OpenBLAS/lapack-netlib/SRC/sgeqp3.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 integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;

/* > \brief \b SGEQP3 */

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

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

/* > \htmlonly */
/* > Download SGEQP3 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgeqp3.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgeqp3.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgeqp3.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

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

/*       SUBROUTINE SGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO ) */

/*       INTEGER            INFO, LDA, LWORK, M, N */
/*       INTEGER            JPVT( * ) */
/*       REAL               A( LDA, * ), TAU( * ), WORK( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGEQP3 computes a QR factorization with column pivoting of a */
/* > matrix A:  A*P = Q*R  using Level 3 BLAS. */
/* > \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 A. */
/* >          On exit, the upper triangle of the array contains the */
/* >          f2cmin(M,N)-by-N upper trapezoidal matrix R; the elements below */
/* >          the diagonal, together with the array TAU, represent the */
/* >          orthogonal matrix Q as a product of f2cmin(M,N) elementary */
/* >          reflectors. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* >          LDA is INTEGER */
/* >          The leading dimension of the array A. LDA >= f2cmax(1,M). */
/* > \endverbatim */
/* > */
/* > \param[in,out] JPVT */
/* > \verbatim */
/* >          JPVT is INTEGER array, dimension (N) */
/* >          On entry, if JPVT(J).ne.0, the J-th column of A is permuted */
/* >          to the front of A*P (a leading column); if JPVT(J)=0, */
/* >          the J-th column of A is a free column. */
/* >          On exit, if JPVT(J)=K, then the J-th column of A*P was the */
/* >          the K-th column of A. */
/* > \endverbatim */
/* > */
/* > \param[out] TAU */
/* > \verbatim */
/* >          TAU is REAL array, dimension (f2cmin(M,N)) */
/* >          The scalar factors of the elementary reflectors. */
/* > \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 >= 3*N+1. */
/* >          For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB */
/* >          is the optimal blocksize. */
/* > */
/* >          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. */
/* > \endverbatim */

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

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

/* > \date December 2016 */

/* > \ingroup realGEcomputational */

/* > \par Further Details: */
/*  ===================== */
/* > */
/* > \verbatim */
/* > */
/* >  The matrix Q is represented as a product of elementary reflectors */
/* > */
/* >     Q = H(1) H(2) . . . H(k), where k = f2cmin(m,n). */
/* > */
/* >  Each H(i) has the form */
/* > */
/* >     H(i) = I - tau * v * v**T */
/* > */
/* >  where tau is a real scalar, and v is a real/complex vector */
/* >  with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in */
/* >  A(i+1:m,i), and tau in TAU(i). */
/* > \endverbatim */

/* > \par Contributors: */
/*  ================== */
/* > */
/* >    G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain */
/* >    X. Sun, Computer Science Dept., Duke University, USA */
/* > */
/*  ===================================================================== */
/* Subroutine */ void sgeqp3_(integer *m, integer *n, real *a, integer *lda, 
	integer *jpvt, real *tau, real *work, integer *lwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;

    /* Local variables */
    integer nfxd;
    extern real snrm2_(integer *, real *, integer *);
    integer j, nbmin, minmn, minws;
    extern /* Subroutine */ void sswap_(integer *, real *, integer *, real *, 
	    integer *), slaqp2_(integer *, integer *, integer *, real *, 
	    integer *, integer *, real *, real *, real *, real *);
    integer jb, na, nb, sm, sn, nx;
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    extern /* Subroutine */ void sgeqrf_(integer *, integer *, real *, integer 
	    *, real *, real *, integer *, integer *);
    integer topbmn, sminmn;
    extern /* Subroutine */ void slaqps_(integer *, integer *, integer *, 
	    integer *, integer *, real *, integer *, integer *, real *, real *
	    , real *, real *, real *, integer *);
    integer lwkopt;
    logical lquery;
    extern /* Subroutine */ void sormqr_(char *, char *, integer *, integer *, 
	    integer *, real *, integer *, real *, real *, integer *, real *, 
	    integer *, integer *);
    integer fjb, iws;


/*  -- 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 input arguments */
/*  ==================== */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --jpvt;
    --tau;
    --work;

    /* Function Body */
    *info = 0;
    lquery = *lwork == -1;
    if (*m < 0) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*lda < f2cmax(1,*m)) {
	*info = -4;
    }

    if (*info == 0) {
	minmn = f2cmin(*m,*n);
	if (minmn == 0) {
	    iws = 1;
	    lwkopt = 1;
	} else {
	    iws = *n * 3 + 1;
	    nb = ilaenv_(&c__1, "SGEQRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, 
		    (ftnlen)1);
	    lwkopt = (*n << 1) + (*n + 1) * nb;
	}
	work[1] = (real) lwkopt;

	if (*lwork < iws && ! lquery) {
	    *info = -8;
	}
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SGEQP3", &i__1, (ftnlen)6);
	return;
    } else if (lquery) {
	return;
    }

/*     Move initial columns up front. */

    nfxd = 1;
    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
	if (jpvt[j] != 0) {
	    if (j != nfxd) {
		sswap_(m, &a[j * a_dim1 + 1], &c__1, &a[nfxd * a_dim1 + 1], &
			c__1);
		jpvt[j] = jpvt[nfxd];
		jpvt[nfxd] = j;
	    } else {
		jpvt[j] = j;
	    }
	    ++nfxd;
	} else {
	    jpvt[j] = j;
	}
/* L10: */
    }
    --nfxd;

/*     Factorize fixed columns */
/*  ======================= */

/*     Compute the QR factorization of fixed columns and update */
/*     remaining columns. */

    if (nfxd > 0) {
	na = f2cmin(*m,nfxd);
/* CC      CALL SGEQR2( M, NA, A, LDA, TAU, WORK, INFO ) */
	sgeqrf_(m, &na, &a[a_offset], lda, &tau[1], &work[1], lwork, info);
/* Computing MAX */
	i__1 = iws, i__2 = (integer) work[1];
	iws = f2cmax(i__1,i__2);
	if (na < *n) {
/* CC         CALL SORM2R( 'Left', 'Transpose', M, N-NA, NA, A, LDA, */
/* CC  $                   TAU, A( 1, NA+1 ), LDA, WORK, INFO ) */
	    i__1 = *n - na;
	    sormqr_("Left", "Transpose", m, &i__1, &na, &a[a_offset], lda, &
		    tau[1], &a[(na + 1) * a_dim1 + 1], lda, &work[1], lwork, 
		    info);
/* Computing MAX */
	    i__1 = iws, i__2 = (integer) work[1];
	    iws = f2cmax(i__1,i__2);
	}
    }

/*     Factorize free columns */
/*  ====================== */

    if (nfxd < minmn) {

	sm = *m - nfxd;
	sn = *n - nfxd;
	sminmn = minmn - nfxd;

/*        Determine the block size. */

	nb = ilaenv_(&c__1, "SGEQRF", " ", &sm, &sn, &c_n1, &c_n1, (ftnlen)6, 
		(ftnlen)1);
	nbmin = 2;
	nx = 0;

	if (nb > 1 && nb < sminmn) {

/*           Determine when to cross over from blocked to unblocked code. */

/* Computing MAX */
	    i__1 = 0, i__2 = ilaenv_(&c__3, "SGEQRF", " ", &sm, &sn, &c_n1, &
		    c_n1, (ftnlen)6, (ftnlen)1);
	    nx = f2cmax(i__1,i__2);


	    if (nx < sminmn) {

/*              Determine if workspace is large enough for blocked code. */

		minws = (sn << 1) + (sn + 1) * nb;
		iws = f2cmax(iws,minws);
		if (*lwork < minws) {

/*                 Not enough workspace to use optimal NB: Reduce NB and */
/*                 determine the minimum value of NB. */

		    nb = (*lwork - (sn << 1)) / (sn + 1);
/* Computing MAX */
		    i__1 = 2, i__2 = ilaenv_(&c__2, "SGEQRF", " ", &sm, &sn, &
			    c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
		    nbmin = f2cmax(i__1,i__2);


		}
	    }
	}

/*        Initialize partial column norms. The first N elements of work */
/*        store the exact column norms. */

	i__1 = *n;
	for (j = nfxd + 1; j <= i__1; ++j) {
	    work[j] = snrm2_(&sm, &a[nfxd + 1 + j * a_dim1], &c__1);
	    work[*n + j] = work[j];
/* L20: */
	}

	if (nb >= nbmin && nb < sminmn && nx < sminmn) {

/*           Use blocked code initially. */

	    j = nfxd + 1;

/*           Compute factorization: while loop. */


	    topbmn = minmn - nx;
L30:
	    if (j <= topbmn) {
/* Computing MIN */
		i__1 = nb, i__2 = topbmn - j + 1;
		jb = f2cmin(i__1,i__2);

/*              Factorize JB columns among columns J:N. */

		i__1 = *n - j + 1;
		i__2 = j - 1;
		i__3 = *n - j + 1;
		slaqps_(m, &i__1, &i__2, &jb, &fjb, &a[j * a_dim1 + 1], lda, &
			jpvt[j], &tau[j], &work[j], &work[*n + j], &work[(*n 
			<< 1) + 1], &work[(*n << 1) + jb + 1], &i__3);

		j += fjb;
		goto L30;
	    }
	} else {
	    j = nfxd + 1;
	}

/*        Use unblocked code to factor the last or only block. */


	if (j <= minmn) {
	    i__1 = *n - j + 1;
	    i__2 = j - 1;
	    slaqp2_(m, &i__1, &i__2, &a[j * a_dim1 + 1], lda, &jpvt[j], &tau[
		    j], &work[j], &work[*n + j], &work[(*n << 1) + 1]);
	}

    }

    work[1] = (real) iws;
    return;

/*     End of SGEQP3 */

} /* sgeqp3_ */