#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 CGELSS solves overdetermined or underdetermined systems for GE matrices */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download CGELSS + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE CGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, */ /* WORK, LWORK, RWORK, INFO ) */ /* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK */ /* REAL RCOND */ /* REAL RWORK( * ), S( * ) */ /* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > CGELSS computes the minimum norm solution to a complex linear */ /* > least squares problem: */ /* > */ /* > Minimize 2-norm(| b - A*x |). */ /* > */ /* > using the singular value decomposition (SVD) 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 effective rank of A is determined by treating as zero those */ /* > singular values which are less than RCOND times the largest singular */ /* > value. */ /* > \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 the matrices B and X. NRHS >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is COMPLEX array, dimension (LDA,N) */ /* > On entry, the M-by-N matrix A. */ /* > On exit, the first f2cmin(m,n) rows of A are overwritten with */ /* > its right singular vectors, stored rowwise. */ /* > \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 COMPLEX array, dimension (LDB,NRHS) */ /* > On entry, the M-by-NRHS right hand side matrix B. */ /* > On exit, B is overwritten by the N-by-NRHS solution matrix X. */ /* > If m >= n and RANK = n, the residual sum-of-squares for */ /* > the solution in the i-th column is given by the sum of */ /* > squares of the modulus of elements n+1:m in that column. */ /* > \endverbatim */ /* > */ /* > \param[in] LDB */ /* > \verbatim */ /* > LDB is INTEGER */ /* > The leading dimension of the array B. LDB >= f2cmax(1,M,N). */ /* > \endverbatim */ /* > */ /* > \param[out] S */ /* > \verbatim */ /* > S is REAL array, dimension (f2cmin(M,N)) */ /* > The singular values of A in decreasing order. */ /* > The condition number of A in the 2-norm = S(1)/S(f2cmin(m,n)). */ /* > \endverbatim */ /* > */ /* > \param[in] RCOND */ /* > \verbatim */ /* > RCOND is REAL */ /* > RCOND is used to determine the effective rank of A. */ /* > Singular values S(i) <= RCOND*S(1) are treated as zero. */ /* > If RCOND < 0, machine precision is used instead. */ /* > \endverbatim */ /* > */ /* > \param[out] RANK */ /* > \verbatim */ /* > RANK is INTEGER */ /* > The effective rank of A, i.e., the number of singular values */ /* > which are greater than RCOND*S(1). */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is COMPLEX 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. LWORK >= 1, and also: */ /* > LWORK >= 2*f2cmin(M,N) + f2cmax(M,N,NRHS) */ /* > For good performance, LWORK should generally be larger. */ /* > */ /* > 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] RWORK */ /* > \verbatim */ /* > RWORK is REAL array, dimension (5*f2cmin(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. */ /* > > 0: the algorithm for computing the SVD failed to converge; */ /* > if INFO = i, i off-diagonal elements of an intermediate */ /* > bidiagonal form did not converge to zero. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date June 2016 */ /* > \ingroup complexGEsolve */ /* ===================================================================== */ /* Subroutine */ int cgelss_(integer *m, integer *n, integer *nrhs, complex * a, integer *lda, complex *b, integer *ldb, real *s, real *rcond, integer *rank, complex *work, integer *lwork, real *rwork, integer * info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3; real r__1; /* Local variables */ real anrm, bnrm; integer itau, lwork_cgebrd__, lwork_cgelqf__, lwork_cgeqrf__, lwork_cungbr__, lwork_cunmbr__, i__, lwork_cunmlq__, lwork_cunmqr__; extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, complex *, integer *); integer iascl, ibscl; extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex * , complex *, integer *, complex *, integer *, complex *, complex * , integer *); integer chunk; real sfmin; extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, complex *, integer *); integer minmn, maxmn, itaup, itauq, mnthr, iwork, bl, ie, il; extern /* Subroutine */ int cgebrd_(integer *, integer *, complex *, integer *, real *, real *, complex *, complex *, complex *, integer *, integer *), slabad_(real *, real *); extern real clange_(char *, integer *, integer *, complex *, integer *, real *); integer mm; extern /* Subroutine */ int cgelqf_(integer *, integer *, complex *, integer *, complex *, complex *, integer *, integer *), clascl_( char *, integer *, integer *, real *, real *, integer *, integer * , complex *, integer *, integer *), cgeqrf_(integer *, integer *, complex *, integer *, complex *, complex *, integer *, integer *); extern real slamch_(char *); extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *), claset_(char *, integer *, integer *, complex *, complex *, complex *, integer *), xerbla_(char *, integer *, ftnlen), cbdsqr_(char *, integer *, integer *, integer *, integer *, real *, real *, complex *, integer *, complex *, integer *, complex *, integer *, real *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); real bignum; extern /* Subroutine */ int cungbr_(char *, integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, integer *), slascl_(char *, integer *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *), cunmbr_(char *, char *, char *, integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, complex *, integer *, integer *), csrscl_(integer *, real *, complex *, integer *), slaset_(char *, integer *, integer *, real *, real *, real *, integer *), cunmlq_(char *, char *, integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, complex *, integer *, integer *); integer ldwork; extern /* Subroutine */ int cunmqr_(char *, char *, integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, complex *, integer *, integer *); integer minwrk, maxwrk; real smlnum; integer irwork; logical lquery; complex dum[1]; real eps, thr; /* -- 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..-- */ /* June 2016 */ /* ===================================================================== */ /* Test the input arguments */ /* 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; --s; --work; --rwork; /* Function Body */ *info = 0; minmn = f2cmin(*m,*n); maxmn = f2cmax(*m,*n); 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 (*ldb < f2cmax(1,maxmn)) { *info = -7; } /* Compute workspace */ /* (Note: Comments in the code beginning "Workspace:" describe the */ /* minimal amount of workspace needed at that point in the code, */ /* as well as the preferred amount for good performance. */ /* CWorkspace refers to complex workspace, and RWorkspace refers */ /* to real workspace. NB refers to the optimal block size for the */ /* immediately following subroutine, as returned by ILAENV.) */ if (*info == 0) { minwrk = 1; maxwrk = 1; if (minmn > 0) { mm = *m; mnthr = ilaenv_(&c__6, "CGELSS", " ", m, n, nrhs, &c_n1, (ftnlen) 6, (ftnlen)1); if (*m >= *n && *m >= mnthr) { /* Path 1a - overdetermined, with many more rows than */ /* columns */ /* Compute space needed for CGEQRF */ cgeqrf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, info); lwork_cgeqrf__ = dum[0].r; /* Compute space needed for CUNMQR */ cunmqr_("L", "C", m, nrhs, n, &a[a_offset], lda, dum, &b[ b_offset], ldb, dum, &c_n1, info); lwork_cunmqr__ = dum[0].r; mm = *n; /* Computing MAX */ i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "CGEQRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = *n + *nrhs * ilaenv_(&c__1, "CUNMQR", "LC", m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)2); maxwrk = f2cmax(i__1,i__2); } if (*m >= *n) { /* Path 1 - overdetermined or exactly determined */ /* Compute space needed for CGEBRD */ cgebrd_(&mm, n, &a[a_offset], lda, &s[1], &s[1], dum, dum, dum, &c_n1, info); lwork_cgebrd__ = dum[0].r; /* Compute space needed for CUNMBR */ cunmbr_("Q", "L", "C", &mm, nrhs, n, &a[a_offset], lda, dum, & b[b_offset], ldb, dum, &c_n1, info); lwork_cunmbr__ = dum[0].r; /* Compute space needed for CUNGBR */ cungbr_("P", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, info); lwork_cungbr__ = dum[0].r; /* Compute total workspace needed */ /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + lwork_cgebrd__; maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + lwork_cunmbr__; maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + lwork_cungbr__; maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = *n * *nrhs; maxwrk = f2cmax(i__1,i__2); minwrk = (*n << 1) + f2cmax(*nrhs,*m); } if (*n > *m) { minwrk = (*m << 1) + f2cmax(*nrhs,*n); if (*n >= mnthr) { /* Path 2a - underdetermined, with many more columns */ /* than rows */ /* Compute space needed for CGELQF */ cgelqf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, info); lwork_cgelqf__ = dum[0].r; /* Compute space needed for CGEBRD */ cgebrd_(m, m, &a[a_offset], lda, &s[1], &s[1], dum, dum, dum, &c_n1, info); lwork_cgebrd__ = dum[0].r; /* Compute space needed for CUNMBR */ cunmbr_("Q", "L", "C", m, nrhs, n, &a[a_offset], lda, dum, &b[b_offset], ldb, dum, &c_n1, info); lwork_cunmbr__ = dum[0].r; /* Compute space needed for CUNGBR */ cungbr_("P", m, m, m, &a[a_offset], lda, dum, dum, &c_n1, info); lwork_cungbr__ = dum[0].r; /* Compute space needed for CUNMLQ */ cunmlq_("L", "C", n, nrhs, m, &a[a_offset], lda, dum, &b[ b_offset], ldb, dum, &c_n1, info); lwork_cunmlq__ = dum[0].r; /* Compute total workspace needed */ maxwrk = *m + lwork_cgelqf__; /* Computing MAX */ i__1 = maxwrk, i__2 = *m * 3 + *m * *m + lwork_cgebrd__; maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = *m * 3 + *m * *m + lwork_cunmbr__; maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = *m * 3 + *m * *m + lwork_cungbr__; maxwrk = f2cmax(i__1,i__2); if (*nrhs > 1) { /* Computing MAX */ i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs; maxwrk = f2cmax(i__1,i__2); } else { /* Computing MAX */ i__1 = maxwrk, i__2 = *m * *m + (*m << 1); maxwrk = f2cmax(i__1,i__2); } /* Computing MAX */ i__1 = maxwrk, i__2 = *m + lwork_cunmlq__; maxwrk = f2cmax(i__1,i__2); } else { /* Path 2 - underdetermined */ /* Compute space needed for CGEBRD */ cgebrd_(m, n, &a[a_offset], lda, &s[1], &s[1], dum, dum, dum, &c_n1, info); lwork_cgebrd__ = dum[0].r; /* Compute space needed for CUNMBR */ cunmbr_("Q", "L", "C", m, nrhs, m, &a[a_offset], lda, dum, &b[b_offset], ldb, dum, &c_n1, info); lwork_cunmbr__ = dum[0].r; /* Compute space needed for CUNGBR */ cungbr_("P", m, n, m, &a[a_offset], lda, dum, dum, &c_n1, info); lwork_cungbr__ = dum[0].r; maxwrk = (*m << 1) + lwork_cgebrd__; /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + lwork_cunmbr__; maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + lwork_cungbr__; maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = *n * *nrhs; maxwrk = f2cmax(i__1,i__2); } } maxwrk = f2cmax(minwrk,maxwrk); } work[1].r = (real) maxwrk, work[1].i = 0.f; if (*lwork < minwrk && ! lquery) { *info = -12; } } if (*info != 0) { i__1 = -(*info); xerbla_("CGELSS", &i__1, (ftnlen)6); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { *rank = 0; return 0; } /* Get machine parameters */ eps = slamch_("P"); sfmin = slamch_("S"); smlnum = sfmin / eps; bignum = 1.f / smlnum; slabad_(&smlnum, &bignum); /* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */ anrm = clange_("M", m, n, &a[a_offset], lda, &rwork[1]); iascl = 0; if (anrm > 0.f && anrm < smlnum) { /* Scale matrix norm up to SMLNUM */ clascl_("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 */ clascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, info); iascl = 2; } else if (anrm == 0.f) { /* Matrix all zero. Return zero solution. */ i__1 = f2cmax(*m,*n); claset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb); slaset_("F", &minmn, &c__1, &c_b59, &c_b59, &s[1], &minmn); *rank = 0; goto L70; } /* Scale B if f2cmax element outside range [SMLNUM,BIGNUM] */ bnrm = clange_("M", m, nrhs, &b[b_offset], ldb, &rwork[1]); ibscl = 0; if (bnrm > 0.f && bnrm < smlnum) { /* Scale matrix norm up to SMLNUM */ clascl_("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 */ clascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb, info); ibscl = 2; } /* Overdetermined case */ if (*m >= *n) { /* Path 1 - overdetermined or exactly determined */ mm = *m; if (*m >= mnthr) { /* Path 1a - overdetermined, with many more rows than columns */ mm = *n; itau = 1; iwork = itau + *n; /* Compute A=Q*R */ /* (CWorkspace: need 2*N, prefer N+N*NB) */ /* (RWorkspace: none) */ i__1 = *lwork - iwork + 1; cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__1, info); /* Multiply B by transpose(Q) */ /* (CWorkspace: need N+NRHS, prefer N+NRHS*NB) */ /* (RWorkspace: none) */ i__1 = *lwork - iwork + 1; cunmqr_("L", "C", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[ b_offset], ldb, &work[iwork], &i__1, info); /* Zero out below R */ if (*n > 1) { i__1 = *n - 1; i__2 = *n - 1; claset_("L", &i__1, &i__2, &c_b1, &c_b1, &a[a_dim1 + 2], lda); } } ie = 1; itauq = 1; itaup = itauq + *n; iwork = itaup + *n; /* Bidiagonalize R in A */ /* (CWorkspace: need 2*N+MM, prefer 2*N+(MM+N)*NB) */ /* (RWorkspace: need N) */ i__1 = *lwork - iwork + 1; cgebrd_(&mm, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq], & work[itaup], &work[iwork], &i__1, info); /* Multiply B by transpose of left bidiagonalizing vectors of R */ /* (CWorkspace: need 2*N+NRHS, prefer 2*N+NRHS*NB) */ /* (RWorkspace: none) */ i__1 = *lwork - iwork + 1; cunmbr_("Q", "L", "C", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], &b[b_offset], ldb, &work[iwork], &i__1, info); /* Generate right bidiagonalizing vectors of R in A */ /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */ /* (RWorkspace: none) */ i__1 = *lwork - iwork + 1; cungbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &work[iwork], & i__1, info); irwork = ie + *n; /* Perform bidiagonal QR iteration */ /* multiply B by transpose of left singular vectors */ /* compute right singular vectors in A */ /* (CWorkspace: none) */ /* (RWorkspace: need BDSPAC) */ cbdsqr_("U", n, n, &c__0, nrhs, &s[1], &rwork[ie], &a[a_offset], lda, dum, &c__1, &b[b_offset], ldb, &rwork[irwork], info); if (*info != 0) { goto L70; } /* Multiply B by reciprocals of singular values */ /* Computing MAX */ r__1 = *rcond * s[1]; thr = f2cmax(r__1,sfmin); if (*rcond < 0.f) { /* Computing MAX */ r__1 = eps * s[1]; thr = f2cmax(r__1,sfmin); } *rank = 0; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (s[i__] > thr) { csrscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); ++(*rank); } else { claset_("F", &c__1, nrhs, &c_b1, &c_b1, &b[i__ + b_dim1], ldb); } /* L10: */ } /* Multiply B by right singular vectors */ /* (CWorkspace: need N, prefer N*NRHS) */ /* (RWorkspace: none) */ if (*lwork >= *ldb * *nrhs && *nrhs > 1) { cgemm_("C", "N", n, nrhs, n, &c_b2, &a[a_offset], lda, &b[ b_offset], ldb, &c_b1, &work[1], ldb); clacpy_("G", n, nrhs, &work[1], ldb, &b[b_offset], ldb) ; } else if (*nrhs > 1) { chunk = *lwork / *n; i__1 = *nrhs; i__2 = chunk; for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { /* Computing MIN */ i__3 = *nrhs - i__ + 1; bl = f2cmin(i__3,chunk); cgemm_("C", "N", n, &bl, n, &c_b2, &a[a_offset], lda, &b[i__ * b_dim1 + 1], ldb, &c_b1, &work[1], n); clacpy_("G", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], ldb); /* L20: */ } } else { cgemv_("C", n, n, &c_b2, &a[a_offset], lda, &b[b_offset], &c__1, & c_b1, &work[1], &c__1); ccopy_(n, &work[1], &c__1, &b[b_offset], &c__1); } } else /* if(complicated condition) */ { /* Computing MAX */ i__2 = f2cmax(*m,*nrhs), i__1 = *n - (*m << 1); if (*n >= mnthr && *lwork >= *m * 3 + *m * *m + f2cmax(i__2,i__1)) { /* Underdetermined case, M much less than N */ /* Path 2a - underdetermined, with many more columns than rows */ /* and sufficient workspace for an efficient algorithm */ ldwork = *m; /* Computing MAX */ i__2 = f2cmax(*m,*nrhs), i__1 = *n - (*m << 1); if (*lwork >= *m * 3 + *m * *lda + f2cmax(i__2,i__1)) { ldwork = *lda; } itau = 1; iwork = *m + 1; /* Compute A=L*Q */ /* (CWorkspace: need 2*M, prefer M+M*NB) */ /* (RWorkspace: none) */ i__2 = *lwork - iwork + 1; cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, info); il = iwork; /* Copy L to WORK(IL), zeroing out above it */ clacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwork); i__2 = *m - 1; i__1 = *m - 1; claset_("U", &i__2, &i__1, &c_b1, &c_b1, &work[il + ldwork], & ldwork); ie = 1; itauq = il + ldwork * *m; itaup = itauq + *m; iwork = itaup + *m; /* Bidiagonalize L in WORK(IL) */ /* (CWorkspace: need M*M+4*M, prefer M*M+3*M+2*M*NB) */ /* (RWorkspace: need M) */ i__2 = *lwork - iwork + 1; cgebrd_(m, m, &work[il], &ldwork, &s[1], &rwork[ie], &work[itauq], &work[itaup], &work[iwork], &i__2, info); /* Multiply B by transpose of left bidiagonalizing vectors of L */ /* (CWorkspace: need M*M+3*M+NRHS, prefer M*M+3*M+NRHS*NB) */ /* (RWorkspace: none) */ i__2 = *lwork - iwork + 1; cunmbr_("Q", "L", "C", m, nrhs, m, &work[il], &ldwork, &work[ itauq], &b[b_offset], ldb, &work[iwork], &i__2, info); /* Generate right bidiagonalizing vectors of R in WORK(IL) */ /* (CWorkspace: need M*M+4*M-1, prefer M*M+3*M+(M-1)*NB) */ /* (RWorkspace: none) */ i__2 = *lwork - iwork + 1; cungbr_("P", m, m, m, &work[il], &ldwork, &work[itaup], &work[ iwork], &i__2, info); irwork = ie + *m; /* Perform bidiagonal QR iteration, computing right singular */ /* vectors of L in WORK(IL) and multiplying B by transpose of */ /* left singular vectors */ /* (CWorkspace: need M*M) */ /* (RWorkspace: need BDSPAC) */ cbdsqr_("U", m, m, &c__0, nrhs, &s[1], &rwork[ie], &work[il], & ldwork, &a[a_offset], lda, &b[b_offset], ldb, &rwork[ irwork], info); if (*info != 0) { goto L70; } /* Multiply B by reciprocals of singular values */ /* Computing MAX */ r__1 = *rcond * s[1]; thr = f2cmax(r__1,sfmin); if (*rcond < 0.f) { /* Computing MAX */ r__1 = eps * s[1]; thr = f2cmax(r__1,sfmin); } *rank = 0; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { if (s[i__] > thr) { csrscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); ++(*rank); } else { claset_("F", &c__1, nrhs, &c_b1, &c_b1, &b[i__ + b_dim1], ldb); } /* L30: */ } iwork = il + *m * ldwork; /* Multiply B by right singular vectors of L in WORK(IL) */ /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NRHS) */ /* (RWorkspace: none) */ if (*lwork >= *ldb * *nrhs + iwork - 1 && *nrhs > 1) { cgemm_("C", "N", m, nrhs, m, &c_b2, &work[il], &ldwork, &b[ b_offset], ldb, &c_b1, &work[iwork], ldb); clacpy_("G", m, nrhs, &work[iwork], ldb, &b[b_offset], ldb); } else if (*nrhs > 1) { chunk = (*lwork - iwork + 1) / *m; i__2 = *nrhs; i__1 = chunk; for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) { /* Computing MIN */ i__3 = *nrhs - i__ + 1; bl = f2cmin(i__3,chunk); cgemm_("C", "N", m, &bl, m, &c_b2, &work[il], &ldwork, &b[ i__ * b_dim1 + 1], ldb, &c_b1, &work[iwork], m); clacpy_("G", m, &bl, &work[iwork], m, &b[i__ * b_dim1 + 1] , ldb); /* L40: */ } } else { cgemv_("C", m, m, &c_b2, &work[il], &ldwork, &b[b_dim1 + 1], & c__1, &c_b1, &work[iwork], &c__1); ccopy_(m, &work[iwork], &c__1, &b[b_dim1 + 1], &c__1); } /* Zero out below first M rows of B */ i__1 = *n - *m; claset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[*m + 1 + b_dim1], ldb); iwork = itau + *m; /* Multiply transpose(Q) by B */ /* (CWorkspace: need M+NRHS, prefer M+NHRS*NB) */ /* (RWorkspace: none) */ i__1 = *lwork - iwork + 1; cunmlq_("L", "C", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[ b_offset], ldb, &work[iwork], &i__1, info); } else { /* Path 2 - remaining underdetermined cases */ ie = 1; itauq = 1; itaup = itauq + *m; iwork = itaup + *m; /* Bidiagonalize A */ /* (CWorkspace: need 3*M, prefer 2*M+(M+N)*NB) */ /* (RWorkspace: need N) */ i__1 = *lwork - iwork + 1; cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq], &work[itaup], &work[iwork], &i__1, info); /* Multiply B by transpose of left bidiagonalizing vectors */ /* (CWorkspace: need 2*M+NRHS, prefer 2*M+NRHS*NB) */ /* (RWorkspace: none) */ i__1 = *lwork - iwork + 1; cunmbr_("Q", "L", "C", m, nrhs, n, &a[a_offset], lda, &work[itauq] , &b[b_offset], ldb, &work[iwork], &i__1, info); /* Generate right bidiagonalizing vectors in A */ /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */ /* (RWorkspace: none) */ i__1 = *lwork - iwork + 1; cungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[ iwork], &i__1, info); irwork = ie + *m; /* Perform bidiagonal QR iteration, */ /* computing right singular vectors of A in A and */ /* multiplying B by transpose of left singular vectors */ /* (CWorkspace: none) */ /* (RWorkspace: need BDSPAC) */ cbdsqr_("L", m, n, &c__0, nrhs, &s[1], &rwork[ie], &a[a_offset], lda, dum, &c__1, &b[b_offset], ldb, &rwork[irwork], info); if (*info != 0) { goto L70; } /* Multiply B by reciprocals of singular values */ /* Computing MAX */ r__1 = *rcond * s[1]; thr = f2cmax(r__1,sfmin); if (*rcond < 0.f) { /* Computing MAX */ r__1 = eps * s[1]; thr = f2cmax(r__1,sfmin); } *rank = 0; i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { if (s[i__] > thr) { csrscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); ++(*rank); } else { claset_("F", &c__1, nrhs, &c_b1, &c_b1, &b[i__ + b_dim1], ldb); } /* L50: */ } /* Multiply B by right singular vectors of A */ /* (CWorkspace: need N, prefer N*NRHS) */ /* (RWorkspace: none) */ if (*lwork >= *ldb * *nrhs && *nrhs > 1) { cgemm_("C", "N", n, nrhs, m, &c_b2, &a[a_offset], lda, &b[ b_offset], ldb, &c_b1, &work[1], ldb); clacpy_("G", n, nrhs, &work[1], ldb, &b[b_offset], ldb); } else if (*nrhs > 1) { chunk = *lwork / *n; i__1 = *nrhs; i__2 = chunk; for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { /* Computing MIN */ i__3 = *nrhs - i__ + 1; bl = f2cmin(i__3,chunk); cgemm_("C", "N", n, &bl, m, &c_b2, &a[a_offset], lda, &b[ i__ * b_dim1 + 1], ldb, &c_b1, &work[1], n); clacpy_("F", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], ldb); /* L60: */ } } else { cgemv_("C", m, n, &c_b2, &a[a_offset], lda, &b[b_offset], & c__1, &c_b1, &work[1], &c__1); ccopy_(n, &work[1], &c__1, &b[b_offset], &c__1); } } } /* Undo scaling */ if (iascl == 1) { clascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb, info); slascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], & minmn, info); } else if (iascl == 2) { clascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb, info); slascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], & minmn, info); } if (ibscl == 1) { clascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb, info); } else if (ibscl == 2) { clascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb, info); } L70: work[1].r = (real) maxwrk, work[1].i = 0.f; return 0; /* End of CGELSS */ } /* cgelss_ */