#include #include #include #include #include #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 int logical; typedef short int shortlogical; 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++ */ #define F2C_proc_par_types 1 #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 \brief \b CBBCSD */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download CBBCSD + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE CBBCSD( 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, RWORK, LRWORK, INFO ) */ /* CHARACTER JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS */ /* INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LRWORK, M, P, Q */ /* REAL B11D( * ), B11E( * ), B12D( * ), B12E( * ), */ /* $ B21D( * ), B21E( * ), B22D( * ), B22E( * ), */ /* $ PHI( * ), THETA( * ), RWORK( * ) */ /* COMPLEX U1( LDU1, * ), U2( LDU2, * ), V1T( LDV1T, * ), */ /* $ V2T( LDV2T, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > CBBCSD computes the CS decomposition of a unitary 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 | ]**H */ /* > = [---------] [---------------] [---------] . */ /* > [ | 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 CUNCSD for details.) */ /* > */ /* > The bidiagonal matrices B11, B12, B21, and B22 are represented */ /* > implicitly by angles THETA(1:Q) and PHI(1:Q-1). */ /* > */ /* > The unitary 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 unitary 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 REAL 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 REAL 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 COMPLEX 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 COMPLEX 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 COMPLEX array, dimension (LDV1T,Q) */ /* > On entry, a Q-by-Q matrix. On exit, V1T is premultiplied */ /* > by the conjugate 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 COMPLEX array, dimension (LDV2T,M-Q) */ /* > On entry, an (M-Q)-by-(M-Q) matrix. On exit, V2T is */ /* > premultiplied by the conjugate 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 REAL array, dimension (Q) */ /* > When CBBCSD converges, B11D contains the cosines of THETA(1), */ /* > ..., THETA(Q). If CBBCSD fails to converge, then B11D */ /* > contains the diagonal of the partially reduced top-left */ /* > block. */ /* > \endverbatim */ /* > */ /* > \param[out] B11E */ /* > \verbatim */ /* > B11E is REAL array, dimension (Q-1) */ /* > When CBBCSD converges, B11E contains zeros. If CBBCSD fails */ /* > to converge, then B11E contains the superdiagonal of the */ /* > partially reduced top-left block. */ /* > \endverbatim */ /* > */ /* > \param[out] B12D */ /* > \verbatim */ /* > B12D is REAL array, dimension (Q) */ /* > When CBBCSD converges, B12D contains the negative sines of */ /* > THETA(1), ..., THETA(Q). If CBBCSD fails to converge, then */ /* > B12D contains the diagonal of the partially reduced top-right */ /* > block. */ /* > \endverbatim */ /* > */ /* > \param[out] B12E */ /* > \verbatim */ /* > B12E is REAL array, dimension (Q-1) */ /* > When CBBCSD converges, B12E contains zeros. If CBBCSD fails */ /* > to converge, then B12E contains the subdiagonal of the */ /* > partially reduced top-right block. */ /* > \endverbatim */ /* > */ /* > \param[out] B21D */ /* > \verbatim */ /* > B21D is REAL array, dimension (Q) */ /* > When CBBCSD converges, B21D contains the negative sines of */ /* > THETA(1), ..., THETA(Q). If CBBCSD fails to converge, then */ /* > B21D contains the diagonal of the partially reduced bottom-left */ /* > block. */ /* > \endverbatim */ /* > */ /* > \param[out] B21E */ /* > \verbatim */ /* > B21E is REAL array, dimension (Q-1) */ /* > When CBBCSD converges, B21E contains zeros. If CBBCSD fails */ /* > to converge, then B21E contains the subdiagonal of the */ /* > partially reduced bottom-left block. */ /* > \endverbatim */ /* > */ /* > \param[out] B22D */ /* > \verbatim */ /* > B22D is REAL array, dimension (Q) */ /* > When CBBCSD converges, B22D contains the negative sines of */ /* > THETA(1), ..., THETA(Q). If CBBCSD fails to converge, then */ /* > B22D contains the diagonal of the partially reduced bottom-right */ /* > block. */ /* > \endverbatim */ /* > */ /* > \param[out] B22E */ /* > \verbatim */ /* > B22E is REAL array, dimension (Q-1) */ /* > When CBBCSD converges, B22E contains zeros. If CBBCSD fails */ /* > to converge, then B22E contains the subdiagonal of the */ /* > partially reduced bottom-right block. */ /* > \endverbatim */ /* > */ /* > \param[out] RWORK */ /* > \verbatim */ /* > RWORK is REAL array, dimension (MAX(1,LRWORK)) */ /* > On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. */ /* > \endverbatim */ /* > */ /* > \param[in] LRWORK */ /* > \verbatim */ /* > LRWORK is INTEGER */ /* > The dimension of the array RWORK. LRWORK >= MAX(1,8*Q). */ /* > */ /* > If LRWORK = -1, then a workspace query is assumed; the */ /* > routine only calculates the optimal size of the RWORK array, */ /* > returns this value as the first entry of the work array, and */ /* > no error message related to LRWORK 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 CBBCSD 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 REAL, 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 complexOTHERcomputational */ /* ===================================================================== */ /* Subroutine */ int cbbcsd_(char *jobu1, char *jobu2, char *jobv1t, char * jobv2t, char *trans, integer *m, integer *p, integer *q, real *theta, real *phi, complex *u1, integer *ldu1, complex *u2, integer *ldu2, complex *v1t, integer *ldv1t, complex *v2t, integer *ldv2t, real * b11d, real *b11e, real *b12d, real *b12e, real *b21d, real *b21e, real *b22d, real *b22e, real *rwork, integer *lrwork, 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; real r__1, r__2, r__3, r__4; doublereal d__1; /* Local variables */ integer imin, mini, imax, iter; real unfl, temp; logical colmajor; real thetamin, thetamax; logical restart11, restart12, restart21, restart22; integer iu1cs, iu2cs; extern /* Subroutine */ int slas2_(real *, real *, real *, real *, real *) ; integer iu1sn, iu2sn, i__, j; real r__; extern /* Subroutine */ int cscal_(integer *, complex *, complex *, integer *); extern logical lsame_(char *, char *); extern /* Subroutine */ int clasr_(char *, char *, char *, integer *, integer *, real *, real *, complex *, integer *), cswap_(integer *, complex *, integer *, complex *, integer *); integer maxit; real dummy, x1, x2, y1, y2; integer lrworkmin, iv1tcs, iv2tcs; logical wantu1, wantu2; integer lrworkopt, iv1tsn, iv2tsn; real mu, nu, sigma11, sigma21; extern real slamch_(char *); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); real thresh, tolmul; extern /* Subroutine */ int mecago_(); logical lquery; real b11bulge; logical wantv1t, wantv2t; real b12bulge, b21bulge, b22bulge, eps, tol; extern /* Subroutine */ int slartgp_(real *, real *, real *, real *, real *), slartgs_(real *, real *, real *, real *, real *); /* -- 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; --rwork; /* Function Body */ *info = 0; lquery = *lrwork == -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) { lrworkmin = 1; rwork[1] = (real) lrworkmin; return 0; } /* 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; lrworkopt = iv2tsn + *q - 1; lrworkmin = lrworkopt; rwork[1] = (real) lrworkopt; if (*lrwork < lrworkmin && ! lquery) { *info = -28; } } if (*info != 0) { i__1 = -(*info); xerbla_("CBBCSD", &i__1, (ftnlen)6); return 0; } else if (lquery) { return 0; } /* Get machine constants */ eps = slamch_("Epsilon"); unfl = slamch_("Safe minimum"); /* Computing MAX */ /* Computing MIN */ d__1 = (doublereal) eps; r__3 = 100.f, r__4 = pow_dd(&d__1, &c_b11); r__1 = 10.f, r__2 = f2cmin(r__3,r__4); tolmul = f2cmax(r__1,r__2); tol = tolmul * eps; /* Computing MAX */ r__1 = tol, r__2 = *q * 6 * *q * unfl; thresh = f2cmax(r__1,r__2); /* Test for negligible sines or cosines */ i__1 = *q; for (i__ = 1; i__ <= i__1; ++i__) { if (theta[i__] < thresh) { theta[i__] = 0.f; } else if (theta[i__] > 1.57079632679489662f - thresh) { theta[i__] = 1.57079632679489662f; } } i__1 = *q - 1; for (i__ = 1; i__ <= i__1; ++i__) { if (phi[i__] < thresh) { phi[i__] = 0.f; } else if (phi[i__] > 1.57079632679489662f - thresh) { phi[i__] = 1.57079632679489662f; } } /* Initial deflation */ imax = *q; while(imax > 1) { if (phi[imax - 1] != 0.f) { myexit_(); } --imax; } imin = imax - 1; if (imin > 1) { while(phi[imin - 1] != 0.f) { --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.f) { ++(*info); } } return 0; } 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 > 1.57079632679489662f - thresh) { /* Zero on diagonals of B11 and B22; induce deflation with a */ /* zero shift */ mu = 0.f; nu = 1.f; } else if (thetamin < thresh) { /* Zero on diagonals of B12 and B22; induce deflation with a */ /* zero shift */ mu = 1.f; nu = 0.f; } else { /* Compute shifts for B11 and B21 and use the lesser */ slas2_(&b11d[imax - 1], &b11e[imax - 1], &b11d[imax], &sigma11, & dummy); slas2_(&b21d[imax - 1], &b21e[imax - 1], &b21d[imax], &sigma21, & dummy); if (sigma11 <= sigma21) { mu = sigma11; /* Computing 2nd power */ r__1 = mu; nu = sqrt(1.f - r__1 * r__1); if (mu < thresh) { mu = 0.f; nu = 1.f; } } else { nu = sigma21; /* Computing 2nd power */ r__1 = nu; mu = sqrt(1.f - r__1 * r__1); if (nu < thresh) { mu = 1.f; nu = 0.f; } } } /* Rotate to produce bulges in B11 and B21 */ if (mu <= nu) { slartgs_(&b11d[imin], &b11e[imin], &mu, &rwork[iv1tcs + imin - 1], &rwork[iv1tsn + imin - 1]); } else { slartgs_(&b21d[imin], &b21e[imin], &nu, &rwork[iv1tcs + imin - 1], &rwork[iv1tsn + imin - 1]); } temp = rwork[iv1tcs + imin - 1] * b11d[imin] + rwork[iv1tsn + imin - 1] * b11e[imin]; b11e[imin] = rwork[iv1tcs + imin - 1] * b11e[imin] - rwork[iv1tsn + imin - 1] * b11d[imin]; b11d[imin] = temp; b11bulge = rwork[iv1tsn + imin - 1] * b11d[imin + 1]; b11d[imin + 1] = rwork[iv1tcs + imin - 1] * b11d[imin + 1]; temp = rwork[iv1tcs + imin - 1] * b21d[imin] + rwork[iv1tsn + imin - 1] * b21e[imin]; b21e[imin] = rwork[iv1tcs + imin - 1] * b21e[imin] - rwork[iv1tsn + imin - 1] * b21d[imin]; b21d[imin] = temp; b21bulge = rwork[iv1tsn + imin - 1] * b21d[imin + 1]; b21d[imin + 1] = rwork[iv1tcs + imin - 1] * b21d[imin + 1]; /* Compute THETA(IMIN) */ /* Computing 2nd power */ r__1 = b21d[imin]; /* Computing 2nd power */ r__2 = b21bulge; /* Computing 2nd power */ r__3 = b11d[imin]; /* Computing 2nd power */ r__4 = b11bulge; theta[imin] = atan2(sqrt(r__1 * r__1 + r__2 * r__2), sqrt(r__3 * r__3 + r__4 * r__4)); /* Chase the bulges in B11(IMIN+1,IMIN) and B21(IMIN+1,IMIN) */ /* Computing 2nd power */ r__1 = b11d[imin]; /* Computing 2nd power */ r__2 = b11bulge; /* Computing 2nd power */ r__3 = thresh; if (r__1 * r__1 + r__2 * r__2 > r__3 * r__3) { slartgp_(&b11bulge, &b11d[imin], &rwork[iu1sn + imin - 1], &rwork[ iu1cs + imin - 1], &r__); } else if (mu <= nu) { slartgs_(&b11e[imin], &b11d[imin + 1], &mu, &rwork[iu1cs + imin - 1], &rwork[iu1sn + imin - 1]); } else { slartgs_(&b12d[imin], &b12e[imin], &nu, &rwork[iu1cs + imin - 1], &rwork[iu1sn + imin - 1]); } /* Computing 2nd power */ r__1 = b21d[imin]; /* Computing 2nd power */ r__2 = b21bulge; /* Computing 2nd power */ r__3 = thresh; if (r__1 * r__1 + r__2 * r__2 > r__3 * r__3) { slartgp_(&b21bulge, &b21d[imin], &rwork[iu2sn + imin - 1], &rwork[ iu2cs + imin - 1], &r__); } else if (nu < mu) { slartgs_(&b21e[imin], &b21d[imin + 1], &nu, &rwork[iu2cs + imin - 1], &rwork[iu2sn + imin - 1]); } else { slartgs_(&b22d[imin], &b22e[imin], &mu, &rwork[iu2cs + imin - 1], &rwork[iu2sn + imin - 1]); } rwork[iu2cs + imin - 1] = -rwork[iu2cs + imin - 1]; rwork[iu2sn + imin - 1] = -rwork[iu2sn + imin - 1]; temp = rwork[iu1cs + imin - 1] * b11e[imin] + rwork[iu1sn + imin - 1] * b11d[imin + 1]; b11d[imin + 1] = rwork[iu1cs + imin - 1] * b11d[imin + 1] - rwork[ iu1sn + imin - 1] * b11e[imin]; b11e[imin] = temp; if (imax > imin + 1) { b11bulge = rwork[iu1sn + imin - 1] * b11e[imin + 1]; b11e[imin + 1] = rwork[iu1cs + imin - 1] * b11e[imin + 1]; } temp = rwork[iu1cs + imin - 1] * b12d[imin] + rwork[iu1sn + imin - 1] * b12e[imin]; b12e[imin] = rwork[iu1cs + imin - 1] * b12e[imin] - rwork[iu1sn + imin - 1] * b12d[imin]; b12d[imin] = temp; b12bulge = rwork[iu1sn + imin - 1] * b12d[imin + 1]; b12d[imin + 1] = rwork[iu1cs + imin - 1] * b12d[imin + 1]; temp = rwork[iu2cs + imin - 1] * b21e[imin] + rwork[iu2sn + imin - 1] * b21d[imin + 1]; b21d[imin + 1] = rwork[iu2cs + imin - 1] * b21d[imin + 1] - rwork[ iu2sn + imin - 1] * b21e[imin]; b21e[imin] = temp; if (imax > imin + 1) { b21bulge = rwork[iu2sn + imin - 1] * b21e[imin + 1]; b21e[imin + 1] = rwork[iu2cs + imin - 1] * b21e[imin + 1]; } temp = rwork[iu2cs + imin - 1] * b22d[imin] + rwork[iu2sn + imin - 1] * b22e[imin]; b22e[imin] = rwork[iu2cs + imin - 1] * b22e[imin] - rwork[iu2sn + imin - 1] * b22d[imin]; b22d[imin] = temp; b22bulge = rwork[iu2sn + imin - 1] * b22d[imin + 1]; b22d[imin + 1] = rwork[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 */ r__1 = x1; /* Computing 2nd power */ r__2 = x2; /* Computing 2nd power */ r__3 = y1; /* Computing 2nd power */ r__4 = y2; phi[i__ - 1] = atan2(sqrt(r__1 * r__1 + r__2 * r__2), sqrt(r__3 * r__3 + r__4 * r__4)); /* Determine if there are bulges to chase or if a new direct */ /* summand has been reached */ /* Computing 2nd power */ r__1 = b11e[i__ - 1]; /* Computing 2nd power */ r__2 = b11bulge; /* Computing 2nd power */ r__3 = thresh; restart11 = r__1 * r__1 + r__2 * r__2 <= r__3 * r__3; /* Computing 2nd power */ r__1 = b21e[i__ - 1]; /* Computing 2nd power */ r__2 = b21bulge; /* Computing 2nd power */ r__3 = thresh; restart21 = r__1 * r__1 + r__2 * r__2 <= r__3 * r__3; /* Computing 2nd power */ r__1 = b12d[i__ - 1]; /* Computing 2nd power */ r__2 = b12bulge; /* Computing 2nd power */ r__3 = thresh; restart12 = r__1 * r__1 + r__2 * r__2 <= r__3 * r__3; /* Computing 2nd power */ r__1 = b22d[i__ - 1]; /* Computing 2nd power */ r__2 = b22bulge; /* Computing 2nd power */ r__3 = thresh; restart22 = r__1 * r__1 + r__2 * r__2 <= r__3 * r__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) { slartgp_(&x2, &x1, &rwork[iv1tsn + i__ - 1], &rwork[iv1tcs + i__ - 1], &r__); } else if (! restart11 && restart21) { slartgp_(&b11bulge, &b11e[i__ - 1], &rwork[iv1tsn + i__ - 1], &rwork[iv1tcs + i__ - 1], &r__); } else if (restart11 && ! restart21) { slartgp_(&b21bulge, &b21e[i__ - 1], &rwork[iv1tsn + i__ - 1], &rwork[iv1tcs + i__ - 1], &r__); } else if (mu <= nu) { slartgs_(&b11d[i__], &b11e[i__], &mu, &rwork[iv1tcs + i__ - 1] , &rwork[iv1tsn + i__ - 1]); } else { slartgs_(&b21d[i__], &b21e[i__], &nu, &rwork[iv1tcs + i__ - 1] , &rwork[iv1tsn + i__ - 1]); } rwork[iv1tcs + i__ - 1] = -rwork[iv1tcs + i__ - 1]; rwork[iv1tsn + i__ - 1] = -rwork[iv1tsn + i__ - 1]; if (! restart12 && ! restart22) { slartgp_(&y2, &y1, &rwork[iv2tsn + i__ - 2], &rwork[iv2tcs + i__ - 2], &r__); } else if (! restart12 && restart22) { slartgp_(&b12bulge, &b12d[i__ - 1], &rwork[iv2tsn + i__ - 2], &rwork[iv2tcs + i__ - 2], &r__); } else if (restart12 && ! restart22) { slartgp_(&b22bulge, &b22d[i__ - 1], &rwork[iv2tsn + i__ - 2], &rwork[iv2tcs + i__ - 2], &r__); } else if (nu < mu) { slartgs_(&b12e[i__ - 1], &b12d[i__], &nu, &rwork[iv2tcs + i__ - 2], &rwork[iv2tsn + i__ - 2]); } else { slartgs_(&b22e[i__ - 1], &b22d[i__], &mu, &rwork[iv2tcs + i__ - 2], &rwork[iv2tsn + i__ - 2]); } temp = rwork[iv1tcs + i__ - 1] * b11d[i__] + rwork[iv1tsn + i__ - 1] * b11e[i__]; b11e[i__] = rwork[iv1tcs + i__ - 1] * b11e[i__] - rwork[iv1tsn + i__ - 1] * b11d[i__]; b11d[i__] = temp; b11bulge = rwork[iv1tsn + i__ - 1] * b11d[i__ + 1]; b11d[i__ + 1] = rwork[iv1tcs + i__ - 1] * b11d[i__ + 1]; temp = rwork[iv1tcs + i__ - 1] * b21d[i__] + rwork[iv1tsn + i__ - 1] * b21e[i__]; b21e[i__] = rwork[iv1tcs + i__ - 1] * b21e[i__] - rwork[iv1tsn + i__ - 1] * b21d[i__]; b21d[i__] = temp; b21bulge = rwork[iv1tsn + i__ - 1] * b21d[i__ + 1]; b21d[i__ + 1] = rwork[iv1tcs + i__ - 1] * b21d[i__ + 1]; temp = rwork[iv2tcs + i__ - 2] * b12e[i__ - 1] + rwork[iv2tsn + i__ - 2] * b12d[i__]; b12d[i__] = rwork[iv2tcs + i__ - 2] * b12d[i__] - rwork[iv2tsn + i__ - 2] * b12e[i__ - 1]; b12e[i__ - 1] = temp; b12bulge = rwork[iv2tsn + i__ - 2] * b12e[i__]; b12e[i__] = rwork[iv2tcs + i__ - 2] * b12e[i__]; temp = rwork[iv2tcs + i__ - 2] * b22e[i__ - 1] + rwork[iv2tsn + i__ - 2] * b22d[i__]; b22d[i__] = rwork[iv2tcs + i__ - 2] * b22d[i__] - rwork[iv2tsn + i__ - 2] * b22e[i__ - 1]; b22e[i__ - 1] = temp; b22bulge = rwork[iv2tsn + i__ - 2] * b22e[i__]; b22e[i__] = rwork[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 */ r__1 = y1; /* Computing 2nd power */ r__2 = y2; /* Computing 2nd power */ r__3 = x1; /* Computing 2nd power */ r__4 = x2; theta[i__] = atan2(sqrt(r__1 * r__1 + r__2 * r__2), sqrt(r__3 * r__3 + r__4 * r__4)); /* Determine if there are bulges to chase or if a new direct */ /* summand has been reached */ /* Computing 2nd power */ r__1 = b11d[i__]; /* Computing 2nd power */ r__2 = b11bulge; /* Computing 2nd power */ r__3 = thresh; restart11 = r__1 * r__1 + r__2 * r__2 <= r__3 * r__3; /* Computing 2nd power */ r__1 = b12e[i__ - 1]; /* Computing 2nd power */ r__2 = b12bulge; /* Computing 2nd power */ r__3 = thresh; restart12 = r__1 * r__1 + r__2 * r__2 <= r__3 * r__3; /* Computing 2nd power */ r__1 = b21d[i__]; /* Computing 2nd power */ r__2 = b21bulge; /* Computing 2nd power */ r__3 = thresh; restart21 = r__1 * r__1 + r__2 * r__2 <= r__3 * r__3; /* Computing 2nd power */ r__1 = b22e[i__ - 1]; /* Computing 2nd power */ r__2 = b22bulge; /* Computing 2nd power */ r__3 = thresh; restart22 = r__1 * r__1 + r__2 * r__2 <= r__3 * r__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) { slartgp_(&x2, &x1, &rwork[iu1sn + i__ - 1], &rwork[iu1cs + i__ - 1], &r__); } else if (! restart11 && restart12) { slartgp_(&b11bulge, &b11d[i__], &rwork[iu1sn + i__ - 1], & rwork[iu1cs + i__ - 1], &r__); } else if (restart11 && ! restart12) { slartgp_(&b12bulge, &b12e[i__ - 1], &rwork[iu1sn + i__ - 1], & rwork[iu1cs + i__ - 1], &r__); } else if (mu <= nu) { slartgs_(&b11e[i__], &b11d[i__ + 1], &mu, &rwork[iu1cs + i__ - 1], &rwork[iu1sn + i__ - 1]); } else { slartgs_(&b12d[i__], &b12e[i__], &nu, &rwork[iu1cs + i__ - 1], &rwork[iu1sn + i__ - 1]); } if (! restart21 && ! restart22) { slartgp_(&y2, &y1, &rwork[iu2sn + i__ - 1], &rwork[iu2cs + i__ - 1], &r__); } else if (! restart21 && restart22) { slartgp_(&b21bulge, &b21d[i__], &rwork[iu2sn + i__ - 1], & rwork[iu2cs + i__ - 1], &r__); } else if (restart21 && ! restart22) { slartgp_(&b22bulge, &b22e[i__ - 1], &rwork[iu2sn + i__ - 1], & rwork[iu2cs + i__ - 1], &r__); } else if (nu < mu) { slartgs_(&b21e[i__], &b21e[i__ + 1], &nu, &rwork[iu2cs + i__ - 1], &rwork[iu2sn + i__ - 1]); } else { slartgs_(&b22d[i__], &b22e[i__], &mu, &rwork[iu2cs + i__ - 1], &rwork[iu2sn + i__ - 1]); } rwork[iu2cs + i__ - 1] = -rwork[iu2cs + i__ - 1]; rwork[iu2sn + i__ - 1] = -rwork[iu2sn + i__ - 1]; temp = rwork[iu1cs + i__ - 1] * b11e[i__] + rwork[iu1sn + i__ - 1] * b11d[i__ + 1]; b11d[i__ + 1] = rwork[iu1cs + i__ - 1] * b11d[i__ + 1] - rwork[ iu1sn + i__ - 1] * b11e[i__]; b11e[i__] = temp; if (i__ < imax - 1) { b11bulge = rwork[iu1sn + i__ - 1] * b11e[i__ + 1]; b11e[i__ + 1] = rwork[iu1cs + i__ - 1] * b11e[i__ + 1]; } temp = rwork[iu2cs + i__ - 1] * b21e[i__] + rwork[iu2sn + i__ - 1] * b21d[i__ + 1]; b21d[i__ + 1] = rwork[iu2cs + i__ - 1] * b21d[i__ + 1] - rwork[ iu2sn + i__ - 1] * b21e[i__]; b21e[i__] = temp; if (i__ < imax - 1) { b21bulge = rwork[iu2sn + i__ - 1] * b21e[i__ + 1]; b21e[i__ + 1] = rwork[iu2cs + i__ - 1] * b21e[i__ + 1]; } temp = rwork[iu1cs + i__ - 1] * b12d[i__] + rwork[iu1sn + i__ - 1] * b12e[i__]; b12e[i__] = rwork[iu1cs + i__ - 1] * b12e[i__] - rwork[iu1sn + i__ - 1] * b12d[i__]; b12d[i__] = temp; b12bulge = rwork[iu1sn + i__ - 1] * b12d[i__ + 1]; b12d[i__ + 1] = rwork[iu1cs + i__ - 1] * b12d[i__ + 1]; temp = rwork[iu2cs + i__ - 1] * b22d[i__] + rwork[iu2sn + i__ - 1] * b22e[i__]; b22e[i__] = rwork[iu2cs + i__ - 1] * b22e[i__] - rwork[iu2sn + i__ - 1] * b22d[i__]; b22d[i__] = temp; b22bulge = rwork[iu2sn + i__ - 1] * b22d[i__ + 1]; b22d[i__ + 1] = rwork[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 */ r__1 = y1; /* Computing 2nd power */ r__2 = y2; phi[imax - 1] = atan2((abs(x1)), sqrt(r__1 * r__1 + r__2 * r__2)); /* Chase bulges from B12(IMAX-1,IMAX) and B22(IMAX-1,IMAX) */ /* Computing 2nd power */ r__1 = b12d[imax - 1]; /* Computing 2nd power */ r__2 = b12bulge; /* Computing 2nd power */ r__3 = thresh; restart12 = r__1 * r__1 + r__2 * r__2 <= r__3 * r__3; /* Computing 2nd power */ r__1 = b22d[imax - 1]; /* Computing 2nd power */ r__2 = b22bulge; /* Computing 2nd power */ r__3 = thresh; restart22 = r__1 * r__1 + r__2 * r__2 <= r__3 * r__3; if (! restart12 && ! restart22) { slartgp_(&y2, &y1, &rwork[iv2tsn + imax - 2], &rwork[iv2tcs + imax - 2], &r__); } else if (! restart12 && restart22) { slartgp_(&b12bulge, &b12d[imax - 1], &rwork[iv2tsn + imax - 2], & rwork[iv2tcs + imax - 2], &r__); } else if (restart12 && ! restart22) { slartgp_(&b22bulge, &b22d[imax - 1], &rwork[iv2tsn + imax - 2], & rwork[iv2tcs + imax - 2], &r__); } else if (nu < mu) { slartgs_(&b12e[imax - 1], &b12d[imax], &nu, &rwork[iv2tcs + imax - 2], &rwork[iv2tsn + imax - 2]); } else { slartgs_(&b22e[imax - 1], &b22d[imax], &mu, &rwork[iv2tcs + imax - 2], &rwork[iv2tsn + imax - 2]); } temp = rwork[iv2tcs + imax - 2] * b12e[imax - 1] + rwork[iv2tsn + imax - 2] * b12d[imax]; b12d[imax] = rwork[iv2tcs + imax - 2] * b12d[imax] - rwork[iv2tsn + imax - 2] * b12e[imax - 1]; b12e[imax - 1] = temp; temp = rwork[iv2tcs + imax - 2] * b22e[imax - 1] + rwork[iv2tsn + imax - 2] * b22d[imax]; b22d[imax] = rwork[iv2tcs + imax - 2] * b22d[imax] - rwork[iv2tsn + imax - 2] * b22e[imax - 1]; b22e[imax - 1] = temp; /* Update singular vectors */ if (wantu1) { if (colmajor) { i__1 = imax - imin + 1; clasr_("R", "V", "F", p, &i__1, &rwork[iu1cs + imin - 1], & rwork[iu1sn + imin - 1], &u1[imin * u1_dim1 + 1], ldu1); } else { i__1 = imax - imin + 1; clasr_("L", "V", "F", &i__1, p, &rwork[iu1cs + imin - 1], & rwork[iu1sn + imin - 1], &u1[imin + u1_dim1], ldu1); } } if (wantu2) { if (colmajor) { i__1 = *m - *p; i__2 = imax - imin + 1; clasr_("R", "V", "F", &i__1, &i__2, &rwork[iu2cs + imin - 1], &rwork[iu2sn + imin - 1], &u2[imin * u2_dim1 + 1], ldu2); } else { i__1 = imax - imin + 1; i__2 = *m - *p; clasr_("L", "V", "F", &i__1, &i__2, &rwork[iu2cs + imin - 1], &rwork[iu2sn + imin - 1], &u2[imin + u2_dim1], ldu2); } } if (wantv1t) { if (colmajor) { i__1 = imax - imin + 1; clasr_("L", "V", "F", &i__1, q, &rwork[iv1tcs + imin - 1], & rwork[iv1tsn + imin - 1], &v1t[imin + v1t_dim1], ldv1t); } else { i__1 = imax - imin + 1; clasr_("R", "V", "F", q, &i__1, &rwork[iv1tcs + imin - 1], & rwork[iv1tsn + imin - 1], &v1t[imin * v1t_dim1 + 1], ldv1t); } } if (wantv2t) { if (colmajor) { i__1 = imax - imin + 1; i__2 = *m - *q; clasr_("L", "V", "F", &i__1, &i__2, &rwork[iv2tcs + imin - 1], &rwork[iv2tsn + imin - 1], &v2t[imin + v2t_dim1], ldv2t); } else { i__1 = *m - *q; i__2 = imax - imin + 1; clasr_("R", "V", "F", &i__1, &i__2, &rwork[iv2tcs + imin - 1], &rwork[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.f) { b11d[imax] = -b11d[imax]; b21d[imax] = -b21d[imax]; if (wantv1t) { if (colmajor) { cscal_(q, &c_b1, &v1t[imax + v1t_dim1], ldv1t); } else { cscal_(q, &c_b1, &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.f) { b12d[imax] = -b12d[imax]; if (wantu1) { if (colmajor) { cscal_(p, &c_b1, &u1[imax * u1_dim1 + 1], &c__1); } else { cscal_(p, &c_b1, &u1[imax + u1_dim1], ldu1); } } } if (b21d[imax] + b22e[imax - 1] > 0.f) { b22d[imax] = -b22d[imax]; if (wantu2) { if (colmajor) { i__1 = *m - *p; cscal_(&i__1, &c_b1, &u2[imax * u2_dim1 + 1], &c__1); } else { i__1 = *m - *p; cscal_(&i__1, &c_b1, &u2[imax + u2_dim1], ldu2); } } } /* Fix signs on B12(IMAX,IMAX) and B22(IMAX,IMAX) */ if (b12d[imax] + b22d[imax] < 0.f) { if (wantv2t) { if (colmajor) { i__1 = *m - *q; cscal_(&i__1, &c_b1, &v2t[imax + v2t_dim1], ldv2t); } else { i__1 = *m - *q; cscal_(&i__1, &c_b1, &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.f; } else if (theta[i__] > 1.57079632679489662f - thresh) { theta[i__] = 1.57079632679489662f; } } i__1 = imax - 1; for (i__ = imin; i__ <= i__1; ++i__) { if (phi[i__] < thresh) { phi[i__] = 0.f; } else if (phi[i__] > 1.57079632679489662f - thresh) { phi[i__] = 1.57079632679489662f; } } /* Deflate */ if (imax > 1) { while(phi[imax - 1] == 0.f) { --imax; if (imax <= 1) { myexit_(); } } } if (imin > imax - 1) { imin = imax - 1; } if (imin > 1) { while(phi[imin - 1] != 0.f) { --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) { cswap_(p, &u1[i__ * u1_dim1 + 1], &c__1, &u1[mini * u1_dim1 + 1], &c__1); } if (wantu2) { i__2 = *m - *p; cswap_(&i__2, &u2[i__ * u2_dim1 + 1], &c__1, &u2[mini * u2_dim1 + 1], &c__1); } if (wantv1t) { cswap_(q, &v1t[i__ + v1t_dim1], ldv1t, &v1t[mini + v1t_dim1], ldv1t); } if (wantv2t) { i__2 = *m - *q; cswap_(&i__2, &v2t[i__ + v2t_dim1], ldv2t, &v2t[mini + v2t_dim1], ldv2t); } } else { if (wantu1) { cswap_(p, &u1[i__ + u1_dim1], ldu1, &u1[mini + u1_dim1], ldu1); } if (wantu2) { i__2 = *m - *p; cswap_(&i__2, &u2[i__ + u2_dim1], ldu2, &u2[mini + u2_dim1], ldu2); } if (wantv1t) { cswap_(q, &v1t[i__ * v1t_dim1 + 1], &c__1, &v1t[mini * v1t_dim1 + 1], &c__1); } if (wantv2t) { i__2 = *m - *q; cswap_(&i__2, &v2t[i__ * v2t_dim1 + 1], &c__1, &v2t[mini * v2t_dim1 + 1], &c__1); } } } } return 0; /* End of CBBCSD */ } /* cbbcsd_ */