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OpenBLAS/lapack-netlib/SRC/sgelss.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__6 = 6;
static integer c_n1 = -1;
static integer c__1 = 1;
static integer c__0 = 0;
static real c_b50 = 0.f;
static real c_b83 = 1.f;
/* > \brief <b> SGELSS solves overdetermined or underdetermined systems for GE matrices</b> */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download SGELSS + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgelss.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgelss.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgelss.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, */
/* WORK, LWORK, INFO ) */
/* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK */
/* REAL RCOND */
/* REAL A( LDA, * ), B( LDB, * ), S( * ), WORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGELSS computes the minimum norm solution to a real linear least */
/* > squares problem: */
/* > */
/* > Minimize 2-norm(| b - A*x |). */
/* > */
/* > using the singular value decomposition (SVD) 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 effective rank of A is determined by treating as zero those */
/* > singular values which are less than RCOND times the largest singular */
/* > value. */
/* > \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 the matrices B and X. NRHS >= 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 first f2cmin(m,n) rows of A are overwritten with */
/* > its right singular vectors, stored rowwise. */
/* > \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 REAL array, dimension (LDB,NRHS) */
/* > On entry, the M-by-NRHS right hand side matrix B. */
/* > On exit, B is overwritten by 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,f2cmax(M,N)). */
/* > \endverbatim */
/* > */
/* > \param[out] S */
/* > \verbatim */
/* > S is REAL array, dimension (f2cmin(M,N)) */
/* > The singular values of A in decreasing order. */
/* > The condition number of A in the 2-norm = S(1)/S(f2cmin(m,n)). */
/* > \endverbatim */
/* > */
/* > \param[in] RCOND */
/* > \verbatim */
/* > RCOND is REAL */
/* > RCOND is used to determine the effective rank of A. */
/* > Singular values S(i) <= RCOND*S(1) are treated as zero. */
/* > If RCOND < 0, machine precision is used instead. */
/* > \endverbatim */
/* > */
/* > \param[out] RANK */
/* > \verbatim */
/* > RANK is INTEGER */
/* > The effective rank of A, i.e., the number of singular values */
/* > which are greater than RCOND*S(1). */
/* > \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 >= 1, and also: */
/* > LWORK >= 3*f2cmin(M,N) + f2cmax( 2*f2cmin(M,N), f2cmax(M,N), NRHS ) */
/* > For good performance, LWORK should generally be larger. */
/* > */
/* > 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. */
/* > > 0: the algorithm for computing the SVD failed to converge; */
/* > if INFO = i, i off-diagonal elements of an intermediate */
/* > bidiagonal form did not converge to zero. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date December 2016 */
/* > \ingroup realGEsolve */
/* ===================================================================== */
/* Subroutine */ void sgelss_(integer *m, integer *n, integer *nrhs, real *a,
integer *lda, real *b, integer *ldb, real *s, real *rcond, integer *
rank, real *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;
real r__1;
/* Local variables */
real anrm, bnrm;
integer itau, lwork_sgebrd__, lwork_sgeqrf__, i__, lwork_sorgbr__,
lwork_sormbr__, lwork_sormlq__, iascl, ibscl, lwork_sormqr__,
chunk;
extern /* Subroutine */ void sgemm_(char *, char *, integer *, integer *,
integer *, real *, real *, integer *, real *, integer *, real *,
real *, integer *);
real sfmin;
integer minmn, maxmn;
extern /* Subroutine */ void sgemv_(char *, integer *, integer *, real *,
real *, integer *, real *, integer *, real *, real *, integer *);
integer itaup, itauq;
extern /* Subroutine */ void srscl_(integer *, real *, real *, integer *);
integer mnthr, iwork;
extern /* Subroutine */ void scopy_(integer *, real *, integer *, real *,
integer *);
integer bl, ie, il;
extern /* Subroutine */ void slabad_(real *, real *);
integer mm, bdspac;
extern /* Subroutine */ void sgebrd_(integer *, integer *, real *, integer
*, real *, real *, real *, real *, real *, integer *, integer *);
extern real slamch_(char *), slange_(char *, integer *, integer *,
real *, integer *, real *);
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
real bignum;
extern /* Subroutine */ void sgelqf_(integer *, integer *, real *, integer
*, real *, real *, integer *, integer *), slascl_(char *, integer
*, integer *, real *, real *, integer *, integer *, real *,
integer *, integer *), sgeqrf_(integer *, integer *, real
*, integer *, real *, real *, integer *, integer *), slacpy_(char
*, integer *, integer *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *,
real *, integer *), sbdsqr_(char *, integer *, integer *,
integer *, integer *, real *, real *, real *, integer *, real *,
integer *, real *, integer *, real *, integer *), sorgbr_(
char *, integer *, integer *, integer *, real *, integer *, real *
, real *, integer *, integer *);
integer ldwork;
extern /* Subroutine */ void sormbr_(char *, char *, char *, integer *,
integer *, integer *, real *, integer *, real *, real *, integer *
, real *, integer *, integer *);
integer minwrk, maxwrk;
real smlnum;
extern /* Subroutine */ void sormlq_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
logical lquery;
extern /* Subroutine */ void sormqr_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
real dum[1], eps, thr;
/* -- 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 */
/* ===================================================================== */
/* Test the input arguments */
/* 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;
--s;
--work;
/* Function Body */
*info = 0;
minmn = f2cmin(*m,*n);
maxmn = f2cmax(*m,*n);
lquery = *lwork == -1;
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 (*ldb < f2cmax(1,maxmn)) {
*info = -7;
}
/* Compute workspace */
/* (Note: Comments in the code beginning "Workspace:" describe the */
/* minimal amount of workspace needed at that point in the code, */
/* as well as the preferred amount for good performance. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV.) */
if (*info == 0) {
minwrk = 1;
maxwrk = 1;
if (minmn > 0) {
mm = *m;
mnthr = ilaenv_(&c__6, "SGELSS", " ", m, n, nrhs, &c_n1, (ftnlen)
6, (ftnlen)1);
if (*m >= *n && *m >= mnthr) {
/* Path 1a - overdetermined, with many more rows than */
/* columns */
/* Compute space needed for SGEQRF */
sgeqrf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, info);
lwork_sgeqrf__ = dum[0];
/* Compute space needed for SORMQR */
sormqr_("L", "T", m, nrhs, n, &a[a_offset], lda, dum, &b[
b_offset], ldb, dum, &c_n1, info);
lwork_sormqr__ = dum[0];
mm = *n;
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + lwork_sgeqrf__;
maxwrk = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + lwork_sormqr__;
maxwrk = f2cmax(i__1,i__2);
}
if (*m >= *n) {
/* Path 1 - overdetermined or exactly determined */
/* Compute workspace needed for SBDSQR */
/* Computing MAX */
i__1 = 1, i__2 = *n * 5;
bdspac = f2cmax(i__1,i__2);
/* Compute space needed for SGEBRD */
sgebrd_(&mm, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum,
&c_n1, info);
lwork_sgebrd__ = dum[0];
/* Compute space needed for SORMBR */
sormbr_("Q", "L", "T", &mm, nrhs, n, &a[a_offset], lda, dum, &
b[b_offset], ldb, dum, &c_n1, info);
lwork_sormbr__ = dum[0];
/* Compute space needed for SORGBR */
sorgbr_("P", n, n, n, &a[a_offset], lda, dum, dum, &c_n1,
info);
lwork_sorgbr__ = dum[0];
/* Compute total workspace needed */
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + lwork_sgebrd__;
maxwrk = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + lwork_sormbr__;
maxwrk = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + lwork_sorgbr__;
maxwrk = f2cmax(i__1,i__2);
maxwrk = f2cmax(maxwrk,bdspac);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * *nrhs;
maxwrk = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = f2cmax(i__1,
i__2);
minwrk = f2cmax(i__1,bdspac);
maxwrk = f2cmax(minwrk,maxwrk);
}
if (*n > *m) {
/* Compute workspace needed for SBDSQR */
/* Computing MAX */
i__1 = 1, i__2 = *m * 5;
bdspac = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *n, i__1 = f2cmax(i__1,
i__2);
minwrk = f2cmax(i__1,bdspac);
if (*n >= mnthr) {
/* Path 2a - underdetermined, with many more columns */
/* than rows */
/* Compute space needed for SGEBRD */
sgebrd_(m, m, &a[a_offset], lda, &s[1], dum, dum, dum,
dum, &c_n1, info);
lwork_sgebrd__ = dum[0];
/* Compute space needed for SORMBR */
sormbr_("Q", "L", "T", m, nrhs, n, &a[a_offset], lda, dum,
&b[b_offset], ldb, dum, &c_n1, info);
lwork_sormbr__ = dum[0];
/* Compute space needed for SORGBR */
sorgbr_("P", m, m, m, &a[a_offset], lda, dum, dum, &c_n1,
info);
lwork_sorgbr__ = dum[0];
/* Compute space needed for SORMLQ */
sormlq_("L", "T", n, nrhs, m, &a[a_offset], lda, dum, &b[
b_offset], ldb, dum, &c_n1, info);
lwork_sormlq__ = dum[0];
/* Compute total workspace needed */
maxwrk = *m + *m * ilaenv_(&c__1, "SGELQF", " ", m, n, &
c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) +
lwork_sgebrd__;
maxwrk = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) +
lwork_sormbr__;
maxwrk = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) +
lwork_sorgbr__;
maxwrk = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + *m + bdspac;
maxwrk = f2cmax(i__1,i__2);
if (*nrhs > 1) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs;
maxwrk = f2cmax(i__1,i__2);
} else {
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 1);
maxwrk = f2cmax(i__1,i__2);
}
/* Computing MAX */
i__1 = maxwrk, i__2 = *m + lwork_sormlq__;
maxwrk = f2cmax(i__1,i__2);
} else {
/* Path 2 - underdetermined */
/* Compute space needed for SGEBRD */
sgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum,
dum, &c_n1, info);
lwork_sgebrd__ = dum[0];
/* Compute space needed for SORMBR */
sormbr_("Q", "L", "T", m, nrhs, m, &a[a_offset], lda, dum,
&b[b_offset], ldb, dum, &c_n1, info);
lwork_sormbr__ = dum[0];
/* Compute space needed for SORGBR */
sorgbr_("P", m, n, m, &a[a_offset], lda, dum, dum, &c_n1,
info);
lwork_sorgbr__ = dum[0];
maxwrk = *m * 3 + lwork_sgebrd__;
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * 3 + lwork_sormbr__;
maxwrk = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * 3 + lwork_sorgbr__;
maxwrk = f2cmax(i__1,i__2);
maxwrk = f2cmax(maxwrk,bdspac);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * *nrhs;
maxwrk = f2cmax(i__1,i__2);
}
}
maxwrk = f2cmax(minwrk,maxwrk);
}
work[1] = (real) maxwrk;
if (*lwork < minwrk && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGELSS", &i__1, (ftnlen)6);
return;
} else if (lquery) {
return;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
*rank = 0;
return;
}
/* Get machine parameters */
eps = slamch_("P");
sfmin = slamch_("S");
smlnum = sfmin / eps;
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
/* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
anrm = slange_("M", m, n, &a[a_offset], lda, &work[1]);
iascl = 0;
if (anrm > 0.f && anrm < smlnum) {
/* Scale matrix norm up to SMLNUM */
slascl_("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 */
slascl_("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);
slaset_("F", &i__1, nrhs, &c_b50, &c_b50, &b[b_offset], ldb);
slaset_("F", &minmn, &c__1, &c_b50, &c_b50, &s[1], &minmn);
*rank = 0;
goto L70;
}
/* Scale B if f2cmax element outside range [SMLNUM,BIGNUM] */
bnrm = slange_("M", m, nrhs, &b[b_offset], ldb, &work[1]);
ibscl = 0;
if (bnrm > 0.f && bnrm < smlnum) {
/* Scale matrix norm up to SMLNUM */
slascl_("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 */
slascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
info);
ibscl = 2;
}
/* Overdetermined case */
if (*m >= *n) {
/* Path 1 - overdetermined or exactly determined */
mm = *m;
if (*m >= mnthr) {
/* Path 1a - overdetermined, with many more rows than columns */
mm = *n;
itau = 1;
iwork = itau + *n;
/* Compute A=Q*R */
/* (Workspace: need 2*N, prefer N+N*NB) */
i__1 = *lwork - iwork + 1;
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__1,
info);
/* Multiply B by transpose(Q) */
/* (Workspace: need N+NRHS, prefer N+NRHS*NB) */
i__1 = *lwork - iwork + 1;
sormqr_("L", "T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[
b_offset], ldb, &work[iwork], &i__1, info);
/* Zero out below R */
if (*n > 1) {
i__1 = *n - 1;
i__2 = *n - 1;
slaset_("L", &i__1, &i__2, &c_b50, &c_b50, &a[a_dim1 + 2],
lda);
}
}
ie = 1;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in A */
/* (Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) */
i__1 = *lwork - iwork + 1;
sgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
work[itaup], &work[iwork], &i__1, info);
/* Multiply B by transpose of left bidiagonalizing vectors of R */
/* (Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) */
i__1 = *lwork - iwork + 1;
sormbr_("Q", "L", "T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq],
&b[b_offset], ldb, &work[iwork], &i__1, info);
/* Generate right bidiagonalizing vectors of R in A */
/* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
i__1 = *lwork - iwork + 1;
sorgbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &work[iwork], &
i__1, info);
iwork = ie + *n;
/* Perform bidiagonal QR iteration */
/* multiply B by transpose of left singular vectors */
/* compute right singular vectors in A */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", n, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], lda,
dum, &c__1, &b[b_offset], ldb, &work[iwork], info);
if (*info != 0) {
goto L70;
}
/* Multiply B by reciprocals of singular values */
/* Computing MAX */
r__1 = *rcond * s[1];
thr = f2cmax(r__1,sfmin);
if (*rcond < 0.f) {
/* Computing MAX */
r__1 = eps * s[1];
thr = f2cmax(r__1,sfmin);
}
*rank = 0;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (s[i__] > thr) {
srscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb);
++(*rank);
} else {
slaset_("F", &c__1, nrhs, &c_b50, &c_b50, &b[i__ + b_dim1],
ldb);
}
/* L10: */
}
/* Multiply B by right singular vectors */
/* (Workspace: need N, prefer N*NRHS) */
if (*lwork >= *ldb * *nrhs && *nrhs > 1) {
sgemm_("T", "N", n, nrhs, n, &c_b83, &a[a_offset], lda, &b[
b_offset], ldb, &c_b50, &work[1], ldb);
slacpy_("G", n, nrhs, &work[1], ldb, &b[b_offset], ldb)
;
} else if (*nrhs > 1) {
chunk = *lwork / *n;
i__1 = *nrhs;
i__2 = chunk;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__3 = *nrhs - i__ + 1;
bl = f2cmin(i__3,chunk);
sgemm_("T", "N", n, &bl, n, &c_b83, &a[a_offset], lda, &b[i__
* b_dim1 + 1], ldb, &c_b50, &work[1], n);
slacpy_("G", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], ldb);
/* L20: */
}
} else {
sgemv_("T", n, n, &c_b83, &a[a_offset], lda, &b[b_offset], &c__1,
&c_b50, &work[1], &c__1);
scopy_(n, &work[1], &c__1, &b[b_offset], &c__1);
}
} else /* if(complicated condition) */ {
/* Computing MAX */
i__2 = *m, i__1 = (*m << 1) - 4, i__2 = f2cmax(i__2,i__1), i__2 = f2cmax(
i__2,*nrhs), i__1 = *n - *m * 3;
if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + f2cmax(i__2,i__1)) {
/* Path 2a - underdetermined, with many more columns than rows */
/* and sufficient workspace for an efficient algorithm */
ldwork = *m;
/* Computing MAX */
/* Computing MAX */
i__3 = *m, i__4 = (*m << 1) - 4, i__3 = f2cmax(i__3,i__4), i__3 =
f2cmax(i__3,*nrhs), i__4 = *n - *m * 3;
i__2 = (*m << 2) + *m * *lda + f2cmax(i__3,i__4), i__1 = *m * *lda +
*m + *m * *nrhs;
if (*lwork >= f2cmax(i__2,i__1)) {
ldwork = *lda;
}
itau = 1;
iwork = *m + 1;
/* Compute A=L*Q */
/* (Workspace: need 2*M, prefer M+M*NB) */
i__2 = *lwork - iwork + 1;
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2,
info);
il = iwork;
/* Copy L to WORK(IL), zeroing out above it */
slacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwork);
i__2 = *m - 1;
i__1 = *m - 1;
slaset_("U", &i__2, &i__1, &c_b50, &c_b50, &work[il + ldwork], &
ldwork);
ie = il + ldwork * *m;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in WORK(IL) */
/* (Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq],
&work[itaup], &work[iwork], &i__2, info);
/* Multiply B by transpose of left bidiagonalizing vectors of L */
/* (Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB) */
i__2 = *lwork - iwork + 1;
sormbr_("Q", "L", "T", m, nrhs, m, &work[il], &ldwork, &work[
itauq], &b[b_offset], ldb, &work[iwork], &i__2, info);
/* Generate right bidiagonalizing vectors of R in WORK(IL) */
/* (Workspace: need M*M+5*M-1, prefer M*M+4*M+(M-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", m, m, m, &work[il], &ldwork, &work[itaup], &work[
iwork], &i__2, info);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, */
/* computing right singular vectors of L in WORK(IL) and */
/* multiplying B by transpose of left singular vectors */
/* (Workspace: need M*M+M+BDSPAC) */
sbdsqr_("U", m, m, &c__0, nrhs, &s[1], &work[ie], &work[il], &
ldwork, &a[a_offset], lda, &b[b_offset], ldb, &work[iwork]
, info);
if (*info != 0) {
goto L70;
}
/* Multiply B by reciprocals of singular values */
/* Computing MAX */
r__1 = *rcond * s[1];
thr = f2cmax(r__1,sfmin);
if (*rcond < 0.f) {
/* Computing MAX */
r__1 = eps * s[1];
thr = f2cmax(r__1,sfmin);
}
*rank = 0;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
if (s[i__] > thr) {
srscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb);
++(*rank);
} else {
slaset_("F", &c__1, nrhs, &c_b50, &c_b50, &b[i__ + b_dim1]
, ldb);
}
/* L30: */
}
iwork = ie;
/* Multiply B by right singular vectors of L in WORK(IL) */
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NRHS) */
if (*lwork >= *ldb * *nrhs + iwork - 1 && *nrhs > 1) {
sgemm_("T", "N", m, nrhs, m, &c_b83, &work[il], &ldwork, &b[
b_offset], ldb, &c_b50, &work[iwork], ldb);
slacpy_("G", m, nrhs, &work[iwork], ldb, &b[b_offset], ldb);
} else if (*nrhs > 1) {
chunk = (*lwork - iwork + 1) / *m;
i__2 = *nrhs;
i__1 = chunk;
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
i__1) {
/* Computing MIN */
i__3 = *nrhs - i__ + 1;
bl = f2cmin(i__3,chunk);
sgemm_("T", "N", m, &bl, m, &c_b83, &work[il], &ldwork, &
b[i__ * b_dim1 + 1], ldb, &c_b50, &work[iwork], m);
slacpy_("G", m, &bl, &work[iwork], m, &b[i__ * b_dim1 + 1]
, ldb);
/* L40: */
}
} else {
sgemv_("T", m, m, &c_b83, &work[il], &ldwork, &b[b_dim1 + 1],
&c__1, &c_b50, &work[iwork], &c__1);
scopy_(m, &work[iwork], &c__1, &b[b_dim1 + 1], &c__1);
}
/* Zero out below first M rows of B */
i__1 = *n - *m;
slaset_("F", &i__1, nrhs, &c_b50, &c_b50, &b[*m + 1 + b_dim1],
ldb);
iwork = itau + *m;
/* Multiply transpose(Q) by B */
/* (Workspace: need M+NRHS, prefer M+NRHS*NB) */
i__1 = *lwork - iwork + 1;
sormlq_("L", "T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[
b_offset], ldb, &work[iwork], &i__1, info);
} else {
/* Path 2 - remaining underdetermined cases */
ie = 1;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize A */
/* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */
i__1 = *lwork - iwork + 1;
sgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
work[itaup], &work[iwork], &i__1, info);
/* Multiply B by transpose of left bidiagonalizing vectors */
/* (Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) */
i__1 = *lwork - iwork + 1;
sormbr_("Q", "L", "T", m, nrhs, n, &a[a_offset], lda, &work[itauq]
, &b[b_offset], ldb, &work[iwork], &i__1, info);
/* Generate right bidiagonalizing vectors in A */
/* (Workspace: need 4*M, prefer 3*M+M*NB) */
i__1 = *lwork - iwork + 1;
sorgbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[
iwork], &i__1, info);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, */
/* computing right singular vectors of A in A and */
/* multiplying B by transpose of left singular vectors */
/* (Workspace: need BDSPAC) */
sbdsqr_("L", m, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset],
lda, dum, &c__1, &b[b_offset], ldb, &work[iwork], info);
if (*info != 0) {
goto L70;
}
/* Multiply B by reciprocals of singular values */
/* Computing MAX */
r__1 = *rcond * s[1];
thr = f2cmax(r__1,sfmin);
if (*rcond < 0.f) {
/* Computing MAX */
r__1 = eps * s[1];
thr = f2cmax(r__1,sfmin);
}
*rank = 0;
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
if (s[i__] > thr) {
srscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb);
++(*rank);
} else {
slaset_("F", &c__1, nrhs, &c_b50, &c_b50, &b[i__ + b_dim1]
, ldb);
}
/* L50: */
}
/* Multiply B by right singular vectors of A */
/* (Workspace: need N, prefer N*NRHS) */
if (*lwork >= *ldb * *nrhs && *nrhs > 1) {
sgemm_("T", "N", n, nrhs, m, &c_b83, &a[a_offset], lda, &b[
b_offset], ldb, &c_b50, &work[1], ldb);
slacpy_("F", n, nrhs, &work[1], ldb, &b[b_offset], ldb);
} else if (*nrhs > 1) {
chunk = *lwork / *n;
i__1 = *nrhs;
i__2 = chunk;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
i__2) {
/* Computing MIN */
i__3 = *nrhs - i__ + 1;
bl = f2cmin(i__3,chunk);
sgemm_("T", "N", n, &bl, m, &c_b83, &a[a_offset], lda, &b[
i__ * b_dim1 + 1], ldb, &c_b50, &work[1], n);
slacpy_("F", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1],
ldb);
/* L60: */
}
} else {
sgemv_("T", m, n, &c_b83, &a[a_offset], lda, &b[b_offset], &
c__1, &c_b50, &work[1], &c__1);
scopy_(n, &work[1], &c__1, &b[b_offset], &c__1);
}
}
}
/* Undo scaling */
if (iascl == 1) {
slascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb,
info);
slascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
minmn, info);
} else if (iascl == 2) {
slascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
info);
slascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
minmn, info);
}
if (ibscl == 1) {
slascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
info);
} else if (ibscl == 2) {
slascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,
info);
}
L70:
work[1] = (real) maxwrk;
return;
/* End of SGELSS */
} /* sgelss_ */
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