#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 ZGESDD */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download ZGESDD + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE ZGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, */ /* WORK, LWORK, RWORK, IWORK, INFO ) */ /* CHARACTER JOBZ */ /* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N */ /* INTEGER IWORK( * ) */ /* DOUBLE PRECISION RWORK( * ), S( * ) */ /* COMPLEX*16 A( LDA, * ), U( LDU, * ), VT( LDVT, * ), */ /* $ WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZGESDD computes the singular value decomposition (SVD) of a complex */ /* > M-by-N matrix A, optionally computing the left and/or right singular */ /* > vectors, by using divide-and-conquer method. The SVD is written */ /* > */ /* > A = U * SIGMA * conjugate-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 unitary matrix, and */ /* > V is an N-by-N unitary 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**H, 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**H 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**H are returned in the arrays U */ /* > and VT; */ /* > = 'O': If M >= N, the first N columns of U are overwritten */ /* > in the array A and all rows of V**H are returned in */ /* > the array VT; */ /* > otherwise, all columns of U are returned in the */ /* > array U and the first M rows of V**H are overwritten */ /* > in the array A; */ /* > = 'N': no columns of U or rows of V**H 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 COMPLEX*16 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**H (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 DOUBLE PRECISION 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 COMPLEX*16 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 */ /* > unitary 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 COMPLEX*16 array, dimension (LDVT,N) */ /* > If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the */ /* > N-by-N unitary matrix V**H; */ /* > if JOBZ = 'S', VT contains the first f2cmin(M,N) rows of */ /* > V**H (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 COMPLEX*16 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 >= 2*mn + mx. */ /* > If JOBZ = 'O', LWORK >= 2*mn*mn + 2*mn + mx. */ /* > If JOBZ = 'S', LWORK >= mn*mn + 3*mn. */ /* > If JOBZ = 'A', LWORK >= mn*mn + 2*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] RWORK */ /* > \verbatim */ /* > RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) */ /* > Let mx = f2cmax(M,N) and mn = f2cmin(M,N). */ /* > If JOBZ = 'N', LRWORK >= 5*mn (LAPACK <= 3.6 needs 7*mn); */ /* > else if mx >> mn, LRWORK >= 5*mn*mn + 5*mn; */ /* > else LRWORK >= f2cmax( 5*mn*mn + 5*mn, */ /* > 2*mx*mn + 2*mn*mn + mn ). */ /* > \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: The updating process of DBDSDC did not converge. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date June 2016 */ /* > \ingroup complex16GEsing */ /* > \par Contributors: */ /* ================== */ /* > */ /* > Ming Gu and Huan Ren, Computer Science Division, University of */ /* > California at Berkeley, USA */ /* > */ /* ===================================================================== */ /* Subroutine */ int zgesdd_(char *jobz, integer *m, integer *n, doublecomplex *a, integer *lda, doublereal *s, doublecomplex *u, integer *ldu, doublecomplex *vt, integer *ldvt, doublecomplex *work, integer *lwork, doublereal *rwork, 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_zgebrd_mm__, lwork_zgebrd_mn__, lwork_zgebrd_nn__, lwork_zgelqf_mn__, lwork_zgeqrf_mn__; doublecomplex cdum[1]; integer iscl; doublereal anrm; integer idum[1], ierr, itau, lwork_zunglq_mn__, lwork_zunglq_nn__, lwork_zungqr_mm__, lwork_zungqr_mn__, irvt, lwork_zunmbr_prc_mm__, lwork_zunmbr_prc_mn__, lwork_zunmbr_prc_nn__, lwork_zunmbr_qln_mm__, lwork_zunmbr_qln_mn__, lwork_zunmbr_qln_nn__, i__; extern logical lsame_(char *, char *); integer chunk, minmn; extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *); integer wrkbl, itaup, itauq; logical wntqa; integer nwork; logical wntqn, wntqo, wntqs; extern /* Subroutine */ int zlacp2_(char *, integer *, integer *, doublereal *, integer *, doublecomplex *, integer *); integer mnthr1, mnthr2, ie; extern /* Subroutine */ int dbdsdc_(char *, char *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, integer *); integer il; extern doublereal dlamch_(char *); integer ir, iu; extern /* Subroutine */ int dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *); integer lwork_zungbr_p_mn__, lwork_zungbr_p_nn__, lwork_zungbr_q_mn__, lwork_zungbr_q_mm__; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); doublereal bignum; extern /* Subroutine */ int zgebrd_(integer *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, integer *); extern logical disnan_(doublereal *); extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *); extern /* Subroutine */ int zgelqf_(integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer * ), zlacrm_(integer *, integer *, doublecomplex *, integer *, doublereal *, integer *, doublecomplex *, integer *, doublereal *) , zlarcm_(integer *, integer *, doublereal *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *), zlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublecomplex *, integer *, integer *), zgeqrf_(integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer * ); integer ldwrkl; extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zlaset_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *); integer ldwrkr, minwrk, ldwrku, maxwrk; extern /* Subroutine */ int zungbr_(char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *); integer ldwkvt; doublereal smlnum; logical wntqas; extern /* Subroutine */ int zunmbr_(char *, char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, integer * ), zunglq_(integer *, integer *, integer * , doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *); logical lquery; integer nrwork; extern /* Subroutine */ int zungqr_(integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *); integer blk; doublereal dum[1], eps; integer iru, ivt; /* -- 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; --rwork; --iwork; /* Function Body */ *info = 0; minmn = f2cmin(*m,*n); mnthr1 = (integer) (minmn * 17. / 9.); mnthr2 = (integer) (minmn * 5. / 3.); wntqa = lsame_(jobz, "A"); wntqs = lsame_(jobz, "S"); wntqas = wntqa || wntqs; wntqo = lsame_(jobz, "O"); wntqn = lsame_(jobz, "N"); lquery = *lwork == -1; minwrk = 1; maxwrk = 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. */ /* CWorkspace refers to complex workspace, and RWorkspace to */ /* real workspace. NB refers to the optimal block size for the */ /* immediately following subroutine, as returned by ILAENV.) */ if (*info == 0) { minwrk = 1; maxwrk = 1; if (*m >= *n && minmn > 0) { /* There is no complex work space needed for bidiagonal SVD */ /* The real work space needed for bidiagonal SVD (dbdsdc) is */ /* BDSPAC = 3*N*N + 4*N for singular values and vectors; */ /* BDSPAC = 4*N for singular values only; */ /* not including e, RU, and RVT matrices. */ /* Compute space preferred for each routine */ zgebrd_(m, n, cdum, m, dum, dum, cdum, cdum, cdum, &c_n1, &ierr); lwork_zgebrd_mn__ = (integer) cdum[0].r; zgebrd_(n, n, cdum, n, dum, dum, cdum, cdum, cdum, &c_n1, &ierr); lwork_zgebrd_nn__ = (integer) cdum[0].r; zgeqrf_(m, n, cdum, m, cdum, cdum, &c_n1, &ierr); lwork_zgeqrf_mn__ = (integer) cdum[0].r; zungbr_("P", n, n, n, cdum, n, cdum, cdum, &c_n1, &ierr); lwork_zungbr_p_nn__ = (integer) cdum[0].r; zungbr_("Q", m, m, n, cdum, m, cdum, cdum, &c_n1, &ierr); lwork_zungbr_q_mm__ = (integer) cdum[0].r; zungbr_("Q", m, n, n, cdum, m, cdum, cdum, &c_n1, &ierr); lwork_zungbr_q_mn__ = (integer) cdum[0].r; zungqr_(m, m, n, cdum, m, cdum, cdum, &c_n1, &ierr); lwork_zungqr_mm__ = (integer) cdum[0].r; zungqr_(m, n, n, cdum, m, cdum, cdum, &c_n1, &ierr); lwork_zungqr_mn__ = (integer) cdum[0].r; zunmbr_("P", "R", "C", n, n, n, cdum, n, cdum, cdum, n, cdum, & c_n1, &ierr); lwork_zunmbr_prc_nn__ = (integer) cdum[0].r; zunmbr_("Q", "L", "N", m, m, n, cdum, m, cdum, cdum, m, cdum, & c_n1, &ierr); lwork_zunmbr_qln_mm__ = (integer) cdum[0].r; zunmbr_("Q", "L", "N", m, n, n, cdum, m, cdum, cdum, m, cdum, & c_n1, &ierr); lwork_zunmbr_qln_mn__ = (integer) cdum[0].r; zunmbr_("Q", "L", "N", n, n, n, cdum, n, cdum, cdum, n, cdum, & c_n1, &ierr); lwork_zunmbr_qln_nn__ = (integer) cdum[0].r; if (*m >= mnthr1) { if (wntqn) { /* Path 1 (M >> N, JOBZ='N') */ maxwrk = *n + lwork_zgeqrf_mn__; /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + lwork_zgebrd_nn__; maxwrk = f2cmax(i__1,i__2); minwrk = *n * 3; } else if (wntqo) { /* Path 2 (M >> N, JOBZ='O') */ wrkbl = *n + lwork_zgeqrf_mn__; /* Computing MAX */ i__1 = wrkbl, i__2 = *n + lwork_zungqr_mn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*n << 1) + lwork_zgebrd_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*n << 1) + lwork_zunmbr_qln_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*n << 1) + lwork_zunmbr_prc_nn__; wrkbl = f2cmax(i__1,i__2); maxwrk = *m * *n + *n * *n + wrkbl; minwrk = (*n << 1) * *n + *n * 3; } else if (wntqs) { /* Path 3 (M >> N, JOBZ='S') */ wrkbl = *n + lwork_zgeqrf_mn__; /* Computing MAX */ i__1 = wrkbl, i__2 = *n + lwork_zungqr_mn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*n << 1) + lwork_zgebrd_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*n << 1) + lwork_zunmbr_qln_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*n << 1) + lwork_zunmbr_prc_nn__; wrkbl = f2cmax(i__1,i__2); maxwrk = *n * *n + wrkbl; minwrk = *n * *n + *n * 3; } else if (wntqa) { /* Path 4 (M >> N, JOBZ='A') */ wrkbl = *n + lwork_zgeqrf_mn__; /* Computing MAX */ i__1 = wrkbl, i__2 = *n + lwork_zungqr_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*n << 1) + lwork_zgebrd_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*n << 1) + lwork_zunmbr_qln_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*n << 1) + lwork_zunmbr_prc_nn__; wrkbl = f2cmax(i__1,i__2); maxwrk = *n * *n + wrkbl; /* Computing MAX */ i__1 = *n * 3, i__2 = *n + *m; minwrk = *n * *n + f2cmax(i__1,i__2); } } else if (*m >= mnthr2) { /* Path 5 (M >> N, but not as much as MNTHR1) */ maxwrk = (*n << 1) + lwork_zgebrd_mn__; minwrk = (*n << 1) + *m; if (wntqo) { /* Path 5o (M >> N, JOBZ='O') */ /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + lwork_zungbr_p_nn__; maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + lwork_zungbr_q_mn__; maxwrk = f2cmax(i__1,i__2); maxwrk += *m * *n; minwrk += *n * *n; } else if (wntqs) { /* Path 5s (M >> N, JOBZ='S') */ /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + lwork_zungbr_p_nn__; maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + lwork_zungbr_q_mn__; maxwrk = f2cmax(i__1,i__2); } else if (wntqa) { /* Path 5a (M >> N, JOBZ='A') */ /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + lwork_zungbr_p_nn__; maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + lwork_zungbr_q_mm__; maxwrk = f2cmax(i__1,i__2); } } else { /* Path 6 (M >= N, but not much larger) */ maxwrk = (*n << 1) + lwork_zgebrd_mn__; minwrk = (*n << 1) + *m; if (wntqo) { /* Path 6o (M >= N, JOBZ='O') */ /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + lwork_zunmbr_prc_nn__; maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + lwork_zunmbr_qln_mn__; maxwrk = f2cmax(i__1,i__2); maxwrk += *m * *n; minwrk += *n * *n; } else if (wntqs) { /* Path 6s (M >= N, JOBZ='S') */ /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + lwork_zunmbr_qln_mn__; maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + lwork_zunmbr_prc_nn__; maxwrk = f2cmax(i__1,i__2); } else if (wntqa) { /* Path 6a (M >= N, JOBZ='A') */ /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + lwork_zunmbr_qln_mm__; maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + lwork_zunmbr_prc_nn__; maxwrk = f2cmax(i__1,i__2); } } } else if (minmn > 0) { /* There is no complex work space needed for bidiagonal SVD */ /* The real work space needed for bidiagonal SVD (dbdsdc) is */ /* BDSPAC = 3*M*M + 4*M for singular values and vectors; */ /* BDSPAC = 4*M for singular values only; */ /* not including e, RU, and RVT matrices. */ /* Compute space preferred for each routine */ zgebrd_(m, n, cdum, m, dum, dum, cdum, cdum, cdum, &c_n1, &ierr); lwork_zgebrd_mn__ = (integer) cdum[0].r; zgebrd_(m, m, cdum, m, dum, dum, cdum, cdum, cdum, &c_n1, &ierr); lwork_zgebrd_mm__ = (integer) cdum[0].r; zgelqf_(m, n, cdum, m, cdum, cdum, &c_n1, &ierr); lwork_zgelqf_mn__ = (integer) cdum[0].r; zungbr_("P", m, n, m, cdum, m, cdum, cdum, &c_n1, &ierr); lwork_zungbr_p_mn__ = (integer) cdum[0].r; zungbr_("P", n, n, m, cdum, n, cdum, cdum, &c_n1, &ierr); lwork_zungbr_p_nn__ = (integer) cdum[0].r; zungbr_("Q", m, m, n, cdum, m, cdum, cdum, &c_n1, &ierr); lwork_zungbr_q_mm__ = (integer) cdum[0].r; zunglq_(m, n, m, cdum, m, cdum, cdum, &c_n1, &ierr); lwork_zunglq_mn__ = (integer) cdum[0].r; zunglq_(n, n, m, cdum, n, cdum, cdum, &c_n1, &ierr); lwork_zunglq_nn__ = (integer) cdum[0].r; zunmbr_("P", "R", "C", m, m, m, cdum, m, cdum, cdum, m, cdum, & c_n1, &ierr); lwork_zunmbr_prc_mm__ = (integer) cdum[0].r; zunmbr_("P", "R", "C", m, n, m, cdum, m, cdum, cdum, m, cdum, & c_n1, &ierr); lwork_zunmbr_prc_mn__ = (integer) cdum[0].r; zunmbr_("P", "R", "C", n, n, m, cdum, n, cdum, cdum, n, cdum, & c_n1, &ierr); lwork_zunmbr_prc_nn__ = (integer) cdum[0].r; zunmbr_("Q", "L", "N", m, m, m, cdum, m, cdum, cdum, m, cdum, & c_n1, &ierr); lwork_zunmbr_qln_mm__ = (integer) cdum[0].r; if (*n >= mnthr1) { if (wntqn) { /* Path 1t (N >> M, JOBZ='N') */ maxwrk = *m + lwork_zgelqf_mn__; /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + lwork_zgebrd_mm__; maxwrk = f2cmax(i__1,i__2); minwrk = *m * 3; } else if (wntqo) { /* Path 2t (N >> M, JOBZ='O') */ wrkbl = *m + lwork_zgelqf_mn__; /* Computing MAX */ i__1 = wrkbl, i__2 = *m + lwork_zunglq_mn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*m << 1) + lwork_zgebrd_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*m << 1) + lwork_zunmbr_qln_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*m << 1) + lwork_zunmbr_prc_mm__; wrkbl = f2cmax(i__1,i__2); maxwrk = *m * *n + *m * *m + wrkbl; minwrk = (*m << 1) * *m + *m * 3; } else if (wntqs) { /* Path 3t (N >> M, JOBZ='S') */ wrkbl = *m + lwork_zgelqf_mn__; /* Computing MAX */ i__1 = wrkbl, i__2 = *m + lwork_zunglq_mn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*m << 1) + lwork_zgebrd_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*m << 1) + lwork_zunmbr_qln_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*m << 1) + lwork_zunmbr_prc_mm__; wrkbl = f2cmax(i__1,i__2); maxwrk = *m * *m + wrkbl; minwrk = *m * *m + *m * 3; } else if (wntqa) { /* Path 4t (N >> M, JOBZ='A') */ wrkbl = *m + lwork_zgelqf_mn__; /* Computing MAX */ i__1 = wrkbl, i__2 = *m + lwork_zunglq_nn__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*m << 1) + lwork_zgebrd_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*m << 1) + lwork_zunmbr_qln_mm__; wrkbl = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*m << 1) + lwork_zunmbr_prc_mm__; wrkbl = f2cmax(i__1,i__2); maxwrk = *m * *m + wrkbl; /* Computing MAX */ i__1 = *m * 3, i__2 = *m + *n; minwrk = *m * *m + f2cmax(i__1,i__2); } } else if (*n >= mnthr2) { /* Path 5t (N >> M, but not as much as MNTHR1) */ maxwrk = (*m << 1) + lwork_zgebrd_mn__; minwrk = (*m << 1) + *n; if (wntqo) { /* Path 5to (N >> M, JOBZ='O') */ /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + lwork_zungbr_q_mm__; maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + lwork_zungbr_p_mn__; maxwrk = f2cmax(i__1,i__2); maxwrk += *m * *n; minwrk += *m * *m; } else if (wntqs) { /* Path 5ts (N >> M, JOBZ='S') */ /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + lwork_zungbr_q_mm__; maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + lwork_zungbr_p_mn__; maxwrk = f2cmax(i__1,i__2); } else if (wntqa) { /* Path 5ta (N >> M, JOBZ='A') */ /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + lwork_zungbr_q_mm__; maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + lwork_zungbr_p_nn__; maxwrk = f2cmax(i__1,i__2); } } else { /* Path 6t (N > M, but not much larger) */ maxwrk = (*m << 1) + lwork_zgebrd_mn__; minwrk = (*m << 1) + *n; if (wntqo) { /* Path 6to (N > M, JOBZ='O') */ /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + lwork_zunmbr_qln_mm__; maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + lwork_zunmbr_prc_mn__; maxwrk = f2cmax(i__1,i__2); maxwrk += *m * *n; minwrk += *m * *m; } else if (wntqs) { /* Path 6ts (N > M, JOBZ='S') */ /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + lwork_zunmbr_qln_mm__; maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + lwork_zunmbr_prc_mn__; maxwrk = f2cmax(i__1,i__2); } else if (wntqa) { /* Path 6ta (N > M, JOBZ='A') */ /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + lwork_zunmbr_qln_mm__; maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + lwork_zunmbr_prc_nn__; maxwrk = f2cmax(i__1,i__2); } } } maxwrk = f2cmax(maxwrk,minwrk); } if (*info == 0) { work[1].r = (doublereal) maxwrk, work[1].i = 0.; if (*lwork < minwrk && ! lquery) { *info = -12; } } if (*info != 0) { i__1 = -(*info); xerbla_("ZGESDD", &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 = dlamch_("P"); smlnum = sqrt(dlamch_("S")) / eps; bignum = 1. / smlnum; /* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */ anrm = zlange_("M", m, n, &a[a_offset], lda, dum); if (disnan_(&anrm)) { *info = -4; return 0; } iscl = 0; if (anrm > 0. && anrm < smlnum) { iscl = 1; zlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, & ierr); } else if (anrm > bignum) { iscl = 1; zlascl_("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 >= mnthr1) { if (wntqn) { /* Path 1 (M >> N, JOBZ='N') */ /* No singular vectors to be computed */ itau = 1; nwork = itau + *n; /* Compute A=Q*R */ /* CWorkspace: need N [tau] + N [work] */ /* CWorkspace: prefer N [tau] + N*NB [work] */ /* RWorkspace: need 0 */ i__1 = *lwork - nwork + 1; zgeqrf_(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; zlaset_("L", &i__1, &i__2, &c_b1, &c_b1, &a[a_dim1 + 2], lda); ie = 1; itauq = 1; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize R in A */ /* CWorkspace: need 2*N [tauq, taup] + N [work] */ /* CWorkspace: prefer 2*N [tauq, taup] + 2*N*NB [work] */ /* RWorkspace: need N [e] */ i__1 = *lwork - nwork + 1; zgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[ itauq], &work[itaup], &work[nwork], &i__1, &ierr); nrwork = ie + *n; /* Perform bidiagonal SVD, compute singular values only */ /* CWorkspace: need 0 */ /* RWorkspace: need N [e] + BDSPAC */ dbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, & c__1, dum, idum, &rwork[nrwork], &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 */ iu = 1; /* WORK(IU) is N by N */ ldwrku = *n; ir = iu + ldwrku * *n; if (*lwork >= *m * *n + *n * *n + *n * 3) { /* WORK(IR) is M by N */ ldwrkr = *m; } else { ldwrkr = (*lwork - *n * *n - *n * 3) / *n; } itau = ir + ldwrkr * *n; nwork = itau + *n; /* Compute A=Q*R */ /* CWorkspace: need N*N [U] + N*N [R] + N [tau] + N [work] */ /* CWorkspace: prefer N*N [U] + N*N [R] + N [tau] + N*NB [work] */ /* RWorkspace: need 0 */ i__1 = *lwork - nwork + 1; zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__1, &ierr); /* Copy R to WORK( IR ), zeroing out below it */ zlacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr); i__1 = *n - 1; i__2 = *n - 1; zlaset_("L", &i__1, &i__2, &c_b1, &c_b1, &work[ir + 1], & ldwrkr); /* Generate Q in A */ /* CWorkspace: need N*N [U] + N*N [R] + N [tau] + N [work] */ /* CWorkspace: prefer N*N [U] + N*N [R] + N [tau] + N*NB [work] */ /* RWorkspace: need 0 */ i__1 = *lwork - nwork + 1; zungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, &ierr); ie = 1; itauq = itau; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize R in WORK(IR) */ /* CWorkspace: need N*N [U] + N*N [R] + 2*N [tauq, taup] + N [work] */ /* CWorkspace: prefer N*N [U] + N*N [R] + 2*N [tauq, taup] + 2*N*NB [work] */ /* RWorkspace: need N [e] */ i__1 = *lwork - nwork + 1; zgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &work[ itauq], &work[itaup], &work[nwork], &i__1, &ierr); /* Perform bidiagonal SVD, computing left singular vectors */ /* of R in WORK(IRU) and computing right singular vectors */ /* of R in WORK(IRVT) */ /* CWorkspace: need 0 */ /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */ iru = ie + *n; irvt = iru + *n * *n; nrwork = irvt + *n * *n; dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, & rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */ /* Overwrite WORK(IU) by the left singular vectors of R */ /* CWorkspace: need N*N [U] + N*N [R] + 2*N [tauq, taup] + N [work] */ /* CWorkspace: prefer N*N [U] + N*N [R] + 2*N [tauq, taup] + N*NB [work] */ /* RWorkspace: need 0 */ zlacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku); i__1 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[ itauq], &work[iu], &ldwrku, &work[nwork], &i__1, & ierr); /* Copy real matrix RWORK(IRVT) to complex matrix VT */ /* Overwrite VT by the right singular vectors of R */ /* CWorkspace: need N*N [U] + N*N [R] + 2*N [tauq, taup] + N [work] */ /* CWorkspace: prefer N*N [U] + N*N [R] + 2*N [tauq, taup] + N*NB [work] */ /* RWorkspace: need 0 */ zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt); i__1 = *lwork - nwork + 1; zunmbr_("P", "R", "C", 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 */ /* CWorkspace: need N*N [U] + N*N [R] */ /* CWorkspace: prefer N*N [U] + M*N [R] */ /* RWorkspace: need 0 */ 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); zgemm_("N", "N", &chunk, n, n, &c_b2, &a[i__ + a_dim1], lda, &work[iu], &ldwrku, &c_b1, &work[ir], & ldwrkr); zlacpy_("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 */ /* CWorkspace: need N*N [R] + N [tau] + N [work] */ /* CWorkspace: prefer N*N [R] + N [tau] + N*NB [work] */ /* RWorkspace: need 0 */ i__2 = *lwork - nwork + 1; zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__2, &ierr); /* Copy R to WORK(IR), zeroing out below it */ zlacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr); i__2 = *n - 1; i__1 = *n - 1; zlaset_("L", &i__2, &i__1, &c_b1, &c_b1, &work[ir + 1], & ldwrkr); /* Generate Q in A */ /* CWorkspace: need N*N [R] + N [tau] + N [work] */ /* CWorkspace: prefer N*N [R] + N [tau] + N*NB [work] */ /* RWorkspace: need 0 */ i__2 = *lwork - nwork + 1; zungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__2, &ierr); ie = 1; itauq = itau; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize R in WORK(IR) */ /* CWorkspace: need N*N [R] + 2*N [tauq, taup] + N [work] */ /* CWorkspace: prefer N*N [R] + 2*N [tauq, taup] + 2*N*NB [work] */ /* RWorkspace: need N [e] */ i__2 = *lwork - nwork + 1; zgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &work[ itauq], &work[itaup], &work[nwork], &i__2, &ierr); /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in RWORK(IRU) and computing right */ /* singular vectors of bidiagonal matrix in RWORK(IRVT) */ /* CWorkspace: need 0 */ /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */ iru = ie + *n; irvt = iru + *n * *n; nrwork = irvt + *n * *n; dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, & rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRU) to complex matrix U */ /* Overwrite U by left singular vectors of R */ /* CWorkspace: need N*N [R] + 2*N [tauq, taup] + N [work] */ /* CWorkspace: prefer N*N [R] + 2*N [tauq, taup] + N*NB [work] */ /* RWorkspace: need 0 */ zlacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu); i__2 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr); /* Copy real matrix RWORK(IRVT) to complex matrix VT */ /* Overwrite VT by right singular vectors of R */ /* CWorkspace: need N*N [R] + 2*N [tauq, taup] + N [work] */ /* CWorkspace: prefer N*N [R] + 2*N [tauq, taup] + N*NB [work] */ /* RWorkspace: need 0 */ zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt); i__2 = *lwork - nwork + 1; zunmbr_("P", "R", "C", 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 */ /* CWorkspace: need N*N [R] */ /* RWorkspace: need 0 */ zlacpy_("F", n, n, &u[u_offset], ldu, &work[ir], &ldwrkr); zgemm_("N", "N", m, n, n, &c_b2, &a[a_offset], lda, &work[ir], &ldwrkr, &c_b1, &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 */ /* CWorkspace: need N*N [U] + N [tau] + N [work] */ /* CWorkspace: prefer N*N [U] + N [tau] + N*NB [work] */ /* RWorkspace: need 0 */ i__2 = *lwork - nwork + 1; zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__2, &ierr); zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu); /* Generate Q in U */ /* CWorkspace: need N*N [U] + N [tau] + M [work] */ /* CWorkspace: prefer N*N [U] + N [tau] + M*NB [work] */ /* RWorkspace: need 0 */ i__2 = *lwork - nwork + 1; zungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &work[nwork], &i__2, &ierr); /* Produce R in A, zeroing out below it */ i__2 = *n - 1; i__1 = *n - 1; zlaset_("L", &i__2, &i__1, &c_b1, &c_b1, &a[a_dim1 + 2], lda); ie = 1; itauq = itau; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize R in A */ /* CWorkspace: need N*N [U] + 2*N [tauq, taup] + N [work] */ /* CWorkspace: prefer N*N [U] + 2*N [tauq, taup] + 2*N*NB [work] */ /* RWorkspace: need N [e] */ i__2 = *lwork - nwork + 1; zgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[ itauq], &work[itaup], &work[nwork], &i__2, &ierr); iru = ie + *n; irvt = iru + *n * *n; nrwork = irvt + *n * *n; /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in RWORK(IRU) and computing right */ /* singular vectors of bidiagonal matrix in RWORK(IRVT) */ /* CWorkspace: need 0 */ /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */ dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, & rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */ /* Overwrite WORK(IU) by left singular vectors of R */ /* CWorkspace: need N*N [U] + 2*N [tauq, taup] + N [work] */ /* CWorkspace: prefer N*N [U] + 2*N [tauq, taup] + N*NB [work] */ /* RWorkspace: need 0 */ zlacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku); i__2 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", n, n, n, &a[a_offset], lda, &work[ itauq], &work[iu], &ldwrku, &work[nwork], &i__2, & ierr); /* Copy real matrix RWORK(IRVT) to complex matrix VT */ /* Overwrite VT by right singular vectors of R */ /* CWorkspace: need N*N [U] + 2*N [tauq, taup] + N [work] */ /* CWorkspace: prefer N*N [U] + 2*N [tauq, taup] + N*NB [work] */ /* RWorkspace: need 0 */ zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt); i__2 = *lwork - nwork + 1; zunmbr_("P", "R", "C", 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 */ /* CWorkspace: need N*N [U] */ /* RWorkspace: need 0 */ zgemm_("N", "N", m, n, n, &c_b2, &u[u_offset], ldu, &work[iu], &ldwrku, &c_b1, &a[a_offset], lda); /* Copy left singular vectors of A from A to U */ zlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu); } } else if (*m >= mnthr2) { /* MNTHR2 <= M < MNTHR1 */ /* Path 5 (M >> N, but not as much as MNTHR1) */ /* Reduce to bidiagonal form without QR decomposition, use */ /* ZUNGBR and matrix multiplication to compute singular vectors */ ie = 1; nrwork = ie + *n; itauq = 1; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize A */ /* CWorkspace: need 2*N [tauq, taup] + M [work] */ /* CWorkspace: prefer 2*N [tauq, taup] + (M+N)*NB [work] */ /* RWorkspace: need N [e] */ i__2 = *lwork - nwork + 1; zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq], &work[itaup], &work[nwork], &i__2, &ierr); if (wntqn) { /* Path 5n (M >> N, JOBZ='N') */ /* Compute singular values only */ /* CWorkspace: need 0 */ /* RWorkspace: need N [e] + BDSPAC */ dbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, & c__1, dum, idum, &rwork[nrwork], &iwork[1], info); } else if (wntqo) { iu = nwork; iru = nrwork; irvt = iru + *n * *n; nrwork = irvt + *n * *n; /* Path 5o (M >> N, JOBZ='O') */ /* Copy A to VT, generate P**H */ /* CWorkspace: need 2*N [tauq, taup] + N [work] */ /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */ /* RWorkspace: need 0 */ zlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt); i__2 = *lwork - nwork + 1; zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], & work[nwork], &i__2, &ierr); /* Generate Q in A */ /* CWorkspace: need 2*N [tauq, taup] + N [work] */ /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */ /* RWorkspace: need 0 */ i__2 = *lwork - nwork + 1; zungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[ nwork], &i__2, &ierr); if (*lwork >= *m * *n + *n * 3) { /* WORK( IU ) is M by N */ ldwrku = *m; } else { /* WORK(IU) is LDWRKU by N */ ldwrku = (*lwork - *n * 3) / *n; } nwork = iu + ldwrku * *n; /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in RWORK(IRU) and computing right */ /* singular vectors of bidiagonal matrix in RWORK(IRVT) */ /* CWorkspace: need 0 */ /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */ dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, & rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1], info); /* Multiply real matrix RWORK(IRVT) by P**H in VT, */ /* storing the result in WORK(IU), copying to VT */ /* CWorkspace: need 2*N [tauq, taup] + N*N [U] */ /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + 2*N*N [rwork] */ zlarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &work[iu] , &ldwrku, &rwork[nrwork]); zlacpy_("F", n, n, &work[iu], &ldwrku, &vt[vt_offset], ldvt); /* Multiply Q in A by real matrix RWORK(IRU), storing the */ /* result in WORK(IU), copying to A */ /* CWorkspace: need 2*N [tauq, taup] + N*N [U] */ /* CWorkspace: prefer 2*N [tauq, taup] + M*N [U] */ /* RWorkspace: need N [e] + N*N [RU] + 2*N*N [rwork] */ /* RWorkspace: prefer N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */ nrwork = irvt; i__2 = *m; i__1 = ldwrku; 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,ldwrku); zlacrm_(&chunk, n, &a[i__ + a_dim1], lda, &rwork[iru], n, &work[iu], &ldwrku, &rwork[nrwork]); zlacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ + a_dim1], lda); /* L20: */ } } else if (wntqs) { /* Path 5s (M >> N, JOBZ='S') */ /* Copy A to VT, generate P**H */ /* CWorkspace: need 2*N [tauq, taup] + N [work] */ /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */ /* RWorkspace: need 0 */ zlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt); i__1 = *lwork - nwork + 1; zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], & work[nwork], &i__1, &ierr); /* Copy A to U, generate Q */ /* CWorkspace: need 2*N [tauq, taup] + N [work] */ /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */ /* RWorkspace: need 0 */ zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu); i__1 = *lwork - nwork + 1; zungbr_("Q", m, n, n, &u[u_offset], ldu, &work[itauq], &work[ nwork], &i__1, &ierr); /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in RWORK(IRU) and computing right */ /* singular vectors of bidiagonal matrix in RWORK(IRVT) */ /* CWorkspace: need 0 */ /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */ iru = nrwork; irvt = iru + *n * *n; nrwork = irvt + *n * *n; dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, & rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1], info); /* Multiply real matrix RWORK(IRVT) by P**H in VT, */ /* storing the result in A, copying to VT */ /* CWorkspace: need 0 */ /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + 2*N*N [rwork] */ zlarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &a[ a_offset], lda, &rwork[nrwork]); zlacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt); /* Multiply Q in U by real matrix RWORK(IRU), storing the */ /* result in A, copying to U */ /* CWorkspace: need 0 */ /* RWorkspace: need N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */ nrwork = irvt; zlacrm_(m, n, &u[u_offset], ldu, &rwork[iru], n, &a[a_offset], lda, &rwork[nrwork]); zlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu); } else { /* Path 5a (M >> N, JOBZ='A') */ /* Copy A to VT, generate P**H */ /* CWorkspace: need 2*N [tauq, taup] + N [work] */ /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */ /* RWorkspace: need 0 */ zlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt); i__1 = *lwork - nwork + 1; zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], & work[nwork], &i__1, &ierr); /* Copy A to U, generate Q */ /* CWorkspace: need 2*N [tauq, taup] + M [work] */ /* CWorkspace: prefer 2*N [tauq, taup] + M*NB [work] */ /* RWorkspace: need 0 */ zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu); i__1 = *lwork - nwork + 1; zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[ nwork], &i__1, &ierr); /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in RWORK(IRU) and computing right */ /* singular vectors of bidiagonal matrix in RWORK(IRVT) */ /* CWorkspace: need 0 */ /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */ iru = nrwork; irvt = iru + *n * *n; nrwork = irvt + *n * *n; dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, & rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1], info); /* Multiply real matrix RWORK(IRVT) by P**H in VT, */ /* storing the result in A, copying to VT */ /* CWorkspace: need 0 */ /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + 2*N*N [rwork] */ zlarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &a[ a_offset], lda, &rwork[nrwork]); zlacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt); /* Multiply Q in U by real matrix RWORK(IRU), storing the */ /* result in A, copying to U */ /* CWorkspace: need 0 */ /* RWorkspace: need N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */ nrwork = irvt; zlacrm_(m, n, &u[u_offset], ldu, &rwork[iru], n, &a[a_offset], lda, &rwork[nrwork]); zlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu); } } else { /* M .LT. MNTHR2 */ /* Path 6 (M >= N, but not much larger) */ /* Reduce to bidiagonal form without QR decomposition */ /* Use ZUNMBR to compute singular vectors */ ie = 1; nrwork = ie + *n; itauq = 1; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize A */ /* CWorkspace: need 2*N [tauq, taup] + M [work] */ /* CWorkspace: prefer 2*N [tauq, taup] + (M+N)*NB [work] */ /* RWorkspace: need N [e] */ i__1 = *lwork - nwork + 1; zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq], &work[itaup], &work[nwork], &i__1, &ierr); if (wntqn) { /* Path 6n (M >= N, JOBZ='N') */ /* Compute singular values only */ /* CWorkspace: need 0 */ /* RWorkspace: need N [e] + BDSPAC */ dbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, & c__1, dum, idum, &rwork[nrwork], &iwork[1], info); } else if (wntqo) { iu = nwork; iru = nrwork; irvt = iru + *n * *n; nrwork = irvt + *n * *n; if (*lwork >= *m * *n + *n * 3) { /* WORK( IU ) is M by N */ ldwrku = *m; } else { /* WORK( IU ) is LDWRKU by N */ ldwrku = (*lwork - *n * 3) / *n; } nwork = iu + ldwrku * *n; /* Path 6o (M >= N, JOBZ='O') */ /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in RWORK(IRU) and computing right */ /* singular vectors of bidiagonal matrix in RWORK(IRVT) */ /* CWorkspace: need 0 */ /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */ dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, & rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRVT) to complex matrix VT */ /* Overwrite VT by right singular vectors of A */ /* CWorkspace: need 2*N [tauq, taup] + N*N [U] + N [work] */ /* CWorkspace: prefer 2*N [tauq, taup] + N*N [U] + N*NB [work] */ /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */ zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt); i__1 = *lwork - nwork + 1; zunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, & ierr); if (*lwork >= *m * *n + *n * 3) { /* Path 6o-fast */ /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */ /* Overwrite WORK(IU) by left singular vectors of A, copying */ /* to A */ /* CWorkspace: need 2*N [tauq, taup] + M*N [U] + N [work] */ /* CWorkspace: prefer 2*N [tauq, taup] + M*N [U] + N*NB [work] */ /* RWorkspace: need N [e] + N*N [RU] */ zlaset_("F", m, n, &c_b1, &c_b1, &work[iu], &ldwrku); zlacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku); i__1 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[ itauq], &work[iu], &ldwrku, &work[nwork], &i__1, & ierr); zlacpy_("F", m, n, &work[iu], &ldwrku, &a[a_offset], lda); } else { /* Path 6o-slow */ /* Generate Q in A */ /* CWorkspace: need 2*N [tauq, taup] + N*N [U] + N [work] */ /* CWorkspace: prefer 2*N [tauq, taup] + N*N [U] + N*NB [work] */ /* RWorkspace: need 0 */ i__1 = *lwork - nwork + 1; zungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], & work[nwork], &i__1, &ierr); /* Multiply Q in A by real matrix RWORK(IRU), storing the */ /* result in WORK(IU), copying to A */ /* CWorkspace: need 2*N [tauq, taup] + N*N [U] */ /* CWorkspace: prefer 2*N [tauq, taup] + M*N [U] */ /* RWorkspace: need N [e] + N*N [RU] + 2*N*N [rwork] */ /* RWorkspace: prefer N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */ nrwork = irvt; i__1 = *m; i__2 = ldwrku; 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,ldwrku); zlacrm_(&chunk, n, &a[i__ + a_dim1], lda, &rwork[iru], n, &work[iu], &ldwrku, &rwork[nrwork]); zlacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ + a_dim1], lda); /* L30: */ } } } else if (wntqs) { /* Path 6s (M >= N, JOBZ='S') */ /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in RWORK(IRU) and computing right */ /* singular vectors of bidiagonal matrix in RWORK(IRVT) */ /* CWorkspace: need 0 */ /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */ iru = nrwork; irvt = iru + *n * *n; nrwork = irvt + *n * *n; dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, & rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRU) to complex matrix U */ /* Overwrite U by left singular vectors of A */ /* CWorkspace: need 2*N [tauq, taup] + N [work] */ /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */ /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */ zlaset_("F", m, n, &c_b1, &c_b1, &u[u_offset], ldu) ; zlacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu); i__2 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr); /* Copy real matrix RWORK(IRVT) to complex matrix VT */ /* Overwrite VT by right singular vectors of A */ /* CWorkspace: need 2*N [tauq, taup] + N [work] */ /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */ /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */ zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt); i__2 = *lwork - nwork + 1; zunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, & ierr); } else { /* Path 6a (M >= N, JOBZ='A') */ /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in RWORK(IRU) and computing right */ /* singular vectors of bidiagonal matrix in RWORK(IRVT) */ /* CWorkspace: need 0 */ /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */ iru = nrwork; irvt = iru + *n * *n; nrwork = irvt + *n * *n; dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, & rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1], info); /* Set the right corner of U to identity matrix */ zlaset_("F", m, m, &c_b1, &c_b1, &u[u_offset], ldu) ; if (*m > *n) { i__2 = *m - *n; i__1 = *m - *n; zlaset_("F", &i__2, &i__1, &c_b1, &c_b2, &u[*n + 1 + (*n + 1) * u_dim1], ldu); } /* Copy real matrix RWORK(IRU) to complex matrix U */ /* Overwrite U by left singular vectors of A */ /* CWorkspace: need 2*N [tauq, taup] + M [work] */ /* CWorkspace: prefer 2*N [tauq, taup] + M*NB [work] */ /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */ zlacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu); i__2 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr); /* Copy real matrix RWORK(IRVT) to complex matrix VT */ /* Overwrite VT by right singular vectors of A */ /* CWorkspace: need 2*N [tauq, taup] + N [work] */ /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */ /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */ zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt); i__2 = *lwork - nwork + 1; zunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, & 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 >= mnthr1) { if (wntqn) { /* Path 1t (N >> M, JOBZ='N') */ /* No singular vectors to be computed */ itau = 1; nwork = itau + *m; /* Compute A=L*Q */ /* CWorkspace: need M [tau] + M [work] */ /* CWorkspace: prefer M [tau] + M*NB [work] */ /* RWorkspace: need 0 */ i__2 = *lwork - nwork + 1; zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__2, &ierr); /* Zero out above L */ i__2 = *m - 1; i__1 = *m - 1; zlaset_("U", &i__2, &i__1, &c_b1, &c_b1, &a[(a_dim1 << 1) + 1] , lda); ie = 1; itauq = 1; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize L in A */ /* CWorkspace: need 2*M [tauq, taup] + M [work] */ /* CWorkspace: prefer 2*M [tauq, taup] + 2*M*NB [work] */ /* RWorkspace: need M [e] */ i__2 = *lwork - nwork + 1; zgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &work[ itauq], &work[itaup], &work[nwork], &i__2, &ierr); nrwork = ie + *m; /* Perform bidiagonal SVD, compute singular values only */ /* CWorkspace: need 0 */ /* RWorkspace: need M [e] + BDSPAC */ dbdsdc_("U", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, & c__1, dum, idum, &rwork[nrwork], &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; ldwkvt = *m; /* WORK(IVT) is M by M */ il = ivt + ldwkvt * *m; if (*lwork >= *m * *n + *m * *m + *m * 3) { /* WORK(IL) M by N */ ldwrkl = *m; chunk = *n; } else { /* WORK(IL) is M by CHUNK */ ldwrkl = *m; chunk = (*lwork - *m * *m - *m * 3) / *m; } itau = il + ldwrkl * chunk; nwork = itau + *m; /* Compute A=L*Q */ /* CWorkspace: need M*M [VT] + M*M [L] + M [tau] + M [work] */ /* CWorkspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work] */ /* RWorkspace: need 0 */ i__2 = *lwork - nwork + 1; zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__2, &ierr); /* Copy L to WORK(IL), zeroing about above it */ zlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl); i__2 = *m - 1; i__1 = *m - 1; zlaset_("U", &i__2, &i__1, &c_b1, &c_b1, &work[il + ldwrkl], & ldwrkl); /* Generate Q in A */ /* CWorkspace: need M*M [VT] + M*M [L] + M [tau] + M [work] */ /* CWorkspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work] */ /* RWorkspace: need 0 */ i__2 = *lwork - nwork + 1; zunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork], &i__2, &ierr); ie = 1; itauq = itau; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize L in WORK(IL) */ /* CWorkspace: need M*M [VT] + M*M [L] + 2*M [tauq, taup] + M [work] */ /* CWorkspace: prefer M*M [VT] + M*M [L] + 2*M [tauq, taup] + 2*M*NB [work] */ /* RWorkspace: need M [e] */ i__2 = *lwork - nwork + 1; zgebrd_(m, m, &work[il], &ldwrkl, &s[1], &rwork[ie], &work[ itauq], &work[itaup], &work[nwork], &i__2, &ierr); /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in RWORK(IRU) and computing right */ /* singular vectors of bidiagonal matrix in RWORK(IRVT) */ /* CWorkspace: need 0 */ /* RWorkspace: need M [e] + M*M [RU] + M*M [RVT] + BDSPAC */ iru = ie + *m; irvt = iru + *m * *m; nrwork = irvt + *m * *m; dbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, & rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */ /* Overwrite WORK(IU) by the left singular vectors of L */ /* CWorkspace: need M*M [VT] + M*M [L] + 2*M [tauq, taup] + M [work] */ /* CWorkspace: prefer M*M [VT] + M*M [L] + 2*M [tauq, taup] + M*NB [work] */ /* RWorkspace: need 0 */ zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu); i__2 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr); /* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) */ /* Overwrite WORK(IVT) by the right singular vectors of L */ /* CWorkspace: need M*M [VT] + M*M [L] + 2*M [tauq, taup] + M [work] */ /* CWorkspace: prefer M*M [VT] + M*M [L] + 2*M [tauq, taup] + M*NB [work] */ /* RWorkspace: need 0 */ zlacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt); i__2 = *lwork - nwork + 1; zunmbr_("P", "R", "C", m, m, m, &work[il], &ldwrkl, &work[ itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2, & ierr); /* Multiply right singular vectors of L in WORK(IL) by Q */ /* in A, storing result in WORK(IL) and copying to A */ /* CWorkspace: need M*M [VT] + M*M [L] */ /* CWorkspace: prefer M*M [VT] + M*N [L] */ /* RWorkspace: need 0 */ 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); zgemm_("N", "N", m, &blk, m, &c_b2, &work[ivt], m, &a[i__ * a_dim1 + 1], lda, &c_b1, &work[il], &ldwrkl); zlacpy_("F", m, &blk, &work[il], &ldwrkl, &a[i__ * a_dim1 + 1], lda); /* L40: */ } } 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 */ /* CWorkspace: need M*M [L] + M [tau] + M [work] */ /* CWorkspace: prefer M*M [L] + M [tau] + M*NB [work] */ /* RWorkspace: need 0 */ i__1 = *lwork - nwork + 1; zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__1, &ierr); /* Copy L to WORK(IL), zeroing out above it */ zlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl); i__1 = *m - 1; i__2 = *m - 1; zlaset_("U", &i__1, &i__2, &c_b1, &c_b1, &work[il + ldwrkl], & ldwrkl); /* Generate Q in A */ /* CWorkspace: need M*M [L] + M [tau] + M [work] */ /* CWorkspace: prefer M*M [L] + M [tau] + M*NB [work] */ /* RWorkspace: need 0 */ i__1 = *lwork - nwork + 1; zunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, &ierr); ie = 1; itauq = itau; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize L in WORK(IL) */ /* CWorkspace: need M*M [L] + 2*M [tauq, taup] + M [work] */ /* CWorkspace: prefer M*M [L] + 2*M [tauq, taup] + 2*M*NB [work] */ /* RWorkspace: need M [e] */ i__1 = *lwork - nwork + 1; zgebrd_(m, m, &work[il], &ldwrkl, &s[1], &rwork[ie], &work[ itauq], &work[itaup], &work[nwork], &i__1, &ierr); /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in RWORK(IRU) and computing right */ /* singular vectors of bidiagonal matrix in RWORK(IRVT) */ /* CWorkspace: need 0 */ /* RWorkspace: need M [e] + M*M [RU] + M*M [RVT] + BDSPAC */ iru = ie + *m; irvt = iru + *m * *m; nrwork = irvt + *m * *m; dbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, & rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRU) to complex matrix U */ /* Overwrite U by left singular vectors of L */ /* CWorkspace: need M*M [L] + 2*M [tauq, taup] + M [work] */ /* CWorkspace: prefer M*M [L] + 2*M [tauq, taup] + M*NB [work] */ /* RWorkspace: need 0 */ zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu); i__1 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr); /* Copy real matrix RWORK(IRVT) to complex matrix VT */ /* Overwrite VT by left singular vectors of L */ /* CWorkspace: need M*M [L] + 2*M [tauq, taup] + M [work] */ /* CWorkspace: prefer M*M [L] + 2*M [tauq, taup] + M*NB [work] */ /* RWorkspace: need 0 */ zlacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt); i__1 = *lwork - nwork + 1; zunmbr_("P", "R", "C", m, m, m, &work[il], &ldwrkl, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, & ierr); /* Copy VT to WORK(IL), multiply right singular vectors of L */ /* in WORK(IL) by Q in A, storing result in VT */ /* CWorkspace: need M*M [L] */ /* RWorkspace: need 0 */ zlacpy_("F", m, m, &vt[vt_offset], ldvt, &work[il], &ldwrkl); zgemm_("N", "N", m, n, m, &c_b2, &work[il], &ldwrkl, &a[ a_offset], lda, &c_b1, &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 */ /* CWorkspace: need M*M [VT] + M [tau] + M [work] */ /* CWorkspace: prefer M*M [VT] + M [tau] + M*NB [work] */ /* RWorkspace: need 0 */ i__1 = *lwork - nwork + 1; zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__1, &ierr); zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt); /* Generate Q in VT */ /* CWorkspace: need M*M [VT] + M [tau] + N [work] */ /* CWorkspace: prefer M*M [VT] + M [tau] + N*NB [work] */ /* RWorkspace: need 0 */ i__1 = *lwork - nwork + 1; zunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &work[ nwork], &i__1, &ierr); /* Produce L in A, zeroing out above it */ i__1 = *m - 1; i__2 = *m - 1; zlaset_("U", &i__1, &i__2, &c_b1, &c_b1, &a[(a_dim1 << 1) + 1] , lda); ie = 1; itauq = itau; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize L in A */ /* CWorkspace: need M*M [VT] + 2*M [tauq, taup] + M [work] */ /* CWorkspace: prefer M*M [VT] + 2*M [tauq, taup] + 2*M*NB [work] */ /* RWorkspace: need M [e] */ i__1 = *lwork - nwork + 1; zgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &work[ itauq], &work[itaup], &work[nwork], &i__1, &ierr); /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in RWORK(IRU) and computing right */ /* singular vectors of bidiagonal matrix in RWORK(IRVT) */ /* CWorkspace: need 0 */ /* RWorkspace: need M [e] + M*M [RU] + M*M [RVT] + BDSPAC */ iru = ie + *m; irvt = iru + *m * *m; nrwork = irvt + *m * *m; dbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, & rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRU) to complex matrix U */ /* Overwrite U by left singular vectors of L */ /* CWorkspace: need M*M [VT] + 2*M [tauq, taup] + M [work] */ /* CWorkspace: prefer M*M [VT] + 2*M [tauq, taup] + M*NB [work] */ /* RWorkspace: need 0 */ zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu); i__1 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", m, m, m, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr); /* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) */ /* Overwrite WORK(IVT) by right singular vectors of L */ /* CWorkspace: need M*M [VT] + 2*M [tauq, taup] + M [work] */ /* CWorkspace: prefer M*M [VT] + 2*M [tauq, taup] + M*NB [work] */ /* RWorkspace: need 0 */ zlacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt); i__1 = *lwork - nwork + 1; zunmbr_("P", "R", "C", m, m, m, &a[a_offset], lda, &work[ itaup], &work[ivt], &ldwkvt, &work[nwork], &i__1, & ierr); /* Multiply right singular vectors of L in WORK(IVT) by */ /* Q in VT, storing result in A */ /* CWorkspace: need M*M [VT] */ /* RWorkspace: need 0 */ zgemm_("N", "N", m, n, m, &c_b2, &work[ivt], &ldwkvt, &vt[ vt_offset], ldvt, &c_b1, &a[a_offset], lda); /* Copy right singular vectors of A from A to VT */ zlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt); } } else if (*n >= mnthr2) { /* MNTHR2 <= N < MNTHR1 */ /* Path 5t (N >> M, but not as much as MNTHR1) */ /* Reduce to bidiagonal form without QR decomposition, use */ /* ZUNGBR and matrix multiplication to compute singular vectors */ ie = 1; nrwork = ie + *m; itauq = 1; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize A */ /* CWorkspace: need 2*M [tauq, taup] + N [work] */ /* CWorkspace: prefer 2*M [tauq, taup] + (M+N)*NB [work] */ /* RWorkspace: need M [e] */ i__1 = *lwork - nwork + 1; zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq], &work[itaup], &work[nwork], &i__1, &ierr); if (wntqn) { /* Path 5tn (N >> M, JOBZ='N') */ /* Compute singular values only */ /* CWorkspace: need 0 */ /* RWorkspace: need M [e] + BDSPAC */ dbdsdc_("L", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, & c__1, dum, idum, &rwork[nrwork], &iwork[1], info); } else if (wntqo) { irvt = nrwork; iru = irvt + *m * *m; nrwork = iru + *m * *m; ivt = nwork; /* Path 5to (N >> M, JOBZ='O') */ /* Copy A to U, generate Q */ /* CWorkspace: need 2*M [tauq, taup] + M [work] */ /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */ /* RWorkspace: need 0 */ zlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu); i__1 = *lwork - nwork + 1; zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[ nwork], &i__1, &ierr); /* Generate P**H in A */ /* CWorkspace: need 2*M [tauq, taup] + M [work] */ /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */ /* RWorkspace: need 0 */ i__1 = *lwork - nwork + 1; zungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[ nwork], &i__1, &ierr); ldwkvt = *m; if (*lwork >= *m * *n + *m * 3) { /* WORK( IVT ) is M by N */ nwork = ivt + ldwkvt * *n; chunk = *n; } else { /* WORK( IVT ) is M by CHUNK */ chunk = (*lwork - *m * 3) / *m; nwork = ivt + ldwkvt * chunk; } /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in RWORK(IRU) and computing right */ /* singular vectors of bidiagonal matrix in RWORK(IRVT) */ /* CWorkspace: need 0 */ /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */ dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, & rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1], info); /* Multiply Q in U by real matrix RWORK(IRVT) */ /* storing the result in WORK(IVT), copying to U */ /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] */ /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + 2*M*M [rwork] */ zlacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &work[ivt], & ldwkvt, &rwork[nrwork]); zlacpy_("F", m, m, &work[ivt], &ldwkvt, &u[u_offset], ldu); /* Multiply RWORK(IRVT) by P**H in A, storing the */ /* result in WORK(IVT), copying to A */ /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] */ /* CWorkspace: prefer 2*M [tauq, taup] + M*N [VT] */ /* RWorkspace: need M [e] + M*M [RVT] + 2*M*M [rwork] */ /* RWorkspace: prefer M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */ nrwork = iru; 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); zlarcm_(m, &blk, &rwork[irvt], m, &a[i__ * a_dim1 + 1], lda, &work[ivt], &ldwkvt, &rwork[nrwork]); zlacpy_("F", m, &blk, &work[ivt], &ldwkvt, &a[i__ * a_dim1 + 1], lda); /* L50: */ } } else if (wntqs) { /* Path 5ts (N >> M, JOBZ='S') */ /* Copy A to U, generate Q */ /* CWorkspace: need 2*M [tauq, taup] + M [work] */ /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */ /* RWorkspace: need 0 */ zlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu); i__2 = *lwork - nwork + 1; zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[ nwork], &i__2, &ierr); /* Copy A to VT, generate P**H */ /* CWorkspace: need 2*M [tauq, taup] + M [work] */ /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */ /* RWorkspace: need 0 */ zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt); i__2 = *lwork - nwork + 1; zungbr_("P", m, n, m, &vt[vt_offset], ldvt, &work[itaup], & work[nwork], &i__2, &ierr); /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in RWORK(IRU) and computing right */ /* singular vectors of bidiagonal matrix in RWORK(IRVT) */ /* CWorkspace: need 0 */ /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */ irvt = nrwork; iru = irvt + *m * *m; nrwork = iru + *m * *m; dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, & rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1], info); /* Multiply Q in U by real matrix RWORK(IRU), storing the */ /* result in A, copying to U */ /* CWorkspace: need 0 */ /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + 2*M*M [rwork] */ zlacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &a[a_offset], lda, &rwork[nrwork]); zlacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu); /* Multiply real matrix RWORK(IRVT) by P**H in VT, */ /* storing the result in A, copying to VT */ /* CWorkspace: need 0 */ /* RWorkspace: need M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */ nrwork = iru; zlarcm_(m, n, &rwork[irvt], m, &vt[vt_offset], ldvt, &a[ a_offset], lda, &rwork[nrwork]); zlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt); } else { /* Path 5ta (N >> M, JOBZ='A') */ /* Copy A to U, generate Q */ /* CWorkspace: need 2*M [tauq, taup] + M [work] */ /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */ /* RWorkspace: need 0 */ zlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu); i__2 = *lwork - nwork + 1; zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[ nwork], &i__2, &ierr); /* Copy A to VT, generate P**H */ /* CWorkspace: need 2*M [tauq, taup] + N [work] */ /* CWorkspace: prefer 2*M [tauq, taup] + N*NB [work] */ /* RWorkspace: need 0 */ zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt); i__2 = *lwork - nwork + 1; zungbr_("P", n, n, m, &vt[vt_offset], ldvt, &work[itaup], & work[nwork], &i__2, &ierr); /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in RWORK(IRU) and computing right */ /* singular vectors of bidiagonal matrix in RWORK(IRVT) */ /* CWorkspace: need 0 */ /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */ irvt = nrwork; iru = irvt + *m * *m; nrwork = iru + *m * *m; dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, & rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1], info); /* Multiply Q in U by real matrix RWORK(IRU), storing the */ /* result in A, copying to U */ /* CWorkspace: need 0 */ /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + 2*M*M [rwork] */ zlacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &a[a_offset], lda, &rwork[nrwork]); zlacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu); /* Multiply real matrix RWORK(IRVT) by P**H in VT, */ /* storing the result in A, copying to VT */ /* CWorkspace: need 0 */ /* RWorkspace: need M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */ nrwork = iru; zlarcm_(m, n, &rwork[irvt], m, &vt[vt_offset], ldvt, &a[ a_offset], lda, &rwork[nrwork]); zlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt); } } else { /* N .LT. MNTHR2 */ /* Path 6t (N > M, but not much larger) */ /* Reduce to bidiagonal form without LQ decomposition */ /* Use ZUNMBR to compute singular vectors */ ie = 1; nrwork = ie + *m; itauq = 1; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize A */ /* CWorkspace: need 2*M [tauq, taup] + N [work] */ /* CWorkspace: prefer 2*M [tauq, taup] + (M+N)*NB [work] */ /* RWorkspace: need M [e] */ i__2 = *lwork - nwork + 1; zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq], &work[itaup], &work[nwork], &i__2, &ierr); if (wntqn) { /* Path 6tn (N > M, JOBZ='N') */ /* Compute singular values only */ /* CWorkspace: need 0 */ /* RWorkspace: need M [e] + BDSPAC */ dbdsdc_("L", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, & c__1, dum, idum, &rwork[nrwork], &iwork[1], info); } else if (wntqo) { /* Path 6to (N > M, JOBZ='O') */ ldwkvt = *m; ivt = nwork; if (*lwork >= *m * *n + *m * 3) { /* WORK( IVT ) is M by N */ zlaset_("F", m, n, &c_b1, &c_b1, &work[ivt], &ldwkvt); nwork = ivt + ldwkvt * *n; } else { /* WORK( IVT ) is M by CHUNK */ chunk = (*lwork - *m * 3) / *m; nwork = ivt + ldwkvt * chunk; } /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in RWORK(IRU) and computing right */ /* singular vectors of bidiagonal matrix in RWORK(IRVT) */ /* CWorkspace: need 0 */ /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */ irvt = nrwork; iru = irvt + *m * *m; nrwork = iru + *m * *m; dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, & rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRU) to complex matrix U */ /* Overwrite U by left singular vectors of A */ /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] + M [work] */ /* CWorkspace: prefer 2*M [tauq, taup] + M*M [VT] + M*NB [work] */ /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] */ zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu); i__2 = *lwork - nwork + 1; zunmbr_("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) { /* Path 6to-fast */ /* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) */ /* Overwrite WORK(IVT) by right singular vectors of A, */ /* copying to A */ /* CWorkspace: need 2*M [tauq, taup] + M*N [VT] + M [work] */ /* CWorkspace: prefer 2*M [tauq, taup] + M*N [VT] + M*NB [work] */ /* RWorkspace: need M [e] + M*M [RVT] */ zlacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt); i__2 = *lwork - nwork + 1; zunmbr_("P", "R", "C", m, n, m, &a[a_offset], lda, &work[ itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2, &ierr); zlacpy_("F", m, n, &work[ivt], &ldwkvt, &a[a_offset], lda); } else { /* Path 6to-slow */ /* Generate P**H in A */ /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] + M [work] */ /* CWorkspace: prefer 2*M [tauq, taup] + M*M [VT] + M*NB [work] */ /* RWorkspace: need 0 */ i__2 = *lwork - nwork + 1; zungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], & work[nwork], &i__2, &ierr); /* Multiply Q in A by real matrix RWORK(IRU), storing the */ /* result in WORK(IU), copying to A */ /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] */ /* CWorkspace: prefer 2*M [tauq, taup] + M*N [VT] */ /* RWorkspace: need M [e] + M*M [RVT] + 2*M*M [rwork] */ /* RWorkspace: prefer M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */ nrwork = iru; 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); zlarcm_(m, &blk, &rwork[irvt], m, &a[i__ * a_dim1 + 1] , lda, &work[ivt], &ldwkvt, &rwork[nrwork]); zlacpy_("F", m, &blk, &work[ivt], &ldwkvt, &a[i__ * a_dim1 + 1], lda); /* L60: */ } } } else if (wntqs) { /* Path 6ts (N > M, JOBZ='S') */ /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in RWORK(IRU) and computing right */ /* singular vectors of bidiagonal matrix in RWORK(IRVT) */ /* CWorkspace: need 0 */ /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */ irvt = nrwork; iru = irvt + *m * *m; nrwork = iru + *m * *m; dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, & rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRU) to complex matrix U */ /* Overwrite U by left singular vectors of A */ /* CWorkspace: need 2*M [tauq, taup] + M [work] */ /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */ /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] */ zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu); i__1 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr); /* Copy real matrix RWORK(IRVT) to complex matrix VT */ /* Overwrite VT by right singular vectors of A */ /* CWorkspace: need 2*M [tauq, taup] + M [work] */ /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */ /* RWorkspace: need M [e] + M*M [RVT] */ zlaset_("F", m, n, &c_b1, &c_b1, &vt[vt_offset], ldvt); zlacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt); i__1 = *lwork - nwork + 1; zunmbr_("P", "R", "C", m, n, m, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, & ierr); } else { /* Path 6ta (N > M, JOBZ='A') */ /* Perform bidiagonal SVD, computing left singular vectors */ /* of bidiagonal matrix in RWORK(IRU) and computing right */ /* singular vectors of bidiagonal matrix in RWORK(IRVT) */ /* CWorkspace: need 0 */ /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */ irvt = nrwork; iru = irvt + *m * *m; nrwork = iru + *m * *m; dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, & rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRU) to complex matrix U */ /* Overwrite U by left singular vectors of A */ /* CWorkspace: need 2*M [tauq, taup] + M [work] */ /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */ /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] */ zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu); i__1 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr); /* Set all of VT to identity matrix */ zlaset_("F", n, n, &c_b1, &c_b2, &vt[vt_offset], ldvt); /* Copy real matrix RWORK(IRVT) to complex matrix VT */ /* Overwrite VT by right singular vectors of A */ /* CWorkspace: need 2*M [tauq, taup] + N [work] */ /* CWorkspace: prefer 2*M [tauq, taup] + N*NB [work] */ /* RWorkspace: need M [e] + M*M [RVT] */ zlacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt); i__1 = *lwork - nwork + 1; zunmbr_("P", "R", "C", 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) { dlascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], & minmn, &ierr); } if (*info != 0 && anrm > bignum) { i__1 = minmn - 1; dlascl_("G", &c__0, &c__0, &bignum, &anrm, &i__1, &c__1, &rwork[ ie], &minmn, &ierr); } if (anrm < smlnum) { dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], & minmn, &ierr); } if (*info != 0 && anrm < smlnum) { i__1 = minmn - 1; dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &i__1, &c__1, &rwork[ ie], &minmn, &ierr); } } /* Return optimal workspace in WORK(1) */ work[1].r = (doublereal) maxwrk, work[1].i = 0.; return 0; /* End of ZGESDD */ } /* zgesdd_ */