#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 SGGSVD3 computes the singular value decomposition (SVD) for OTHER matrices */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SGGSVD3 + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SGGSVD3( JOBU, JOBV, JOBQ, M, N, P, K, L, A, LDA, B, */ /* LDB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK, */ /* LWORK, IWORK, INFO ) */ /* CHARACTER JOBQ, JOBU, JOBV */ /* INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P, LWORK */ /* INTEGER IWORK( * ) */ /* REAL A( LDA, * ), ALPHA( * ), B( LDB, * ), */ /* $ BETA( * ), Q( LDQ, * ), U( LDU, * ), */ /* $ V( LDV, * ), WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SGGSVD3 computes the generalized singular value decomposition (GSVD) */ /* > of an M-by-N real matrix A and P-by-N real matrix B: */ /* > */ /* > U**T*A*Q = D1*( 0 R ), V**T*B*Q = D2*( 0 R ) */ /* > */ /* > where U, V and Q are orthogonal matrices. */ /* > Let K+L = the effective numerical rank of the matrix (A**T,B**T)**T, */ /* > then R is a K+L-by-K+L nonsingular upper triangular matrix, D1 and */ /* > D2 are M-by-(K+L) and P-by-(K+L) "diagonal" matrices and of the */ /* > following structures, respectively: */ /* > */ /* > 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 ) */ /* > L ( 0 0 R22 ) */ /* > */ /* > 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. */ /* > */ /* > (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 routine computes C, S, R, and optionally the orthogonal */ /* > transformation matrices U, V and Q. */ /* > */ /* > In particular, if B is an N-by-N nonsingular matrix, then the GSVD of */ /* > A and B implicitly gives the SVD of A*inv(B): */ /* > A*inv(B) = U*(D1*inv(D2))*V**T. */ /* > If ( A**T,B**T)**T has orthonormal columns, then the GSVD of A and B is */ /* > also equal to the CS decomposition of A and B. Furthermore, the GSVD */ /* > can be used to derive the solution of the eigenvalue problem: */ /* > A**T*A x = lambda* B**T*B x. */ /* > In some literature, the GSVD of A and B is presented in the form */ /* > U**T*A*X = ( 0 D1 ), V**T*B*X = ( 0 D2 ) */ /* > where U and V are orthogonal and X is nonsingular, D1 and D2 are */ /* > ``diagonal''. The former GSVD form can be converted to the latter */ /* > form by taking the nonsingular matrix X as */ /* > */ /* > X = Q*( I 0 ) */ /* > ( 0 inv(R) ). */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] JOBU */ /* > \verbatim */ /* > JOBU is CHARACTER*1 */ /* > = 'U': Orthogonal matrix U is computed; */ /* > = 'N': U is not computed. */ /* > \endverbatim */ /* > */ /* > \param[in] JOBV */ /* > \verbatim */ /* > JOBV is CHARACTER*1 */ /* > = 'V': Orthogonal matrix V is computed; */ /* > = 'N': V is not computed. */ /* > \endverbatim */ /* > */ /* > \param[in] JOBQ */ /* > \verbatim */ /* > JOBQ is CHARACTER*1 */ /* > = 'Q': Orthogonal matrix Q is computed; */ /* > = '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] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The number of columns of the matrices A and B. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] P */ /* > \verbatim */ /* > P is INTEGER */ /* > The number of rows of the matrix B. P >= 0. */ /* > \endverbatim */ /* > */ /* > \param[out] K */ /* > \verbatim */ /* > K is INTEGER */ /* > \endverbatim */ /* > */ /* > \param[out] L */ /* > \verbatim */ /* > L is INTEGER */ /* > */ /* > On exit, K and L specify the dimension of the subblocks */ /* > described in Purpose. */ /* > K + L = effective numerical rank of (A**T,B**T)**T. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is REAL array, dimension (LDA,N) */ /* > On entry, the M-by-N matrix A. */ /* > On exit, A 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 REAL array, dimension (LDB,N) */ /* > On entry, the P-by-N matrix B. */ /* > On exit, B contains the triangular matrix R if M-K-L < 0. */ /* > 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[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) = C, */ /* > BETA(K+1:K+L) = 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 */ /* > and */ /* > ALPHA(K+L+1:N) = 0 */ /* > BETA(K+L+1:N) = 0 */ /* > \endverbatim */ /* > */ /* > \param[out] U */ /* > \verbatim */ /* > U is REAL array, dimension (LDU,M) */ /* > If JOBU = 'U', U contains the M-by-M orthogonal matrix 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[out] V */ /* > \verbatim */ /* > V is REAL array, dimension (LDV,P) */ /* > If JOBV = 'V', V contains the P-by-P orthogonal matrix 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[out] Q */ /* > \verbatim */ /* > Q is REAL array, dimension (LDQ,N) */ /* > If JOBQ = 'Q', Q contains the N-by-N orthogonal matrix 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 REAL 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. */ /* > */ /* > 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] IWORK */ /* > \verbatim */ /* > IWORK is INTEGER array, dimension (N) */ /* > On exit, IWORK stores the sorting information. More */ /* > precisely, the following loop will sort ALPHA */ /* > for I = K+1, f2cmin(M,K+L) */ /* > swap ALPHA(I) and ALPHA(IWORK(I)) */ /* > endfor */ /* > such that ALPHA(1) >= ALPHA(2) >= ... >= ALPHA(N). */ /* > \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 INFO = 1, the Jacobi-type procedure failed to */ /* > converge. For further details, see subroutine STGSJA. */ /* > \endverbatim */ /* > \par Internal Parameters: */ /* ========================= */ /* > */ /* > \verbatim */ /* > TOLA REAL */ /* > TOLB REAL */ /* > TOLA and TOLB are the thresholds to determine the effective */ /* > rank of (A**T,B**T)**T. Generally, they are set to */ /* > TOLA = MAX(M,N)*norm(A)*MACHEPS, */ /* > TOLB = MAX(P,N)*norm(B)*MACHEPS. */ /* > The size of TOLA and TOLB may affect the size of backward */ /* > errors of the decomposition. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date August 2015 */ /* > \ingroup realGEsing */ /* > \par Contributors: */ /* ================== */ /* > */ /* > Ming Gu and Huan Ren, Computer Science Division, University of */ /* > California at Berkeley, USA */ /* > */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > SGGSVD3 replaces the deprecated subroutine SGGSVD. */ /* > */ /* ===================================================================== */ /* Subroutine */ int sggsvd3_(char *jobu, char *jobv, char *jobq, integer *m, integer *n, integer *p, integer *k, integer *l, real *a, integer *lda, real *b, integer *ldb, real *alpha, real *beta, real *u, integer * ldu, real *v, integer *ldv, real *q, integer *ldq, real *work, integer *lwork, integer *iwork, 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; /* Local variables */ integer ibnd; real tola; integer isub; real tolb, unfl, temp, smax; integer ncallmycycle, i__, j; extern logical lsame_(char *, char *); real anorm, bnorm; logical wantq; extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, integer *); logical wantu, wantv; extern real slamch_(char *), slange_(char *, integer *, integer *, real *, integer *, real *); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), stgsja_( char *, char *, char *, integer *, integer *, integer *, integer * , integer *, real *, integer *, real *, integer *, real *, real *, real *, real *, real *, integer *, real *, integer *, real *, integer *, real *, integer *, integer *); integer lwkopt; logical lquery; extern /* Subroutine */ int sggsvp3_(char *, char *, char *, integer *, integer *, integer *, real *, integer *, real *, integer *, real * , real *, integer *, integer *, real *, integer *, real *, integer *, real *, integer *, integer *, real *, real *, integer * , integer *); real ulp; /* -- LAPACK driver 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..-- */ /* August 2015 */ /* ===================================================================== */ /* 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; --iwork; /* Function Body */ wantu = lsame_(jobu, "U"); wantv = lsame_(jobv, "V"); wantq = lsame_(jobq, "Q"); lquery = *lwork == -1; lwkopt = 1; /* Test the input arguments */ *info = 0; if (! (wantu || lsame_(jobu, "N"))) { *info = -1; } else if (! (wantv || lsame_(jobv, "N"))) { *info = -2; } else if (! (wantq || lsame_(jobq, "N"))) { *info = -3; } else if (*m < 0) { *info = -4; } else if (*n < 0) { *info = -5; } else if (*p < 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 = -16; } else if (*ldv < 1 || wantv && *ldv < *p) { *info = -18; } else if (*ldq < 1 || wantq && *ldq < *n) { *info = -20; } else if (*lwork < 1 && ! lquery) { *info = -24; } /* Compute workspace */ if (*info == 0) { sggsvp3_(jobu, jobv, jobq, m, p, n, &a[a_offset], lda, &b[b_offset], ldb, &tola, &tolb, k, l, &u[u_offset], ldu, &v[v_offset], ldv, &q[q_offset], ldq, &iwork[1], &work[1], &work[1], &c_n1, info); lwkopt = *n + (integer) work[1]; /* Computing MAX */ i__1 = *n << 1; lwkopt = f2cmax(i__1,lwkopt); lwkopt = f2cmax(1,lwkopt); work[1] = (real) lwkopt; } if (*info != 0) { i__1 = -(*info); xerbla_("SGGSVD3", &i__1, (ftnlen)7); return 0; } if (lquery) { return 0; } /* Compute the Frobenius norm of matrices A and B */ anorm = slange_("1", m, n, &a[a_offset], lda, &work[1]); bnorm = slange_("1", p, n, &b[b_offset], ldb, &work[1]); /* Get machine precision and set up threshold for determining */ /* the effective numerical rank of the matrices A and B. */ ulp = slamch_("Precision"); unfl = slamch_("Safe Minimum"); tola = f2cmax(*m,*n) * f2cmax(anorm,unfl) * ulp; tolb = f2cmax(*p,*n) * f2cmax(bnorm,unfl) * ulp; /* Preprocessing */ i__1 = *lwork - *n; sggsvp3_(jobu, jobv, jobq, m, p, n, &a[a_offset], lda, &b[b_offset], ldb, &tola, &tolb, k, l, &u[u_offset], ldu, &v[v_offset], ldv, &q[ q_offset], ldq, &iwork[1], &work[1], &work[*n + 1], &i__1, info); /* Compute the GSVD of two upper "triangular" matrices */ stgsja_(jobu, jobv, jobq, m, p, n, k, l, &a[a_offset], lda, &b[b_offset], ldb, &tola, &tolb, &alpha[1], &beta[1], &u[u_offset], ldu, &v[ v_offset], ldv, &q[q_offset], ldq, &work[1], &ncallmycycle, info); /* Sort the singular values and store the pivot indices in IWORK */ /* Copy ALPHA to WORK, then sort ALPHA in WORK */ scopy_(n, &alpha[1], &c__1, &work[1], &c__1); /* Computing MIN */ i__1 = *l, i__2 = *m - *k; ibnd = f2cmin(i__1,i__2); i__1 = ibnd; for (i__ = 1; i__ <= i__1; ++i__) { /* Scan for largest ALPHA(K+I) */ isub = i__; smax = work[*k + i__]; i__2 = ibnd; for (j = i__ + 1; j <= i__2; ++j) { temp = work[*k + j]; if (temp > smax) { isub = j; smax = temp; } /* L10: */ } if (isub != i__) { work[*k + isub] = work[*k + i__]; work[*k + i__] = smax; iwork[*k + i__] = *k + isub; } else { iwork[*k + i__] = *k + i__; } /* L20: */ } work[1] = (real) lwkopt; return 0; /* End of SGGSVD3 */ } /* sggsvd3_ */