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OpenBLAS/lapack-netlib/SRC/sgelsd.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__9 = 9;
static integer c__0 = 0;
static integer c__6 = 6;
static integer c_n1 = -1;
static integer c__1 = 1;
static real c_b81 = 0.f;
/* > \brief <b> SGELSD computes the minimum-norm solution to a linear least squares problem for GE matrices</b
> */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download SGELSD + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgelsd.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgelsd.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgelsd.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, */
/* RANK, WORK, LWORK, IWORK, INFO ) */
/* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK */
/* REAL RCOND */
/* INTEGER IWORK( * ) */
/* REAL A( LDA, * ), B( LDB, * ), S( * ), WORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGELSD 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 problem is solved in three steps: */
/* > (1) Reduce the coefficient matrix A to bidiagonal form with */
/* > Householder transformations, reducing the original problem */
/* > into a "bidiagonal least squares problem" (BLS) */
/* > (2) Solve the BLS using a divide and conquer approach. */
/* > (3) Apply back all the Householder transformations to solve */
/* > the original least squares problem. */
/* > */
/* > The effective rank of A is determined by treating as zero those */
/* > singular values which are less than RCOND times the largest singular */
/* > value. */
/* > */
/* > The divide and conquer algorithm makes very mild assumptions about */
/* > floating point arithmetic. It will work on machines with a guard */
/* > digit in add/subtract, or on those binary machines without guard */
/* > digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
/* > Cray-2. It could conceivably fail on hexadecimal or decimal machines */
/* > without guard digits, but we know of none. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] M */
/* > \verbatim */
/* > M is INTEGER */
/* > The number of rows of A. M >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The number of columns of 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, A has been destroyed. */
/* > \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 must be at least 1. */
/* > The exact minimum amount of workspace needed depends on M, */
/* > N and NRHS. As long as LWORK is at least */
/* > 12*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2, */
/* > if M is greater than or equal to N or */
/* > 12*M + 2*M*SMLSIZ + 8*M*NLVL + M*NRHS + (SMLSIZ+1)**2, */
/* > if M is less than N, the code will execute correctly. */
/* > SMLSIZ is returned by ILAENV and is equal to the maximum */
/* > size of the subproblems at the bottom of the computation */
/* > tree (usually about 25), and */
/* > NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 ) */
/* > 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 array WORK and the */
/* > minimum size of the array IWORK, and returns these values as */
/* > the first entries of the WORK and IWORK arrays, and no error */
/* > message related to LWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */
/* > LIWORK >= f2cmax(1, 3*MINMN*NLVL + 11*MINMN), */
/* > where MINMN = MIN( M,N ). */
/* > On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK. */
/* > \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 June 2017 */
/* > \ingroup realGEsolve */
/* > \par Contributors: */
/* ================== */
/* > */
/* > Ming Gu and Ren-Cang Li, Computer Science Division, University of */
/* > California at Berkeley, USA \n */
/* > Osni Marques, LBNL/NERSC, USA \n */
/* ===================================================================== */
/* Subroutine */ void sgelsd_(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 *iwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;
/* Local variables */
real anrm, bnrm;
integer itau, nlvl, iascl, ibscl;
real sfmin;
integer minmn, maxmn, itaup, itauq, mnthr, nwork, ie, il;
extern /* Subroutine */ void slabad_(real *, real *);
integer mm;
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 *), slalsd_(char *, integer
*, integer *, integer *, real *, real *, real *, integer *, real *
, integer *, real *, integer *, integer *), slascl_(char *
, integer *, integer *, real *, real *, integer *, integer *,
real *, integer *, integer *);
integer wlalsd;
extern /* Subroutine */ void 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 *);
integer ldwork;
extern /* Subroutine */ void sormbr_(char *, char *, char *, integer *,
integer *, integer *, real *, integer *, real *, real *, integer *
, real *, integer *, integer *);
integer liwork, minwrk, maxwrk;
real smlnum;
extern /* Subroutine */ void sormlq_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
logical lquery;
integer smlsiz;
extern /* Subroutine */ void sormqr_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
real eps;
/* -- LAPACK driver routine (version 3.7.1) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* June 2017 */
/* ===================================================================== */
/* Test the input arguments. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--s;
--work;
--iwork;
fprintf(stdout,"start of SGELSD\n");
/* 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;
liwork = 1;
if (minmn > 0) {
smlsiz = ilaenv_(&c__9, "SGELSD", " ", &c__0, &c__0, &c__0, &c__0,
(ftnlen)6, (ftnlen)1);
mnthr = ilaenv_(&c__6, "SGELSD", " ", m, n, nrhs, &c_n1, (ftnlen)
6, (ftnlen)1);
/* Computing MAX */
i__1 = (integer) (logf((real) minmn / (real) (smlsiz + 1)) / logf(
2.f)) + 1;
nlvl = f2cmax(i__1,0);
liwork = minmn * 3 * nlvl + minmn * 11;
mm = *m;
if (*m >= *n && *m >= mnthr) {
/* Path 1a - overdetermined, with many more rows than */
/* columns. */
mm = *n;
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "SGEQRF",
" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + *nrhs * ilaenv_(&c__1, "SORMQR",
"LT", m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)2);
maxwrk = f2cmax(i__1,i__2);
}
if (*m >= *n) {
/* Path 1 - overdetermined or exactly determined. */
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + (mm + *n) * ilaenv_(&c__1,
"SGEBRD", " ", &mm, n, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
maxwrk = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + *nrhs * ilaenv_(&c__1, "SORMBR"
, "QLT", &mm, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3);
maxwrk = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + (*n - 1) * ilaenv_(&c__1,
"SORMBR", "PLN", n, nrhs, n, &c_n1, (ftnlen)6, (
ftnlen)3);
maxwrk = f2cmax(i__1,i__2);
/* Computing 2nd power */
i__1 = smlsiz + 1;
wlalsd = *n * 9 + (*n << 1) * smlsiz + (*n << 3) * nlvl + *n *
*nrhs + i__1 * i__1;
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + wlalsd;
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), i__2 = *n * 3 + wlalsd;
minwrk = f2cmax(i__1,i__2);
}
if (*n > *m) {
/* Computing 2nd power */
i__1 = smlsiz + 1;
wlalsd = *m * 9 + (*m << 1) * smlsiz + (*m << 3) * nlvl + *m *
*nrhs + i__1 * i__1;
if (*n >= mnthr) {
/* Path 2a - underdetermined, with many more columns */
/* than rows. */
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) + (*m << 1) *
ilaenv_(&c__1, "SGEBRD", " ", m, m, &c_n1, &c_n1,
(ftnlen)6, (ftnlen)1);
maxwrk = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *nrhs *
ilaenv_(&c__1, "SORMBR", "QLT", m, nrhs, m, &c_n1,
(ftnlen)6, (ftnlen)3);
maxwrk = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m - 1) *
ilaenv_(&c__1, "SORMBR", "PLN", m, nrhs, m, &c_n1,
(ftnlen)6, (ftnlen)3);
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 + *nrhs * ilaenv_(&c__1, "SORMLQ"
, "LT", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)2);
maxwrk = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + wlalsd;
maxwrk = f2cmax(i__1,i__2);
/* XXX: Ensure the Path 2a case below is triggered. The workspace */
/* calculation should use queries for all routines eventually. */
/* 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__1 = maxwrk, i__2 = (*m << 2) + *m * *m + f2cmax(i__3,i__4)
;
maxwrk = f2cmax(i__1,i__2);
} else {
/* Path 2 - remaining underdetermined cases. */
maxwrk = *m * 3 + (*n + *m) * ilaenv_(&c__1, "SGEBRD",
" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * 3 + *nrhs * ilaenv_(&c__1,
"SORMBR", "QLT", m, nrhs, n, &c_n1, (ftnlen)6, (
ftnlen)3);
maxwrk = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * 3 + *m * ilaenv_(&c__1, "SORM"
"BR", "PLN", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)
3);
maxwrk = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * 3 + wlalsd;
maxwrk = f2cmax(i__1,i__2);
}
/* Computing MAX */
i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *m, i__1 = f2cmax(i__1,
i__2), i__2 = *m * 3 + wlalsd;
minwrk = f2cmax(i__1,i__2);
}
}
minwrk = f2cmin(minwrk,maxwrk);
work[1] = (real) maxwrk;
iwork[1] = liwork;
if (*lwork < minwrk && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGELSD", &i__1, (ftnlen)6);
return;
} else if (lquery) {
return;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0) {
fprintf(stdout,"SGELSD quickreturn rank=0\n");
*rank = 0;
return;
}
/* Get machine parameters. */
eps = slamch_("P");
sfmin = slamch_("S");
smlnum = sfmin / eps;
bignum = 1.f / smlnum;
// FILE *bla=fopen("/tmp/bla","w");
//fprintf(bla,"SGELSD eps=%g sfmin=%g smlnum=%g bignum=%g\n",eps,sfmin,smlnum,bignum);
//fclose(bla);
slabad_(&smlnum, &bignum);
/* Scale A if f2cmax entry 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. */
fprintf(stdout,"scaling A up to SML\n");
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. */
fprintf(stdout,"scaling A down to BIG\n");
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. */
fprintf(stdout,"A is zero soln\n");
i__1 = f2cmax(*m,*n);
slaset_("F", &i__1, nrhs, &c_b81, &c_b81, &b[b_offset], ldb);
slaset_("F", &minmn, &c__1, &c_b81, &c_b81, &s[1], &c__1);
*rank = 0;
goto L10;
}
/* Scale B if f2cmax entry 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. */
fprintf(stdout,"scaling B up to SML\n");
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. */
fprintf(stdout,"scaling B down to BIG\n");
slascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
info);
ibscl = 2;
}
/* If M < N make sure certain entries of B are zero. */
if (*m < *n) {
i__1 = *n - *m;
fprintf(stdout,"zeroing parts of B \n");
slaset_("F", &i__1, nrhs, &c_b81, &c_b81, &b[*m + 1 + b_dim1], ldb);
}
/* Overdetermined case. */
if (*m >= *n) {
fprintf(stdout,"overdetermined, path 1 \n");
/* Path 1 - overdetermined or exactly determined. */
mm = *m;
if (*m >= mnthr) {
/* Path 1a - overdetermined, with many more rows than columns. */
fprintf(stdout,"overdetermined, path 1a \n");
mm = *n;
itau = 1;
nwork = itau + *n;
/* Compute A=Q*R. */
/* (Workspace: need 2*N, prefer N+N*NB) */
i__1 = *lwork - nwork + 1;
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1,
info);
/* Multiply B by transpose(Q). */
/* (Workspace: need N+NRHS, prefer N+NRHS*NB) */
i__1 = *lwork - nwork + 1;
sormqr_("L", "T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[
b_offset], ldb, &work[nwork], &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_b81, &c_b81, &a[a_dim1 + 2],
lda);
}
}
ie = 1;
itauq = ie + *n;
itaup = itauq + *n;
nwork = itaup + *n;
/* Bidiagonalize R in A. */
/* (Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) */
i__1 = *lwork - nwork + 1;
sgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
work[itaup], &work[nwork], &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 - nwork + 1;
sormbr_("Q", "L", "T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq],
&b[b_offset], ldb, &work[nwork], &i__1, info);
/* Solve the bidiagonal least squares problem. */
slalsd_("U", &smlsiz, n, nrhs, &s[1], &work[ie], &b[b_offset], ldb,
rcond, rank, &work[nwork], &iwork[1], info);
if (*info != 0) {
fprintf(stdout,"info !=0 nach slalsd\n");
goto L10;
}
/* Multiply B by right bidiagonalizing vectors of R. */
i__1 = *lwork - nwork + 1;
sormbr_("P", "L", "N", n, nrhs, n, &a[a_offset], lda, &work[itaup], &
b[b_offset], ldb, &work[nwork], &i__1, info);
} else /* if(complicated condition) */ {
fprintf(stdout,"not overdetermined \n");
/* Computing MAX */
i__1 = *m, i__2 = (*m << 1) - 4, i__1 = f2cmax(i__1,i__2), i__1 = f2cmax(
i__1,*nrhs), i__2 = *n - *m * 3, i__1 = f2cmax(i__1,i__2);
if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + f2cmax(i__1,wlalsd)) {
/* Path 2a - underdetermined, with many more columns than rows */
/* and sufficient workspace for an efficient algorithm. */
fprintf(stdout,"not overdetermined, path 2a\n");
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__1 = (*m << 2) + *m * *lda + f2cmax(i__3,i__4), i__2 = *m * *lda +
*m + *m * *nrhs, i__1 = f2cmax(i__1,i__2), i__2 = (*m << 2)
+ *m * *lda + wlalsd;
if (*lwork >= f2cmax(i__1,i__2)) {
ldwork = *lda;
}
itau = 1;
nwork = *m + 1;
/* Compute A=L*Q. */
/* (Workspace: need 2*M, prefer M+M*NB) */
i__1 = *lwork - nwork + 1;
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1,
info);
il = nwork;
/* Copy L to WORK(IL), zeroing out above its diagonal. */
slacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwork);
i__1 = *m - 1;
i__2 = *m - 1;
slaset_("U", &i__1, &i__2, &c_b81, &c_b81, &work[il + ldwork], &
ldwork);
ie = il + ldwork * *m;
itauq = ie + *m;
itaup = itauq + *m;
nwork = itaup + *m;
/* Bidiagonalize L in WORK(IL). */
/* (Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) */
i__1 = *lwork - nwork + 1;
sgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq],
&work[itaup], &work[nwork], &i__1, 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__1 = *lwork - nwork + 1;
sormbr_("Q", "L", "T", m, nrhs, m, &work[il], &ldwork, &work[
itauq], &b[b_offset], ldb, &work[nwork], &i__1, info);
/* Solve the bidiagonal least squares problem. */
slalsd_("U", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset],
ldb, rcond, rank, &work[nwork], &iwork[1], info);
if (*info != 0) {
goto L10;
}
/* Multiply B by right bidiagonalizing vectors of L. */
i__1 = *lwork - nwork + 1;
sormbr_("P", "L", "N", m, nrhs, m, &work[il], &ldwork, &work[
itaup], &b[b_offset], ldb, &work[nwork], &i__1, info);
/* Zero out below first M rows of B. */
i__1 = *n - *m;
slaset_("F", &i__1, nrhs, &c_b81, &c_b81, &b[*m + 1 + b_dim1],
ldb);
nwork = itau + *m;
/* Multiply transpose(Q) by B. */
/* (Workspace: need M+NRHS, prefer M+NRHS*NB) */
i__1 = *lwork - nwork + 1;
sormlq_("L", "T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[
b_offset], ldb, &work[nwork], &i__1, info);
} else {
/* Path 2 - remaining underdetermined cases. */
fprintf(stdout,"other underdetermined, path 2");
ie = 1;
itauq = ie + *m;
itaup = itauq + *m;
nwork = itaup + *m;
/* Bidiagonalize A. */
/* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */
i__1 = *lwork - nwork + 1;
sgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
work[itaup], &work[nwork], &i__1, info);
/* Multiply B by transpose of left bidiagonalizing vectors. */
/* (Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) */
i__1 = *lwork - nwork + 1;
sormbr_("Q", "L", "T", m, nrhs, n, &a[a_offset], lda, &work[itauq]
, &b[b_offset], ldb, &work[nwork], &i__1, info);
/* Solve the bidiagonal least squares problem. */
slalsd_("L", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset],
ldb, rcond, rank, &work[nwork], &iwork[1], info);
if (*info != 0) {
goto L10;
}
/* Multiply B by right bidiagonalizing vectors of A. */
i__1 = *lwork - nwork + 1;
sormbr_("P", "L", "N", n, nrhs, m, &a[a_offset], lda, &work[itaup]
, &b[b_offset], ldb, &work[nwork], &i__1, info);
}
}
/* Undo scaling. */
if (iascl == 1) {
fprintf(stdout," unscaling a1\n");
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) {
fprintf(stdout," unscaling a2\n");
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) {
fprintf(stdout," unscaling b1\n");
slascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
info);
} else if (ibscl == 2) {
fprintf(stdout," unscaling b2\n");
slascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,
info);
}
L10:
work[1] = (real) maxwrk;
iwork[1] = liwork;
fprintf(stdout, "end of SGELSD\n");
return;
/* End of SGELSD */
} /* sgelsd_ */
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