1160 lines
31 KiB
C
1160 lines
31 KiB
C
#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;
|
|
|
|
/* > \brief \b DGBBRD */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DGBBRD + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgbbrd.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgbbrd.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgbbrd.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DGBBRD( 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 */
|
|
/* DOUBLE PRECISION AB( LDAB, * ), C( LDC, * ), D( * ), E( * ), */
|
|
/* $ PT( LDPT, * ), Q( LDQ, * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DGBBRD 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (f2cmin(M,N)) */
|
|
/* > The diagonal elements of the bidiagonal matrix B. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] E */
|
|
/* > \verbatim */
|
|
/* > E is DOUBLE PRECISION array, dimension (f2cmin(M,N)-1) */
|
|
/* > The superdiagonal elements of the bidiagonal matrix B. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] Q */
|
|
/* > \verbatim */
|
|
/* > Q is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 doubleGBcomputational */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dgbbrd_(char *vect, integer *m, integer *n, integer *ncc,
|
|
integer *kl, integer *ku, doublereal *ab, integer *ldab, doublereal *
|
|
d__, doublereal *e, doublereal *q, integer *ldq, doublereal *pt,
|
|
integer *ldpt, doublereal *c__, integer *ldc, doublereal *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 drot_(integer *, doublereal *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *);
|
|
integer i__, j, l;
|
|
extern logical lsame_(char *, char *);
|
|
logical wantb, wantc;
|
|
integer minmn;
|
|
logical wantq;
|
|
integer j1, j2, kb;
|
|
doublereal ra, rb;
|
|
integer kk;
|
|
doublereal rc;
|
|
integer ml, mn, nr, mu;
|
|
doublereal rs;
|
|
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 *), dlartv_(integer *, doublereal *,
|
|
integer *, doublereal *, integer *, doublereal *, doublereal *,
|
|
integer *);
|
|
integer kb1, ml0;
|
|
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_("DGBBRD", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Initialize Q and P**T to the unit matrix, if needed */
|
|
|
|
if (wantq) {
|
|
dlaset_("Full", m, m, &c_b8, &c_b9, &q[q_offset], ldq);
|
|
}
|
|
if (wantpt) {
|
|
dlaset_("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) {
|
|
dlargv_(&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) {
|
|
dlartv_(&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 */
|
|
|
|
dlartg_(&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;
|
|
drot_(&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)
|
|
{
|
|
drot_(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)
|
|
{
|
|
drot_(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) {
|
|
dlargv_(&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) {
|
|
dlartv_(&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 */
|
|
|
|
dlartg_(&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);
|
|
drot_(&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)
|
|
{
|
|
drot_(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__) {
|
|
dlartg_(&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) {
|
|
drot_(m, &q[i__ * q_dim1 + 1], &c__1, &q[(i__ + 1) * q_dim1 +
|
|
1], &c__1, &rc, &rs);
|
|
}
|
|
if (wantc) {
|
|
drot_(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__) {
|
|
dlartg_(&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) {
|
|
drot_(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.;
|
|
/* L140: */
|
|
}
|
|
i__1 = minmn;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
d__[i__] = ab[i__ * ab_dim1 + 1];
|
|
/* L150: */
|
|
}
|
|
}
|
|
return;
|
|
|
|
/* End of DGBBRD */
|
|
|
|
} /* dgbbrd_ */
|
|
|