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OpenBLAS/lapack-netlib/SRC/DEPRECATED/cgelsx.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 int logical;
typedef short int shortlogical;
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 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++ */
#define F2C_proc_par_types 1
/* -- 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 complex c_b1 = {0.f,0.f};
static complex c_b2 = {1.f,0.f};
static integer c__0 = 0;
static integer c__2 = 2;
static integer c__1 = 1;
/* > \brief <b> CGELSX solves overdetermined or underdetermined systems for GE matrices</b> */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download CGELSX + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgelsx.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgelsx.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgelsx.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE CGELSX( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, */
/* WORK, RWORK, INFO ) */
/* INTEGER INFO, LDA, LDB, M, N, NRHS, RANK */
/* REAL RCOND */
/* INTEGER JPVT( * ) */
/* REAL RWORK( * ) */
/* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > This routine is deprecated and has been replaced by routine CGELSY. */
/* > */
/* > CGELSX computes the minimum-norm solution to a complex linear least */
/* > squares problem: */
/* > minimize || A * X - B || */
/* > using a complete orthogonal factorization of A. A is an M-by-N */
/* > matrix which may be rank-deficient. */
/* > */
/* > 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. */
/* > */
/* > The routine first computes a QR factorization with column pivoting: */
/* > A * P = Q * [ R11 R12 ] */
/* > [ 0 R22 ] */
/* > with R11 defined as the largest leading submatrix whose estimated */
/* > condition number is less than 1/RCOND. The order of R11, RANK, */
/* > is the effective rank of A. */
/* > */
/* > Then, R22 is considered to be negligible, and R12 is annihilated */
/* > by unitary transformations from the right, arriving at the */
/* > complete orthogonal factorization: */
/* > A * P = Q * [ T11 0 ] * Z */
/* > [ 0 0 ] */
/* > The minimum-norm solution is then */
/* > X = P * Z**H [ inv(T11)*Q1**H*B ] */
/* > [ 0 ] */
/* > where Q1 consists of the first RANK columns of Q. */
/* > \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] NRHS */
/* > \verbatim */
/* > NRHS is INTEGER */
/* > The number of right hand sides, i.e., the number of */
/* > columns of matrices B and X. NRHS >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* > A is COMPLEX array, dimension (LDA,N) */
/* > On entry, the M-by-N matrix A. */
/* > On exit, A has been overwritten by details of its */
/* > complete orthogonal factorization. */
/* > \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 COMPLEX array, dimension (LDB,NRHS) */
/* > On entry, the M-by-NRHS right hand side matrix B. */
/* > On exit, the N-by-NRHS solution matrix X. */
/* > If m >= n and RANK = n, the residual sum-of-squares for */
/* > the solution in the i-th column is given by the sum of */
/* > squares of elements N+1:M in that column. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* > LDB is INTEGER */
/* > The leading dimension of the array B. LDB >= f2cmax(1,M,N). */
/* > \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 an */
/* > initial column, otherwise it is a free column. Before */
/* > the QR factorization of A, all initial columns are */
/* > permuted to the leading positions; only the remaining */
/* > free columns are moved as a result of column pivoting */
/* > during the factorization. */
/* > On exit, if JPVT(i) = k, then the i-th column of A*P */
/* > was the k-th column of A. */
/* > \endverbatim */
/* > */
/* > \param[in] RCOND */
/* > \verbatim */
/* > RCOND is REAL */
/* > RCOND is used to determine the effective rank of A, which */
/* > is defined as the order of the largest leading triangular */
/* > submatrix R11 in the QR factorization with pivoting of A, */
/* > whose estimated condition number < 1/RCOND. */
/* > \endverbatim */
/* > */
/* > \param[out] RANK */
/* > \verbatim */
/* > RANK is INTEGER */
/* > The effective rank of A, i.e., the order of the submatrix */
/* > R11. This is the same as the order of the submatrix T11 */
/* > in the complete orthogonal factorization of A. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is COMPLEX array, dimension */
/* > (f2cmin(M,N) + f2cmax( N, 2*f2cmin(M,N)+NRHS )), */
/* > \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 complexGEsolve */
/* ===================================================================== */
/* Subroutine */ void cgelsx_(integer *m, integer *n, integer *nrhs, complex *
a, integer *lda, complex *b, integer *ldb, integer *jpvt, real *rcond,
integer *rank, complex *work, real *rwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
complex q__1;
/* Local variables */
real anrm, bnrm, smin, smax;
integer i__, j, k, iascl, ibscl, ismin, ismax;
complex c1, c2;
extern /* Subroutine */ void ctrsm_(char *, char *, char *, char *,
integer *, integer *, complex *, complex *, integer *, complex *,
integer *), claic1_(integer *,
integer *, complex *, real *, complex *, complex *, real *,
complex *, complex *);
complex s1, s2, t1, t2;
extern /* Subroutine */ void cunm2r_(char *, char *, integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *), slabad_(real *, real *);
extern real clange_(char *, integer *, integer *, complex *, integer *,
real *);
integer mn;
extern /* Subroutine */ void clascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, complex *, integer *, integer *), cgeqpf_(integer *, integer *, complex *, integer *,
integer *, complex *, complex *, real *, integer *);
extern real slamch_(char *);
extern /* Subroutine */ void claset_(char *, integer *, integer *, complex
*, complex *, complex *, integer *);
extern int xerbla_(char *, integer *, ftnlen);
real bignum;
extern /* Subroutine */ void clatzm_(char *, integer *, integer *, complex
*, integer *, complex *, complex *, complex *, integer *, complex
*);
real sminpr;
extern /* Subroutine */ void ctzrqf_(integer *, integer *, complex *,
integer *, complex *, integer *);
real smaxpr, smlnum;
/* -- LAPACK driver 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 */
/* ===================================================================== */
/* 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;
--jpvt;
--work;
--rwork;
/* Function Body */
mn = f2cmin(*m,*n);
ismin = mn + 1;
ismax = (mn << 1) + 1;
/* Test the input arguments. */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*lda < f2cmax(1,*m)) {
*info = -5;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = f2cmax(1,*m);
if (*ldb < f2cmax(i__1,*n)) {
*info = -7;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGELSX", &i__1, 6);
return;
}
/* Quick return if possible */
/* Computing MIN */
i__1 = f2cmin(*m,*n);
if (f2cmin(i__1,*nrhs) == 0) {
*rank = 0;
return;
}
/* Get machine parameters */
smlnum = slamch_("S") / slamch_("P");
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
/* Scale A, B if f2cmax elements outside range [SMLNUM,BIGNUM] */
anrm = clange_("M", m, n, &a[a_offset], lda, &rwork[1]);
iascl = 0;
if (anrm > 0.f && anrm < smlnum) {
/* Scale matrix norm up to SMLNUM */
clascl_("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 */
clascl_("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);
claset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
*rank = 0;
goto L100;
}
bnrm = clange_("M", m, nrhs, &b[b_offset], ldb, &rwork[1]);
ibscl = 0;
if (bnrm > 0.f && bnrm < smlnum) {
/* Scale matrix norm up to SMLNUM */
clascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb,
info);
ibscl = 1;
} else if (bnrm > bignum) {
/* Scale matrix norm down to BIGNUM */
clascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
info);
ibscl = 2;
}
/* Compute QR factorization with column pivoting of A: */
/* A * P = Q * R */
cgeqpf_(m, n, &a[a_offset], lda, &jpvt[1], &work[1], &work[mn + 1], &
rwork[1], info);
/* complex workspace MN+N. Real workspace 2*N. Details of Householder */
/* rotations stored in WORK(1:MN). */
/* Determine RANK using incremental condition estimation */
i__1 = ismin;
work[i__1].r = 1.f, work[i__1].i = 0.f;
i__1 = ismax;
work[i__1].r = 1.f, work[i__1].i = 0.f;
smax = c_abs(&a[a_dim1 + 1]);
smin = smax;
if (c_abs(&a[a_dim1 + 1]) == 0.f) {
*rank = 0;
i__1 = f2cmax(*m,*n);
claset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
goto L100;
} else {
*rank = 1;
}
L10:
if (*rank < mn) {
i__ = *rank + 1;
claic1_(&c__2, rank, &work[ismin], &smin, &a[i__ * a_dim1 + 1], &a[
i__ + i__ * a_dim1], &sminpr, &s1, &c1);
claic1_(&c__1, rank, &work[ismax], &smax, &a[i__ * a_dim1 + 1], &a[
i__ + i__ * a_dim1], &smaxpr, &s2, &c2);
if (smaxpr * *rcond <= sminpr) {
i__1 = *rank;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = ismin + i__ - 1;
i__3 = ismin + i__ - 1;
q__1.r = s1.r * work[i__3].r - s1.i * work[i__3].i, q__1.i =
s1.r * work[i__3].i + s1.i * work[i__3].r;
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
i__2 = ismax + i__ - 1;
i__3 = ismax + i__ - 1;
q__1.r = s2.r * work[i__3].r - s2.i * work[i__3].i, q__1.i =
s2.r * work[i__3].i + s2.i * work[i__3].r;
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
/* L20: */
}
i__1 = ismin + *rank;
work[i__1].r = c1.r, work[i__1].i = c1.i;
i__1 = ismax + *rank;
work[i__1].r = c2.r, work[i__1].i = c2.i;
smin = sminpr;
smax = smaxpr;
++(*rank);
goto L10;
}
}
/* Logically partition R = [ R11 R12 ] */
/* [ 0 R22 ] */
/* where R11 = R(1:RANK,1:RANK) */
/* [R11,R12] = [ T11, 0 ] * Y */
if (*rank < *n) {
ctzrqf_(rank, n, &a[a_offset], lda, &work[mn + 1], info);
}
/* Details of Householder rotations stored in WORK(MN+1:2*MN) */
/* B(1:M,1:NRHS) := Q**H * B(1:M,1:NRHS) */
cunm2r_("Left", "Conjugate transpose", m, nrhs, &mn, &a[a_offset], lda, &
work[1], &b[b_offset], ldb, &work[(mn << 1) + 1], info);
/* workspace NRHS */
/* B(1:RANK,1:NRHS) := inv(T11) * B(1:RANK,1:NRHS) */
ctrsm_("Left", "Upper", "No transpose", "Non-unit", rank, nrhs, &c_b2, &a[
a_offset], lda, &b[b_offset], ldb);
i__1 = *n;
for (i__ = *rank + 1; i__ <= i__1; ++i__) {
i__2 = *nrhs;
for (j = 1; j <= i__2; ++j) {
i__3 = i__ + j * b_dim1;
b[i__3].r = 0.f, b[i__3].i = 0.f;
/* L30: */
}
/* L40: */
}
/* B(1:N,1:NRHS) := Y**H * B(1:N,1:NRHS) */
if (*rank < *n) {
i__1 = *rank;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = *n - *rank + 1;
r_cnjg(&q__1, &work[mn + i__]);
clatzm_("Left", &i__2, nrhs, &a[i__ + (*rank + 1) * a_dim1], lda,
&q__1, &b[i__ + b_dim1], &b[*rank + 1 + b_dim1], ldb, &
work[(mn << 1) + 1]);
/* L50: */
}
}
/* workspace NRHS */
/* B(1:N,1:NRHS) := P * B(1:N,1:NRHS) */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = (mn << 1) + i__;
work[i__3].r = 1.f, work[i__3].i = 0.f;
/* L60: */
}
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = (mn << 1) + i__;
if (work[i__3].r == 1.f && work[i__3].i == 0.f) {
if (jpvt[i__] != i__) {
k = i__;
i__3 = k + j * b_dim1;
t1.r = b[i__3].r, t1.i = b[i__3].i;
i__3 = jpvt[k] + j * b_dim1;
t2.r = b[i__3].r, t2.i = b[i__3].i;
L70:
i__3 = jpvt[k] + j * b_dim1;
b[i__3].r = t1.r, b[i__3].i = t1.i;
i__3 = (mn << 1) + k;
work[i__3].r = 0.f, work[i__3].i = 0.f;
t1.r = t2.r, t1.i = t2.i;
k = jpvt[k];
i__3 = jpvt[k] + j * b_dim1;
t2.r = b[i__3].r, t2.i = b[i__3].i;
if (jpvt[k] != i__) {
goto L70;
}
i__3 = i__ + j * b_dim1;
b[i__3].r = t1.r, b[i__3].i = t1.i;
i__3 = (mn << 1) + k;
work[i__3].r = 0.f, work[i__3].i = 0.f;
}
}
/* L80: */
}
/* L90: */
}
/* Undo scaling */
if (iascl == 1) {
clascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb,
info);
clascl_("U", &c__0, &c__0, &smlnum, &anrm, rank, rank, &a[a_offset],
lda, info);
} else if (iascl == 2) {
clascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
info);
clascl_("U", &c__0, &c__0, &bignum, &anrm, rank, rank, &a[a_offset],
lda, info);
}
if (ibscl == 1) {
clascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
info);
} else if (ibscl == 2) {
clascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,
info);
}
L100:
return;
/* End of CGELSX */
} /* cgelsx_ */
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