#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 DLALS0 applies back multiplying factors in solving the least squares problem using divide and c onquer SVD approach. Used by sgelsd. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download DLALS0 + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE DLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, */ /* PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, */ /* POLES, DIFL, DIFR, Z, K, C, S, WORK, INFO ) */ /* INTEGER GIVPTR, ICOMPQ, INFO, K, LDB, LDBX, LDGCOL, */ /* $ LDGNUM, NL, NR, NRHS, SQRE */ /* DOUBLE PRECISION C, S */ /* INTEGER GIVCOL( LDGCOL, * ), PERM( * ) */ /* DOUBLE PRECISION B( LDB, * ), BX( LDBX, * ), DIFL( * ), */ /* $ DIFR( LDGNUM, * ), GIVNUM( LDGNUM, * ), */ /* $ POLES( LDGNUM, * ), WORK( * ), Z( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > DLALS0 applies back the multiplying factors of either the left or the */ /* > right singular vector matrix of a diagonal matrix appended by a row */ /* > to the right hand side matrix B in solving the least squares problem */ /* > using the divide-and-conquer SVD approach. */ /* > */ /* > For the left singular vector matrix, three types of orthogonal */ /* > matrices are involved: */ /* > */ /* > (1L) Givens rotations: the number of such rotations is GIVPTR; the */ /* > pairs of columns/rows they were applied to are stored in GIVCOL; */ /* > and the C- and S-values of these rotations are stored in GIVNUM. */ /* > */ /* > (2L) Permutation. The (NL+1)-st row of B is to be moved to the first */ /* > row, and for J=2:N, PERM(J)-th row of B is to be moved to the */ /* > J-th row. */ /* > */ /* > (3L) The left singular vector matrix of the remaining matrix. */ /* > */ /* > For the right singular vector matrix, four types of orthogonal */ /* > matrices are involved: */ /* > */ /* > (1R) The right singular vector matrix of the remaining matrix. */ /* > */ /* > (2R) If SQRE = 1, one extra Givens rotation to generate the right */ /* > null space. */ /* > */ /* > (3R) The inverse transformation of (2L). */ /* > */ /* > (4R) The inverse transformation of (1L). */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] ICOMPQ */ /* > \verbatim */ /* > ICOMPQ is INTEGER */ /* > Specifies whether singular vectors are to be computed in */ /* > factored form: */ /* > = 0: Left singular vector matrix. */ /* > = 1: Right singular vector matrix. */ /* > \endverbatim */ /* > */ /* > \param[in] NL */ /* > \verbatim */ /* > NL is INTEGER */ /* > The row dimension of the upper block. NL >= 1. */ /* > \endverbatim */ /* > */ /* > \param[in] NR */ /* > \verbatim */ /* > NR is INTEGER */ /* > The row dimension of the lower block. NR >= 1. */ /* > \endverbatim */ /* > */ /* > \param[in] SQRE */ /* > \verbatim */ /* > SQRE is INTEGER */ /* > = 0: the lower block is an NR-by-NR square matrix. */ /* > = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */ /* > */ /* > The bidiagonal matrix has row dimension N = NL + NR + 1, */ /* > and column dimension M = N + SQRE. */ /* > \endverbatim */ /* > */ /* > \param[in] NRHS */ /* > \verbatim */ /* > NRHS is INTEGER */ /* > The number of columns of B and BX. NRHS must be at least 1. */ /* > \endverbatim */ /* > */ /* > \param[in,out] B */ /* > \verbatim */ /* > B is DOUBLE PRECISION array, dimension ( LDB, NRHS ) */ /* > On input, B contains the right hand sides of the least */ /* > squares problem in rows 1 through M. On output, B contains */ /* > the solution X in rows 1 through N. */ /* > \endverbatim */ /* > */ /* > \param[in] LDB */ /* > \verbatim */ /* > LDB is INTEGER */ /* > The leading dimension of B. LDB must be at least */ /* > f2cmax(1,MAX( M, N ) ). */ /* > \endverbatim */ /* > */ /* > \param[out] BX */ /* > \verbatim */ /* > BX is DOUBLE PRECISION array, dimension ( LDBX, NRHS ) */ /* > \endverbatim */ /* > */ /* > \param[in] LDBX */ /* > \verbatim */ /* > LDBX is INTEGER */ /* > The leading dimension of BX. */ /* > \endverbatim */ /* > */ /* > \param[in] PERM */ /* > \verbatim */ /* > PERM is INTEGER array, dimension ( N ) */ /* > The permutations (from deflation and sorting) applied */ /* > to the two blocks. */ /* > \endverbatim */ /* > */ /* > \param[in] GIVPTR */ /* > \verbatim */ /* > GIVPTR is INTEGER */ /* > The number of Givens rotations which took place in this */ /* > subproblem. */ /* > \endverbatim */ /* > */ /* > \param[in] GIVCOL */ /* > \verbatim */ /* > GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) */ /* > Each pair of numbers indicates a pair of rows/columns */ /* > involved in a Givens rotation. */ /* > \endverbatim */ /* > */ /* > \param[in] LDGCOL */ /* > \verbatim */ /* > LDGCOL is INTEGER */ /* > The leading dimension of GIVCOL, must be at least N. */ /* > \endverbatim */ /* > */ /* > \param[in] GIVNUM */ /* > \verbatim */ /* > GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */ /* > Each number indicates the C or S value used in the */ /* > corresponding Givens rotation. */ /* > \endverbatim */ /* > */ /* > \param[in] LDGNUM */ /* > \verbatim */ /* > LDGNUM is INTEGER */ /* > The leading dimension of arrays DIFR, POLES and */ /* > GIVNUM, must be at least K. */ /* > \endverbatim */ /* > */ /* > \param[in] POLES */ /* > \verbatim */ /* > POLES is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */ /* > On entry, POLES(1:K, 1) contains the new singular */ /* > values obtained from solving the secular equation, and */ /* > POLES(1:K, 2) is an array containing the poles in the secular */ /* > equation. */ /* > \endverbatim */ /* > */ /* > \param[in] DIFL */ /* > \verbatim */ /* > DIFL is DOUBLE PRECISION array, dimension ( K ). */ /* > On entry, DIFL(I) is the distance between I-th updated */ /* > (undeflated) singular value and the I-th (undeflated) old */ /* > singular value. */ /* > \endverbatim */ /* > */ /* > \param[in] DIFR */ /* > \verbatim */ /* > DIFR is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). */ /* > On entry, DIFR(I, 1) contains the distances between I-th */ /* > updated (undeflated) singular value and the I+1-th */ /* > (undeflated) old singular value. And DIFR(I, 2) is the */ /* > normalizing factor for the I-th right singular vector. */ /* > \endverbatim */ /* > */ /* > \param[in] Z */ /* > \verbatim */ /* > Z is DOUBLE PRECISION array, dimension ( K ) */ /* > Contain the components of the deflation-adjusted updating row */ /* > vector. */ /* > \endverbatim */ /* > */ /* > \param[in] K */ /* > \verbatim */ /* > K is INTEGER */ /* > Contains the dimension of the non-deflated matrix, */ /* > This is the order of the related secular equation. 1 <= K <=N. */ /* > \endverbatim */ /* > */ /* > \param[in] C */ /* > \verbatim */ /* > C is DOUBLE PRECISION */ /* > C contains garbage if SQRE =0 and the C-value of a Givens */ /* > rotation related to the right null space if SQRE = 1. */ /* > \endverbatim */ /* > */ /* > \param[in] S */ /* > \verbatim */ /* > S is DOUBLE PRECISION */ /* > S contains garbage if SQRE =0 and the S-value of a Givens */ /* > rotation related to the right null space if SQRE = 1. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is DOUBLE PRECISION array, dimension ( K ) */ /* > \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 doubleOTHERcomputational */ /* > \par Contributors: */ /* ================== */ /* > */ /* > Ming Gu and Ren-Cang Li, Computer Science Division, University of */ /* > California at Berkeley, USA \n */ /* > Osni Marques, LBNL/NERSC, USA \n */ /* ===================================================================== */ /* Subroutine */ int dlals0_(integer *icompq, integer *nl, integer *nr, integer *sqre, integer *nrhs, doublereal *b, integer *ldb, doublereal *bx, integer *ldbx, integer *perm, integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum, integer *ldgnum, doublereal * poles, doublereal *difl, doublereal *difr, doublereal *z__, integer * k, doublereal *c__, doublereal *s, doublereal *work, integer *info) { /* System generated locals */ integer givcol_dim1, givcol_offset, b_dim1, b_offset, bx_dim1, bx_offset, difr_dim1, difr_offset, givnum_dim1, givnum_offset, poles_dim1, poles_offset, i__1, i__2; doublereal d__1; /* Local variables */ doublereal temp; extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *); extern doublereal dnrm2_(integer *, doublereal *, integer *); integer i__, j, m, n; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); doublereal diflj, difrj, dsigj; extern /* Subroutine */ int dgemv_(char *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *), dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); extern doublereal dlamc3_(doublereal *, doublereal *); doublereal dj; extern /* Subroutine */ int dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *), dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *), xerbla_(char *, integer *, ftnlen); doublereal dsigjp; integer nlp1; /* -- 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 */ b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; bx_dim1 = *ldbx; bx_offset = 1 + bx_dim1 * 1; bx -= bx_offset; --perm; givcol_dim1 = *ldgcol; givcol_offset = 1 + givcol_dim1 * 1; givcol -= givcol_offset; difr_dim1 = *ldgnum; difr_offset = 1 + difr_dim1 * 1; difr -= difr_offset; poles_dim1 = *ldgnum; poles_offset = 1 + poles_dim1 * 1; poles -= poles_offset; givnum_dim1 = *ldgnum; givnum_offset = 1 + givnum_dim1 * 1; givnum -= givnum_offset; --difl; --z__; --work; /* Function Body */ *info = 0; n = *nl + *nr + 1; if (*icompq < 0 || *icompq > 1) { *info = -1; } else if (*nl < 1) { *info = -2; } else if (*nr < 1) { *info = -3; } else if (*sqre < 0 || *sqre > 1) { *info = -4; } else if (*nrhs < 1) { *info = -5; } else if (*ldb < n) { *info = -7; } else if (*ldbx < n) { *info = -9; } else if (*givptr < 0) { *info = -11; } else if (*ldgcol < n) { *info = -13; } else if (*ldgnum < n) { *info = -15; //} else if (*k < 1) { } else if (*k < 0) { *info = -20; } if (*info != 0) { i__1 = -(*info); xerbla_("DLALS0", &i__1, (ftnlen)6); return 0; } m = n + *sqre; nlp1 = *nl + 1; if (*icompq == 0) { /* Apply back orthogonal transformations from the left. */ /* Step (1L): apply back the Givens rotations performed. */ i__1 = *givptr; for (i__ = 1; i__ <= i__1; ++i__) { drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, & b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ + (givnum_dim1 << 1)], &givnum[i__ + givnum_dim1]); /* L10: */ } /* Step (2L): permute rows of B. */ dcopy_(nrhs, &b[nlp1 + b_dim1], ldb, &bx[bx_dim1 + 1], ldbx); i__1 = n; for (i__ = 2; i__ <= i__1; ++i__) { dcopy_(nrhs, &b[perm[i__] + b_dim1], ldb, &bx[i__ + bx_dim1], ldbx); /* L20: */ } /* Step (3L): apply the inverse of the left singular vector */ /* matrix to BX. */ if (*k == 1) { dcopy_(nrhs, &bx[bx_offset], ldbx, &b[b_offset], ldb); if (z__[1] < 0.) { dscal_(nrhs, &c_b5, &b[b_offset], ldb); } } else { i__1 = *k; for (j = 1; j <= i__1; ++j) { diflj = difl[j]; dj = poles[j + poles_dim1]; dsigj = -poles[j + (poles_dim1 << 1)]; if (j < *k) { difrj = -difr[j + difr_dim1]; dsigjp = -poles[j + 1 + (poles_dim1 << 1)]; } if (z__[j] == 0. || poles[j + (poles_dim1 << 1)] == 0.) { work[j] = 0.; } else { work[j] = -poles[j + (poles_dim1 << 1)] * z__[j] / diflj / (poles[j + (poles_dim1 << 1)] + dj); } i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] == 0.) { work[i__] = 0.; } else { work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__] / (dlamc3_(&poles[i__ + (poles_dim1 << 1)], & dsigj) - diflj) / (poles[i__ + (poles_dim1 << 1)] + dj); } /* L30: */ } i__2 = *k; for (i__ = j + 1; i__ <= i__2; ++i__) { if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] == 0.) { work[i__] = 0.; } else { work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__] / (dlamc3_(&poles[i__ + (poles_dim1 << 1)], & dsigjp) + difrj) / (poles[i__ + (poles_dim1 << 1)] + dj); } /* L40: */ } work[1] = -1.; temp = dnrm2_(k, &work[1], &c__1); dgemv_("T", k, nrhs, &c_b11, &bx[bx_offset], ldbx, &work[1], & c__1, &c_b13, &b[j + b_dim1], ldb); dlascl_("G", &c__0, &c__0, &temp, &c_b11, &c__1, nrhs, &b[j + b_dim1], ldb, info); /* L50: */ } } /* Move the deflated rows of BX to B also. */ if (*k < f2cmax(m,n)) { i__1 = n - *k; dlacpy_("A", &i__1, nrhs, &bx[*k + 1 + bx_dim1], ldbx, &b[*k + 1 + b_dim1], ldb); } } else { /* Apply back the right orthogonal transformations. */ /* Step (1R): apply back the new right singular vector matrix */ /* to B. */ if (*k == 1) { dcopy_(nrhs, &b[b_offset], ldb, &bx[bx_offset], ldbx); } else { i__1 = *k; for (j = 1; j <= i__1; ++j) { dsigj = poles[j + (poles_dim1 << 1)]; if (z__[j] == 0.) { work[j] = 0.; } else { work[j] = -z__[j] / difl[j] / (dsigj + poles[j + poles_dim1]) / difr[j + (difr_dim1 << 1)]; } i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { if (z__[j] == 0.) { work[i__] = 0.; } else { d__1 = -poles[i__ + 1 + (poles_dim1 << 1)]; work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difr[ i__ + difr_dim1]) / (dsigj + poles[i__ + poles_dim1]) / difr[i__ + (difr_dim1 << 1)]; } /* L60: */ } i__2 = *k; for (i__ = j + 1; i__ <= i__2; ++i__) { if (z__[j] == 0.) { work[i__] = 0.; } else { d__1 = -poles[i__ + (poles_dim1 << 1)]; work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difl[ i__]) / (dsigj + poles[i__ + poles_dim1]) / difr[i__ + (difr_dim1 << 1)]; } /* L70: */ } dgemv_("T", k, nrhs, &c_b11, &b[b_offset], ldb, &work[1], & c__1, &c_b13, &bx[j + bx_dim1], ldbx); /* L80: */ } } /* Step (2R): if SQRE = 1, apply back the rotation that is */ /* related to the right null space of the subproblem. */ if (*sqre == 1) { dcopy_(nrhs, &b[m + b_dim1], ldb, &bx[m + bx_dim1], ldbx); drot_(nrhs, &bx[bx_dim1 + 1], ldbx, &bx[m + bx_dim1], ldbx, c__, s); } if (*k < f2cmax(m,n)) { i__1 = n - *k; dlacpy_("A", &i__1, nrhs, &b[*k + 1 + b_dim1], ldb, &bx[*k + 1 + bx_dim1], ldbx); } /* Step (3R): permute rows of B. */ dcopy_(nrhs, &bx[bx_dim1 + 1], ldbx, &b[nlp1 + b_dim1], ldb); if (*sqre == 1) { dcopy_(nrhs, &bx[m + bx_dim1], ldbx, &b[m + b_dim1], ldb); } i__1 = n; for (i__ = 2; i__ <= i__1; ++i__) { dcopy_(nrhs, &bx[i__ + bx_dim1], ldbx, &b[perm[i__] + b_dim1], ldb); /* L90: */ } /* Step (4R): apply back the Givens rotations performed. */ for (i__ = *givptr; i__ >= 1; --i__) { d__1 = -givnum[i__ + givnum_dim1]; drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, & b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ + (givnum_dim1 << 1)], &d__1); /* L100: */ } } return 0; /* End of DLALS0 */ } /* dlals0_ */