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OpenBLAS/lapack-netlib/SRC/sgeqp3.c

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#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <complex.h>
#ifdef complex
#undef complex
#endif
#ifdef I
#undef I
#endif
#if defined(_WIN64)
typedef long long BLASLONG;
typedef unsigned long long BLASULONG;
#else
typedef long BLASLONG;
typedef unsigned long BLASULONG;
#endif
#ifdef LAPACK_ILP64
typedef BLASLONG blasint;
#if defined(_WIN64)
#define blasabs(x) llabs(x)
#else
#define blasabs(x) labs(x)
#endif
#else
typedef int blasint;
#define blasabs(x) abs(x)
#endif
typedef blasint integer;
typedef unsigned int uinteger;
typedef char *address;
typedef short int shortint;
typedef float real;
typedef double doublereal;
typedef struct { real r, i; } complex;
typedef struct { doublereal r, i; } doublecomplex;
#ifdef _MSC_VER
static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
#else
static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
#endif
#define pCf(z) (*_pCf(z))
#define pCd(z) (*_pCd(z))
typedef blasint logical;
typedef char logical1;
typedef char integer1;
#define TRUE_ (1)
#define FALSE_ (0)
/* Extern is for use with -E */
#ifndef Extern
#define Extern extern
#endif
/* I/O stuff */
typedef int flag;
typedef int ftnlen;
typedef int ftnint;
/*external read, write*/
typedef struct
{ flag cierr;
ftnint ciunit;
flag ciend;
char *cifmt;
ftnint cirec;
} cilist;
/*internal read, write*/
typedef struct
{ flag icierr;
char *iciunit;
flag iciend;
char *icifmt;
ftnint icirlen;
ftnint icirnum;
} icilist;
/*open*/
typedef struct
{ flag oerr;
ftnint ounit;
char *ofnm;
ftnlen ofnmlen;
char *osta;
char *oacc;
char *ofm;
ftnint orl;
char *oblnk;
} olist;
/*close*/
typedef struct
{ flag cerr;
ftnint cunit;
char *csta;
} cllist;
/*rewind, backspace, endfile*/
typedef struct
{ flag aerr;
ftnint aunit;
} alist;
/* inquire */
typedef struct
{ flag inerr;
ftnint inunit;
char *infile;
ftnlen infilen;
ftnint *inex; /*parameters in standard's order*/
ftnint *inopen;
ftnint *innum;
ftnint *innamed;
char *inname;
ftnlen innamlen;
char *inacc;
ftnlen inacclen;
char *inseq;
ftnlen inseqlen;
char *indir;
ftnlen indirlen;
char *infmt;
ftnlen infmtlen;
char *inform;
ftnint informlen;
char *inunf;
ftnlen inunflen;
ftnint *inrecl;
ftnint *innrec;
char *inblank;
ftnlen inblanklen;
} inlist;
#define VOID void
union Multitype { /* for multiple entry points */
integer1 g;
shortint h;
integer i;
/* longint j; */
real r;
doublereal d;
complex c;
doublecomplex z;
};
typedef union Multitype Multitype;
struct Vardesc { /* for Namelist */
char *name;
char *addr;
ftnlen *dims;
int type;
};
typedef struct Vardesc Vardesc;
struct Namelist {
char *name;
Vardesc **vars;
int nvars;
};
typedef struct Namelist Namelist;
#define abs(x) ((x) >= 0 ? (x) : -(x))
#define dabs(x) (fabs(x))
#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
#define dmin(a,b) (f2cmin(a,b))
#define dmax(a,b) (f2cmax(a,b))
#define bit_test(a,b) ((a) >> (b) & 1)
#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
#define abort_() { sig_die("Fortran abort routine called", 1); }
#define c_abs(z) (cabsf(Cf(z)))
#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
#ifdef _MSC_VER
#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
#else
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#endif
#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
#define d_abs(x) (fabs(*(x)))
#define d_acos(x) (acos(*(x)))
#define d_asin(x) (asin(*(x)))
#define d_atan(x) (atan(*(x)))
#define d_atn2(x, y) (atan2(*(x),*(y)))
#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
#define d_cos(x) (cos(*(x)))
#define d_cosh(x) (cosh(*(x)))
#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
#define d_exp(x) (exp(*(x)))
#define d_imag(z) (cimag(Cd(z)))
#define r_imag(z) (cimagf(Cf(z)))
#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define d_log(x) (log(*(x)))
#define d_mod(x, y) (fmod(*(x), *(y)))
#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
#define d_nint(x) u_nint(*(x))
#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
#define d_sign(a,b) u_sign(*(a),*(b))
#define r_sign(a,b) u_sign(*(a),*(b))
#define d_sin(x) (sin(*(x)))
#define d_sinh(x) (sinh(*(x)))
#define d_sqrt(x) (sqrt(*(x)))
#define d_tan(x) (tan(*(x)))
#define d_tanh(x) (tanh(*(x)))
#define i_abs(x) abs(*(x))
#define i_dnnt(x) ((integer)u_nint(*(x)))
#define i_len(s, n) (n)
#define i_nint(x) ((integer)u_nint(*(x)))
#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
#define 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_ */
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