#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 SORBDB */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SORBDB + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, */ /* X21, LDX21, X22, LDX22, THETA, PHI, TAUP1, */ /* TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO ) */ /* CHARACTER SIGNS, TRANS */ /* INTEGER INFO, LDX11, LDX12, LDX21, LDX22, LWORK, M, P, */ /* $ Q */ /* REAL PHI( * ), THETA( * ) */ /* REAL TAUP1( * ), TAUP2( * ), TAUQ1( * ), TAUQ2( * ), */ /* $ WORK( * ), X11( LDX11, * ), X12( LDX12, * ), */ /* $ X21( LDX21, * ), X22( LDX22, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SORBDB simultaneously bidiagonalizes the blocks of an M-by-M */ /* > partitioned orthogonal matrix X: */ /* > */ /* > [ B11 | B12 0 0 ] */ /* > [ X11 | X12 ] [ P1 | ] [ 0 | 0 -I 0 ] [ Q1 | ]**T */ /* > X = [-----------] = [---------] [----------------] [---------] . */ /* > [ X21 | X22 ] [ | P2 ] [ B21 | B22 0 0 ] [ | Q2 ] */ /* > [ 0 | 0 0 I ] */ /* > */ /* > X11 is P-by-Q. Q must be no larger than P, M-P, or M-Q. (If this is */ /* > not the case, then X must be transposed and/or permuted. This can be */ /* > done in constant time using the TRANS and SIGNS options. See SORCSD */ /* > for details.) */ /* > */ /* > The orthogonal matrices P1, P2, Q1, and Q2 are P-by-P, (M-P)-by- */ /* > (M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. They are */ /* > represented implicitly by Householder vectors. */ /* > */ /* > B11, B12, B21, and B22 are Q-by-Q bidiagonal matrices represented */ /* > implicitly by angles THETA, PHI. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \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 <= */ /* > MIN(P,M-P,M-Q). */ /* > \endverbatim */ /* > */ /* > \param[in,out] X11 */ /* > \verbatim */ /* > X11 is REAL array, dimension (LDX11,Q) */ /* > On entry, the top-left block of the orthogonal matrix to be */ /* > reduced. On exit, the form depends on TRANS: */ /* > If TRANS = 'N', then */ /* > the columns of tril(X11) specify reflectors for P1, */ /* > the rows of triu(X11,1) specify reflectors for Q1; */ /* > else TRANS = 'T', and */ /* > the rows of triu(X11) specify reflectors for P1, */ /* > the columns of tril(X11,-1) specify reflectors for Q1. */ /* > \endverbatim */ /* > */ /* > \param[in] LDX11 */ /* > \verbatim */ /* > LDX11 is INTEGER */ /* > The leading dimension of X11. If TRANS = 'N', then LDX11 >= */ /* > P; else LDX11 >= Q. */ /* > \endverbatim */ /* > */ /* > \param[in,out] X12 */ /* > \verbatim */ /* > X12 is REAL array, dimension (LDX12,M-Q) */ /* > On entry, the top-right block of the orthogonal matrix to */ /* > be reduced. On exit, the form depends on TRANS: */ /* > If TRANS = 'N', then */ /* > the rows of triu(X12) specify the first P reflectors for */ /* > Q2; */ /* > else TRANS = 'T', and */ /* > the columns of tril(X12) specify the first P reflectors */ /* > for Q2. */ /* > \endverbatim */ /* > */ /* > \param[in] LDX12 */ /* > \verbatim */ /* > LDX12 is INTEGER */ /* > The leading dimension of X12. If TRANS = 'N', then LDX12 >= */ /* > P; else LDX11 >= M-Q. */ /* > \endverbatim */ /* > */ /* > \param[in,out] X21 */ /* > \verbatim */ /* > X21 is REAL array, dimension (LDX21,Q) */ /* > On entry, the bottom-left block of the orthogonal matrix to */ /* > be reduced. On exit, the form depends on TRANS: */ /* > If TRANS = 'N', then */ /* > the columns of tril(X21) specify reflectors for P2; */ /* > else TRANS = 'T', and */ /* > the rows of triu(X21) specify reflectors for P2. */ /* > \endverbatim */ /* > */ /* > \param[in] LDX21 */ /* > \verbatim */ /* > LDX21 is INTEGER */ /* > The leading dimension of X21. If TRANS = 'N', then LDX21 >= */ /* > M-P; else LDX21 >= Q. */ /* > \endverbatim */ /* > */ /* > \param[in,out] X22 */ /* > \verbatim */ /* > X22 is REAL array, dimension (LDX22,M-Q) */ /* > On entry, the bottom-right block of the orthogonal matrix to */ /* > be reduced. On exit, the form depends on TRANS: */ /* > If TRANS = 'N', then */ /* > the rows of triu(X22(Q+1:M-P,P+1:M-Q)) specify the last */ /* > M-P-Q reflectors for Q2, */ /* > else TRANS = 'T', and */ /* > the columns of tril(X22(P+1:M-Q,Q+1:M-P)) specify the last */ /* > M-P-Q reflectors for P2. */ /* > \endverbatim */ /* > */ /* > \param[in] LDX22 */ /* > \verbatim */ /* > LDX22 is INTEGER */ /* > The leading dimension of X22. If TRANS = 'N', then LDX22 >= */ /* > M-P; else LDX22 >= M-Q. */ /* > \endverbatim */ /* > */ /* > \param[out] THETA */ /* > \verbatim */ /* > THETA is REAL array, dimension (Q) */ /* > The entries of the bidiagonal blocks B11, B12, B21, B22 can */ /* > be computed from the angles THETA and PHI. See Further */ /* > Details. */ /* > \endverbatim */ /* > */ /* > \param[out] PHI */ /* > \verbatim */ /* > PHI is REAL array, dimension (Q-1) */ /* > The entries of the bidiagonal blocks B11, B12, B21, B22 can */ /* > be computed from the angles THETA and PHI. See Further */ /* > Details. */ /* > \endverbatim */ /* > */ /* > \param[out] TAUP1 */ /* > \verbatim */ /* > TAUP1 is REAL array, dimension (P) */ /* > The scalar factors of the elementary reflectors that define */ /* > P1. */ /* > \endverbatim */ /* > */ /* > \param[out] TAUP2 */ /* > \verbatim */ /* > TAUP2 is REAL array, dimension (M-P) */ /* > The scalar factors of the elementary reflectors that define */ /* > P2. */ /* > \endverbatim */ /* > */ /* > \param[out] TAUQ1 */ /* > \verbatim */ /* > TAUQ1 is REAL array, dimension (Q) */ /* > The scalar factors of the elementary reflectors that define */ /* > Q1. */ /* > \endverbatim */ /* > */ /* > \param[out] TAUQ2 */ /* > \verbatim */ /* > TAUQ2 is REAL array, dimension (M-Q) */ /* > The scalar factors of the elementary reflectors that define */ /* > Q2. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is REAL array, dimension (LWORK) */ /* > \endverbatim */ /* > */ /* > \param[in] LWORK */ /* > \verbatim */ /* > LWORK is INTEGER */ /* > The dimension of the array WORK. LWORK >= M-Q. */ /* > */ /* > If LWORK = -1, then a workspace query is assumed; the routine */ /* > only calculates the optimal size of the WORK array, returns */ /* > this value as the first entry of the WORK array, and no error */ /* > message related to LWORK is issued by XERBLA. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit. */ /* > < 0: if INFO = -i, the i-th argument had an illegal value. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup realOTHERcomputational */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > The bidiagonal blocks B11, B12, B21, and B22 are represented */ /* > implicitly by angles THETA(1), ..., THETA(Q) and PHI(1), ..., */ /* > PHI(Q-1). B11 and B21 are upper bidiagonal, while B21 and B22 are */ /* > lower bidiagonal. Every entry in each bidiagonal band is a product */ /* > of a sine or cosine of a THETA with a sine or cosine of a PHI. See */ /* > [1] or SORCSD for details. */ /* > */ /* > P1, P2, Q1, and Q2 are represented as products of elementary */ /* > reflectors. See SORCSD for details on generating P1, P2, Q1, and Q2 */ /* > using SORGQR and SORGLQ. */ /* > \endverbatim */ /* > \par References: */ /* ================ */ /* > */ /* > [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. */ /* > Algorithms, 50(1):33-65, 2009. */ /* > */ /* ===================================================================== */ /* Subroutine */ int sorbdb_(char *trans, char *signs, integer *m, integer *p, integer *q, real *x11, integer *ldx11, real *x12, integer *ldx12, real *x21, integer *ldx21, real *x22, integer *ldx22, real *theta, real *phi, real *taup1, real *taup2, real *tauq1, real *tauq2, real * work, integer *lwork, integer *info) { /* System generated locals */ integer x11_dim1, x11_offset, x12_dim1, x12_offset, x21_dim1, x21_offset, x22_dim1, x22_offset, i__1, i__2, i__3; real r__1; /* Local variables */ logical colmajor; integer lworkmin, lworkopt; extern real snrm2_(integer *, real *, integer *); integer i__; extern logical lsame_(char *, char *); extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *), slarf_(char *, integer *, integer *, real *, integer *, real *, real *, integer *, real *), saxpy_(integer *, real *, real *, integer *, real *, integer *); real z1, z2, z3, z4; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); logical lquery; extern /* Subroutine */ int slarfgp_(integer *, real *, real *, integer *, real *); /* -- 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 */ /* ==================================================================== */ /* 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; --phi; --taup1; --taup2; --tauq1; --tauq2; --work; /* Function Body */ *info = 0; colmajor = ! lsame_(trans, "T"); if (! lsame_(signs, "O")) { z1 = 1.f; z2 = 1.f; z3 = 1.f; z4 = 1.f; } else { z1 = 1.f; z2 = -1.f; z3 = 1.f; z4 = -1.f; } lquery = *lwork == -1; if (*m < 0) { *info = -3; } else if (*p < 0 || *p > *m) { *info = -4; } else if (*q < 0 || *q > *p || *q > *m - *p || *q > *m - *q) { *info = -5; } else if (colmajor && *ldx11 < f2cmax(1,*p)) { *info = -7; } else if (! colmajor && *ldx11 < f2cmax(1,*q)) { *info = -7; } else if (colmajor && *ldx12 < f2cmax(1,*p)) { *info = -9; } else /* if(complicated condition) */ { /* Computing MAX */ i__1 = 1, i__2 = *m - *q; if (! colmajor && *ldx12 < f2cmax(i__1,i__2)) { *info = -9; } else /* if(complicated condition) */ { /* Computing MAX */ i__1 = 1, i__2 = *m - *p; if (colmajor && *ldx21 < f2cmax(i__1,i__2)) { *info = -11; } else if (! colmajor && *ldx21 < f2cmax(1,*q)) { *info = -11; } else /* if(complicated condition) */ { /* Computing MAX */ i__1 = 1, i__2 = *m - *p; if (colmajor && *ldx22 < f2cmax(i__1,i__2)) { *info = -13; } else /* if(complicated condition) */ { /* Computing MAX */ i__1 = 1, i__2 = *m - *q; if (! colmajor && *ldx22 < f2cmax(i__1,i__2)) { *info = -13; } } } } } /* Compute workspace */ if (*info == 0) { lworkopt = *m - *q; lworkmin = *m - *q; work[1] = (real) lworkopt; if (*lwork < lworkmin && ! lquery) { *info = -21; } } if (*info != 0) { i__1 = -(*info); xerbla_("xORBDB", &i__1, (ftnlen)6); return 0; } else if (lquery) { return 0; } /* Handle column-major and row-major separately */ if (colmajor) { /* Reduce columns 1, ..., Q of X11, X12, X21, and X22 */ i__1 = *q; for (i__ = 1; i__ <= i__1; ++i__) { if (i__ == 1) { i__2 = *p - i__ + 1; sscal_(&i__2, &z1, &x11[i__ + i__ * x11_dim1], &c__1); } else { i__2 = *p - i__ + 1; r__1 = z1 * cos(phi[i__ - 1]); sscal_(&i__2, &r__1, &x11[i__ + i__ * x11_dim1], &c__1); i__2 = *p - i__ + 1; r__1 = -z1 * z3 * z4 * sin(phi[i__ - 1]); saxpy_(&i__2, &r__1, &x12[i__ + (i__ - 1) * x12_dim1], &c__1, &x11[i__ + i__ * x11_dim1], &c__1); } if (i__ == 1) { i__2 = *m - *p - i__ + 1; sscal_(&i__2, &z2, &x21[i__ + i__ * x21_dim1], &c__1); } else { i__2 = *m - *p - i__ + 1; r__1 = z2 * cos(phi[i__ - 1]); sscal_(&i__2, &r__1, &x21[i__ + i__ * x21_dim1], &c__1); i__2 = *m - *p - i__ + 1; r__1 = -z2 * z3 * z4 * sin(phi[i__ - 1]); saxpy_(&i__2, &r__1, &x22[i__ + (i__ - 1) * x22_dim1], &c__1, &x21[i__ + i__ * x21_dim1], &c__1); } i__2 = *m - *p - i__ + 1; i__3 = *p - i__ + 1; theta[i__] = atan2(snrm2_(&i__2, &x21[i__ + i__ * x21_dim1], & c__1), snrm2_(&i__3, &x11[i__ + i__ * x11_dim1], &c__1)); if (*p > i__) { i__2 = *p - i__ + 1; slarfgp_(&i__2, &x11[i__ + i__ * x11_dim1], &x11[i__ + 1 + i__ * x11_dim1], &c__1, &taup1[i__]); } else if (*p == i__) { i__2 = *p - i__ + 1; slarfgp_(&i__2, &x11[i__ + i__ * x11_dim1], &x11[i__ + i__ * x11_dim1], &c__1, &taup1[i__]); } x11[i__ + i__ * x11_dim1] = 1.f; if (*m - *p > i__) { i__2 = *m - *p - i__ + 1; slarfgp_(&i__2, &x21[i__ + i__ * x21_dim1], &x21[i__ + 1 + i__ * x21_dim1], &c__1, &taup2[i__]); } else if (*m - *p == i__) { i__2 = *m - *p - i__ + 1; slarfgp_(&i__2, &x21[i__ + i__ * x21_dim1], &x21[i__ + i__ * x21_dim1], &c__1, &taup2[i__]); } x21[i__ + i__ * x21_dim1] = 1.f; if (*q > i__) { i__2 = *p - i__ + 1; i__3 = *q - i__; slarf_("L", &i__2, &i__3, &x11[i__ + i__ * x11_dim1], &c__1, & taup1[i__], &x11[i__ + (i__ + 1) * x11_dim1], ldx11, & work[1]); } if (*m - *q + 1 > i__) { i__2 = *p - i__ + 1; i__3 = *m - *q - i__ + 1; slarf_("L", &i__2, &i__3, &x11[i__ + i__ * x11_dim1], &c__1, & taup1[i__], &x12[i__ + i__ * x12_dim1], ldx12, &work[ 1]); } if (*q > i__) { i__2 = *m - *p - i__ + 1; i__3 = *q - i__; slarf_("L", &i__2, &i__3, &x21[i__ + i__ * x21_dim1], &c__1, & taup2[i__], &x21[i__ + (i__ + 1) * x21_dim1], ldx21, & work[1]); } if (*m - *q + 1 > i__) { i__2 = *m - *p - i__ + 1; i__3 = *m - *q - i__ + 1; slarf_("L", &i__2, &i__3, &x21[i__ + i__ * x21_dim1], &c__1, & taup2[i__], &x22[i__ + i__ * x22_dim1], ldx22, &work[ 1]); } if (i__ < *q) { i__2 = *q - i__; r__1 = -z1 * z3 * sin(theta[i__]); sscal_(&i__2, &r__1, &x11[i__ + (i__ + 1) * x11_dim1], ldx11); i__2 = *q - i__; r__1 = z2 * z3 * cos(theta[i__]); saxpy_(&i__2, &r__1, &x21[i__ + (i__ + 1) * x21_dim1], ldx21, &x11[i__ + (i__ + 1) * x11_dim1], ldx11); } i__2 = *m - *q - i__ + 1; r__1 = -z1 * z4 * sin(theta[i__]); sscal_(&i__2, &r__1, &x12[i__ + i__ * x12_dim1], ldx12); i__2 = *m - *q - i__ + 1; r__1 = z2 * z4 * cos(theta[i__]); saxpy_(&i__2, &r__1, &x22[i__ + i__ * x22_dim1], ldx22, &x12[i__ + i__ * x12_dim1], ldx12); if (i__ < *q) { i__2 = *q - i__; i__3 = *m - *q - i__ + 1; phi[i__] = atan2(snrm2_(&i__2, &x11[i__ + (i__ + 1) * x11_dim1], ldx11), snrm2_(&i__3, &x12[i__ + i__ * x12_dim1], ldx12)); } if (i__ < *q) { if (*q - i__ == 1) { i__2 = *q - i__; slarfgp_(&i__2, &x11[i__ + (i__ + 1) * x11_dim1], &x11[ i__ + (i__ + 1) * x11_dim1], ldx11, &tauq1[i__]); } else { i__2 = *q - i__; slarfgp_(&i__2, &x11[i__ + (i__ + 1) * x11_dim1], &x11[ i__ + (i__ + 2) * x11_dim1], ldx11, &tauq1[i__]); } x11[i__ + (i__ + 1) * x11_dim1] = 1.f; } if (*q + i__ - 1 < *m) { if (*m - *q == i__) { i__2 = *m - *q - i__ + 1; slarfgp_(&i__2, &x12[i__ + i__ * x12_dim1], &x12[i__ + i__ * x12_dim1], ldx12, &tauq2[i__]); } else { i__2 = *m - *q - i__ + 1; slarfgp_(&i__2, &x12[i__ + i__ * x12_dim1], &x12[i__ + ( i__ + 1) * x12_dim1], ldx12, &tauq2[i__]); } } x12[i__ + i__ * x12_dim1] = 1.f; if (i__ < *q) { i__2 = *p - i__; i__3 = *q - i__; slarf_("R", &i__2, &i__3, &x11[i__ + (i__ + 1) * x11_dim1], ldx11, &tauq1[i__], &x11[i__ + 1 + (i__ + 1) * x11_dim1], ldx11, &work[1]); i__2 = *m - *p - i__; i__3 = *q - i__; slarf_("R", &i__2, &i__3, &x11[i__ + (i__ + 1) * x11_dim1], ldx11, &tauq1[i__], &x21[i__ + 1 + (i__ + 1) * x21_dim1], ldx21, &work[1]); } if (*p > i__) { i__2 = *p - i__; i__3 = *m - *q - i__ + 1; slarf_("R", &i__2, &i__3, &x12[i__ + i__ * x12_dim1], ldx12, & tauq2[i__], &x12[i__ + 1 + i__ * x12_dim1], ldx12, & work[1]); } if (*m - *p > i__) { i__2 = *m - *p - i__; i__3 = *m - *q - i__ + 1; slarf_("R", &i__2, &i__3, &x12[i__ + i__ * x12_dim1], ldx12, & tauq2[i__], &x22[i__ + 1 + i__ * x22_dim1], ldx22, & work[1]); } } /* Reduce columns Q + 1, ..., P of X12, X22 */ i__1 = *p; for (i__ = *q + 1; i__ <= i__1; ++i__) { i__2 = *m - *q - i__ + 1; r__1 = -z1 * z4; sscal_(&i__2, &r__1, &x12[i__ + i__ * x12_dim1], ldx12); if (i__ >= *m - *q) { i__2 = *m - *q - i__ + 1; slarfgp_(&i__2, &x12[i__ + i__ * x12_dim1], &x12[i__ + i__ * x12_dim1], ldx12, &tauq2[i__]); } else { i__2 = *m - *q - i__ + 1; slarfgp_(&i__2, &x12[i__ + i__ * x12_dim1], &x12[i__ + (i__ + 1) * x12_dim1], ldx12, &tauq2[i__]); } x12[i__ + i__ * x12_dim1] = 1.f; if (*p > i__) { i__2 = *p - i__; i__3 = *m - *q - i__ + 1; slarf_("R", &i__2, &i__3, &x12[i__ + i__ * x12_dim1], ldx12, & tauq2[i__], &x12[i__ + 1 + i__ * x12_dim1], ldx12, & work[1]); } if (*m - *p - *q >= 1) { i__2 = *m - *p - *q; i__3 = *m - *q - i__ + 1; slarf_("R", &i__2, &i__3, &x12[i__ + i__ * x12_dim1], ldx12, & tauq2[i__], &x22[*q + 1 + i__ * x22_dim1], ldx22, & work[1]); } } /* Reduce columns P + 1, ..., M - Q of X12, X22 */ i__1 = *m - *p - *q; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *m - *p - *q - i__ + 1; r__1 = z2 * z4; sscal_(&i__2, &r__1, &x22[*q + i__ + (*p + i__) * x22_dim1], ldx22); if (i__ == *m - *p - *q) { i__2 = *m - *p - *q - i__ + 1; slarfgp_(&i__2, &x22[*q + i__ + (*p + i__) * x22_dim1], &x22[* q + i__ + (*p + i__) * x22_dim1], ldx22, &tauq2[*p + i__]); } else { i__2 = *m - *p - *q - i__ + 1; slarfgp_(&i__2, &x22[*q + i__ + (*p + i__) * x22_dim1], &x22[* q + i__ + (*p + i__ + 1) * x22_dim1], ldx22, &tauq2[* p + i__]); } x22[*q + i__ + (*p + i__) * x22_dim1] = 1.f; if (i__ < *m - *p - *q) { i__2 = *m - *p - *q - i__; i__3 = *m - *p - *q - i__ + 1; slarf_("R", &i__2, &i__3, &x22[*q + i__ + (*p + i__) * x22_dim1], ldx22, &tauq2[*p + i__], &x22[*q + i__ + 1 + (*p + i__) * x22_dim1], ldx22, &work[1]); } } } else { /* Reduce columns 1, ..., Q of X11, X12, X21, X22 */ i__1 = *q; for (i__ = 1; i__ <= i__1; ++i__) { if (i__ == 1) { i__2 = *p - i__ + 1; sscal_(&i__2, &z1, &x11[i__ + i__ * x11_dim1], ldx11); } else { i__2 = *p - i__ + 1; r__1 = z1 * cos(phi[i__ - 1]); sscal_(&i__2, &r__1, &x11[i__ + i__ * x11_dim1], ldx11); i__2 = *p - i__ + 1; r__1 = -z1 * z3 * z4 * sin(phi[i__ - 1]); saxpy_(&i__2, &r__1, &x12[i__ - 1 + i__ * x12_dim1], ldx12, & x11[i__ + i__ * x11_dim1], ldx11); } if (i__ == 1) { i__2 = *m - *p - i__ + 1; sscal_(&i__2, &z2, &x21[i__ + i__ * x21_dim1], ldx21); } else { i__2 = *m - *p - i__ + 1; r__1 = z2 * cos(phi[i__ - 1]); sscal_(&i__2, &r__1, &x21[i__ + i__ * x21_dim1], ldx21); i__2 = *m - *p - i__ + 1; r__1 = -z2 * z3 * z4 * sin(phi[i__ - 1]); saxpy_(&i__2, &r__1, &x22[i__ - 1 + i__ * x22_dim1], ldx22, & x21[i__ + i__ * x21_dim1], ldx21); } i__2 = *m - *p - i__ + 1; i__3 = *p - i__ + 1; theta[i__] = atan2(snrm2_(&i__2, &x21[i__ + i__ * x21_dim1], ldx21), snrm2_(&i__3, &x11[i__ + i__ * x11_dim1], ldx11)); i__2 = *p - i__ + 1; slarfgp_(&i__2, &x11[i__ + i__ * x11_dim1], &x11[i__ + (i__ + 1) * x11_dim1], ldx11, &taup1[i__]); x11[i__ + i__ * x11_dim1] = 1.f; if (i__ == *m - *p) { i__2 = *m - *p - i__ + 1; slarfgp_(&i__2, &x21[i__ + i__ * x21_dim1], &x21[i__ + i__ * x21_dim1], ldx21, &taup2[i__]); } else { i__2 = *m - *p - i__ + 1; slarfgp_(&i__2, &x21[i__ + i__ * x21_dim1], &x21[i__ + (i__ + 1) * x21_dim1], ldx21, &taup2[i__]); } x21[i__ + i__ * x21_dim1] = 1.f; if (*q > i__) { i__2 = *q - i__; i__3 = *p - i__ + 1; slarf_("R", &i__2, &i__3, &x11[i__ + i__ * x11_dim1], ldx11, & taup1[i__], &x11[i__ + 1 + i__ * x11_dim1], ldx11, & work[1]); } if (*m - *q + 1 > i__) { i__2 = *m - *q - i__ + 1; i__3 = *p - i__ + 1; slarf_("R", &i__2, &i__3, &x11[i__ + i__ * x11_dim1], ldx11, & taup1[i__], &x12[i__ + i__ * x12_dim1], ldx12, &work[ 1]); } if (*q > i__) { i__2 = *q - i__; i__3 = *m - *p - i__ + 1; slarf_("R", &i__2, &i__3, &x21[i__ + i__ * x21_dim1], ldx21, & taup2[i__], &x21[i__ + 1 + i__ * x21_dim1], ldx21, & work[1]); } if (*m - *q + 1 > i__) { i__2 = *m - *q - i__ + 1; i__3 = *m - *p - i__ + 1; slarf_("R", &i__2, &i__3, &x21[i__ + i__ * x21_dim1], ldx21, & taup2[i__], &x22[i__ + i__ * x22_dim1], ldx22, &work[ 1]); } if (i__ < *q) { i__2 = *q - i__; r__1 = -z1 * z3 * sin(theta[i__]); sscal_(&i__2, &r__1, &x11[i__ + 1 + i__ * x11_dim1], &c__1); i__2 = *q - i__; r__1 = z2 * z3 * cos(theta[i__]); saxpy_(&i__2, &r__1, &x21[i__ + 1 + i__ * x21_dim1], &c__1, & x11[i__ + 1 + i__ * x11_dim1], &c__1); } i__2 = *m - *q - i__ + 1; r__1 = -z1 * z4 * sin(theta[i__]); sscal_(&i__2, &r__1, &x12[i__ + i__ * x12_dim1], &c__1); i__2 = *m - *q - i__ + 1; r__1 = z2 * z4 * cos(theta[i__]); saxpy_(&i__2, &r__1, &x22[i__ + i__ * x22_dim1], &c__1, &x12[i__ + i__ * x12_dim1], &c__1); if (i__ < *q) { i__2 = *q - i__; i__3 = *m - *q - i__ + 1; phi[i__] = atan2(snrm2_(&i__2, &x11[i__ + 1 + i__ * x11_dim1], &c__1), snrm2_(&i__3, &x12[i__ + i__ * x12_dim1], & c__1)); } if (i__ < *q) { if (*q - i__ == 1) { i__2 = *q - i__; slarfgp_(&i__2, &x11[i__ + 1 + i__ * x11_dim1], &x11[i__ + 1 + i__ * x11_dim1], &c__1, &tauq1[i__]); } else { i__2 = *q - i__; slarfgp_(&i__2, &x11[i__ + 1 + i__ * x11_dim1], &x11[i__ + 2 + i__ * x11_dim1], &c__1, &tauq1[i__]); } x11[i__ + 1 + i__ * x11_dim1] = 1.f; } if (*m - *q > i__) { i__2 = *m - *q - i__ + 1; slarfgp_(&i__2, &x12[i__ + i__ * x12_dim1], &x12[i__ + 1 + i__ * x12_dim1], &c__1, &tauq2[i__]); } else { i__2 = *m - *q - i__ + 1; slarfgp_(&i__2, &x12[i__ + i__ * x12_dim1], &x12[i__ + i__ * x12_dim1], &c__1, &tauq2[i__]); } x12[i__ + i__ * x12_dim1] = 1.f; if (i__ < *q) { i__2 = *q - i__; i__3 = *p - i__; slarf_("L", &i__2, &i__3, &x11[i__ + 1 + i__ * x11_dim1], & c__1, &tauq1[i__], &x11[i__ + 1 + (i__ + 1) * x11_dim1], ldx11, &work[1]); i__2 = *q - i__; i__3 = *m - *p - i__; slarf_("L", &i__2, &i__3, &x11[i__ + 1 + i__ * x11_dim1], & c__1, &tauq1[i__], &x21[i__ + 1 + (i__ + 1) * x21_dim1], ldx21, &work[1]); } i__2 = *m - *q - i__ + 1; i__3 = *p - i__; slarf_("L", &i__2, &i__3, &x12[i__ + i__ * x12_dim1], &c__1, & tauq2[i__], &x12[i__ + (i__ + 1) * x12_dim1], ldx12, & work[1]); if (*m - *p - i__ > 0) { i__2 = *m - *q - i__ + 1; i__3 = *m - *p - i__; slarf_("L", &i__2, &i__3, &x12[i__ + i__ * x12_dim1], &c__1, & tauq2[i__], &x22[i__ + (i__ + 1) * x22_dim1], ldx22, & work[1]); } } /* Reduce columns Q + 1, ..., P of X12, X22 */ i__1 = *p; for (i__ = *q + 1; i__ <= i__1; ++i__) { i__2 = *m - *q - i__ + 1; r__1 = -z1 * z4; sscal_(&i__2, &r__1, &x12[i__ + i__ * x12_dim1], &c__1); i__2 = *m - *q - i__ + 1; slarfgp_(&i__2, &x12[i__ + i__ * x12_dim1], &x12[i__ + 1 + i__ * x12_dim1], &c__1, &tauq2[i__]); x12[i__ + i__ * x12_dim1] = 1.f; if (*p > i__) { i__2 = *m - *q - i__ + 1; i__3 = *p - i__; slarf_("L", &i__2, &i__3, &x12[i__ + i__ * x12_dim1], &c__1, & tauq2[i__], &x12[i__ + (i__ + 1) * x12_dim1], ldx12, & work[1]); } if (*m - *p - *q >= 1) { i__2 = *m - *q - i__ + 1; i__3 = *m - *p - *q; slarf_("L", &i__2, &i__3, &x12[i__ + i__ * x12_dim1], &c__1, & tauq2[i__], &x22[i__ + (*q + 1) * x22_dim1], ldx22, & work[1]); } } /* Reduce columns P + 1, ..., M - Q of X12, X22 */ i__1 = *m - *p - *q; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *m - *p - *q - i__ + 1; r__1 = z2 * z4; sscal_(&i__2, &r__1, &x22[*p + i__ + (*q + i__) * x22_dim1], & c__1); if (*m - *p - *q == i__) { i__2 = *m - *p - *q - i__ + 1; slarfgp_(&i__2, &x22[*p + i__ + (*q + i__) * x22_dim1], &x22[* p + i__ + (*q + i__) * x22_dim1], &c__1, &tauq2[*p + i__]); x22[*p + i__ + (*q + i__) * x22_dim1] = 1.f; } else { i__2 = *m - *p - *q - i__ + 1; slarfgp_(&i__2, &x22[*p + i__ + (*q + i__) * x22_dim1], &x22[* p + i__ + 1 + (*q + i__) * x22_dim1], &c__1, &tauq2[* p + i__]); x22[*p + i__ + (*q + i__) * x22_dim1] = 1.f; i__2 = *m - *p - *q - i__ + 1; i__3 = *m - *p - *q - i__; slarf_("L", &i__2, &i__3, &x22[*p + i__ + (*q + i__) * x22_dim1], &c__1, &tauq2[*p + i__], &x22[*p + i__ + (* q + i__ + 1) * x22_dim1], ldx22, &work[1]); } } } return 0; /* End of SORBDB */ } /* sorbdb_ */