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OpenBLAS/lapack-netlib/SRC/dbbcsd.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_b10 = -.125;
static doublereal c_b35 = -1.;
static integer c__1 = 1;
/* > \brief \b DBBCSD */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DBBCSD + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dbbcsd.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dbbcsd.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dbbcsd.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE DBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, */
/* THETA, PHI, U1, LDU1, U2, LDU2, V1T, LDV1T, */
/* V2T, LDV2T, B11D, B11E, B12D, B12E, B21D, B21E, */
/* B22D, B22E, WORK, LWORK, INFO ) */
/* CHARACTER JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS */
/* INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LWORK, M, P, Q */
/* DOUBLE PRECISION B11D( * ), B11E( * ), B12D( * ), B12E( * ), */
/* $ B21D( * ), B21E( * ), B22D( * ), B22E( * ), */
/* $ PHI( * ), THETA( * ), WORK( * ) */
/* DOUBLE PRECISION U1( LDU1, * ), U2( LDU2, * ), V1T( LDV1T, * ), */
/* $ V2T( LDV2T, * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > DBBCSD computes the CS decomposition of an orthogonal matrix in */
/* > bidiagonal-block form, */
/* > */
/* > */
/* > [ B11 | B12 0 0 ] */
/* > [ 0 | 0 -I 0 ] */
/* > X = [----------------] */
/* > [ B21 | B22 0 0 ] */
/* > [ 0 | 0 0 I ] */
/* > */
/* > [ C | -S 0 0 ] */
/* > [ U1 | ] [ 0 | 0 -I 0 ] [ V1 | ]**T */
/* > = [---------] [---------------] [---------] . */
/* > [ | U2 ] [ S | C 0 0 ] [ | V2 ] */
/* > [ 0 | 0 0 I ] */
/* > */
/* > X is M-by-M, its top-left block is P-by-Q, and Q must be no larger */
/* > than P, M-P, or M-Q. (If Q is not the smallest index, then X must be */
/* > transposed and/or permuted. This can be done in constant time using */
/* > the TRANS and SIGNS options. See DORCSD for details.) */
/* > */
/* > The bidiagonal matrices B11, B12, B21, and B22 are represented */
/* > implicitly by angles THETA(1:Q) and PHI(1:Q-1). */
/* > */
/* > The orthogonal matrices U1, U2, V1T, and V2T are input/output. */
/* > The input matrices are pre- or post-multiplied by the appropriate */
/* > singular vector matrices. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] JOBU1 */
/* > \verbatim */
/* > JOBU1 is CHARACTER */
/* > = 'Y': U1 is updated; */
/* > otherwise: U1 is not updated. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBU2 */
/* > \verbatim */
/* > JOBU2 is CHARACTER */
/* > = 'Y': U2 is updated; */
/* > otherwise: U2 is not updated. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBV1T */
/* > \verbatim */
/* > JOBV1T is CHARACTER */
/* > = 'Y': V1T is updated; */
/* > otherwise: V1T is not updated. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBV2T */
/* > \verbatim */
/* > JOBV2T is CHARACTER */
/* > = 'Y': V2T is updated; */
/* > otherwise: V2T is not updated. */
/* > \endverbatim */
/* > */
/* > \param[in] TRANS */
/* > \verbatim */
/* > TRANS is CHARACTER */
/* > = 'T': X, U1, U2, V1T, and V2T are stored in row-major */
/* > order; */
/* > otherwise: X, U1, U2, V1T, and V2T are stored in column- */
/* > major order. */
/* > \endverbatim */
/* > */
/* > \param[in] M */
/* > \verbatim */
/* > M is INTEGER */
/* > The number of rows and columns in X, the orthogonal matrix in */
/* > bidiagonal-block form. */
/* > \endverbatim */
/* > */
/* > \param[in] P */
/* > \verbatim */
/* > P is INTEGER */
/* > The number of rows in the top-left block of X. 0 <= P <= M. */
/* > \endverbatim */
/* > */
/* > \param[in] Q */
/* > \verbatim */
/* > Q is INTEGER */
/* > The number of columns in the top-left block of X. */
/* > 0 <= Q <= MIN(P,M-P,M-Q). */
/* > \endverbatim */
/* > */
/* > \param[in,out] THETA */
/* > \verbatim */
/* > THETA is DOUBLE PRECISION array, dimension (Q) */
/* > On entry, the angles THETA(1),...,THETA(Q) that, along with */
/* > PHI(1), ...,PHI(Q-1), define the matrix in bidiagonal-block */
/* > form. On exit, the angles whose cosines and sines define the */
/* > diagonal blocks in the CS decomposition. */
/* > \endverbatim */
/* > */
/* > \param[in,out] PHI */
/* > \verbatim */
/* > PHI is DOUBLE PRECISION array, dimension (Q-1) */
/* > The angles PHI(1),...,PHI(Q-1) that, along with THETA(1),..., */
/* > THETA(Q), define the matrix in bidiagonal-block form. */
/* > \endverbatim */
/* > */
/* > \param[in,out] U1 */
/* > \verbatim */
/* > U1 is DOUBLE PRECISION array, dimension (LDU1,P) */
/* > On entry, a P-by-P matrix. On exit, U1 is postmultiplied */
/* > by the left singular vector matrix common to [ B11 ; 0 ] and */
/* > [ B12 0 0 ; 0 -I 0 0 ]. */
/* > \endverbatim */
/* > */
/* > \param[in] LDU1 */
/* > \verbatim */
/* > LDU1 is INTEGER */
/* > The leading dimension of the array U1, LDU1 >= MAX(1,P). */
/* > \endverbatim */
/* > */
/* > \param[in,out] U2 */
/* > \verbatim */
/* > U2 is DOUBLE PRECISION array, dimension (LDU2,M-P) */
/* > On entry, an (M-P)-by-(M-P) matrix. On exit, U2 is */
/* > postmultiplied by the left singular vector matrix common to */
/* > [ B21 ; 0 ] and [ B22 0 0 ; 0 0 I ]. */
/* > \endverbatim */
/* > */
/* > \param[in] LDU2 */
/* > \verbatim */
/* > LDU2 is INTEGER */
/* > The leading dimension of the array U2, LDU2 >= MAX(1,M-P). */
/* > \endverbatim */
/* > */
/* > \param[in,out] V1T */
/* > \verbatim */
/* > V1T is DOUBLE PRECISION array, dimension (LDV1T,Q) */
/* > On entry, a Q-by-Q matrix. On exit, V1T is premultiplied */
/* > by the transpose of the right singular vector */
/* > matrix common to [ B11 ; 0 ] and [ B21 ; 0 ]. */
/* > \endverbatim */
/* > */
/* > \param[in] LDV1T */
/* > \verbatim */
/* > LDV1T is INTEGER */
/* > The leading dimension of the array V1T, LDV1T >= MAX(1,Q). */
/* > \endverbatim */
/* > */
/* > \param[in,out] V2T */
/* > \verbatim */
/* > V2T is DOUBLE PRECISION array, dimension (LDV2T,M-Q) */
/* > On entry, an (M-Q)-by-(M-Q) matrix. On exit, V2T is */
/* > premultiplied by the transpose of the right */
/* > singular vector matrix common to [ B12 0 0 ; 0 -I 0 ] and */
/* > [ B22 0 0 ; 0 0 I ]. */
/* > \endverbatim */
/* > */
/* > \param[in] LDV2T */
/* > \verbatim */
/* > LDV2T is INTEGER */
/* > The leading dimension of the array V2T, LDV2T >= MAX(1,M-Q). */
/* > \endverbatim */
/* > */
/* > \param[out] B11D */
/* > \verbatim */
/* > B11D is DOUBLE PRECISION array, dimension (Q) */
/* > When DBBCSD converges, B11D contains the cosines of THETA(1), */
/* > ..., THETA(Q). If DBBCSD fails to converge, then B11D */
/* > contains the diagonal of the partially reduced top-left */
/* > block. */
/* > \endverbatim */
/* > */
/* > \param[out] B11E */
/* > \verbatim */
/* > B11E is DOUBLE PRECISION array, dimension (Q-1) */
/* > When DBBCSD converges, B11E contains zeros. If DBBCSD fails */
/* > to converge, then B11E contains the superdiagonal of the */
/* > partially reduced top-left block. */
/* > \endverbatim */
/* > */
/* > \param[out] B12D */
/* > \verbatim */
/* > B12D is DOUBLE PRECISION array, dimension (Q) */
/* > When DBBCSD converges, B12D contains the negative sines of */
/* > THETA(1), ..., THETA(Q). If DBBCSD fails to converge, then */
/* > B12D contains the diagonal of the partially reduced top-right */
/* > block. */
/* > \endverbatim */
/* > */
/* > \param[out] B12E */
/* > \verbatim */
/* > B12E is DOUBLE PRECISION array, dimension (Q-1) */
/* > When DBBCSD converges, B12E contains zeros. If DBBCSD fails */
/* > to converge, then B12E contains the subdiagonal of the */
/* > partially reduced top-right block. */
/* > \endverbatim */
/* > */
/* > \param[out] B21D */
/* > \verbatim */
/* > B21D is DOUBLE PRECISION array, dimension (Q) */
/* > When DBBCSD converges, B21D contains the negative sines of */
/* > THETA(1), ..., THETA(Q). If DBBCSD fails to converge, then */
/* > B21D contains the diagonal of the partially reduced bottom-left */
/* > block. */
/* > \endverbatim */
/* > */
/* > \param[out] B21E */
/* > \verbatim */
/* > B21E is DOUBLE PRECISION array, dimension (Q-1) */
/* > When DBBCSD converges, B21E contains zeros. If DBBCSD fails */
/* > to converge, then B21E contains the subdiagonal of the */
/* > partially reduced bottom-left block. */
/* > \endverbatim */
/* > */
/* > \param[out] B22D */
/* > \verbatim */
/* > B22D is DOUBLE PRECISION array, dimension (Q) */
/* > When DBBCSD converges, B22D contains the negative sines of */
/* > THETA(1), ..., THETA(Q). If DBBCSD fails to converge, then */
/* > B22D contains the diagonal of the partially reduced bottom-right */
/* > block. */
/* > \endverbatim */
/* > */
/* > \param[out] B22E */
/* > \verbatim */
/* > B22E is DOUBLE PRECISION array, dimension (Q-1) */
/* > When DBBCSD converges, B22E contains zeros. If DBBCSD fails */
/* > to converge, then B22E contains the subdiagonal of the */
/* > partially reduced bottom-right block. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* > LWORK is INTEGER */
/* > The dimension of the array WORK. LWORK >= MAX(1,8*Q). */
/* > */
/* > If LWORK = -1, then a workspace query is assumed; the */
/* > routine only calculates the optimal size of the WORK array, */
/* > returns this value as the first entry of the work array, and */
/* > no error message related to LWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit. */
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > > 0: if DBBCSD did not converge, INFO specifies the number */
/* > of nonzero entries in PHI, and B11D, B11E, etc., */
/* > contain the partially reduced matrix. */
/* > \endverbatim */
/* > \par Internal Parameters: */
/* ========================= */
/* > */
/* > \verbatim */
/* > TOLMUL DOUBLE PRECISION, default = MAX(10,MIN(100,EPS**(-1/8))) */
/* > TOLMUL controls the convergence criterion of the QR loop. */
/* > Angles THETA(i), PHI(i) are rounded to 0 or PI/2 when they */
/* > are within TOLMUL*EPS of either bound. */
/* > \endverbatim */
/* > \par References: */
/* ================ */
/* > */
/* > [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. */
/* > Algorithms, 50(1):33-65, 2009. */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date June 2016 */
/* > \ingroup doubleOTHERcomputational */
/* ===================================================================== */
/* Subroutine */ void dbbcsd_(char *jobu1, char *jobu2, char *jobv1t, char *
jobv2t, char *trans, integer *m, integer *p, integer *q, doublereal *
theta, doublereal *phi, doublereal *u1, integer *ldu1, doublereal *u2,
integer *ldu2, doublereal *v1t, integer *ldv1t, doublereal *v2t,
integer *ldv2t, doublereal *b11d, doublereal *b11e, doublereal *b12d,
doublereal *b12e, doublereal *b21d, doublereal *b21e, doublereal *
b22d, doublereal *b22e, doublereal *work, integer *lwork, integer *
info)
{
/* System generated locals */
integer u1_dim1, u1_offset, u2_dim1, u2_offset, v1t_dim1, v1t_offset,
v2t_dim1, v2t_offset, i__1, i__2;
doublereal d__1, d__2, d__3, d__4;
/* Local variables */
integer imin, mini, imax, iter;
doublereal unfl, temp;
logical colmajor;
doublereal thetamin, thetamax;
logical restart11, restart12, restart21, restart22;
extern /* Subroutine */ void dlas2_(doublereal *, doublereal *, doublereal
*, doublereal *, doublereal *);
integer lworkmin, iu1cs, iu2cs, iu1sn, iu2sn, lworkopt, i__, j;
doublereal r__;
extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *,
integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ void dlasr_(char *, char *, char *, integer *,
integer *, doublereal *, doublereal *, doublereal *, integer *), dswap_(integer *, doublereal *, integer *
, doublereal *, integer *);
integer maxit;
doublereal dummy, x1, x2, y1, y2;
integer iv1tcs, iv2tcs;
logical wantu1, wantu2;
integer iv1tsn, iv2tsn;
extern doublereal dlamch_(char *);
doublereal mu, nu, sigma11, sigma21;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
doublereal thresh, tolmul;
extern /* Subroutine */ void mecago_();
logical lquery;
doublereal b11bulge;
logical wantv1t, wantv2t;
doublereal b12bulge, b21bulge, b22bulge, eps, tol;
extern /* Subroutine */ void dlartgp_(doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *), dlartgs_(doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *);
/* -- LAPACK computational routine (version 3.7.1) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* June 2016 */
/* =================================================================== */
/* Test input arguments */
/* Parameter adjustments */
--theta;
--phi;
u1_dim1 = *ldu1;
u1_offset = 1 + u1_dim1 * 1;
u1 -= u1_offset;
u2_dim1 = *ldu2;
u2_offset = 1 + u2_dim1 * 1;
u2 -= u2_offset;
v1t_dim1 = *ldv1t;
v1t_offset = 1 + v1t_dim1 * 1;
v1t -= v1t_offset;
v2t_dim1 = *ldv2t;
v2t_offset = 1 + v2t_dim1 * 1;
v2t -= v2t_offset;
--b11d;
--b11e;
--b12d;
--b12e;
--b21d;
--b21e;
--b22d;
--b22e;
--work;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
wantu1 = lsame_(jobu1, "Y");
wantu2 = lsame_(jobu2, "Y");
wantv1t = lsame_(jobv1t, "Y");
wantv2t = lsame_(jobv2t, "Y");
colmajor = ! lsame_(trans, "T");
if (*m < 0) {
*info = -6;
} else if (*p < 0 || *p > *m) {
*info = -7;
} else if (*q < 0 || *q > *m) {
*info = -8;
} else if (*q > *p || *q > *m - *p || *q > *m - *q) {
*info = -8;
} else if (wantu1 && *ldu1 < *p) {
*info = -12;
} else if (wantu2 && *ldu2 < *m - *p) {
*info = -14;
} else if (wantv1t && *ldv1t < *q) {
*info = -16;
} else if (wantv2t && *ldv2t < *m - *q) {
*info = -18;
}
/* Quick return if Q = 0 */
if (*info == 0 && *q == 0) {
lworkmin = 1;
work[1] = (doublereal) lworkmin;
return;
}
/* Compute workspace */
if (*info == 0) {
iu1cs = 1;
iu1sn = iu1cs + *q;
iu2cs = iu1sn + *q;
iu2sn = iu2cs + *q;
iv1tcs = iu2sn + *q;
iv1tsn = iv1tcs + *q;
iv2tcs = iv1tsn + *q;
iv2tsn = iv2tcs + *q;
lworkopt = iv2tsn + *q - 1;
lworkmin = lworkopt;
work[1] = (doublereal) lworkopt;
if (*lwork < lworkmin && ! lquery) {
*info = -28;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DBBCSD", &i__1, (ftnlen)6);
return;
} else if (lquery) {
return;
}
/* Get machine constants */
eps = dlamch_("Epsilon");
unfl = dlamch_("Safe minimum");
/* Computing MAX */
/* Computing MIN */
d__3 = 100., d__4 = pow_dd(&eps, &c_b10);
d__1 = 10., d__2 = f2cmin(d__3,d__4);
tolmul = f2cmax(d__1,d__2);
tol = tolmul * eps;
/* Computing MAX */
d__1 = tol, d__2 = *q * 6 * *q * unfl;
thresh = f2cmax(d__1,d__2);
/* Test for negligible sines or cosines */
i__1 = *q;
for (i__ = 1; i__ <= i__1; ++i__) {
if (theta[i__] < thresh) {
theta[i__] = 0.;
} else if (theta[i__] > 1.57079632679489662 - thresh) {
theta[i__] = 1.57079632679489662;
}
}
i__1 = *q - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
if (phi[i__] < thresh) {
phi[i__] = 0.;
} else if (phi[i__] > 1.57079632679489662 - thresh) {
phi[i__] = 1.57079632679489662;
}
}
/* Initial deflation */
imax = *q;
while(imax > 1) {
if (phi[imax - 1] != 0.) {
myexit_();
}
--imax;
}
imin = imax - 1;
if (imin > 1) {
while(phi[imin - 1] != 0.) {
--imin;
if (imin <= 1) {
myexit_();
}
}
}
/* Initialize iteration counter */
maxit = *q * 6 * *q;
iter = 0;
/* Begin main iteration loop */
while(imax > 1) {
/* Compute the matrix entries */
b11d[imin] = cos(theta[imin]);
b21d[imin] = -sin(theta[imin]);
i__1 = imax - 1;
for (i__ = imin; i__ <= i__1; ++i__) {
b11e[i__] = -sin(theta[i__]) * sin(phi[i__]);
b11d[i__ + 1] = cos(theta[i__ + 1]) * cos(phi[i__]);
b12d[i__] = sin(theta[i__]) * cos(phi[i__]);
b12e[i__] = cos(theta[i__ + 1]) * sin(phi[i__]);
b21e[i__] = -cos(theta[i__]) * sin(phi[i__]);
b21d[i__ + 1] = -sin(theta[i__ + 1]) * cos(phi[i__]);
b22d[i__] = cos(theta[i__]) * cos(phi[i__]);
b22e[i__] = -sin(theta[i__ + 1]) * sin(phi[i__]);
}
b12d[imax] = sin(theta[imax]);
b22d[imax] = cos(theta[imax]);
/* Abort if not converging; otherwise, increment ITER */
if (iter > maxit) {
*info = 0;
i__1 = *q;
for (i__ = 1; i__ <= i__1; ++i__) {
if (phi[i__] != 0.) {
++(*info);
}
}
return;
}
iter = iter + imax - imin;
/* Compute shifts */
thetamax = theta[imin];
thetamin = theta[imin];
i__1 = imax;
for (i__ = imin + 1; i__ <= i__1; ++i__) {
if (theta[i__] > thetamax) {
thetamax = theta[i__];
}
if (theta[i__] < thetamin) {
thetamin = theta[i__];
}
}
if (thetamax > 1.57079632679489662 - thresh) {
/* Zero on diagonals of B11 and B22; induce deflation with a */
/* zero shift */
mu = 0.;
nu = 1.;
} else if (thetamin < thresh) {
/* Zero on diagonals of B12 and B22; induce deflation with a */
/* zero shift */
mu = 1.;
nu = 0.;
} else {
/* Compute shifts for B11 and B21 and use the lesser */
dlas2_(&b11d[imax - 1], &b11e[imax - 1], &b11d[imax], &sigma11, &
dummy);
dlas2_(&b21d[imax - 1], &b21e[imax - 1], &b21d[imax], &sigma21, &
dummy);
if (sigma11 <= sigma21) {
mu = sigma11;
/* Computing 2nd power */
d__1 = mu;
nu = sqrt(1. - d__1 * d__1);
if (mu < thresh) {
mu = 0.;
nu = 1.;
}
} else {
nu = sigma21;
/* Computing 2nd power */
d__1 = nu;
mu = sqrt(1.f - d__1 * d__1);
if (nu < thresh) {
mu = 1.;
nu = 0.;
}
}
}
/* Rotate to produce bulges in B11 and B21 */
if (mu <= nu) {
dlartgs_(&b11d[imin], &b11e[imin], &mu, &work[iv1tcs + imin - 1],
&work[iv1tsn + imin - 1]);
} else {
dlartgs_(&b21d[imin], &b21e[imin], &nu, &work[iv1tcs + imin - 1],
&work[iv1tsn + imin - 1]);
}
temp = work[iv1tcs + imin - 1] * b11d[imin] + work[iv1tsn + imin - 1]
* b11e[imin];
b11e[imin] = work[iv1tcs + imin - 1] * b11e[imin] - work[iv1tsn +
imin - 1] * b11d[imin];
b11d[imin] = temp;
b11bulge = work[iv1tsn + imin - 1] * b11d[imin + 1];
b11d[imin + 1] = work[iv1tcs + imin - 1] * b11d[imin + 1];
temp = work[iv1tcs + imin - 1] * b21d[imin] + work[iv1tsn + imin - 1]
* b21e[imin];
b21e[imin] = work[iv1tcs + imin - 1] * b21e[imin] - work[iv1tsn +
imin - 1] * b21d[imin];
b21d[imin] = temp;
b21bulge = work[iv1tsn + imin - 1] * b21d[imin + 1];
b21d[imin + 1] = work[iv1tcs + imin - 1] * b21d[imin + 1];
/* Compute THETA(IMIN) */
/* Computing 2nd power */
d__1 = b21d[imin];
/* Computing 2nd power */
d__2 = b21bulge;
/* Computing 2nd power */
d__3 = b11d[imin];
/* Computing 2nd power */
d__4 = b11bulge;
theta[imin] = atan2(sqrt(d__1 * d__1 + d__2 * d__2), sqrt(d__3 * d__3
+ d__4 * d__4));
/* Chase the bulges in B11(IMIN+1,IMIN) and B21(IMIN+1,IMIN) */
/* Computing 2nd power */
d__1 = b11d[imin];
/* Computing 2nd power */
d__2 = b11bulge;
/* Computing 2nd power */
d__3 = thresh;
if (d__1 * d__1 + d__2 * d__2 > d__3 * d__3) {
dlartgp_(&b11bulge, &b11d[imin], &work[iu1sn + imin - 1], &work[
iu1cs + imin - 1], &r__);
} else if (mu <= nu) {
dlartgs_(&b11e[imin], &b11d[imin + 1], &mu, &work[iu1cs + imin -
1], &work[iu1sn + imin - 1]);
} else {
dlartgs_(&b12d[imin], &b12e[imin], &nu, &work[iu1cs + imin - 1], &
work[iu1sn + imin - 1]);
}
/* Computing 2nd power */
d__1 = b21d[imin];
/* Computing 2nd power */
d__2 = b21bulge;
/* Computing 2nd power */
d__3 = thresh;
if (d__1 * d__1 + d__2 * d__2 > d__3 * d__3) {
dlartgp_(&b21bulge, &b21d[imin], &work[iu2sn + imin - 1], &work[
iu2cs + imin - 1], &r__);
} else if (nu < mu) {
dlartgs_(&b21e[imin], &b21d[imin + 1], &nu, &work[iu2cs + imin -
1], &work[iu2sn + imin - 1]);
} else {
dlartgs_(&b22d[imin], &b22e[imin], &mu, &work[iu2cs + imin - 1], &
work[iu2sn + imin - 1]);
}
work[iu2cs + imin - 1] = -work[iu2cs + imin - 1];
work[iu2sn + imin - 1] = -work[iu2sn + imin - 1];
temp = work[iu1cs + imin - 1] * b11e[imin] + work[iu1sn + imin - 1] *
b11d[imin + 1];
b11d[imin + 1] = work[iu1cs + imin - 1] * b11d[imin + 1] - work[iu1sn
+ imin - 1] * b11e[imin];
b11e[imin] = temp;
if (imax > imin + 1) {
b11bulge = work[iu1sn + imin - 1] * b11e[imin + 1];
b11e[imin + 1] = work[iu1cs + imin - 1] * b11e[imin + 1];
}
temp = work[iu1cs + imin - 1] * b12d[imin] + work[iu1sn + imin - 1] *
b12e[imin];
b12e[imin] = work[iu1cs + imin - 1] * b12e[imin] - work[iu1sn + imin
- 1] * b12d[imin];
b12d[imin] = temp;
b12bulge = work[iu1sn + imin - 1] * b12d[imin + 1];
b12d[imin + 1] = work[iu1cs + imin - 1] * b12d[imin + 1];
temp = work[iu2cs + imin - 1] * b21e[imin] + work[iu2sn + imin - 1] *
b21d[imin + 1];
b21d[imin + 1] = work[iu2cs + imin - 1] * b21d[imin + 1] - work[iu2sn
+ imin - 1] * b21e[imin];
b21e[imin] = temp;
if (imax > imin + 1) {
b21bulge = work[iu2sn + imin - 1] * b21e[imin + 1];
b21e[imin + 1] = work[iu2cs + imin - 1] * b21e[imin + 1];
}
temp = work[iu2cs + imin - 1] * b22d[imin] + work[iu2sn + imin - 1] *
b22e[imin];
b22e[imin] = work[iu2cs + imin - 1] * b22e[imin] - work[iu2sn + imin
- 1] * b22d[imin];
b22d[imin] = temp;
b22bulge = work[iu2sn + imin - 1] * b22d[imin + 1];
b22d[imin + 1] = work[iu2cs + imin - 1] * b22d[imin + 1];
/* Inner loop: chase bulges from B11(IMIN,IMIN+2), */
/* B12(IMIN,IMIN+1), B21(IMIN,IMIN+2), and B22(IMIN,IMIN+1) to */
/* bottom-right */
i__1 = imax - 1;
for (i__ = imin + 1; i__ <= i__1; ++i__) {
/* Compute PHI(I-1) */
x1 = sin(theta[i__ - 1]) * b11e[i__ - 1] + cos(theta[i__ - 1]) *
b21e[i__ - 1];
x2 = sin(theta[i__ - 1]) * b11bulge + cos(theta[i__ - 1]) *
b21bulge;
y1 = sin(theta[i__ - 1]) * b12d[i__ - 1] + cos(theta[i__ - 1]) *
b22d[i__ - 1];
y2 = sin(theta[i__ - 1]) * b12bulge + cos(theta[i__ - 1]) *
b22bulge;
/* Computing 2nd power */
d__1 = x1;
/* Computing 2nd power */
d__2 = x2;
/* Computing 2nd power */
d__3 = y1;
/* Computing 2nd power */
d__4 = y2;
phi[i__ - 1] = atan2(sqrt(d__1 * d__1 + d__2 * d__2), sqrt(d__3 *
d__3 + d__4 * d__4));
/* Determine if there are bulges to chase or if a new direct */
/* summand has been reached */
/* Computing 2nd power */
d__1 = b11e[i__ - 1];
/* Computing 2nd power */
d__2 = b11bulge;
/* Computing 2nd power */
d__3 = thresh;
restart11 = d__1 * d__1 + d__2 * d__2 <= d__3 * d__3;
/* Computing 2nd power */
d__1 = b21e[i__ - 1];
/* Computing 2nd power */
d__2 = b21bulge;
/* Computing 2nd power */
d__3 = thresh;
restart21 = d__1 * d__1 + d__2 * d__2 <= d__3 * d__3;
/* Computing 2nd power */
d__1 = b12d[i__ - 1];
/* Computing 2nd power */
d__2 = b12bulge;
/* Computing 2nd power */
d__3 = thresh;
restart12 = d__1 * d__1 + d__2 * d__2 <= d__3 * d__3;
/* Computing 2nd power */
d__1 = b22d[i__ - 1];
/* Computing 2nd power */
d__2 = b22bulge;
/* Computing 2nd power */
d__3 = thresh;
restart22 = d__1 * d__1 + d__2 * d__2 <= d__3 * d__3;
/* If possible, chase bulges from B11(I-1,I+1), B12(I-1,I), */
/* B21(I-1,I+1), and B22(I-1,I). If necessary, restart bulge- */
/* chasing by applying the original shift again. */
if (! restart11 && ! restart21) {
dlartgp_(&x2, &x1, &work[iv1tsn + i__ - 1], &work[iv1tcs +
i__ - 1], &r__);
} else if (! restart11 && restart21) {
dlartgp_(&b11bulge, &b11e[i__ - 1], &work[iv1tsn + i__ - 1], &
work[iv1tcs + i__ - 1], &r__);
} else if (restart11 && ! restart21) {
dlartgp_(&b21bulge, &b21e[i__ - 1], &work[iv1tsn + i__ - 1], &
work[iv1tcs + i__ - 1], &r__);
} else if (mu <= nu) {
dlartgs_(&b11d[i__], &b11e[i__], &mu, &work[iv1tcs + i__ - 1],
&work[iv1tsn + i__ - 1]);
} else {
dlartgs_(&b21d[i__], &b21e[i__], &nu, &work[iv1tcs + i__ - 1],
&work[iv1tsn + i__ - 1]);
}
work[iv1tcs + i__ - 1] = -work[iv1tcs + i__ - 1];
work[iv1tsn + i__ - 1] = -work[iv1tsn + i__ - 1];
if (! restart12 && ! restart22) {
dlartgp_(&y2, &y1, &work[iv2tsn + i__ - 2], &work[iv2tcs +
i__ - 2], &r__);
} else if (! restart12 && restart22) {
dlartgp_(&b12bulge, &b12d[i__ - 1], &work[iv2tsn + i__ - 2], &
work[iv2tcs + i__ - 2], &r__);
} else if (restart12 && ! restart22) {
dlartgp_(&b22bulge, &b22d[i__ - 1], &work[iv2tsn + i__ - 2], &
work[iv2tcs + i__ - 2], &r__);
} else if (nu < mu) {
dlartgs_(&b12e[i__ - 1], &b12d[i__], &nu, &work[iv2tcs + i__
- 2], &work[iv2tsn + i__ - 2]);
} else {
dlartgs_(&b22e[i__ - 1], &b22d[i__], &mu, &work[iv2tcs + i__
- 2], &work[iv2tsn + i__ - 2]);
}
temp = work[iv1tcs + i__ - 1] * b11d[i__] + work[iv1tsn + i__ - 1]
* b11e[i__];
b11e[i__] = work[iv1tcs + i__ - 1] * b11e[i__] - work[iv1tsn +
i__ - 1] * b11d[i__];
b11d[i__] = temp;
b11bulge = work[iv1tsn + i__ - 1] * b11d[i__ + 1];
b11d[i__ + 1] = work[iv1tcs + i__ - 1] * b11d[i__ + 1];
temp = work[iv1tcs + i__ - 1] * b21d[i__] + work[iv1tsn + i__ - 1]
* b21e[i__];
b21e[i__] = work[iv1tcs + i__ - 1] * b21e[i__] - work[iv1tsn +
i__ - 1] * b21d[i__];
b21d[i__] = temp;
b21bulge = work[iv1tsn + i__ - 1] * b21d[i__ + 1];
b21d[i__ + 1] = work[iv1tcs + i__ - 1] * b21d[i__ + 1];
temp = work[iv2tcs + i__ - 2] * b12e[i__ - 1] + work[iv2tsn + i__
- 2] * b12d[i__];
b12d[i__] = work[iv2tcs + i__ - 2] * b12d[i__] - work[iv2tsn +
i__ - 2] * b12e[i__ - 1];
b12e[i__ - 1] = temp;
b12bulge = work[iv2tsn + i__ - 2] * b12e[i__];
b12e[i__] = work[iv2tcs + i__ - 2] * b12e[i__];
temp = work[iv2tcs + i__ - 2] * b22e[i__ - 1] + work[iv2tsn + i__
- 2] * b22d[i__];
b22d[i__] = work[iv2tcs + i__ - 2] * b22d[i__] - work[iv2tsn +
i__ - 2] * b22e[i__ - 1];
b22e[i__ - 1] = temp;
b22bulge = work[iv2tsn + i__ - 2] * b22e[i__];
b22e[i__] = work[iv2tcs + i__ - 2] * b22e[i__];
/* Compute THETA(I) */
x1 = cos(phi[i__ - 1]) * b11d[i__] + sin(phi[i__ - 1]) * b12e[i__
- 1];
x2 = cos(phi[i__ - 1]) * b11bulge + sin(phi[i__ - 1]) * b12bulge;
y1 = cos(phi[i__ - 1]) * b21d[i__] + sin(phi[i__ - 1]) * b22e[i__
- 1];
y2 = cos(phi[i__ - 1]) * b21bulge + sin(phi[i__ - 1]) * b22bulge;
/* Computing 2nd power */
d__1 = y1;
/* Computing 2nd power */
d__2 = y2;
/* Computing 2nd power */
d__3 = x1;
/* Computing 2nd power */
d__4 = x2;
theta[i__] = atan2(sqrt(d__1 * d__1 + d__2 * d__2), sqrt(d__3 *
d__3 + d__4 * d__4));
/* Determine if there are bulges to chase or if a new direct */
/* summand has been reached */
/* Computing 2nd power */
d__1 = b11d[i__];
/* Computing 2nd power */
d__2 = b11bulge;
/* Computing 2nd power */
d__3 = thresh;
restart11 = d__1 * d__1 + d__2 * d__2 <= d__3 * d__3;
/* Computing 2nd power */
d__1 = b12e[i__ - 1];
/* Computing 2nd power */
d__2 = b12bulge;
/* Computing 2nd power */
d__3 = thresh;
restart12 = d__1 * d__1 + d__2 * d__2 <= d__3 * d__3;
/* Computing 2nd power */
d__1 = b21d[i__];
/* Computing 2nd power */
d__2 = b21bulge;
/* Computing 2nd power */
d__3 = thresh;
restart21 = d__1 * d__1 + d__2 * d__2 <= d__3 * d__3;
/* Computing 2nd power */
d__1 = b22e[i__ - 1];
/* Computing 2nd power */
d__2 = b22bulge;
/* Computing 2nd power */
d__3 = thresh;
restart22 = d__1 * d__1 + d__2 * d__2 <= d__3 * d__3;
/* If possible, chase bulges from B11(I+1,I), B12(I+1,I-1), */
/* B21(I+1,I), and B22(I+1,I-1). If necessary, restart bulge- */
/* chasing by applying the original shift again. */
if (! restart11 && ! restart12) {
dlartgp_(&x2, &x1, &work[iu1sn + i__ - 1], &work[iu1cs + i__
- 1], &r__);
} else if (! restart11 && restart12) {
dlartgp_(&b11bulge, &b11d[i__], &work[iu1sn + i__ - 1], &work[
iu1cs + i__ - 1], &r__);
} else if (restart11 && ! restart12) {
dlartgp_(&b12bulge, &b12e[i__ - 1], &work[iu1sn + i__ - 1], &
work[iu1cs + i__ - 1], &r__);
} else if (mu <= nu) {
dlartgs_(&b11e[i__], &b11d[i__ + 1], &mu, &work[iu1cs + i__ -
1], &work[iu1sn + i__ - 1]);
} else {
dlartgs_(&b12d[i__], &b12e[i__], &nu, &work[iu1cs + i__ - 1],
&work[iu1sn + i__ - 1]);
}
if (! restart21 && ! restart22) {
dlartgp_(&y2, &y1, &work[iu2sn + i__ - 1], &work[iu2cs + i__
- 1], &r__);
} else if (! restart21 && restart22) {
dlartgp_(&b21bulge, &b21d[i__], &work[iu2sn + i__ - 1], &work[
iu2cs + i__ - 1], &r__);
} else if (restart21 && ! restart22) {
dlartgp_(&b22bulge, &b22e[i__ - 1], &work[iu2sn + i__ - 1], &
work[iu2cs + i__ - 1], &r__);
} else if (nu < mu) {
dlartgs_(&b21e[i__], &b21e[i__ + 1], &nu, &work[iu2cs + i__ -
1], &work[iu2sn + i__ - 1]);
} else {
dlartgs_(&b22d[i__], &b22e[i__], &mu, &work[iu2cs + i__ - 1],
&work[iu2sn + i__ - 1]);
}
work[iu2cs + i__ - 1] = -work[iu2cs + i__ - 1];
work[iu2sn + i__ - 1] = -work[iu2sn + i__ - 1];
temp = work[iu1cs + i__ - 1] * b11e[i__] + work[iu1sn + i__ - 1] *
b11d[i__ + 1];
b11d[i__ + 1] = work[iu1cs + i__ - 1] * b11d[i__ + 1] - work[
iu1sn + i__ - 1] * b11e[i__];
b11e[i__] = temp;
if (i__ < imax - 1) {
b11bulge = work[iu1sn + i__ - 1] * b11e[i__ + 1];
b11e[i__ + 1] = work[iu1cs + i__ - 1] * b11e[i__ + 1];
}
temp = work[iu2cs + i__ - 1] * b21e[i__] + work[iu2sn + i__ - 1] *
b21d[i__ + 1];
b21d[i__ + 1] = work[iu2cs + i__ - 1] * b21d[i__ + 1] - work[
iu2sn + i__ - 1] * b21e[i__];
b21e[i__] = temp;
if (i__ < imax - 1) {
b21bulge = work[iu2sn + i__ - 1] * b21e[i__ + 1];
b21e[i__ + 1] = work[iu2cs + i__ - 1] * b21e[i__ + 1];
}
temp = work[iu1cs + i__ - 1] * b12d[i__] + work[iu1sn + i__ - 1] *
b12e[i__];
b12e[i__] = work[iu1cs + i__ - 1] * b12e[i__] - work[iu1sn + i__
- 1] * b12d[i__];
b12d[i__] = temp;
b12bulge = work[iu1sn + i__ - 1] * b12d[i__ + 1];
b12d[i__ + 1] = work[iu1cs + i__ - 1] * b12d[i__ + 1];
temp = work[iu2cs + i__ - 1] * b22d[i__] + work[iu2sn + i__ - 1] *
b22e[i__];
b22e[i__] = work[iu2cs + i__ - 1] * b22e[i__] - work[iu2sn + i__
- 1] * b22d[i__];
b22d[i__] = temp;
b22bulge = work[iu2sn + i__ - 1] * b22d[i__ + 1];
b22d[i__ + 1] = work[iu2cs + i__ - 1] * b22d[i__ + 1];
}
/* Compute PHI(IMAX-1) */
x1 = sin(theta[imax - 1]) * b11e[imax - 1] + cos(theta[imax - 1]) *
b21e[imax - 1];
y1 = sin(theta[imax - 1]) * b12d[imax - 1] + cos(theta[imax - 1]) *
b22d[imax - 1];
y2 = sin(theta[imax - 1]) * b12bulge + cos(theta[imax - 1]) *
b22bulge;
/* Computing 2nd power */
d__1 = y1;
/* Computing 2nd power */
d__2 = y2;
phi[imax - 1] = atan2((abs(x1)), sqrt(d__1 * d__1 + d__2 * d__2));
/* Chase bulges from B12(IMAX-1,IMAX) and B22(IMAX-1,IMAX) */
/* Computing 2nd power */
d__1 = b12d[imax - 1];
/* Computing 2nd power */
d__2 = b12bulge;
/* Computing 2nd power */
d__3 = thresh;
restart12 = d__1 * d__1 + d__2 * d__2 <= d__3 * d__3;
/* Computing 2nd power */
d__1 = b22d[imax - 1];
/* Computing 2nd power */
d__2 = b22bulge;
/* Computing 2nd power */
d__3 = thresh;
restart22 = d__1 * d__1 + d__2 * d__2 <= d__3 * d__3;
if (! restart12 && ! restart22) {
dlartgp_(&y2, &y1, &work[iv2tsn + imax - 2], &work[iv2tcs + imax
- 2], &r__);
} else if (! restart12 && restart22) {
dlartgp_(&b12bulge, &b12d[imax - 1], &work[iv2tsn + imax - 2], &
work[iv2tcs + imax - 2], &r__);
} else if (restart12 && ! restart22) {
dlartgp_(&b22bulge, &b22d[imax - 1], &work[iv2tsn + imax - 2], &
work[iv2tcs + imax - 2], &r__);
} else if (nu < mu) {
dlartgs_(&b12e[imax - 1], &b12d[imax], &nu, &work[iv2tcs + imax -
2], &work[iv2tsn + imax - 2]);
} else {
dlartgs_(&b22e[imax - 1], &b22d[imax], &mu, &work[iv2tcs + imax -
2], &work[iv2tsn + imax - 2]);
}
temp = work[iv2tcs + imax - 2] * b12e[imax - 1] + work[iv2tsn + imax
- 2] * b12d[imax];
b12d[imax] = work[iv2tcs + imax - 2] * b12d[imax] - work[iv2tsn +
imax - 2] * b12e[imax - 1];
b12e[imax - 1] = temp;
temp = work[iv2tcs + imax - 2] * b22e[imax - 1] + work[iv2tsn + imax
- 2] * b22d[imax];
b22d[imax] = work[iv2tcs + imax - 2] * b22d[imax] - work[iv2tsn +
imax - 2] * b22e[imax - 1];
b22e[imax - 1] = temp;
/* Update singular vectors */
if (wantu1) {
if (colmajor) {
i__1 = imax - imin + 1;
dlasr_("R", "V", "F", p, &i__1, &work[iu1cs + imin - 1], &
work[iu1sn + imin - 1], &u1[imin * u1_dim1 + 1], ldu1);
} else {
i__1 = imax - imin + 1;
dlasr_("L", "V", "F", &i__1, p, &work[iu1cs + imin - 1], &
work[iu1sn + imin - 1], &u1[imin + u1_dim1], ldu1);
}
}
if (wantu2) {
if (colmajor) {
i__1 = *m - *p;
i__2 = imax - imin + 1;
dlasr_("R", "V", "F", &i__1, &i__2, &work[iu2cs + imin - 1], &
work[iu2sn + imin - 1], &u2[imin * u2_dim1 + 1], ldu2);
} else {
i__1 = imax - imin + 1;
i__2 = *m - *p;
dlasr_("L", "V", "F", &i__1, &i__2, &work[iu2cs + imin - 1], &
work[iu2sn + imin - 1], &u2[imin + u2_dim1], ldu2);
}
}
if (wantv1t) {
if (colmajor) {
i__1 = imax - imin + 1;
dlasr_("L", "V", "F", &i__1, q, &work[iv1tcs + imin - 1], &
work[iv1tsn + imin - 1], &v1t[imin + v1t_dim1], ldv1t);
} else {
i__1 = imax - imin + 1;
dlasr_("R", "V", "F", q, &i__1, &work[iv1tcs + imin - 1], &
work[iv1tsn + imin - 1], &v1t[imin * v1t_dim1 + 1],
ldv1t);
}
}
if (wantv2t) {
if (colmajor) {
i__1 = imax - imin + 1;
i__2 = *m - *q;
dlasr_("L", "V", "F", &i__1, &i__2, &work[iv2tcs + imin - 1],
&work[iv2tsn + imin - 1], &v2t[imin + v2t_dim1],
ldv2t);
} else {
i__1 = *m - *q;
i__2 = imax - imin + 1;
dlasr_("R", "V", "F", &i__1, &i__2, &work[iv2tcs + imin - 1],
&work[iv2tsn + imin - 1], &v2t[imin * v2t_dim1 + 1],
ldv2t);
}
}
/* Fix signs on B11(IMAX-1,IMAX) and B21(IMAX-1,IMAX) */
if (b11e[imax - 1] + b21e[imax - 1] > 0.) {
b11d[imax] = -b11d[imax];
b21d[imax] = -b21d[imax];
if (wantv1t) {
if (colmajor) {
dscal_(q, &c_b35, &v1t[imax + v1t_dim1], ldv1t);
} else {
dscal_(q, &c_b35, &v1t[imax * v1t_dim1 + 1], &c__1);
}
}
}
/* Compute THETA(IMAX) */
x1 = cos(phi[imax - 1]) * b11d[imax] + sin(phi[imax - 1]) * b12e[imax
- 1];
y1 = cos(phi[imax - 1]) * b21d[imax] + sin(phi[imax - 1]) * b22e[imax
- 1];
theta[imax] = atan2((abs(y1)), (abs(x1)));
/* Fix signs on B11(IMAX,IMAX), B12(IMAX,IMAX-1), B21(IMAX,IMAX), */
/* and B22(IMAX,IMAX-1) */
if (b11d[imax] + b12e[imax - 1] < 0.) {
b12d[imax] = -b12d[imax];
if (wantu1) {
if (colmajor) {
dscal_(p, &c_b35, &u1[imax * u1_dim1 + 1], &c__1);
} else {
dscal_(p, &c_b35, &u1[imax + u1_dim1], ldu1);
}
}
}
if (b21d[imax] + b22e[imax - 1] > 0.) {
b22d[imax] = -b22d[imax];
if (wantu2) {
if (colmajor) {
i__1 = *m - *p;
dscal_(&i__1, &c_b35, &u2[imax * u2_dim1 + 1], &c__1);
} else {
i__1 = *m - *p;
dscal_(&i__1, &c_b35, &u2[imax + u2_dim1], ldu2);
}
}
}
/* Fix signs on B12(IMAX,IMAX) and B22(IMAX,IMAX) */
if (b12d[imax] + b22d[imax] < 0.) {
if (wantv2t) {
if (colmajor) {
i__1 = *m - *q;
dscal_(&i__1, &c_b35, &v2t[imax + v2t_dim1], ldv2t);
} else {
i__1 = *m - *q;
dscal_(&i__1, &c_b35, &v2t[imax * v2t_dim1 + 1], &c__1);
}
}
}
/* Test for negligible sines or cosines */
i__1 = imax;
for (i__ = imin; i__ <= i__1; ++i__) {
if (theta[i__] < thresh) {
theta[i__] = 0.;
} else if (theta[i__] > 1.57079632679489662 - thresh) {
theta[i__] = 1.57079632679489662;
}
}
i__1 = imax - 1;
for (i__ = imin; i__ <= i__1; ++i__) {
if (phi[i__] < thresh) {
phi[i__] = 0.;
} else if (phi[i__] > 1.57079632679489662 - thresh) {
phi[i__] = 1.57079632679489662;
}
}
/* Deflate */
if (imax > 1) {
while(phi[imax - 1] == 0.) {
--imax;
if (imax <= 1) {
myexit_();
}
}
}
if (imin > imax - 1) {
imin = imax - 1;
}
if (imin > 1) {
while(phi[imin - 1] != 0.) {
--imin;
if (imin <= 1) {
myexit_();
}
}
}
/* Repeat main iteration loop */
}
/* Postprocessing: order THETA from least to greatest */
i__1 = *q;
for (i__ = 1; i__ <= i__1; ++i__) {
mini = i__;
thetamin = theta[i__];
i__2 = *q;
for (j = i__ + 1; j <= i__2; ++j) {
if (theta[j] < thetamin) {
mini = j;
thetamin = theta[j];
}
}
if (mini != i__) {
theta[mini] = theta[i__];
theta[i__] = thetamin;
if (colmajor) {
if (wantu1) {
dswap_(p, &u1[i__ * u1_dim1 + 1], &c__1, &u1[mini *
u1_dim1 + 1], &c__1);
}
if (wantu2) {
i__2 = *m - *p;
dswap_(&i__2, &u2[i__ * u2_dim1 + 1], &c__1, &u2[mini *
u2_dim1 + 1], &c__1);
}
if (wantv1t) {
dswap_(q, &v1t[i__ + v1t_dim1], ldv1t, &v1t[mini +
v1t_dim1], ldv1t);
}
if (wantv2t) {
i__2 = *m - *q;
dswap_(&i__2, &v2t[i__ + v2t_dim1], ldv2t, &v2t[mini +
v2t_dim1], ldv2t);
}
} else {
if (wantu1) {
dswap_(p, &u1[i__ + u1_dim1], ldu1, &u1[mini + u1_dim1],
ldu1);
}
if (wantu2) {
i__2 = *m - *p;
dswap_(&i__2, &u2[i__ + u2_dim1], ldu2, &u2[mini +
u2_dim1], ldu2);
}
if (wantv1t) {
dswap_(q, &v1t[i__ * v1t_dim1 + 1], &c__1, &v1t[mini *
v1t_dim1 + 1], &c__1);
}
if (wantv2t) {
i__2 = *m - *q;
dswap_(&i__2, &v2t[i__ * v2t_dim1 + 1], &c__1, &v2t[mini *
v2t_dim1 + 1], &c__1);
}
}
}
}
return;
/* End of DBBCSD */
} /* dbbcsd_ */
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