#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 SGESVDX computes the singular value decomposition (SVD) for GE matrices */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SGESVDX + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SGESVDX( JOBU, JOBVT, RANGE, M, N, A, LDA, VL, VU, */ /* $ IL, IU, NS, S, U, LDU, VT, LDVT, WORK, */ /* $ LWORK, IWORK, INFO ) */ /* CHARACTER JOBU, JOBVT, RANGE */ /* INTEGER IL, INFO, IU, LDA, LDU, LDVT, LWORK, M, N, NS */ /* REAL VL, VU */ /* INTEGER IWORK( * ) */ /* REAL A( LDA, * ), S( * ), U( LDU, * ), */ /* $ VT( LDVT, * ), WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SGESVDX computes the singular value decomposition (SVD) of a real */ /* > M-by-N matrix A, optionally computing the left and/or right singular */ /* > vectors. 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. */ /* > */ /* > SGESVDX uses an eigenvalue problem for obtaining the SVD, which */ /* > allows for the computation of a subset of singular values and */ /* > vectors. See SBDSVDX for details. */ /* > */ /* > Note that the routine returns V**T, not V. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] JOBU */ /* > \verbatim */ /* > JOBU is CHARACTER*1 */ /* > Specifies options for computing all or part of the matrix U: */ /* > = 'V': the first f2cmin(m,n) columns of U (the left singular */ /* > vectors) or as specified by RANGE are returned in */ /* > the array U; */ /* > = 'N': no columns of U (no left singular vectors) are */ /* > computed. */ /* > \endverbatim */ /* > */ /* > \param[in] JOBVT */ /* > \verbatim */ /* > JOBVT is CHARACTER*1 */ /* > Specifies options for computing all or part of the matrix */ /* > V**T: */ /* > = 'V': the first f2cmin(m,n) rows of V**T (the right singular */ /* > vectors) or as specified by RANGE are returned in */ /* > the array VT; */ /* > = 'N': no rows of V**T (no right singular vectors) are */ /* > computed. */ /* > \endverbatim */ /* > */ /* > \param[in] RANGE */ /* > \verbatim */ /* > RANGE is CHARACTER*1 */ /* > = 'A': all singular values will be found. */ /* > = 'V': all singular values in the half-open interval (VL,VU] */ /* > will be found. */ /* > = 'I': the IL-th through IU-th singular values will be found. */ /* > \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, 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[in] VL */ /* > \verbatim */ /* > VL is REAL */ /* > If RANGE='V', the lower bound of the interval to */ /* > be searched for singular values. VU > VL. */ /* > Not referenced if RANGE = 'A' or 'I'. */ /* > \endverbatim */ /* > */ /* > \param[in] VU */ /* > \verbatim */ /* > VU is REAL */ /* > If RANGE='V', the upper bound of the interval to */ /* > be searched for singular values. VU > VL. */ /* > Not referenced if RANGE = 'A' or 'I'. */ /* > \endverbatim */ /* > */ /* > \param[in] IL */ /* > \verbatim */ /* > IL is INTEGER */ /* > If RANGE='I', the index of the */ /* > smallest singular value to be returned. */ /* > 1 <= IL <= IU <= f2cmin(M,N), if f2cmin(M,N) > 0. */ /* > Not referenced if RANGE = 'A' or 'V'. */ /* > \endverbatim */ /* > */ /* > \param[in] IU */ /* > \verbatim */ /* > IU is INTEGER */ /* > If RANGE='I', the index of the */ /* > largest singular value to be returned. */ /* > 1 <= IL <= IU <= f2cmin(M,N), if f2cmin(M,N) > 0. */ /* > Not referenced if RANGE = 'A' or 'V'. */ /* > \endverbatim */ /* > */ /* > \param[out] NS */ /* > \verbatim */ /* > NS is INTEGER */ /* > The total number of singular values found, */ /* > 0 <= NS <= f2cmin(M,N). */ /* > If RANGE = 'A', NS = f2cmin(M,N); if RANGE = 'I', NS = IU-IL+1. */ /* > \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) */ /* > If JOBU = 'V', U contains columns of U (the left singular */ /* > vectors, stored columnwise) as specified by RANGE; if */ /* > JOBU = 'N', U is not referenced. */ /* > Note: The user must ensure that UCOL >= NS; if RANGE = 'V', */ /* > the exact value of NS is not known in advance and an upper */ /* > bound must be used. */ /* > \endverbatim */ /* > */ /* > \param[in] LDU */ /* > \verbatim */ /* > LDU is INTEGER */ /* > The leading dimension of the array U. LDU >= 1; if */ /* > JOBU = 'V', LDU >= M. */ /* > \endverbatim */ /* > */ /* > \param[out] VT */ /* > \verbatim */ /* > VT is REAL array, dimension (LDVT,N) */ /* > If JOBVT = 'V', VT contains the rows of V**T (the right singular */ /* > vectors, stored rowwise) as specified by RANGE; if JOBVT = 'N', */ /* > VT is not referenced. */ /* > Note: The user must ensure that LDVT >= NS; if RANGE = 'V', */ /* > the exact value of NS is not known in advance and an upper */ /* > bound must be used. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVT */ /* > \verbatim */ /* > LDVT is INTEGER */ /* > The leading dimension of the array VT. LDVT >= 1; if */ /* > JOBVT = 'V', LDVT >= NS (see above). */ /* > \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 >= MAX(1,MIN(M,N)*(MIN(M,N)+4)) for the paths (see */ /* > comments inside the code): */ /* > - PATH 1 (M much larger than N) */ /* > - PATH 1t (N much larger than M) */ /* > LWORK >= MAX(1,MIN(M,N)*2+MAX(M,N)) for the other paths. */ /* > For good performance, LWORK should generally be larger. */ /* > */ /* > If LWORK = -1, then a workspace query is assumed; the routine */ /* > only calculates the optimal size of the WORK array, returns */ /* > this value as the first entry of the WORK array, and no error */ /* > message related to LWORK is issued by XERBLA. */ /* > \endverbatim */ /* > */ /* > \param[out] IWORK */ /* > \verbatim */ /* > IWORK is INTEGER array, dimension (12*MIN(M,N)) */ /* > If INFO = 0, the first NS elements of IWORK are zero. If INFO > 0, */ /* > then IWORK contains the indices of the eigenvectors that failed */ /* > to converge in SBDSVDX/SSTEVX. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit */ /* > < 0: if INFO = -i, the i-th argument had an illegal value */ /* > > 0: if INFO = i, then i eigenvectors failed to converge */ /* > in SBDSVDX/SSTEVX. */ /* > if INFO = N*2 + 1, an internal error occurred in */ /* > SBDSVDX */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date June 2016 */ /* > \ingroup realGEsing */ /* ===================================================================== */ /* Subroutine */ int sgesvdx_(char *jobu, char *jobvt, char *range, integer * m, integer *n, real *a, integer *lda, real *vl, real *vu, integer *il, integer *iu, integer *ns, real *s, real *u, integer *ldu, real *vt, integer *ldvt, real *work, integer *lwork, integer *iwork, integer * info) { /* System generated locals */ address a__1[2]; integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1[2], i__2, i__3; char ch__1[2]; /* Local variables */ integer iscl; logical alls, inds; integer ilqf; real anrm; integer ierr, iqrf, itau; char jobz[1]; logical vals; integer i__, j; extern logical lsame_(char *, char *); integer iltgk, itemp, minmn, itaup, itauq, iutgk, itgkz, mnthr; extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, integer *); logical wantu; integer id, ie; 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 *), slascl_(char *, integer *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *); real abstol; extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer *, real *, real *, integer *, integer *), slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *); char rngtgk[1]; extern /* Subroutine */ int slaset_(char *, integer *, integer *, real *, real *, real *, integer *), sormbr_(char *, char *, char * , integer *, integer *, integer *, real *, integer *, real *, real *, integer *, real *, integer *, integer *); integer minwrk, maxwrk; real smlnum; extern /* Subroutine */ int sormlq_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, real *, integer *, real *, integer *, integer *); logical lquery, wantvt; extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, real *, integer *, real *, integer *, integer *); real dum[1], eps; extern /* Subroutine */ int sbdsvdx_(char *, char *, char *, integer *, real *, real *, real *, real *, integer *, integer *, integer *, real *, real *, integer *, real *, integer *, integer *); /* -- LAPACK driver routine (version 3.8.0) -- */ /* -- 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 */ *ns = 0; *info = 0; abstol = slamch_("S") * 2; lquery = *lwork == -1; minmn = f2cmin(*m,*n); wantu = lsame_(jobu, "V"); wantvt = lsame_(jobvt, "V"); if (wantu || wantvt) { *(unsigned char *)jobz = 'V'; } else { *(unsigned char *)jobz = 'N'; } alls = lsame_(range, "A"); vals = lsame_(range, "V"); inds = lsame_(range, "I"); *info = 0; if (! lsame_(jobu, "V") && ! lsame_(jobu, "N")) { *info = -1; } else if (! lsame_(jobvt, "V") && ! lsame_(jobvt, "N")) { *info = -2; } else if (! (alls || vals || inds)) { *info = -3; } else if (*m < 0) { *info = -4; } else if (*n < 0) { *info = -5; } else if (*m > *lda) { *info = -7; } else if (minmn > 0) { if (vals) { if (*vl < 0.f) { *info = -8; } else if (*vu <= *vl) { *info = -9; } } else if (inds) { if (*il < 1 || *il > f2cmax(1,minmn)) { *info = -10; } else if (*iu < f2cmin(minmn,*il) || *iu > minmn) { *info = -11; } } if (*info == 0) { if (wantu && *ldu < *m) { *info = -15; } else if (wantvt) { if (inds) { if (*ldvt < *iu - *il + 1) { *info = -17; } } else if (*ldvt < minmn) { *info = -17; } } } } /* 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; if (minmn > 0) { if (*m >= *n) { /* Writing concatenation */ i__1[0] = 1, a__1[0] = jobu; i__1[1] = 1, a__1[1] = jobvt; s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); mnthr = ilaenv_(&c__6, "SGESVD", ch__1, m, n, &c__0, &c__0, ( ftnlen)6, (ftnlen)2); if (*m >= mnthr) { /* Path 1 (M much larger than N) */ maxwrk = *n + *n * ilaenv_(&c__1, "SGEQRF", " ", m, n, & c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__2 = maxwrk, i__3 = *n * (*n + 5) + (*n << 1) * ilaenv_( &c__1, "SGEBRD", " ", n, n, &c_n1, &c_n1, (ftnlen) 6, (ftnlen)1); maxwrk = f2cmax(i__2,i__3); if (wantu) { /* Computing MAX */ i__2 = maxwrk, i__3 = *n * (*n * 3 + 6) + *n * ilaenv_(&c__1, "SORMQR", " ", n, n, &c_n1, & c_n1, (ftnlen)6, (ftnlen)1); maxwrk = f2cmax(i__2,i__3); } if (wantvt) { /* Computing MAX */ i__2 = maxwrk, i__3 = *n * (*n * 3 + 6) + *n * ilaenv_(&c__1, "SORMLQ", " ", n, n, &c_n1, & c_n1, (ftnlen)6, (ftnlen)1); maxwrk = f2cmax(i__2,i__3); } minwrk = *n * (*n * 3 + 20); } else { /* Path 2 (M at least N, but not much larger) */ maxwrk = (*n << 2) + (*m + *n) * ilaenv_(&c__1, "SGEBRD", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); if (wantu) { /* Computing MAX */ i__2 = maxwrk, i__3 = *n * ((*n << 1) + 5) + *n * ilaenv_(&c__1, "SORMQR", " ", n, n, &c_n1, & c_n1, (ftnlen)6, (ftnlen)1); maxwrk = f2cmax(i__2,i__3); } if (wantvt) { /* Computing MAX */ i__2 = maxwrk, i__3 = *n * ((*n << 1) + 5) + *n * ilaenv_(&c__1, "SORMLQ", " ", n, n, &c_n1, & c_n1, (ftnlen)6, (ftnlen)1); maxwrk = f2cmax(i__2,i__3); } /* Computing MAX */ i__2 = *n * ((*n << 1) + 19), i__3 = (*n << 2) + *m; minwrk = f2cmax(i__2,i__3); } } else { /* Writing concatenation */ i__1[0] = 1, a__1[0] = jobu; i__1[1] = 1, a__1[1] = jobvt; s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); mnthr = ilaenv_(&c__6, "SGESVD", ch__1, m, n, &c__0, &c__0, ( ftnlen)6, (ftnlen)2); if (*n >= mnthr) { /* Path 1t (N much larger than M) */ maxwrk = *m + *m * ilaenv_(&c__1, "SGELQF", " ", m, n, & c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__2 = maxwrk, i__3 = *m * (*m + 5) + (*m << 1) * ilaenv_( &c__1, "SGEBRD", " ", m, m, &c_n1, &c_n1, (ftnlen) 6, (ftnlen)1); maxwrk = f2cmax(i__2,i__3); if (wantu) { /* Computing MAX */ i__2 = maxwrk, i__3 = *m * (*m * 3 + 6) + *m * ilaenv_(&c__1, "SORMQR", " ", m, m, &c_n1, & c_n1, (ftnlen)6, (ftnlen)1); maxwrk = f2cmax(i__2,i__3); } if (wantvt) { /* Computing MAX */ i__2 = maxwrk, i__3 = *m * (*m * 3 + 6) + *m * ilaenv_(&c__1, "SORMLQ", " ", m, m, &c_n1, & c_n1, (ftnlen)6, (ftnlen)1); maxwrk = f2cmax(i__2,i__3); } minwrk = *m * (*m * 3 + 20); } else { /* Path 2t (N at least M, but not much larger) */ maxwrk = (*m << 2) + (*m + *n) * ilaenv_(&c__1, "SGEBRD", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); if (wantu) { /* Computing MAX */ i__2 = maxwrk, i__3 = *m * ((*m << 1) + 5) + *m * ilaenv_(&c__1, "SORMQR", " ", m, m, &c_n1, & c_n1, (ftnlen)6, (ftnlen)1); maxwrk = f2cmax(i__2,i__3); } if (wantvt) { /* Computing MAX */ i__2 = maxwrk, i__3 = *m * ((*m << 1) + 5) + *m * ilaenv_(&c__1, "SORMLQ", " ", m, m, &c_n1, & c_n1, (ftnlen)6, (ftnlen)1); maxwrk = f2cmax(i__2,i__3); } /* Computing MAX */ i__2 = *m * ((*m << 1) + 19), i__3 = (*m << 2) + *n; minwrk = f2cmax(i__2,i__3); } } } maxwrk = f2cmax(maxwrk,minwrk); work[1] = (real) maxwrk; if (*lwork < minwrk && ! lquery) { *info = -19; } } if (*info != 0) { i__2 = -(*info); xerbla_("SGESVDX", &i__2, (ftnlen)7); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { return 0; } /* Set singular values indices accord to RANGE. */ if (alls) { *(unsigned char *)rngtgk = 'I'; iltgk = 1; iutgk = f2cmin(*m,*n); } else if (inds) { *(unsigned char *)rngtgk = 'I'; iltgk = *il; iutgk = *iu; } else { *(unsigned char *)rngtgk = 'V'; iltgk = 0; iutgk = 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); iscl = 0; if (anrm > 0.f && anrm < smlnum) { iscl = 1; slascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, info); } else if (anrm > bignum) { iscl = 1; slascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, info); } if (*m >= *n) { /* A has at least as many rows as columns. If A has sufficiently */ /* more rows than columns, first reduce A using the QR */ /* decomposition. */ if (*m >= mnthr) { /* Path 1 (M much larger than N): */ /* A = Q * R = Q * ( QB * B * PB**T ) */ /* = Q * ( QB * ( UB * S * VB**T ) * PB**T ) */ /* U = Q * QB * UB; V**T = VB**T * PB**T */ /* Compute A=Q*R */ /* (Workspace: need 2*N, prefer N+N*NB) */ itau = 1; itemp = itau + *n; i__2 = *lwork - itemp + 1; sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[itemp], &i__2, info); /* Copy R into WORK and bidiagonalize it: */ /* (Workspace: need N*N+5*N, prefer N*N+4*N+2*N*NB) */ iqrf = itemp; id = iqrf + *n * *n; ie = id + *n; itauq = ie + *n; itaup = itauq + *n; itemp = itaup + *n; slacpy_("U", n, n, &a[a_offset], lda, &work[iqrf], n); i__2 = *n - 1; i__3 = *n - 1; slaset_("L", &i__2, &i__3, &c_b109, &c_b109, &work[iqrf + 1], n); i__2 = *lwork - itemp + 1; sgebrd_(n, n, &work[iqrf], n, &work[id], &work[ie], &work[itauq], &work[itaup], &work[itemp], &i__2, info); /* Solve eigenvalue problem TGK*Z=Z*S. */ /* (Workspace: need 14*N + 2*N*(N+1)) */ itgkz = itemp; itemp = itgkz + *n * ((*n << 1) + 1); i__2 = *n << 1; sbdsvdx_("U", jobz, rngtgk, n, &work[id], &work[ie], vl, vu, & iltgk, &iutgk, ns, &s[1], &work[itgkz], &i__2, &work[ itemp], &iwork[1], info); /* If needed, compute left singular vectors. */ if (wantu) { j = itgkz; i__2 = *ns; for (i__ = 1; i__ <= i__2; ++i__) { scopy_(n, &work[j], &c__1, &u[i__ * u_dim1 + 1], &c__1); j += *n << 1; } i__2 = *m - *n; slaset_("A", &i__2, ns, &c_b109, &c_b109, &u[*n + 1 + u_dim1], ldu); /* Call SORMBR to compute QB*UB. */ /* (Workspace in WORK( ITEMP ): need N, prefer N*NB) */ i__2 = *lwork - itemp + 1; sormbr_("Q", "L", "N", n, ns, n, &work[iqrf], n, &work[itauq], &u[u_offset], ldu, &work[itemp], &i__2, info); /* Call SORMQR to compute Q*(QB*UB). */ /* (Workspace in WORK( ITEMP ): need N, prefer N*NB) */ i__2 = *lwork - itemp + 1; sormqr_("L", "N", m, ns, n, &a[a_offset], lda, &work[itau], & u[u_offset], ldu, &work[itemp], &i__2, info); } /* If needed, compute right singular vectors. */ if (wantvt) { j = itgkz + *n; i__2 = *ns; for (i__ = 1; i__ <= i__2; ++i__) { scopy_(n, &work[j], &c__1, &vt[i__ + vt_dim1], ldvt); j += *n << 1; } /* Call SORMBR to compute VB**T * PB**T */ /* (Workspace in WORK( ITEMP ): need N, prefer N*NB) */ i__2 = *lwork - itemp + 1; sormbr_("P", "R", "T", ns, n, n, &work[iqrf], n, &work[itaup], &vt[vt_offset], ldvt, &work[itemp], &i__2, info); } } else { /* Path 2 (M at least N, but not much larger) */ /* Reduce A to bidiagonal form without QR decomposition */ /* A = QB * B * PB**T = QB * ( UB * S * VB**T ) * PB**T */ /* U = QB * UB; V**T = VB**T * PB**T */ /* Bidiagonalize A */ /* (Workspace: need 4*N+M, prefer 4*N+(M+N)*NB) */ id = 1; ie = id + *n; itauq = ie + *n; itaup = itauq + *n; itemp = itaup + *n; i__2 = *lwork - itemp + 1; sgebrd_(m, n, &a[a_offset], lda, &work[id], &work[ie], &work[ itauq], &work[itaup], &work[itemp], &i__2, info); /* Solve eigenvalue problem TGK*Z=Z*S. */ /* (Workspace: need 14*N + 2*N*(N+1)) */ itgkz = itemp; itemp = itgkz + *n * ((*n << 1) + 1); i__2 = *n << 1; sbdsvdx_("U", jobz, rngtgk, n, &work[id], &work[ie], vl, vu, & iltgk, &iutgk, ns, &s[1], &work[itgkz], &i__2, &work[ itemp], &iwork[1], info); /* If needed, compute left singular vectors. */ if (wantu) { j = itgkz; i__2 = *ns; for (i__ = 1; i__ <= i__2; ++i__) { scopy_(n, &work[j], &c__1, &u[i__ * u_dim1 + 1], &c__1); j += *n << 1; } i__2 = *m - *n; slaset_("A", &i__2, ns, &c_b109, &c_b109, &u[*n + 1 + u_dim1], ldu); /* Call SORMBR to compute QB*UB. */ /* (Workspace in WORK( ITEMP ): need N, prefer N*NB) */ i__2 = *lwork - itemp + 1; sormbr_("Q", "L", "N", m, ns, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[itemp], &i__2, &ierr); } /* If needed, compute right singular vectors. */ if (wantvt) { j = itgkz + *n; i__2 = *ns; for (i__ = 1; i__ <= i__2; ++i__) { scopy_(n, &work[j], &c__1, &vt[i__ + vt_dim1], ldvt); j += *n << 1; } /* Call SORMBR to compute VB**T * PB**T */ /* (Workspace in WORK( ITEMP ): need N, prefer N*NB) */ i__2 = *lwork - itemp + 1; sormbr_("P", "R", "T", ns, n, n, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[itemp], &i__2, & ierr); } } } else { /* A has more columns than rows. If A has sufficiently more */ /* columns than rows, first reduce A using the LQ decomposition. */ if (*n >= mnthr) { /* Path 1t (N much larger than M): */ /* A = L * Q = ( QB * B * PB**T ) * Q */ /* = ( QB * ( UB * S * VB**T ) * PB**T ) * Q */ /* U = QB * UB ; V**T = VB**T * PB**T * Q */ /* Compute A=L*Q */ /* (Workspace: need 2*M, prefer M+M*NB) */ itau = 1; itemp = itau + *m; i__2 = *lwork - itemp + 1; sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[itemp], &i__2, info); /* Copy L into WORK and bidiagonalize it: */ /* (Workspace in WORK( ITEMP ): need M*M+5*N, prefer M*M+4*M+2*M*NB) */ ilqf = itemp; id = ilqf + *m * *m; ie = id + *m; itauq = ie + *m; itaup = itauq + *m; itemp = itaup + *m; slacpy_("L", m, m, &a[a_offset], lda, &work[ilqf], m); i__2 = *m - 1; i__3 = *m - 1; slaset_("U", &i__2, &i__3, &c_b109, &c_b109, &work[ilqf + *m], m); i__2 = *lwork - itemp + 1; sgebrd_(m, m, &work[ilqf], m, &work[id], &work[ie], &work[itauq], &work[itaup], &work[itemp], &i__2, info); /* Solve eigenvalue problem TGK*Z=Z*S. */ /* (Workspace: need 2*M*M+14*M) */ itgkz = itemp; itemp = itgkz + *m * ((*m << 1) + 1); i__2 = *m << 1; sbdsvdx_("U", jobz, rngtgk, m, &work[id], &work[ie], vl, vu, & iltgk, &iutgk, ns, &s[1], &work[itgkz], &i__2, &work[ itemp], &iwork[1], info); /* If needed, compute left singular vectors. */ if (wantu) { j = itgkz; i__2 = *ns; for (i__ = 1; i__ <= i__2; ++i__) { scopy_(m, &work[j], &c__1, &u[i__ * u_dim1 + 1], &c__1); j += *m << 1; } /* Call SORMBR to compute QB*UB. */ /* (Workspace in WORK( ITEMP ): need M, prefer M*NB) */ i__2 = *lwork - itemp + 1; sormbr_("Q", "L", "N", m, ns, m, &work[ilqf], m, &work[itauq], &u[u_offset], ldu, &work[itemp], &i__2, info); } /* If needed, compute right singular vectors. */ if (wantvt) { j = itgkz + *m; i__2 = *ns; for (i__ = 1; i__ <= i__2; ++i__) { scopy_(m, &work[j], &c__1, &vt[i__ + vt_dim1], ldvt); j += *m << 1; } i__2 = *n - *m; slaset_("A", ns, &i__2, &c_b109, &c_b109, &vt[(*m + 1) * vt_dim1 + 1], ldvt); /* Call SORMBR to compute (VB**T)*(PB**T) */ /* (Workspace in WORK( ITEMP ): need M, prefer M*NB) */ i__2 = *lwork - itemp + 1; sormbr_("P", "R", "T", ns, m, m, &work[ilqf], m, &work[itaup], &vt[vt_offset], ldvt, &work[itemp], &i__2, info); /* Call SORMLQ to compute ((VB**T)*(PB**T))*Q. */ /* (Workspace in WORK( ITEMP ): need M, prefer M*NB) */ i__2 = *lwork - itemp + 1; sormlq_("R", "N", ns, n, m, &a[a_offset], lda, &work[itau], & vt[vt_offset], ldvt, &work[itemp], &i__2, info); } } else { /* Path 2t (N greater than M, but not much larger) */ /* Reduce to bidiagonal form without LQ decomposition */ /* A = QB * B * PB**T = QB * ( UB * S * VB**T ) * PB**T */ /* U = QB * UB; V**T = VB**T * PB**T */ /* Bidiagonalize A */ /* (Workspace: need 4*M+N, prefer 4*M+(M+N)*NB) */ id = 1; ie = id + *m; itauq = ie + *m; itaup = itauq + *m; itemp = itaup + *m; i__2 = *lwork - itemp + 1; sgebrd_(m, n, &a[a_offset], lda, &work[id], &work[ie], &work[ itauq], &work[itaup], &work[itemp], &i__2, info); /* Solve eigenvalue problem TGK*Z=Z*S. */ /* (Workspace: need 2*M*M+14*M) */ itgkz = itemp; itemp = itgkz + *m * ((*m << 1) + 1); i__2 = *m << 1; sbdsvdx_("L", jobz, rngtgk, m, &work[id], &work[ie], vl, vu, & iltgk, &iutgk, ns, &s[1], &work[itgkz], &i__2, &work[ itemp], &iwork[1], info); /* If needed, compute left singular vectors. */ if (wantu) { j = itgkz; i__2 = *ns; for (i__ = 1; i__ <= i__2; ++i__) { scopy_(m, &work[j], &c__1, &u[i__ * u_dim1 + 1], &c__1); j += *m << 1; } /* Call SORMBR to compute QB*UB. */ /* (Workspace in WORK( ITEMP ): need M, prefer M*NB) */ i__2 = *lwork - itemp + 1; sormbr_("Q", "L", "N", m, ns, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[itemp], &i__2, info); } /* If needed, compute right singular vectors. */ if (wantvt) { j = itgkz + *m; i__2 = *ns; for (i__ = 1; i__ <= i__2; ++i__) { scopy_(m, &work[j], &c__1, &vt[i__ + vt_dim1], ldvt); j += *m << 1; } i__2 = *n - *m; slaset_("A", ns, &i__2, &c_b109, &c_b109, &vt[(*m + 1) * vt_dim1 + 1], ldvt); /* Call SORMBR to compute VB**T * PB**T */ /* (Workspace in WORK( ITEMP ): need M, prefer M*NB) */ i__2 = *lwork - itemp + 1; sormbr_("P", "R", "T", ns, n, m, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[itemp], &i__2, info); } } } /* Undo scaling if necessary */ if (iscl == 1) { if (anrm > bignum) { slascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], & minmn, info); } if (anrm < smlnum) { slascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], & minmn, info); } } /* Return optimal workspace in WORK(1) */ work[1] = (real) maxwrk; return 0; /* End of SGESVDX */ } /* sgesvdx_ */