#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 DGELSY solves overdetermined or underdetermined systems for GE matrices */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download DGELSY + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE DGELSY( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, */ /* WORK, LWORK, INFO ) */ /* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK */ /* DOUBLE PRECISION RCOND */ /* INTEGER JPVT( * ) */ /* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > DGELSY computes the minimum-norm solution to a real linear least */ /* > squares problem: */ /* > minimize || A * X - B || */ /* > using a complete orthogonal factorization of A. A is an M-by-N */ /* > matrix which may be rank-deficient. */ /* > */ /* > Several right hand side vectors b and solution vectors x can be */ /* > handled in a single call; they are stored as the columns of the */ /* > M-by-NRHS right hand side matrix B and the N-by-NRHS solution */ /* > matrix X. */ /* > */ /* > The routine first computes a QR factorization with column pivoting: */ /* > A * P = Q * [ R11 R12 ] */ /* > [ 0 R22 ] */ /* > with R11 defined as the largest leading submatrix whose estimated */ /* > condition number is less than 1/RCOND. The order of R11, RANK, */ /* > is the effective rank of A. */ /* > */ /* > Then, R22 is considered to be negligible, and R12 is annihilated */ /* > by orthogonal transformations from the right, arriving at the */ /* > complete orthogonal factorization: */ /* > A * P = Q * [ T11 0 ] * Z */ /* > [ 0 0 ] */ /* > The minimum-norm solution is then */ /* > X = P * Z**T [ inv(T11)*Q1**T*B ] */ /* > [ 0 ] */ /* > where Q1 consists of the first RANK columns of Q. */ /* > */ /* > This routine is basically identical to the original xGELSX except */ /* > three differences: */ /* > o The call to the subroutine xGEQPF has been substituted by the */ /* > the call to the subroutine xGEQP3. This subroutine is a Blas-3 */ /* > version of the QR factorization with column pivoting. */ /* > o Matrix B (the right hand side) is updated with Blas-3. */ /* > o The permutation of matrix B (the right hand side) is faster and */ /* > more simple. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \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] NRHS */ /* > \verbatim */ /* > NRHS is INTEGER */ /* > The number of right hand sides, i.e., the number of */ /* > columns of matrices B and X. NRHS >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is DOUBLE PRECISION array, dimension (LDA,N) */ /* > On entry, the M-by-N matrix A. */ /* > On exit, A has been overwritten by details of its */ /* > complete orthogonal factorization. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */ /* > \endverbatim */ /* > */ /* > \param[in,out] B */ /* > \verbatim */ /* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */ /* > On entry, the M-by-NRHS right hand side matrix B. */ /* > On exit, the N-by-NRHS solution matrix X. */ /* > \endverbatim */ /* > */ /* > \param[in] LDB */ /* > \verbatim */ /* > LDB is INTEGER */ /* > The leading dimension of the array B. LDB >= f2cmax(1,M,N). */ /* > \endverbatim */ /* > */ /* > \param[in,out] JPVT */ /* > \verbatim */ /* > JPVT is INTEGER array, dimension (N) */ /* > On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted */ /* > to the front of AP, otherwise column i is a free column. */ /* > On exit, if JPVT(i) = k, then the i-th column of AP */ /* > was the k-th column of A. */ /* > \endverbatim */ /* > */ /* > \param[in] RCOND */ /* > \verbatim */ /* > RCOND is DOUBLE PRECISION */ /* > RCOND is used to determine the effective rank of A, which */ /* > is defined as the order of the largest leading triangular */ /* > submatrix R11 in the QR factorization with pivoting of A, */ /* > whose estimated condition number < 1/RCOND. */ /* > \endverbatim */ /* > */ /* > \param[out] RANK */ /* > \verbatim */ /* > RANK is INTEGER */ /* > The effective rank of A, i.e., the order of the submatrix */ /* > R11. This is the same as the order of the submatrix T11 */ /* > in the complete orthogonal factorization of A. */ /* > \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. */ /* > \endverbatim */ /* > */ /* > \param[in] LWORK */ /* > \verbatim */ /* > LWORK is INTEGER */ /* > The dimension of the array WORK. */ /* > The unblocked strategy requires that: */ /* > LWORK >= MAX( MN+3*N+1, 2*MN+NRHS ), */ /* > where MN = f2cmin( M, N ). */ /* > The block algorithm requires that: */ /* > LWORK >= MAX( MN+2*N+NB*(N+1), 2*MN+NB*NRHS ), */ /* > where NB is an upper bound on the blocksize returned */ /* > by ILAENV for the routines DGEQP3, DTZRZF, STZRQF, DORMQR, */ /* > and DORMRZ. */ /* > */ /* > 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 doubleGEsolve */ /* > \par Contributors: */ /* ================== */ /* > */ /* > A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA \n */ /* > E. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain \n */ /* > G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain \n */ /* > */ /* ===================================================================== */ /* Subroutine */ int dgelsy_(integer *m, integer *n, integer *nrhs, doublereal *a, integer *lda, doublereal *b, integer *ldb, integer * jpvt, doublereal *rcond, integer *rank, doublereal *work, integer * lwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2; doublereal d__1, d__2; /* Local variables */ doublereal anrm, bnrm, smin, smax; integer i__, j, iascl, ibscl; extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); integer ismin, ismax; doublereal c1, c2; extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *), dlaic1_( integer *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *); doublereal wsize, s1, s2; extern /* Subroutine */ int dgeqp3_(integer *, integer *, doublereal *, integer *, integer *, doublereal *, doublereal *, integer *, integer *), dlabad_(doublereal *, doublereal *); integer nb; extern doublereal dlamch_(char *), dlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *); integer mn; extern /* Subroutine */ int dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *), dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *), xerbla_(char *, integer *, ftnlen); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); doublereal bignum; integer lwkmin, nb1, nb2, nb3, nb4; extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *); doublereal sminpr, smaxpr, smlnum; extern /* Subroutine */ int dormrz_(char *, char *, integer *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *); integer lwkopt; logical lquery; extern /* Subroutine */ int dtzrzf_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *); /* -- LAPACK driver routine (version 3.7.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* December 2016 */ /* ===================================================================== */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; --jpvt; --work; /* Function Body */ mn = f2cmin(*m,*n); ismin = mn + 1; ismax = (mn << 1) + 1; /* Test the input arguments. */ *info = 0; lquery = *lwork == -1; if (*m < 0) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*nrhs < 0) { *info = -3; } else if (*lda < f2cmax(1,*m)) { *info = -5; } else /* if(complicated condition) */ { /* Computing MAX */ i__1 = f2cmax(1,*m); if (*ldb < f2cmax(i__1,*n)) { *info = -7; } } /* Figure out optimal block size */ if (*info == 0) { if (mn == 0 || *nrhs == 0) { lwkmin = 1; lwkopt = 1; } else { nb1 = ilaenv_(&c__1, "DGEQRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); nb2 = ilaenv_(&c__1, "DGERQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); nb3 = ilaenv_(&c__1, "DORMQR", " ", m, n, nrhs, &c_n1, (ftnlen)6, (ftnlen)1); nb4 = ilaenv_(&c__1, "DORMRQ", " ", m, n, nrhs, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = f2cmax(nb1,nb2), i__1 = f2cmax(i__1,nb3); nb = f2cmax(i__1,nb4); /* Computing MAX */ i__1 = mn << 1, i__2 = *n + 1, i__1 = f2cmax(i__1,i__2), i__2 = mn + *nrhs; lwkmin = mn + f2cmax(i__1,i__2); /* Computing MAX */ i__1 = lwkmin, i__2 = mn + (*n << 1) + nb * (*n + 1), i__1 = f2cmax( i__1,i__2), i__2 = (mn << 1) + nb * *nrhs; lwkopt = f2cmax(i__1,i__2); } work[1] = (doublereal) lwkopt; if (*lwork < lwkmin && ! lquery) { *info = -12; } } if (*info != 0) { i__1 = -(*info); xerbla_("DGELSY", &i__1, (ftnlen)6); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (mn == 0 || *nrhs == 0) { *rank = 0; return 0; } /* Get machine parameters */ smlnum = dlamch_("S") / dlamch_("P"); bignum = 1. / smlnum; dlabad_(&smlnum, &bignum); /* Scale A, B if f2cmax entries outside range [SMLNUM,BIGNUM] */ anrm = dlange_("M", m, n, &a[a_offset], lda, &work[1]); iascl = 0; if (anrm > 0. && anrm < smlnum) { /* Scale matrix norm up to SMLNUM */ dlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, info); iascl = 1; } else if (anrm > bignum) { /* Scale matrix norm down to BIGNUM */ dlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, info); iascl = 2; } else if (anrm == 0.) { /* Matrix all zero. Return zero solution. */ i__1 = f2cmax(*m,*n); dlaset_("F", &i__1, nrhs, &c_b31, &c_b31, &b[b_offset], ldb); *rank = 0; goto L70; } bnrm = dlange_("M", m, nrhs, &b[b_offset], ldb, &work[1]); ibscl = 0; if (bnrm > 0. && bnrm < smlnum) { /* Scale matrix norm up to SMLNUM */ dlascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb, info); ibscl = 1; } else if (bnrm > bignum) { /* Scale matrix norm down to BIGNUM */ dlascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb, info); ibscl = 2; } /* Compute QR factorization with column pivoting of A: */ /* A * P = Q * R */ i__1 = *lwork - mn; dgeqp3_(m, n, &a[a_offset], lda, &jpvt[1], &work[1], &work[mn + 1], &i__1, info); wsize = mn + work[mn + 1]; /* workspace: MN+2*N+NB*(N+1). */ /* Details of Householder rotations stored in WORK(1:MN). */ /* Determine RANK using incremental condition estimation */ work[ismin] = 1.; work[ismax] = 1.; smax = (d__1 = a[a_dim1 + 1], abs(d__1)); smin = smax; if ((d__1 = a[a_dim1 + 1], abs(d__1)) == 0.) { *rank = 0; i__1 = f2cmax(*m,*n); dlaset_("F", &i__1, nrhs, &c_b31, &c_b31, &b[b_offset], ldb); goto L70; } else { *rank = 1; } L10: if (*rank < mn) { i__ = *rank + 1; dlaic1_(&c__2, rank, &work[ismin], &smin, &a[i__ * a_dim1 + 1], &a[ i__ + i__ * a_dim1], &sminpr, &s1, &c1); dlaic1_(&c__1, rank, &work[ismax], &smax, &a[i__ * a_dim1 + 1], &a[ i__ + i__ * a_dim1], &smaxpr, &s2, &c2); if (smaxpr * *rcond <= sminpr) { i__1 = *rank; for (i__ = 1; i__ <= i__1; ++i__) { work[ismin + i__ - 1] = s1 * work[ismin + i__ - 1]; work[ismax + i__ - 1] = s2 * work[ismax + i__ - 1]; /* L20: */ } work[ismin + *rank] = c1; work[ismax + *rank] = c2; smin = sminpr; smax = smaxpr; ++(*rank); goto L10; } } /* workspace: 3*MN. */ /* Logically partition R = [ R11 R12 ] */ /* [ 0 R22 ] */ /* where R11 = R(1:RANK,1:RANK) */ /* [R11,R12] = [ T11, 0 ] * Y */ if (*rank < *n) { i__1 = *lwork - (mn << 1); dtzrzf_(rank, n, &a[a_offset], lda, &work[mn + 1], &work[(mn << 1) + 1], &i__1, info); } /* workspace: 2*MN. */ /* Details of Householder rotations stored in WORK(MN+1:2*MN) */ /* B(1:M,1:NRHS) := Q**T * B(1:M,1:NRHS) */ i__1 = *lwork - (mn << 1); dormqr_("Left", "Transpose", m, nrhs, &mn, &a[a_offset], lda, &work[1], & b[b_offset], ldb, &work[(mn << 1) + 1], &i__1, info); /* Computing MAX */ d__1 = wsize, d__2 = (mn << 1) + work[(mn << 1) + 1]; wsize = f2cmax(d__1,d__2); /* workspace: 2*MN+NB*NRHS. */ /* B(1:RANK,1:NRHS) := inv(T11) * B(1:RANK,1:NRHS) */ dtrsm_("Left", "Upper", "No transpose", "Non-unit", rank, nrhs, &c_b54, & a[a_offset], lda, &b[b_offset], ldb); i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = *rank + 1; i__ <= i__2; ++i__) { b[i__ + j * b_dim1] = 0.; /* L30: */ } /* L40: */ } /* B(1:N,1:NRHS) := Y**T * B(1:N,1:NRHS) */ if (*rank < *n) { i__1 = *n - *rank; i__2 = *lwork - (mn << 1); dormrz_("Left", "Transpose", n, nrhs, rank, &i__1, &a[a_offset], lda, &work[mn + 1], &b[b_offset], ldb, &work[(mn << 1) + 1], &i__2, info); } /* workspace: 2*MN+NRHS. */ /* B(1:N,1:NRHS) := P * B(1:N,1:NRHS) */ i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { work[jpvt[i__]] = b[i__ + j * b_dim1]; /* L50: */ } dcopy_(n, &work[1], &c__1, &b[j * b_dim1 + 1], &c__1); /* L60: */ } /* workspace: N. */ /* Undo scaling */ if (iascl == 1) { dlascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb, info); dlascl_("U", &c__0, &c__0, &smlnum, &anrm, rank, rank, &a[a_offset], lda, info); } else if (iascl == 2) { dlascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb, info); dlascl_("U", &c__0, &c__0, &bignum, &anrm, rank, rank, &a[a_offset], lda, info); } if (ibscl == 1) { dlascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb, info); } else if (ibscl == 2) { dlascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb, info); } L70: work[1] = (doublereal) lwkopt; return 0; /* End of DGELSY */ } /* dgelsy_ */