#include #include #include #include #include #ifdef complex #undef complex #endif #ifdef I #undef I #endif #if defined(_WIN64) typedef long long BLASLONG; typedef unsigned long long BLASULONG; #else typedef long BLASLONG; typedef unsigned long BLASULONG; #endif #ifdef LAPACK_ILP64 typedef BLASLONG blasint; #if defined(_WIN64) #define blasabs(x) llabs(x) #else #define blasabs(x) labs(x) #endif #else typedef int blasint; #define blasabs(x) abs(x) #endif typedef blasint integer; typedef unsigned int uinteger; typedef char *address; typedef short int shortint; typedef float real; typedef double doublereal; typedef struct { real r, i; } complex; typedef struct { doublereal r, i; } doublecomplex; #ifdef _MSC_VER static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;} static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;} static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;} static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;} #else static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;} static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;} static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;} static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;} #endif #define pCf(z) (*_pCf(z)) #define pCd(z) (*_pCd(z)) typedef int logical; typedef short int shortlogical; typedef char logical1; typedef char integer1; #define TRUE_ (1) #define FALSE_ (0) /* Extern is for use with -E */ #ifndef Extern #define Extern extern #endif /* I/O stuff */ typedef int flag; typedef int ftnlen; typedef int ftnint; /*external read, write*/ typedef struct { flag cierr; ftnint ciunit; flag ciend; char *cifmt; ftnint cirec; } cilist; /*internal read, write*/ typedef struct { flag icierr; char *iciunit; flag iciend; char *icifmt; ftnint icirlen; ftnint icirnum; } icilist; /*open*/ typedef struct { flag oerr; ftnint ounit; char *ofnm; ftnlen ofnmlen; char *osta; char *oacc; char *ofm; ftnint orl; char *oblnk; } olist; /*close*/ typedef struct { flag cerr; ftnint cunit; char *csta; } cllist; /*rewind, backspace, endfile*/ typedef struct { flag aerr; ftnint aunit; } alist; /* inquire */ typedef struct { flag inerr; ftnint inunit; char *infile; ftnlen infilen; ftnint *inex; /*parameters in standard's order*/ ftnint *inopen; ftnint *innum; ftnint *innamed; char *inname; ftnlen innamlen; char *inacc; ftnlen inacclen; char *inseq; ftnlen inseqlen; char *indir; ftnlen indirlen; char *infmt; ftnlen infmtlen; char *inform; ftnint informlen; char *inunf; ftnlen inunflen; ftnint *inrecl; ftnint *innrec; char *inblank; ftnlen inblanklen; } inlist; #define VOID void union Multitype { /* for multiple entry points */ integer1 g; shortint h; integer i; /* longint j; */ real r; doublereal d; complex c; doublecomplex z; }; typedef union Multitype Multitype; struct Vardesc { /* for Namelist */ char *name; char *addr; ftnlen *dims; int type; }; typedef struct Vardesc Vardesc; struct Namelist { char *name; Vardesc **vars; int nvars; }; typedef struct Namelist Namelist; #define abs(x) ((x) >= 0 ? (x) : -(x)) #define dabs(x) (fabs(x)) #define f2cmin(a,b) ((a) <= (b) ? (a) : (b)) #define f2cmax(a,b) ((a) >= (b) ? (a) : (b)) #define dmin(a,b) (f2cmin(a,b)) #define dmax(a,b) (f2cmax(a,b)) #define bit_test(a,b) ((a) >> (b) & 1) #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b))) #define bit_set(a,b) ((a) | ((uinteger)1 << (b))) #define abort_() { sig_die("Fortran abort routine called", 1); } #define c_abs(z) (cabsf(Cf(z))) #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); } #ifdef _MSC_VER #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);} #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);} #else #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);} #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);} #endif #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));} #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));} #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));} //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));} #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));} #define d_abs(x) (fabs(*(x))) #define d_acos(x) (acos(*(x))) #define d_asin(x) (asin(*(x))) #define d_atan(x) (atan(*(x))) #define d_atn2(x, y) (atan2(*(x),*(y))) #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); } #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); } #define d_cos(x) (cos(*(x))) #define d_cosh(x) (cosh(*(x))) #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 ) #define d_exp(x) (exp(*(x))) #define d_imag(z) (cimag(Cd(z))) #define r_imag(z) (cimagf(Cf(z))) #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define d_log(x) (log(*(x))) #define d_mod(x, y) (fmod(*(x), *(y))) #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x))) #define d_nint(x) u_nint(*(x)) #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a))) #define d_sign(a,b) u_sign(*(a),*(b)) #define r_sign(a,b) u_sign(*(a),*(b)) #define d_sin(x) (sin(*(x))) #define d_sinh(x) (sinh(*(x))) #define d_sqrt(x) (sqrt(*(x))) #define d_tan(x) (tan(*(x))) #define d_tanh(x) (tanh(*(x))) #define i_abs(x) abs(*(x)) #define i_dnnt(x) ((integer)u_nint(*(x))) #define i_len(s, n) (n) #define i_nint(x) ((integer)u_nint(*(x))) #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b))) #define pow_dd(ap, bp) ( pow(*(ap), *(bp))) #define pow_si(B,E) spow_ui(*(B),*(E)) #define pow_ri(B,E) spow_ui(*(B),*(E)) #define pow_di(B,E) dpow_ui(*(B),*(E)) #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));} #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));} #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));} #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; } #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d)))) #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; } #define sig_die(s, kill) { exit(1); } #define s_stop(s, n) {exit(0);} static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n"; #define z_abs(z) (cabs(Cd(z))) #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));} #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));} #define myexit_() break; #define mycycle() continue; #define myceiling(w) {ceil(w)} #define myhuge(w) {HUGE_VAL} //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);} #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)} /* procedure parameter types for -A and -C++ */ #define F2C_proc_par_types 1 #ifdef __cplusplus typedef logical (*L_fp)(...); #else typedef logical (*L_fp)(); #endif static float spow_ui(float x, integer n) { float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static double dpow_ui(double x, integer n) { double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #ifdef _MSC_VER static _Fcomplex cpow_ui(complex x, integer n) { complex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i; for(u = n; ; ) { if(u & 01) pow.r *= x.r, pow.i *= x.i; if(u >>= 1) x.r *= x.r, x.i *= x.i; else break; } } _Fcomplex p={pow.r, pow.i}; return p; } #else static _Complex float cpow_ui(_Complex float x, integer n) { _Complex float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif #ifdef _MSC_VER static _Dcomplex zpow_ui(_Dcomplex x, integer n) { _Dcomplex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1]; for(u = n; ; ) { if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1]; if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1]; else break; } } _Dcomplex p = {pow._Val[0], pow._Val[1]}; return p; } #else static _Complex double zpow_ui(_Complex double x, integer n) { _Complex double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif static integer pow_ii(integer x, integer n) { integer pow; unsigned long int u; if (n <= 0) { if (n == 0 || x == 1) pow = 1; else if (x != -1) pow = x == 0 ? 1/x : 0; else n = -n; } if ((n > 0) || !(n == 0 || x == 1 || x != -1)) { u = n; for(pow = 1; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static integer dmaxloc_(double *w, integer s, integer e, integer *n) { double m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static integer smaxloc_(float *w, integer s, integer e, integer *n) { float m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) { integer n = *n_, incx = *incx_, incy = *incy_, i; #ifdef _MSC_VER _Fcomplex zdotc = {0.0, 0.0}; if (incx == 1 && incy == 1) { for (i=0;i \brief \b SGESDD */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SGESDD + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, */ /* WORK, LWORK, IWORK, INFO ) */ /* CHARACTER JOBZ */ /* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N */ /* INTEGER IWORK( * ) */ /* REAL A( LDA, * ), S( * ), U( LDU, * ), */ /* $ VT( LDVT, * ), WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SGESDD computes the singular value decomposition (SVD) of a real */ /* > M-by-N matrix A, optionally computing the left and right singular */ /* > vectors. If singular vectors are desired, it uses a */ /* > divide-and-conquer algorithm. */ /* > */ /* > The SVD is written */ /* > */ /* > A = U * SIGMA * transpose(V) */ /* > */ /* > where SIGMA is an M-by-N matrix which is zero except for its */ /* > f2cmin(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and */ /* > V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA */ /* > are the singular values of A; they are real and non-negative, and */ /* > are returned in descending order. The first f2cmin(m,n) columns of */ /* > U and V are the left and right singular vectors of A. */ /* > */ /* > Note that the routine returns VT = V**T, not V. */ /* > */ /* > 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] JOBZ */ /* > \verbatim */ /* > JOBZ is CHARACTER*1 */ /* > Specifies options for computing all or part of the matrix U: */ /* > = 'A': all M columns of U and all N rows of V**T are */ /* > returned in the arrays U and VT; */ /* > = 'S': the first f2cmin(M,N) columns of U and the first */ /* > f2cmin(M,N) rows of V**T are returned in the arrays U */ /* > and VT; */ /* > = 'O': If M >= N, the first N columns of U are overwritten */ /* > on the array A and all rows of V**T are returned in */ /* > the array VT; */ /* > otherwise, all columns of U are returned in the */ /* > array U and the first M rows of V**T are overwritten */ /* > in the array A; */ /* > = 'N': no columns of U or rows of V**T are computed. */ /* > \endverbatim */ /* > */ /* > \param[in] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The number of rows of the input matrix A. M >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The number of columns of the input matrix A. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is REAL array, dimension (LDA,N) */ /* > On entry, the M-by-N matrix A. */ /* > On exit, */ /* > if JOBZ = 'O', A is overwritten with the first N columns */ /* > of U (the left singular vectors, stored */ /* > columnwise) if M >= N; */ /* > A is overwritten with the first M rows */ /* > of V**T (the right singular vectors, stored */ /* > rowwise) otherwise. */ /* > if JOBZ .ne. 'O', the contents of A are destroyed. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */ /* > \endverbatim */ /* > */ /* > \param[out] S */ /* > \verbatim */ /* > S is REAL array, dimension (f2cmin(M,N)) */ /* > The singular values of A, sorted so that S(i) >= S(i+1). */ /* > \endverbatim */ /* > */ /* > \param[out] U */ /* > \verbatim */ /* > U is REAL array, dimension (LDU,UCOL) */ /* > UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; */ /* > UCOL = f2cmin(M,N) if JOBZ = 'S'. */ /* > If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M */ /* > orthogonal matrix U; */ /* > if JOBZ = 'S', U contains the first f2cmin(M,N) columns of U */ /* > (the left singular vectors, stored columnwise); */ /* > if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDU */ /* > \verbatim */ /* > LDU is INTEGER */ /* > The leading dimension of the array U. LDU >= 1; if */ /* > JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M. */ /* > \endverbatim */ /* > */ /* > \param[out] VT */ /* > \verbatim */ /* > VT is REAL array, dimension (LDVT,N) */ /* > If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the */ /* > N-by-N orthogonal matrix V**T; */ /* > if JOBZ = 'S', VT contains the first f2cmin(M,N) rows of */ /* > V**T (the right singular vectors, stored rowwise); */ /* > if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVT */ /* > \verbatim */ /* > LDVT is INTEGER */ /* > The leading dimension of the array VT. LDVT >= 1; */ /* > if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; */ /* > if JOBZ = 'S', LDVT >= f2cmin(M,N). */ /* > \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 >= 1. */ /* > If LWORK = -1, a workspace query is assumed. The optimal */ /* > size for the WORK array is calculated and stored in WORK(1), */ /* > and no other work except argument checking is performed. */ /* > */ /* > Let mx = f2cmax(M,N) and mn = f2cmin(M,N). */ /* > If JOBZ = 'N', LWORK >= 3*mn + f2cmax( mx, 7*mn ). */ /* > If JOBZ = 'O', LWORK >= 3*mn + f2cmax( mx, 5*mn*mn + 4*mn ). */ /* > If JOBZ = 'S', LWORK >= 4*mn*mn + 7*mn. */ /* > If JOBZ = 'A', LWORK >= 4*mn*mn + 6*mn + mx. */ /* > These are not tight minimums in all cases; see comments inside code. */ /* > For good performance, LWORK should generally be larger; */ /* > a query is recommended. */ /* > \endverbatim */ /* > */ /* > \param[out] IWORK */ /* > \verbatim */ /* > IWORK is INTEGER array, dimension (8*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: SBDSDC did not converge, updating process failed. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date June 2016 */ /* > \ingroup realGEsing */ /* > \par Contributors: */ /* ================== */ /* > */ /* > Ming Gu and Huan Ren, Computer Science Division, University of */ /* > California at Berkeley, USA */ /* > */ /* ===================================================================== */ /* Subroutine */ int sgesdd_(char *jobz, integer *m, integer *n, real *a, integer *lda, real *s, real *u, integer *ldu, real *vt, integer *ldvt, real *work, integer *lwork, integer *iwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1, i__2, i__3; /* Local variables */ integer lwork_sgelqf_mn__, lwork_sgeqrf_mn__, iscl, lwork_sorglq_mn__, lwork_sorglq_nn__; real anrm; integer idum[1], ierr, itau, lwork_sorgqr_mm__, lwork_sorgqr_mn__, lwork_sormbr_qln_mm__, lwork_sormbr_qln_mn__, lwork_sormbr_qln_nn__, lwork_sormbr_prt_mm__, lwork_sormbr_prt_mn__, lwork_sormbr_prt_nn__, i__; extern logical lsame_(char *, char *); integer chunk; extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *); integer minmn, wrkbl, itaup, itauq, mnthr; logical wntqa; integer nwork; logical wntqn, wntqo, wntqs; integer ie, il, ir, bdspac, iu, lwork_sorgbr_p_mm__; extern /* Subroutine */ int sbdsdc_(char *, char *, integer *, real *, real *, real *, integer *, real *, integer *, real *, integer *, real *, integer *, integer *); integer lwork_sorgbr_q_nn__; 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); real bignum; extern /* Subroutine */ int sgelqf_(integer *, integer *, real *, integer *, real *, real *, integer *, integer *), slascl_(char *, integer *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *), 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 *); extern logical sisnan_(real *); extern /* Subroutine */ int sorgbr_(char *, integer *, integer *, integer *, real *, integer *, real *, real *, integer *, integer *); integer ldwrkl; extern /* Subroutine */ int sormbr_(char *, char *, char *, integer *, integer *, integer *, real *, integer *, real *, real *, integer * , real *, integer *, integer *); integer ldwrkr, minwrk, ldwrku, maxwrk; extern /* Subroutine */ int sorglq_(integer *, integer *, integer *, real *, integer *, real *, real *, integer *, integer *); integer ldwkvt; real smlnum; logical wntqas; extern /* Subroutine */ int sorgqr_(integer *, integer *, integer *, real *, integer *, real *, real *, integer *, integer *); logical lquery; integer blk; real dum[1], eps; integer ivt, lwork_sgebrd_mm__, lwork_sgebrd_mn__, lwork_sgebrd_nn__; /* -- 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; --s; u_dim1 = *ldu; u_offset = 1 + u_dim1 * 1; u -= u_offset; vt_dim1 = *ldvt; vt_offset = 1 + vt_dim1 * 1; vt -= vt_offset; --work; --iwork; /* Function Body */ *info = 0; minmn = f2cmin(*m,*n); wntqa = lsame_(jobz, "A"); wntqs = lsame_(jobz, "S"); wntqas = wntqa || wntqs; wntqo = lsame_(jobz, "O"); wntqn = lsame_(jobz, "N"); lquery = *lwork == -1; if (! (wntqa || wntqs || wntqo || wntqn)) { *info = -1; } else if (*m < 0) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*lda < f2cmax(1,*m)) { *info = -5; } else if (*ldu < 1 || wntqas && *ldu < *m || wntqo && *m < *n && *ldu < * m) { *info = -8; } else if (*ldvt < 1 || wntqa && *ldvt < *n || wntqs && *ldvt < minmn || wntqo && *m >= *n && *ldvt < *n) { *info = -10; } /* Compute workspace */ /* Note: Comments in the code beginning "Workspace:" describe the */ /* minimal amount of workspace allocated 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; bdspac = 0; mnthr = (integer) (minmn * 11.f / 6.f); if (*m >= *n && minmn > 0) { /* Compute space needed for SBDSDC */ if (wntqn) { /* sbdsdc needs only 4*N (or 6*N for uplo=L for LAPACK <= 3.6) */ /* keep 7*N for backwards compatibility. */ bdspac = *n * 7; } else { bdspac = *n * 3 * *n + (*n << 2); } /* Compute space preferred for each routine */ sgebrd_(m, n, dum, m, dum, dum, dum, dum, dum, &c_n1, &ierr); lwork_sgebrd_mn__ = (integer) dum[0]; sgebrd_(n, n, dum, n, dum, dum, dum, dum, dum, &c_n1, &ierr); lwork_sgebrd_nn__ = (integer) dum[0]; sgeqrf_(m, n, dum, m, dum, dum, &c_n1, &ierr); lwork_sgeqrf_mn__ = (integer) dum[0]; sorgbr_("Q", n, n, n, dum, n, dum, dum, &c_n1, &ierr); lwork_sorgbr_q_nn__ = (integer) dum[0]; sorgqr_(m, m, n, dum, m, dum, dum, &c_n1, &ierr); lwork_sorgqr_mm__ = (integer) dum[0]; sorgqr_(m, n, n, dum, m, dum, dum, &c_n1, &ierr); lwork_sorgqr_mn__ = (integer) dum[0]; sormbr_("P", "R", "T", n, n, n, dum, n, dum, dum, n, dum, &c_n1, & ierr); lwork_sormbr_prt_nn__ = (integer) dum[0]; sormbr_("Q", "L", "N", n, n, n, dum, n, dum, dum, n, dum, &c_n1, & ierr); lwork_sormbr_qln_nn__ = (integer) dum[0]; sormbr_("Q", "L", "N", m, n, n, dum, m, dum, dum, m, dum, &c_n1, & ierr); lwork_sormbr_qln_mn__ = (integer) dum[0]; sormbr_("Q", "L", "N", m, m, n, dum, m, dum, dum, m, dum, &c_n1, & ierr); lwork_sormbr_qln_mm__ = (integer) dum[0]; if (*m >= mnthr) { if (wntqn) { /* Path 1 (M >> N, JOBZ='N') */ wrkbl = *n + lwork_sgeqrf_mn__; /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + lwork_sgebrd_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = bdspac + *n; maxwrk = f2cmax(i__1,i__2); minwrk = bdspac + *n; } else if (wntqo) { /* Path 2 (M >> N, JOBZ='O') */ wrkbl = *n + lwork_sgeqrf_mn__; /* Computing MAX */ i__1 = wrkbl, i__2 = *n + lwork_sorgqr_mn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + lwork_sgebrd_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_qln_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_prt_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + bdspac; wrkbl = f2cmax(i__1,i__2); maxwrk = wrkbl + (*n << 1) * *n; minwrk = bdspac + (*n << 1) * *n + *n * 3; } else if (wntqs) { /* Path 3 (M >> N, JOBZ='S') */ wrkbl = *n + lwork_sgeqrf_mn__; /* Computing MAX */ i__1 = wrkbl, i__2 = *n + lwork_sorgqr_mn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + lwork_sgebrd_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_qln_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_prt_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + bdspac; wrkbl = f2cmax(i__1,i__2); maxwrk = wrkbl + *n * *n; minwrk = bdspac + *n * *n + *n * 3; } else if (wntqa) { /* Path 4 (M >> N, JOBZ='A') */ wrkbl = *n + lwork_sgeqrf_mn__; /* Computing MAX */ i__1 = wrkbl, i__2 = *n + lwork_sorgqr_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + lwork_sgebrd_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_qln_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_prt_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + bdspac; wrkbl = f2cmax(i__1,i__2); maxwrk = wrkbl + *n * *n; /* Computing MAX */ i__1 = *n * 3 + bdspac, i__2 = *n + *m; minwrk = *n * *n + f2cmax(i__1,i__2); } } else { /* Path 5 (M >= N, but not much larger) */ wrkbl = *n * 3 + lwork_sgebrd_mn__; if (wntqn) { /* Path 5n (M >= N, jobz='N') */ /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + bdspac; maxwrk = f2cmax(i__1,i__2); minwrk = *n * 3 + f2cmax(*m,bdspac); } else if (wntqo) { /* Path 5o (M >= N, jobz='O') */ /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_prt_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_qln_mn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + bdspac; wrkbl = f2cmax(i__1,i__2); maxwrk = wrkbl + *m * *n; /* Computing MAX */ i__1 = *m, i__2 = *n * *n + bdspac; minwrk = *n * 3 + f2cmax(i__1,i__2); } else if (wntqs) { /* Path 5s (M >= N, jobz='S') */ /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_qln_mn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_prt_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + bdspac; maxwrk = f2cmax(i__1,i__2); minwrk = *n * 3 + f2cmax(*m,bdspac); } else if (wntqa) { /* Path 5a (M >= N, jobz='A') */ /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_qln_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_prt_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *n * 3 + bdspac; maxwrk = f2cmax(i__1,i__2); minwrk = *n * 3 + f2cmax(*m,bdspac); } } } else if (minmn > 0) { /* Compute space needed for SBDSDC */ if (wntqn) { /* sbdsdc needs only 4*N (or 6*N for uplo=L for LAPACK <= 3.6) */ /* keep 7*N for backwards compatibility. */ bdspac = *m * 7; } else { bdspac = *m * 3 * *m + (*m << 2); } /* Compute space preferred for each routine */ sgebrd_(m, n, dum, m, dum, dum, dum, dum, dum, &c_n1, &ierr); lwork_sgebrd_mn__ = (integer) dum[0]; sgebrd_(m, m, &a[a_offset], m, &s[1], dum, dum, dum, dum, &c_n1, & ierr); lwork_sgebrd_mm__ = (integer) dum[0]; sgelqf_(m, n, &a[a_offset], m, dum, dum, &c_n1, &ierr); lwork_sgelqf_mn__ = (integer) dum[0]; sorglq_(n, n, m, dum, n, dum, dum, &c_n1, &ierr); lwork_sorglq_nn__ = (integer) dum[0]; sorglq_(m, n, m, &a[a_offset], m, dum, dum, &c_n1, &ierr); lwork_sorglq_mn__ = (integer) dum[0]; sorgbr_("P", m, m, m, &a[a_offset], n, dum, dum, &c_n1, &ierr); lwork_sorgbr_p_mm__ = (integer) dum[0]; sormbr_("P", "R", "T", m, m, m, dum, m, dum, dum, m, dum, &c_n1, & ierr); lwork_sormbr_prt_mm__ = (integer) dum[0]; sormbr_("P", "R", "T", m, n, m, dum, m, dum, dum, m, dum, &c_n1, & ierr); lwork_sormbr_prt_mn__ = (integer) dum[0]; sormbr_("P", "R", "T", n, n, m, dum, n, dum, dum, n, dum, &c_n1, & ierr); lwork_sormbr_prt_nn__ = (integer) dum[0]; sormbr_("Q", "L", "N", m, m, m, dum, m, dum, dum, m, dum, &c_n1, & ierr); lwork_sormbr_qln_mm__ = (integer) dum[0]; if (*n >= mnthr) { if (wntqn) { /* Path 1t (N >> M, JOBZ='N') */ wrkbl = *m + lwork_sgelqf_mn__; /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + lwork_sgebrd_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = bdspac + *m; maxwrk = f2cmax(i__1,i__2); minwrk = bdspac + *m; } else if (wntqo) { /* Path 2t (N >> M, JOBZ='O') */ wrkbl = *m + lwork_sgelqf_mn__; /* Computing MAX */ i__1 = wrkbl, i__2 = *m + lwork_sorglq_mn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + lwork_sgebrd_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_qln_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_prt_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + bdspac; wrkbl = f2cmax(i__1,i__2); maxwrk = wrkbl + (*m << 1) * *m; minwrk = bdspac + (*m << 1) * *m + *m * 3; } else if (wntqs) { /* Path 3t (N >> M, JOBZ='S') */ wrkbl = *m + lwork_sgelqf_mn__; /* Computing MAX */ i__1 = wrkbl, i__2 = *m + lwork_sorglq_mn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + lwork_sgebrd_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_qln_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_prt_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + bdspac; wrkbl = f2cmax(i__1,i__2); maxwrk = wrkbl + *m * *m; minwrk = bdspac + *m * *m + *m * 3; } else if (wntqa) { /* Path 4t (N >> M, JOBZ='A') */ wrkbl = *m + lwork_sgelqf_mn__; /* Computing MAX */ i__1 = wrkbl, i__2 = *m + lwork_sorglq_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + lwork_sgebrd_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_qln_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_prt_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + bdspac; wrkbl = f2cmax(i__1,i__2); maxwrk = wrkbl + *m * *m; /* Computing MAX */ i__1 = *m * 3 + bdspac, i__2 = *m + *n; minwrk = *m * *m + f2cmax(i__1,i__2); } } else { /* Path 5t (N > M, but not much larger) */ wrkbl = *m * 3 + lwork_sgebrd_mn__; if (wntqn) { /* Path 5tn (N > M, jobz='N') */ /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + bdspac; maxwrk = f2cmax(i__1,i__2); minwrk = *m * 3 + f2cmax(*n,bdspac); } else if (wntqo) { /* Path 5to (N > M, jobz='O') */ /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_qln_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_prt_mn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + bdspac; wrkbl = f2cmax(i__1,i__2); maxwrk = wrkbl + *m * *n; /* Computing MAX */ i__1 = *n, i__2 = *m * *m + bdspac; minwrk = *m * 3 + f2cmax(i__1,i__2); } else if (wntqs) { /* Path 5ts (N > M, jobz='S') */ /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_qln_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_prt_mn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + bdspac; maxwrk = f2cmax(i__1,i__2); minwrk = *m * 3 + f2cmax(*n,bdspac); } else if (wntqa) { /* Path 5ta (N > M, jobz='A') */ /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_qln_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_prt_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = *m * 3 + bdspac; maxwrk = f2cmax(i__1,i__2); minwrk = *m * 3 + f2cmax(*n,bdspac); } } } maxwrk = f2cmax(maxwrk,minwrk); work[1] = (real) maxwrk; if (*lwork < minwrk && ! lquery) { *info = -12; } } if (*info != 0) { i__1 = -(*info); xerbla_("SGESDD", &i__1, (ftnlen)6); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { return 0; } /* Get machine constants */ eps = slamch_("P"); smlnum = sqrt(slamch_("S")) / eps; bignum = 1.f / smlnum; /* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */ anrm = slange_("M", m, n, &a[a_offset], lda, dum); if (sisnan_(&anrm)) { *info = -4; return 0; } iscl = 0; if (anrm > 0.f && anrm < smlnum) { iscl = 1; slascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, & ierr); } else if (anrm > bignum) { iscl = 1; slascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, & ierr); } if (*m >= *n) { /* A has at least as many rows as columns. If A has sufficiently */ /* more rows than columns, first reduce using the QR */ /* decomposition (if sufficient workspace available) */ if (*m >= mnthr) { if (wntqn) { /* Path 1 (M >> N, JOBZ='N') */ /* No singular vectors to be computed */ itau = 1; nwork = itau + *n; /* Compute A=Q*R */ /* Workspace: need N [tau] + N [work] */ /* Workspace: prefer N [tau] + N*NB [work] */ i__1 = *lwork - nwork + 1; sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__1, &ierr); /* Zero out below R */ i__1 = *n - 1; i__2 = *n - 1; slaset_("L", &i__1, &i__2, &c_b63, &c_b63, &a[a_dim1 + 2], lda); ie = 1; itauq = ie + *n; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize R in A */ /* Workspace: need 3*N [e, tauq, taup] + N [work] */ /* Workspace: prefer 3*N [e, tauq, taup] + 2*N*NB [work] */ i__1 = *lwork - nwork + 1; sgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[ itauq], &work[itaup], &work[nwork], &i__1, &ierr); nwork = ie + *n; /* Perform bidiagonal SVD, computing singular values only */ /* Workspace: need N [e] + BDSPAC */ sbdsdc_("U", "N", n, &s[1], &work[ie], dum, &c__1, dum, &c__1, dum, idum, &work[nwork], &iwork[1], info); } else if (wntqo) { /* Path 2 (M >> N, JOBZ = 'O') */ /* N left singular vectors to be overwritten on A and */ /* N right singular vectors to be computed in VT */ ir = 1; /* WORK(IR) is LDWRKR by N */ if (*lwork >= *lda * *n + *n * *n + *n * 3 + bdspac) { ldwrkr = *lda; } else { ldwrkr = (*lwork - *n * *n - *n * 3 - bdspac) / *n; } itau = ir + ldwrkr * *n; nwork = itau + *n; /* Compute A=Q*R */ /* Workspace: need N*N [R] + N [tau] + N [work] */ /* Workspace: prefer N*N [R] + N [tau] + N*NB [work] */ i__1 = *lwork - nwork + 1; sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__1, &ierr); /* Copy R to WORK(IR), zeroing out below it */ slacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr); i__1 = *n - 1; i__2 = *n - 1; slaset_("L", &i__1, &i__2, &c_b63, &c_b63, &work[ir + 1], & ldwrkr); /* Generate Q in A */ /* Workspace: need N*N [R] + N [tau] + N [work] */ /* Workspace: prefer N*N [R] + N [tau] + N*NB [work] */ i__1 = *lwork - nwork + 1; sorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, &ierr); ie = itau; itauq = ie + *n; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize R in WORK(IR) */ /* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N [work] */ /* Workspace: prefer N*N [R] + 3*N [e, tauq, taup] + 2*N*NB [work] */ i__1 = *lwork - nwork + 1; sgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[ itauq], &work[itaup], &work[nwork], &i__1, &ierr); /* WORK(IU) is N by N */ iu = nwork; nwork = iu + *n * *n; /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in WORK(IU) and computing right */ /* singular vectors of bidiagonal matrix in VT */ /* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N*N [U] + BDSPAC */ sbdsdc_("U", "I", n, &s[1], &work[ie], &work[iu], n, &vt[ vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], info); /* Overwrite WORK(IU) by left singular vectors of R */ /* and VT by right singular vectors of R */ /* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N*N [U] + N [work] */ /* Workspace: prefer N*N [R] + 3*N [e, tauq, taup] + N*N [U] + N*NB [work] */ i__1 = *lwork - nwork + 1; sormbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[ itauq], &work[iu], n, &work[nwork], &i__1, &ierr); i__1 = *lwork - nwork + 1; sormbr_("P", "R", "T", n, n, n, &work[ir], &ldwrkr, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, & ierr); /* Multiply Q in A by left singular vectors of R in */ /* WORK(IU), storing result in WORK(IR) and copying to A */ /* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N*N [U] */ /* Workspace: prefer M*N [R] + 3*N [e, tauq, taup] + N*N [U] */ i__1 = *m; i__2 = ldwrkr; for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { /* Computing MIN */ i__3 = *m - i__ + 1; chunk = f2cmin(i__3,ldwrkr); sgemm_("N", "N", &chunk, n, n, &c_b84, &a[i__ + a_dim1], lda, &work[iu], n, &c_b63, &work[ir], &ldwrkr); slacpy_("F", &chunk, n, &work[ir], &ldwrkr, &a[i__ + a_dim1], lda); /* L10: */ } } else if (wntqs) { /* Path 3 (M >> N, JOBZ='S') */ /* N left singular vectors to be computed in U and */ /* N right singular vectors to be computed in VT */ ir = 1; /* WORK(IR) is N by N */ ldwrkr = *n; itau = ir + ldwrkr * *n; nwork = itau + *n; /* Compute A=Q*R */ /* Workspace: need N*N [R] + N [tau] + N [work] */ /* Workspace: prefer N*N [R] + N [tau] + N*NB [work] */ i__2 = *lwork - nwork + 1; sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__2, &ierr); /* Copy R to WORK(IR), zeroing out below it */ slacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr); i__2 = *n - 1; i__1 = *n - 1; slaset_("L", &i__2, &i__1, &c_b63, &c_b63, &work[ir + 1], & ldwrkr); /* Generate Q in A */ /* Workspace: need N*N [R] + N [tau] + N [work] */ /* Workspace: prefer N*N [R] + N [tau] + N*NB [work] */ i__2 = *lwork - nwork + 1; sorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__2, &ierr); ie = itau; itauq = ie + *n; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize R in WORK(IR) */ /* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N [work] */ /* Workspace: prefer N*N [R] + 3*N [e, tauq, taup] + 2*N*NB [work] */ i__2 = *lwork - nwork + 1; sgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[ itauq], &work[itaup], &work[nwork], &i__2, &ierr); /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagoal matrix in U and computing right singular */ /* vectors of bidiagonal matrix in VT */ /* Workspace: need N*N [R] + 3*N [e, tauq, taup] + BDSPAC */ sbdsdc_("U", "I", n, &s[1], &work[ie], &u[u_offset], ldu, &vt[ vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], info); /* Overwrite U by left singular vectors of R and VT */ /* by right singular vectors of R */ /* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N [work] */ /* Workspace: prefer N*N [R] + 3*N [e, tauq, taup] + N*NB [work] */ i__2 = *lwork - nwork + 1; sormbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr); i__2 = *lwork - nwork + 1; sormbr_("P", "R", "T", n, n, n, &work[ir], &ldwrkr, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, & ierr); /* Multiply Q in A by left singular vectors of R in */ /* WORK(IR), storing result in U */ /* Workspace: need N*N [R] */ slacpy_("F", n, n, &u[u_offset], ldu, &work[ir], &ldwrkr); sgemm_("N", "N", m, n, n, &c_b84, &a[a_offset], lda, &work[ir] , &ldwrkr, &c_b63, &u[u_offset], ldu); } else if (wntqa) { /* Path 4 (M >> N, JOBZ='A') */ /* M left singular vectors to be computed in U and */ /* N right singular vectors to be computed in VT */ iu = 1; /* WORK(IU) is N by N */ ldwrku = *n; itau = iu + ldwrku * *n; nwork = itau + *n; /* Compute A=Q*R, copying result to U */ /* Workspace: need N*N [U] + N [tau] + N [work] */ /* Workspace: prefer N*N [U] + N [tau] + N*NB [work] */ i__2 = *lwork - nwork + 1; sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__2, &ierr); slacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu); /* Generate Q in U */ /* Workspace: need N*N [U] + N [tau] + M [work] */ /* Workspace: prefer N*N [U] + N [tau] + M*NB [work] */ i__2 = *lwork - nwork + 1; sorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &work[nwork], &i__2, &ierr); /* Produce R in A, zeroing out other entries */ i__2 = *n - 1; i__1 = *n - 1; slaset_("L", &i__2, &i__1, &c_b63, &c_b63, &a[a_dim1 + 2], lda); ie = itau; itauq = ie + *n; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize R in A */ /* Workspace: need N*N [U] + 3*N [e, tauq, taup] + N [work] */ /* Workspace: prefer N*N [U] + 3*N [e, tauq, taup] + 2*N*NB [work] */ i__2 = *lwork - nwork + 1; sgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[ itauq], &work[itaup], &work[nwork], &i__2, &ierr); /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in WORK(IU) and computing right */ /* singular vectors of bidiagonal matrix in VT */ /* Workspace: need N*N [U] + 3*N [e, tauq, taup] + BDSPAC */ sbdsdc_("U", "I", n, &s[1], &work[ie], &work[iu], n, &vt[ vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], info); /* Overwrite WORK(IU) by left singular vectors of R and VT */ /* by right singular vectors of R */ /* Workspace: need N*N [U] + 3*N [e, tauq, taup] + N [work] */ /* Workspace: prefer N*N [U] + 3*N [e, tauq, taup] + N*NB [work] */ i__2 = *lwork - nwork + 1; sormbr_("Q", "L", "N", n, n, n, &a[a_offset], lda, &work[ itauq], &work[iu], &ldwrku, &work[nwork], &i__2, & ierr); i__2 = *lwork - nwork + 1; sormbr_("P", "R", "T", n, n, n, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, & ierr); /* Multiply Q in U by left singular vectors of R in */ /* WORK(IU), storing result in A */ /* Workspace: need N*N [U] */ sgemm_("N", "N", m, n, n, &c_b84, &u[u_offset], ldu, &work[iu] , &ldwrku, &c_b63, &a[a_offset], lda); /* Copy left singular vectors of A from A to U */ slacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu); } } else { /* M .LT. MNTHR */ /* Path 5 (M >= N, but not much larger) */ /* Reduce to bidiagonal form without QR decomposition */ ie = 1; itauq = ie + *n; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize A */ /* Workspace: need 3*N [e, tauq, taup] + M [work] */ /* Workspace: prefer 3*N [e, tauq, taup] + (M+N)*NB [work] */ i__2 = *lwork - nwork + 1; sgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & work[itaup], &work[nwork], &i__2, &ierr); if (wntqn) { /* Path 5n (M >= N, JOBZ='N') */ /* Perform bidiagonal SVD, only computing singular values */ /* Workspace: need 3*N [e, tauq, taup] + BDSPAC */ sbdsdc_("U", "N", n, &s[1], &work[ie], dum, &c__1, dum, &c__1, dum, idum, &work[nwork], &iwork[1], info); } else if (wntqo) { /* Path 5o (M >= N, JOBZ='O') */ iu = nwork; if (*lwork >= *m * *n + *n * 3 + bdspac) { /* WORK( IU ) is M by N */ ldwrku = *m; nwork = iu + ldwrku * *n; slaset_("F", m, n, &c_b63, &c_b63, &work[iu], &ldwrku); /* IR is unused; silence compile warnings */ ir = -1; } else { /* WORK( IU ) is N by N */ ldwrku = *n; nwork = iu + ldwrku * *n; /* WORK(IR) is LDWRKR by N */ ir = nwork; ldwrkr = (*lwork - *n * *n - *n * 3) / *n; } nwork = iu + ldwrku * *n; /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in WORK(IU) and computing right */ /* singular vectors of bidiagonal matrix in VT */ /* Workspace: need 3*N [e, tauq, taup] + N*N [U] + BDSPAC */ sbdsdc_("U", "I", n, &s[1], &work[ie], &work[iu], &ldwrku, & vt[vt_offset], ldvt, dum, idum, &work[nwork], &iwork[ 1], info); /* Overwrite VT by right singular vectors of A */ /* Workspace: need 3*N [e, tauq, taup] + N*N [U] + N [work] */ /* Workspace: prefer 3*N [e, tauq, taup] + N*N [U] + N*NB [work] */ i__2 = *lwork - nwork + 1; sormbr_("P", "R", "T", n, n, n, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, & ierr); if (*lwork >= *m * *n + *n * 3 + bdspac) { /* Path 5o-fast */ /* Overwrite WORK(IU) by left singular vectors of A */ /* Workspace: need 3*N [e, tauq, taup] + M*N [U] + N [work] */ /* Workspace: prefer 3*N [e, tauq, taup] + M*N [U] + N*NB [work] */ i__2 = *lwork - nwork + 1; sormbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[ itauq], &work[iu], &ldwrku, &work[nwork], &i__2, & ierr); /* Copy left singular vectors of A from WORK(IU) to A */ slacpy_("F", m, n, &work[iu], &ldwrku, &a[a_offset], lda); } else { /* Path 5o-slow */ /* Generate Q in A */ /* Workspace: need 3*N [e, tauq, taup] + N*N [U] + N [work] */ /* Workspace: prefer 3*N [e, tauq, taup] + N*N [U] + N*NB [work] */ i__2 = *lwork - nwork + 1; sorgbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], & work[nwork], &i__2, &ierr); /* Multiply Q in A by left singular vectors of */ /* bidiagonal matrix in WORK(IU), storing result in */ /* WORK(IR) and copying to A */ /* Workspace: need 3*N [e, tauq, taup] + N*N [U] + NB*N [R] */ /* Workspace: prefer 3*N [e, tauq, taup] + N*N [U] + M*N [R] */ i__2 = *m; i__1 = ldwrkr; for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) { /* Computing MIN */ i__3 = *m - i__ + 1; chunk = f2cmin(i__3,ldwrkr); sgemm_("N", "N", &chunk, n, n, &c_b84, &a[i__ + a_dim1], lda, &work[iu], &ldwrku, &c_b63, & work[ir], &ldwrkr); slacpy_("F", &chunk, n, &work[ir], &ldwrkr, &a[i__ + a_dim1], lda); /* L20: */ } } } else if (wntqs) { /* Path 5s (M >= N, JOBZ='S') */ /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in U and computing right singular */ /* vectors of bidiagonal matrix in VT */ /* Workspace: need 3*N [e, tauq, taup] + BDSPAC */ slaset_("F", m, n, &c_b63, &c_b63, &u[u_offset], ldu); sbdsdc_("U", "I", n, &s[1], &work[ie], &u[u_offset], ldu, &vt[ vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], info); /* Overwrite U by left singular vectors of A and VT */ /* by right singular vectors of A */ /* Workspace: need 3*N [e, tauq, taup] + N [work] */ /* Workspace: prefer 3*N [e, tauq, taup] + N*NB [work] */ i__1 = *lwork - nwork + 1; sormbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr); i__1 = *lwork - nwork + 1; sormbr_("P", "R", "T", n, n, n, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, & ierr); } else if (wntqa) { /* Path 5a (M >= N, JOBZ='A') */ /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in U and computing right singular */ /* vectors of bidiagonal matrix in VT */ /* Workspace: need 3*N [e, tauq, taup] + BDSPAC */ slaset_("F", m, m, &c_b63, &c_b63, &u[u_offset], ldu); sbdsdc_("U", "I", n, &s[1], &work[ie], &u[u_offset], ldu, &vt[ vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], info); /* Set the right corner of U to identity matrix */ if (*m > *n) { i__1 = *m - *n; i__2 = *m - *n; slaset_("F", &i__1, &i__2, &c_b63, &c_b84, &u[*n + 1 + (* n + 1) * u_dim1], ldu); } /* Overwrite U by left singular vectors of A and VT */ /* by right singular vectors of A */ /* Workspace: need 3*N [e, tauq, taup] + M [work] */ /* Workspace: prefer 3*N [e, tauq, taup] + M*NB [work] */ i__1 = *lwork - nwork + 1; sormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr); i__1 = *lwork - nwork + 1; sormbr_("P", "R", "T", n, n, m, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, & ierr); } } } else { /* A has more columns than rows. If A has sufficiently more */ /* columns than rows, first reduce using the LQ decomposition (if */ /* sufficient workspace available) */ if (*n >= mnthr) { if (wntqn) { /* Path 1t (N >> M, JOBZ='N') */ /* No singular vectors to be computed */ itau = 1; nwork = itau + *m; /* Compute A=L*Q */ /* Workspace: need M [tau] + M [work] */ /* Workspace: prefer M [tau] + M*NB [work] */ i__1 = *lwork - nwork + 1; sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__1, &ierr); /* Zero out above L */ i__1 = *m - 1; i__2 = *m - 1; slaset_("U", &i__1, &i__2, &c_b63, &c_b63, &a[(a_dim1 << 1) + 1], lda); ie = 1; itauq = ie + *m; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize L in A */ /* Workspace: need 3*M [e, tauq, taup] + M [work] */ /* Workspace: prefer 3*M [e, tauq, taup] + 2*M*NB [work] */ i__1 = *lwork - nwork + 1; sgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[ itauq], &work[itaup], &work[nwork], &i__1, &ierr); nwork = ie + *m; /* Perform bidiagonal SVD, computing singular values only */ /* Workspace: need M [e] + BDSPAC */ sbdsdc_("U", "N", m, &s[1], &work[ie], dum, &c__1, dum, &c__1, dum, idum, &work[nwork], &iwork[1], info); } else if (wntqo) { /* Path 2t (N >> M, JOBZ='O') */ /* M right singular vectors to be overwritten on A and */ /* M left singular vectors to be computed in U */ ivt = 1; /* WORK(IVT) is M by M */ /* WORK(IL) is M by M; it is later resized to M by chunk for gemm */ il = ivt + *m * *m; if (*lwork >= *m * *n + *m * *m + *m * 3 + bdspac) { ldwrkl = *m; chunk = *n; } else { ldwrkl = *m; chunk = (*lwork - *m * *m) / *m; } itau = il + ldwrkl * *m; nwork = itau + *m; /* Compute A=L*Q */ /* Workspace: need M*M [VT] + M*M [L] + M [tau] + M [work] */ /* Workspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work] */ i__1 = *lwork - nwork + 1; sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__1, &ierr); /* Copy L to WORK(IL), zeroing about above it */ slacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl); i__1 = *m - 1; i__2 = *m - 1; slaset_("U", &i__1, &i__2, &c_b63, &c_b63, &work[il + ldwrkl], &ldwrkl); /* Generate Q in A */ /* Workspace: need M*M [VT] + M*M [L] + M [tau] + M [work] */ /* Workspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work] */ i__1 = *lwork - nwork + 1; sorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, &ierr); ie = itau; itauq = ie + *m; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize L in WORK(IL) */ /* Workspace: need M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + M [work] */ /* Workspace: prefer M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + 2*M*NB [work] */ i__1 = *lwork - nwork + 1; sgebrd_(m, m, &work[il], &ldwrkl, &s[1], &work[ie], &work[ itauq], &work[itaup], &work[nwork], &i__1, &ierr); /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in U, and computing right singular */ /* vectors of bidiagonal matrix in WORK(IVT) */ /* Workspace: need M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + BDSPAC */ sbdsdc_("U", "I", m, &s[1], &work[ie], &u[u_offset], ldu, & work[ivt], m, dum, idum, &work[nwork], &iwork[1], info); /* Overwrite U by left singular vectors of L and WORK(IVT) */ /* by right singular vectors of L */ /* Workspace: need M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + M [work] */ /* Workspace: prefer M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + M*NB [work] */ i__1 = *lwork - nwork + 1; sormbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr); i__1 = *lwork - nwork + 1; sormbr_("P", "R", "T", m, m, m, &work[il], &ldwrkl, &work[ itaup], &work[ivt], m, &work[nwork], &i__1, &ierr); /* Multiply right singular vectors of L in WORK(IVT) by Q */ /* in A, storing result in WORK(IL) and copying to A */ /* Workspace: need M*M [VT] + M*M [L] */ /* Workspace: prefer M*M [VT] + M*N [L] */ /* At this point, L is resized as M by chunk. */ i__1 = *n; i__2 = chunk; for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { /* Computing MIN */ i__3 = *n - i__ + 1; blk = f2cmin(i__3,chunk); sgemm_("N", "N", m, &blk, m, &c_b84, &work[ivt], m, &a[ i__ * a_dim1 + 1], lda, &c_b63, &work[il], & ldwrkl); slacpy_("F", m, &blk, &work[il], &ldwrkl, &a[i__ * a_dim1 + 1], lda); /* L30: */ } } else if (wntqs) { /* Path 3t (N >> M, JOBZ='S') */ /* M right singular vectors to be computed in VT and */ /* M left singular vectors to be computed in U */ il = 1; /* WORK(IL) is M by M */ ldwrkl = *m; itau = il + ldwrkl * *m; nwork = itau + *m; /* Compute A=L*Q */ /* Workspace: need M*M [L] + M [tau] + M [work] */ /* Workspace: prefer M*M [L] + M [tau] + M*NB [work] */ i__2 = *lwork - nwork + 1; sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__2, &ierr); /* Copy L to WORK(IL), zeroing out above it */ slacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl); i__2 = *m - 1; i__1 = *m - 1; slaset_("U", &i__2, &i__1, &c_b63, &c_b63, &work[il + ldwrkl], &ldwrkl); /* Generate Q in A */ /* Workspace: need M*M [L] + M [tau] + M [work] */ /* Workspace: prefer M*M [L] + M [tau] + M*NB [work] */ i__2 = *lwork - nwork + 1; sorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork], &i__2, &ierr); ie = itau; itauq = ie + *m; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize L in WORK(IU). */ /* Workspace: need M*M [L] + 3*M [e, tauq, taup] + M [work] */ /* Workspace: prefer M*M [L] + 3*M [e, tauq, taup] + 2*M*NB [work] */ i__2 = *lwork - nwork + 1; sgebrd_(m, m, &work[il], &ldwrkl, &s[1], &work[ie], &work[ itauq], &work[itaup], &work[nwork], &i__2, &ierr); /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in U and computing right singular */ /* vectors of bidiagonal matrix in VT */ /* Workspace: need M*M [L] + 3*M [e, tauq, taup] + BDSPAC */ sbdsdc_("U", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &vt[ vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], info); /* Overwrite U by left singular vectors of L and VT */ /* by right singular vectors of L */ /* Workspace: need M*M [L] + 3*M [e, tauq, taup] + M [work] */ /* Workspace: prefer M*M [L] + 3*M [e, tauq, taup] + M*NB [work] */ i__2 = *lwork - nwork + 1; sormbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr); i__2 = *lwork - nwork + 1; sormbr_("P", "R", "T", m, m, m, &work[il], &ldwrkl, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, & ierr); /* Multiply right singular vectors of L in WORK(IL) by */ /* Q in A, storing result in VT */ /* Workspace: need M*M [L] */ slacpy_("F", m, m, &vt[vt_offset], ldvt, &work[il], &ldwrkl); sgemm_("N", "N", m, n, m, &c_b84, &work[il], &ldwrkl, &a[ a_offset], lda, &c_b63, &vt[vt_offset], ldvt); } else if (wntqa) { /* Path 4t (N >> M, JOBZ='A') */ /* N right singular vectors to be computed in VT and */ /* M left singular vectors to be computed in U */ ivt = 1; /* WORK(IVT) is M by M */ ldwkvt = *m; itau = ivt + ldwkvt * *m; nwork = itau + *m; /* Compute A=L*Q, copying result to VT */ /* Workspace: need M*M [VT] + M [tau] + M [work] */ /* Workspace: prefer M*M [VT] + M [tau] + M*NB [work] */ i__2 = *lwork - nwork + 1; sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__2, &ierr); slacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt); /* Generate Q in VT */ /* Workspace: need M*M [VT] + M [tau] + N [work] */ /* Workspace: prefer M*M [VT] + M [tau] + N*NB [work] */ i__2 = *lwork - nwork + 1; sorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &work[ nwork], &i__2, &ierr); /* Produce L in A, zeroing out other entries */ i__2 = *m - 1; i__1 = *m - 1; slaset_("U", &i__2, &i__1, &c_b63, &c_b63, &a[(a_dim1 << 1) + 1], lda); ie = itau; itauq = ie + *m; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize L in A */ /* Workspace: need M*M [VT] + 3*M [e, tauq, taup] + M [work] */ /* Workspace: prefer M*M [VT] + 3*M [e, tauq, taup] + 2*M*NB [work] */ i__2 = *lwork - nwork + 1; sgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[ itauq], &work[itaup], &work[nwork], &i__2, &ierr); /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in U and computing right singular */ /* vectors of bidiagonal matrix in WORK(IVT) */ /* Workspace: need M*M [VT] + 3*M [e, tauq, taup] + BDSPAC */ sbdsdc_("U", "I", m, &s[1], &work[ie], &u[u_offset], ldu, & work[ivt], &ldwkvt, dum, idum, &work[nwork], &iwork[1] , info); /* Overwrite U by left singular vectors of L and WORK(IVT) */ /* by right singular vectors of L */ /* Workspace: need M*M [VT] + 3*M [e, tauq, taup]+ M [work] */ /* Workspace: prefer M*M [VT] + 3*M [e, tauq, taup]+ M*NB [work] */ i__2 = *lwork - nwork + 1; sormbr_("Q", "L", "N", m, m, m, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr); i__2 = *lwork - nwork + 1; sormbr_("P", "R", "T", m, m, m, &a[a_offset], lda, &work[ itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2, & ierr); /* Multiply right singular vectors of L in WORK(IVT) by */ /* Q in VT, storing result in A */ /* Workspace: need M*M [VT] */ sgemm_("N", "N", m, n, m, &c_b84, &work[ivt], &ldwkvt, &vt[ vt_offset], ldvt, &c_b63, &a[a_offset], lda); /* Copy right singular vectors of A from A to VT */ slacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt); } } else { /* N .LT. MNTHR */ /* Path 5t (N > M, but not much larger) */ /* Reduce to bidiagonal form without LQ decomposition */ ie = 1; itauq = ie + *m; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize A */ /* Workspace: need 3*M [e, tauq, taup] + N [work] */ /* Workspace: prefer 3*M [e, tauq, taup] + (M+N)*NB [work] */ i__2 = *lwork - nwork + 1; sgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & work[itaup], &work[nwork], &i__2, &ierr); if (wntqn) { /* Path 5tn (N > M, JOBZ='N') */ /* Perform bidiagonal SVD, only computing singular values */ /* Workspace: need 3*M [e, tauq, taup] + BDSPAC */ sbdsdc_("L", "N", m, &s[1], &work[ie], dum, &c__1, dum, &c__1, dum, idum, &work[nwork], &iwork[1], info); } else if (wntqo) { /* Path 5to (N > M, JOBZ='O') */ ldwkvt = *m; ivt = nwork; if (*lwork >= *m * *n + *m * 3 + bdspac) { /* WORK( IVT ) is M by N */ slaset_("F", m, n, &c_b63, &c_b63, &work[ivt], &ldwkvt); nwork = ivt + ldwkvt * *n; /* IL is unused; silence compile warnings */ il = -1; } else { /* WORK( IVT ) is M by M */ nwork = ivt + ldwkvt * *m; il = nwork; /* WORK(IL) is M by CHUNK */ chunk = (*lwork - *m * *m - *m * 3) / *m; } /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in U and computing right singular */ /* vectors of bidiagonal matrix in WORK(IVT) */ /* Workspace: need 3*M [e, tauq, taup] + M*M [VT] + BDSPAC */ sbdsdc_("L", "I", m, &s[1], &work[ie], &u[u_offset], ldu, & work[ivt], &ldwkvt, dum, idum, &work[nwork], &iwork[1] , info); /* Overwrite U by left singular vectors of A */ /* Workspace: need 3*M [e, tauq, taup] + M*M [VT] + M [work] */ /* Workspace: prefer 3*M [e, tauq, taup] + M*M [VT] + M*NB [work] */ i__2 = *lwork - nwork + 1; sormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr); if (*lwork >= *m * *n + *m * 3 + bdspac) { /* Path 5to-fast */ /* Overwrite WORK(IVT) by left singular vectors of A */ /* Workspace: need 3*M [e, tauq, taup] + M*N [VT] + M [work] */ /* Workspace: prefer 3*M [e, tauq, taup] + M*N [VT] + M*NB [work] */ i__2 = *lwork - nwork + 1; sormbr_("P", "R", "T", m, n, m, &a[a_offset], lda, &work[ itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2, &ierr); /* Copy right singular vectors of A from WORK(IVT) to A */ slacpy_("F", m, n, &work[ivt], &ldwkvt, &a[a_offset], lda); } else { /* Path 5to-slow */ /* Generate P**T in A */ /* Workspace: need 3*M [e, tauq, taup] + M*M [VT] + M [work] */ /* Workspace: prefer 3*M [e, tauq, taup] + M*M [VT] + M*NB [work] */ i__2 = *lwork - nwork + 1; sorgbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], & work[nwork], &i__2, &ierr); /* Multiply Q in A by right singular vectors of */ /* bidiagonal matrix in WORK(IVT), storing result in */ /* WORK(IL) and copying to A */ /* Workspace: need 3*M [e, tauq, taup] + M*M [VT] + M*NB [L] */ /* Workspace: prefer 3*M [e, tauq, taup] + M*M [VT] + M*N [L] */ i__2 = *n; i__1 = chunk; for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) { /* Computing MIN */ i__3 = *n - i__ + 1; blk = f2cmin(i__3,chunk); sgemm_("N", "N", m, &blk, m, &c_b84, &work[ivt], & ldwkvt, &a[i__ * a_dim1 + 1], lda, &c_b63, & work[il], m); slacpy_("F", m, &blk, &work[il], m, &a[i__ * a_dim1 + 1], lda); /* L40: */ } } } else if (wntqs) { /* Path 5ts (N > M, JOBZ='S') */ /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in U and computing right singular */ /* vectors of bidiagonal matrix in VT */ /* Workspace: need 3*M [e, tauq, taup] + BDSPAC */ slaset_("F", m, n, &c_b63, &c_b63, &vt[vt_offset], ldvt); sbdsdc_("L", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &vt[ vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], info); /* Overwrite U by left singular vectors of A and VT */ /* by right singular vectors of A */ /* Workspace: need 3*M [e, tauq, taup] + M [work] */ /* Workspace: prefer 3*M [e, tauq, taup] + M*NB [work] */ i__1 = *lwork - nwork + 1; sormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr); i__1 = *lwork - nwork + 1; sormbr_("P", "R", "T", m, n, m, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, & ierr); } else if (wntqa) { /* Path 5ta (N > M, JOBZ='A') */ /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in U and computing right singular */ /* vectors of bidiagonal matrix in VT */ /* Workspace: need 3*M [e, tauq, taup] + BDSPAC */ slaset_("F", n, n, &c_b63, &c_b63, &vt[vt_offset], ldvt); sbdsdc_("L", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &vt[ vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], info); /* Set the right corner of VT to identity matrix */ if (*n > *m) { i__1 = *n - *m; i__2 = *n - *m; slaset_("F", &i__1, &i__2, &c_b63, &c_b84, &vt[*m + 1 + (* m + 1) * vt_dim1], ldvt); } /* Overwrite U by left singular vectors of A and VT */ /* by right singular vectors of A */ /* Workspace: need 3*M [e, tauq, taup] + N [work] */ /* Workspace: prefer 3*M [e, tauq, taup] + N*NB [work] */ i__1 = *lwork - nwork + 1; sormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr); i__1 = *lwork - nwork + 1; sormbr_("P", "R", "T", n, n, m, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, & ierr); } } } /* Undo scaling if necessary */ if (iscl == 1) { if (anrm > bignum) { slascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], & minmn, &ierr); } if (anrm < smlnum) { slascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], & minmn, &ierr); } } /* Return optimal workspace in WORK(1) */ work[1] = (real) maxwrk; return 0; /* End of SGESDD */ } /* sgesdd_ */