floraachy
/
OpenBLAS
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity
OpenBLAS/lapack-netlib/SRC/DEPRECATED/cgeqpf.c

630 lines
17 KiB
C
Raw Permalink Blame History

#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 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);}
#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++ */
/* -- 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;
/* > \brief \b CGEQPF */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download CGEQPF + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeqpf.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeqpf.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeqpf.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE CGEQPF( M, N, A, LDA, JPVT, TAU, WORK, RWORK, INFO ) */
/* INTEGER INFO, LDA, M, N */
/* INTEGER JPVT( * ) */
/* REAL RWORK( * ) */
/* COMPLEX A( LDA, * ), TAU( * ), WORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > This routine is deprecated and has been replaced by routine CGEQP3. */
/* > */
/* > CGEQPF computes a QR factorization with column pivoting of a */
/* > complex M-by-N matrix A: A*P = Q*R. */
/* > \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 COMPLEX 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 triangular matrix R; the elements */
/* > below the diagonal, together with the array TAU, */
/* > represent the unitary 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(i) .ne. 0, the i-th column of A is permuted */
/* > to the front of A*P (a leading column); if JPVT(i) = 0, */
/* > the i-th column of A is a free column. */
/* > On exit, if JPVT(i) = k, then the i-th column of A*P */
/* > was the k-th column of A. */
/* > \endverbatim */
/* > */
/* > \param[out] TAU */
/* > \verbatim */
/* > TAU is COMPLEX array, dimension (f2cmin(M,N)) */
/* > The scalar factors of the elementary reflectors. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is COMPLEX array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] RWORK */
/* > \verbatim */
/* > RWORK is REAL array, dimension (2*N) */
/* > \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 complexGEcomputational */
/* > \par Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > The matrix Q is represented as a product of elementary reflectors */
/* > */
/* > Q = H(1) H(2) . . . H(n) */
/* > */
/* > Each H(i) has the form */
/* > */
/* > H = I - tau * v * v**H */
/* > */
/* > where tau is a complex scalar, and v is a 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). */
/* > */
/* > The matrix P is represented in jpvt as follows: If */
/* > jpvt(j) = i */
/* > then the jth column of P is the ith canonical unit vector. */
/* > */
/* > Partial column norm updating strategy modified by */
/* > Z. Drmac and Z. Bujanovic, Dept. of Mathematics, */
/* > University of Zagreb, Croatia. */
/* > -- April 2011 -- */
/* > For more details see LAPACK Working Note 176. */
/* > \endverbatim */
/* > */
/* ===================================================================== */
/* Subroutine */ void cgeqpf_(integer *m, integer *n, complex *a, integer *lda,
integer *jpvt, complex *tau, complex *work, real *rwork, integer *
info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
real r__1, r__2;
complex q__1;
/* Local variables */
real temp, temp2;
integer i__, j;
real tol3z;
extern /* Subroutine */ void clarf_(char *, integer *, integer *, complex *
, integer *, complex *, complex *, integer *, complex *),
cswap_(integer *, complex *, integer *, complex *, integer *);
integer itemp;
extern /* Subroutine */ void cgeqr2_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *);
extern real scnrm2_(integer *, complex *, integer *);
extern /* Subroutine */ void cunm2r_(char *, char *, integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *);
integer ma, mn;
extern /* Subroutine */ void clarfg_(integer *, complex *, complex *,
integer *, complex *);
extern real slamch_(char *);
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
extern integer isamax_(integer *, real *, integer *);
complex aii;
integer pvt;
/* -- 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 arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--jpvt;
--tau;
--work;
--rwork;
/* 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_("CGEQPF", &i__1, 6);
return;
}
mn = f2cmin(*m,*n);
tol3z = sqrt(slamch_("Epsilon"));
/* Move initial columns up front */
itemp = 1;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (jpvt[i__] != 0) {
if (i__ != itemp) {
cswap_(m, &a[i__ * a_dim1 + 1], &c__1, &a[itemp * a_dim1 + 1],
&c__1);
jpvt[i__] = jpvt[itemp];
jpvt[itemp] = i__;
} else {
jpvt[i__] = i__;
}
++itemp;
} else {
jpvt[i__] = i__;
}
/* L10: */
}
--itemp;
/* Compute the QR factorization and update remaining columns */
if (itemp > 0) {
ma = f2cmin(itemp,*m);
cgeqr2_(m, &ma, &a[a_offset], lda, &tau[1], &work[1], info);
if (ma < *n) {
i__1 = *n - ma;
cunm2r_("Left", "Conjugate transpose", m, &i__1, &ma, &a[a_offset]
, lda, &tau[1], &a[(ma + 1) * a_dim1 + 1], lda, &work[1],
info);
}
}
if (itemp < mn) {
/* Initialize partial column norms. The first n elements of */
/* work store the exact column norms. */
i__1 = *n;
for (i__ = itemp + 1; i__ <= i__1; ++i__) {
i__2 = *m - itemp;
rwork[i__] = scnrm2_(&i__2, &a[itemp + 1 + i__ * a_dim1], &c__1);
rwork[*n + i__] = rwork[i__];
/* L20: */
}
/* Compute factorization */
i__1 = mn;
for (i__ = itemp + 1; i__ <= i__1; ++i__) {
/* Determine ith pivot column and swap if necessary */
i__2 = *n - i__ + 1;
pvt = i__ - 1 + isamax_(&i__2, &rwork[i__], &c__1);
if (pvt != i__) {
cswap_(m, &a[pvt * a_dim1 + 1], &c__1, &a[i__ * a_dim1 + 1], &
c__1);
itemp = jpvt[pvt];
jpvt[pvt] = jpvt[i__];
jpvt[i__] = itemp;
rwork[pvt] = rwork[i__];
rwork[*n + pvt] = rwork[*n + i__];
}
/* Generate elementary reflector H(i) */
i__2 = i__ + i__ * a_dim1;
aii.r = a[i__2].r, aii.i = a[i__2].i;
i__2 = *m - i__ + 1;
/* Computing MIN */
i__3 = i__ + 1;
clarfg_(&i__2, &aii, &a[f2cmin(i__3,*m) + i__ * a_dim1], &c__1, &tau[
i__]);
i__2 = i__ + i__ * a_dim1;
a[i__2].r = aii.r, a[i__2].i = aii.i;
if (i__ < *n) {
/* Apply H(i) to A(i:m,i+1:n) from the left */
i__2 = i__ + i__ * a_dim1;
aii.r = a[i__2].r, aii.i = a[i__2].i;
i__2 = i__ + i__ * a_dim1;
a[i__2].r = 1.f, a[i__2].i = 0.f;
i__2 = *m - i__ + 1;
i__3 = *n - i__;
r_cnjg(&q__1, &tau[i__]);
clarf_("Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &
q__1, &a[i__ + (i__ + 1) * a_dim1], lda, &work[1]);
i__2 = i__ + i__ * a_dim1;
a[i__2].r = aii.r, a[i__2].i = aii.i;
}
/* Update partial column norms */
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
if (rwork[j] != 0.f) {
/* NOTE: The following 4 lines follow from the analysis in */
/* Lapack Working Note 176. */
temp = c_abs(&a[i__ + j * a_dim1]) / rwork[j];
/* Computing MAX */
r__1 = 0.f, r__2 = (temp + 1.f) * (1.f - temp);
temp = f2cmax(r__1,r__2);
/* Computing 2nd power */
r__1 = rwork[j] / rwork[*n + j];
temp2 = temp * (r__1 * r__1);
if (temp2 <= tol3z) {
if (*m - i__ > 0) {
i__3 = *m - i__;
rwork[j] = scnrm2_(&i__3, &a[i__ + 1 + j * a_dim1]
, &c__1);
rwork[*n + j] = rwork[j];
} else {
rwork[j] = 0.f;
rwork[*n + j] = 0.f;
}
} else {
rwork[j] *= sqrt(temp);
}
}
/* L30: */
}
/* L40: */
}
}
return;
/* End of CGEQPF */
} /* cgeqpf_ */
Reference in New Issue View Git Blame Copy Permalink