)] + dj);
}
/* L40: */
}
rwork[1] = -1.f;
temp = snrm2_(k, &rwork[1], &c__1);
/* Since B and BX are complex, the following call to SGEMV */
/* is performed in two steps (real and imaginary parts). */
/* CALL SGEMV( 'T', K, NRHS, ONE, BX, LDBX, WORK, 1, ZERO, */
/* $ B( J, 1 ), LDB ) */
i__ = *k + (*nrhs << 1);
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = *k;
for (jrow = 1; jrow <= i__3; ++jrow) {
++i__;
i__4 = jrow + jcol * bx_dim1;
rwork[i__] = bx[i__4].r;
/* L50: */
}
/* L60: */
}
sgemv_("T", k, nrhs, &c_b13, &rwork[*k + 1 + (*nrhs << 1)], k,
&rwork[1], &c__1, &c_b15, &rwork[*k + 1], &c__1);
i__ = *k + (*nrhs << 1);
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = *k;
for (jrow = 1; jrow <= i__3; ++jrow) {
++i__;
rwork[i__] = r_imag(&bx[jrow + jcol * bx_dim1]);
/* L70: */
}
/* L80: */
}
sgemv_("T", k, nrhs, &c_b13, &rwork[*k + 1 + (*nrhs << 1)], k,
&rwork[1], &c__1, &c_b15, &rwork[*k + 1 + *nrhs], &
c__1);
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = j + jcol * b_dim1;
i__4 = jcol + *k;
i__5 = jcol + *k + *nrhs;
q__1.r = rwork[i__4], q__1.i = rwork[i__5];
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L90: */
}
clascl_("G", &c__0, &c__0, &temp, &c_b13, &c__1, nrhs, &b[j +
b_dim1], ldb, info);
/* L100: */
}
}
/* Move the deflated rows of BX to B also. */
if (*k < f2cmax(m,n)) {
i__1 = n - *k;
clacpy_("A", &i__1, nrhs, &bx[*k + 1 + bx_dim1], ldbx, &b[*k + 1
+ b_dim1], ldb);
}
} else {
/* Apply back the right orthogonal transformations. */
/* Step (1R): apply back the new right singular vector matrix */
/* to B. */
if (*k == 1) {
ccopy_(nrhs, &b[b_offset], ldb, &bx[bx_offset], ldbx);
} else {
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
dsigj = poles[j + (poles_dim1 << 1)];
if (z__[j] == 0.f) {
rwork[j] = 0.f;
} else {
rwork[j] = -z__[j] / difl[j] / (dsigj + poles[j +
poles_dim1]) / difr[j + (difr_dim1 << 1)];
}
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
if (z__[j] == 0.f) {
rwork[i__] = 0.f;
} else {
r__1 = -poles[i__ + 1 + (poles_dim1 << 1)];
rwork[i__] = z__[j] / (slamc3_(&dsigj, &r__1) - difr[
i__ + difr_dim1]) / (dsigj + poles[i__ +
poles_dim1]) / difr[i__ + (difr_dim1 << 1)];
}
/* L110: */
}
i__2 = *k;
for (i__ = j + 1; i__ <= i__2; ++i__) {
if (z__[j] == 0.f) {
rwork[i__] = 0.f;
} else {
r__1 = -poles[i__ + (poles_dim1 << 1)];
rwork[i__] = z__[j] / (slamc3_(&dsigj, &r__1) - difl[
i__]) / (dsigj + poles[i__ + poles_dim1]) /
difr[i__ + (difr_dim1 << 1)];
}
/* L120: */
}
/* Since B and BX are complex, the following call to SGEMV */
/* is performed in two steps (real and imaginary parts). */
/* CALL SGEMV( 'T', K, NRHS, ONE, B, LDB, WORK, 1, ZERO, */
/* $ BX( J, 1 ), LDBX ) */
i__ = *k + (*nrhs << 1);
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = *k;
for (jrow = 1; jrow <= i__3; ++jrow) {
++i__;
i__4 = jrow + jcol * b_dim1;
rwork[i__] = b[i__4].r;
/* L130: */
}
/* L140: */
}
sgemv_("T", k, nrhs, &c_b13, &rwork[*k + 1 + (*nrhs << 1)], k,
&rwork[1], &c__1, &c_b15, &rwork[*k + 1], &c__1);
i__ = *k + (*nrhs << 1);
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = *k;
for (jrow = 1; jrow <= i__3; ++jrow) {
++i__;
rwork[i__] = r_imag(&b[jrow + jcol * b_dim1]);
/* L150: */
}
/* L160: */
}
sgemv_("T", k, nrhs, &c_b13, &rwork[*k + 1 + (*nrhs << 1)], k,
&rwork[1], &c__1, &c_b15, &rwork[*k + 1 + *nrhs], &
c__1);
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = j + jcol * bx_dim1;
i__4 = jcol + *k;
i__5 = jcol + *k + *nrhs;
q__1.r = rwork[i__4], q__1.i = rwork[i__5];
bx[i__3].r = q__1.r, bx[i__3].i = q__1.i;
/* L170: */
}
/* L180: */
}
}
/* Step (2R): if SQRE = 1, apply back the rotation that is */
/* related to the right null space of the subproblem. */
if (*sqre == 1) {
ccopy_(nrhs, &b[m + b_dim1], ldb, &bx[m + bx_dim1], ldbx);
csrot_(nrhs, &bx[bx_dim1 + 1], ldbx, &bx[m + bx_dim1], ldbx, c__,
s);
}
if (*k < f2cmax(m,n)) {
i__1 = n - *k;
clacpy_("A", &i__1, nrhs, &b[*k + 1 + b_dim1], ldb, &bx[*k + 1 +
bx_dim1], ldbx);
}
/* Step (3R): permute rows of B. */
ccopy_(nrhs, &bx[bx_dim1 + 1], ldbx, &b[nlp1 + b_dim1], ldb);
if (*sqre == 1) {
ccopy_(nrhs, &bx[m + bx_dim1], ldbx, &b[m + b_dim1], ldb);
}
i__1 = n;
for (i__ = 2; i__ <= i__1; ++i__) {
ccopy_(nrhs, &bx[i__ + bx_dim1], ldbx, &b[perm[i__] + b_dim1],
ldb);
/* L190: */
}
/* Step (4R): apply back the Givens rotations performed. */
for (i__ = *givptr; i__ >= 1; --i__) {
r__1 = -givnum[i__ + givnum_dim1];
csrot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, &
b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ +
(givnum_dim1 << 1)], &r__1);
/* L200: */
}
}
return;
/* End of CLALS0 */
} /* clals0_ */