#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 DORCSD */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download DORCSD + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE DORCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, */ /* SIGNS, M, P, Q, X11, LDX11, X12, */ /* LDX12, X21, LDX21, X22, LDX22, THETA, */ /* U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, */ /* LDV2T, WORK, LWORK, IWORK, INFO ) */ /* CHARACTER JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS */ /* INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12, */ /* $ LDX21, LDX22, LWORK, M, P, Q */ /* INTEGER IWORK( * ) */ /* DOUBLE PRECISION THETA( * ) */ /* DOUBLE PRECISION U1( LDU1, * ), U2( LDU2, * ), V1T( LDV1T, * ), */ /* $ V2T( LDV2T, * ), WORK( * ), X11( LDX11, * ), */ /* $ X12( LDX12, * ), X21( LDX21, * ), X22( LDX22, */ /* $ * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > DORCSD computes the CS decomposition of an M-by-M partitioned */ /* > orthogonal matrix X: */ /* > */ /* > [ I 0 0 | 0 0 0 ] */ /* > [ 0 C 0 | 0 -S 0 ] */ /* > [ X11 | X12 ] [ U1 | ] [ 0 0 0 | 0 0 -I ] [ V1 | ]**T */ /* > X = [-----------] = [---------] [---------------------] [---------] . */ /* > [ X21 | X22 ] [ | U2 ] [ 0 0 0 | I 0 0 ] [ | V2 ] */ /* > [ 0 S 0 | 0 C 0 ] */ /* > [ 0 0 I | 0 0 0 ] */ /* > */ /* > X11 is P-by-Q. The orthogonal matrices U1, U2, V1, and V2 are P-by-P, */ /* > (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are */ /* > R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in */ /* > which R = MIN(P,M-P,Q,M-Q). */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] JOBU1 */ /* > \verbatim */ /* > JOBU1 is CHARACTER */ /* > = 'Y': U1 is computed; */ /* > otherwise: U1 is not computed. */ /* > \endverbatim */ /* > */ /* > \param[in] JOBU2 */ /* > \verbatim */ /* > JOBU2 is CHARACTER */ /* > = 'Y': U2 is computed; */ /* > otherwise: U2 is not computed. */ /* > \endverbatim */ /* > */ /* > \param[in] JOBV1T */ /* > \verbatim */ /* > JOBV1T is CHARACTER */ /* > = 'Y': V1T is computed; */ /* > otherwise: V1T is not computed. */ /* > \endverbatim */ /* > */ /* > \param[in] JOBV2T */ /* > \verbatim */ /* > JOBV2T is CHARACTER */ /* > = 'Y': V2T is computed; */ /* > otherwise: V2T is not computed. */ /* > \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] SIGNS */ /* > \verbatim */ /* > SIGNS is CHARACTER */ /* > = 'O': The lower-left block is made nonpositive (the */ /* > "other" convention); */ /* > otherwise: The upper-right block is made nonpositive (the */ /* > "default" convention). */ /* > \endverbatim */ /* > */ /* > \param[in] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The number of rows and columns in X. */ /* > \endverbatim */ /* > */ /* > \param[in] P */ /* > \verbatim */ /* > P is INTEGER */ /* > The number of rows in X11 and X12. 0 <= P <= M. */ /* > \endverbatim */ /* > */ /* > \param[in] Q */ /* > \verbatim */ /* > Q is INTEGER */ /* > The number of columns in X11 and X21. 0 <= Q <= M. */ /* > \endverbatim */ /* > */ /* > \param[in,out] X11 */ /* > \verbatim */ /* > X11 is DOUBLE PRECISION array, dimension (LDX11,Q) */ /* > On entry, part of the orthogonal matrix whose CSD is desired. */ /* > \endverbatim */ /* > */ /* > \param[in] LDX11 */ /* > \verbatim */ /* > LDX11 is INTEGER */ /* > The leading dimension of X11. LDX11 >= MAX(1,P). */ /* > \endverbatim */ /* > */ /* > \param[in,out] X12 */ /* > \verbatim */ /* > X12 is DOUBLE PRECISION array, dimension (LDX12,M-Q) */ /* > On entry, part of the orthogonal matrix whose CSD is desired. */ /* > \endverbatim */ /* > */ /* > \param[in] LDX12 */ /* > \verbatim */ /* > LDX12 is INTEGER */ /* > The leading dimension of X12. LDX12 >= MAX(1,P). */ /* > \endverbatim */ /* > */ /* > \param[in,out] X21 */ /* > \verbatim */ /* > X21 is DOUBLE PRECISION array, dimension (LDX21,Q) */ /* > On entry, part of the orthogonal matrix whose CSD is desired. */ /* > \endverbatim */ /* > */ /* > \param[in] LDX21 */ /* > \verbatim */ /* > LDX21 is INTEGER */ /* > The leading dimension of X11. LDX21 >= MAX(1,M-P). */ /* > \endverbatim */ /* > */ /* > \param[in,out] X22 */ /* > \verbatim */ /* > X22 is DOUBLE PRECISION array, dimension (LDX22,M-Q) */ /* > On entry, part of the orthogonal matrix whose CSD is desired. */ /* > \endverbatim */ /* > */ /* > \param[in] LDX22 */ /* > \verbatim */ /* > LDX22 is INTEGER */ /* > The leading dimension of X11. LDX22 >= MAX(1,M-P). */ /* > \endverbatim */ /* > */ /* > \param[out] THETA */ /* > \verbatim */ /* > THETA is DOUBLE PRECISION array, dimension (R), in which R = */ /* > MIN(P,M-P,Q,M-Q). */ /* > C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and */ /* > S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ). */ /* > \endverbatim */ /* > */ /* > \param[out] U1 */ /* > \verbatim */ /* > U1 is DOUBLE PRECISION array, dimension (LDU1,P) */ /* > If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1. */ /* > \endverbatim */ /* > */ /* > \param[in] LDU1 */ /* > \verbatim */ /* > LDU1 is INTEGER */ /* > The leading dimension of U1. If JOBU1 = 'Y', LDU1 >= */ /* > MAX(1,P). */ /* > \endverbatim */ /* > */ /* > \param[out] U2 */ /* > \verbatim */ /* > U2 is DOUBLE PRECISION array, dimension (LDU2,M-P) */ /* > If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal */ /* > matrix U2. */ /* > \endverbatim */ /* > */ /* > \param[in] LDU2 */ /* > \verbatim */ /* > LDU2 is INTEGER */ /* > The leading dimension of U2. If JOBU2 = 'Y', LDU2 >= */ /* > MAX(1,M-P). */ /* > \endverbatim */ /* > */ /* > \param[out] V1T */ /* > \verbatim */ /* > V1T is DOUBLE PRECISION array, dimension (LDV1T,Q) */ /* > If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal */ /* > matrix V1**T. */ /* > \endverbatim */ /* > */ /* > \param[in] LDV1T */ /* > \verbatim */ /* > LDV1T is INTEGER */ /* > The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >= */ /* > MAX(1,Q). */ /* > \endverbatim */ /* > */ /* > \param[out] V2T */ /* > \verbatim */ /* > V2T is DOUBLE PRECISION array, dimension (LDV2T,M-Q) */ /* > If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) orthogonal */ /* > matrix V2**T. */ /* > \endverbatim */ /* > */ /* > \param[in] LDV2T */ /* > \verbatim */ /* > LDV2T is INTEGER */ /* > The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >= */ /* > MAX(1,M-Q). */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ /* > If INFO > 0 on exit, WORK(2:R) contains the values PHI(1), */ /* > ..., PHI(R-1) that, together with THETA(1), ..., THETA(R), */ /* > define the matrix in intermediate bidiagonal-block form */ /* > remaining after nonconvergence. INFO specifies the number */ /* > of nonzero PHI's. */ /* > \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 (M-MIN(P, M-P, Q, M-Q)) */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit. */ /* > < 0: if INFO = -i, the i-th argument had an illegal value. */ /* > > 0: DBBCSD did not converge. See the description of WORK */ /* > above for details. */ /* > \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 2017 */ /* > \ingroup doubleOTHERcomputational */ /* ===================================================================== */ /* Subroutine */ int dorcsd_(char *jobu1, char *jobu2, char *jobv1t, char * jobv2t, char *trans, char *signs, integer *m, integer *p, integer *q, doublereal *x11, integer *ldx11, doublereal *x12, integer *ldx12, doublereal *x21, integer *ldx21, doublereal *x22, integer *ldx22, doublereal *theta, doublereal *u1, integer *ldu1, doublereal *u2, integer *ldu2, doublereal *v1t, integer *ldv1t, doublereal *v2t, integer *ldv2t, doublereal *work, integer *lwork, integer *iwork, integer *info) { /* System generated locals */ integer u1_dim1, u1_offset, u2_dim1, u2_offset, v1t_dim1, v1t_offset, v2t_dim1, v2t_offset, x11_dim1, x11_offset, x12_dim1, x12_offset, x21_dim1, x21_offset, x22_dim1, x22_offset, i__1, i__2, i__3, i__4, i__5, i__6; /* Local variables */ integer ib11d, ib11e, ib12d, ib12e, ib21d, ib21e, ib22d, ib22e, iphi; logical colmajor; integer lworkmin; logical defaultsigns; integer lworkopt, i__, j; extern logical lsame_(char *, char *); integer childinfo, lbbcsdworkmin, itaup1, itaup2, itauq1, itauq2, lorbdbworkmin, lbbcsdworkopt; logical wantu1, wantu2; extern /* Subroutine */ int dbbcsd_(char *, char *, char *, char *, char * , integer *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, integer *); integer ibbcsd, lorbdbworkopt; extern /* Subroutine */ int dorbdb_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, integer *); integer iorbdb, lorglqworkmin, lorgqrworkmin; extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *), xerbla_(char *, integer *, ftnlen), dlapmr_(logical *, integer *, integer *, doublereal *, integer *, integer *), dlapmt_(logical *, integer *, integer *, doublereal *, integer *, integer *); integer lorglqworkopt; extern /* Subroutine */ int dorglq_(integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *); integer lorgqrworkopt, iorglq; extern /* Subroutine */ int dorgqr_(integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *); integer iorgqr; char signst[1], transt[1]; integer lbbcsdwork; logical lquery; integer lorbdbwork, lorglqwork, lorgqrwork; logical wantv1t, wantv2t; /* -- 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 2017 */ /* =================================================================== */ /* Test input arguments */ /* Parameter adjustments */ x11_dim1 = *ldx11; x11_offset = 1 + x11_dim1 * 1; x11 -= x11_offset; x12_dim1 = *ldx12; x12_offset = 1 + x12_dim1 * 1; x12 -= x12_offset; x21_dim1 = *ldx21; x21_offset = 1 + x21_dim1 * 1; x21 -= x21_offset; x22_dim1 = *ldx22; x22_offset = 1 + x22_dim1 * 1; x22 -= x22_offset; --theta; 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; --work; --iwork; /* Function Body */ *info = 0; wantu1 = lsame_(jobu1, "Y"); wantu2 = lsame_(jobu2, "Y"); wantv1t = lsame_(jobv1t, "Y"); wantv2t = lsame_(jobv2t, "Y"); colmajor = ! lsame_(trans, "T"); defaultsigns = ! lsame_(signs, "O"); lquery = *lwork == -1; if (*m < 0) { *info = -7; } else if (*p < 0 || *p > *m) { *info = -8; } else if (*q < 0 || *q > *m) { *info = -9; } else if (colmajor && *ldx11 < f2cmax(1,*p)) { *info = -11; } else if (! colmajor && *ldx11 < f2cmax(1,*q)) { *info = -11; } else if (colmajor && *ldx12 < f2cmax(1,*p)) { *info = -13; } else /* if(complicated condition) */ { /* Computing MAX */ i__1 = 1, i__2 = *m - *q; if (! colmajor && *ldx12 < f2cmax(i__1,i__2)) { *info = -13; } else /* if(complicated condition) */ { /* Computing MAX */ i__1 = 1, i__2 = *m - *p; if (colmajor && *ldx21 < f2cmax(i__1,i__2)) { *info = -15; } else if (! colmajor && *ldx21 < f2cmax(1,*q)) { *info = -15; } else /* if(complicated condition) */ { /* Computing MAX */ i__1 = 1, i__2 = *m - *p; if (colmajor && *ldx22 < f2cmax(i__1,i__2)) { *info = -17; } else /* if(complicated condition) */ { /* Computing MAX */ i__1 = 1, i__2 = *m - *q; if (! colmajor && *ldx22 < f2cmax(i__1,i__2)) { *info = -17; } else if (wantu1 && *ldu1 < *p) { *info = -20; } else if (wantu2 && *ldu2 < *m - *p) { *info = -22; } else if (wantv1t && *ldv1t < *q) { *info = -24; } else if (wantv2t && *ldv2t < *m - *q) { *info = -26; } } } } } /* Work with transpose if convenient */ /* Computing MIN */ i__1 = *p, i__2 = *m - *p; /* Computing MIN */ i__3 = *q, i__4 = *m - *q; if (*info == 0 && f2cmin(i__1,i__2) < f2cmin(i__3,i__4)) { if (colmajor) { *(unsigned char *)transt = 'T'; } else { *(unsigned char *)transt = 'N'; } if (defaultsigns) { *(unsigned char *)signst = 'O'; } else { *(unsigned char *)signst = 'D'; } dorcsd_(jobv1t, jobv2t, jobu1, jobu2, transt, signst, m, q, p, &x11[ x11_offset], ldx11, &x21[x21_offset], ldx21, &x12[x12_offset], ldx12, &x22[x22_offset], ldx22, &theta[1], &v1t[v1t_offset], ldv1t, &v2t[v2t_offset], ldv2t, &u1[u1_offset], ldu1, &u2[ u2_offset], ldu2, &work[1], lwork, &iwork[1], info); return 0; } /* Work with permutation [ 0 I; I 0 ] * X * [ 0 I; I 0 ] if */ /* convenient */ if (*info == 0 && *m - *q < *q) { if (defaultsigns) { *(unsigned char *)signst = 'O'; } else { *(unsigned char *)signst = 'D'; } i__1 = *m - *p; i__2 = *m - *q; dorcsd_(jobu2, jobu1, jobv2t, jobv1t, trans, signst, m, &i__1, &i__2, &x22[x22_offset], ldx22, &x21[x21_offset], ldx21, &x12[ x12_offset], ldx12, &x11[x11_offset], ldx11, &theta[1], &u2[ u2_offset], ldu2, &u1[u1_offset], ldu1, &v2t[v2t_offset], ldv2t, &v1t[v1t_offset], ldv1t, &work[1], lwork, &iwork[1], info); return 0; } /* Compute workspace */ if (*info == 0) { iphi = 2; /* Computing MAX */ i__1 = 1, i__2 = *q - 1; itaup1 = iphi + f2cmax(i__1,i__2); itaup2 = itaup1 + f2cmax(1,*p); /* Computing MAX */ i__1 = 1, i__2 = *m - *p; itauq1 = itaup2 + f2cmax(i__1,i__2); itauq2 = itauq1 + f2cmax(1,*q); /* Computing MAX */ i__1 = 1, i__2 = *m - *q; iorgqr = itauq2 + f2cmax(i__1,i__2); i__1 = *m - *q; i__2 = *m - *q; i__3 = *m - *q; /* Computing MAX */ i__5 = 1, i__6 = *m - *q; i__4 = f2cmax(i__5,i__6); dorgqr_(&i__1, &i__2, &i__3, &u1[u1_offset], &i__4, &u1[u1_offset], & work[1], &c_n1, &childinfo); lorgqrworkopt = (integer) work[1]; /* Computing MAX */ i__1 = 1, i__2 = *m - *q; lorgqrworkmin = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = 1, i__2 = *m - *q; iorglq = itauq2 + f2cmax(i__1,i__2); i__1 = *m - *q; i__2 = *m - *q; i__3 = *m - *q; /* Computing MAX */ i__5 = 1, i__6 = *m - *q; i__4 = f2cmax(i__5,i__6); dorglq_(&i__1, &i__2, &i__3, &u1[u1_offset], &i__4, &u1[u1_offset], & work[1], &c_n1, &childinfo); lorglqworkopt = (integer) work[1]; /* Computing MAX */ i__1 = 1, i__2 = *m - *q; lorglqworkmin = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = 1, i__2 = *m - *q; iorbdb = itauq2 + f2cmax(i__1,i__2); dorbdb_(trans, signs, m, p, q, &x11[x11_offset], ldx11, &x12[ x12_offset], ldx12, &x21[x21_offset], ldx21, &x22[x22_offset], ldx22, &theta[1], &v1t[v1t_offset], &u1[u1_offset], &u2[ u2_offset], &v1t[v1t_offset], &v2t[v2t_offset], &work[1], & c_n1, &childinfo); lorbdbworkopt = (integer) work[1]; lorbdbworkmin = lorbdbworkopt; /* Computing MAX */ i__1 = 1, i__2 = *m - *q; ib11d = itauq2 + f2cmax(i__1,i__2); ib11e = ib11d + f2cmax(1,*q); /* Computing MAX */ i__1 = 1, i__2 = *q - 1; ib12d = ib11e + f2cmax(i__1,i__2); ib12e = ib12d + f2cmax(1,*q); /* Computing MAX */ i__1 = 1, i__2 = *q - 1; ib21d = ib12e + f2cmax(i__1,i__2); ib21e = ib21d + f2cmax(1,*q); /* Computing MAX */ i__1 = 1, i__2 = *q - 1; ib22d = ib21e + f2cmax(i__1,i__2); ib22e = ib22d + f2cmax(1,*q); /* Computing MAX */ i__1 = 1, i__2 = *q - 1; ibbcsd = ib22e + f2cmax(i__1,i__2); dbbcsd_(jobu1, jobu2, jobv1t, jobv2t, trans, m, p, q, &theta[1], & theta[1], &u1[u1_offset], ldu1, &u2[u2_offset], ldu2, &v1t[ v1t_offset], ldv1t, &v2t[v2t_offset], ldv2t, &u1[u1_offset], & u1[u1_offset], &u1[u1_offset], &u1[u1_offset], &u1[u1_offset], &u1[u1_offset], &u1[u1_offset], &u1[u1_offset], &work[1], & c_n1, &childinfo); lbbcsdworkopt = (integer) work[1]; lbbcsdworkmin = lbbcsdworkopt; /* Computing MAX */ i__1 = iorgqr + lorgqrworkopt, i__2 = iorglq + lorglqworkopt, i__1 = f2cmax(i__1,i__2), i__2 = iorbdb + lorbdbworkopt, i__1 = f2cmax( i__1,i__2), i__2 = ibbcsd + lbbcsdworkopt; lworkopt = f2cmax(i__1,i__2) - 1; /* Computing MAX */ i__1 = iorgqr + lorgqrworkmin, i__2 = iorglq + lorglqworkmin, i__1 = f2cmax(i__1,i__2), i__2 = iorbdb + lorbdbworkopt, i__1 = f2cmax( i__1,i__2), i__2 = ibbcsd + lbbcsdworkmin; lworkmin = f2cmax(i__1,i__2) - 1; work[1] = (doublereal) f2cmax(lworkopt,lworkmin); if (*lwork < lworkmin && ! lquery) { *info = -22; } else { lorgqrwork = *lwork - iorgqr + 1; lorglqwork = *lwork - iorglq + 1; lorbdbwork = *lwork - iorbdb + 1; lbbcsdwork = *lwork - ibbcsd + 1; } } /* Abort if any illegal arguments */ if (*info != 0) { i__1 = -(*info); xerbla_("DORCSD", &i__1, (ftnlen)6); return 0; } else if (lquery) { return 0; } /* Transform to bidiagonal block form */ dorbdb_(trans, signs, m, p, q, &x11[x11_offset], ldx11, &x12[x12_offset], ldx12, &x21[x21_offset], ldx21, &x22[x22_offset], ldx22, &theta[1] , &work[iphi], &work[itaup1], &work[itaup2], &work[itauq1], &work[ itauq2], &work[iorbdb], &lorbdbwork, &childinfo); /* Accumulate Householder reflectors */ if (colmajor) { if (wantu1 && *p > 0) { dlacpy_("L", p, q, &x11[x11_offset], ldx11, &u1[u1_offset], ldu1); dorgqr_(p, p, q, &u1[u1_offset], ldu1, &work[itaup1], &work[ iorgqr], &lorgqrwork, info); } if (wantu2 && *m - *p > 0) { i__1 = *m - *p; dlacpy_("L", &i__1, q, &x21[x21_offset], ldx21, &u2[u2_offset], ldu2); i__1 = *m - *p; i__2 = *m - *p; dorgqr_(&i__1, &i__2, q, &u2[u2_offset], ldu2, &work[itaup2], & work[iorgqr], &lorgqrwork, info); } if (wantv1t && *q > 0) { i__1 = *q - 1; i__2 = *q - 1; dlacpy_("U", &i__1, &i__2, &x11[(x11_dim1 << 1) + 1], ldx11, &v1t[ (v1t_dim1 << 1) + 2], ldv1t); v1t[v1t_dim1 + 1] = 1.; i__1 = *q; for (j = 2; j <= i__1; ++j) { v1t[j * v1t_dim1 + 1] = 0.; v1t[j + v1t_dim1] = 0.; } i__1 = *q - 1; i__2 = *q - 1; i__3 = *q - 1; dorglq_(&i__1, &i__2, &i__3, &v1t[(v1t_dim1 << 1) + 2], ldv1t, & work[itauq1], &work[iorglq], &lorglqwork, info); } if (wantv2t && *m - *q > 0) { i__1 = *m - *q; dlacpy_("U", p, &i__1, &x12[x12_offset], ldx12, &v2t[v2t_offset], ldv2t); if (*m - *p > *q) { i__1 = *m - *p - *q; i__2 = *m - *p - *q; dlacpy_("U", &i__1, &i__2, &x22[*q + 1 + (*p + 1) * x22_dim1], ldx22, &v2t[*p + 1 + (*p + 1) * v2t_dim1], ldv2t); } if (*m > *q) { i__1 = *m - *q; i__2 = *m - *q; i__3 = *m - *q; dorglq_(&i__1, &i__2, &i__3, &v2t[v2t_offset], ldv2t, &work[ itauq2], &work[iorglq], &lorglqwork, info); } } } else { if (wantu1 && *p > 0) { dlacpy_("U", q, p, &x11[x11_offset], ldx11, &u1[u1_offset], ldu1); dorglq_(p, p, q, &u1[u1_offset], ldu1, &work[itaup1], &work[ iorglq], &lorglqwork, info); } if (wantu2 && *m - *p > 0) { i__1 = *m - *p; dlacpy_("U", q, &i__1, &x21[x21_offset], ldx21, &u2[u2_offset], ldu2); i__1 = *m - *p; i__2 = *m - *p; dorglq_(&i__1, &i__2, q, &u2[u2_offset], ldu2, &work[itaup2], & work[iorglq], &lorglqwork, info); } if (wantv1t && *q > 0) { i__1 = *q - 1; i__2 = *q - 1; dlacpy_("L", &i__1, &i__2, &x11[x11_dim1 + 2], ldx11, &v1t[( v1t_dim1 << 1) + 2], ldv1t); v1t[v1t_dim1 + 1] = 1.; i__1 = *q; for (j = 2; j <= i__1; ++j) { v1t[j * v1t_dim1 + 1] = 0.; v1t[j + v1t_dim1] = 0.; } i__1 = *q - 1; i__2 = *q - 1; i__3 = *q - 1; dorgqr_(&i__1, &i__2, &i__3, &v1t[(v1t_dim1 << 1) + 2], ldv1t, & work[itauq1], &work[iorgqr], &lorgqrwork, info); } if (wantv2t && *m - *q > 0) { i__1 = *m - *q; dlacpy_("L", &i__1, p, &x12[x12_offset], ldx12, &v2t[v2t_offset], ldv2t); i__1 = *m - *p - *q; i__2 = *m - *p - *q; dlacpy_("L", &i__1, &i__2, &x22[*p + 1 + (*q + 1) * x22_dim1], ldx22, &v2t[*p + 1 + (*p + 1) * v2t_dim1], ldv2t); i__1 = *m - *q; i__2 = *m - *q; i__3 = *m - *q; dorgqr_(&i__1, &i__2, &i__3, &v2t[v2t_offset], ldv2t, &work[ itauq2], &work[iorgqr], &lorgqrwork, info); } } /* Compute the CSD of the matrix in bidiagonal-block form */ dbbcsd_(jobu1, jobu2, jobv1t, jobv2t, trans, m, p, q, &theta[1], &work[ iphi], &u1[u1_offset], ldu1, &u2[u2_offset], ldu2, &v1t[ v1t_offset], ldv1t, &v2t[v2t_offset], ldv2t, &work[ib11d], &work[ ib11e], &work[ib12d], &work[ib12e], &work[ib21d], &work[ib21e], & work[ib22d], &work[ib22e], &work[ibbcsd], &lbbcsdwork, info); /* Permute rows and columns to place identity submatrices in top- */ /* left corner of (1,1)-block and/or bottom-right corner of (1,2)- */ /* block and/or bottom-right corner of (2,1)-block and/or top-left */ /* corner of (2,2)-block */ if (*q > 0 && wantu2) { i__1 = *q; for (i__ = 1; i__ <= i__1; ++i__) { iwork[i__] = *m - *p - *q + i__; } i__1 = *m - *p; for (i__ = *q + 1; i__ <= i__1; ++i__) { iwork[i__] = i__ - *q; } if (colmajor) { i__1 = *m - *p; i__2 = *m - *p; dlapmt_(&c_false, &i__1, &i__2, &u2[u2_offset], ldu2, &iwork[1]); } else { i__1 = *m - *p; i__2 = *m - *p; dlapmr_(&c_false, &i__1, &i__2, &u2[u2_offset], ldu2, &iwork[1]); } } if (*m > 0 && wantv2t) { i__1 = *p; for (i__ = 1; i__ <= i__1; ++i__) { iwork[i__] = *m - *p - *q + i__; } i__1 = *m - *q; for (i__ = *p + 1; i__ <= i__1; ++i__) { iwork[i__] = i__ - *p; } if (! colmajor) { i__1 = *m - *q; i__2 = *m - *q; dlapmt_(&c_false, &i__1, &i__2, &v2t[v2t_offset], ldv2t, &iwork[1] ); } else { i__1 = *m - *q; i__2 = *m - *q; dlapmr_(&c_false, &i__1, &i__2, &v2t[v2t_offset], ldv2t, &iwork[1] ); } } return 0; /* End DORCSD */ } /* dorcsd_ */