OpenBLAS/lapack-netlib/SRC/sgelst.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]/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++ */


#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_n1 = -1;
static real c_b12 = 0.f;
static integer c__2 = 2;
static integer c__0 = 0;

/* > \brief <b> SGELST solves overdetermined or underdetermined systems for GE matrices using QR or LQ factori
zation with compact WY representation of Q.</b> */

/*  =========== DOCUMENTATION =========== */

/* Online html documentation available at */
/*            http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */
/* > Download SGELST + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgelst.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgelst.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgelst.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

/*  Definition: */
/*  =========== */

/*       SUBROUTINE SGELST( TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK, */
/*                          INFO ) */

/*       CHARACTER          TRANS */
/*       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS */
/*       REAL               A( LDA, * ), B( LDB, * ), WORK( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGELST solves overdetermined or underdetermined real linear systems */
/* > involving an M-by-N matrix A, or its transpose, using a QR or LQ */
/* > factorization of A with compact WY representation of Q. */
/* > It is assumed that A has full rank. */
/* > */
/* > The following options are provided: */
/* > */
/* > 1. If TRANS = 'N' and m >= n:  find the least squares solution of */
/* >    an overdetermined system, i.e., solve the least squares problem */
/* >                 minimize || B - A*X ||. */
/* > */
/* > 2. If TRANS = 'N' and m < n:  find the minimum norm solution of */
/* >    an underdetermined system A * X = B. */
/* > */
/* > 3. If TRANS = 'T' and m >= n:  find the minimum norm solution of */
/* >    an underdetermined system A**T * X = B. */
/* > */
/* > 4. If TRANS = 'T' and m < n:  find the least squares solution of */
/* >    an overdetermined system, i.e., solve the least squares problem */
/* >                 minimize || B - A**T * X ||. */
/* > */
/* > Several right hand side vectors b and solution vectors x can be */
/* > handled in a single call; they are stored as the columns of the */
/* > M-by-NRHS right hand side matrix B and the N-by-NRHS solution */
/* > matrix X. */
/* > \endverbatim */

/*  Arguments: */
/*  ========== */

/* > \param[in] TRANS */
/* > \verbatim */
/* >          TRANS is CHARACTER*1 */
/* >          = 'N': the linear system involves A; */
/* >          = 'T': the linear system involves A**T. */
/* > \endverbatim */
/* > */
/* > \param[in] M */
/* > \verbatim */
/* >          M is INTEGER */
/* >          The number of rows of the matrix A.  M >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The number of columns of the matrix A.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] NRHS */
/* > \verbatim */
/* >          NRHS is INTEGER */
/* >          The number of right hand sides, i.e., the number of */
/* >          columns of the matrices B and X. NRHS >=0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* >          A is REAL array, dimension (LDA,N) */
/* >          On entry, the M-by-N matrix A. */
/* >          On exit, */
/* >            if M >= N, A is overwritten by details of its QR */
/* >                       factorization as returned by SGEQRT; */
/* >            if M <  N, A is overwritten by details of its LQ */
/* >                       factorization as returned by SGELQT. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* >          LDA is INTEGER */
/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
/* > \endverbatim */
/* > */
/* > \param[in,out] B */
/* > \verbatim */
/* >          B is REAL array, dimension (LDB,NRHS) */
/* >          On entry, the matrix B of right hand side vectors, stored */
/* >          columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS */
/* >          if TRANS = 'T'. */
/* >          On exit, if INFO = 0, B is overwritten by the solution */
/* >          vectors, stored columnwise: */
/* >          if TRANS = 'N' and m >= n, rows 1 to n of B contain the least */
/* >          squares solution vectors; the residual sum of squares for the */
/* >          solution in each column is given by the sum of squares of */
/* >          elements N+1 to M in that column; */
/* >          if TRANS = 'N' and m < n, rows 1 to N of B contain the */
/* >          minimum norm solution vectors; */
/* >          if TRANS = 'T' and m >= n, rows 1 to M of B contain the */
/* >          minimum norm solution vectors; */
/* >          if TRANS = 'T' and m < n, rows 1 to M of B contain the */
/* >          least squares solution vectors; the residual sum of squares */
/* >          for the solution in each column is given by the sum of */
/* >          squares of elements M+1 to N in that column. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* >          LDB is INTEGER */
/* >          The leading dimension of the array B. LDB >= MAX(1,M,N). */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is REAL array, dimension (MAX(1,LWORK)) */
/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* >          LWORK is INTEGER */
/* >          The dimension of the array WORK. */
/* >          LWORK >= f2cmax( 1, MN + f2cmax( MN, NRHS ) ). */
/* >          For optimal performance, */
/* >          LWORK >= f2cmax( 1, (MN + f2cmax( MN, NRHS ))*NB ). */
/* >          where MN = f2cmin(M,N) and NB is the optimum block size. */
/* > */
/* >          If LWORK = -1, then a workspace query is assumed; the routine */
/* >          only calculates the optimal size of the WORK array, returns */
/* >          this value as the first entry of the WORK array, and no error */
/* >          message related to LWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* >          INFO is INTEGER */
/* >          = 0:  successful exit */
/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
/* >          > 0:  if INFO =  i, the i-th diagonal element of the */
/* >                triangular factor of A is zero, so that A does not have */
/* >                full rank; the least squares solution could not be */
/* >                computed. */
/* > \endverbatim */

/*  Authors: */
/*  ======== */

/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */

/* > \ingroup realGEsolve */

/* > \par Contributors: */
/*  ================== */
/* > */
/* > \verbatim */
/* > */
/* >  November 2022,  Igor Kozachenko, */
/* >                  Computer Science Division, */
/* >                  University of California, Berkeley */
/* > \endverbatim */

/*  ===================================================================== */
/* Subroutine */ void sgelst_(char *trans, integer *m, integer *n, integer *
	nrhs, real *a, integer *lda, real *b, integer *ldb, real *work, 
	integer *lwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;

    /* Local variables */
    real anrm, bnrm;
    integer brow;
    logical tpsd;
    integer i__, j, iascl, ibscl;
    extern logical lsame_(char *, char *);
    integer nbmin;
    real rwork[1];
    integer lwopt, nb;
    extern /* Subroutine */ void slabad_(real *, real *);
    integer mn;
    extern real slamch_(char *), slange_(char *, integer *, integer *,
	     real *, integer *, real *);
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    integer scllen;
    real bignum;
    extern /* Subroutine */ void slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *), slaset_(char *, integer *, integer *, real *, real *, 
	    real *, integer *), sgelqt_(integer *, integer *, integer 
	    *, real *, integer *, real *, integer *, real *, integer *);
    integer mnnrhs;
    extern /* Subroutine */ void sgeqrt_(integer *, integer *, integer *, real 
	    *, integer *, real *, integer *, real *, integer *);
    real smlnum;
    logical lquery;
    extern /* Subroutine */ void strtrs_(char *, char *, char *, integer *, 
	    integer *, real *, integer *, real *, integer *, integer *);
    extern void sgemlqt_(char *, char *, integer *, 
	    integer *, integer *, integer *, real *, integer *, real *, 
	    integer *, real *, integer *, real *, integer *), 
	    sgemqrt_(char *, char *, integer *, integer *, integer *, integer 
	    *, real *, integer *, real *, integer *, real *, integer *, real *
	    , integer *);


/*  -- LAPACK driver routine -- */
/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */


/*  ===================================================================== */


/*     Test the input arguments. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    --work;

    /* Function Body */
    *info = 0;
    mn = f2cmin(*m,*n);
    lquery = *lwork == -1;
    if (! (lsame_(trans, "N") || lsame_(trans, "T"))) {
	*info = -1;
    } else if (*m < 0) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*nrhs < 0) {
	*info = -4;
    } else if (*lda < f2cmax(1,*m)) {
	*info = -6;
    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__1 = f2cmax(1,*m);
	if (*ldb < f2cmax(i__1,*n)) {
	    *info = -8;
	} else /* if(complicated condition) */ {
/* Computing MAX */
	    i__1 = 1, i__2 = mn + f2cmax(mn,*nrhs);
	    if (*lwork < f2cmax(i__1,i__2) && ! lquery) {
		*info = -10;
	    }
	}
    }

/*     Figure out optimal block size and optimal workspace size */

    if (*info == 0 || *info == -10) {

	tpsd = TRUE_;
	if (lsame_(trans, "N")) {
	    tpsd = FALSE_;
	}

	nb = ilaenv_(&c__1, "SGELST", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (
		ftnlen)1);

	mnnrhs = f2cmax(mn,*nrhs);
/* Computing MAX */
	i__1 = 1, i__2 = (mn + mnnrhs) * nb;
	lwopt = f2cmax(i__1,i__2);
	work[1] = (real) lwopt;

    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SGELST ", &i__1, 6);
	return;
    } else if (lquery) {
	return;
    }

/*     Quick return if possible */

/* Computing MIN */
    i__1 = f2cmin(*m,*n);
    if (f2cmin(i__1,*nrhs) == 0) {
	i__1 = f2cmax(*m,*n);
	slaset_("Full", &i__1, nrhs, &c_b12, &c_b12, &b[b_offset], ldb);
	work[1] = (real) lwopt;
	return;
    }

/*     *GEQRT and *GELQT routines cannot accept NB larger than f2cmin(M,N) */

    if (nb > mn) {
	nb = mn;
    }

/*     Determine the block size from the supplied LWORK */
/*     ( at this stage we know that LWORK >= (minimum required workspace, */
/*     but it may be less than optimal) */

/* Computing MIN */
    i__1 = nb, i__2 = *lwork / (mn + mnnrhs);
    nb = f2cmin(i__1,i__2);

/*     The minimum value of NB, when blocked code is used */

/* Computing MAX */
    i__1 = 2, i__2 = ilaenv_(&c__2, "SGELST", " ", m, n, &c_n1, &c_n1, (
	    ftnlen)6, (ftnlen)1);
    nbmin = f2cmax(i__1,i__2);

    if (nb < nbmin) {
	nb = 1;
    }

/*     Get machine parameters */

    smlnum = slamch_("S") / slamch_("P");
    bignum = 1.f / smlnum;
    slabad_(&smlnum, &bignum);

/*     Scale A, B if f2cmax element outside range [SMLNUM,BIGNUM] */

    anrm = slange_("M", m, n, &a[a_offset], lda, rwork);
    iascl = 0;
    if (anrm > 0.f && anrm < smlnum) {

/*        Scale matrix norm up to SMLNUM */

	slascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, 
		info);
	iascl = 1;
    } else if (anrm > bignum) {

/*        Scale matrix norm down to BIGNUM */

	slascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, 
		info);
	iascl = 2;
    } else if (anrm == 0.f) {

/*        Matrix all zero. Return zero solution. */

	i__1 = f2cmax(*m,*n);
	slaset_("Full", &i__1, nrhs, &c_b12, &c_b12, &b[b_offset], ldb);
	work[1] = (real) lwopt;
	return;
    }

    brow = *m;
    if (tpsd) {
	brow = *n;
    }
    bnrm = slange_("M", &brow, nrhs, &b[b_offset], ldb, rwork);
    ibscl = 0;
    if (bnrm > 0.f && bnrm < smlnum) {

/*        Scale matrix norm up to SMLNUM */

	slascl_("G", &c__0, &c__0, &bnrm, &smlnum, &brow, nrhs, &b[b_offset], 
		ldb, info);
	ibscl = 1;
    } else if (bnrm > bignum) {

/*        Scale matrix norm down to BIGNUM */

	slascl_("G", &c__0, &c__0, &bnrm, &bignum, &brow, nrhs, &b[b_offset], 
		ldb, info);
	ibscl = 2;
    }

    if (*m >= *n) {

/*        M > N: */
/*        Compute the blocked QR factorization of A, */
/*        using the compact WY representation of Q, */
/*        workspace at least N, optimally N*NB. */

	sgeqrt_(m, n, &nb, &a[a_offset], lda, &work[1], &nb, &work[mn * nb + 
		1], info);

	if (! tpsd) {

/*           M > N, A is not transposed: */
/*           Overdetermined system of equations, */
/*           least-squares problem, f2cmin || A * X - B ||. */

/*           Compute B(1:M,1:NRHS) := Q**T * B(1:M,1:NRHS), */
/*           using the compact WY representation of Q, */
/*           workspace at least NRHS, optimally NRHS*NB. */

	    sgemqrt_("Left", "Transpose", m, nrhs, n, &nb, &a[a_offset], lda, 
		    &work[1], &nb, &b[b_offset], ldb, &work[mn * nb + 1], 
		    info);

/*           Compute B(1:N,1:NRHS) := inv(R) * B(1:N,1:NRHS) */

	    strtrs_("Upper", "No transpose", "Non-unit", n, nrhs, &a[a_offset]
		    , lda, &b[b_offset], ldb, info);

	    if (*info > 0) {
		return;
	    }

	    scllen = *n;

	} else {

/*           M > N, A is transposed: */
/*           Underdetermined system of equations, */
/*           minimum norm solution of A**T * X = B. */

/*           Compute B := inv(R**T) * B in two row blocks of B. */

/*           Block 1: B(1:N,1:NRHS) := inv(R**T) * B(1:N,1:NRHS) */

	    strtrs_("Upper", "Transpose", "Non-unit", n, nrhs, &a[a_offset], 
		    lda, &b[b_offset], ldb, info);

	    if (*info > 0) {
		return;
	    }

/*           Block 2: Zero out all rows below the N-th row in B: */
/*           B(N+1:M,1:NRHS) = ZERO */

	    i__1 = *nrhs;
	    for (j = 1; j <= i__1; ++j) {
		i__2 = *m;
		for (i__ = *n + 1; i__ <= i__2; ++i__) {
		    b[i__ + j * b_dim1] = 0.f;
		}
	    }

/*           Compute B(1:M,1:NRHS) := Q(1:N,:) * B(1:N,1:NRHS), */
/*           using the compact WY representation of Q, */
/*           workspace at least NRHS, optimally NRHS*NB. */

	    sgemqrt_("Left", "No transpose", m, nrhs, n, &nb, &a[a_offset], 
		    lda, &work[1], &nb, &b[b_offset], ldb, &work[mn * nb + 1],
		     info);

	    scllen = *m;

	}

    } else {

/*        M < N: */
/*        Compute the blocked LQ factorization of A, */
/*        using the compact WY representation of Q, */
/*        workspace at least M, optimally M*NB. */

	sgelqt_(m, n, &nb, &a[a_offset], lda, &work[1], &nb, &work[mn * nb + 
		1], info);

	if (! tpsd) {

/*           M < N, A is not transposed: */
/*           Underdetermined system of equations, */
/*           minimum norm solution of A * X = B. */

/*           Compute B := inv(L) * B in two row blocks of B. */

/*           Block 1: B(1:M,1:NRHS) := inv(L) * B(1:M,1:NRHS) */

	    strtrs_("Lower", "No transpose", "Non-unit", m, nrhs, &a[a_offset]
		    , lda, &b[b_offset], ldb, info);

	    if (*info > 0) {
		return;
	    }

/*           Block 2: Zero out all rows below the M-th row in B: */
/*           B(M+1:N,1:NRHS) = ZERO */

	    i__1 = *nrhs;
	    for (j = 1; j <= i__1; ++j) {
		i__2 = *n;
		for (i__ = *m + 1; i__ <= i__2; ++i__) {
		    b[i__ + j * b_dim1] = 0.f;
		}
	    }

/*           Compute B(1:N,1:NRHS) := Q(1:N,:)**T * B(1:M,1:NRHS), */
/*           using the compact WY representation of Q, */
/*           workspace at least NRHS, optimally NRHS*NB. */

	    sgemlqt_("Left", "Transpose", n, nrhs, m, &nb, &a[a_offset], lda, 
		    &work[1], &nb, &b[b_offset], ldb, &work[mn * nb + 1], 
		    info);

	    scllen = *n;

	} else {

/*           M < N, A is transposed: */
/*           Overdetermined system of equations, */
/*           least-squares problem, f2cmin || A**T * X - B ||. */

/*           Compute B(1:N,1:NRHS) := Q * B(1:N,1:NRHS), */
/*           using the compact WY representation of Q, */
/*           workspace at least NRHS, optimally NRHS*NB. */

	    sgemlqt_("Left", "No transpose", n, nrhs, m, &nb, &a[a_offset], 
		    lda, &work[1], &nb, &b[b_offset], ldb, &work[mn * nb + 1],
		     info);

/*           Compute B(1:M,1:NRHS) := inv(L**T) * B(1:M,1:NRHS) */

	    strtrs_("Lower", "Transpose", "Non-unit", m, nrhs, &a[a_offset], 
		    lda, &b[b_offset], ldb, info);

	    if (*info > 0) {
		return;
	    }

	    scllen = *m;

	}

    }

/*     Undo scaling */

    if (iascl == 1) {
	slascl_("G", &c__0, &c__0, &anrm, &smlnum, &scllen, nrhs, &b[b_offset]
		, ldb, info);
    } else if (iascl == 2) {
	slascl_("G", &c__0, &c__0, &anrm, &bignum, &scllen, nrhs, &b[b_offset]
		, ldb, info);
    }
    if (ibscl == 1) {
	slascl_("G", &c__0, &c__0, &smlnum, &bnrm, &scllen, nrhs, &b[b_offset]
		, ldb, info);
    } else if (ibscl == 2) {
	slascl_("G", &c__0, &c__0, &bignum, &bnrm, &scllen, nrhs, &b[b_offset]
		, ldb, info);
    }

    work[1] = (real) lwopt;

    return;

/*     End of SGELST */

} /* sgelst_ */