#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]/Cd(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 CTGSJA */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download CTGSJA + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE CTGSJA( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B, */ /* LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV, */ /* Q, LDQ, WORK, NCALL MYCYCLE, INFO ) */ /* CHARACTER JOBQ, JOBU, JOBV */ /* INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, */ /* $ NCALL MYCYCLE, P */ /* REAL TOLA, TOLB */ /* REAL ALPHA( * ), BETA( * ) */ /* COMPLEX A( LDA, * ), B( LDB, * ), Q( LDQ, * ), */ /* $ U( LDU, * ), V( LDV, * ), WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > CTGSJA computes the generalized singular value decomposition (GSVD) */ /* > of two complex upper triangular (or trapezoidal) matrices A and B. */ /* > */ /* > On entry, it is assumed that matrices A and B have the following */ /* > forms, which may be obtained by the preprocessing subroutine CGGSVP */ /* > from a general M-by-N matrix A and P-by-N matrix B: */ /* > */ /* > N-K-L K L */ /* > A = K ( 0 A12 A13 ) if M-K-L >= 0; */ /* > L ( 0 0 A23 ) */ /* > M-K-L ( 0 0 0 ) */ /* > */ /* > N-K-L K L */ /* > A = K ( 0 A12 A13 ) if M-K-L < 0; */ /* > M-K ( 0 0 A23 ) */ /* > */ /* > N-K-L K L */ /* > B = L ( 0 0 B13 ) */ /* > P-L ( 0 0 0 ) */ /* > */ /* > where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular */ /* > upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0, */ /* > otherwise A23 is (M-K)-by-L upper trapezoidal. */ /* > */ /* > On exit, */ /* > */ /* > U**H *A*Q = D1*( 0 R ), V**H *B*Q = D2*( 0 R ), */ /* > */ /* > where U, V and Q are unitary matrices. */ /* > R is a nonsingular upper triangular matrix, and D1 */ /* > and D2 are ``diagonal'' matrices, which are of the following */ /* > structures: */ /* > */ /* > If M-K-L >= 0, */ /* > */ /* > K L */ /* > D1 = K ( I 0 ) */ /* > L ( 0 C ) */ /* > M-K-L ( 0 0 ) */ /* > */ /* > K L */ /* > D2 = L ( 0 S ) */ /* > P-L ( 0 0 ) */ /* > */ /* > N-K-L K L */ /* > ( 0 R ) = K ( 0 R11 R12 ) K */ /* > L ( 0 0 R22 ) L */ /* > */ /* > where */ /* > */ /* > C = diag( ALPHA(K+1), ... , ALPHA(K+L) ), */ /* > S = diag( BETA(K+1), ... , BETA(K+L) ), */ /* > C**2 + S**2 = I. */ /* > */ /* > R is stored in A(1:K+L,N-K-L+1:N) on exit. */ /* > */ /* > If M-K-L < 0, */ /* > */ /* > K M-K K+L-M */ /* > D1 = K ( I 0 0 ) */ /* > M-K ( 0 C 0 ) */ /* > */ /* > K M-K K+L-M */ /* > D2 = M-K ( 0 S 0 ) */ /* > K+L-M ( 0 0 I ) */ /* > P-L ( 0 0 0 ) */ /* > */ /* > N-K-L K M-K K+L-M */ /* > ( 0 R ) = K ( 0 R11 R12 R13 ) */ /* > M-K ( 0 0 R22 R23 ) */ /* > K+L-M ( 0 0 0 R33 ) */ /* > */ /* > where */ /* > C = diag( ALPHA(K+1), ... , ALPHA(M) ), */ /* > S = diag( BETA(K+1), ... , BETA(M) ), */ /* > C**2 + S**2 = I. */ /* > */ /* > R = ( R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N) and R33 is stored */ /* > ( 0 R22 R23 ) */ /* > in B(M-K+1:L,N+M-K-L+1:N) on exit. */ /* > */ /* > The computation of the unitary transformation matrices U, V or Q */ /* > is optional. These matrices may either be formed explicitly, or they */ /* > may be postmultiplied into input matrices U1, V1, or Q1. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] JOBU */ /* > \verbatim */ /* > JOBU is CHARACTER*1 */ /* > = 'U': U must contain a unitary matrix U1 on entry, and */ /* > the product U1*U is returned; */ /* > = 'I': U is initialized to the unit matrix, and the */ /* > unitary matrix U is returned; */ /* > = 'N': U is not computed. */ /* > \endverbatim */ /* > */ /* > \param[in] JOBV */ /* > \verbatim */ /* > JOBV is CHARACTER*1 */ /* > = 'V': V must contain a unitary matrix V1 on entry, and */ /* > the product V1*V is returned; */ /* > = 'I': V is initialized to the unit matrix, and the */ /* > unitary matrix V is returned; */ /* > = 'N': V is not computed. */ /* > \endverbatim */ /* > */ /* > \param[in] JOBQ */ /* > \verbatim */ /* > JOBQ is CHARACTER*1 */ /* > = 'Q': Q must contain a unitary matrix Q1 on entry, and */ /* > the product Q1*Q is returned; */ /* > = 'I': Q is initialized to the unit matrix, and the */ /* > unitary matrix Q is returned; */ /* > = 'N': Q is not computed. */ /* > \endverbatim */ /* > */ /* > \param[in] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The number of rows of the matrix A. M >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] P */ /* > \verbatim */ /* > P is INTEGER */ /* > The number of rows of the matrix B. P >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The number of columns of the matrices A and B. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] K */ /* > \verbatim */ /* > K is INTEGER */ /* > \endverbatim */ /* > */ /* > \param[in] L */ /* > \verbatim */ /* > L is INTEGER */ /* > */ /* > K and L specify the subblocks in the input matrices A and B: */ /* > A23 = A(K+1:MIN(K+L,M),N-L+1:N) and B13 = B(1:L,,N-L+1:N) */ /* > of A and B, whose GSVD is going to be computed by CTGSJA. */ /* > See Further Details. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is COMPLEX array, dimension (LDA,N) */ /* > On entry, the M-by-N matrix A. */ /* > On exit, A(N-K+1:N,1:MIN(K+L,M) ) contains the triangular */ /* > matrix R or part of R. See Purpose for details. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */ /* > \endverbatim */ /* > */ /* > \param[in,out] B */ /* > \verbatim */ /* > B is COMPLEX array, dimension (LDB,N) */ /* > On entry, the P-by-N matrix B. */ /* > On exit, if necessary, B(M-K+1:L,N+M-K-L+1:N) contains */ /* > a part of R. See Purpose for details. */ /* > \endverbatim */ /* > */ /* > \param[in] LDB */ /* > \verbatim */ /* > LDB is INTEGER */ /* > The leading dimension of the array B. LDB >= f2cmax(1,P). */ /* > \endverbatim */ /* > */ /* > \param[in] TOLA */ /* > \verbatim */ /* > TOLA is REAL */ /* > \endverbatim */ /* > */ /* > \param[in] TOLB */ /* > \verbatim */ /* > TOLB is REAL */ /* > */ /* > TOLA and TOLB are the convergence criteria for the Jacobi- */ /* > Kogbetliantz iteration procedure. Generally, they are the */ /* > same as used in the preprocessing step, say */ /* > TOLA = MAX(M,N)*norm(A)*MACHEPS, */ /* > TOLB = MAX(P,N)*norm(B)*MACHEPS. */ /* > \endverbatim */ /* > */ /* > \param[out] ALPHA */ /* > \verbatim */ /* > ALPHA is REAL array, dimension (N) */ /* > \endverbatim */ /* > */ /* > \param[out] BETA */ /* > \verbatim */ /* > BETA is REAL array, dimension (N) */ /* > */ /* > On exit, ALPHA and BETA contain the generalized singular */ /* > value pairs of A and B; */ /* > ALPHA(1:K) = 1, */ /* > BETA(1:K) = 0, */ /* > and if M-K-L >= 0, */ /* > ALPHA(K+1:K+L) = diag(C), */ /* > BETA(K+1:K+L) = diag(S), */ /* > or if M-K-L < 0, */ /* > ALPHA(K+1:M)= C, ALPHA(M+1:K+L)= 0 */ /* > BETA(K+1:M) = S, BETA(M+1:K+L) = 1. */ /* > Furthermore, if K+L < N, */ /* > ALPHA(K+L+1:N) = 0 */ /* > BETA(K+L+1:N) = 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] U */ /* > \verbatim */ /* > U is COMPLEX array, dimension (LDU,M) */ /* > On entry, if JOBU = 'U', U must contain a matrix U1 (usually */ /* > the unitary matrix returned by CGGSVP). */ /* > On exit, */ /* > if JOBU = 'I', U contains the unitary matrix U; */ /* > if JOBU = 'U', U contains the product U1*U. */ /* > If JOBU = 'N', U is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDU */ /* > \verbatim */ /* > LDU is INTEGER */ /* > The leading dimension of the array U. LDU >= f2cmax(1,M) if */ /* > JOBU = 'U'; LDU >= 1 otherwise. */ /* > \endverbatim */ /* > */ /* > \param[in,out] V */ /* > \verbatim */ /* > V is COMPLEX array, dimension (LDV,P) */ /* > On entry, if JOBV = 'V', V must contain a matrix V1 (usually */ /* > the unitary matrix returned by CGGSVP). */ /* > On exit, */ /* > if JOBV = 'I', V contains the unitary matrix V; */ /* > if JOBV = 'V', V contains the product V1*V. */ /* > If JOBV = 'N', V is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDV */ /* > \verbatim */ /* > LDV is INTEGER */ /* > The leading dimension of the array V. LDV >= f2cmax(1,P) if */ /* > JOBV = 'V'; LDV >= 1 otherwise. */ /* > \endverbatim */ /* > */ /* > \param[in,out] Q */ /* > \verbatim */ /* > Q is COMPLEX array, dimension (LDQ,N) */ /* > On entry, if JOBQ = 'Q', Q must contain a matrix Q1 (usually */ /* > the unitary matrix returned by CGGSVP). */ /* > On exit, */ /* > if JOBQ = 'I', Q contains the unitary matrix Q; */ /* > if JOBQ = 'Q', Q contains the product Q1*Q. */ /* > If JOBQ = 'N', Q is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDQ */ /* > \verbatim */ /* > LDQ is INTEGER */ /* > The leading dimension of the array Q. LDQ >= f2cmax(1,N) if */ /* > JOBQ = 'Q'; LDQ >= 1 otherwise. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is COMPLEX array, dimension (2*N) */ /* > \endverbatim */ /* > */ /* > \param[out] NCALL MYCYCLE */ /* > \verbatim */ /* > NCALL MYCYCLE is INTEGER */ /* > The number of cycles required for convergence. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit */ /* > < 0: if INFO = -i, the i-th argument had an illegal value. */ /* > = 1: the procedure does not converge after MAXIT cycles. */ /* > \endverbatim */ /* > \par Internal Parameters: */ /* ========================= */ /* > */ /* > \verbatim */ /* > MAXIT INTEGER */ /* > MAXIT specifies the total loops that the iterative procedure */ /* > may take. If after MAXIT cycles, the routine fails to */ /* > converge, we return INFO = 1. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup complexOTHERcomputational */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > CTGSJA essentially uses a variant of Kogbetliantz algorithm to reduce */ /* > f2cmin(L,M-K)-by-L triangular (or trapezoidal) matrix A23 and L-by-L */ /* > matrix B13 to the form: */ /* > */ /* > U1**H *A13*Q1 = C1*R1; V1**H *B13*Q1 = S1*R1, */ /* > */ /* > where U1, V1 and Q1 are unitary matrix. */ /* > C1 and S1 are diagonal matrices satisfying */ /* > */ /* > C1**2 + S1**2 = I, */ /* > */ /* > and R1 is an L-by-L nonsingular upper triangular matrix. */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int ctgsja_(char *jobu, char *jobv, char *jobq, integer *m, integer *p, integer *n, integer *k, integer *l, complex *a, integer * lda, complex *b, integer *ldb, real *tola, real *tolb, real *alpha, real *beta, complex *u, integer *ldu, complex *v, integer *ldv, complex *q, integer *ldq, complex *work, integer *ncallmycycle, integer *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, u_dim1, u_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4; real r__1; complex q__1; /* Local variables */ extern /* Subroutine */ int crot_(integer *, complex *, integer *, complex *, integer *, real *, complex *); integer kcallmycycle, i__, j; real gamma; extern logical lsame_(char *, char *); extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, complex *, integer *); logical initq; real a1, a3, b1; logical initu, initv, wantq, upper; real b3, error; logical wantu, wantv; real ssmin; complex a2, b2; extern /* Subroutine */ int clags2_(logical *, real *, complex *, real *, real *, complex *, real *, real *, complex *, real *, complex *, real *, complex *), clapll_(integer *, complex *, integer *, complex *, integer *, real *), csscal_(integer *, real *, complex *, integer *), claset_(char *, integer *, integer *, complex *, complex *, complex *, integer *), xerbla_(char *, integer *, ftnlen), slartg_(real *, real *, real *, real *, real *); // extern integer myhuge_(real *); real csq, csu, csv; complex snq; real rwk; complex snu, snv; /* -- LAPACK computational routine (version 3.7.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* December 2016 */ /* ===================================================================== */ /* Decode and test the input parameters */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; --alpha; --beta; u_dim1 = *ldu; u_offset = 1 + u_dim1 * 1; u -= u_offset; v_dim1 = *ldv; v_offset = 1 + v_dim1 * 1; v -= v_offset; q_dim1 = *ldq; q_offset = 1 + q_dim1 * 1; q -= q_offset; --work; /* Function Body */ initu = lsame_(jobu, "I"); wantu = initu || lsame_(jobu, "U"); initv = lsame_(jobv, "I"); wantv = initv || lsame_(jobv, "V"); initq = lsame_(jobq, "I"); wantq = initq || lsame_(jobq, "Q"); *info = 0; if (! (initu || wantu || lsame_(jobu, "N"))) { *info = -1; } else if (! (initv || wantv || lsame_(jobv, "N"))) { *info = -2; } else if (! (initq || wantq || lsame_(jobq, "N"))) { *info = -3; } else if (*m < 0) { *info = -4; } else if (*p < 0) { *info = -5; } else if (*n < 0) { *info = -6; } else if (*lda < f2cmax(1,*m)) { *info = -10; } else if (*ldb < f2cmax(1,*p)) { *info = -12; } else if (*ldu < 1 || wantu && *ldu < *m) { *info = -18; } else if (*ldv < 1 || wantv && *ldv < *p) { *info = -20; } else if (*ldq < 1 || wantq && *ldq < *n) { *info = -22; } if (*info != 0) { i__1 = -(*info); xerbla_("CTGSJA", &i__1, (ftnlen)6); return 0; } /* Initialize U, V and Q, if necessary */ if (initu) { claset_("Full", m, m, &c_b1, &c_b2, &u[u_offset], ldu); } if (initv) { claset_("Full", p, p, &c_b1, &c_b2, &v[v_offset], ldv); } if (initq) { claset_("Full", n, n, &c_b1, &c_b2, &q[q_offset], ldq); } /* Loop until convergence */ upper = FALSE_; for (kcallmycycle = 1; kcallmycycle <= 40; ++kcallmycycle) { upper = ! upper; i__1 = *l - 1; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *l; for (j = i__ + 1; j <= i__2; ++j) { a1 = 0.f; a2.r = 0.f, a2.i = 0.f; a3 = 0.f; if (*k + i__ <= *m) { i__3 = *k + i__ + (*n - *l + i__) * a_dim1; a1 = a[i__3].r; } if (*k + j <= *m) { i__3 = *k + j + (*n - *l + j) * a_dim1; a3 = a[i__3].r; } i__3 = i__ + (*n - *l + i__) * b_dim1; b1 = b[i__3].r; i__3 = j + (*n - *l + j) * b_dim1; b3 = b[i__3].r; if (upper) { if (*k + i__ <= *m) { i__3 = *k + i__ + (*n - *l + j) * a_dim1; a2.r = a[i__3].r, a2.i = a[i__3].i; } i__3 = i__ + (*n - *l + j) * b_dim1; b2.r = b[i__3].r, b2.i = b[i__3].i; } else { if (*k + j <= *m) { i__3 = *k + j + (*n - *l + i__) * a_dim1; a2.r = a[i__3].r, a2.i = a[i__3].i; } i__3 = j + (*n - *l + i__) * b_dim1; b2.r = b[i__3].r, b2.i = b[i__3].i; } clags2_(&upper, &a1, &a2, &a3, &b1, &b2, &b3, &csu, &snu, & csv, &snv, &csq, &snq); /* Update (K+I)-th and (K+J)-th rows of matrix A: U**H *A */ if (*k + j <= *m) { r_cnjg(&q__1, &snu); crot_(l, &a[*k + j + (*n - *l + 1) * a_dim1], lda, &a[*k + i__ + (*n - *l + 1) * a_dim1], lda, &csu, &q__1) ; } /* Update I-th and J-th rows of matrix B: V**H *B */ r_cnjg(&q__1, &snv); crot_(l, &b[j + (*n - *l + 1) * b_dim1], ldb, &b[i__ + (*n - * l + 1) * b_dim1], ldb, &csv, &q__1); /* Update (N-L+I)-th and (N-L+J)-th columns of matrices */ /* A and B: A*Q and B*Q */ /* Computing MIN */ i__4 = *k + *l; i__3 = f2cmin(i__4,*m); crot_(&i__3, &a[(*n - *l + j) * a_dim1 + 1], &c__1, &a[(*n - * l + i__) * a_dim1 + 1], &c__1, &csq, &snq); crot_(l, &b[(*n - *l + j) * b_dim1 + 1], &c__1, &b[(*n - *l + i__) * b_dim1 + 1], &c__1, &csq, &snq); if (upper) { if (*k + i__ <= *m) { i__3 = *k + i__ + (*n - *l + j) * a_dim1; a[i__3].r = 0.f, a[i__3].i = 0.f; } i__3 = i__ + (*n - *l + j) * b_dim1; b[i__3].r = 0.f, b[i__3].i = 0.f; } else { if (*k + j <= *m) { i__3 = *k + j + (*n - *l + i__) * a_dim1; a[i__3].r = 0.f, a[i__3].i = 0.f; } i__3 = j + (*n - *l + i__) * b_dim1; b[i__3].r = 0.f, b[i__3].i = 0.f; } /* Ensure that the diagonal elements of A and B are real. */ if (*k + i__ <= *m) { i__3 = *k + i__ + (*n - *l + i__) * a_dim1; i__4 = *k + i__ + (*n - *l + i__) * a_dim1; r__1 = a[i__4].r; a[i__3].r = r__1, a[i__3].i = 0.f; } if (*k + j <= *m) { i__3 = *k + j + (*n - *l + j) * a_dim1; i__4 = *k + j + (*n - *l + j) * a_dim1; r__1 = a[i__4].r; a[i__3].r = r__1, a[i__3].i = 0.f; } i__3 = i__ + (*n - *l + i__) * b_dim1; i__4 = i__ + (*n - *l + i__) * b_dim1; r__1 = b[i__4].r; b[i__3].r = r__1, b[i__3].i = 0.f; i__3 = j + (*n - *l + j) * b_dim1; i__4 = j + (*n - *l + j) * b_dim1; r__1 = b[i__4].r; b[i__3].r = r__1, b[i__3].i = 0.f; /* Update unitary matrices U, V, Q, if desired. */ if (wantu && *k + j <= *m) { crot_(m, &u[(*k + j) * u_dim1 + 1], &c__1, &u[(*k + i__) * u_dim1 + 1], &c__1, &csu, &snu); } if (wantv) { crot_(p, &v[j * v_dim1 + 1], &c__1, &v[i__ * v_dim1 + 1], &c__1, &csv, &snv); } if (wantq) { crot_(n, &q[(*n - *l + j) * q_dim1 + 1], &c__1, &q[(*n - * l + i__) * q_dim1 + 1], &c__1, &csq, &snq); } /* L10: */ } /* L20: */ } if (! upper) { /* The matrices A13 and B13 were lower triangular at the start */ /* of the cycle, and are now upper triangular. */ /* Convergence test: test the parallelism of the corresponding */ /* rows of A and B. */ error = 0.f; /* Computing MIN */ i__2 = *l, i__3 = *m - *k; i__1 = f2cmin(i__2,i__3); for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *l - i__ + 1; ccopy_(&i__2, &a[*k + i__ + (*n - *l + i__) * a_dim1], lda, & work[1], &c__1); i__2 = *l - i__ + 1; ccopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &work[* l + 1], &c__1); i__2 = *l - i__ + 1; clapll_(&i__2, &work[1], &c__1, &work[*l + 1], &c__1, &ssmin); error = f2cmax(error,ssmin); /* L30: */ } if (abs(error) <= f2cmin(*tola,*tolb)) { goto L50; } } /* End of cycle loop */ /* L40: */ } /* The algorithm has not converged after MAXIT cycles. */ *info = 1; goto L100; L50: /* If ERROR <= MIN(TOLA,TOLB), then the algorithm has converged. */ /* Compute the generalized singular value pairs (ALPHA, BETA), and */ /* set the triangular matrix R to array A. */ i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { alpha[i__] = 1.f; beta[i__] = 0.f; /* L60: */ } /* Computing MIN */ i__2 = *l, i__3 = *m - *k; i__1 = f2cmin(i__2,i__3); for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *k + i__ + (*n - *l + i__) * a_dim1; a1 = a[i__2].r; i__2 = i__ + (*n - *l + i__) * b_dim1; b1 = b[i__2].r; gamma = b1 / a1; if (gamma <= (real) myhuge_(&c_b3) && gamma >= -((real) myhuge_(&c_b3) )) { if (gamma < 0.f) { i__2 = *l - i__ + 1; csscal_(&i__2, &c_b40, &b[i__ + (*n - *l + i__) * b_dim1], ldb); if (wantv) { csscal_(p, &c_b40, &v[i__ * v_dim1 + 1], &c__1); } } r__1 = abs(gamma); slartg_(&r__1, &c_b43, &beta[*k + i__], &alpha[*k + i__], &rwk); if (alpha[*k + i__] >= beta[*k + i__]) { i__2 = *l - i__ + 1; r__1 = 1.f / alpha[*k + i__]; csscal_(&i__2, &r__1, &a[*k + i__ + (*n - *l + i__) * a_dim1], lda); } else { i__2 = *l - i__ + 1; r__1 = 1.f / beta[*k + i__]; csscal_(&i__2, &r__1, &b[i__ + (*n - *l + i__) * b_dim1], ldb) ; i__2 = *l - i__ + 1; ccopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &a[*k + i__ + (*n - *l + i__) * a_dim1], lda); } } else { alpha[*k + i__] = 0.f; beta[*k + i__] = 1.f; i__2 = *l - i__ + 1; ccopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &a[*k + i__ + (*n - *l + i__) * a_dim1], lda); } /* L70: */ } /* Post-assignment */ i__1 = *k + *l; for (i__ = *m + 1; i__ <= i__1; ++i__) { alpha[i__] = 0.f; beta[i__] = 1.f; /* L80: */ } if (*k + *l < *n) { i__1 = *n; for (i__ = *k + *l + 1; i__ <= i__1; ++i__) { alpha[i__] = 0.f; beta[i__] = 0.f; /* L90: */ } } L100: *ncallmycycle = kcallmycycle; return 0; /* End of CTGSJA */ } /* ctgsja_ */