OpenBLAS/lapack-netlib/SRC/sgetrf2.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 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);}
#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)}


/*  -- 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 real c_b13 = 1.f;
static real c_b16 = -1.f;

/* > \brief \b SGETRF2 */

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

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

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

/*        SUBROUTINE SGETRF2( M, N, A, LDA, IPIV, INFO ) */

/*       INTEGER            INFO, LDA, M, N */
/*       INTEGER            IPIV( * ) */
/*       REAL               A( LDA, * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGETRF2 computes an LU factorization of a general M-by-N matrix A */
/* > using partial pivoting with row interchanges. */
/* > */
/* > The factorization has the form */
/* >    A = P * L * U */
/* > where P is a permutation matrix, L is lower triangular with unit */
/* > diagonal elements (lower trapezoidal if m > n), and U is upper */
/* > triangular (upper trapezoidal if m < n). */
/* > */
/* > This is the recursive version of the algorithm. It divides */
/* > the matrix into four submatrices: */
/* > */
/* >        [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2 */
/* >    A = [ -----|----- ]  with n1 = f2cmin(m,n)/2 */
/* >        [  A21 | A22  ]       n2 = n-n1 */
/* > */
/* >                                       [ A11 ] */
/* > The subroutine calls itself to factor [ --- ], */
/* >                                       [ A12 ] */
/* >                 [ A12 ] */
/* > do the swaps on [ --- ], solve A12, update A22, */
/* >                 [ A22 ] */
/* > */
/* > then calls itself to factor A22 and do the swaps on A21. */
/* > */
/* > \endverbatim */

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

/* > \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,out] A */
/* > \verbatim */
/* >          A is REAL array, dimension (LDA,N) */
/* >          On entry, the M-by-N matrix to be factored. */
/* >          On exit, the factors L and U from the factorization */
/* >          A = P*L*U; the unit diagonal elements of L are not stored. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* >          LDA is INTEGER */
/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
/* > \endverbatim */
/* > */
/* > \param[out] IPIV */
/* > \verbatim */
/* >          IPIV is INTEGER array, dimension (f2cmin(M,N)) */
/* >          The pivot indices; for 1 <= i <= f2cmin(M,N), row i of the */
/* >          matrix was interchanged with row IPIV(i). */
/* > \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, U(i,i) is exactly zero. The factorization */
/* >                has been completed, but the factor U is exactly */
/* >                singular, and division by zero will occur if it is used */
/* >                to solve a system of equations. */
/* > \endverbatim */

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

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

/* > \date June 2016 */

/* > \ingroup realGEcomputational */

/*  ===================================================================== */
/* Subroutine */ void sgetrf2_(integer *m, integer *n, real *a, integer *lda, 
	integer *ipiv, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2;
    real r__1;

    /* Local variables */
    real temp;
    integer i__, iinfo;
    extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *), 
	    sgemm_(char *, char *, integer *, integer *, integer *, real *, 
	    real *, integer *, real *, integer *, real *, real *, integer *);
    real sfmin;
    integer n1, n2;
    extern /* Subroutine */ void strsm_(char *, char *, char *, char *, 
	    integer *, integer *, real *, real *, integer *, real *, integer *
	    );
    extern real slamch_(char *);
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    extern integer isamax_(integer *, real *, integer *);
    extern /* Subroutine */ int slaswp_(integer *, real *, integer *, integer 
	    *, integer *, integer *, integer *);


/*  -- LAPACK computational routine (version 3.7.1) -- */
/*  -- 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 */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --ipiv;

    /* Function Body */
    *info = 0;
    if (*m < 0) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*lda < f2cmax(1,*m)) {
	*info = -4;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SGETRF2", &i__1, (ftnlen)7);
	return;
    }

/*     Quick return if possible */

    if (*m == 0 || *n == 0) {
	return;
    }
    if (*m == 1) {

/*        Use unblocked code for one row case */
/*        Just need to handle IPIV and INFO */

	ipiv[1] = 1;
	if (a[a_dim1 + 1] == 0.f) {
	    *info = 1;
	}

    } else if (*n == 1) {

/*        Use unblocked code for one column case */


/*        Compute machine safe minimum */

	sfmin = slamch_("S");

/*        Find pivot and test for singularity */

	i__ = isamax_(m, &a[a_dim1 + 1], &c__1);
	ipiv[1] = i__;
	if (a[i__ + a_dim1] != 0.f) {

/*           Apply the interchange */

	    if (i__ != 1) {
		temp = a[a_dim1 + 1];
		a[a_dim1 + 1] = a[i__ + a_dim1];
		a[i__ + a_dim1] = temp;
	    }

/*           Compute elements 2:M of the column */

	    if ((r__1 = a[a_dim1 + 1], abs(r__1)) >= sfmin) {
		i__1 = *m - 1;
		r__1 = 1.f / a[a_dim1 + 1];
		sscal_(&i__1, &r__1, &a[a_dim1 + 2], &c__1);
	    } else {
		i__1 = *m - 1;
		for (i__ = 1; i__ <= i__1; ++i__) {
		    a[i__ + 1 + a_dim1] /= a[a_dim1 + 1];
/* L10: */
		}
	    }

	} else {
	    *info = 1;
	}

    } else {

/*        Use recursive code */

	n1 = f2cmin(*m,*n) / 2;
	n2 = *n - n1;

/*               [ A11 ] */
/*        Factor [ --- ] */
/*               [ A21 ] */

	sgetrf2_(m, &n1, &a[a_offset], lda, &ipiv[1], &iinfo);
	if (*info == 0 && iinfo > 0) {
	    *info = iinfo;
	}

/*                              [ A12 ] */
/*        Apply interchanges to [ --- ] */
/*                              [ A22 ] */

	slaswp_(&n2, &a[(n1 + 1) * a_dim1 + 1], lda, &c__1, &n1, &ipiv[1], &
		c__1);

/*        Solve A12 */

	strsm_("L", "L", "N", "U", &n1, &n2, &c_b13, &a[a_offset], lda, &a[(
		n1 + 1) * a_dim1 + 1], lda);

/*        Update A22 */

	i__1 = *m - n1;
	sgemm_("N", "N", &i__1, &n2, &n1, &c_b16, &a[n1 + 1 + a_dim1], lda, &
		a[(n1 + 1) * a_dim1 + 1], lda, &c_b13, &a[n1 + 1 + (n1 + 1) * 
		a_dim1], lda);

/*        Factor A22 */

	i__1 = *m - n1;
	sgetrf2_(&i__1, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &ipiv[n1 + 
		1], &iinfo);

/*        Adjust INFO and the pivot indices */

	if (*info == 0 && iinfo > 0) {
	    *info = iinfo + n1;
	}
	i__1 = f2cmin(*m,*n);
	for (i__ = n1 + 1; i__ <= i__1; ++i__) {
	    ipiv[i__] += n1;
/* L20: */
	}

/*        Apply interchanges to A21 */

	i__1 = n1 + 1;
	i__2 = f2cmin(*m,*n);
	slaswp_(&n1, &a[a_dim1 + 1], lda, &i__1, &i__2, &ipiv[1], &c__1);

    }
    return;

/*     End of SGETRF2 */

} /* sgetrf2_ */