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OpenBLAS/lapack-netlib/SRC/sgbbrd.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 real c_b8 = 0.f;
static real c_b9 = 1.f;
static integer c__1 = 1;
/* > \brief \b SGBBRD */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download SGBBRD + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgbbrd.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgbbrd.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgbbrd.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, */
/* LDQ, PT, LDPT, C, LDC, WORK, INFO ) */
/* CHARACTER VECT */
/* INTEGER INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC */
/* REAL AB( LDAB, * ), C( LDC, * ), D( * ), E( * ), */
/* $ PT( LDPT, * ), Q( LDQ, * ), WORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGBBRD reduces a real general m-by-n band matrix A to upper */
/* > bidiagonal form B by an orthogonal transformation: Q**T * A * P = B. */
/* > */
/* > The routine computes B, and optionally forms Q or P**T, or computes */
/* > Q**T*C for a given matrix C. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] VECT */
/* > \verbatim */
/* > VECT is CHARACTER*1 */
/* > Specifies whether or not the matrices Q and P**T are to be */
/* > formed. */
/* > = 'N': do not form Q or P**T; */
/* > = 'Q': form Q only; */
/* > = 'P': form P**T only; */
/* > = 'B': form both. */
/* > \endverbatim */
/* > */
/* > \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] NCC */
/* > \verbatim */
/* > NCC is INTEGER */
/* > The number of columns of the matrix C. NCC >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] KL */
/* > \verbatim */
/* > KL is INTEGER */
/* > The number of subdiagonals of the matrix A. KL >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] KU */
/* > \verbatim */
/* > KU is INTEGER */
/* > The number of superdiagonals of the matrix A. KU >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] AB */
/* > \verbatim */
/* > AB is REAL array, dimension (LDAB,N) */
/* > On entry, the m-by-n band matrix A, stored in rows 1 to */
/* > KL+KU+1. The j-th column of A is stored in the j-th column of */
/* > the array AB as follows: */
/* > AB(ku+1+i-j,j) = A(i,j) for f2cmax(1,j-ku)<=i<=f2cmin(m,j+kl). */
/* > On exit, A is overwritten by values generated during the */
/* > reduction. */
/* > \endverbatim */
/* > */
/* > \param[in] LDAB */
/* > \verbatim */
/* > LDAB is INTEGER */
/* > The leading dimension of the array A. LDAB >= KL+KU+1. */
/* > \endverbatim */
/* > */
/* > \param[out] D */
/* > \verbatim */
/* > D is REAL array, dimension (f2cmin(M,N)) */
/* > The diagonal elements of the bidiagonal matrix B. */
/* > \endverbatim */
/* > */
/* > \param[out] E */
/* > \verbatim */
/* > E is REAL array, dimension (f2cmin(M,N)-1) */
/* > The superdiagonal elements of the bidiagonal matrix B. */
/* > \endverbatim */
/* > */
/* > \param[out] Q */
/* > \verbatim */
/* > Q is REAL array, dimension (LDQ,M) */
/* > If VECT = 'Q' or 'B', the m-by-m orthogonal matrix Q. */
/* > If VECT = 'N' or 'P', the array Q is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDQ */
/* > \verbatim */
/* > LDQ is INTEGER */
/* > The leading dimension of the array Q. */
/* > LDQ >= f2cmax(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise. */
/* > \endverbatim */
/* > */
/* > \param[out] PT */
/* > \verbatim */
/* > PT is REAL array, dimension (LDPT,N) */
/* > If VECT = 'P' or 'B', the n-by-n orthogonal matrix P'. */
/* > If VECT = 'N' or 'Q', the array PT is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDPT */
/* > \verbatim */
/* > LDPT is INTEGER */
/* > The leading dimension of the array PT. */
/* > LDPT >= f2cmax(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise. */
/* > \endverbatim */
/* > */
/* > \param[in,out] C */
/* > \verbatim */
/* > C is REAL array, dimension (LDC,NCC) */
/* > On entry, an m-by-ncc matrix C. */
/* > On exit, C is overwritten by Q**T*C. */
/* > C is not referenced if NCC = 0. */
/* > \endverbatim */
/* > */
/* > \param[in] LDC */
/* > \verbatim */
/* > LDC is INTEGER */
/* > The leading dimension of the array C. */
/* > LDC >= f2cmax(1,M) if NCC > 0; LDC >= 1 if NCC = 0. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is REAL array, dimension (2*f2cmax(M,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 realGBcomputational */
/* ===================================================================== */
/* Subroutine */ void sgbbrd_(char *vect, integer *m, integer *n, integer *ncc,
integer *kl, integer *ku, real *ab, integer *ldab, real *d__, real *
e, real *q, integer *ldq, real *pt, integer *ldpt, real *c__, integer
*ldc, real *work, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, c_dim1, c_offset, pt_dim1, pt_offset, q_dim1,
q_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7;
/* Local variables */
integer inca;
extern /* Subroutine */ void srot_(integer *, real *, integer *, real *,
integer *, real *, real *);
integer i__, j, l;
extern logical lsame_(char *, char *);
logical wantb, wantc;
integer minmn;
logical wantq;
integer j1, j2, kb;
real ra, rb, rc;
integer kk, ml, mn, nr, mu;
real rs;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
extern void slaset_(
char *, integer *, integer *, real *, real *, real *, integer *), slartg_(real *, real *, real *, real *, real *);
integer kb1;
extern /* Subroutine */ void slargv_(integer *, real *, integer *, real *,
integer *, real *, integer *);
integer ml0;
extern /* Subroutine */ void slartv_(integer *, real *, integer *, real *,
integer *, real *, real *, integer *);
logical wantpt;
integer mu0, klm, kun, nrt, klu1;
/* -- 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 parameters */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1 * 1;
ab -= ab_offset;
--d__;
--e;
q_dim1 = *ldq;
q_offset = 1 + q_dim1 * 1;
q -= q_offset;
pt_dim1 = *ldpt;
pt_offset = 1 + pt_dim1 * 1;
pt -= pt_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
--work;
/* Function Body */
wantb = lsame_(vect, "B");
wantq = lsame_(vect, "Q") || wantb;
wantpt = lsame_(vect, "P") || wantb;
wantc = *ncc > 0;
klu1 = *kl + *ku + 1;
*info = 0;
if (! wantq && ! wantpt && ! lsame_(vect, "N")) {
*info = -1;
} else if (*m < 0) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*ncc < 0) {
*info = -4;
} else if (*kl < 0) {
*info = -5;
} else if (*ku < 0) {
*info = -6;
} else if (*ldab < klu1) {
*info = -8;
} else if (*ldq < 1 || wantq && *ldq < f2cmax(1,*m)) {
*info = -12;
} else if (*ldpt < 1 || wantpt && *ldpt < f2cmax(1,*n)) {
*info = -14;
} else if (*ldc < 1 || wantc && *ldc < f2cmax(1,*m)) {
*info = -16;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGBBRD", &i__1, (ftnlen)6);
return;
}
/* Initialize Q and P**T to the unit matrix, if needed */
if (wantq) {
slaset_("Full", m, m, &c_b8, &c_b9, &q[q_offset], ldq);
}
if (wantpt) {
slaset_("Full", n, n, &c_b8, &c_b9, &pt[pt_offset], ldpt);
}
/* Quick return if possible. */
if (*m == 0 || *n == 0) {
return;
}
minmn = f2cmin(*m,*n);
if (*kl + *ku > 1) {
/* Reduce to upper bidiagonal form if KU > 0; if KU = 0, reduce */
/* first to lower bidiagonal form and then transform to upper */
/* bidiagonal */
if (*ku > 0) {
ml0 = 1;
mu0 = 2;
} else {
ml0 = 2;
mu0 = 1;
}
/* Wherever possible, plane rotations are generated and applied in */
/* vector operations of length NR over the index set J1:J2:KLU1. */
/* The sines of the plane rotations are stored in WORK(1:f2cmax(m,n)) */
/* and the cosines in WORK(f2cmax(m,n)+1:2*f2cmax(m,n)). */
mn = f2cmax(*m,*n);
/* Computing MIN */
i__1 = *m - 1;
klm = f2cmin(i__1,*kl);
/* Computing MIN */
i__1 = *n - 1;
kun = f2cmin(i__1,*ku);
kb = klm + kun;
kb1 = kb + 1;
inca = kb1 * *ldab;
nr = 0;
j1 = klm + 2;
j2 = 1 - kun;
i__1 = minmn;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Reduce i-th column and i-th row of matrix to bidiagonal form */
ml = klm + 1;
mu = kun + 1;
i__2 = kb;
for (kk = 1; kk <= i__2; ++kk) {
j1 += kb;
j2 += kb;
/* generate plane rotations to annihilate nonzero elements */
/* which have been created below the band */
if (nr > 0) {
slargv_(&nr, &ab[klu1 + (j1 - klm - 1) * ab_dim1], &inca,
&work[j1], &kb1, &work[mn + j1], &kb1);
}
/* apply plane rotations from the left */
i__3 = kb;
for (l = 1; l <= i__3; ++l) {
if (j2 - klm + l - 1 > *n) {
nrt = nr - 1;
} else {
nrt = nr;
}
if (nrt > 0) {
slartv_(&nrt, &ab[klu1 - l + (j1 - klm + l - 1) *
ab_dim1], &inca, &ab[klu1 - l + 1 + (j1 - klm
+ l - 1) * ab_dim1], &inca, &work[mn + j1], &
work[j1], &kb1);
}
/* L10: */
}
if (ml > ml0) {
if (ml <= *m - i__ + 1) {
/* generate plane rotation to annihilate a(i+ml-1,i) */
/* within the band, and apply rotation from the left */
slartg_(&ab[*ku + ml - 1 + i__ * ab_dim1], &ab[*ku +
ml + i__ * ab_dim1], &work[mn + i__ + ml - 1],
&work[i__ + ml - 1], &ra);
ab[*ku + ml - 1 + i__ * ab_dim1] = ra;
if (i__ < *n) {
/* Computing MIN */
i__4 = *ku + ml - 2, i__5 = *n - i__;
i__3 = f2cmin(i__4,i__5);
i__6 = *ldab - 1;
i__7 = *ldab - 1;
srot_(&i__3, &ab[*ku + ml - 2 + (i__ + 1) *
ab_dim1], &i__6, &ab[*ku + ml - 1 + (i__
+ 1) * ab_dim1], &i__7, &work[mn + i__ +
ml - 1], &work[i__ + ml - 1]);
}
}
++nr;
j1 -= kb1;
}
if (wantq) {
/* accumulate product of plane rotations in Q */
i__3 = j2;
i__4 = kb1;
for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4)
{
srot_(m, &q[(j - 1) * q_dim1 + 1], &c__1, &q[j *
q_dim1 + 1], &c__1, &work[mn + j], &work[j]);
/* L20: */
}
}
if (wantc) {
/* apply plane rotations to C */
i__4 = j2;
i__3 = kb1;
for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3)
{
srot_(ncc, &c__[j - 1 + c_dim1], ldc, &c__[j + c_dim1]
, ldc, &work[mn + j], &work[j]);
/* L30: */
}
}
if (j2 + kun > *n) {
/* adjust J2 to keep within the bounds of the matrix */
--nr;
j2 -= kb1;
}
i__3 = j2;
i__4 = kb1;
for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
/* create nonzero element a(j-1,j+ku) above the band */
/* and store it in WORK(n+1:2*n) */
work[j + kun] = work[j] * ab[(j + kun) * ab_dim1 + 1];
ab[(j + kun) * ab_dim1 + 1] = work[mn + j] * ab[(j + kun)
* ab_dim1 + 1];
/* L40: */
}
/* generate plane rotations to annihilate nonzero elements */
/* which have been generated above the band */
if (nr > 0) {
slargv_(&nr, &ab[(j1 + kun - 1) * ab_dim1 + 1], &inca, &
work[j1 + kun], &kb1, &work[mn + j1 + kun], &kb1);
}
/* apply plane rotations from the right */
i__4 = kb;
for (l = 1; l <= i__4; ++l) {
if (j2 + l - 1 > *m) {
nrt = nr - 1;
} else {
nrt = nr;
}
if (nrt > 0) {
slartv_(&nrt, &ab[l + 1 + (j1 + kun - 1) * ab_dim1], &
inca, &ab[l + (j1 + kun) * ab_dim1], &inca, &
work[mn + j1 + kun], &work[j1 + kun], &kb1);
}
/* L50: */
}
if (ml == ml0 && mu > mu0) {
if (mu <= *n - i__ + 1) {
/* generate plane rotation to annihilate a(i,i+mu-1) */
/* within the band, and apply rotation from the right */
slartg_(&ab[*ku - mu + 3 + (i__ + mu - 2) * ab_dim1],
&ab[*ku - mu + 2 + (i__ + mu - 1) * ab_dim1],
&work[mn + i__ + mu - 1], &work[i__ + mu - 1],
&ra);
ab[*ku - mu + 3 + (i__ + mu - 2) * ab_dim1] = ra;
/* Computing MIN */
i__3 = *kl + mu - 2, i__5 = *m - i__;
i__4 = f2cmin(i__3,i__5);
srot_(&i__4, &ab[*ku - mu + 4 + (i__ + mu - 2) *
ab_dim1], &c__1, &ab[*ku - mu + 3 + (i__ + mu
- 1) * ab_dim1], &c__1, &work[mn + i__ + mu -
1], &work[i__ + mu - 1]);
}
++nr;
j1 -= kb1;
}
if (wantpt) {
/* accumulate product of plane rotations in P**T */
i__4 = j2;
i__3 = kb1;
for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3)
{
srot_(n, &pt[j + kun - 1 + pt_dim1], ldpt, &pt[j +
kun + pt_dim1], ldpt, &work[mn + j + kun], &
work[j + kun]);
/* L60: */
}
}
if (j2 + kb > *m) {
/* adjust J2 to keep within the bounds of the matrix */
--nr;
j2 -= kb1;
}
i__3 = j2;
i__4 = kb1;
for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
/* create nonzero element a(j+kl+ku,j+ku-1) below the */
/* band and store it in WORK(1:n) */
work[j + kb] = work[j + kun] * ab[klu1 + (j + kun) *
ab_dim1];
ab[klu1 + (j + kun) * ab_dim1] = work[mn + j + kun] * ab[
klu1 + (j + kun) * ab_dim1];
/* L70: */
}
if (ml > ml0) {
--ml;
} else {
--mu;
}
/* L80: */
}
/* L90: */
}
}
if (*ku == 0 && *kl > 0) {
/* A has been reduced to lower bidiagonal form */
/* Transform lower bidiagonal form to upper bidiagonal by applying */
/* plane rotations from the left, storing diagonal elements in D */
/* and off-diagonal elements in E */
/* Computing MIN */
i__2 = *m - 1;
i__1 = f2cmin(i__2,*n);
for (i__ = 1; i__ <= i__1; ++i__) {
slartg_(&ab[i__ * ab_dim1 + 1], &ab[i__ * ab_dim1 + 2], &rc, &rs,
&ra);
d__[i__] = ra;
if (i__ < *n) {
e[i__] = rs * ab[(i__ + 1) * ab_dim1 + 1];
ab[(i__ + 1) * ab_dim1 + 1] = rc * ab[(i__ + 1) * ab_dim1 + 1]
;
}
if (wantq) {
srot_(m, &q[i__ * q_dim1 + 1], &c__1, &q[(i__ + 1) * q_dim1 +
1], &c__1, &rc, &rs);
}
if (wantc) {
srot_(ncc, &c__[i__ + c_dim1], ldc, &c__[i__ + 1 + c_dim1],
ldc, &rc, &rs);
}
/* L100: */
}
if (*m <= *n) {
d__[*m] = ab[*m * ab_dim1 + 1];
}
} else if (*ku > 0) {
/* A has been reduced to upper bidiagonal form */
if (*m < *n) {
/* Annihilate a(m,m+1) by applying plane rotations from the */
/* right, storing diagonal elements in D and off-diagonal */
/* elements in E */
rb = ab[*ku + (*m + 1) * ab_dim1];
for (i__ = *m; i__ >= 1; --i__) {
slartg_(&ab[*ku + 1 + i__ * ab_dim1], &rb, &rc, &rs, &ra);
d__[i__] = ra;
if (i__ > 1) {
rb = -rs * ab[*ku + i__ * ab_dim1];
e[i__ - 1] = rc * ab[*ku + i__ * ab_dim1];
}
if (wantpt) {
srot_(n, &pt[i__ + pt_dim1], ldpt, &pt[*m + 1 + pt_dim1],
ldpt, &rc, &rs);
}
/* L110: */
}
} else {
/* Copy off-diagonal elements to E and diagonal elements to D */
i__1 = minmn - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
e[i__] = ab[*ku + (i__ + 1) * ab_dim1];
/* L120: */
}
i__1 = minmn;
for (i__ = 1; i__ <= i__1; ++i__) {
d__[i__] = ab[*ku + 1 + i__ * ab_dim1];
/* L130: */
}
}
} else {
/* A is diagonal. Set elements of E to zero and copy diagonal */
/* elements to D. */
i__1 = minmn - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
e[i__] = 0.f;
/* L140: */
}
i__1 = minmn;
for (i__ = 1; i__ <= i__1; ++i__) {
d__[i__] = ab[i__ * ab_dim1 + 1];
/* L150: */
}
}
return;
/* End of SGBBRD */
} /* sgbbrd_ */
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