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OpenBLAS/lapack-netlib/SRC/dsbgst.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 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);}
static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
#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++ */
#ifdef __cplusplus
typedef logical (*L_fp)(...);
#else
typedef logical (*L_fp)();
#endif
static float spow_ui(float x, integer n) {
float pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static double dpow_ui(double x, integer n) {
double pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#ifdef _MSC_VER
static _Fcomplex cpow_ui(complex x, integer n) {
complex pow={1.0,0.0}; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
for(u = n; ; ) {
if(u & 01) pow.r *= x.r, pow.i *= x.i;
if(u >>= 1) x.r *= x.r, x.i *= x.i;
else break;
}
}
_Fcomplex p={pow.r, pow.i};
return p;
}
#else
static _Complex float cpow_ui(_Complex float x, integer n) {
_Complex float pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#endif
#ifdef _MSC_VER
static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
_Dcomplex pow={1.0,0.0}; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
for(u = n; ; ) {
if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
else break;
}
}
_Dcomplex p = {pow._Val[0], pow._Val[1]};
return p;
}
#else
static _Complex double zpow_ui(_Complex double x, integer n) {
_Complex double pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#endif
static integer pow_ii(integer x, integer n) {
integer pow; unsigned long int u;
if (n <= 0) {
if (n == 0 || x == 1) pow = 1;
else if (x != -1) pow = x == 0 ? 1/x : 0;
else n = -n;
}
if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
u = n;
for(pow = 1; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static integer dmaxloc_(double *w, integer s, integer e, integer *n)
{
double m; integer i, mi;
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
if (w[i-1]>m) mi=i ,m=w[i-1];
return mi-s+1;
}
static integer smaxloc_(float *w, integer s, integer e, integer *n)
{
float m; integer i, mi;
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
if (w[i-1]>m) mi=i ,m=w[i-1];
return mi-s+1;
}
static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Fcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
}
}
pCf(z) = zdotc;
}
#else
_Complex float zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
}
}
pCf(z) = zdotc;
}
#endif
static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Dcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
}
}
pCd(z) = zdotc;
}
#else
_Complex double zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
}
}
pCd(z) = zdotc;
}
#endif
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Fcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
}
}
pCf(z) = zdotc;
}
#else
_Complex float zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cf(&x[i]) * Cf(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
}
}
pCf(z) = zdotc;
}
#endif
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Dcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
}
}
pCd(z) = zdotc;
}
#else
_Complex double zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cd(&x[i]) * Cd(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
}
}
pCd(z) = zdotc;
}
#endif
/* -- 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 doublereal c_b8 = 0.;
static doublereal c_b9 = 1.;
static integer c__1 = 1;
static doublereal c_b20 = -1.;
/* > \brief \b DSBGST */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DSBGST + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsbgst.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsbgst.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsbgst.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE DSBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, */
/* LDX, WORK, INFO ) */
/* CHARACTER UPLO, VECT */
/* INTEGER INFO, KA, KB, LDAB, LDBB, LDX, N */
/* DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), WORK( * ), */
/* $ X( LDX, * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > DSBGST reduces a real symmetric-definite banded generalized */
/* > eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, */
/* > such that C has the same bandwidth as A. */
/* > */
/* > B must have been previously factorized as S**T*S by DPBSTF, using a */
/* > split Cholesky factorization. A is overwritten by C = X**T*A*X, where */
/* > X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the */
/* > bandwidth of A. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] VECT */
/* > \verbatim */
/* > VECT is CHARACTER*1 */
/* > = 'N': do not form the transformation matrix X; */
/* > = 'V': form X. */
/* > \endverbatim */
/* > */
/* > \param[in] UPLO */
/* > \verbatim */
/* > UPLO is CHARACTER*1 */
/* > = 'U': Upper triangle of A is stored; */
/* > = 'L': Lower triangle of A is stored. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrices A and B. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] KA */
/* > \verbatim */
/* > KA is INTEGER */
/* > The number of superdiagonals of the matrix A if UPLO = 'U', */
/* > or the number of subdiagonals if UPLO = 'L'. KA >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] KB */
/* > \verbatim */
/* > KB is INTEGER */
/* > The number of superdiagonals of the matrix B if UPLO = 'U', */
/* > or the number of subdiagonals if UPLO = 'L'. KA >= KB >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] AB */
/* > \verbatim */
/* > AB is DOUBLE PRECISION array, dimension (LDAB,N) */
/* > On entry, the upper or lower triangle of the symmetric band */
/* > matrix A, stored in the first ka+1 rows of the array. The */
/* > j-th column of A is stored in the j-th column of the array AB */
/* > as follows: */
/* > if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for f2cmax(1,j-ka)<=i<=j; */
/* > if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=f2cmin(n,j+ka). */
/* > */
/* > On exit, the transformed matrix X**T*A*X, stored in the same */
/* > format as A. */
/* > \endverbatim */
/* > */
/* > \param[in] LDAB */
/* > \verbatim */
/* > LDAB is INTEGER */
/* > The leading dimension of the array AB. LDAB >= KA+1. */
/* > \endverbatim */
/* > */
/* > \param[in] BB */
/* > \verbatim */
/* > BB is DOUBLE PRECISION array, dimension (LDBB,N) */
/* > The banded factor S from the split Cholesky factorization of */
/* > B, as returned by DPBSTF, stored in the first KB+1 rows of */
/* > the array. */
/* > \endverbatim */
/* > */
/* > \param[in] LDBB */
/* > \verbatim */
/* > LDBB is INTEGER */
/* > The leading dimension of the array BB. LDBB >= KB+1. */
/* > \endverbatim */
/* > */
/* > \param[out] X */
/* > \verbatim */
/* > X is DOUBLE PRECISION array, dimension (LDX,N) */
/* > If VECT = 'V', the n-by-n matrix X. */
/* > If VECT = 'N', the array X is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDX */
/* > \verbatim */
/* > LDX is INTEGER */
/* > The leading dimension of the array X. */
/* > LDX >= f2cmax(1,N) if VECT = 'V'; LDX >= 1 otherwise. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is DOUBLE PRECISION 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 doubleOTHERcomputational */
/* ===================================================================== */
/* Subroutine */ void dsbgst_(char *vect, char *uplo, integer *n, integer *ka,
integer *kb, doublereal *ab, integer *ldab, doublereal *bb, integer *
ldbb, doublereal *x, integer *ldx, doublereal *work, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, bb_dim1, bb_offset, x_dim1, x_offset, i__1,
i__2, i__3, i__4;
doublereal d__1;
/* Local variables */
integer inca;
extern /* Subroutine */ void dger_(integer *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *), drot_(integer *, doublereal *, integer *, doublereal *
, integer *, doublereal *, doublereal *);
integer i__, j, k, l, m;
doublereal t;
extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *,
integer *);
extern logical lsame_(char *, char *);
integer i0, i1;
logical upper;
integer i2, j1, j2;
logical wantx;
extern /* Subroutine */ void dlar2v_(integer *, doublereal *, doublereal *,
doublereal *, integer *, doublereal *, doublereal *, integer *);
doublereal ra;
integer nr, nx;
extern /* Subroutine */ void dlaset_(char *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *),
dlartg_(doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *);
extern int xerbla_(char *, integer *, ftnlen);
extern void dlargv_(
integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *);
logical update;
extern /* Subroutine */ void dlartv_(integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *);
integer ka1, kb1;
doublereal ra1;
integer j1t, j2t;
doublereal bii;
integer kbt, nrt;
/* -- 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;
bb_dim1 = *ldbb;
bb_offset = 1 + bb_dim1 * 1;
bb -= bb_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1 * 1;
x -= x_offset;
--work;
/* Function Body */
wantx = lsame_(vect, "V");
upper = lsame_(uplo, "U");
ka1 = *ka + 1;
kb1 = *kb + 1;
*info = 0;
if (! wantx && ! lsame_(vect, "N")) {
*info = -1;
} else if (! upper && ! lsame_(uplo, "L")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*ka < 0) {
*info = -4;
} else if (*kb < 0 || *kb > *ka) {
*info = -5;
} else if (*ldab < *ka + 1) {
*info = -7;
} else if (*ldbb < *kb + 1) {
*info = -9;
} else if (*ldx < 1 || wantx && *ldx < f2cmax(1,*n)) {
*info = -11;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DSBGST", &i__1, (ftnlen)6);
return;
}
/* Quick return if possible */
if (*n == 0) {
return;
}
inca = *ldab * ka1;
/* Initialize X to the unit matrix, if needed */
if (wantx) {
dlaset_("Full", n, n, &c_b8, &c_b9, &x[x_offset], ldx);
}
/* Set M to the splitting point m. It must be the same value as is */
/* used in DPBSTF. The chosen value allows the arrays WORK and RWORK */
/* to be of dimension (N). */
m = (*n + *kb) / 2;
/* The routine works in two phases, corresponding to the two halves */
/* of the split Cholesky factorization of B as S**T*S where */
/* S = ( U ) */
/* ( M L ) */
/* with U upper triangular of order m, and L lower triangular of */
/* order n-m. S has the same bandwidth as B. */
/* S is treated as a product of elementary matrices: */
/* S = S(m)*S(m-1)*...*S(2)*S(1)*S(m+1)*S(m+2)*...*S(n-1)*S(n) */
/* where S(i) is determined by the i-th row of S. */
/* In phase 1, the index i takes the values n, n-1, ... , m+1; */
/* in phase 2, it takes the values 1, 2, ... , m. */
/* For each value of i, the current matrix A is updated by forming */
/* inv(S(i))**T*A*inv(S(i)). This creates a triangular bulge outside */
/* the band of A. The bulge is then pushed down toward the bottom of */
/* A in phase 1, and up toward the top of A in phase 2, by applying */
/* plane rotations. */
/* There are kb*(kb+1)/2 elements in the bulge, but at most 2*kb-1 */
/* of them are linearly independent, so annihilating a bulge requires */
/* only 2*kb-1 plane rotations. The rotations are divided into a 1st */
/* set of kb-1 rotations, and a 2nd set of kb rotations. */
/* Wherever possible, rotations are generated and applied in vector */
/* operations of length NR between the indices J1 and J2 (sometimes */
/* replaced by modified values NRT, J1T or J2T). */
/* The cosines and sines of the rotations are stored in the array */
/* WORK. The cosines of the 1st set of rotations are stored in */
/* elements n+2:n+m-kb-1 and the sines of the 1st set in elements */
/* 2:m-kb-1; the cosines of the 2nd set are stored in elements */
/* n+m-kb+1:2*n and the sines of the second set in elements m-kb+1:n. */
/* The bulges are not formed explicitly; nonzero elements outside the */
/* band are created only when they are required for generating new */
/* rotations; they are stored in the array WORK, in positions where */
/* they are later overwritten by the sines of the rotations which */
/* annihilate them. */
/* **************************** Phase 1 ***************************** */
/* The logical structure of this phase is: */
/* UPDATE = .TRUE. */
/* DO I = N, M + 1, -1 */
/* use S(i) to update A and create a new bulge */
/* apply rotations to push all bulges KA positions downward */
/* END DO */
/* UPDATE = .FALSE. */
/* DO I = M + KA + 1, N - 1 */
/* apply rotations to push all bulges KA positions downward */
/* END DO */
/* To avoid duplicating code, the two loops are merged. */
update = TRUE_;
i__ = *n + 1;
L10:
if (update) {
--i__;
/* Computing MIN */
i__1 = *kb, i__2 = i__ - 1;
kbt = f2cmin(i__1,i__2);
i0 = i__ - 1;
/* Computing MIN */
i__1 = *n, i__2 = i__ + *ka;
i1 = f2cmin(i__1,i__2);
i2 = i__ - kbt + ka1;
if (i__ < m + 1) {
update = FALSE_;
++i__;
i0 = m;
if (*ka == 0) {
goto L480;
}
goto L10;
}
} else {
i__ += *ka;
if (i__ > *n - 1) {
goto L480;
}
}
if (upper) {
/* Transform A, working with the upper triangle */
if (update) {
/* Form inv(S(i))**T * A * inv(S(i)) */
bii = bb[kb1 + i__ * bb_dim1];
i__1 = i1;
for (j = i__; j <= i__1; ++j) {
ab[i__ - j + ka1 + j * ab_dim1] /= bii;
/* L20: */
}
/* Computing MAX */
i__1 = 1, i__2 = i__ - *ka;
i__3 = i__;
for (j = f2cmax(i__1,i__2); j <= i__3; ++j) {
ab[j - i__ + ka1 + i__ * ab_dim1] /= bii;
/* L30: */
}
i__3 = i__ - 1;
for (k = i__ - kbt; k <= i__3; ++k) {
i__1 = k;
for (j = i__ - kbt; j <= i__1; ++j) {
ab[j - k + ka1 + k * ab_dim1] = ab[j - k + ka1 + k *
ab_dim1] - bb[j - i__ + kb1 + i__ * bb_dim1] * ab[
k - i__ + ka1 + i__ * ab_dim1] - bb[k - i__ + kb1
+ i__ * bb_dim1] * ab[j - i__ + ka1 + i__ *
ab_dim1] + ab[ka1 + i__ * ab_dim1] * bb[j - i__ +
kb1 + i__ * bb_dim1] * bb[k - i__ + kb1 + i__ *
bb_dim1];
/* L40: */
}
/* Computing MAX */
i__1 = 1, i__2 = i__ - *ka;
i__4 = i__ - kbt - 1;
for (j = f2cmax(i__1,i__2); j <= i__4; ++j) {
ab[j - k + ka1 + k * ab_dim1] -= bb[k - i__ + kb1 + i__ *
bb_dim1] * ab[j - i__ + ka1 + i__ * ab_dim1];
/* L50: */
}
/* L60: */
}
i__3 = i1;
for (j = i__; j <= i__3; ++j) {
/* Computing MAX */
i__4 = j - *ka, i__1 = i__ - kbt;
i__2 = i__ - 1;
for (k = f2cmax(i__4,i__1); k <= i__2; ++k) {
ab[k - j + ka1 + j * ab_dim1] -= bb[k - i__ + kb1 + i__ *
bb_dim1] * ab[i__ - j + ka1 + j * ab_dim1];
/* L70: */
}
/* L80: */
}
if (wantx) {
/* post-multiply X by inv(S(i)) */
i__3 = *n - m;
d__1 = 1. / bii;
dscal_(&i__3, &d__1, &x[m + 1 + i__ * x_dim1], &c__1);
if (kbt > 0) {
i__3 = *n - m;
dger_(&i__3, &kbt, &c_b20, &x[m + 1 + i__ * x_dim1], &
c__1, &bb[kb1 - kbt + i__ * bb_dim1], &c__1, &x[m
+ 1 + (i__ - kbt) * x_dim1], ldx);
}
}
/* store a(i,i1) in RA1 for use in next loop over K */
ra1 = ab[i__ - i1 + ka1 + i1 * ab_dim1];
}
/* Generate and apply vectors of rotations to chase all the */
/* existing bulges KA positions down toward the bottom of the */
/* band */
i__3 = *kb - 1;
for (k = 1; k <= i__3; ++k) {
if (update) {
/* Determine the rotations which would annihilate the bulge */
/* which has in theory just been created */
if (i__ - k + *ka < *n && i__ - k > 1) {
/* generate rotation to annihilate a(i,i-k+ka+1) */
dlartg_(&ab[k + 1 + (i__ - k + *ka) * ab_dim1], &ra1, &
work[*n + i__ - k + *ka - m], &work[i__ - k + *ka
- m], &ra);
/* create nonzero element a(i-k,i-k+ka+1) outside the */
/* band and store it in WORK(i-k) */
t = -bb[kb1 - k + i__ * bb_dim1] * ra1;
work[i__ - k] = work[*n + i__ - k + *ka - m] * t - work[
i__ - k + *ka - m] * ab[(i__ - k + *ka) * ab_dim1
+ 1];
ab[(i__ - k + *ka) * ab_dim1 + 1] = work[i__ - k + *ka -
m] * t + work[*n + i__ - k + *ka - m] * ab[(i__ -
k + *ka) * ab_dim1 + 1];
ra1 = ra;
}
}
/* Computing MAX */
i__2 = 1, i__4 = k - i0 + 2;
j2 = i__ - k - 1 + f2cmax(i__2,i__4) * ka1;
nr = (*n - j2 + *ka) / ka1;
j1 = j2 + (nr - 1) * ka1;
if (update) {
/* Computing MAX */
i__2 = j2, i__4 = i__ + (*ka << 1) - k + 1;
j2t = f2cmax(i__2,i__4);
} else {
j2t = j2;
}
nrt = (*n - j2t + *ka) / ka1;
i__2 = j1;
i__4 = ka1;
for (j = j2t; i__4 < 0 ? j >= i__2 : j <= i__2; j += i__4) {
/* create nonzero element a(j-ka,j+1) outside the band */
/* and store it in WORK(j-m) */
work[j - m] *= ab[(j + 1) * ab_dim1 + 1];
ab[(j + 1) * ab_dim1 + 1] = work[*n + j - m] * ab[(j + 1) *
ab_dim1 + 1];
/* L90: */
}
/* generate rotations in 1st set to annihilate elements which */
/* have been created outside the band */
if (nrt > 0) {
dlargv_(&nrt, &ab[j2t * ab_dim1 + 1], &inca, &work[j2t - m], &
ka1, &work[*n + j2t - m], &ka1);
}
if (nr > 0) {
/* apply rotations in 1st set from the right */
i__4 = *ka - 1;
for (l = 1; l <= i__4; ++l) {
dlartv_(&nr, &ab[ka1 - l + j2 * ab_dim1], &inca, &ab[*ka
- l + (j2 + 1) * ab_dim1], &inca, &work[*n + j2 -
m], &work[j2 - m], &ka1);
/* L100: */
}
/* apply rotations in 1st set from both sides to diagonal */
/* blocks */
dlar2v_(&nr, &ab[ka1 + j2 * ab_dim1], &ab[ka1 + (j2 + 1) *
ab_dim1], &ab[*ka + (j2 + 1) * ab_dim1], &inca, &work[
*n + j2 - m], &work[j2 - m], &ka1);
}
/* start applying rotations in 1st set from the left */
i__4 = *kb - k + 1;
for (l = *ka - 1; l >= i__4; --l) {
nrt = (*n - j2 + l) / ka1;
if (nrt > 0) {
dlartv_(&nrt, &ab[l + (j2 + ka1 - l) * ab_dim1], &inca, &
ab[l + 1 + (j2 + ka1 - l) * ab_dim1], &inca, &
work[*n + j2 - m], &work[j2 - m], &ka1);
}
/* L110: */
}
if (wantx) {
/* post-multiply X by product of rotations in 1st set */
i__4 = j1;
i__2 = ka1;
for (j = j2; i__2 < 0 ? j >= i__4 : j <= i__4; j += i__2) {
i__1 = *n - m;
drot_(&i__1, &x[m + 1 + j * x_dim1], &c__1, &x[m + 1 + (j
+ 1) * x_dim1], &c__1, &work[*n + j - m], &work[j
- m]);
/* L120: */
}
}
/* L130: */
}
if (update) {
if (i2 <= *n && kbt > 0) {
/* create nonzero element a(i-kbt,i-kbt+ka+1) outside the */
/* band and store it in WORK(i-kbt) */
work[i__ - kbt] = -bb[kb1 - kbt + i__ * bb_dim1] * ra1;
}
}
for (k = *kb; k >= 1; --k) {
if (update) {
/* Computing MAX */
i__3 = 2, i__2 = k - i0 + 1;
j2 = i__ - k - 1 + f2cmax(i__3,i__2) * ka1;
} else {
/* Computing MAX */
i__3 = 1, i__2 = k - i0 + 1;
j2 = i__ - k - 1 + f2cmax(i__3,i__2) * ka1;
}
/* finish applying rotations in 2nd set from the left */
for (l = *kb - k; l >= 1; --l) {
nrt = (*n - j2 + *ka + l) / ka1;
if (nrt > 0) {
dlartv_(&nrt, &ab[l + (j2 - l + 1) * ab_dim1], &inca, &ab[
l + 1 + (j2 - l + 1) * ab_dim1], &inca, &work[*n
+ j2 - *ka], &work[j2 - *ka], &ka1);
}
/* L140: */
}
nr = (*n - j2 + *ka) / ka1;
j1 = j2 + (nr - 1) * ka1;
i__3 = j2;
i__2 = -ka1;
for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j += i__2) {
work[j] = work[j - *ka];
work[*n + j] = work[*n + j - *ka];
/* L150: */
}
i__2 = j1;
i__3 = ka1;
for (j = j2; i__3 < 0 ? j >= i__2 : j <= i__2; j += i__3) {
/* create nonzero element a(j-ka,j+1) outside the band */
/* and store it in WORK(j) */
work[j] *= ab[(j + 1) * ab_dim1 + 1];
ab[(j + 1) * ab_dim1 + 1] = work[*n + j] * ab[(j + 1) *
ab_dim1 + 1];
/* L160: */
}
if (update) {
if (i__ - k < *n - *ka && k <= kbt) {
work[i__ - k + *ka] = work[i__ - k];
}
}
/* L170: */
}
for (k = *kb; k >= 1; --k) {
/* Computing MAX */
i__3 = 1, i__2 = k - i0 + 1;
j2 = i__ - k - 1 + f2cmax(i__3,i__2) * ka1;
nr = (*n - j2 + *ka) / ka1;
j1 = j2 + (nr - 1) * ka1;
if (nr > 0) {
/* generate rotations in 2nd set to annihilate elements */
/* which have been created outside the band */
dlargv_(&nr, &ab[j2 * ab_dim1 + 1], &inca, &work[j2], &ka1, &
work[*n + j2], &ka1);
/* apply rotations in 2nd set from the right */
i__3 = *ka - 1;
for (l = 1; l <= i__3; ++l) {
dlartv_(&nr, &ab[ka1 - l + j2 * ab_dim1], &inca, &ab[*ka
- l + (j2 + 1) * ab_dim1], &inca, &work[*n + j2],
&work[j2], &ka1);
/* L180: */
}
/* apply rotations in 2nd set from both sides to diagonal */
/* blocks */
dlar2v_(&nr, &ab[ka1 + j2 * ab_dim1], &ab[ka1 + (j2 + 1) *
ab_dim1], &ab[*ka + (j2 + 1) * ab_dim1], &inca, &work[
*n + j2], &work[j2], &ka1);
}
/* start applying rotations in 2nd set from the left */
i__3 = *kb - k + 1;
for (l = *ka - 1; l >= i__3; --l) {
nrt = (*n - j2 + l) / ka1;
if (nrt > 0) {
dlartv_(&nrt, &ab[l + (j2 + ka1 - l) * ab_dim1], &inca, &
ab[l + 1 + (j2 + ka1 - l) * ab_dim1], &inca, &
work[*n + j2], &work[j2], &ka1);
}
/* L190: */
}
if (wantx) {
/* post-multiply X by product of rotations in 2nd set */
i__3 = j1;
i__2 = ka1;
for (j = j2; i__2 < 0 ? j >= i__3 : j <= i__3; j += i__2) {
i__4 = *n - m;
drot_(&i__4, &x[m + 1 + j * x_dim1], &c__1, &x[m + 1 + (j
+ 1) * x_dim1], &c__1, &work[*n + j], &work[j]);
/* L200: */
}
}
/* L210: */
}
i__2 = *kb - 1;
for (k = 1; k <= i__2; ++k) {
/* Computing MAX */
i__3 = 1, i__4 = k - i0 + 2;
j2 = i__ - k - 1 + f2cmax(i__3,i__4) * ka1;
/* finish applying rotations in 1st set from the left */
for (l = *kb - k; l >= 1; --l) {
nrt = (*n - j2 + l) / ka1;
if (nrt > 0) {
dlartv_(&nrt, &ab[l + (j2 + ka1 - l) * ab_dim1], &inca, &
ab[l + 1 + (j2 + ka1 - l) * ab_dim1], &inca, &
work[*n + j2 - m], &work[j2 - m], &ka1);
}
/* L220: */
}
/* L230: */
}
if (*kb > 1) {
i__2 = i__ - *kb + (*ka << 1) + 1;
for (j = *n - 1; j >= i__2; --j) {
work[*n + j - m] = work[*n + j - *ka - m];
work[j - m] = work[j - *ka - m];
/* L240: */
}
}
} else {
/* Transform A, working with the lower triangle */
if (update) {
/* Form inv(S(i))**T * A * inv(S(i)) */
bii = bb[i__ * bb_dim1 + 1];
i__2 = i1;
for (j = i__; j <= i__2; ++j) {
ab[j - i__ + 1 + i__ * ab_dim1] /= bii;
/* L250: */
}
/* Computing MAX */
i__2 = 1, i__3 = i__ - *ka;
i__4 = i__;
for (j = f2cmax(i__2,i__3); j <= i__4; ++j) {
ab[i__ - j + 1 + j * ab_dim1] /= bii;
/* L260: */
}
i__4 = i__ - 1;
for (k = i__ - kbt; k <= i__4; ++k) {
i__2 = k;
for (j = i__ - kbt; j <= i__2; ++j) {
ab[k - j + 1 + j * ab_dim1] = ab[k - j + 1 + j * ab_dim1]
- bb[i__ - j + 1 + j * bb_dim1] * ab[i__ - k + 1
+ k * ab_dim1] - bb[i__ - k + 1 + k * bb_dim1] *
ab[i__ - j + 1 + j * ab_dim1] + ab[i__ * ab_dim1
+ 1] * bb[i__ - j + 1 + j * bb_dim1] * bb[i__ - k
+ 1 + k * bb_dim1];
/* L270: */
}
/* Computing MAX */
i__2 = 1, i__3 = i__ - *ka;
i__1 = i__ - kbt - 1;
for (j = f2cmax(i__2,i__3); j <= i__1; ++j) {
ab[k - j + 1 + j * ab_dim1] -= bb[i__ - k + 1 + k *
bb_dim1] * ab[i__ - j + 1 + j * ab_dim1];
/* L280: */
}
/* L290: */
}
i__4 = i1;
for (j = i__; j <= i__4; ++j) {
/* Computing MAX */
i__1 = j - *ka, i__2 = i__ - kbt;
i__3 = i__ - 1;
for (k = f2cmax(i__1,i__2); k <= i__3; ++k) {
ab[j - k + 1 + k * ab_dim1] -= bb[i__ - k + 1 + k *
bb_dim1] * ab[j - i__ + 1 + i__ * ab_dim1];
/* L300: */
}
/* L310: */
}
if (wantx) {
/* post-multiply X by inv(S(i)) */
i__4 = *n - m;
d__1 = 1. / bii;
dscal_(&i__4, &d__1, &x[m + 1 + i__ * x_dim1], &c__1);
if (kbt > 0) {
i__4 = *n - m;
i__3 = *ldbb - 1;
dger_(&i__4, &kbt, &c_b20, &x[m + 1 + i__ * x_dim1], &
c__1, &bb[kbt + 1 + (i__ - kbt) * bb_dim1], &i__3,
&x[m + 1 + (i__ - kbt) * x_dim1], ldx);
}
}
/* store a(i1,i) in RA1 for use in next loop over K */
ra1 = ab[i1 - i__ + 1 + i__ * ab_dim1];
}
/* Generate and apply vectors of rotations to chase all the */
/* existing bulges KA positions down toward the bottom of the */
/* band */
i__4 = *kb - 1;
for (k = 1; k <= i__4; ++k) {
if (update) {
/* Determine the rotations which would annihilate the bulge */
/* which has in theory just been created */
if (i__ - k + *ka < *n && i__ - k > 1) {
/* generate rotation to annihilate a(i-k+ka+1,i) */
dlartg_(&ab[ka1 - k + i__ * ab_dim1], &ra1, &work[*n +
i__ - k + *ka - m], &work[i__ - k + *ka - m], &ra)
;
/* create nonzero element a(i-k+ka+1,i-k) outside the */
/* band and store it in WORK(i-k) */
t = -bb[k + 1 + (i__ - k) * bb_dim1] * ra1;
work[i__ - k] = work[*n + i__ - k + *ka - m] * t - work[
i__ - k + *ka - m] * ab[ka1 + (i__ - k) * ab_dim1]
;
ab[ka1 + (i__ - k) * ab_dim1] = work[i__ - k + *ka - m] *
t + work[*n + i__ - k + *ka - m] * ab[ka1 + (i__
- k) * ab_dim1];
ra1 = ra;
}
}
/* Computing MAX */
i__3 = 1, i__1 = k - i0 + 2;
j2 = i__ - k - 1 + f2cmax(i__3,i__1) * ka1;
nr = (*n - j2 + *ka) / ka1;
j1 = j2 + (nr - 1) * ka1;
if (update) {
/* Computing MAX */
i__3 = j2, i__1 = i__ + (*ka << 1) - k + 1;
j2t = f2cmax(i__3,i__1);
} else {
j2t = j2;
}
nrt = (*n - j2t + *ka) / ka1;
i__3 = j1;
i__1 = ka1;
for (j = j2t; i__1 < 0 ? j >= i__3 : j <= i__3; j += i__1) {
/* create nonzero element a(j+1,j-ka) outside the band */
/* and store it in WORK(j-m) */
work[j - m] *= ab[ka1 + (j - *ka + 1) * ab_dim1];
ab[ka1 + (j - *ka + 1) * ab_dim1] = work[*n + j - m] * ab[ka1
+ (j - *ka + 1) * ab_dim1];
/* L320: */
}
/* generate rotations in 1st set to annihilate elements which */
/* have been created outside the band */
if (nrt > 0) {
dlargv_(&nrt, &ab[ka1 + (j2t - *ka) * ab_dim1], &inca, &work[
j2t - m], &ka1, &work[*n + j2t - m], &ka1);
}
if (nr > 0) {
/* apply rotations in 1st set from the left */
i__1 = *ka - 1;
for (l = 1; l <= i__1; ++l) {
dlartv_(&nr, &ab[l + 1 + (j2 - l) * ab_dim1], &inca, &ab[
l + 2 + (j2 - l) * ab_dim1], &inca, &work[*n + j2
- m], &work[j2 - m], &ka1);
/* L330: */
}
/* apply rotations in 1st set from both sides to diagonal */
/* blocks */
dlar2v_(&nr, &ab[j2 * ab_dim1 + 1], &ab[(j2 + 1) * ab_dim1 +
1], &ab[j2 * ab_dim1 + 2], &inca, &work[*n + j2 - m],
&work[j2 - m], &ka1);
}
/* start applying rotations in 1st set from the right */
i__1 = *kb - k + 1;
for (l = *ka - 1; l >= i__1; --l) {
nrt = (*n - j2 + l) / ka1;
if (nrt > 0) {
dlartv_(&nrt, &ab[ka1 - l + 1 + j2 * ab_dim1], &inca, &ab[
ka1 - l + (j2 + 1) * ab_dim1], &inca, &work[*n +
j2 - m], &work[j2 - m], &ka1);
}
/* L340: */
}
if (wantx) {
/* post-multiply X by product of rotations in 1st set */
i__1 = j1;
i__3 = ka1;
for (j = j2; i__3 < 0 ? j >= i__1 : j <= i__1; j += i__3) {
i__2 = *n - m;
drot_(&i__2, &x[m + 1 + j * x_dim1], &c__1, &x[m + 1 + (j
+ 1) * x_dim1], &c__1, &work[*n + j - m], &work[j
- m]);
/* L350: */
}
}
/* L360: */
}
if (update) {
if (i2 <= *n && kbt > 0) {
/* create nonzero element a(i-kbt+ka+1,i-kbt) outside the */
/* band and store it in WORK(i-kbt) */
work[i__ - kbt] = -bb[kbt + 1 + (i__ - kbt) * bb_dim1] * ra1;
}
}
for (k = *kb; k >= 1; --k) {
if (update) {
/* Computing MAX */
i__4 = 2, i__3 = k - i0 + 1;
j2 = i__ - k - 1 + f2cmax(i__4,i__3) * ka1;
} else {
/* Computing MAX */
i__4 = 1, i__3 = k - i0 + 1;
j2 = i__ - k - 1 + f2cmax(i__4,i__3) * ka1;
}
/* finish applying rotations in 2nd set from the right */
for (l = *kb - k; l >= 1; --l) {
nrt = (*n - j2 + *ka + l) / ka1;
if (nrt > 0) {
dlartv_(&nrt, &ab[ka1 - l + 1 + (j2 - *ka) * ab_dim1], &
inca, &ab[ka1 - l + (j2 - *ka + 1) * ab_dim1], &
inca, &work[*n + j2 - *ka], &work[j2 - *ka], &ka1)
;
}
/* L370: */
}
nr = (*n - j2 + *ka) / ka1;
j1 = j2 + (nr - 1) * ka1;
i__4 = j2;
i__3 = -ka1;
for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) {
work[j] = work[j - *ka];
work[*n + j] = work[*n + j - *ka];
/* L380: */
}
i__3 = j1;
i__4 = ka1;
for (j = j2; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
/* create nonzero element a(j+1,j-ka) outside the band */
/* and store it in WORK(j) */
work[j] *= ab[ka1 + (j - *ka + 1) * ab_dim1];
ab[ka1 + (j - *ka + 1) * ab_dim1] = work[*n + j] * ab[ka1 + (
j - *ka + 1) * ab_dim1];
/* L390: */
}
if (update) {
if (i__ - k < *n - *ka && k <= kbt) {
work[i__ - k + *ka] = work[i__ - k];
}
}
/* L400: */
}
for (k = *kb; k >= 1; --k) {
/* Computing MAX */
i__4 = 1, i__3 = k - i0 + 1;
j2 = i__ - k - 1 + f2cmax(i__4,i__3) * ka1;
nr = (*n - j2 + *ka) / ka1;
j1 = j2 + (nr - 1) * ka1;
if (nr > 0) {
/* generate rotations in 2nd set to annihilate elements */
/* which have been created outside the band */
dlargv_(&nr, &ab[ka1 + (j2 - *ka) * ab_dim1], &inca, &work[j2]
, &ka1, &work[*n + j2], &ka1);
/* apply rotations in 2nd set from the left */
i__4 = *ka - 1;
for (l = 1; l <= i__4; ++l) {
dlartv_(&nr, &ab[l + 1 + (j2 - l) * ab_dim1], &inca, &ab[
l + 2 + (j2 - l) * ab_dim1], &inca, &work[*n + j2]
, &work[j2], &ka1);
/* L410: */
}
/* apply rotations in 2nd set from both sides to diagonal */
/* blocks */
dlar2v_(&nr, &ab[j2 * ab_dim1 + 1], &ab[(j2 + 1) * ab_dim1 +
1], &ab[j2 * ab_dim1 + 2], &inca, &work[*n + j2], &
work[j2], &ka1);
}
/* start applying rotations in 2nd set from the right */
i__4 = *kb - k + 1;
for (l = *ka - 1; l >= i__4; --l) {
nrt = (*n - j2 + l) / ka1;
if (nrt > 0) {
dlartv_(&nrt, &ab[ka1 - l + 1 + j2 * ab_dim1], &inca, &ab[
ka1 - l + (j2 + 1) * ab_dim1], &inca, &work[*n +
j2], &work[j2], &ka1);
}
/* L420: */
}
if (wantx) {
/* post-multiply X by product of rotations in 2nd set */
i__4 = j1;
i__3 = ka1;
for (j = j2; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) {
i__1 = *n - m;
drot_(&i__1, &x[m + 1 + j * x_dim1], &c__1, &x[m + 1 + (j
+ 1) * x_dim1], &c__1, &work[*n + j], &work[j]);
/* L430: */
}
}
/* L440: */
}
i__3 = *kb - 1;
for (k = 1; k <= i__3; ++k) {
/* Computing MAX */
i__4 = 1, i__1 = k - i0 + 2;
j2 = i__ - k - 1 + f2cmax(i__4,i__1) * ka1;
/* finish applying rotations in 1st set from the right */
for (l = *kb - k; l >= 1; --l) {
nrt = (*n - j2 + l) / ka1;
if (nrt > 0) {
dlartv_(&nrt, &ab[ka1 - l + 1 + j2 * ab_dim1], &inca, &ab[
ka1 - l + (j2 + 1) * ab_dim1], &inca, &work[*n +
j2 - m], &work[j2 - m], &ka1);
}
/* L450: */
}
/* L460: */
}
if (*kb > 1) {
i__3 = i__ - *kb + (*ka << 1) + 1;
for (j = *n - 1; j >= i__3; --j) {
work[*n + j - m] = work[*n + j - *ka - m];
work[j - m] = work[j - *ka - m];
/* L470: */
}
}
}
goto L10;
L480:
/* **************************** Phase 2 ***************************** */
/* The logical structure of this phase is: */
/* UPDATE = .TRUE. */
/* DO I = 1, M */
/* use S(i) to update A and create a new bulge */
/* apply rotations to push all bulges KA positions upward */
/* END DO */
/* UPDATE = .FALSE. */
/* DO I = M - KA - 1, 2, -1 */
/* apply rotations to push all bulges KA positions upward */
/* END DO */
/* To avoid duplicating code, the two loops are merged. */
update = TRUE_;
i__ = 0;
L490:
if (update) {
++i__;
/* Computing MIN */
i__3 = *kb, i__4 = m - i__;
kbt = f2cmin(i__3,i__4);
i0 = i__ + 1;
/* Computing MAX */
i__3 = 1, i__4 = i__ - *ka;
i1 = f2cmax(i__3,i__4);
i2 = i__ + kbt - ka1;
if (i__ > m) {
update = FALSE_;
--i__;
i0 = m + 1;
if (*ka == 0) {
return;
}
goto L490;
}
} else {
i__ -= *ka;
if (i__ < 2) {
return;
}
}
if (i__ < m - kbt) {
nx = m;
} else {
nx = *n;
}
if (upper) {
/* Transform A, working with the upper triangle */
if (update) {
/* Form inv(S(i))**T * A * inv(S(i)) */
bii = bb[kb1 + i__ * bb_dim1];
i__3 = i__;
for (j = i1; j <= i__3; ++j) {
ab[j - i__ + ka1 + i__ * ab_dim1] /= bii;
/* L500: */
}
/* Computing MIN */
i__4 = *n, i__1 = i__ + *ka;
i__3 = f2cmin(i__4,i__1);
for (j = i__; j <= i__3; ++j) {
ab[i__ - j + ka1 + j * ab_dim1] /= bii;
/* L510: */
}
i__3 = i__ + kbt;
for (k = i__ + 1; k <= i__3; ++k) {
i__4 = i__ + kbt;
for (j = k; j <= i__4; ++j) {
ab[k - j + ka1 + j * ab_dim1] = ab[k - j + ka1 + j *
ab_dim1] - bb[i__ - j + kb1 + j * bb_dim1] * ab[
i__ - k + ka1 + k * ab_dim1] - bb[i__ - k + kb1 +
k * bb_dim1] * ab[i__ - j + ka1 + j * ab_dim1] +
ab[ka1 + i__ * ab_dim1] * bb[i__ - j + kb1 + j *
bb_dim1] * bb[i__ - k + kb1 + k * bb_dim1];
/* L520: */
}
/* Computing MIN */
i__1 = *n, i__2 = i__ + *ka;
i__4 = f2cmin(i__1,i__2);
for (j = i__ + kbt + 1; j <= i__4; ++j) {
ab[k - j + ka1 + j * ab_dim1] -= bb[i__ - k + kb1 + k *
bb_dim1] * ab[i__ - j + ka1 + j * ab_dim1];
/* L530: */
}
/* L540: */
}
i__3 = i__;
for (j = i1; j <= i__3; ++j) {
/* Computing MIN */
i__1 = j + *ka, i__2 = i__ + kbt;
i__4 = f2cmin(i__1,i__2);
for (k = i__ + 1; k <= i__4; ++k) {
ab[j - k + ka1 + k * ab_dim1] -= bb[i__ - k + kb1 + k *
bb_dim1] * ab[j - i__ + ka1 + i__ * ab_dim1];
/* L550: */
}
/* L560: */
}
if (wantx) {
/* post-multiply X by inv(S(i)) */
d__1 = 1. / bii;
dscal_(&nx, &d__1, &x[i__ * x_dim1 + 1], &c__1);
if (kbt > 0) {
i__3 = *ldbb - 1;
dger_(&nx, &kbt, &c_b20, &x[i__ * x_dim1 + 1], &c__1, &bb[
*kb + (i__ + 1) * bb_dim1], &i__3, &x[(i__ + 1) *
x_dim1 + 1], ldx);
}
}
/* store a(i1,i) in RA1 for use in next loop over K */
ra1 = ab[i1 - i__ + ka1 + i__ * ab_dim1];
}
/* Generate and apply vectors of rotations to chase all the */
/* existing bulges KA positions up toward the top of the band */
i__3 = *kb - 1;
for (k = 1; k <= i__3; ++k) {
if (update) {
/* Determine the rotations which would annihilate the bulge */
/* which has in theory just been created */
if (i__ + k - ka1 > 0 && i__ + k < m) {
/* generate rotation to annihilate a(i+k-ka-1,i) */
dlartg_(&ab[k + 1 + i__ * ab_dim1], &ra1, &work[*n + i__
+ k - *ka], &work[i__ + k - *ka], &ra);
/* create nonzero element a(i+k-ka-1,i+k) outside the */
/* band and store it in WORK(m-kb+i+k) */
t = -bb[kb1 - k + (i__ + k) * bb_dim1] * ra1;
work[m - *kb + i__ + k] = work[*n + i__ + k - *ka] * t -
work[i__ + k - *ka] * ab[(i__ + k) * ab_dim1 + 1];
ab[(i__ + k) * ab_dim1 + 1] = work[i__ + k - *ka] * t +
work[*n + i__ + k - *ka] * ab[(i__ + k) * ab_dim1
+ 1];
ra1 = ra;
}
}
/* Computing MAX */
i__4 = 1, i__1 = k + i0 - m + 1;
j2 = i__ + k + 1 - f2cmax(i__4,i__1) * ka1;
nr = (j2 + *ka - 1) / ka1;
j1 = j2 - (nr - 1) * ka1;
if (update) {
/* Computing MIN */
i__4 = j2, i__1 = i__ - (*ka << 1) + k - 1;
j2t = f2cmin(i__4,i__1);
} else {
j2t = j2;
}
nrt = (j2t + *ka - 1) / ka1;
i__4 = j2t;
i__1 = ka1;
for (j = j1; i__1 < 0 ? j >= i__4 : j <= i__4; j += i__1) {
/* create nonzero element a(j-1,j+ka) outside the band */
/* and store it in WORK(j) */
work[j] *= ab[(j + *ka - 1) * ab_dim1 + 1];
ab[(j + *ka - 1) * ab_dim1 + 1] = work[*n + j] * ab[(j + *ka
- 1) * ab_dim1 + 1];
/* L570: */
}
/* generate rotations in 1st set to annihilate elements which */
/* have been created outside the band */
if (nrt > 0) {
dlargv_(&nrt, &ab[(j1 + *ka) * ab_dim1 + 1], &inca, &work[j1],
&ka1, &work[*n + j1], &ka1);
}
if (nr > 0) {
/* apply rotations in 1st set from the left */
i__1 = *ka - 1;
for (l = 1; l <= i__1; ++l) {
dlartv_(&nr, &ab[ka1 - l + (j1 + l) * ab_dim1], &inca, &
ab[*ka - l + (j1 + l) * ab_dim1], &inca, &work[*n
+ j1], &work[j1], &ka1);
/* L580: */
}
/* apply rotations in 1st set from both sides to diagonal */
/* blocks */
dlar2v_(&nr, &ab[ka1 + j1 * ab_dim1], &ab[ka1 + (j1 - 1) *
ab_dim1], &ab[*ka + j1 * ab_dim1], &inca, &work[*n +
j1], &work[j1], &ka1);
}
/* start applying rotations in 1st set from the right */
i__1 = *kb - k + 1;
for (l = *ka - 1; l >= i__1; --l) {
nrt = (j2 + l - 1) / ka1;
j1t = j2 - (nrt - 1) * ka1;
if (nrt > 0) {
dlartv_(&nrt, &ab[l + j1t * ab_dim1], &inca, &ab[l + 1 + (
j1t - 1) * ab_dim1], &inca, &work[*n + j1t], &
work[j1t], &ka1);
}
/* L590: */
}
if (wantx) {
/* post-multiply X by product of rotations in 1st set */
i__1 = j2;
i__4 = ka1;
for (j = j1; i__4 < 0 ? j >= i__1 : j <= i__1; j += i__4) {
drot_(&nx, &x[j * x_dim1 + 1], &c__1, &x[(j - 1) * x_dim1
+ 1], &c__1, &work[*n + j], &work[j]);
/* L600: */
}
}
/* L610: */
}
if (update) {
if (i2 > 0 && kbt > 0) {
/* create nonzero element a(i+kbt-ka-1,i+kbt) outside the */
/* band and store it in WORK(m-kb+i+kbt) */
work[m - *kb + i__ + kbt] = -bb[kb1 - kbt + (i__ + kbt) *
bb_dim1] * ra1;
}
}
for (k = *kb; k >= 1; --k) {
if (update) {
/* Computing MAX */
i__3 = 2, i__4 = k + i0 - m;
j2 = i__ + k + 1 - f2cmax(i__3,i__4) * ka1;
} else {
/* Computing MAX */
i__3 = 1, i__4 = k + i0 - m;
j2 = i__ + k + 1 - f2cmax(i__3,i__4) * ka1;
}
/* finish applying rotations in 2nd set from the right */
for (l = *kb - k; l >= 1; --l) {
nrt = (j2 + *ka + l - 1) / ka1;
j1t = j2 - (nrt - 1) * ka1;
if (nrt > 0) {
dlartv_(&nrt, &ab[l + (j1t + *ka) * ab_dim1], &inca, &ab[
l + 1 + (j1t + *ka - 1) * ab_dim1], &inca, &work[*
n + m - *kb + j1t + *ka], &work[m - *kb + j1t + *
ka], &ka1);
}
/* L620: */
}
nr = (j2 + *ka - 1) / ka1;
j1 = j2 - (nr - 1) * ka1;
i__3 = j2;
i__4 = ka1;
for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
work[m - *kb + j] = work[m - *kb + j + *ka];
work[*n + m - *kb + j] = work[*n + m - *kb + j + *ka];
/* L630: */
}
i__4 = j2;
i__3 = ka1;
for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) {
/* create nonzero element a(j-1,j+ka) outside the band */
/* and store it in WORK(m-kb+j) */
work[m - *kb + j] *= ab[(j + *ka - 1) * ab_dim1 + 1];
ab[(j + *ka - 1) * ab_dim1 + 1] = work[*n + m - *kb + j] * ab[
(j + *ka - 1) * ab_dim1 + 1];
/* L640: */
}
if (update) {
if (i__ + k > ka1 && k <= kbt) {
work[m - *kb + i__ + k - *ka] = work[m - *kb + i__ + k];
}
}
/* L650: */
}
for (k = *kb; k >= 1; --k) {
/* Computing MAX */
i__3 = 1, i__4 = k + i0 - m;
j2 = i__ + k + 1 - f2cmax(i__3,i__4) * ka1;
nr = (j2 + *ka - 1) / ka1;
j1 = j2 - (nr - 1) * ka1;
if (nr > 0) {
/* generate rotations in 2nd set to annihilate elements */
/* which have been created outside the band */
dlargv_(&nr, &ab[(j1 + *ka) * ab_dim1 + 1], &inca, &work[m - *
kb + j1], &ka1, &work[*n + m - *kb + j1], &ka1);
/* apply rotations in 2nd set from the left */
i__3 = *ka - 1;
for (l = 1; l <= i__3; ++l) {
dlartv_(&nr, &ab[ka1 - l + (j1 + l) * ab_dim1], &inca, &
ab[*ka - l + (j1 + l) * ab_dim1], &inca, &work[*n
+ m - *kb + j1], &work[m - *kb + j1], &ka1);
/* L660: */
}
/* apply rotations in 2nd set from both sides to diagonal */
/* blocks */
dlar2v_(&nr, &ab[ka1 + j1 * ab_dim1], &ab[ka1 + (j1 - 1) *
ab_dim1], &ab[*ka + j1 * ab_dim1], &inca, &work[*n +
m - *kb + j1], &work[m - *kb + j1], &ka1);
}
/* start applying rotations in 2nd set from the right */
i__3 = *kb - k + 1;
for (l = *ka - 1; l >= i__3; --l) {
nrt = (j2 + l - 1) / ka1;
j1t = j2 - (nrt - 1) * ka1;
if (nrt > 0) {
dlartv_(&nrt, &ab[l + j1t * ab_dim1], &inca, &ab[l + 1 + (
j1t - 1) * ab_dim1], &inca, &work[*n + m - *kb +
j1t], &work[m - *kb + j1t], &ka1);
}
/* L670: */
}
if (wantx) {
/* post-multiply X by product of rotations in 2nd set */
i__3 = j2;
i__4 = ka1;
for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
drot_(&nx, &x[j * x_dim1 + 1], &c__1, &x[(j - 1) * x_dim1
+ 1], &c__1, &work[*n + m - *kb + j], &work[m - *
kb + j]);
/* L680: */
}
}
/* L690: */
}
i__4 = *kb - 1;
for (k = 1; k <= i__4; ++k) {
/* Computing MAX */
i__3 = 1, i__1 = k + i0 - m + 1;
j2 = i__ + k + 1 - f2cmax(i__3,i__1) * ka1;
/* finish applying rotations in 1st set from the right */
for (l = *kb - k; l >= 1; --l) {
nrt = (j2 + l - 1) / ka1;
j1t = j2 - (nrt - 1) * ka1;
if (nrt > 0) {
dlartv_(&nrt, &ab[l + j1t * ab_dim1], &inca, &ab[l + 1 + (
j1t - 1) * ab_dim1], &inca, &work[*n + j1t], &
work[j1t], &ka1);
}
/* L700: */
}
/* L710: */
}
if (*kb > 1) {
/* Computing MIN */
i__3 = i__ + *kb;
i__4 = f2cmin(i__3,m) - (*ka << 1) - 1;
for (j = 2; j <= i__4; ++j) {
work[*n + j] = work[*n + j + *ka];
work[j] = work[j + *ka];
/* L720: */
}
}
} else {
/* Transform A, working with the lower triangle */
if (update) {
/* Form inv(S(i))**T * A * inv(S(i)) */
bii = bb[i__ * bb_dim1 + 1];
i__4 = i__;
for (j = i1; j <= i__4; ++j) {
ab[i__ - j + 1 + j * ab_dim1] /= bii;
/* L730: */
}
/* Computing MIN */
i__3 = *n, i__1 = i__ + *ka;
i__4 = f2cmin(i__3,i__1);
for (j = i__; j <= i__4; ++j) {
ab[j - i__ + 1 + i__ * ab_dim1] /= bii;
/* L740: */
}
i__4 = i__ + kbt;
for (k = i__ + 1; k <= i__4; ++k) {
i__3 = i__ + kbt;
for (j = k; j <= i__3; ++j) {
ab[j - k + 1 + k * ab_dim1] = ab[j - k + 1 + k * ab_dim1]
- bb[j - i__ + 1 + i__ * bb_dim1] * ab[k - i__ +
1 + i__ * ab_dim1] - bb[k - i__ + 1 + i__ *
bb_dim1] * ab[j - i__ + 1 + i__ * ab_dim1] + ab[
i__ * ab_dim1 + 1] * bb[j - i__ + 1 + i__ *
bb_dim1] * bb[k - i__ + 1 + i__ * bb_dim1];
/* L750: */
}
/* Computing MIN */
i__1 = *n, i__2 = i__ + *ka;
i__3 = f2cmin(i__1,i__2);
for (j = i__ + kbt + 1; j <= i__3; ++j) {
ab[j - k + 1 + k * ab_dim1] -= bb[k - i__ + 1 + i__ *
bb_dim1] * ab[j - i__ + 1 + i__ * ab_dim1];
/* L760: */
}
/* L770: */
}
i__4 = i__;
for (j = i1; j <= i__4; ++j) {
/* Computing MIN */
i__1 = j + *ka, i__2 = i__ + kbt;
i__3 = f2cmin(i__1,i__2);
for (k = i__ + 1; k <= i__3; ++k) {
ab[k - j + 1 + j * ab_dim1] -= bb[k - i__ + 1 + i__ *
bb_dim1] * ab[i__ - j + 1 + j * ab_dim1];
/* L780: */
}
/* L790: */
}
if (wantx) {
/* post-multiply X by inv(S(i)) */
d__1 = 1. / bii;
dscal_(&nx, &d__1, &x[i__ * x_dim1 + 1], &c__1);
if (kbt > 0) {
dger_(&nx, &kbt, &c_b20, &x[i__ * x_dim1 + 1], &c__1, &bb[
i__ * bb_dim1 + 2], &c__1, &x[(i__ + 1) * x_dim1
+ 1], ldx);
}
}
/* store a(i,i1) in RA1 for use in next loop over K */
ra1 = ab[i__ - i1 + 1 + i1 * ab_dim1];
}
/* Generate and apply vectors of rotations to chase all the */
/* existing bulges KA positions up toward the top of the band */
i__4 = *kb - 1;
for (k = 1; k <= i__4; ++k) {
if (update) {
/* Determine the rotations which would annihilate the bulge */
/* which has in theory just been created */
if (i__ + k - ka1 > 0 && i__ + k < m) {
/* generate rotation to annihilate a(i,i+k-ka-1) */
dlartg_(&ab[ka1 - k + (i__ + k - *ka) * ab_dim1], &ra1, &
work[*n + i__ + k - *ka], &work[i__ + k - *ka], &
ra);
/* create nonzero element a(i+k,i+k-ka-1) outside the */
/* band and store it in WORK(m-kb+i+k) */
t = -bb[k + 1 + i__ * bb_dim1] * ra1;
work[m - *kb + i__ + k] = work[*n + i__ + k - *ka] * t -
work[i__ + k - *ka] * ab[ka1 + (i__ + k - *ka) *
ab_dim1];
ab[ka1 + (i__ + k - *ka) * ab_dim1] = work[i__ + k - *ka]
* t + work[*n + i__ + k - *ka] * ab[ka1 + (i__ +
k - *ka) * ab_dim1];
ra1 = ra;
}
}
/* Computing MAX */
i__3 = 1, i__1 = k + i0 - m + 1;
j2 = i__ + k + 1 - f2cmax(i__3,i__1) * ka1;
nr = (j2 + *ka - 1) / ka1;
j1 = j2 - (nr - 1) * ka1;
if (update) {
/* Computing MIN */
i__3 = j2, i__1 = i__ - (*ka << 1) + k - 1;
j2t = f2cmin(i__3,i__1);
} else {
j2t = j2;
}
nrt = (j2t + *ka - 1) / ka1;
i__3 = j2t;
i__1 = ka1;
for (j = j1; i__1 < 0 ? j >= i__3 : j <= i__3; j += i__1) {
/* create nonzero element a(j+ka,j-1) outside the band */
/* and store it in WORK(j) */
work[j] *= ab[ka1 + (j - 1) * ab_dim1];
ab[ka1 + (j - 1) * ab_dim1] = work[*n + j] * ab[ka1 + (j - 1)
* ab_dim1];
/* L800: */
}
/* generate rotations in 1st set to annihilate elements which */
/* have been created outside the band */
if (nrt > 0) {
dlargv_(&nrt, &ab[ka1 + j1 * ab_dim1], &inca, &work[j1], &ka1,
&work[*n + j1], &ka1);
}
if (nr > 0) {
/* apply rotations in 1st set from the right */
i__1 = *ka - 1;
for (l = 1; l <= i__1; ++l) {
dlartv_(&nr, &ab[l + 1 + j1 * ab_dim1], &inca, &ab[l + 2
+ (j1 - 1) * ab_dim1], &inca, &work[*n + j1], &
work[j1], &ka1);
/* L810: */
}
/* apply rotations in 1st set from both sides to diagonal */
/* blocks */
dlar2v_(&nr, &ab[j1 * ab_dim1 + 1], &ab[(j1 - 1) * ab_dim1 +
1], &ab[(j1 - 1) * ab_dim1 + 2], &inca, &work[*n + j1]
, &work[j1], &ka1);
}
/* start applying rotations in 1st set from the left */
i__1 = *kb - k + 1;
for (l = *ka - 1; l >= i__1; --l) {
nrt = (j2 + l - 1) / ka1;
j1t = j2 - (nrt - 1) * ka1;
if (nrt > 0) {
dlartv_(&nrt, &ab[ka1 - l + 1 + (j1t - ka1 + l) * ab_dim1]
, &inca, &ab[ka1 - l + (j1t - ka1 + l) * ab_dim1],
&inca, &work[*n + j1t], &work[j1t], &ka1);
}
/* L820: */
}
if (wantx) {
/* post-multiply X by product of rotations in 1st set */
i__1 = j2;
i__3 = ka1;
for (j = j1; i__3 < 0 ? j >= i__1 : j <= i__1; j += i__3) {
drot_(&nx, &x[j * x_dim1 + 1], &c__1, &x[(j - 1) * x_dim1
+ 1], &c__1, &work[*n + j], &work[j]);
/* L830: */
}
}
/* L840: */
}
if (update) {
if (i2 > 0 && kbt > 0) {
/* create nonzero element a(i+kbt,i+kbt-ka-1) outside the */
/* band and store it in WORK(m-kb+i+kbt) */
work[m - *kb + i__ + kbt] = -bb[kbt + 1 + i__ * bb_dim1] *
ra1;
}
}
for (k = *kb; k >= 1; --k) {
if (update) {
/* Computing MAX */
i__4 = 2, i__3 = k + i0 - m;
j2 = i__ + k + 1 - f2cmax(i__4,i__3) * ka1;
} else {
/* Computing MAX */
i__4 = 1, i__3 = k + i0 - m;
j2 = i__ + k + 1 - f2cmax(i__4,i__3) * ka1;
}
/* finish applying rotations in 2nd set from the left */
for (l = *kb - k; l >= 1; --l) {
nrt = (j2 + *ka + l - 1) / ka1;
j1t = j2 - (nrt - 1) * ka1;
if (nrt > 0) {
dlartv_(&nrt, &ab[ka1 - l + 1 + (j1t + l - 1) * ab_dim1],
&inca, &ab[ka1 - l + (j1t + l - 1) * ab_dim1], &
inca, &work[*n + m - *kb + j1t + *ka], &work[m - *
kb + j1t + *ka], &ka1);
}
/* L850: */
}
nr = (j2 + *ka - 1) / ka1;
j1 = j2 - (nr - 1) * ka1;
i__4 = j2;
i__3 = ka1;
for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) {
work[m - *kb + j] = work[m - *kb + j + *ka];
work[*n + m - *kb + j] = work[*n + m - *kb + j + *ka];
/* L860: */
}
i__3 = j2;
i__4 = ka1;
for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
/* create nonzero element a(j+ka,j-1) outside the band */
/* and store it in WORK(m-kb+j) */
work[m - *kb + j] *= ab[ka1 + (j - 1) * ab_dim1];
ab[ka1 + (j - 1) * ab_dim1] = work[*n + m - *kb + j] * ab[ka1
+ (j - 1) * ab_dim1];
/* L870: */
}
if (update) {
if (i__ + k > ka1 && k <= kbt) {
work[m - *kb + i__ + k - *ka] = work[m - *kb + i__ + k];
}
}
/* L880: */
}
for (k = *kb; k >= 1; --k) {
/* Computing MAX */
i__4 = 1, i__3 = k + i0 - m;
j2 = i__ + k + 1 - f2cmax(i__4,i__3) * ka1;
nr = (j2 + *ka - 1) / ka1;
j1 = j2 - (nr - 1) * ka1;
if (nr > 0) {
/* generate rotations in 2nd set to annihilate elements */
/* which have been created outside the band */
dlargv_(&nr, &ab[ka1 + j1 * ab_dim1], &inca, &work[m - *kb +
j1], &ka1, &work[*n + m - *kb + j1], &ka1);
/* apply rotations in 2nd set from the right */
i__4 = *ka - 1;
for (l = 1; l <= i__4; ++l) {
dlartv_(&nr, &ab[l + 1 + j1 * ab_dim1], &inca, &ab[l + 2
+ (j1 - 1) * ab_dim1], &inca, &work[*n + m - *kb
+ j1], &work[m - *kb + j1], &ka1);
/* L890: */
}
/* apply rotations in 2nd set from both sides to diagonal */
/* blocks */
dlar2v_(&nr, &ab[j1 * ab_dim1 + 1], &ab[(j1 - 1) * ab_dim1 +
1], &ab[(j1 - 1) * ab_dim1 + 2], &inca, &work[*n + m
- *kb + j1], &work[m - *kb + j1], &ka1);
}
/* start applying rotations in 2nd set from the left */
i__4 = *kb - k + 1;
for (l = *ka - 1; l >= i__4; --l) {
nrt = (j2 + l - 1) / ka1;
j1t = j2 - (nrt - 1) * ka1;
if (nrt > 0) {
dlartv_(&nrt, &ab[ka1 - l + 1 + (j1t - ka1 + l) * ab_dim1]
, &inca, &ab[ka1 - l + (j1t - ka1 + l) * ab_dim1],
&inca, &work[*n + m - *kb + j1t], &work[m - *kb
+ j1t], &ka1);
}
/* L900: */
}
if (wantx) {
/* post-multiply X by product of rotations in 2nd set */
i__4 = j2;
i__3 = ka1;
for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) {
drot_(&nx, &x[j * x_dim1 + 1], &c__1, &x[(j - 1) * x_dim1
+ 1], &c__1, &work[*n + m - *kb + j], &work[m - *
kb + j]);
/* L910: */
}
}
/* L920: */
}
i__3 = *kb - 1;
for (k = 1; k <= i__3; ++k) {
/* Computing MAX */
i__4 = 1, i__1 = k + i0 - m + 1;
j2 = i__ + k + 1 - f2cmax(i__4,i__1) * ka1;
/* finish applying rotations in 1st set from the left */
for (l = *kb - k; l >= 1; --l) {
nrt = (j2 + l - 1) / ka1;
j1t = j2 - (nrt - 1) * ka1;
if (nrt > 0) {
dlartv_(&nrt, &ab[ka1 - l + 1 + (j1t - ka1 + l) * ab_dim1]
, &inca, &ab[ka1 - l + (j1t - ka1 + l) * ab_dim1],
&inca, &work[*n + j1t], &work[j1t], &ka1);
}
/* L930: */
}
/* L940: */
}
if (*kb > 1) {
/* Computing MIN */
i__4 = i__ + *kb;
i__3 = f2cmin(i__4,m) - (*ka << 1) - 1;
for (j = 2; j <= i__3; ++j) {
work[*n + j] = work[*n + j + *ka];
work[j] = work[j + *ka];
/* L950: */
}
}
}
goto L490;
/* End of DSBGST */
} /* dsbgst_ */
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