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|
- #include <math.h>
- #include <stdlib.h>
- #include <string.h>
- #include <stdio.h>
- #include <complex.h>
- #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<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
- zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
- zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
- }
- }
- pCf(z) = zdotc;
- }
- #else
- _Complex float zdotc = 0.0;
- if (incx == 1 && incy == 1) {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
- }
- }
- pCf(z) = zdotc;
- }
- #endif
- static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
- integer n = *n_, incx = *incx_, incy = *incy_, i;
- #ifdef _MSC_VER
- _Dcomplex zdotc = {0.0, 0.0};
- if (incx == 1 && incy == 1) {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
- zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
- zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
- }
- }
- pCd(z) = zdotc;
- }
- #else
- _Complex double zdotc = 0.0;
- if (incx == 1 && incy == 1) {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
- }
- }
- pCd(z) = zdotc;
- }
- #endif
- static inline void cdotu_(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<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
- zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
- zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
- }
- }
- pCf(z) = zdotc;
- }
- #else
- _Complex float zdotc = 0.0;
- if (incx == 1 && incy == 1) {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += Cf(&x[i]) * Cf(&y[i]);
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
- }
- }
- pCf(z) = zdotc;
- }
- #endif
- static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
- integer n = *n_, incx = *incx_, incy = *incy_, i;
- #ifdef _MSC_VER
- _Dcomplex zdotc = {0.0, 0.0};
- if (incx == 1 && incy == 1) {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
- zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
- zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
- }
- }
- pCd(z) = zdotc;
- }
- #else
- _Complex double zdotc = 0.0;
- if (incx == 1 && incy == 1) {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += Cd(&x[i]) * Cd(&y[i]);
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
- }
- }
- pCd(z) = zdotc;
- }
- #endif
- /* -- translated by f2c (version 20000121).
- You must link the resulting object file with the libraries:
- -lf2c -lm (in that order)
- */
-
-
-
-
- /* Table of constant values */
-
- static complex c_b1 = {0.f,0.f};
- static complex c_b2 = {1.f,0.f};
- static integer c__6 = 6;
- static integer c__0 = 0;
- static integer c__2 = 2;
- static integer c_n1 = -1;
- static integer c__1 = 1;
-
- /* > \brief <b> CGESVD computes the singular value decomposition (SVD) for GE matrices</b> */
-
- /* =========== DOCUMENTATION =========== */
-
- /* Online html documentation available at */
- /* http://www.netlib.org/lapack/explore-html/ */
-
- /* > \htmlonly */
- /* > Download CGESVD + dependencies */
- /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgesvd.
- f"> */
- /* > [TGZ]</a> */
- /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgesvd.
- f"> */
- /* > [ZIP]</a> */
- /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgesvd.
- f"> */
- /* > [TXT]</a> */
- /* > \endhtmlonly */
-
- /* Definition: */
- /* =========== */
-
- /* SUBROUTINE CGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, */
- /* WORK, LWORK, RWORK, INFO ) */
-
- /* CHARACTER JOBU, JOBVT */
- /* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N */
- /* REAL RWORK( * ), S( * ) */
- /* COMPLEX A( LDA, * ), U( LDU, * ), VT( LDVT, * ), */
- /* $ WORK( * ) */
-
-
- /* > \par Purpose: */
- /* ============= */
- /* > */
- /* > \verbatim */
- /* > */
- /* > CGESVD computes the singular value decomposition (SVD) of a complex */
- /* > M-by-N matrix A, optionally computing the left and/or right singular */
- /* > vectors. 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 V**H, not V. */
- /* > \endverbatim */
-
- /* Arguments: */
- /* ========== */
-
- /* > \param[in] JOBU */
- /* > \verbatim */
- /* > JOBU is CHARACTER*1 */
- /* > Specifies options for computing all or part of the matrix U: */
- /* > = 'A': all M columns of U are returned in array U: */
- /* > = 'S': the first f2cmin(m,n) columns of U (the left singular */
- /* > vectors) are returned in the array U; */
- /* > = 'O': the first f2cmin(m,n) columns of U (the left singular */
- /* > vectors) are overwritten on the array A; */
- /* > = '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**H: */
- /* > = 'A': all N rows of V**H are returned in the array VT; */
- /* > = 'S': the first f2cmin(m,n) rows of V**H (the right singular */
- /* > vectors) are returned in the array VT; */
- /* > = 'O': the first f2cmin(m,n) rows of V**H (the right singular */
- /* > vectors) are overwritten on the array A; */
- /* > = 'N': no rows of V**H (no right singular vectors) are */
- /* > computed. */
- /* > */
- /* > JOBVT and JOBU cannot both be 'O'. */
- /* > \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 array, dimension (LDA,N) */
- /* > On entry, the M-by-N matrix A. */
- /* > On exit, */
- /* > if JOBU = 'O', A is overwritten with the first f2cmin(m,n) */
- /* > columns of U (the left singular vectors, */
- /* > stored columnwise); */
- /* > if JOBVT = 'O', A is overwritten with the first f2cmin(m,n) */
- /* > rows of V**H (the right singular vectors, */
- /* > stored rowwise); */
- /* > if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A */
- /* > are destroyed. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] LDA */
- /* > \verbatim */
- /* > LDA is INTEGER */
- /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
- /* > \endverbatim */
- /* > */
- /* > \param[out] S */
- /* > \verbatim */
- /* > S is REAL array, dimension (f2cmin(M,N)) */
- /* > The singular values of A, sorted so that S(i) >= S(i+1). */
- /* > \endverbatim */
- /* > */
- /* > \param[out] U */
- /* > \verbatim */
- /* > U is COMPLEX array, dimension (LDU,UCOL) */
- /* > (LDU,M) if JOBU = 'A' or (LDU,f2cmin(M,N)) if JOBU = 'S'. */
- /* > If JOBU = 'A', U contains the M-by-M unitary matrix U; */
- /* > if JOBU = 'S', U contains the first f2cmin(m,n) columns of U */
- /* > (the left singular vectors, stored columnwise); */
- /* > if JOBU = 'N' or 'O', U is not referenced. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] LDU */
- /* > \verbatim */
- /* > LDU is INTEGER */
- /* > The leading dimension of the array U. LDU >= 1; if */
- /* > JOBU = 'S' or 'A', LDU >= M. */
- /* > \endverbatim */
- /* > */
- /* > \param[out] VT */
- /* > \verbatim */
- /* > VT is COMPLEX array, dimension (LDVT,N) */
- /* > If JOBVT = 'A', VT contains the N-by-N unitary matrix */
- /* > V**H; */
- /* > if JOBVT = 'S', VT contains the first f2cmin(m,n) rows of */
- /* > V**H (the right singular vectors, stored rowwise); */
- /* > if JOBVT = 'N' or 'O', VT is not referenced. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] LDVT */
- /* > \verbatim */
- /* > LDVT is INTEGER */
- /* > The leading dimension of the array VT. LDVT >= 1; if */
- /* > JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= f2cmin(M,N). */
- /* > \endverbatim */
- /* > */
- /* > \param[out] WORK */
- /* > \verbatim */
- /* > WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
- /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] LWORK */
- /* > \verbatim */
- /* > LWORK is INTEGER */
- /* > The dimension of the array WORK. */
- /* > LWORK >= MAX(1,2*MIN(M,N)+MAX(M,N)). */
- /* > For good performance, LWORK should generally be larger. */
- /* > */
- /* > If LWORK = -1, then a workspace query is assumed; the routine */
- /* > only calculates the optimal size of the WORK array, returns */
- /* > this value as the first entry of the WORK array, and no error */
- /* > message related to LWORK is issued by XERBLA. */
- /* > \endverbatim */
- /* > */
- /* > \param[out] RWORK */
- /* > \verbatim */
- /* > RWORK is REAL array, dimension (5*f2cmin(M,N)) */
- /* > On exit, if INFO > 0, RWORK(1:MIN(M,N)-1) contains the */
- /* > unconverged superdiagonal elements of an upper bidiagonal */
- /* > matrix B whose diagonal is in S (not necessarily sorted). */
- /* > B satisfies A = U * B * VT, so it has the same singular */
- /* > values as A, and singular vectors related by U and VT. */
- /* > \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 CBDSQR did not converge, INFO specifies how many */
- /* > superdiagonals of an intermediate bidiagonal form B */
- /* > did not converge to zero. See the description of RWORK */
- /* > above for details. */
- /* > \endverbatim */
-
- /* Authors: */
- /* ======== */
-
- /* > \author Univ. of Tennessee */
- /* > \author Univ. of California Berkeley */
- /* > \author Univ. of Colorado Denver */
- /* > \author NAG Ltd. */
-
- /* > \date April 2012 */
-
- /* > \ingroup complexGEsing */
-
- /* ===================================================================== */
- /* Subroutine */ int cgesvd_(char *jobu, char *jobvt, integer *m, integer *n,
- complex *a, integer *lda, real *s, complex *u, integer *ldu, complex *
- vt, integer *ldvt, complex *work, integer *lwork, real *rwork,
- 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, i__4;
- char ch__1[2];
-
- /* Local variables */
- complex cdum[1];
- integer iscl;
- real anrm;
- integer ierr, itau, ncvt, nrvt, lwork_cgebrd__, lwork_cgelqf__,
- lwork_cgeqrf__, i__;
- extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *,
- integer *, complex *, complex *, integer *, complex *, integer *,
- complex *, complex *, integer *);
- extern logical lsame_(char *, char *);
- integer chunk, minmn, wrkbl, itaup, itauq, mnthr, iwork;
- logical wntua, wntva, wntun, wntuo, wntvn, wntvo, wntus, wntvs;
- integer ie;
- extern /* Subroutine */ int cgebrd_(integer *, integer *, complex *,
- integer *, real *, real *, complex *, complex *, complex *,
- integer *, integer *);
- extern real clange_(char *, integer *, integer *, complex *, integer *,
- real *);
- integer ir, iu;
- extern /* Subroutine */ int cgelqf_(integer *, integer *, complex *,
- integer *, complex *, complex *, integer *, integer *), clascl_(
- char *, integer *, integer *, real *, real *, integer *, integer *
- , complex *, integer *, integer *), cgeqrf_(integer *,
- integer *, complex *, integer *, complex *, complex *, integer *,
- integer *);
- extern real slamch_(char *);
- extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
- *, integer *, complex *, integer *), claset_(char *,
- integer *, integer *, complex *, complex *, complex *, integer *), cbdsqr_(char *, integer *, integer *, integer *, integer
- *, real *, real *, complex *, integer *, complex *, integer *,
- complex *, integer *, real *, integer *), xerbla_(char *,
- integer *, ftnlen), cungbr_(char *, integer *, integer *, integer
- *, complex *, integer *, complex *, complex *, integer *, integer
- *);
- real bignum;
- extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
- real *, integer *, integer *, real *, integer *, integer *);
- extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
- integer *, integer *, ftnlen, ftnlen);
- extern /* Subroutine */ int cunmbr_(char *, char *, char *, integer *,
- integer *, integer *, complex *, integer *, complex *, complex *,
- integer *, complex *, integer *, integer *), cunglq_(integer *, integer *, integer *, complex *,
- integer *, complex *, complex *, integer *, integer *), cungqr_(
- integer *, integer *, integer *, complex *, integer *, complex *,
- complex *, integer *, integer *);
- integer ldwrkr, minwrk, ldwrku, maxwrk;
- real smlnum;
- integer irwork;
- logical lquery, wntuas, wntvas;
- integer lwork_cungbr_p__, lwork_cungbr_q__, lwork_cunglq_n__,
- lwork_cunglq_m__, lwork_cungqr_m__, lwork_cungqr_n__, blk, ncu;
- real dum[1], eps;
- integer nru;
-
-
- /* -- 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..-- */
- /* April 2012 */
-
-
- /* ===================================================================== */
-
-
- /* 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;
-
- /* Function Body */
- *info = 0;
- minmn = f2cmin(*m,*n);
- wntua = lsame_(jobu, "A");
- wntus = lsame_(jobu, "S");
- wntuas = wntua || wntus;
- wntuo = lsame_(jobu, "O");
- wntun = lsame_(jobu, "N");
- wntva = lsame_(jobvt, "A");
- wntvs = lsame_(jobvt, "S");
- wntvas = wntva || wntvs;
- wntvo = lsame_(jobvt, "O");
- wntvn = lsame_(jobvt, "N");
- lquery = *lwork == -1;
-
- if (! (wntua || wntus || wntuo || wntun)) {
- *info = -1;
- } else if (! (wntva || wntvs || wntvo || wntvn) || wntvo && wntuo) {
- *info = -2;
- } else if (*m < 0) {
- *info = -3;
- } else if (*n < 0) {
- *info = -4;
- } else if (*lda < f2cmax(1,*m)) {
- *info = -6;
- } else if (*ldu < 1 || wntuas && *ldu < *m) {
- *info = -9;
- } else if (*ldvt < 1 || wntva && *ldvt < *n || wntvs && *ldvt < minmn) {
- *info = -11;
- }
-
- /* Compute workspace */
- /* (Note: Comments in the code beginning "Workspace:" describe the */
- /* minimal amount of workspace needed at that point in the code, */
- /* as well as the preferred amount for good performance. */
- /* CWorkspace refers to complex workspace, and RWorkspace 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) {
-
- /* Space needed for ZBDSQR is BDSPAC = 5*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, "CGESVD", ch__1, m, n, &c__0, &c__0, (
- ftnlen)6, (ftnlen)2);
- /* Compute space needed for CGEQRF */
- cgeqrf_(m, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
- lwork_cgeqrf__ = (integer) cdum[0].r;
- /* Compute space needed for CUNGQR */
- cungqr_(m, n, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
- lwork_cungqr_n__ = (integer) cdum[0].r;
- cungqr_(m, m, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
- lwork_cungqr_m__ = (integer) cdum[0].r;
- /* Compute space needed for CGEBRD */
- cgebrd_(n, n, &a[a_offset], lda, &s[1], dum, cdum, cdum, cdum, &
- c_n1, &ierr);
- lwork_cgebrd__ = (integer) cdum[0].r;
- /* Compute space needed for CUNGBR */
- cungbr_("P", n, n, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
- lwork_cungbr_p__ = (integer) cdum[0].r;
- cungbr_("Q", n, n, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
- lwork_cungbr_q__ = (integer) cdum[0].r;
-
- /* 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, "CGESVD", ch__1, m, n, &c__0, &c__0, (
- ftnlen)6, (ftnlen)2);
- if (*m >= mnthr) {
- if (wntun) {
-
- /* Path 1 (M much larger than N, JOBU='N') */
-
- maxwrk = *n + lwork_cgeqrf__;
- /* Computing MAX */
- i__2 = maxwrk, i__3 = (*n << 1) + lwork_cgebrd__;
- maxwrk = f2cmax(i__2,i__3);
- if (wntvo || wntvas) {
- /* Computing MAX */
- i__2 = maxwrk, i__3 = (*n << 1) + lwork_cungbr_p__;
- maxwrk = f2cmax(i__2,i__3);
- }
- minwrk = *n * 3;
- } else if (wntuo && wntvn) {
-
- /* Path 2 (M much larger than N, JOBU='O', JOBVT='N') */
-
- wrkbl = *n + lwork_cgeqrf__;
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n + lwork_cungqr_n__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n;
- maxwrk = f2cmax(i__2,i__3);
- minwrk = (*n << 1) + *m;
- } else if (wntuo && wntvas) {
-
- /* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or */
- /* 'A') */
-
- wrkbl = *n + lwork_cgeqrf__;
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n + lwork_cungqr_n__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_p__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n;
- maxwrk = f2cmax(i__2,i__3);
- minwrk = (*n << 1) + *m;
- } else if (wntus && wntvn) {
-
- /* Path 4 (M much larger than N, JOBU='S', JOBVT='N') */
-
- wrkbl = *n + lwork_cgeqrf__;
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n + lwork_cungqr_n__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
- wrkbl = f2cmax(i__2,i__3);
- maxwrk = *n * *n + wrkbl;
- minwrk = (*n << 1) + *m;
- } else if (wntus && wntvo) {
-
- /* Path 5 (M much larger than N, JOBU='S', JOBVT='O') */
-
- wrkbl = *n + lwork_cgeqrf__;
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n + lwork_cungqr_n__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_p__;
- wrkbl = f2cmax(i__2,i__3);
- maxwrk = (*n << 1) * *n + wrkbl;
- minwrk = (*n << 1) + *m;
- } else if (wntus && wntvas) {
-
- /* Path 6 (M much larger than N, JOBU='S', JOBVT='S' or */
- /* 'A') */
-
- wrkbl = *n + lwork_cgeqrf__;
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n + lwork_cungqr_n__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_p__;
- wrkbl = f2cmax(i__2,i__3);
- maxwrk = *n * *n + wrkbl;
- minwrk = (*n << 1) + *m;
- } else if (wntua && wntvn) {
-
- /* Path 7 (M much larger than N, JOBU='A', JOBVT='N') */
-
- wrkbl = *n + lwork_cgeqrf__;
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n + lwork_cungqr_m__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
- wrkbl = f2cmax(i__2,i__3);
- maxwrk = *n * *n + wrkbl;
- minwrk = (*n << 1) + *m;
- } else if (wntua && wntvo) {
-
- /* Path 8 (M much larger than N, JOBU='A', JOBVT='O') */
-
- wrkbl = *n + lwork_cgeqrf__;
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n + lwork_cungqr_m__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_p__;
- wrkbl = f2cmax(i__2,i__3);
- maxwrk = (*n << 1) * *n + wrkbl;
- minwrk = (*n << 1) + *m;
- } else if (wntua && wntvas) {
-
- /* Path 9 (M much larger than N, JOBU='A', JOBVT='S' or */
- /* 'A') */
-
- wrkbl = *n + lwork_cgeqrf__;
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n + lwork_cungqr_m__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_p__;
- wrkbl = f2cmax(i__2,i__3);
- maxwrk = *n * *n + wrkbl;
- minwrk = (*n << 1) + *m;
- }
- } else {
-
- /* Path 10 (M at least N, but not much larger) */
-
- cgebrd_(m, n, &a[a_offset], lda, &s[1], dum, cdum, cdum, cdum,
- &c_n1, &ierr);
- lwork_cgebrd__ = (integer) cdum[0].r;
- maxwrk = (*n << 1) + lwork_cgebrd__;
- if (wntus || wntuo) {
- cungbr_("Q", m, n, n, &a[a_offset], lda, cdum, cdum, &
- c_n1, &ierr);
- lwork_cungbr_q__ = (integer) cdum[0].r;
- /* Computing MAX */
- i__2 = maxwrk, i__3 = (*n << 1) + lwork_cungbr_q__;
- maxwrk = f2cmax(i__2,i__3);
- }
- if (wntua) {
- cungbr_("Q", m, m, n, &a[a_offset], lda, cdum, cdum, &
- c_n1, &ierr);
- lwork_cungbr_q__ = (integer) cdum[0].r;
- /* Computing MAX */
- i__2 = maxwrk, i__3 = (*n << 1) + lwork_cungbr_q__;
- maxwrk = f2cmax(i__2,i__3);
- }
- if (! wntvn) {
- /* Computing MAX */
- i__2 = maxwrk, i__3 = (*n << 1) + lwork_cungbr_p__;
- maxwrk = f2cmax(i__2,i__3);
- }
- minwrk = (*n << 1) + *m;
- }
- } else if (minmn > 0) {
-
- /* Space needed for CBDSQR is BDSPAC = 5*M */
-
- /* 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, "CGESVD", ch__1, m, n, &c__0, &c__0, (
- ftnlen)6, (ftnlen)2);
- /* Compute space needed for CGELQF */
- cgelqf_(m, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
- lwork_cgelqf__ = (integer) cdum[0].r;
- /* Compute space needed for CUNGLQ */
- cunglq_(n, n, m, cdum, n, cdum, cdum, &c_n1, &ierr);
- lwork_cunglq_n__ = (integer) cdum[0].r;
- cunglq_(m, n, m, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
- lwork_cunglq_m__ = (integer) cdum[0].r;
- /* Compute space needed for CGEBRD */
- cgebrd_(m, m, &a[a_offset], lda, &s[1], dum, cdum, cdum, cdum, &
- c_n1, &ierr);
- lwork_cgebrd__ = (integer) cdum[0].r;
- /* Compute space needed for CUNGBR P */
- cungbr_("P", m, m, m, &a[a_offset], n, cdum, cdum, &c_n1, &ierr);
- lwork_cungbr_p__ = (integer) cdum[0].r;
- /* Compute space needed for CUNGBR Q */
- cungbr_("Q", m, m, m, &a[a_offset], n, cdum, cdum, &c_n1, &ierr);
- lwork_cungbr_q__ = (integer) cdum[0].r;
- if (*n >= mnthr) {
- if (wntvn) {
-
- /* Path 1t(N much larger than M, JOBVT='N') */
-
- maxwrk = *m + lwork_cgelqf__;
- /* Computing MAX */
- i__2 = maxwrk, i__3 = (*m << 1) + lwork_cgebrd__;
- maxwrk = f2cmax(i__2,i__3);
- if (wntuo || wntuas) {
- /* Computing MAX */
- i__2 = maxwrk, i__3 = (*m << 1) + lwork_cungbr_q__;
- maxwrk = f2cmax(i__2,i__3);
- }
- minwrk = *m * 3;
- } else if (wntvo && wntun) {
-
- /* Path 2t(N much larger than M, JOBU='N', JOBVT='O') */
-
- wrkbl = *m + lwork_cgelqf__;
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m + lwork_cunglq_m__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n;
- maxwrk = f2cmax(i__2,i__3);
- minwrk = (*m << 1) + *n;
- } else if (wntvo && wntuas) {
-
- /* Path 3t(N much larger than M, JOBU='S' or 'A', */
- /* JOBVT='O') */
-
- wrkbl = *m + lwork_cgelqf__;
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m + lwork_cunglq_m__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_q__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n;
- maxwrk = f2cmax(i__2,i__3);
- minwrk = (*m << 1) + *n;
- } else if (wntvs && wntun) {
-
- /* Path 4t(N much larger than M, JOBU='N', JOBVT='S') */
-
- wrkbl = *m + lwork_cgelqf__;
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m + lwork_cunglq_m__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
- wrkbl = f2cmax(i__2,i__3);
- maxwrk = *m * *m + wrkbl;
- minwrk = (*m << 1) + *n;
- } else if (wntvs && wntuo) {
-
- /* Path 5t(N much larger than M, JOBU='O', JOBVT='S') */
-
- wrkbl = *m + lwork_cgelqf__;
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m + lwork_cunglq_m__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_q__;
- wrkbl = f2cmax(i__2,i__3);
- maxwrk = (*m << 1) * *m + wrkbl;
- minwrk = (*m << 1) + *n;
- } else if (wntvs && wntuas) {
-
- /* Path 6t(N much larger than M, JOBU='S' or 'A', */
- /* JOBVT='S') */
-
- wrkbl = *m + lwork_cgelqf__;
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m + lwork_cunglq_m__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_q__;
- wrkbl = f2cmax(i__2,i__3);
- maxwrk = *m * *m + wrkbl;
- minwrk = (*m << 1) + *n;
- } else if (wntva && wntun) {
-
- /* Path 7t(N much larger than M, JOBU='N', JOBVT='A') */
-
- wrkbl = *m + lwork_cgelqf__;
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m + lwork_cunglq_n__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
- wrkbl = f2cmax(i__2,i__3);
- maxwrk = *m * *m + wrkbl;
- minwrk = (*m << 1) + *n;
- } else if (wntva && wntuo) {
-
- /* Path 8t(N much larger than M, JOBU='O', JOBVT='A') */
-
- wrkbl = *m + lwork_cgelqf__;
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m + lwork_cunglq_n__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_q__;
- wrkbl = f2cmax(i__2,i__3);
- maxwrk = (*m << 1) * *m + wrkbl;
- minwrk = (*m << 1) + *n;
- } else if (wntva && wntuas) {
-
- /* Path 9t(N much larger than M, JOBU='S' or 'A', */
- /* JOBVT='A') */
-
- wrkbl = *m + lwork_cgelqf__;
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m + lwork_cunglq_n__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
- wrkbl = f2cmax(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_q__;
- wrkbl = f2cmax(i__2,i__3);
- maxwrk = *m * *m + wrkbl;
- minwrk = (*m << 1) + *n;
- }
- } else {
-
- /* Path 10t(N greater than M, but not much larger) */
-
- cgebrd_(m, n, &a[a_offset], lda, &s[1], dum, cdum, cdum, cdum,
- &c_n1, &ierr);
- lwork_cgebrd__ = (integer) cdum[0].r;
- maxwrk = (*m << 1) + lwork_cgebrd__;
- if (wntvs || wntvo) {
- /* Compute space needed for CUNGBR P */
- cungbr_("P", m, n, m, &a[a_offset], n, cdum, cdum, &c_n1,
- &ierr);
- lwork_cungbr_p__ = (integer) cdum[0].r;
- /* Computing MAX */
- i__2 = maxwrk, i__3 = (*m << 1) + lwork_cungbr_p__;
- maxwrk = f2cmax(i__2,i__3);
- }
- if (wntva) {
- cungbr_("P", n, n, m, &a[a_offset], n, cdum, cdum, &c_n1,
- &ierr);
- lwork_cungbr_p__ = (integer) cdum[0].r;
- /* Computing MAX */
- i__2 = maxwrk, i__3 = (*m << 1) + lwork_cungbr_p__;
- maxwrk = f2cmax(i__2,i__3);
- }
- if (! wntun) {
- /* Computing MAX */
- i__2 = maxwrk, i__3 = (*m << 1) + lwork_cungbr_q__;
- maxwrk = f2cmax(i__2,i__3);
- }
- minwrk = (*m << 1) + *n;
- }
- }
- maxwrk = f2cmax(minwrk,maxwrk);
- work[1].r = (real) maxwrk, work[1].i = 0.f;
-
- if (*lwork < minwrk && ! lquery) {
- *info = -13;
- }
- }
-
- if (*info != 0) {
- i__2 = -(*info);
- xerbla_("CGESVD", &i__2, (ftnlen)6);
- return 0;
- } else if (lquery) {
- return 0;
- }
-
- /* Quick return if possible */
-
- if (*m == 0 || *n == 0) {
- return 0;
- }
-
- /* Get machine constants */
-
- eps = slamch_("P");
- smlnum = sqrt(slamch_("S")) / eps;
- bignum = 1.f / smlnum;
-
- /* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
-
- anrm = clange_("M", m, n, &a[a_offset], lda, dum);
- iscl = 0;
- if (anrm > 0.f && anrm < smlnum) {
- iscl = 1;
- clascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, &
- ierr);
- } else if (anrm > bignum) {
- iscl = 1;
- clascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, &
- ierr);
- }
-
- if (*m >= *n) {
-
- /* A has at least as many rows as columns. If A has sufficiently */
- /* more rows than columns, first reduce using the QR */
- /* decomposition (if sufficient workspace available) */
-
- if (*m >= mnthr) {
-
- if (wntun) {
-
- /* Path 1 (M much larger than N, JOBU='N') */
- /* No left singular vectors to be computed */
-
- itau = 1;
- iwork = itau + *n;
-
- /* Compute A=Q*R */
- /* (CWorkspace: need 2*N, prefer N+N*NB) */
- /* (RWorkspace: need 0) */
-
- i__2 = *lwork - iwork + 1;
- cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &
- i__2, &ierr);
-
- /* Zero out below R */
-
- if (*n > 1) {
- i__2 = *n - 1;
- i__3 = *n - 1;
- claset_("L", &i__2, &i__3, &c_b1, &c_b1, &a[a_dim1 + 2],
- lda);
- }
- ie = 1;
- itauq = 1;
- itaup = itauq + *n;
- iwork = itaup + *n;
-
- /* Bidiagonalize R in A */
- /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
- /* (RWorkspace: need N) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
- itauq], &work[itaup], &work[iwork], &i__2, &ierr);
- ncvt = 0;
- if (wntvo || wntvas) {
-
- /* If right singular vectors desired, generate P'. */
- /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &
- work[iwork], &i__2, &ierr);
- ncvt = *n;
- }
- irwork = ie + *n;
-
- /* Perform bidiagonal QR iteration, computing right */
- /* singular vectors of A in A if desired */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", n, &ncvt, &c__0, &c__0, &s[1], &rwork[ie], &a[
- a_offset], lda, cdum, &c__1, cdum, &c__1, &rwork[
- irwork], info);
-
- /* If right singular vectors desired in VT, copy them there */
-
- if (wntvas) {
- clacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- }
-
- } else if (wntuo && wntvn) {
-
- /* Path 2 (M much larger than N, JOBU='O', JOBVT='N') */
- /* N left singular vectors to be overwritten on A and */
- /* no right singular vectors to be computed */
-
- if (*lwork >= *n * *n + *n * 3) {
-
- /* Sufficient workspace for a fast algorithm */
-
- ir = 1;
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *lda * *n;
- if (*lwork >= f2cmax(i__2,i__3) + *lda * *n) {
-
- /* WORK(IU) is LDA by N, WORK(IR) is LDA by N */
-
- ldwrku = *lda;
- ldwrkr = *lda;
- } else /* if(complicated condition) */ {
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *lda * *n;
- if (*lwork >= f2cmax(i__2,i__3) + *n * *n) {
-
- /* WORK(IU) is LDA by N, WORK(IR) is N by N */
-
- ldwrku = *lda;
- ldwrkr = *n;
- } else {
-
- /* WORK(IU) is LDWRKU by N, WORK(IR) is N by N */
-
- ldwrku = (*lwork - *n * *n) / *n;
- ldwrkr = *n;
- }
- }
- itau = ir + ldwrkr * *n;
- iwork = itau + *n;
-
- /* Compute A=Q*R */
- /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
- , &i__2, &ierr);
-
- /* Copy R to WORK(IR) and zero out below it */
-
- clacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
- i__2 = *n - 1;
- i__3 = *n - 1;
- claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[ir + 1], &
- ldwrkr);
-
- /* Generate Q in A */
- /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *n;
- iwork = itaup + *n;
-
- /* Bidiagonalize R in WORK(IR) */
- /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
- /* (RWorkspace: need N) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &i__2, &
- ierr);
-
- /* Generate left vectors bidiagonalizing R */
- /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
- /* (RWorkspace: need 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], &
- work[iwork], &i__2, &ierr);
- irwork = ie + *n;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of R in WORK(IR) */
- /* (CWorkspace: need N*N) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", n, &c__0, n, &c__0, &s[1], &rwork[ie], cdum,
- &c__1, &work[ir], &ldwrkr, cdum, &c__1, &rwork[
- irwork], info);
- iu = itauq;
-
- /* Multiply Q in A by left singular vectors of R in */
- /* WORK(IR), storing result in WORK(IU) and copying to A */
- /* (CWorkspace: need N*N+N, prefer N*N+M*N) */
- /* (RWorkspace: 0) */
-
- i__2 = *m;
- i__3 = ldwrku;
- for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
- i__3) {
- /* Computing MIN */
- i__4 = *m - i__ + 1;
- chunk = f2cmin(i__4,ldwrku);
- cgemm_("N", "N", &chunk, n, n, &c_b2, &a[i__ + a_dim1]
- , lda, &work[ir], &ldwrkr, &c_b1, &work[iu], &
- ldwrku);
- clacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
- a_dim1], lda);
- /* L10: */
- }
-
- } else {
-
- /* Insufficient workspace for a fast algorithm */
-
- ie = 1;
- itauq = 1;
- itaup = itauq + *n;
- iwork = itaup + *n;
-
- /* Bidiagonalize A */
- /* (CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB) */
- /* (RWorkspace: N) */
-
- i__3 = *lwork - iwork + 1;
- cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
- itauq], &work[itaup], &work[iwork], &i__3, &ierr);
-
- /* Generate left vectors bidiagonalizing A */
- /* (CWorkspace: need 3*N, prefer 2*N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__3 = *lwork - iwork + 1;
- cungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &
- work[iwork], &i__3, &ierr);
- irwork = ie + *n;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in A */
- /* (CWorkspace: need 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", n, &c__0, m, &c__0, &s[1], &rwork[ie], cdum,
- &c__1, &a[a_offset], lda, cdum, &c__1, &rwork[
- irwork], info);
-
- }
-
- } else if (wntuo && wntvas) {
-
- /* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or 'A') */
- /* N left singular vectors to be overwritten on A and */
- /* N right singular vectors to be computed in VT */
-
- if (*lwork >= *n * *n + *n * 3) {
-
- /* Sufficient workspace for a fast algorithm */
-
- ir = 1;
- /* Computing MAX */
- i__3 = wrkbl, i__2 = *lda * *n;
- if (*lwork >= f2cmax(i__3,i__2) + *lda * *n) {
-
- /* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
-
- ldwrku = *lda;
- ldwrkr = *lda;
- } else /* if(complicated condition) */ {
- /* Computing MAX */
- i__3 = wrkbl, i__2 = *lda * *n;
- if (*lwork >= f2cmax(i__3,i__2) + *n * *n) {
-
- /* WORK(IU) is LDA by N and WORK(IR) is N by N */
-
- ldwrku = *lda;
- ldwrkr = *n;
- } else {
-
- /* WORK(IU) is LDWRKU by N and WORK(IR) is N by N */
-
- ldwrku = (*lwork - *n * *n) / *n;
- ldwrkr = *n;
- }
- }
- itau = ir + ldwrkr * *n;
- iwork = itau + *n;
-
- /* Compute A=Q*R */
- /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__3 = *lwork - iwork + 1;
- cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
- , &i__3, &ierr);
-
- /* Copy R to VT, zeroing out below it */
-
- clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- if (*n > 1) {
- i__3 = *n - 1;
- i__2 = *n - 1;
- claset_("L", &i__3, &i__2, &c_b1, &c_b1, &vt[vt_dim1
- + 2], ldvt);
- }
-
- /* Generate Q in A */
- /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__3 = *lwork - iwork + 1;
- cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__3, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *n;
- iwork = itaup + *n;
-
- /* Bidiagonalize R in VT, copying result to WORK(IR) */
- /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
- /* (RWorkspace: need N) */
-
- i__3 = *lwork - iwork + 1;
- cgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &i__3, &
- ierr);
- clacpy_("L", n, n, &vt[vt_offset], ldvt, &work[ir], &
- ldwrkr);
-
- /* Generate left vectors bidiagonalizing R in WORK(IR) */
- /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__3 = *lwork - iwork + 1;
- cungbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], &
- work[iwork], &i__3, &ierr);
-
- /* Generate right vectors bidiagonalizing R in VT */
- /* (CWorkspace: need N*N+3*N-1, prefer N*N+2*N+(N-1)*NB) */
- /* (RWorkspace: 0) */
-
- i__3 = *lwork - iwork + 1;
- cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup],
- &work[iwork], &i__3, &ierr);
- irwork = ie + *n;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of R in WORK(IR) and computing right */
- /* singular vectors of R in VT */
- /* (CWorkspace: need N*N) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", n, n, n, &c__0, &s[1], &rwork[ie], &vt[
- vt_offset], ldvt, &work[ir], &ldwrkr, cdum, &c__1,
- &rwork[irwork], info);
- iu = itauq;
-
- /* Multiply Q in A by left singular vectors of R in */
- /* WORK(IR), storing result in WORK(IU) and copying to A */
- /* (CWorkspace: need N*N+N, prefer N*N+M*N) */
- /* (RWorkspace: 0) */
-
- i__3 = *m;
- i__2 = ldwrku;
- for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ +=
- i__2) {
- /* Computing MIN */
- i__4 = *m - i__ + 1;
- chunk = f2cmin(i__4,ldwrku);
- cgemm_("N", "N", &chunk, n, n, &c_b2, &a[i__ + a_dim1]
- , lda, &work[ir], &ldwrkr, &c_b1, &work[iu], &
- ldwrku);
- clacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
- a_dim1], lda);
- /* L20: */
- }
-
- } else {
-
- /* Insufficient workspace for a fast algorithm */
-
- itau = 1;
- iwork = itau + *n;
-
- /* Compute A=Q*R */
- /* (CWorkspace: need 2*N, prefer N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
- , &i__2, &ierr);
-
- /* Copy R to VT, zeroing out below it */
-
- clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- if (*n > 1) {
- i__2 = *n - 1;
- i__3 = *n - 1;
- claset_("L", &i__2, &i__3, &c_b1, &c_b1, &vt[vt_dim1
- + 2], ldvt);
- }
-
- /* Generate Q in A */
- /* (CWorkspace: need 2*N, prefer N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *n;
- iwork = itaup + *n;
-
- /* Bidiagonalize R in VT */
- /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
- /* (RWorkspace: N) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &i__2, &
- ierr);
-
- /* Multiply Q in A by left vectors bidiagonalizing R */
- /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunmbr_("Q", "R", "N", m, n, n, &vt[vt_offset], ldvt, &
- work[itauq], &a[a_offset], lda, &work[iwork], &
- i__2, &ierr);
-
- /* Generate right vectors bidiagonalizing R in VT */
- /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup],
- &work[iwork], &i__2, &ierr);
- irwork = ie + *n;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in A and computing right */
- /* singular vectors of A in VT */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", n, n, m, &c__0, &s[1], &rwork[ie], &vt[
- vt_offset], ldvt, &a[a_offset], lda, cdum, &c__1,
- &rwork[irwork], info);
-
- }
-
- } else if (wntus) {
-
- if (wntvn) {
-
- /* Path 4 (M much larger than N, JOBU='S', JOBVT='N') */
- /* N left singular vectors to be computed in U and */
- /* no right singular vectors to be computed */
-
- if (*lwork >= *n * *n + *n * 3) {
-
- /* Sufficient workspace for a fast algorithm */
-
- ir = 1;
- if (*lwork >= wrkbl + *lda * *n) {
-
- /* WORK(IR) is LDA by N */
-
- ldwrkr = *lda;
- } else {
-
- /* WORK(IR) is N by N */
-
- ldwrkr = *n;
- }
- itau = ir + ldwrkr * *n;
- iwork = itau + *n;
-
- /* Compute A=Q*R */
- /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
-
- /* Copy R to WORK(IR), zeroing out below it */
-
- clacpy_("U", n, n, &a[a_offset], lda, &work[ir], &
- ldwrkr);
- i__2 = *n - 1;
- i__3 = *n - 1;
- claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[ir + 1]
- , &ldwrkr);
-
- /* Generate Q in A */
- /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *n;
- iwork = itaup + *n;
-
- /* Bidiagonalize R in WORK(IR) */
- /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
- /* (RWorkspace: need N) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
-
- /* Generate left vectors bidiagonalizing R in WORK(IR) */
- /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq]
- , &work[iwork], &i__2, &ierr);
- irwork = ie + *n;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of R in WORK(IR) */
- /* (CWorkspace: need N*N) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", n, &c__0, n, &c__0, &s[1], &rwork[ie],
- cdum, &c__1, &work[ir], &ldwrkr, cdum, &c__1,
- &rwork[irwork], info);
-
- /* Multiply Q in A by left singular vectors of R in */
- /* WORK(IR), storing result in U */
- /* (CWorkspace: need N*N) */
- /* (RWorkspace: 0) */
-
- cgemm_("N", "N", m, n, n, &c_b2, &a[a_offset], lda, &
- work[ir], &ldwrkr, &c_b1, &u[u_offset], ldu);
-
- } else {
-
- /* Insufficient workspace for a fast algorithm */
-
- itau = 1;
- iwork = itau + *n;
-
- /* Compute A=Q*R, copying result to U */
- /* (CWorkspace: need 2*N, prefer N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
-
- /* Generate Q in U */
- /* (CWorkspace: need 2*N, prefer N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *n;
- iwork = itaup + *n;
-
- /* Zero out below R in A */
-
- if (*n > 1) {
- i__2 = *n - 1;
- i__3 = *n - 1;
- claset_("L", &i__2, &i__3, &c_b1, &c_b1, &a[
- a_dim1 + 2], lda);
- }
-
- /* Bidiagonalize R in A */
- /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
- /* (RWorkspace: need N) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
-
- /* Multiply Q in U by left vectors bidiagonalizing R */
- /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunmbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
- work[itauq], &u[u_offset], ldu, &work[iwork],
- &i__2, &ierr)
- ;
- irwork = ie + *n;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in U */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", n, &c__0, m, &c__0, &s[1], &rwork[ie],
- cdum, &c__1, &u[u_offset], ldu, cdum, &c__1, &
- rwork[irwork], info);
-
- }
-
- } else if (wntvo) {
-
- /* Path 5 (M much larger than N, JOBU='S', JOBVT='O') */
- /* N left singular vectors to be computed in U and */
- /* N right singular vectors to be overwritten on A */
-
- if (*lwork >= (*n << 1) * *n + *n * 3) {
-
- /* Sufficient workspace for a fast algorithm */
-
- iu = 1;
- if (*lwork >= wrkbl + (*lda << 1) * *n) {
-
- /* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
-
- ldwrku = *lda;
- ir = iu + ldwrku * *n;
- ldwrkr = *lda;
- } else if (*lwork >= wrkbl + (*lda + *n) * *n) {
-
- /* WORK(IU) is LDA by N and WORK(IR) is N by N */
-
- ldwrku = *lda;
- ir = iu + ldwrku * *n;
- ldwrkr = *n;
- } else {
-
- /* WORK(IU) is N by N and WORK(IR) is N by N */
-
- ldwrku = *n;
- ir = iu + ldwrku * *n;
- ldwrkr = *n;
- }
- itau = ir + ldwrkr * *n;
- iwork = itau + *n;
-
- /* Compute A=Q*R */
- /* (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
-
- /* Copy R to WORK(IU), zeroing out below it */
-
- clacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
- ldwrku);
- i__2 = *n - 1;
- i__3 = *n - 1;
- claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[iu + 1]
- , &ldwrku);
-
- /* Generate Q in A */
- /* (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *n;
- iwork = itaup + *n;
-
- /* Bidiagonalize R in WORK(IU), copying result to */
- /* WORK(IR) */
- /* (CWorkspace: need 2*N*N+3*N, */
- /* prefer 2*N*N+2*N+2*N*NB) */
- /* (RWorkspace: need N) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(n, n, &work[iu], &ldwrku, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- clacpy_("U", n, n, &work[iu], &ldwrku, &work[ir], &
- ldwrkr);
-
- /* Generate left bidiagonalizing vectors in WORK(IU) */
- /* (CWorkspace: need 2*N*N+3*N, prefer 2*N*N+2*N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
- , &work[iwork], &i__2, &ierr);
-
- /* Generate right bidiagonalizing vectors in WORK(IR) */
- /* (CWorkspace: need 2*N*N+3*N-1, */
- /* prefer 2*N*N+2*N+(N-1)*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("P", n, n, n, &work[ir], &ldwrkr, &work[itaup]
- , &work[iwork], &i__2, &ierr);
- irwork = ie + *n;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of R in WORK(IU) and computing */
- /* right singular vectors of R in WORK(IR) */
- /* (CWorkspace: need 2*N*N) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", n, n, n, &c__0, &s[1], &rwork[ie], &work[
- ir], &ldwrkr, &work[iu], &ldwrku, cdum, &c__1,
- &rwork[irwork], info);
-
- /* Multiply Q in A by left singular vectors of R in */
- /* WORK(IU), storing result in U */
- /* (CWorkspace: need N*N) */
- /* (RWorkspace: 0) */
-
- cgemm_("N", "N", m, n, n, &c_b2, &a[a_offset], lda, &
- work[iu], &ldwrku, &c_b1, &u[u_offset], ldu);
-
- /* Copy right singular vectors of R to A */
- /* (CWorkspace: need N*N) */
- /* (RWorkspace: 0) */
-
- clacpy_("F", n, n, &work[ir], &ldwrkr, &a[a_offset],
- lda);
-
- } else {
-
- /* Insufficient workspace for a fast algorithm */
-
- itau = 1;
- iwork = itau + *n;
-
- /* Compute A=Q*R, copying result to U */
- /* (CWorkspace: need 2*N, prefer N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
-
- /* Generate Q in U */
- /* (CWorkspace: need 2*N, prefer N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *n;
- iwork = itaup + *n;
-
- /* Zero out below R in A */
-
- if (*n > 1) {
- i__2 = *n - 1;
- i__3 = *n - 1;
- claset_("L", &i__2, &i__3, &c_b1, &c_b1, &a[
- a_dim1 + 2], lda);
- }
-
- /* Bidiagonalize R in A */
- /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
- /* (RWorkspace: need N) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
-
- /* Multiply Q in U by left vectors bidiagonalizing R */
- /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunmbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
- work[itauq], &u[u_offset], ldu, &work[iwork],
- &i__2, &ierr)
- ;
-
- /* Generate right vectors bidiagonalizing R in A */
- /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("P", n, n, n, &a[a_offset], lda, &work[itaup],
- &work[iwork], &i__2, &ierr);
- irwork = ie + *n;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in U and computing right */
- /* singular vectors of A in A */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", n, n, m, &c__0, &s[1], &rwork[ie], &a[
- a_offset], lda, &u[u_offset], ldu, cdum, &
- c__1, &rwork[irwork], info);
-
- }
-
- } else if (wntvas) {
-
- /* Path 6 (M much larger than N, JOBU='S', JOBVT='S' */
- /* or 'A') */
- /* N left singular vectors to be computed in U and */
- /* N right singular vectors to be computed in VT */
-
- if (*lwork >= *n * *n + *n * 3) {
-
- /* Sufficient workspace for a fast algorithm */
-
- iu = 1;
- if (*lwork >= wrkbl + *lda * *n) {
-
- /* WORK(IU) is LDA by N */
-
- ldwrku = *lda;
- } else {
-
- /* WORK(IU) is N by N */
-
- ldwrku = *n;
- }
- itau = iu + ldwrku * *n;
- iwork = itau + *n;
-
- /* Compute A=Q*R */
- /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
-
- /* Copy R to WORK(IU), zeroing out below it */
-
- clacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
- ldwrku);
- i__2 = *n - 1;
- i__3 = *n - 1;
- claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[iu + 1]
- , &ldwrku);
-
- /* Generate Q in A */
- /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *n;
- iwork = itaup + *n;
-
- /* Bidiagonalize R in WORK(IU), copying result to VT */
- /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
- /* (RWorkspace: need N) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(n, n, &work[iu], &ldwrku, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- clacpy_("U", n, n, &work[iu], &ldwrku, &vt[vt_offset],
- ldvt);
-
- /* Generate left bidiagonalizing vectors in WORK(IU) */
- /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
- , &work[iwork], &i__2, &ierr);
-
- /* Generate right bidiagonalizing vectors in VT */
- /* (CWorkspace: need N*N+3*N-1, */
- /* prefer N*N+2*N+(N-1)*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
- itaup], &work[iwork], &i__2, &ierr)
- ;
- irwork = ie + *n;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of R in WORK(IU) and computing */
- /* right singular vectors of R in VT */
- /* (CWorkspace: need N*N) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", n, n, n, &c__0, &s[1], &rwork[ie], &vt[
- vt_offset], ldvt, &work[iu], &ldwrku, cdum, &
- c__1, &rwork[irwork], info);
-
- /* Multiply Q in A by left singular vectors of R in */
- /* WORK(IU), storing result in U */
- /* (CWorkspace: need N*N) */
- /* (RWorkspace: 0) */
-
- cgemm_("N", "N", m, n, n, &c_b2, &a[a_offset], lda, &
- work[iu], &ldwrku, &c_b1, &u[u_offset], ldu);
-
- } else {
-
- /* Insufficient workspace for a fast algorithm */
-
- itau = 1;
- iwork = itau + *n;
-
- /* Compute A=Q*R, copying result to U */
- /* (CWorkspace: need 2*N, prefer N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
-
- /* Generate Q in U */
- /* (CWorkspace: need 2*N, prefer N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
- work[iwork], &i__2, &ierr);
-
- /* Copy R to VT, zeroing out below it */
-
- clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- if (*n > 1) {
- i__2 = *n - 1;
- i__3 = *n - 1;
- claset_("L", &i__2, &i__3, &c_b1, &c_b1, &vt[
- vt_dim1 + 2], ldvt);
- }
- ie = 1;
- itauq = itau;
- itaup = itauq + *n;
- iwork = itaup + *n;
-
- /* Bidiagonalize R in VT */
- /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
- /* (RWorkspace: need N) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &rwork[ie],
- &work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
-
- /* Multiply Q in U by left bidiagonalizing vectors */
- /* in VT */
- /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunmbr_("Q", "R", "N", m, n, n, &vt[vt_offset], ldvt,
- &work[itauq], &u[u_offset], ldu, &work[iwork],
- &i__2, &ierr);
-
- /* Generate right bidiagonalizing vectors in VT */
- /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
- itaup], &work[iwork], &i__2, &ierr)
- ;
- irwork = ie + *n;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in U and computing right */
- /* singular vectors of A in VT */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", n, n, m, &c__0, &s[1], &rwork[ie], &vt[
- vt_offset], ldvt, &u[u_offset], ldu, cdum, &
- c__1, &rwork[irwork], info);
-
- }
-
- }
-
- } else if (wntua) {
-
- if (wntvn) {
-
- /* Path 7 (M much larger than N, JOBU='A', JOBVT='N') */
- /* M left singular vectors to be computed in U and */
- /* no right singular vectors to be computed */
-
- /* Computing MAX */
- i__2 = *n + *m, i__3 = *n * 3;
- if (*lwork >= *n * *n + f2cmax(i__2,i__3)) {
-
- /* Sufficient workspace for a fast algorithm */
-
- ir = 1;
- if (*lwork >= wrkbl + *lda * *n) {
-
- /* WORK(IR) is LDA by N */
-
- ldwrkr = *lda;
- } else {
-
- /* WORK(IR) is N by N */
-
- ldwrkr = *n;
- }
- itau = ir + ldwrkr * *n;
- iwork = itau + *n;
-
- /* Compute A=Q*R, copying result to U */
- /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
-
- /* Copy R to WORK(IR), zeroing out below it */
-
- clacpy_("U", n, n, &a[a_offset], lda, &work[ir], &
- ldwrkr);
- i__2 = *n - 1;
- i__3 = *n - 1;
- claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[ir + 1]
- , &ldwrkr);
-
- /* Generate Q in U */
- /* (CWorkspace: need N*N+N+M, prefer N*N+N+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *n;
- iwork = itaup + *n;
-
- /* Bidiagonalize R in WORK(IR) */
- /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
- /* (RWorkspace: need N) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
-
- /* Generate left bidiagonalizing vectors in WORK(IR) */
- /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq]
- , &work[iwork], &i__2, &ierr);
- irwork = ie + *n;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of R in WORK(IR) */
- /* (CWorkspace: need N*N) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", n, &c__0, n, &c__0, &s[1], &rwork[ie],
- cdum, &c__1, &work[ir], &ldwrkr, cdum, &c__1,
- &rwork[irwork], info);
-
- /* Multiply Q in U by left singular vectors of R in */
- /* WORK(IR), storing result in A */
- /* (CWorkspace: need N*N) */
- /* (RWorkspace: 0) */
-
- cgemm_("N", "N", m, n, n, &c_b2, &u[u_offset], ldu, &
- work[ir], &ldwrkr, &c_b1, &a[a_offset], lda);
-
- /* Copy left singular vectors of A from A to U */
-
- clacpy_("F", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
-
- } else {
-
- /* Insufficient workspace for a fast algorithm */
-
- itau = 1;
- iwork = itau + *n;
-
- /* Compute A=Q*R, copying result to U */
- /* (CWorkspace: need 2*N, prefer N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
-
- /* Generate Q in U */
- /* (CWorkspace: need N+M, prefer N+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *n;
- iwork = itaup + *n;
-
- /* Zero out below R in A */
-
- if (*n > 1) {
- i__2 = *n - 1;
- i__3 = *n - 1;
- claset_("L", &i__2, &i__3, &c_b1, &c_b1, &a[
- a_dim1 + 2], lda);
- }
-
- /* Bidiagonalize R in A */
- /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
- /* (RWorkspace: need N) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
-
- /* Multiply Q in U by left bidiagonalizing vectors */
- /* in A */
- /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunmbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
- work[itauq], &u[u_offset], ldu, &work[iwork],
- &i__2, &ierr)
- ;
- irwork = ie + *n;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in U */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", n, &c__0, m, &c__0, &s[1], &rwork[ie],
- cdum, &c__1, &u[u_offset], ldu, cdum, &c__1, &
- rwork[irwork], info);
-
- }
-
- } else if (wntvo) {
-
- /* Path 8 (M much larger than N, JOBU='A', JOBVT='O') */
- /* M left singular vectors to be computed in U and */
- /* N right singular vectors to be overwritten on A */
-
- /* Computing MAX */
- i__2 = *n + *m, i__3 = *n * 3;
- if (*lwork >= (*n << 1) * *n + f2cmax(i__2,i__3)) {
-
- /* Sufficient workspace for a fast algorithm */
-
- iu = 1;
- if (*lwork >= wrkbl + (*lda << 1) * *n) {
-
- /* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
-
- ldwrku = *lda;
- ir = iu + ldwrku * *n;
- ldwrkr = *lda;
- } else if (*lwork >= wrkbl + (*lda + *n) * *n) {
-
- /* WORK(IU) is LDA by N and WORK(IR) is N by N */
-
- ldwrku = *lda;
- ir = iu + ldwrku * *n;
- ldwrkr = *n;
- } else {
-
- /* WORK(IU) is N by N and WORK(IR) is N by N */
-
- ldwrku = *n;
- ir = iu + ldwrku * *n;
- ldwrkr = *n;
- }
- itau = ir + ldwrkr * *n;
- iwork = itau + *n;
-
- /* Compute A=Q*R, copying result to U */
- /* (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
-
- /* Generate Q in U */
- /* (CWorkspace: need 2*N*N+N+M, prefer 2*N*N+N+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
- work[iwork], &i__2, &ierr);
-
- /* Copy R to WORK(IU), zeroing out below it */
-
- clacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
- ldwrku);
- i__2 = *n - 1;
- i__3 = *n - 1;
- claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[iu + 1]
- , &ldwrku);
- ie = 1;
- itauq = itau;
- itaup = itauq + *n;
- iwork = itaup + *n;
-
- /* Bidiagonalize R in WORK(IU), copying result to */
- /* WORK(IR) */
- /* (CWorkspace: need 2*N*N+3*N, */
- /* prefer 2*N*N+2*N+2*N*NB) */
- /* (RWorkspace: need N) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(n, n, &work[iu], &ldwrku, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- clacpy_("U", n, n, &work[iu], &ldwrku, &work[ir], &
- ldwrkr);
-
- /* Generate left bidiagonalizing vectors in WORK(IU) */
- /* (CWorkspace: need 2*N*N+3*N, prefer 2*N*N+2*N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
- , &work[iwork], &i__2, &ierr);
-
- /* Generate right bidiagonalizing vectors in WORK(IR) */
- /* (CWorkspace: need 2*N*N+3*N-1, */
- /* prefer 2*N*N+2*N+(N-1)*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("P", n, n, n, &work[ir], &ldwrkr, &work[itaup]
- , &work[iwork], &i__2, &ierr);
- irwork = ie + *n;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of R in WORK(IU) and computing */
- /* right singular vectors of R in WORK(IR) */
- /* (CWorkspace: need 2*N*N) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", n, n, n, &c__0, &s[1], &rwork[ie], &work[
- ir], &ldwrkr, &work[iu], &ldwrku, cdum, &c__1,
- &rwork[irwork], info);
-
- /* Multiply Q in U by left singular vectors of R in */
- /* WORK(IU), storing result in A */
- /* (CWorkspace: need N*N) */
- /* (RWorkspace: 0) */
-
- cgemm_("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 */
-
- clacpy_("F", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
-
- /* Copy right singular vectors of R from WORK(IR) to A */
-
- clacpy_("F", n, n, &work[ir], &ldwrkr, &a[a_offset],
- lda);
-
- } else {
-
- /* Insufficient workspace for a fast algorithm */
-
- itau = 1;
- iwork = itau + *n;
-
- /* Compute A=Q*R, copying result to U */
- /* (CWorkspace: need 2*N, prefer N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
-
- /* Generate Q in U */
- /* (CWorkspace: need N+M, prefer N+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *n;
- iwork = itaup + *n;
-
- /* Zero out below R in A */
-
- if (*n > 1) {
- i__2 = *n - 1;
- i__3 = *n - 1;
- claset_("L", &i__2, &i__3, &c_b1, &c_b1, &a[
- a_dim1 + 2], lda);
- }
-
- /* Bidiagonalize R in A */
- /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
- /* (RWorkspace: need N) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
-
- /* Multiply Q in U by left bidiagonalizing vectors */
- /* in A */
- /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunmbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
- work[itauq], &u[u_offset], ldu, &work[iwork],
- &i__2, &ierr)
- ;
-
- /* Generate right bidiagonalizing vectors in A */
- /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("P", n, n, n, &a[a_offset], lda, &work[itaup],
- &work[iwork], &i__2, &ierr);
- irwork = ie + *n;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in U and computing right */
- /* singular vectors of A in A */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", n, n, m, &c__0, &s[1], &rwork[ie], &a[
- a_offset], lda, &u[u_offset], ldu, cdum, &
- c__1, &rwork[irwork], info);
-
- }
-
- } else if (wntvas) {
-
- /* Path 9 (M much larger than N, JOBU='A', JOBVT='S' */
- /* or 'A') */
- /* M left singular vectors to be computed in U and */
- /* N right singular vectors to be computed in VT */
-
- /* Computing MAX */
- i__2 = *n + *m, i__3 = *n * 3;
- if (*lwork >= *n * *n + f2cmax(i__2,i__3)) {
-
- /* Sufficient workspace for a fast algorithm */
-
- iu = 1;
- if (*lwork >= wrkbl + *lda * *n) {
-
- /* WORK(IU) is LDA by N */
-
- ldwrku = *lda;
- } else {
-
- /* WORK(IU) is N by N */
-
- ldwrku = *n;
- }
- itau = iu + ldwrku * *n;
- iwork = itau + *n;
-
- /* Compute A=Q*R, copying result to U */
- /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
-
- /* Generate Q in U */
- /* (CWorkspace: need N*N+N+M, prefer N*N+N+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
- work[iwork], &i__2, &ierr);
-
- /* Copy R to WORK(IU), zeroing out below it */
-
- clacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
- ldwrku);
- i__2 = *n - 1;
- i__3 = *n - 1;
- claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[iu + 1]
- , &ldwrku);
- ie = 1;
- itauq = itau;
- itaup = itauq + *n;
- iwork = itaup + *n;
-
- /* Bidiagonalize R in WORK(IU), copying result to VT */
- /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
- /* (RWorkspace: need N) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(n, n, &work[iu], &ldwrku, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- clacpy_("U", n, n, &work[iu], &ldwrku, &vt[vt_offset],
- ldvt);
-
- /* Generate left bidiagonalizing vectors in WORK(IU) */
- /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
- , &work[iwork], &i__2, &ierr);
-
- /* Generate right bidiagonalizing vectors in VT */
- /* (CWorkspace: need N*N+3*N-1, */
- /* prefer N*N+2*N+(N-1)*NB) */
- /* (RWorkspace: need 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
- itaup], &work[iwork], &i__2, &ierr)
- ;
- irwork = ie + *n;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of R in WORK(IU) and computing */
- /* right singular vectors of R in VT */
- /* (CWorkspace: need N*N) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", n, n, n, &c__0, &s[1], &rwork[ie], &vt[
- vt_offset], ldvt, &work[iu], &ldwrku, cdum, &
- c__1, &rwork[irwork], info);
-
- /* Multiply Q in U by left singular vectors of R in */
- /* WORK(IU), storing result in A */
- /* (CWorkspace: need N*N) */
- /* (RWorkspace: 0) */
-
- cgemm_("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 */
-
- clacpy_("F", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
-
- } else {
-
- /* Insufficient workspace for a fast algorithm */
-
- itau = 1;
- iwork = itau + *n;
-
- /* Compute A=Q*R, copying result to U */
- /* (CWorkspace: need 2*N, prefer N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
-
- /* Generate Q in U */
- /* (CWorkspace: need N+M, prefer N+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
- work[iwork], &i__2, &ierr);
-
- /* Copy R from A to VT, zeroing out below it */
-
- clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- if (*n > 1) {
- i__2 = *n - 1;
- i__3 = *n - 1;
- claset_("L", &i__2, &i__3, &c_b1, &c_b1, &vt[
- vt_dim1 + 2], ldvt);
- }
- ie = 1;
- itauq = itau;
- itaup = itauq + *n;
- iwork = itaup + *n;
-
- /* Bidiagonalize R in VT */
- /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
- /* (RWorkspace: need N) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &rwork[ie],
- &work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
-
- /* Multiply Q in U by left bidiagonalizing vectors */
- /* in VT */
- /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunmbr_("Q", "R", "N", m, n, n, &vt[vt_offset], ldvt,
- &work[itauq], &u[u_offset], ldu, &work[iwork],
- &i__2, &ierr);
-
- /* Generate right bidiagonalizing vectors in VT */
- /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
- itaup], &work[iwork], &i__2, &ierr)
- ;
- irwork = ie + *n;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in U and computing right */
- /* singular vectors of A in VT */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", n, n, m, &c__0, &s[1], &rwork[ie], &vt[
- vt_offset], ldvt, &u[u_offset], ldu, cdum, &
- c__1, &rwork[irwork], info);
-
- }
-
- }
-
- }
-
- } else {
-
- /* M .LT. MNTHR */
-
- /* Path 10 (M at least N, but not much larger) */
- /* Reduce to bidiagonal form without QR decomposition */
-
- ie = 1;
- itauq = 1;
- itaup = itauq + *n;
- iwork = itaup + *n;
-
- /* Bidiagonalize A */
- /* (CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB) */
- /* (RWorkspace: need N) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
- &work[itaup], &work[iwork], &i__2, &ierr);
- if (wntuas) {
-
- /* If left singular vectors desired in U, copy result to U */
- /* and generate left bidiagonalizing vectors in U */
- /* (CWorkspace: need 2*N+NCU, prefer 2*N+NCU*NB) */
- /* (RWorkspace: 0) */
-
- clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
- if (wntus) {
- ncu = *n;
- }
- if (wntua) {
- ncu = *m;
- }
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", m, &ncu, n, &u[u_offset], ldu, &work[itauq], &
- work[iwork], &i__2, &ierr);
- }
- if (wntvas) {
-
- /* If right singular vectors desired in VT, copy result to */
- /* VT and generate right bidiagonalizing vectors in VT */
- /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
- /* (RWorkspace: 0) */
-
- clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
- i__2 = *lwork - iwork + 1;
- cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
- work[iwork], &i__2, &ierr);
- }
- if (wntuo) {
-
- /* If left singular vectors desired in A, generate left */
- /* bidiagonalizing vectors in A */
- /* (CWorkspace: need 3*N, prefer 2*N+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[
- iwork], &i__2, &ierr);
- }
- if (wntvo) {
-
- /* If right singular vectors desired in A, generate right */
- /* bidiagonalizing vectors in A */
- /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &work[
- iwork], &i__2, &ierr);
- }
- irwork = ie + *n;
- if (wntuas || wntuo) {
- nru = *m;
- }
- if (wntun) {
- nru = 0;
- }
- if (wntvas || wntvo) {
- ncvt = *n;
- }
- if (wntvn) {
- ncvt = 0;
- }
- if (! wntuo && ! wntvo) {
-
- /* Perform bidiagonal QR iteration, if desired, computing */
- /* left singular vectors in U and computing right singular */
- /* vectors in VT */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", n, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &vt[
- vt_offset], ldvt, &u[u_offset], ldu, cdum, &c__1, &
- rwork[irwork], info);
- } else if (! wntuo && wntvo) {
-
- /* Perform bidiagonal QR iteration, if desired, computing */
- /* left singular vectors in U and computing right singular */
- /* vectors in A */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", n, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &a[
- a_offset], lda, &u[u_offset], ldu, cdum, &c__1, &
- rwork[irwork], info);
- } else {
-
- /* Perform bidiagonal QR iteration, if desired, computing */
- /* left singular vectors in A and computing right singular */
- /* vectors in VT */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", n, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &vt[
- vt_offset], ldvt, &a[a_offset], lda, cdum, &c__1, &
- rwork[irwork], info);
- }
-
- }
-
- } else {
-
- /* A has more columns than rows. If A has sufficiently more */
- /* columns than rows, first reduce using the LQ decomposition (if */
- /* sufficient workspace available) */
-
- if (*n >= mnthr) {
-
- if (wntvn) {
-
- /* Path 1t(N much larger than M, JOBVT='N') */
- /* No right singular vectors to be computed */
-
- itau = 1;
- iwork = itau + *m;
-
- /* Compute A=L*Q */
- /* (CWorkspace: need 2*M, prefer M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &
- i__2, &ierr);
-
- /* Zero out above L */
-
- i__2 = *m - 1;
- i__3 = *m - 1;
- claset_("U", &i__2, &i__3, &c_b1, &c_b1, &a[(a_dim1 << 1) + 1]
- , lda);
- ie = 1;
- itauq = 1;
- itaup = itauq + *m;
- iwork = itaup + *m;
-
- /* Bidiagonalize L in A */
- /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
- /* (RWorkspace: need M) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &work[
- itauq], &work[itaup], &work[iwork], &i__2, &ierr);
- if (wntuo || wntuas) {
-
- /* If left singular vectors desired, generate Q */
- /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", m, m, m, &a[a_offset], lda, &work[itauq], &
- work[iwork], &i__2, &ierr);
- }
- irwork = ie + *m;
- nru = 0;
- if (wntuo || wntuas) {
- nru = *m;
- }
-
- /* Perform bidiagonal QR iteration, computing left singular */
- /* vectors of A in A if desired */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", m, &c__0, &nru, &c__0, &s[1], &rwork[ie], cdum, &
- c__1, &a[a_offset], lda, cdum, &c__1, &rwork[irwork],
- info);
-
- /* If left singular vectors desired in U, copy them there */
-
- if (wntuas) {
- clacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu);
- }
-
- } else if (wntvo && wntun) {
-
- /* Path 2t(N much larger than M, JOBU='N', JOBVT='O') */
- /* M right singular vectors to be overwritten on A and */
- /* no left singular vectors to be computed */
-
- if (*lwork >= *m * *m + *m * 3) {
-
- /* Sufficient workspace for a fast algorithm */
-
- ir = 1;
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *lda * *n;
- if (*lwork >= f2cmax(i__2,i__3) + *lda * *m) {
-
- /* WORK(IU) is LDA by N and WORK(IR) is LDA by M */
-
- ldwrku = *lda;
- chunk = *n;
- ldwrkr = *lda;
- } else /* if(complicated condition) */ {
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *lda * *n;
- if (*lwork >= f2cmax(i__2,i__3) + *m * *m) {
-
- /* WORK(IU) is LDA by N and WORK(IR) is M by M */
-
- ldwrku = *lda;
- chunk = *n;
- ldwrkr = *m;
- } else {
-
- /* WORK(IU) is M by CHUNK and WORK(IR) is M by M */
-
- ldwrku = *m;
- chunk = (*lwork - *m * *m) / *m;
- ldwrkr = *m;
- }
- }
- itau = ir + ldwrkr * *m;
- iwork = itau + *m;
-
- /* Compute A=L*Q */
- /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
- , &i__2, &ierr);
-
- /* Copy L to WORK(IR) and zero out above it */
-
- clacpy_("L", m, m, &a[a_offset], lda, &work[ir], &ldwrkr);
- i__2 = *m - 1;
- i__3 = *m - 1;
- claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[ir +
- ldwrkr], &ldwrkr);
-
- /* Generate Q in A */
- /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *m;
- iwork = itaup + *m;
-
- /* Bidiagonalize L in WORK(IR) */
- /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
- /* (RWorkspace: need M) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &i__2, &
- ierr);
-
- /* Generate right vectors bidiagonalizing L */
- /* (CWorkspace: need M*M+3*M-1, prefer M*M+2*M+(M-1)*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup], &
- work[iwork], &i__2, &ierr);
- irwork = ie + *m;
-
- /* Perform bidiagonal QR iteration, computing right */
- /* singular vectors of L in WORK(IR) */
- /* (CWorkspace: need M*M) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", m, m, &c__0, &c__0, &s[1], &rwork[ie], &work[
- ir], &ldwrkr, cdum, &c__1, cdum, &c__1, &rwork[
- irwork], info);
- iu = itauq;
-
- /* Multiply right singular vectors of L in WORK(IR) by Q */
- /* in A, storing result in WORK(IU) and copying to A */
- /* (CWorkspace: need M*M+M, prefer M*M+M*N) */
- /* (RWorkspace: 0) */
-
- i__2 = *n;
- i__3 = chunk;
- for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
- i__3) {
- /* Computing MIN */
- i__4 = *n - i__ + 1;
- blk = f2cmin(i__4,chunk);
- cgemm_("N", "N", m, &blk, m, &c_b2, &work[ir], &
- ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b1, &
- work[iu], &ldwrku);
- clacpy_("F", m, &blk, &work[iu], &ldwrku, &a[i__ *
- a_dim1 + 1], lda);
- /* L30: */
- }
-
- } else {
-
- /* Insufficient workspace for a fast algorithm */
-
- ie = 1;
- itauq = 1;
- itaup = itauq + *m;
- iwork = itaup + *m;
-
- /* Bidiagonalize A */
- /* (CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB) */
- /* (RWorkspace: need M) */
-
- i__3 = *lwork - iwork + 1;
- cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
- itauq], &work[itaup], &work[iwork], &i__3, &ierr);
-
- /* Generate right vectors bidiagonalizing A */
- /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__3 = *lwork - iwork + 1;
- cungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &
- work[iwork], &i__3, &ierr);
- irwork = ie + *m;
-
- /* Perform bidiagonal QR iteration, computing right */
- /* singular vectors of A in A */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("L", m, n, &c__0, &c__0, &s[1], &rwork[ie], &a[
- a_offset], lda, cdum, &c__1, cdum, &c__1, &rwork[
- irwork], info);
-
- }
-
- } else if (wntvo && wntuas) {
-
- /* Path 3t(N much larger than M, JOBU='S' or 'A', JOBVT='O') */
- /* M right singular vectors to be overwritten on A and */
- /* M left singular vectors to be computed in U */
-
- if (*lwork >= *m * *m + *m * 3) {
-
- /* Sufficient workspace for a fast algorithm */
-
- ir = 1;
- /* Computing MAX */
- i__3 = wrkbl, i__2 = *lda * *n;
- if (*lwork >= f2cmax(i__3,i__2) + *lda * *m) {
-
- /* WORK(IU) is LDA by N and WORK(IR) is LDA by M */
-
- ldwrku = *lda;
- chunk = *n;
- ldwrkr = *lda;
- } else /* if(complicated condition) */ {
- /* Computing MAX */
- i__3 = wrkbl, i__2 = *lda * *n;
- if (*lwork >= f2cmax(i__3,i__2) + *m * *m) {
-
- /* WORK(IU) is LDA by N and WORK(IR) is M by M */
-
- ldwrku = *lda;
- chunk = *n;
- ldwrkr = *m;
- } else {
-
- /* WORK(IU) is M by CHUNK and WORK(IR) is M by M */
-
- ldwrku = *m;
- chunk = (*lwork - *m * *m) / *m;
- ldwrkr = *m;
- }
- }
- itau = ir + ldwrkr * *m;
- iwork = itau + *m;
-
- /* Compute A=L*Q */
- /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__3 = *lwork - iwork + 1;
- cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
- , &i__3, &ierr);
-
- /* Copy L to U, zeroing about above it */
-
- clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
- i__3 = *m - 1;
- i__2 = *m - 1;
- claset_("U", &i__3, &i__2, &c_b1, &c_b1, &u[(u_dim1 << 1)
- + 1], ldu);
-
- /* Generate Q in A */
- /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__3 = *lwork - iwork + 1;
- cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__3, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *m;
- iwork = itaup + *m;
-
- /* Bidiagonalize L in U, copying result to WORK(IR) */
- /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
- /* (RWorkspace: need M) */
-
- i__3 = *lwork - iwork + 1;
- cgebrd_(m, m, &u[u_offset], ldu, &s[1], &rwork[ie], &work[
- itauq], &work[itaup], &work[iwork], &i__3, &ierr);
- clacpy_("U", m, m, &u[u_offset], ldu, &work[ir], &ldwrkr);
-
- /* Generate right vectors bidiagonalizing L in WORK(IR) */
- /* (CWorkspace: need M*M+3*M-1, prefer M*M+2*M+(M-1)*NB) */
- /* (RWorkspace: 0) */
-
- i__3 = *lwork - iwork + 1;
- cungbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup], &
- work[iwork], &i__3, &ierr);
-
- /* Generate left vectors bidiagonalizing L in U */
- /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__3 = *lwork - iwork + 1;
- cungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq], &
- work[iwork], &i__3, &ierr);
- irwork = ie + *m;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of L in U, and computing right */
- /* singular vectors of L in WORK(IR) */
- /* (CWorkspace: need M*M) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", m, m, m, &c__0, &s[1], &rwork[ie], &work[ir],
- &ldwrkr, &u[u_offset], ldu, cdum, &c__1, &rwork[
- irwork], info);
- iu = itauq;
-
- /* Multiply right singular vectors of L in WORK(IR) by Q */
- /* in A, storing result in WORK(IU) and copying to A */
- /* (CWorkspace: need M*M+M, prefer M*M+M*N)) */
- /* (RWorkspace: 0) */
-
- i__3 = *n;
- i__2 = chunk;
- for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ +=
- i__2) {
- /* Computing MIN */
- i__4 = *n - i__ + 1;
- blk = f2cmin(i__4,chunk);
- cgemm_("N", "N", m, &blk, m, &c_b2, &work[ir], &
- ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b1, &
- work[iu], &ldwrku);
- clacpy_("F", m, &blk, &work[iu], &ldwrku, &a[i__ *
- a_dim1 + 1], lda);
- /* L40: */
- }
-
- } else {
-
- /* Insufficient workspace for a fast algorithm */
-
- itau = 1;
- iwork = itau + *m;
-
- /* Compute A=L*Q */
- /* (CWorkspace: need 2*M, prefer M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
- , &i__2, &ierr);
-
- /* Copy L to U, zeroing out above it */
-
- clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
- i__2 = *m - 1;
- i__3 = *m - 1;
- claset_("U", &i__2, &i__3, &c_b1, &c_b1, &u[(u_dim1 << 1)
- + 1], ldu);
-
- /* Generate Q in A */
- /* (CWorkspace: need 2*M, prefer M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *m;
- iwork = itaup + *m;
-
- /* Bidiagonalize L in U */
- /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
- /* (RWorkspace: need M) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(m, m, &u[u_offset], ldu, &s[1], &rwork[ie], &work[
- itauq], &work[itaup], &work[iwork], &i__2, &ierr);
-
- /* Multiply right vectors bidiagonalizing L by Q in A */
- /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunmbr_("P", "L", "C", m, n, m, &u[u_offset], ldu, &work[
- itaup], &a[a_offset], lda, &work[iwork], &i__2, &
- ierr);
-
- /* Generate left vectors bidiagonalizing L in U */
- /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq], &
- work[iwork], &i__2, &ierr);
- irwork = ie + *m;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in U and computing right */
- /* singular vectors of A in A */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", m, n, m, &c__0, &s[1], &rwork[ie], &a[
- a_offset], lda, &u[u_offset], ldu, cdum, &c__1, &
- rwork[irwork], info);
-
- }
-
- } else if (wntvs) {
-
- if (wntun) {
-
- /* Path 4t(N much larger than M, JOBU='N', JOBVT='S') */
- /* M right singular vectors to be computed in VT and */
- /* no left singular vectors to be computed */
-
- if (*lwork >= *m * *m + *m * 3) {
-
- /* Sufficient workspace for a fast algorithm */
-
- ir = 1;
- if (*lwork >= wrkbl + *lda * *m) {
-
- /* WORK(IR) is LDA by M */
-
- ldwrkr = *lda;
- } else {
-
- /* WORK(IR) is M by M */
-
- ldwrkr = *m;
- }
- itau = ir + ldwrkr * *m;
- iwork = itau + *m;
-
- /* Compute A=L*Q */
- /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
-
- /* Copy L to WORK(IR), zeroing out above it */
-
- clacpy_("L", m, m, &a[a_offset], lda, &work[ir], &
- ldwrkr);
- i__2 = *m - 1;
- i__3 = *m - 1;
- claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[ir +
- ldwrkr], &ldwrkr);
-
- /* Generate Q in A */
- /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *m;
- iwork = itaup + *m;
-
- /* Bidiagonalize L in WORK(IR) */
- /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
- /* (RWorkspace: need M) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
-
- /* Generate right vectors bidiagonalizing L in */
- /* WORK(IR) */
- /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+(M-1)*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup]
- , &work[iwork], &i__2, &ierr);
- irwork = ie + *m;
-
- /* Perform bidiagonal QR iteration, computing right */
- /* singular vectors of L in WORK(IR) */
- /* (CWorkspace: need M*M) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", m, m, &c__0, &c__0, &s[1], &rwork[ie], &
- work[ir], &ldwrkr, cdum, &c__1, cdum, &c__1, &
- rwork[irwork], info);
-
- /* Multiply right singular vectors of L in WORK(IR) by */
- /* Q in A, storing result in VT */
- /* (CWorkspace: need M*M) */
- /* (RWorkspace: 0) */
-
- cgemm_("N", "N", m, n, m, &c_b2, &work[ir], &ldwrkr, &
- a[a_offset], lda, &c_b1, &vt[vt_offset], ldvt);
-
- } else {
-
- /* Insufficient workspace for a fast algorithm */
-
- itau = 1;
- iwork = itau + *m;
-
- /* Compute A=L*Q */
- /* (CWorkspace: need 2*M, prefer M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
-
- /* Copy result to VT */
-
- clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
-
- /* Generate Q in VT */
- /* (CWorkspace: need 2*M, prefer M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *m;
- iwork = itaup + *m;
-
- /* Zero out above L in A */
-
- i__2 = *m - 1;
- i__3 = *m - 1;
- claset_("U", &i__2, &i__3, &c_b1, &c_b1, &a[(a_dim1 <<
- 1) + 1], lda);
-
- /* Bidiagonalize L in A */
- /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
- /* (RWorkspace: need M) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
-
- /* Multiply right vectors bidiagonalizing L by Q in VT */
- /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunmbr_("P", "L", "C", m, n, m, &a[a_offset], lda, &
- work[itaup], &vt[vt_offset], ldvt, &work[
- iwork], &i__2, &ierr);
- irwork = ie + *m;
-
- /* Perform bidiagonal QR iteration, computing right */
- /* singular vectors of A in VT */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", m, n, &c__0, &c__0, &s[1], &rwork[ie], &
- vt[vt_offset], ldvt, cdum, &c__1, cdum, &c__1,
- &rwork[irwork], info);
-
- }
-
- } else if (wntuo) {
-
- /* Path 5t(N much larger than M, JOBU='O', JOBVT='S') */
- /* M right singular vectors to be computed in VT and */
- /* M left singular vectors to be overwritten on A */
-
- if (*lwork >= (*m << 1) * *m + *m * 3) {
-
- /* Sufficient workspace for a fast algorithm */
-
- iu = 1;
- if (*lwork >= wrkbl + (*lda << 1) * *m) {
-
- /* WORK(IU) is LDA by M and WORK(IR) is LDA by M */
-
- ldwrku = *lda;
- ir = iu + ldwrku * *m;
- ldwrkr = *lda;
- } else if (*lwork >= wrkbl + (*lda + *m) * *m) {
-
- /* WORK(IU) is LDA by M and WORK(IR) is M by M */
-
- ldwrku = *lda;
- ir = iu + ldwrku * *m;
- ldwrkr = *m;
- } else {
-
- /* WORK(IU) is M by M and WORK(IR) is M by M */
-
- ldwrku = *m;
- ir = iu + ldwrku * *m;
- ldwrkr = *m;
- }
- itau = ir + ldwrkr * *m;
- iwork = itau + *m;
-
- /* Compute A=L*Q */
- /* (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
-
- /* Copy L to WORK(IU), zeroing out below it */
-
- clacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
- ldwrku);
- i__2 = *m - 1;
- i__3 = *m - 1;
- claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[iu +
- ldwrku], &ldwrku);
-
- /* Generate Q in A */
- /* (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *m;
- iwork = itaup + *m;
-
- /* Bidiagonalize L in WORK(IU), copying result to */
- /* WORK(IR) */
- /* (CWorkspace: need 2*M*M+3*M, */
- /* prefer 2*M*M+2*M+2*M*NB) */
- /* (RWorkspace: need M) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(m, m, &work[iu], &ldwrku, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- clacpy_("L", m, m, &work[iu], &ldwrku, &work[ir], &
- ldwrkr);
-
- /* Generate right bidiagonalizing vectors in WORK(IU) */
- /* (CWorkspace: need 2*M*M+3*M-1, */
- /* prefer 2*M*M+2*M+(M-1)*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
- , &work[iwork], &i__2, &ierr);
-
- /* Generate left bidiagonalizing vectors in WORK(IR) */
- /* (CWorkspace: need 2*M*M+3*M, prefer 2*M*M+2*M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", m, m, m, &work[ir], &ldwrkr, &work[itauq]
- , &work[iwork], &i__2, &ierr);
- irwork = ie + *m;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of L in WORK(IR) and computing */
- /* right singular vectors of L in WORK(IU) */
- /* (CWorkspace: need 2*M*M) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", m, m, m, &c__0, &s[1], &rwork[ie], &work[
- iu], &ldwrku, &work[ir], &ldwrkr, cdum, &c__1,
- &rwork[irwork], info);
-
- /* Multiply right singular vectors of L in WORK(IU) by */
- /* Q in A, storing result in VT */
- /* (CWorkspace: need M*M) */
- /* (RWorkspace: 0) */
-
- cgemm_("N", "N", m, n, m, &c_b2, &work[iu], &ldwrku, &
- a[a_offset], lda, &c_b1, &vt[vt_offset], ldvt);
-
- /* Copy left singular vectors of L to A */
- /* (CWorkspace: need M*M) */
- /* (RWorkspace: 0) */
-
- clacpy_("F", m, m, &work[ir], &ldwrkr, &a[a_offset],
- lda);
-
- } else {
-
- /* Insufficient workspace for a fast algorithm */
-
- itau = 1;
- iwork = itau + *m;
-
- /* Compute A=L*Q, copying result to VT */
- /* (CWorkspace: need 2*M, prefer M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
-
- /* Generate Q in VT */
- /* (CWorkspace: need 2*M, prefer M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *m;
- iwork = itaup + *m;
-
- /* Zero out above L in A */
-
- i__2 = *m - 1;
- i__3 = *m - 1;
- claset_("U", &i__2, &i__3, &c_b1, &c_b1, &a[(a_dim1 <<
- 1) + 1], lda);
-
- /* Bidiagonalize L in A */
- /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
- /* (RWorkspace: need M) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
-
- /* Multiply right vectors bidiagonalizing L by Q in VT */
- /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunmbr_("P", "L", "C", m, n, m, &a[a_offset], lda, &
- work[itaup], &vt[vt_offset], ldvt, &work[
- iwork], &i__2, &ierr);
-
- /* Generate left bidiagonalizing vectors of L in A */
- /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", m, m, m, &a[a_offset], lda, &work[itauq],
- &work[iwork], &i__2, &ierr);
- irwork = ie + *m;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in A and computing right */
- /* singular vectors of A in VT */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", m, n, m, &c__0, &s[1], &rwork[ie], &vt[
- vt_offset], ldvt, &a[a_offset], lda, cdum, &
- c__1, &rwork[irwork], info);
-
- }
-
- } else if (wntuas) {
-
- /* Path 6t(N much larger than M, JOBU='S' or 'A', */
- /* JOBVT='S') */
- /* M right singular vectors to be computed in VT and */
- /* M left singular vectors to be computed in U */
-
- if (*lwork >= *m * *m + *m * 3) {
-
- /* Sufficient workspace for a fast algorithm */
-
- iu = 1;
- if (*lwork >= wrkbl + *lda * *m) {
-
- /* WORK(IU) is LDA by N */
-
- ldwrku = *lda;
- } else {
-
- /* WORK(IU) is LDA by M */
-
- ldwrku = *m;
- }
- itau = iu + ldwrku * *m;
- iwork = itau + *m;
-
- /* Compute A=L*Q */
- /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
-
- /* Copy L to WORK(IU), zeroing out above it */
-
- clacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
- ldwrku);
- i__2 = *m - 1;
- i__3 = *m - 1;
- claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[iu +
- ldwrku], &ldwrku);
-
- /* Generate Q in A */
- /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *m;
- iwork = itaup + *m;
-
- /* Bidiagonalize L in WORK(IU), copying result to U */
- /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
- /* (RWorkspace: need M) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(m, m, &work[iu], &ldwrku, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- clacpy_("L", m, m, &work[iu], &ldwrku, &u[u_offset],
- ldu);
-
- /* Generate right bidiagonalizing vectors in WORK(IU) */
- /* (CWorkspace: need M*M+3*M-1, */
- /* prefer M*M+2*M+(M-1)*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
- , &work[iwork], &i__2, &ierr);
-
- /* Generate left bidiagonalizing vectors in U */
- /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
- &work[iwork], &i__2, &ierr);
- irwork = ie + *m;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of L in U and computing right */
- /* singular vectors of L in WORK(IU) */
- /* (CWorkspace: need M*M) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", m, m, m, &c__0, &s[1], &rwork[ie], &work[
- iu], &ldwrku, &u[u_offset], ldu, cdum, &c__1,
- &rwork[irwork], info);
-
- /* Multiply right singular vectors of L in WORK(IU) by */
- /* Q in A, storing result in VT */
- /* (CWorkspace: need M*M) */
- /* (RWorkspace: 0) */
-
- cgemm_("N", "N", m, n, m, &c_b2, &work[iu], &ldwrku, &
- a[a_offset], lda, &c_b1, &vt[vt_offset], ldvt);
-
- } else {
-
- /* Insufficient workspace for a fast algorithm */
-
- itau = 1;
- iwork = itau + *m;
-
- /* Compute A=L*Q, copying result to VT */
- /* (CWorkspace: need 2*M, prefer M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
-
- /* Generate Q in VT */
- /* (CWorkspace: need 2*M, prefer M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
- work[iwork], &i__2, &ierr);
-
- /* Copy L to U, zeroing out above it */
-
- clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset],
- ldu);
- i__2 = *m - 1;
- i__3 = *m - 1;
- claset_("U", &i__2, &i__3, &c_b1, &c_b1, &u[(u_dim1 <<
- 1) + 1], ldu);
- ie = 1;
- itauq = itau;
- itaup = itauq + *m;
- iwork = itaup + *m;
-
- /* Bidiagonalize L in U */
- /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
- /* (RWorkspace: need M) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(m, m, &u[u_offset], ldu, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
-
- /* Multiply right bidiagonalizing vectors in U by Q */
- /* in VT */
- /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunmbr_("P", "L", "C", m, n, m, &u[u_offset], ldu, &
- work[itaup], &vt[vt_offset], ldvt, &work[
- iwork], &i__2, &ierr);
-
- /* Generate left bidiagonalizing vectors in U */
- /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
- &work[iwork], &i__2, &ierr);
- irwork = ie + *m;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in U and computing right */
- /* singular vectors of A in VT */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", m, n, m, &c__0, &s[1], &rwork[ie], &vt[
- vt_offset], ldvt, &u[u_offset], ldu, cdum, &
- c__1, &rwork[irwork], info);
-
- }
-
- }
-
- } else if (wntva) {
-
- if (wntun) {
-
- /* Path 7t(N much larger than M, JOBU='N', JOBVT='A') */
- /* N right singular vectors to be computed in VT and */
- /* no left singular vectors to be computed */
-
- /* Computing MAX */
- i__2 = *n + *m, i__3 = *m * 3;
- if (*lwork >= *m * *m + f2cmax(i__2,i__3)) {
-
- /* Sufficient workspace for a fast algorithm */
-
- ir = 1;
- if (*lwork >= wrkbl + *lda * *m) {
-
- /* WORK(IR) is LDA by M */
-
- ldwrkr = *lda;
- } else {
-
- /* WORK(IR) is M by M */
-
- ldwrkr = *m;
- }
- itau = ir + ldwrkr * *m;
- iwork = itau + *m;
-
- /* Compute A=L*Q, copying result to VT */
- /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
-
- /* Copy L to WORK(IR), zeroing out above it */
-
- clacpy_("L", m, m, &a[a_offset], lda, &work[ir], &
- ldwrkr);
- i__2 = *m - 1;
- i__3 = *m - 1;
- claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[ir +
- ldwrkr], &ldwrkr);
-
- /* Generate Q in VT */
- /* (CWorkspace: need M*M+M+N, prefer M*M+M+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *m;
- iwork = itaup + *m;
-
- /* Bidiagonalize L in WORK(IR) */
- /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
- /* (RWorkspace: need M) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
-
- /* Generate right bidiagonalizing vectors in WORK(IR) */
- /* (CWorkspace: need M*M+3*M-1, */
- /* prefer M*M+2*M+(M-1)*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup]
- , &work[iwork], &i__2, &ierr);
- irwork = ie + *m;
-
- /* Perform bidiagonal QR iteration, computing right */
- /* singular vectors of L in WORK(IR) */
- /* (CWorkspace: need M*M) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", m, m, &c__0, &c__0, &s[1], &rwork[ie], &
- work[ir], &ldwrkr, cdum, &c__1, cdum, &c__1, &
- rwork[irwork], info);
-
- /* Multiply right singular vectors of L in WORK(IR) by */
- /* Q in VT, storing result in A */
- /* (CWorkspace: need M*M) */
- /* (RWorkspace: 0) */
-
- cgemm_("N", "N", m, n, m, &c_b2, &work[ir], &ldwrkr, &
- vt[vt_offset], ldvt, &c_b1, &a[a_offset], lda);
-
- /* Copy right singular vectors of A from A to VT */
-
- clacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
-
- } else {
-
- /* Insufficient workspace for a fast algorithm */
-
- itau = 1;
- iwork = itau + *m;
-
- /* Compute A=L*Q, copying result to VT */
- /* (CWorkspace: need 2*M, prefer M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
-
- /* Generate Q in VT */
- /* (CWorkspace: need M+N, prefer M+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *m;
- iwork = itaup + *m;
-
- /* Zero out above L in A */
-
- i__2 = *m - 1;
- i__3 = *m - 1;
- claset_("U", &i__2, &i__3, &c_b1, &c_b1, &a[(a_dim1 <<
- 1) + 1], lda);
-
- /* Bidiagonalize L in A */
- /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
- /* (RWorkspace: need M) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
-
- /* Multiply right bidiagonalizing vectors in A by Q */
- /* in VT */
- /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunmbr_("P", "L", "C", m, n, m, &a[a_offset], lda, &
- work[itaup], &vt[vt_offset], ldvt, &work[
- iwork], &i__2, &ierr);
- irwork = ie + *m;
-
- /* Perform bidiagonal QR iteration, computing right */
- /* singular vectors of A in VT */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", m, n, &c__0, &c__0, &s[1], &rwork[ie], &
- vt[vt_offset], ldvt, cdum, &c__1, cdum, &c__1,
- &rwork[irwork], info);
-
- }
-
- } else if (wntuo) {
-
- /* Path 8t(N much larger than M, JOBU='O', JOBVT='A') */
- /* N right singular vectors to be computed in VT and */
- /* M left singular vectors to be overwritten on A */
-
- /* Computing MAX */
- i__2 = *n + *m, i__3 = *m * 3;
- if (*lwork >= (*m << 1) * *m + f2cmax(i__2,i__3)) {
-
- /* Sufficient workspace for a fast algorithm */
-
- iu = 1;
- if (*lwork >= wrkbl + (*lda << 1) * *m) {
-
- /* WORK(IU) is LDA by M and WORK(IR) is LDA by M */
-
- ldwrku = *lda;
- ir = iu + ldwrku * *m;
- ldwrkr = *lda;
- } else if (*lwork >= wrkbl + (*lda + *m) * *m) {
-
- /* WORK(IU) is LDA by M and WORK(IR) is M by M */
-
- ldwrku = *lda;
- ir = iu + ldwrku * *m;
- ldwrkr = *m;
- } else {
-
- /* WORK(IU) is M by M and WORK(IR) is M by M */
-
- ldwrku = *m;
- ir = iu + ldwrku * *m;
- ldwrkr = *m;
- }
- itau = ir + ldwrkr * *m;
- iwork = itau + *m;
-
- /* Compute A=L*Q, copying result to VT */
- /* (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
-
- /* Generate Q in VT */
- /* (CWorkspace: need 2*M*M+M+N, prefer 2*M*M+M+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
- work[iwork], &i__2, &ierr);
-
- /* Copy L to WORK(IU), zeroing out above it */
-
- clacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
- ldwrku);
- i__2 = *m - 1;
- i__3 = *m - 1;
- claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[iu +
- ldwrku], &ldwrku);
- ie = 1;
- itauq = itau;
- itaup = itauq + *m;
- iwork = itaup + *m;
-
- /* Bidiagonalize L in WORK(IU), copying result to */
- /* WORK(IR) */
- /* (CWorkspace: need 2*M*M+3*M, */
- /* prefer 2*M*M+2*M+2*M*NB) */
- /* (RWorkspace: need M) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(m, m, &work[iu], &ldwrku, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- clacpy_("L", m, m, &work[iu], &ldwrku, &work[ir], &
- ldwrkr);
-
- /* Generate right bidiagonalizing vectors in WORK(IU) */
- /* (CWorkspace: need 2*M*M+3*M-1, */
- /* prefer 2*M*M+2*M+(M-1)*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
- , &work[iwork], &i__2, &ierr);
-
- /* Generate left bidiagonalizing vectors in WORK(IR) */
- /* (CWorkspace: need 2*M*M+3*M, prefer 2*M*M+2*M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", m, m, m, &work[ir], &ldwrkr, &work[itauq]
- , &work[iwork], &i__2, &ierr);
- irwork = ie + *m;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of L in WORK(IR) and computing */
- /* right singular vectors of L in WORK(IU) */
- /* (CWorkspace: need 2*M*M) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", m, m, m, &c__0, &s[1], &rwork[ie], &work[
- iu], &ldwrku, &work[ir], &ldwrkr, cdum, &c__1,
- &rwork[irwork], info);
-
- /* Multiply right singular vectors of L in WORK(IU) by */
- /* Q in VT, storing result in A */
- /* (CWorkspace: need M*M) */
- /* (RWorkspace: 0) */
-
- cgemm_("N", "N", m, n, m, &c_b2, &work[iu], &ldwrku, &
- vt[vt_offset], ldvt, &c_b1, &a[a_offset], lda);
-
- /* Copy right singular vectors of A from A to VT */
-
- clacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
-
- /* Copy left singular vectors of A from WORK(IR) to A */
-
- clacpy_("F", m, m, &work[ir], &ldwrkr, &a[a_offset],
- lda);
-
- } else {
-
- /* Insufficient workspace for a fast algorithm */
-
- itau = 1;
- iwork = itau + *m;
-
- /* Compute A=L*Q, copying result to VT */
- /* (CWorkspace: need 2*M, prefer M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
-
- /* Generate Q in VT */
- /* (CWorkspace: need M+N, prefer M+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *m;
- iwork = itaup + *m;
-
- /* Zero out above L in A */
-
- i__2 = *m - 1;
- i__3 = *m - 1;
- claset_("U", &i__2, &i__3, &c_b1, &c_b1, &a[(a_dim1 <<
- 1) + 1], lda);
-
- /* Bidiagonalize L in A */
- /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
- /* (RWorkspace: need M) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
-
- /* Multiply right bidiagonalizing vectors in A by Q */
- /* in VT */
- /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunmbr_("P", "L", "C", m, n, m, &a[a_offset], lda, &
- work[itaup], &vt[vt_offset], ldvt, &work[
- iwork], &i__2, &ierr);
-
- /* Generate left bidiagonalizing vectors in A */
- /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", m, m, m, &a[a_offset], lda, &work[itauq],
- &work[iwork], &i__2, &ierr);
- irwork = ie + *m;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in A and computing right */
- /* singular vectors of A in VT */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", m, n, m, &c__0, &s[1], &rwork[ie], &vt[
- vt_offset], ldvt, &a[a_offset], lda, cdum, &
- c__1, &rwork[irwork], info);
-
- }
-
- } else if (wntuas) {
-
- /* Path 9t(N much larger than M, JOBU='S' or 'A', */
- /* JOBVT='A') */
- /* N right singular vectors to be computed in VT and */
- /* M left singular vectors to be computed in U */
-
- /* Computing MAX */
- i__2 = *n + *m, i__3 = *m * 3;
- if (*lwork >= *m * *m + f2cmax(i__2,i__3)) {
-
- /* Sufficient workspace for a fast algorithm */
-
- iu = 1;
- if (*lwork >= wrkbl + *lda * *m) {
-
- /* WORK(IU) is LDA by M */
-
- ldwrku = *lda;
- } else {
-
- /* WORK(IU) is M by M */
-
- ldwrku = *m;
- }
- itau = iu + ldwrku * *m;
- iwork = itau + *m;
-
- /* Compute A=L*Q, copying result to VT */
- /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
-
- /* Generate Q in VT */
- /* (CWorkspace: need M*M+M+N, prefer M*M+M+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
- work[iwork], &i__2, &ierr);
-
- /* Copy L to WORK(IU), zeroing out above it */
-
- clacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
- ldwrku);
- i__2 = *m - 1;
- i__3 = *m - 1;
- claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[iu +
- ldwrku], &ldwrku);
- ie = 1;
- itauq = itau;
- itaup = itauq + *m;
- iwork = itaup + *m;
-
- /* Bidiagonalize L in WORK(IU), copying result to U */
- /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
- /* (RWorkspace: need M) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(m, m, &work[iu], &ldwrku, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- clacpy_("L", m, m, &work[iu], &ldwrku, &u[u_offset],
- ldu);
-
- /* Generate right bidiagonalizing vectors in WORK(IU) */
- /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+(M-1)*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
- , &work[iwork], &i__2, &ierr);
-
- /* Generate left bidiagonalizing vectors in U */
- /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
- &work[iwork], &i__2, &ierr);
- irwork = ie + *m;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of L in U and computing right */
- /* singular vectors of L in WORK(IU) */
- /* (CWorkspace: need M*M) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", m, m, m, &c__0, &s[1], &rwork[ie], &work[
- iu], &ldwrku, &u[u_offset], ldu, cdum, &c__1,
- &rwork[irwork], info);
-
- /* Multiply right singular vectors of L in WORK(IU) by */
- /* Q in VT, storing result in A */
- /* (CWorkspace: need M*M) */
- /* (RWorkspace: 0) */
-
- cgemm_("N", "N", m, n, m, &c_b2, &work[iu], &ldwrku, &
- vt[vt_offset], ldvt, &c_b1, &a[a_offset], lda);
-
- /* Copy right singular vectors of A from A to VT */
-
- clacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
-
- } else {
-
- /* Insufficient workspace for a fast algorithm */
-
- itau = 1;
- iwork = itau + *m;
-
- /* Compute A=L*Q, copying result to VT */
- /* (CWorkspace: need 2*M, prefer M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
-
- /* Generate Q in VT */
- /* (CWorkspace: need M+N, prefer M+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
- work[iwork], &i__2, &ierr);
-
- /* Copy L to U, zeroing out above it */
-
- clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset],
- ldu);
- i__2 = *m - 1;
- i__3 = *m - 1;
- claset_("U", &i__2, &i__3, &c_b1, &c_b1, &u[(u_dim1 <<
- 1) + 1], ldu);
- ie = 1;
- itauq = itau;
- itaup = itauq + *m;
- iwork = itaup + *m;
-
- /* Bidiagonalize L in U */
- /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
- /* (RWorkspace: need M) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(m, m, &u[u_offset], ldu, &s[1], &rwork[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
-
- /* Multiply right bidiagonalizing vectors in U by Q */
- /* in VT */
- /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cunmbr_("P", "L", "C", m, n, m, &u[u_offset], ldu, &
- work[itaup], &vt[vt_offset], ldvt, &work[
- iwork], &i__2, &ierr);
-
- /* Generate left bidiagonalizing vectors in U */
- /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
- &work[iwork], &i__2, &ierr);
- irwork = ie + *m;
-
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in U and computing right */
- /* singular vectors of A in VT */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("U", m, n, m, &c__0, &s[1], &rwork[ie], &vt[
- vt_offset], ldvt, &u[u_offset], ldu, cdum, &
- c__1, &rwork[irwork], info);
-
- }
-
- }
-
- }
-
- } else {
-
- /* N .LT. MNTHR */
-
- /* Path 10t(N greater than M, but not much larger) */
- /* Reduce to bidiagonal form without LQ decomposition */
-
- ie = 1;
- itauq = 1;
- itaup = itauq + *m;
- iwork = itaup + *m;
-
- /* Bidiagonalize A */
- /* (CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB) */
- /* (RWorkspace: M) */
-
- i__2 = *lwork - iwork + 1;
- cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
- &work[itaup], &work[iwork], &i__2, &ierr);
- if (wntuas) {
-
- /* If left singular vectors desired in U, copy result to U */
- /* and generate left bidiagonalizing vectors in U */
- /* (CWorkspace: need 3*M-1, prefer 2*M+(M-1)*NB) */
- /* (RWorkspace: 0) */
-
- clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
- iwork], &i__2, &ierr);
- }
- if (wntvas) {
-
- /* If right singular vectors desired in VT, copy result to */
- /* VT and generate right bidiagonalizing vectors in VT */
- /* (CWorkspace: need 2*M+NRVT, prefer 2*M+NRVT*NB) */
- /* (RWorkspace: 0) */
-
- clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
- if (wntva) {
- nrvt = *n;
- }
- if (wntvs) {
- nrvt = *m;
- }
- i__2 = *lwork - iwork + 1;
- cungbr_("P", &nrvt, n, m, &vt[vt_offset], ldvt, &work[itaup],
- &work[iwork], &i__2, &ierr);
- }
- if (wntuo) {
-
- /* If left singular vectors desired in A, generate left */
- /* bidiagonalizing vectors in A */
- /* (CWorkspace: need 3*M-1, prefer 2*M+(M-1)*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("Q", m, m, n, &a[a_offset], lda, &work[itauq], &work[
- iwork], &i__2, &ierr);
- }
- if (wntvo) {
-
- /* If right singular vectors desired in A, generate right */
- /* bidiagonalizing vectors in A */
- /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
- /* (RWorkspace: 0) */
-
- i__2 = *lwork - iwork + 1;
- cungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[
- iwork], &i__2, &ierr);
- }
- irwork = ie + *m;
- if (wntuas || wntuo) {
- nru = *m;
- }
- if (wntun) {
- nru = 0;
- }
- if (wntvas || wntvo) {
- ncvt = *n;
- }
- if (wntvn) {
- ncvt = 0;
- }
- if (! wntuo && ! wntvo) {
-
- /* Perform bidiagonal QR iteration, if desired, computing */
- /* left singular vectors in U and computing right singular */
- /* vectors in VT */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("L", m, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &vt[
- vt_offset], ldvt, &u[u_offset], ldu, cdum, &c__1, &
- rwork[irwork], info);
- } else if (! wntuo && wntvo) {
-
- /* Perform bidiagonal QR iteration, if desired, computing */
- /* left singular vectors in U and computing right singular */
- /* vectors in A */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("L", m, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &a[
- a_offset], lda, &u[u_offset], ldu, cdum, &c__1, &
- rwork[irwork], info);
- } else {
-
- /* Perform bidiagonal QR iteration, if desired, computing */
- /* left singular vectors in A and computing right singular */
- /* vectors in VT */
- /* (CWorkspace: 0) */
- /* (RWorkspace: need BDSPAC) */
-
- cbdsqr_("L", m, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &vt[
- vt_offset], ldvt, &a[a_offset], lda, cdum, &c__1, &
- rwork[irwork], 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, &ierr);
- }
- if (*info != 0 && anrm > bignum) {
- i__2 = minmn - 1;
- slascl_("G", &c__0, &c__0, &bignum, &anrm, &i__2, &c__1, &rwork[
- ie], &minmn, &ierr);
- }
- if (anrm < smlnum) {
- slascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
- minmn, &ierr);
- }
- if (*info != 0 && anrm < smlnum) {
- i__2 = minmn - 1;
- slascl_("G", &c__0, &c__0, &smlnum, &anrm, &i__2, &c__1, &rwork[
- ie], &minmn, &ierr);
- }
- }
-
- /* Return optimal workspace in WORK(1) */
-
- work[1].r = (real) maxwrk, work[1].i = 0.f;
-
- return 0;
-
- /* End of CGESVD */
-
- } /* cgesvd_ */
-
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