#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 SGELSD computes the minimum-norm solution to a linear least squares problem for GE matrices */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SGELSD + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, */ /* RANK, WORK, LWORK, IWORK, INFO ) */ /* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK */ /* REAL RCOND */ /* INTEGER IWORK( * ) */ /* REAL A( LDA, * ), B( LDB, * ), S( * ), WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SGELSD computes the minimum-norm solution to a real 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 problem is solved in three steps: */ /* > (1) Reduce the coefficient matrix A to bidiagonal form with */ /* > Householder transformations, reducing the original problem */ /* > into a "bidiagonal least squares problem" (BLS) */ /* > (2) Solve the BLS using a divide and conquer approach. */ /* > (3) Apply back all the Householder transformations to solve */ /* > the original least squares problem. */ /* > */ /* > The effective rank of A is determined by treating as zero those */ /* > singular values which are less than RCOND times the largest singular */ /* > value. */ /* > */ /* > The divide and conquer algorithm makes very mild assumptions about */ /* > floating point arithmetic. It will work on machines with a guard */ /* > digit in add/subtract, or on those binary machines without guard */ /* > digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */ /* > Cray-2. It could conceivably fail on hexadecimal or decimal machines */ /* > without guard digits, but we know of none. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The number of rows of A. M >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The number of columns of 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 REAL array, dimension (LDA,N) */ /* > On entry, the M-by-N matrix A. */ /* > On exit, A has been destroyed. */ /* > \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 REAL 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 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,f2cmax(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 REAL 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 must be at least 1. */ /* > The exact minimum amount of workspace needed depends on M, */ /* > N and NRHS. As long as LWORK is at least */ /* > 12*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2, */ /* > if M is greater than or equal to N or */ /* > 12*M + 2*M*SMLSIZ + 8*M*NLVL + M*NRHS + (SMLSIZ+1)**2, */ /* > if M is less than N, the code will execute correctly. */ /* > SMLSIZ is returned by ILAENV and is equal to the maximum */ /* > size of the subproblems at the bottom of the computation */ /* > tree (usually about 25), and */ /* > NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 ) */ /* > 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 array WORK and the */ /* > minimum size of the array IWORK, and returns these values as */ /* > the first entries of the WORK and IWORK arrays, and no error */ /* > message related to LWORK is issued by XERBLA. */ /* > \endverbatim */ /* > */ /* > \param[out] IWORK */ /* > \verbatim */ /* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */ /* > LIWORK >= f2cmax(1, 3*MINMN*NLVL + 11*MINMN), */ /* > where MINMN = MIN( M,N ). */ /* > On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK. */ /* > \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 2017 */ /* > \ingroup realGEsolve */ /* > \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 sgelsd_(integer *m, integer *n, integer *nrhs, real *a, integer *lda, real *b, integer *ldb, real *s, real *rcond, integer * rank, real *work, integer *lwork, integer *iwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4; /* Local variables */ real anrm, bnrm; integer itau, nlvl, iascl, ibscl; real sfmin; integer minmn, maxmn, itaup, itauq, mnthr, nwork, ie, il; extern /* Subroutine */ int slabad_(real *, real *); integer mm; extern /* Subroutine */ int sgebrd_(integer *, integer *, real *, integer *, real *, real *, real *, real *, real *, integer *, integer *); extern real slamch_(char *), slange_(char *, integer *, integer *, real *, integer *, real *); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); real bignum; extern /* Subroutine */ int sgelqf_(integer *, integer *, real *, integer *, real *, real *, integer *, integer *), slalsd_(char *, integer *, integer *, integer *, real *, real *, real *, integer *, real * , integer *, real *, integer *, integer *), slascl_(char * , integer *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *); integer wlalsd; extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer *, real *, real *, integer *, integer *), slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *, real *, integer *); integer ldwork; extern /* Subroutine */ int sormbr_(char *, char *, char *, integer *, integer *, integer *, real *, integer *, real *, real *, integer * , real *, integer *, integer *); integer liwork, minwrk, maxwrk; real smlnum; extern /* Subroutine */ int sormlq_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, real *, integer *, real *, integer *, integer *); logical lquery; integer smlsiz; extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, real *, integer *, real *, integer *, integer *); real eps; /* -- LAPACK driver routine (version 3.7.1) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* June 2017 */ /* ===================================================================== */ /* Test the input arguments. */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; --s; --work; --iwork; fprintf(stdout,"start of SGELSD\n"); /* 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. */ /* NB refers to the optimal block size for the immediately */ /* following subroutine, as returned by ILAENV.) */ if (*info == 0) { minwrk = 1; maxwrk = 1; liwork = 1; if (minmn > 0) { smlsiz = ilaenv_(&c__9, "SGELSD", " ", &c__0, &c__0, &c__0, &c__0, (ftnlen)6, (ftnlen)1); mnthr = ilaenv_(&c__6, "SGELSD", " ", m, n, nrhs, &c_n1, (ftnlen) 6, (ftnlen)1); /* Computing MAX */ i__1 = (integer) (logf((real) minmn / (real) (smlsiz + 1)) / logf( 2.f)) + 1; nlvl = f2cmax(i__1,0); liwork = minmn * 3 * nlvl + minmn * 11; mm = *m; if (*m >= *n && *m >= mnthr) { /* Path 1a - overdetermined, with many more rows than */ /* columns. */ mm = *n; /* Computing MAX */ i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "SGEQRF", " ", 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, "SORMQR", "LT", m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)2); maxwrk = f2cmax(i__1,i__2); } if (*m >= *n) { /* Path 1 - overdetermined or exactly determined. */ /* Computing MAX */ i__1 = maxwrk, i__2 = *n * 3 + (mm + *n) * ilaenv_(&c__1, "SGEBRD", " ", &mm, n, &c_n1, &c_n1, (ftnlen)6, ( ftnlen)1); maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = *n * 3 + *nrhs * ilaenv_(&c__1, "SORMBR" , "QLT", &mm, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3); maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = *n * 3 + (*n - 1) * ilaenv_(&c__1, "SORMBR", "PLN", n, nrhs, n, &c_n1, (ftnlen)6, ( ftnlen)3); maxwrk = f2cmax(i__1,i__2); /* Computing 2nd power */ i__1 = smlsiz + 1; wlalsd = *n * 9 + (*n << 1) * smlsiz + (*n << 3) * nlvl + *n * *nrhs + i__1 * i__1; /* Computing MAX */ i__1 = maxwrk, i__2 = *n * 3 + wlalsd; maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = f2cmax(i__1, i__2), i__2 = *n * 3 + wlalsd; minwrk = f2cmax(i__1,i__2); } if (*n > *m) { /* Computing 2nd power */ i__1 = smlsiz + 1; wlalsd = *m * 9 + (*m << 1) * smlsiz + (*m << 3) * nlvl + *m * *nrhs + i__1 * i__1; if (*n >= mnthr) { /* Path 2a - underdetermined, with many more columns */ /* than rows. */ maxwrk = *m + *m * ilaenv_(&c__1, "SGELQF", " ", m, n, & c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m << 1) * ilaenv_(&c__1, "SGEBRD", " ", m, m, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *nrhs * ilaenv_(&c__1, "SORMBR", "QLT", m, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)3); maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m - 1) * ilaenv_(&c__1, "SORMBR", "PLN", m, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)3); 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 + *nrhs * ilaenv_(&c__1, "SORMLQ" , "LT", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)2); maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + wlalsd; maxwrk = f2cmax(i__1,i__2); /* XXX: Ensure the Path 2a case below is triggered. The workspace */ /* calculation should use queries for all routines eventually. */ /* Computing MAX */ /* Computing MAX */ i__3 = *m, i__4 = (*m << 1) - 4, i__3 = f2cmax(i__3,i__4), i__3 = f2cmax(i__3,*nrhs), i__4 = *n - *m * 3; i__1 = maxwrk, i__2 = (*m << 2) + *m * *m + f2cmax(i__3,i__4) ; maxwrk = f2cmax(i__1,i__2); } else { /* Path 2 - remaining underdetermined cases. */ maxwrk = *m * 3 + (*n + *m) * ilaenv_(&c__1, "SGEBRD", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = maxwrk, i__2 = *m * 3 + *nrhs * ilaenv_(&c__1, "SORMBR", "QLT", m, nrhs, n, &c_n1, (ftnlen)6, ( ftnlen)3); maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = *m * 3 + *m * ilaenv_(&c__1, "SORM" "BR", "PLN", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen) 3); maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = *m * 3 + wlalsd; maxwrk = f2cmax(i__1,i__2); } /* Computing MAX */ i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *m, i__1 = f2cmax(i__1, i__2), i__2 = *m * 3 + wlalsd; minwrk = f2cmax(i__1,i__2); } } minwrk = f2cmin(minwrk,maxwrk); work[1] = (real) maxwrk; iwork[1] = liwork; if (*lwork < minwrk && ! lquery) { *info = -12; } } if (*info != 0) { i__1 = -(*info); xerbla_("SGELSD", &i__1, (ftnlen)6); return 0; } else if (lquery) { return 0; } /* Quick return if possible. */ if (*m == 0 || *n == 0) { fprintf(stdout,"SGELSD quickreturn rank=0\n"); *rank = 0; return 0; } /* Get machine parameters. */ eps = slamch_("P"); sfmin = slamch_("S"); smlnum = sfmin / eps; bignum = 1.f / smlnum; // FILE *bla=fopen("/tmp/bla","w"); //fprintf(bla,"SGELSD eps=%g sfmin=%g smlnum=%g bignum=%g\n",eps,sfmin,smlnum,bignum); //fclose(bla); slabad_(&smlnum, &bignum); /* Scale A if f2cmax entry outside range [SMLNUM,BIGNUM]. */ anrm = slange_("M", m, n, &a[a_offset], lda, &work[1]); iascl = 0; if (anrm > 0.f && anrm < smlnum) { /* Scale matrix norm up to SMLNUM. */ fprintf(stdout,"scaling A up to SML\n"); slascl_("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. */ fprintf(stdout,"scaling A down to BIG\n"); slascl_("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. */ fprintf(stdout,"A is zero soln\n"); i__1 = f2cmax(*m,*n); slaset_("F", &i__1, nrhs, &c_b81, &c_b81, &b[b_offset], ldb); slaset_("F", &minmn, &c__1, &c_b81, &c_b81, &s[1], &c__1); *rank = 0; goto L10; } /* Scale B if f2cmax entry outside range [SMLNUM,BIGNUM]. */ bnrm = slange_("M", m, nrhs, &b[b_offset], ldb, &work[1]); ibscl = 0; if (bnrm > 0.f && bnrm < smlnum) { /* Scale matrix norm up to SMLNUM. */ fprintf(stdout,"scaling B up to SML\n"); slascl_("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. */ fprintf(stdout,"scaling B down to BIG\n"); slascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb, info); ibscl = 2; } /* If M < N make sure certain entries of B are zero. */ if (*m < *n) { i__1 = *n - *m; fprintf(stdout,"zeroing parts of B \n"); slaset_("F", &i__1, nrhs, &c_b81, &c_b81, &b[*m + 1 + b_dim1], ldb); } /* Overdetermined case. */ if (*m >= *n) { fprintf(stdout,"overdetermined, path 1 \n"); /* Path 1 - overdetermined or exactly determined. */ mm = *m; if (*m >= mnthr) { /* Path 1a - overdetermined, with many more rows than columns. */ fprintf(stdout,"overdetermined, path 1a \n"); mm = *n; itau = 1; nwork = itau + *n; /* Compute A=Q*R. */ /* (Workspace: need 2*N, prefer N+N*NB) */ i__1 = *lwork - nwork + 1; sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, info); /* Multiply B by transpose(Q). */ /* (Workspace: need N+NRHS, prefer N+NRHS*NB) */ i__1 = *lwork - nwork + 1; sormqr_("L", "T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[ b_offset], ldb, &work[nwork], &i__1, info); /* Zero out below R. */ if (*n > 1) { i__1 = *n - 1; i__2 = *n - 1; slaset_("L", &i__1, &i__2, &c_b81, &c_b81, &a[a_dim1 + 2], lda); } } ie = 1; itauq = ie + *n; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize R in A. */ /* (Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) */ i__1 = *lwork - nwork + 1; sgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & work[itaup], &work[nwork], &i__1, info); /* Multiply B by transpose of left bidiagonalizing vectors of R. */ /* (Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) */ i__1 = *lwork - nwork + 1; sormbr_("Q", "L", "T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], &b[b_offset], ldb, &work[nwork], &i__1, info); /* Solve the bidiagonal least squares problem. */ slalsd_("U", &smlsiz, n, nrhs, &s[1], &work[ie], &b[b_offset], ldb, rcond, rank, &work[nwork], &iwork[1], info); if (*info != 0) { fprintf(stdout,"info !=0 nach slalsd\n"); goto L10; } /* Multiply B by right bidiagonalizing vectors of R. */ i__1 = *lwork - nwork + 1; sormbr_("P", "L", "N", n, nrhs, n, &a[a_offset], lda, &work[itaup], & b[b_offset], ldb, &work[nwork], &i__1, info); } else /* if(complicated condition) */ { fprintf(stdout,"not overdetermined \n"); /* Computing MAX */ i__1 = *m, i__2 = (*m << 1) - 4, i__1 = f2cmax(i__1,i__2), i__1 = f2cmax( i__1,*nrhs), i__2 = *n - *m * 3, i__1 = f2cmax(i__1,i__2); if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + f2cmax(i__1,wlalsd)) { /* Path 2a - underdetermined, with many more columns than rows */ /* and sufficient workspace for an efficient algorithm. */ fprintf(stdout,"not overdetermined, path 2a\n"); ldwork = *m; /* Computing MAX */ /* Computing MAX */ i__3 = *m, i__4 = (*m << 1) - 4, i__3 = f2cmax(i__3,i__4), i__3 = f2cmax(i__3,*nrhs), i__4 = *n - *m * 3; i__1 = (*m << 2) + *m * *lda + f2cmax(i__3,i__4), i__2 = *m * *lda + *m + *m * *nrhs, i__1 = f2cmax(i__1,i__2), i__2 = (*m << 2) + *m * *lda + wlalsd; if (*lwork >= f2cmax(i__1,i__2)) { ldwork = *lda; } itau = 1; nwork = *m + 1; /* Compute A=L*Q. */ /* (Workspace: need 2*M, prefer M+M*NB) */ i__1 = *lwork - nwork + 1; sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, info); il = nwork; /* Copy L to WORK(IL), zeroing out above its diagonal. */ slacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwork); i__1 = *m - 1; i__2 = *m - 1; slaset_("U", &i__1, &i__2, &c_b81, &c_b81, &work[il + ldwork], & ldwork); ie = il + ldwork * *m; itauq = ie + *m; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize L in WORK(IL). */ /* (Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) */ i__1 = *lwork - nwork + 1; sgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq], &work[itaup], &work[nwork], &i__1, info); /* Multiply B by transpose of left bidiagonalizing vectors of L. */ /* (Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB) */ i__1 = *lwork - nwork + 1; sormbr_("Q", "L", "T", m, nrhs, m, &work[il], &ldwork, &work[ itauq], &b[b_offset], ldb, &work[nwork], &i__1, info); /* Solve the bidiagonal least squares problem. */ slalsd_("U", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset], ldb, rcond, rank, &work[nwork], &iwork[1], info); if (*info != 0) { goto L10; } /* Multiply B by right bidiagonalizing vectors of L. */ i__1 = *lwork - nwork + 1; sormbr_("P", "L", "N", m, nrhs, m, &work[il], &ldwork, &work[ itaup], &b[b_offset], ldb, &work[nwork], &i__1, info); /* Zero out below first M rows of B. */ i__1 = *n - *m; slaset_("F", &i__1, nrhs, &c_b81, &c_b81, &b[*m + 1 + b_dim1], ldb); nwork = itau + *m; /* Multiply transpose(Q) by B. */ /* (Workspace: need M+NRHS, prefer M+NRHS*NB) */ i__1 = *lwork - nwork + 1; sormlq_("L", "T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[ b_offset], ldb, &work[nwork], &i__1, info); } else { /* Path 2 - remaining underdetermined cases. */ fprintf(stdout,"other underdetermined, path 2"); ie = 1; itauq = ie + *m; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize A. */ /* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */ i__1 = *lwork - nwork + 1; sgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & work[itaup], &work[nwork], &i__1, info); /* Multiply B by transpose of left bidiagonalizing vectors. */ /* (Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) */ i__1 = *lwork - nwork + 1; sormbr_("Q", "L", "T", m, nrhs, n, &a[a_offset], lda, &work[itauq] , &b[b_offset], ldb, &work[nwork], &i__1, info); /* Solve the bidiagonal least squares problem. */ slalsd_("L", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset], ldb, rcond, rank, &work[nwork], &iwork[1], info); if (*info != 0) { goto L10; } /* Multiply B by right bidiagonalizing vectors of A. */ i__1 = *lwork - nwork + 1; sormbr_("P", "L", "N", n, nrhs, m, &a[a_offset], lda, &work[itaup] , &b[b_offset], ldb, &work[nwork], &i__1, info); } } /* Undo scaling. */ if (iascl == 1) { fprintf(stdout," unscaling a1\n"); slascl_("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) { fprintf(stdout," unscaling a2\n"); slascl_("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) { fprintf(stdout," unscaling b1\n"); slascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb, info); } else if (ibscl == 2) { fprintf(stdout," unscaling b2\n"); slascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb, info); } L10: work[1] = (real) maxwrk; iwork[1] = liwork; fprintf(stdout, "end of SGELSD\n"); return 0; /* End of SGELSD */ } /* sgelsd_ */