#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 DGBBRD */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download DGBBRD + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE DGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, */ /* LDQ, PT, LDPT, C, LDC, WORK, INFO ) */ /* CHARACTER VECT */ /* INTEGER INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC */ /* DOUBLE PRECISION AB( LDAB, * ), C( LDC, * ), D( * ), E( * ), */ /* $ PT( LDPT, * ), Q( LDQ, * ), WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > DGBBRD reduces a real general m-by-n band matrix A to upper */ /* > bidiagonal form B by an orthogonal transformation: Q**T * A * P = B. */ /* > */ /* > The routine computes B, and optionally forms Q or P**T, or computes */ /* > Q**T*C for a given matrix C. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] VECT */ /* > \verbatim */ /* > VECT is CHARACTER*1 */ /* > Specifies whether or not the matrices Q and P**T are to be */ /* > formed. */ /* > = 'N': do not form Q or P**T; */ /* > = 'Q': form Q only; */ /* > = 'P': form P**T only; */ /* > = 'B': form both. */ /* > \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 matrix A. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] NCC */ /* > \verbatim */ /* > NCC is INTEGER */ /* > The number of columns of the matrix C. NCC >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] KL */ /* > \verbatim */ /* > KL is INTEGER */ /* > The number of subdiagonals of the matrix A. KL >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] KU */ /* > \verbatim */ /* > KU is INTEGER */ /* > The number of superdiagonals of the matrix A. KU >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] AB */ /* > \verbatim */ /* > AB is DOUBLE PRECISION array, dimension (LDAB,N) */ /* > On entry, the m-by-n band matrix A, stored in rows 1 to */ /* > KL+KU+1. The j-th column of A is stored in the j-th column of */ /* > the array AB as follows: */ /* > AB(ku+1+i-j,j) = A(i,j) for f2cmax(1,j-ku)<=i<=f2cmin(m,j+kl). */ /* > On exit, A is overwritten by values generated during the */ /* > reduction. */ /* > \endverbatim */ /* > */ /* > \param[in] LDAB */ /* > \verbatim */ /* > LDAB is INTEGER */ /* > The leading dimension of the array A. LDAB >= KL+KU+1. */ /* > \endverbatim */ /* > */ /* > \param[out] D */ /* > \verbatim */ /* > D is DOUBLE PRECISION array, dimension (f2cmin(M,N)) */ /* > The diagonal elements of the bidiagonal matrix B. */ /* > \endverbatim */ /* > */ /* > \param[out] E */ /* > \verbatim */ /* > E is DOUBLE PRECISION array, dimension (f2cmin(M,N)-1) */ /* > The superdiagonal elements of the bidiagonal matrix B. */ /* > \endverbatim */ /* > */ /* > \param[out] Q */ /* > \verbatim */ /* > Q is DOUBLE PRECISION array, dimension (LDQ,M) */ /* > If VECT = 'Q' or 'B', the m-by-m orthogonal matrix Q. */ /* > If VECT = 'N' or 'P', the array Q is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDQ */ /* > \verbatim */ /* > LDQ is INTEGER */ /* > The leading dimension of the array Q. */ /* > LDQ >= f2cmax(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise. */ /* > \endverbatim */ /* > */ /* > \param[out] PT */ /* > \verbatim */ /* > PT is DOUBLE PRECISION array, dimension (LDPT,N) */ /* > If VECT = 'P' or 'B', the n-by-n orthogonal matrix P'. */ /* > If VECT = 'N' or 'Q', the array PT is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDPT */ /* > \verbatim */ /* > LDPT is INTEGER */ /* > The leading dimension of the array PT. */ /* > LDPT >= f2cmax(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise. */ /* > \endverbatim */ /* > */ /* > \param[in,out] C */ /* > \verbatim */ /* > C is DOUBLE PRECISION array, dimension (LDC,NCC) */ /* > On entry, an m-by-ncc matrix C. */ /* > On exit, C is overwritten by Q**T*C. */ /* > C is not referenced if NCC = 0. */ /* > \endverbatim */ /* > */ /* > \param[in] LDC */ /* > \verbatim */ /* > LDC is INTEGER */ /* > The leading dimension of the array C. */ /* > LDC >= f2cmax(1,M) if NCC > 0; LDC >= 1 if NCC = 0. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is DOUBLE PRECISION array, dimension (2*f2cmax(M,N)) */ /* > \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 doubleGBcomputational */ /* ===================================================================== */ /* Subroutine */ int dgbbrd_(char *vect, integer *m, integer *n, integer *ncc, integer *kl, integer *ku, doublereal *ab, integer *ldab, doublereal * d__, doublereal *e, doublereal *q, integer *ldq, doublereal *pt, integer *ldpt, doublereal *c__, integer *ldc, doublereal *work, integer *info) { /* System generated locals */ integer ab_dim1, ab_offset, c_dim1, c_offset, pt_dim1, pt_offset, q_dim1, q_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7; /* Local variables */ integer inca; extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *); integer i__, j, l; extern logical lsame_(char *, char *); logical wantb, wantc; integer minmn; logical wantq; integer j1, j2, kb; doublereal ra, rb; integer kk; doublereal rc; integer ml, mn, nr, mu; doublereal rs; extern /* Subroutine */ int dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *), dlartg_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *), xerbla_(char *, integer *, ftnlen), dlargv_( integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *), dlartv_(integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *); integer kb1, ml0; logical wantpt; integer mu0, klm, kun, nrt, klu1; /* -- 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 the input parameters */ /* Parameter adjustments */ ab_dim1 = *ldab; ab_offset = 1 + ab_dim1 * 1; ab -= ab_offset; --d__; --e; q_dim1 = *ldq; q_offset = 1 + q_dim1 * 1; q -= q_offset; pt_dim1 = *ldpt; pt_offset = 1 + pt_dim1 * 1; pt -= pt_offset; c_dim1 = *ldc; c_offset = 1 + c_dim1 * 1; c__ -= c_offset; --work; /* Function Body */ wantb = lsame_(vect, "B"); wantq = lsame_(vect, "Q") || wantb; wantpt = lsame_(vect, "P") || wantb; wantc = *ncc > 0; klu1 = *kl + *ku + 1; *info = 0; if (! wantq && ! wantpt && ! lsame_(vect, "N")) { *info = -1; } else if (*m < 0) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*ncc < 0) { *info = -4; } else if (*kl < 0) { *info = -5; } else if (*ku < 0) { *info = -6; } else if (*ldab < klu1) { *info = -8; } else if (*ldq < 1 || wantq && *ldq < f2cmax(1,*m)) { *info = -12; } else if (*ldpt < 1 || wantpt && *ldpt < f2cmax(1,*n)) { *info = -14; } else if (*ldc < 1 || wantc && *ldc < f2cmax(1,*m)) { *info = -16; } if (*info != 0) { i__1 = -(*info); xerbla_("DGBBRD", &i__1, (ftnlen)6); return 0; } /* Initialize Q and P**T to the unit matrix, if needed */ if (wantq) { dlaset_("Full", m, m, &c_b8, &c_b9, &q[q_offset], ldq); } if (wantpt) { dlaset_("Full", n, n, &c_b8, &c_b9, &pt[pt_offset], ldpt); } /* Quick return if possible. */ if (*m == 0 || *n == 0) { return 0; } minmn = f2cmin(*m,*n); if (*kl + *ku > 1) { /* Reduce to upper bidiagonal form if KU > 0; if KU = 0, reduce */ /* first to lower bidiagonal form and then transform to upper */ /* bidiagonal */ if (*ku > 0) { ml0 = 1; mu0 = 2; } else { ml0 = 2; mu0 = 1; } /* Wherever possible, plane rotations are generated and applied in */ /* vector operations of length NR over the index set J1:J2:KLU1. */ /* The sines of the plane rotations are stored in WORK(1:f2cmax(m,n)) */ /* and the cosines in WORK(f2cmax(m,n)+1:2*f2cmax(m,n)). */ mn = f2cmax(*m,*n); /* Computing MIN */ i__1 = *m - 1; klm = f2cmin(i__1,*kl); /* Computing MIN */ i__1 = *n - 1; kun = f2cmin(i__1,*ku); kb = klm + kun; kb1 = kb + 1; inca = kb1 * *ldab; nr = 0; j1 = klm + 2; j2 = 1 - kun; i__1 = minmn; for (i__ = 1; i__ <= i__1; ++i__) { /* Reduce i-th column and i-th row of matrix to bidiagonal form */ ml = klm + 1; mu = kun + 1; i__2 = kb; for (kk = 1; kk <= i__2; ++kk) { j1 += kb; j2 += kb; /* generate plane rotations to annihilate nonzero elements */ /* which have been created below the band */ if (nr > 0) { dlargv_(&nr, &ab[klu1 + (j1 - klm - 1) * ab_dim1], &inca, &work[j1], &kb1, &work[mn + j1], &kb1); } /* apply plane rotations from the left */ i__3 = kb; for (l = 1; l <= i__3; ++l) { if (j2 - klm + l - 1 > *n) { nrt = nr - 1; } else { nrt = nr; } if (nrt > 0) { dlartv_(&nrt, &ab[klu1 - l + (j1 - klm + l - 1) * ab_dim1], &inca, &ab[klu1 - l + 1 + (j1 - klm + l - 1) * ab_dim1], &inca, &work[mn + j1], & work[j1], &kb1); } /* L10: */ } if (ml > ml0) { if (ml <= *m - i__ + 1) { /* generate plane rotation to annihilate a(i+ml-1,i) */ /* within the band, and apply rotation from the left */ dlartg_(&ab[*ku + ml - 1 + i__ * ab_dim1], &ab[*ku + ml + i__ * ab_dim1], &work[mn + i__ + ml - 1], &work[i__ + ml - 1], &ra); ab[*ku + ml - 1 + i__ * ab_dim1] = ra; if (i__ < *n) { /* Computing MIN */ i__4 = *ku + ml - 2, i__5 = *n - i__; i__3 = f2cmin(i__4,i__5); i__6 = *ldab - 1; i__7 = *ldab - 1; drot_(&i__3, &ab[*ku + ml - 2 + (i__ + 1) * ab_dim1], &i__6, &ab[*ku + ml - 1 + (i__ + 1) * ab_dim1], &i__7, &work[mn + i__ + ml - 1], &work[i__ + ml - 1]); } } ++nr; j1 -= kb1; } if (wantq) { /* accumulate product of plane rotations in Q */ i__3 = j2; i__4 = kb1; for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) { drot_(m, &q[(j - 1) * q_dim1 + 1], &c__1, &q[j * q_dim1 + 1], &c__1, &work[mn + j], &work[j]); /* L20: */ } } if (wantc) { /* apply plane rotations to C */ i__4 = j2; i__3 = kb1; for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) { drot_(ncc, &c__[j - 1 + c_dim1], ldc, &c__[j + c_dim1] , ldc, &work[mn + j], &work[j]); /* L30: */ } } if (j2 + kun > *n) { /* adjust J2 to keep within the bounds of the matrix */ --nr; j2 -= kb1; } i__3 = j2; i__4 = kb1; for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) { /* create nonzero element a(j-1,j+ku) above the band */ /* and store it in WORK(n+1:2*n) */ work[j + kun] = work[j] * ab[(j + kun) * ab_dim1 + 1]; ab[(j + kun) * ab_dim1 + 1] = work[mn + j] * ab[(j + kun) * ab_dim1 + 1]; /* L40: */ } /* generate plane rotations to annihilate nonzero elements */ /* which have been generated above the band */ if (nr > 0) { dlargv_(&nr, &ab[(j1 + kun - 1) * ab_dim1 + 1], &inca, & work[j1 + kun], &kb1, &work[mn + j1 + kun], &kb1); } /* apply plane rotations from the right */ i__4 = kb; for (l = 1; l <= i__4; ++l) { if (j2 + l - 1 > *m) { nrt = nr - 1; } else { nrt = nr; } if (nrt > 0) { dlartv_(&nrt, &ab[l + 1 + (j1 + kun - 1) * ab_dim1], & inca, &ab[l + (j1 + kun) * ab_dim1], &inca, & work[mn + j1 + kun], &work[j1 + kun], &kb1); } /* L50: */ } if (ml == ml0 && mu > mu0) { if (mu <= *n - i__ + 1) { /* generate plane rotation to annihilate a(i,i+mu-1) */ /* within the band, and apply rotation from the right */ dlartg_(&ab[*ku - mu + 3 + (i__ + mu - 2) * ab_dim1], &ab[*ku - mu + 2 + (i__ + mu - 1) * ab_dim1], &work[mn + i__ + mu - 1], &work[i__ + mu - 1], &ra); ab[*ku - mu + 3 + (i__ + mu - 2) * ab_dim1] = ra; /* Computing MIN */ i__3 = *kl + mu - 2, i__5 = *m - i__; i__4 = f2cmin(i__3,i__5); drot_(&i__4, &ab[*ku - mu + 4 + (i__ + mu - 2) * ab_dim1], &c__1, &ab[*ku - mu + 3 + (i__ + mu - 1) * ab_dim1], &c__1, &work[mn + i__ + mu - 1], &work[i__ + mu - 1]); } ++nr; j1 -= kb1; } if (wantpt) { /* accumulate product of plane rotations in P**T */ i__4 = j2; i__3 = kb1; for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) { drot_(n, &pt[j + kun - 1 + pt_dim1], ldpt, &pt[j + kun + pt_dim1], ldpt, &work[mn + j + kun], & work[j + kun]); /* L60: */ } } if (j2 + kb > *m) { /* adjust J2 to keep within the bounds of the matrix */ --nr; j2 -= kb1; } i__3 = j2; i__4 = kb1; for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) { /* create nonzero element a(j+kl+ku,j+ku-1) below the */ /* band and store it in WORK(1:n) */ work[j + kb] = work[j + kun] * ab[klu1 + (j + kun) * ab_dim1]; ab[klu1 + (j + kun) * ab_dim1] = work[mn + j + kun] * ab[ klu1 + (j + kun) * ab_dim1]; /* L70: */ } if (ml > ml0) { --ml; } else { --mu; } /* L80: */ } /* L90: */ } } if (*ku == 0 && *kl > 0) { /* A has been reduced to lower bidiagonal form */ /* Transform lower bidiagonal form to upper bidiagonal by applying */ /* plane rotations from the left, storing diagonal elements in D */ /* and off-diagonal elements in E */ /* Computing MIN */ i__2 = *m - 1; i__1 = f2cmin(i__2,*n); for (i__ = 1; i__ <= i__1; ++i__) { dlartg_(&ab[i__ * ab_dim1 + 1], &ab[i__ * ab_dim1 + 2], &rc, &rs, &ra); d__[i__] = ra; if (i__ < *n) { e[i__] = rs * ab[(i__ + 1) * ab_dim1 + 1]; ab[(i__ + 1) * ab_dim1 + 1] = rc * ab[(i__ + 1) * ab_dim1 + 1] ; } if (wantq) { drot_(m, &q[i__ * q_dim1 + 1], &c__1, &q[(i__ + 1) * q_dim1 + 1], &c__1, &rc, &rs); } if (wantc) { drot_(ncc, &c__[i__ + c_dim1], ldc, &c__[i__ + 1 + c_dim1], ldc, &rc, &rs); } /* L100: */ } if (*m <= *n) { d__[*m] = ab[*m * ab_dim1 + 1]; } } else if (*ku > 0) { /* A has been reduced to upper bidiagonal form */ if (*m < *n) { /* Annihilate a(m,m+1) by applying plane rotations from the */ /* right, storing diagonal elements in D and off-diagonal */ /* elements in E */ rb = ab[*ku + (*m + 1) * ab_dim1]; for (i__ = *m; i__ >= 1; --i__) { dlartg_(&ab[*ku + 1 + i__ * ab_dim1], &rb, &rc, &rs, &ra); d__[i__] = ra; if (i__ > 1) { rb = -rs * ab[*ku + i__ * ab_dim1]; e[i__ - 1] = rc * ab[*ku + i__ * ab_dim1]; } if (wantpt) { drot_(n, &pt[i__ + pt_dim1], ldpt, &pt[*m + 1 + pt_dim1], ldpt, &rc, &rs); } /* L110: */ } } else { /* Copy off-diagonal elements to E and diagonal elements to D */ i__1 = minmn - 1; for (i__ = 1; i__ <= i__1; ++i__) { e[i__] = ab[*ku + (i__ + 1) * ab_dim1]; /* L120: */ } i__1 = minmn; for (i__ = 1; i__ <= i__1; ++i__) { d__[i__] = ab[*ku + 1 + i__ * ab_dim1]; /* L130: */ } } } else { /* A is diagonal. Set elements of E to zero and copy diagonal */ /* elements to D. */ i__1 = minmn - 1; for (i__ = 1; i__ <= i__1; ++i__) { e[i__] = 0.; /* L140: */ } i__1 = minmn; for (i__ = 1; i__ <= i__1; ++i__) { d__[i__] = ab[i__ * ab_dim1 + 1]; /* L150: */ } } return 0; /* End of DGBBRD */ } /* dgbbrd_ */