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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_n1 = -1;
- static integer c__0 = 0;
- static integer c__1 = 1;
-
- /* > \brief \b CGESDD */
-
- /* =========== DOCUMENTATION =========== */
-
- /* Online html documentation available at */
- /* http://www.netlib.org/lapack/explore-html/ */
-
- /* > \htmlonly */
- /* > Download CGESDD + dependencies */
- /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgesdd.
- f"> */
- /* > [TGZ]</a> */
- /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgesdd.
- f"> */
- /* > [ZIP]</a> */
- /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgesdd.
- f"> */
- /* > [TXT]</a> */
- /* > \endhtmlonly */
-
- /* Definition: */
- /* =========== */
-
- /* SUBROUTINE CGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, */
- /* WORK, LWORK, RWORK, IWORK, INFO ) */
-
- /* CHARACTER JOBZ */
- /* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N */
- /* INTEGER IWORK( * ) */
- /* REAL RWORK( * ), S( * ) */
- /* COMPLEX A( LDA, * ), U( LDU, * ), VT( LDVT, * ), */
- /* $ WORK( * ) */
-
-
- /* > \par Purpose: */
- /* ============= */
- /* > */
- /* > \verbatim */
- /* > */
- /* > CGESDD computes the singular value decomposition (SVD) of a complex */
- /* > M-by-N matrix A, optionally computing the left and/or right singular */
- /* > vectors, by using divide-and-conquer method. The SVD is written */
- /* > */
- /* > A = U * SIGMA * conjugate-transpose(V) */
- /* > */
- /* > where SIGMA is an M-by-N matrix which is zero except for its */
- /* > f2cmin(m,n) diagonal elements, U is an M-by-M unitary matrix, and */
- /* > V is an N-by-N unitary matrix. The diagonal elements of SIGMA */
- /* > are the singular values of A; they are real and non-negative, and */
- /* > are returned in descending order. The first f2cmin(m,n) columns of */
- /* > U and V are the left and right singular vectors of A. */
- /* > */
- /* > Note that the routine returns VT = V**H, not V. */
- /* > */
- /* > The divide and conquer algorithm makes very mild assumptions about */
- /* > floating point arithmetic. It will work on machines with a guard */
- /* > digit in add/subtract, or on those binary machines without guard */
- /* > digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
- /* > Cray-2. It could conceivably fail on hexadecimal or decimal machines */
- /* > without guard digits, but we know of none. */
- /* > \endverbatim */
-
- /* Arguments: */
- /* ========== */
-
- /* > \param[in] JOBZ */
- /* > \verbatim */
- /* > JOBZ is CHARACTER*1 */
- /* > Specifies options for computing all or part of the matrix U: */
- /* > = 'A': all M columns of U and all N rows of V**H are */
- /* > returned in the arrays U and VT; */
- /* > = 'S': the first f2cmin(M,N) columns of U and the first */
- /* > f2cmin(M,N) rows of V**H are returned in the arrays U */
- /* > and VT; */
- /* > = 'O': If M >= N, the first N columns of U are overwritten */
- /* > in the array A and all rows of V**H are returned in */
- /* > the array VT; */
- /* > otherwise, all columns of U are returned in the */
- /* > array U and the first M rows of V**H are overwritten */
- /* > in the array A; */
- /* > = 'N': no columns of U or rows of V**H are computed. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] M */
- /* > \verbatim */
- /* > M is INTEGER */
- /* > The number of rows of the input matrix A. M >= 0. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] N */
- /* > \verbatim */
- /* > N is INTEGER */
- /* > The number of columns of the input matrix A. N >= 0. */
- /* > \endverbatim */
- /* > */
- /* > \param[in,out] A */
- /* > \verbatim */
- /* > A is COMPLEX array, dimension (LDA,N) */
- /* > On entry, the M-by-N matrix A. */
- /* > On exit, */
- /* > if JOBZ = 'O', A is overwritten with the first N columns */
- /* > of U (the left singular vectors, stored */
- /* > columnwise) if M >= N; */
- /* > A is overwritten with the first M rows */
- /* > of V**H (the right singular vectors, stored */
- /* > rowwise) otherwise. */
- /* > if JOBZ .ne. 'O', the contents of A are destroyed. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] LDA */
- /* > \verbatim */
- /* > LDA is INTEGER */
- /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
- /* > \endverbatim */
- /* > */
- /* > \param[out] S */
- /* > \verbatim */
- /* > S is 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) */
- /* > UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; */
- /* > UCOL = f2cmin(M,N) if JOBZ = 'S'. */
- /* > If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M */
- /* > unitary matrix U; */
- /* > if JOBZ = 'S', U contains the first f2cmin(M,N) columns of U */
- /* > (the left singular vectors, stored columnwise); */
- /* > if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] LDU */
- /* > \verbatim */
- /* > LDU is INTEGER */
- /* > The leading dimension of the array U. LDU >= 1; */
- /* > if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M. */
- /* > \endverbatim */
- /* > */
- /* > \param[out] VT */
- /* > \verbatim */
- /* > VT is COMPLEX array, dimension (LDVT,N) */
- /* > If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the */
- /* > N-by-N unitary matrix V**H; */
- /* > if JOBZ = 'S', VT contains the first f2cmin(M,N) rows of */
- /* > V**H (the right singular vectors, stored rowwise); */
- /* > if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] LDVT */
- /* > \verbatim */
- /* > LDVT is INTEGER */
- /* > The leading dimension of the array VT. LDVT >= 1; */
- /* > if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; */
- /* > if JOBZ = 'S', LDVT >= f2cmin(M,N). */
- /* > \endverbatim */
- /* > */
- /* > \param[out] WORK */
- /* > \verbatim */
- /* > WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
- /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] LWORK */
- /* > \verbatim */
- /* > LWORK is INTEGER */
- /* > The dimension of the array WORK. LWORK >= 1. */
- /* > If LWORK = -1, a workspace query is assumed. The optimal */
- /* > size for the WORK array is calculated and stored in WORK(1), */
- /* > and no other work except argument checking is performed. */
- /* > */
- /* > Let mx = f2cmax(M,N) and mn = f2cmin(M,N). */
- /* > If JOBZ = 'N', LWORK >= 2*mn + mx. */
- /* > If JOBZ = 'O', LWORK >= 2*mn*mn + 2*mn + mx. */
- /* > If JOBZ = 'S', LWORK >= mn*mn + 3*mn. */
- /* > If JOBZ = 'A', LWORK >= mn*mn + 2*mn + mx. */
- /* > These are not tight minimums in all cases; see comments inside code. */
- /* > For good performance, LWORK should generally be larger; */
- /* > a query is recommended. */
- /* > \endverbatim */
- /* > */
- /* > \param[out] RWORK */
- /* > \verbatim */
- /* > RWORK is REAL array, dimension (MAX(1,LRWORK)) */
- /* > Let mx = f2cmax(M,N) and mn = f2cmin(M,N). */
- /* > If JOBZ = 'N', LRWORK >= 5*mn (LAPACK <= 3.6 needs 7*mn); */
- /* > else if mx >> mn, LRWORK >= 5*mn*mn + 5*mn; */
- /* > else LRWORK >= f2cmax( 5*mn*mn + 5*mn, */
- /* > 2*mx*mn + 2*mn*mn + mn ). */
- /* > \endverbatim */
- /* > */
- /* > \param[out] IWORK */
- /* > \verbatim */
- /* > IWORK is INTEGER array, dimension (8*f2cmin(M,N)) */
- /* > \endverbatim */
- /* > */
- /* > \param[out] INFO */
- /* > \verbatim */
- /* > INFO is INTEGER */
- /* > = 0: successful exit. */
- /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
- /* > > 0: The updating process of SBDSDC did not converge. */
- /* > \endverbatim */
-
- /* Authors: */
- /* ======== */
-
- /* > \author Univ. of Tennessee */
- /* > \author Univ. of California Berkeley */
- /* > \author Univ. of Colorado Denver */
- /* > \author NAG Ltd. */
-
- /* > \date June 2016 */
-
- /* > \ingroup complexGEsing */
-
- /* > \par Contributors: */
- /* ================== */
- /* > */
- /* > Ming Gu and Huan Ren, Computer Science Division, University of */
- /* > California at Berkeley, USA */
- /* > */
- /* ===================================================================== */
- /* Subroutine */ void cgesdd_(char *jobz, 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 *iwork,
- integer *info)
- {
- /* System generated locals */
- integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1,
- i__2, i__3;
-
- /* Local variables */
- integer lwork_cunglq_mn__, lwork_cunglq_nn__, lwork_cungqr_mm__,
- lwork_cungqr_mn__;
- complex cdum[1];
- integer iscl, lwork_cunmbr_prc_mm__, lwork_cunmbr_prc_mn__,
- lwork_cunmbr_prc_nn__;
- real anrm;
- integer ierr, itau, lwork_cunmbr_qln_mm__, lwork_cunmbr_qln_mn__,
- lwork_cunmbr_qln_nn__, idum[1], irvt, i__;
- extern /* Subroutine */ void 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;
- logical wntqa;
- integer nwork;
- extern /* Subroutine */ void clacp2_(char *, integer *, integer *, real *,
- integer *, complex *, integer *);
- logical wntqn, wntqo, wntqs;
- integer mnthr1, mnthr2, ie, lwork_cungbr_p_mn__, il, lwork_cungbr_p_nn__,
- lwork_cungbr_q_mn__, lwork_cungbr_q_mm__;
- extern /* Subroutine */ void cgebrd_(integer *, integer *, complex *,
- integer *, real *, real *, complex *, complex *, complex *,
- integer *, integer *);
- integer ir;
- extern real clange_(char *, integer *, integer *, complex *, integer *,
- real *);
- integer iu;
- extern /* Subroutine */ void cgelqf_(integer *, integer *, complex *,
- integer *, complex *, complex *, integer *, integer *), clacrm_(
- integer *, integer *, complex *, integer *, real *, integer *,
- complex *, integer *, real *), clarcm_(integer *, integer *, real
- *, integer *, complex *, integer *, complex *, integer *, real *),
- clascl_(char *, integer *, integer *, real *, real *, integer *,
- integer *, complex *, integer *, integer *), sbdsdc_(char
- *, char *, integer *, real *, real *, real *, integer *, real *,
- integer *, real *, integer *, real *, integer *, integer *), cgeqrf_(integer *, integer *, complex *, integer
- *, complex *, complex *, integer *, integer *);
- extern real slamch_(char *);
- extern /* Subroutine */ void clacpy_(char *, integer *, integer *, complex
- *, integer *, complex *, integer *), claset_(char *,
- integer *, integer *, complex *, complex *, complex *, integer *);
- extern int xerbla_(char *, integer *, ftnlen);
- extern void cungbr_(char *,
- integer *, integer *, integer *, complex *, integer *, complex *,
- complex *, integer *, integer *);
- real bignum;
- extern /* Subroutine */ void slascl_(char *, integer *, integer *, real *,
- real *, integer *, integer *, real *, integer *, integer *), 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 *);
- extern logical sisnan_(real *);
- integer ldwrkl;
- extern /* Subroutine */ void cungqr_(integer *, integer *, integer *,
- complex *, integer *, complex *, complex *, integer *, integer *);
- integer ldwrkr, minwrk, ldwrku, maxwrk, ldwkvt;
- real smlnum;
- logical wntqas, lquery;
- integer nrwork, blk;
- real dum[1], eps;
- integer iru, ivt, lwork_cgebrd_mm__, lwork_cgebrd_mn__, lwork_cgebrd_nn__,
- lwork_cgelqf_mn__, lwork_cgeqrf_mn__;
-
-
- /* -- LAPACK driver routine (version 3.7.0) -- */
- /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
- /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
- /* June 2016 */
-
-
- /* ===================================================================== */
-
-
- /* Test the input arguments */
-
- /* Parameter adjustments */
- a_dim1 = *lda;
- a_offset = 1 + a_dim1 * 1;
- a -= a_offset;
- --s;
- u_dim1 = *ldu;
- u_offset = 1 + u_dim1 * 1;
- u -= u_offset;
- vt_dim1 = *ldvt;
- vt_offset = 1 + vt_dim1 * 1;
- vt -= vt_offset;
- --work;
- --rwork;
- --iwork;
-
- /* Function Body */
- *info = 0;
- minmn = f2cmin(*m,*n);
- mnthr1 = (integer) (minmn * 17.f / 9.f);
- mnthr2 = (integer) (minmn * 5.f / 3.f);
- wntqa = lsame_(jobz, "A");
- wntqs = lsame_(jobz, "S");
- wntqas = wntqa || wntqs;
- wntqo = lsame_(jobz, "O");
- wntqn = lsame_(jobz, "N");
- lquery = *lwork == -1;
- minwrk = 1;
- maxwrk = 1;
-
- if (! (wntqa || wntqs || wntqo || wntqn)) {
- *info = -1;
- } else if (*m < 0) {
- *info = -2;
- } else if (*n < 0) {
- *info = -3;
- } else if (*lda < f2cmax(1,*m)) {
- *info = -5;
- } else if (*ldu < 1 || wntqas && *ldu < *m || wntqo && *m < *n && *ldu < *
- m) {
- *info = -8;
- } else if (*ldvt < 1 || wntqa && *ldvt < *n || wntqs && *ldvt < minmn ||
- wntqo && *m >= *n && *ldvt < *n) {
- *info = -10;
- }
-
- /* Compute workspace */
- /* Note: Comments in the code beginning "Workspace:" describe the */
- /* minimal amount of workspace allocated at that point in the code, */
- /* as well as the preferred amount for good performance. */
- /* CWorkspace refers to complex workspace, and RWorkspace to */
- /* real workspace. NB refers to the optimal block size for the */
- /* immediately following subroutine, as returned by ILAENV.) */
-
- if (*info == 0) {
- minwrk = 1;
- maxwrk = 1;
- if (*m >= *n && minmn > 0) {
-
- /* There is no complex work space needed for bidiagonal SVD */
- /* The real work space needed for bidiagonal SVD (sbdsdc) is */
- /* BDSPAC = 3*N*N + 4*N for singular values and vectors; */
- /* BDSPAC = 4*N for singular values only; */
- /* not including e, RU, and RVT matrices. */
-
- /* Compute space preferred for each routine */
- cgebrd_(m, n, cdum, m, dum, dum, cdum, cdum, cdum, &c_n1, &ierr);
- lwork_cgebrd_mn__ = (integer) cdum[0].r;
-
- cgebrd_(n, n, cdum, n, dum, dum, cdum, cdum, cdum, &c_n1, &ierr);
- lwork_cgebrd_nn__ = (integer) cdum[0].r;
-
- cgeqrf_(m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
- lwork_cgeqrf_mn__ = (integer) cdum[0].r;
-
- cungbr_("P", n, n, n, cdum, n, cdum, cdum, &c_n1, &ierr);
- lwork_cungbr_p_nn__ = (integer) cdum[0].r;
-
- cungbr_("Q", m, m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
- lwork_cungbr_q_mm__ = (integer) cdum[0].r;
-
- cungbr_("Q", m, n, n, cdum, m, cdum, cdum, &c_n1, &ierr);
- lwork_cungbr_q_mn__ = (integer) cdum[0].r;
-
- cungqr_(m, m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
- lwork_cungqr_mm__ = (integer) cdum[0].r;
-
- cungqr_(m, n, n, cdum, m, cdum, cdum, &c_n1, &ierr);
- lwork_cungqr_mn__ = (integer) cdum[0].r;
-
- cunmbr_("P", "R", "C", n, n, n, cdum, n, cdum, cdum, n, cdum, &
- c_n1, &ierr);
- lwork_cunmbr_prc_nn__ = (integer) cdum[0].r;
-
- cunmbr_("Q", "L", "N", m, m, n, cdum, m, cdum, cdum, m, cdum, &
- c_n1, &ierr);
- lwork_cunmbr_qln_mm__ = (integer) cdum[0].r;
-
- cunmbr_("Q", "L", "N", m, n, n, cdum, m, cdum, cdum, m, cdum, &
- c_n1, &ierr);
- lwork_cunmbr_qln_mn__ = (integer) cdum[0].r;
-
- cunmbr_("Q", "L", "N", n, n, n, cdum, n, cdum, cdum, n, cdum, &
- c_n1, &ierr);
- lwork_cunmbr_qln_nn__ = (integer) cdum[0].r;
-
- if (*m >= mnthr1) {
- if (wntqn) {
-
- /* Path 1 (M >> N, JOBZ='N') */
-
- maxwrk = *n + lwork_cgeqrf_mn__;
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*n << 1) + lwork_cgebrd_nn__;
- maxwrk = f2cmax(i__1,i__2);
- minwrk = *n * 3;
- } else if (wntqo) {
-
- /* Path 2 (M >> N, JOBZ='O') */
-
- wrkbl = *n + lwork_cgeqrf_mn__;
- /* Computing MAX */
- i__1 = wrkbl, i__2 = *n + lwork_cungqr_mn__;
- wrkbl = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = wrkbl, i__2 = (*n << 1) + lwork_cgebrd_nn__;
- wrkbl = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = wrkbl, i__2 = (*n << 1) + lwork_cunmbr_qln_nn__;
- wrkbl = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = wrkbl, i__2 = (*n << 1) + lwork_cunmbr_prc_nn__;
- wrkbl = f2cmax(i__1,i__2);
- maxwrk = *m * *n + *n * *n + wrkbl;
- minwrk = (*n << 1) * *n + *n * 3;
- } else if (wntqs) {
-
- /* Path 3 (M >> N, JOBZ='S') */
-
- wrkbl = *n + lwork_cgeqrf_mn__;
- /* Computing MAX */
- i__1 = wrkbl, i__2 = *n + lwork_cungqr_mn__;
- wrkbl = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = wrkbl, i__2 = (*n << 1) + lwork_cgebrd_nn__;
- wrkbl = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = wrkbl, i__2 = (*n << 1) + lwork_cunmbr_qln_nn__;
- wrkbl = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = wrkbl, i__2 = (*n << 1) + lwork_cunmbr_prc_nn__;
- wrkbl = f2cmax(i__1,i__2);
- maxwrk = *n * *n + wrkbl;
- minwrk = *n * *n + *n * 3;
- } else if (wntqa) {
-
- /* Path 4 (M >> N, JOBZ='A') */
-
- wrkbl = *n + lwork_cgeqrf_mn__;
- /* Computing MAX */
- i__1 = wrkbl, i__2 = *n + lwork_cungqr_mm__;
- wrkbl = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = wrkbl, i__2 = (*n << 1) + lwork_cgebrd_nn__;
- wrkbl = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = wrkbl, i__2 = (*n << 1) + lwork_cunmbr_qln_nn__;
- wrkbl = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = wrkbl, i__2 = (*n << 1) + lwork_cunmbr_prc_nn__;
- wrkbl = f2cmax(i__1,i__2);
- maxwrk = *n * *n + wrkbl;
- /* Computing MAX */
- i__1 = *n * 3, i__2 = *n + *m;
- minwrk = *n * *n + f2cmax(i__1,i__2);
- }
- } else if (*m >= mnthr2) {
-
- /* Path 5 (M >> N, but not as much as MNTHR1) */
-
- maxwrk = (*n << 1) + lwork_cgebrd_mn__;
- minwrk = (*n << 1) + *m;
- if (wntqo) {
- /* Path 5o (M >> N, JOBZ='O') */
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*n << 1) + lwork_cungbr_p_nn__;
- maxwrk = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*n << 1) + lwork_cungbr_q_mn__;
- maxwrk = f2cmax(i__1,i__2);
- maxwrk += *m * *n;
- minwrk += *n * *n;
- } else if (wntqs) {
- /* Path 5s (M >> N, JOBZ='S') */
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*n << 1) + lwork_cungbr_p_nn__;
- maxwrk = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*n << 1) + lwork_cungbr_q_mn__;
- maxwrk = f2cmax(i__1,i__2);
- } else if (wntqa) {
- /* Path 5a (M >> N, JOBZ='A') */
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*n << 1) + lwork_cungbr_p_nn__;
- maxwrk = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*n << 1) + lwork_cungbr_q_mm__;
- maxwrk = f2cmax(i__1,i__2);
- }
- } else {
-
- /* Path 6 (M >= N, but not much larger) */
-
- maxwrk = (*n << 1) + lwork_cgebrd_mn__;
- minwrk = (*n << 1) + *m;
- if (wntqo) {
- /* Path 6o (M >= N, JOBZ='O') */
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*n << 1) + lwork_cunmbr_prc_nn__;
- maxwrk = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*n << 1) + lwork_cunmbr_qln_mn__;
- maxwrk = f2cmax(i__1,i__2);
- maxwrk += *m * *n;
- minwrk += *n * *n;
- } else if (wntqs) {
- /* Path 6s (M >= N, JOBZ='S') */
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*n << 1) + lwork_cunmbr_qln_mn__;
- maxwrk = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*n << 1) + lwork_cunmbr_prc_nn__;
- maxwrk = f2cmax(i__1,i__2);
- } else if (wntqa) {
- /* Path 6a (M >= N, JOBZ='A') */
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*n << 1) + lwork_cunmbr_qln_mm__;
- maxwrk = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*n << 1) + lwork_cunmbr_prc_nn__;
- maxwrk = f2cmax(i__1,i__2);
- }
- }
- } else if (minmn > 0) {
-
- /* There is no complex work space needed for bidiagonal SVD */
- /* The real work space needed for bidiagonal SVD (sbdsdc) is */
- /* BDSPAC = 3*M*M + 4*M for singular values and vectors; */
- /* BDSPAC = 4*M for singular values only; */
- /* not including e, RU, and RVT matrices. */
-
- /* Compute space preferred for each routine */
- cgebrd_(m, n, cdum, m, dum, dum, cdum, cdum, cdum, &c_n1, &ierr);
- lwork_cgebrd_mn__ = (integer) cdum[0].r;
-
- cgebrd_(m, m, cdum, m, dum, dum, cdum, cdum, cdum, &c_n1, &ierr);
- lwork_cgebrd_mm__ = (integer) cdum[0].r;
-
- cgelqf_(m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
- lwork_cgelqf_mn__ = (integer) cdum[0].r;
-
- cungbr_("P", m, n, m, cdum, m, cdum, cdum, &c_n1, &ierr);
- lwork_cungbr_p_mn__ = (integer) cdum[0].r;
-
- cungbr_("P", n, n, m, cdum, n, cdum, cdum, &c_n1, &ierr);
- lwork_cungbr_p_nn__ = (integer) cdum[0].r;
-
- cungbr_("Q", m, m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
- lwork_cungbr_q_mm__ = (integer) cdum[0].r;
-
- cunglq_(m, n, m, cdum, m, cdum, cdum, &c_n1, &ierr);
- lwork_cunglq_mn__ = (integer) cdum[0].r;
-
- cunglq_(n, n, m, cdum, n, cdum, cdum, &c_n1, &ierr);
- lwork_cunglq_nn__ = (integer) cdum[0].r;
-
- cunmbr_("P", "R", "C", m, m, m, cdum, m, cdum, cdum, m, cdum, &
- c_n1, &ierr);
- lwork_cunmbr_prc_mm__ = (integer) cdum[0].r;
-
- cunmbr_("P", "R", "C", m, n, m, cdum, m, cdum, cdum, m, cdum, &
- c_n1, &ierr);
- lwork_cunmbr_prc_mn__ = (integer) cdum[0].r;
-
- cunmbr_("P", "R", "C", n, n, m, cdum, n, cdum, cdum, n, cdum, &
- c_n1, &ierr);
- lwork_cunmbr_prc_nn__ = (integer) cdum[0].r;
-
- cunmbr_("Q", "L", "N", m, m, m, cdum, m, cdum, cdum, m, cdum, &
- c_n1, &ierr);
- lwork_cunmbr_qln_mm__ = (integer) cdum[0].r;
-
- if (*n >= mnthr1) {
- if (wntqn) {
-
- /* Path 1t (N >> M, JOBZ='N') */
-
- maxwrk = *m + lwork_cgelqf_mn__;
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*m << 1) + lwork_cgebrd_mm__;
- maxwrk = f2cmax(i__1,i__2);
- minwrk = *m * 3;
- } else if (wntqo) {
-
- /* Path 2t (N >> M, JOBZ='O') */
-
- wrkbl = *m + lwork_cgelqf_mn__;
- /* Computing MAX */
- i__1 = wrkbl, i__2 = *m + lwork_cunglq_mn__;
- wrkbl = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = wrkbl, i__2 = (*m << 1) + lwork_cgebrd_mm__;
- wrkbl = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = wrkbl, i__2 = (*m << 1) + lwork_cunmbr_qln_mm__;
- wrkbl = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = wrkbl, i__2 = (*m << 1) + lwork_cunmbr_prc_mm__;
- wrkbl = f2cmax(i__1,i__2);
- maxwrk = *m * *n + *m * *m + wrkbl;
- minwrk = (*m << 1) * *m + *m * 3;
- } else if (wntqs) {
-
- /* Path 3t (N >> M, JOBZ='S') */
-
- wrkbl = *m + lwork_cgelqf_mn__;
- /* Computing MAX */
- i__1 = wrkbl, i__2 = *m + lwork_cunglq_mn__;
- wrkbl = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = wrkbl, i__2 = (*m << 1) + lwork_cgebrd_mm__;
- wrkbl = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = wrkbl, i__2 = (*m << 1) + lwork_cunmbr_qln_mm__;
- wrkbl = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = wrkbl, i__2 = (*m << 1) + lwork_cunmbr_prc_mm__;
- wrkbl = f2cmax(i__1,i__2);
- maxwrk = *m * *m + wrkbl;
- minwrk = *m * *m + *m * 3;
- } else if (wntqa) {
-
- /* Path 4t (N >> M, JOBZ='A') */
-
- wrkbl = *m + lwork_cgelqf_mn__;
- /* Computing MAX */
- i__1 = wrkbl, i__2 = *m + lwork_cunglq_nn__;
- wrkbl = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = wrkbl, i__2 = (*m << 1) + lwork_cgebrd_mm__;
- wrkbl = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = wrkbl, i__2 = (*m << 1) + lwork_cunmbr_qln_mm__;
- wrkbl = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = wrkbl, i__2 = (*m << 1) + lwork_cunmbr_prc_mm__;
- wrkbl = f2cmax(i__1,i__2);
- maxwrk = *m * *m + wrkbl;
- /* Computing MAX */
- i__1 = *m * 3, i__2 = *m + *n;
- minwrk = *m * *m + f2cmax(i__1,i__2);
- }
- } else if (*n >= mnthr2) {
-
- /* Path 5t (N >> M, but not as much as MNTHR1) */
-
- maxwrk = (*m << 1) + lwork_cgebrd_mn__;
- minwrk = (*m << 1) + *n;
- if (wntqo) {
- /* Path 5to (N >> M, JOBZ='O') */
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*m << 1) + lwork_cungbr_q_mm__;
- maxwrk = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*m << 1) + lwork_cungbr_p_mn__;
- maxwrk = f2cmax(i__1,i__2);
- maxwrk += *m * *n;
- minwrk += *m * *m;
- } else if (wntqs) {
- /* Path 5ts (N >> M, JOBZ='S') */
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*m << 1) + lwork_cungbr_q_mm__;
- maxwrk = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*m << 1) + lwork_cungbr_p_mn__;
- maxwrk = f2cmax(i__1,i__2);
- } else if (wntqa) {
- /* Path 5ta (N >> M, JOBZ='A') */
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*m << 1) + lwork_cungbr_q_mm__;
- maxwrk = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*m << 1) + lwork_cungbr_p_nn__;
- maxwrk = f2cmax(i__1,i__2);
- }
- } else {
-
- /* Path 6t (N > M, but not much larger) */
-
- maxwrk = (*m << 1) + lwork_cgebrd_mn__;
- minwrk = (*m << 1) + *n;
- if (wntqo) {
- /* Path 6to (N > M, JOBZ='O') */
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*m << 1) + lwork_cunmbr_qln_mm__;
- maxwrk = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*m << 1) + lwork_cunmbr_prc_mn__;
- maxwrk = f2cmax(i__1,i__2);
- maxwrk += *m * *n;
- minwrk += *m * *m;
- } else if (wntqs) {
- /* Path 6ts (N > M, JOBZ='S') */
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*m << 1) + lwork_cunmbr_qln_mm__;
- maxwrk = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*m << 1) + lwork_cunmbr_prc_mn__;
- maxwrk = f2cmax(i__1,i__2);
- } else if (wntqa) {
- /* Path 6ta (N > M, JOBZ='A') */
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*m << 1) + lwork_cunmbr_qln_mm__;
- maxwrk = f2cmax(i__1,i__2);
- /* Computing MAX */
- i__1 = maxwrk, i__2 = (*m << 1) + lwork_cunmbr_prc_nn__;
- maxwrk = f2cmax(i__1,i__2);
- }
- }
- }
- maxwrk = f2cmax(maxwrk,minwrk);
- }
- if (*info == 0) {
- work[1].r = (real) maxwrk, work[1].i = 0.f;
- if (*lwork < minwrk && ! lquery) {
- *info = -12;
- }
- }
-
- if (*info != 0) {
- i__1 = -(*info);
- xerbla_("CGESDD", &i__1, (ftnlen)6);
- return;
- } else if (lquery) {
- return;
- }
-
- /* Quick return if possible */
-
- if (*m == 0 || *n == 0) {
- return;
- }
-
- /* 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);
- if (sisnan_(&anrm)) {
- *info = -4;
- return;
- }
- 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 >= mnthr1) {
-
- if (wntqn) {
-
- /* Path 1 (M >> N, JOBZ='N') */
- /* No singular vectors to be computed */
-
- itau = 1;
- nwork = itau + *n;
-
- /* Compute A=Q*R */
- /* CWorkspace: need N [tau] + N [work] */
- /* CWorkspace: prefer N [tau] + N*NB [work] */
- /* RWorkspace: need 0 */
-
- i__1 = *lwork - nwork + 1;
- cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
- i__1, &ierr);
-
- /* Zero out below R */
-
- i__1 = *n - 1;
- i__2 = *n - 1;
- claset_("L", &i__1, &i__2, &c_b1, &c_b1, &a[a_dim1 + 2], lda);
- ie = 1;
- itauq = 1;
- itaup = itauq + *n;
- nwork = itaup + *n;
-
- /* Bidiagonalize R in A */
- /* CWorkspace: need 2*N [tauq, taup] + N [work] */
- /* CWorkspace: prefer 2*N [tauq, taup] + 2*N*NB [work] */
- /* RWorkspace: need N [e] */
-
- i__1 = *lwork - nwork + 1;
- cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
- itauq], &work[itaup], &work[nwork], &i__1, &ierr);
- nrwork = ie + *n;
-
- /* Perform bidiagonal SVD, compute singular values only */
- /* CWorkspace: need 0 */
- /* RWorkspace: need N [e] + BDSPAC */
-
- sbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, &
- c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
-
- } else if (wntqo) {
-
- /* Path 2 (M >> N, JOBZ='O') */
- /* N left singular vectors to be overwritten on A and */
- /* N right singular vectors to be computed in VT */
-
- iu = 1;
-
- /* WORK(IU) is N by N */
-
- ldwrku = *n;
- ir = iu + ldwrku * *n;
- if (*lwork >= *m * *n + *n * *n + *n * 3) {
-
- /* WORK(IR) is M by N */
-
- ldwrkr = *m;
- } else {
- ldwrkr = (*lwork - *n * *n - *n * 3) / *n;
- }
- itau = ir + ldwrkr * *n;
- nwork = itau + *n;
-
- /* Compute A=Q*R */
- /* CWorkspace: need N*N [U] + N*N [R] + N [tau] + N [work] */
- /* CWorkspace: prefer N*N [U] + N*N [R] + N [tau] + N*NB [work] */
- /* RWorkspace: need 0 */
-
- i__1 = *lwork - nwork + 1;
- cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
- i__1, &ierr);
-
- /* Copy R to WORK( IR ), zeroing out below it */
-
- clacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
- i__1 = *n - 1;
- i__2 = *n - 1;
- claset_("L", &i__1, &i__2, &c_b1, &c_b1, &work[ir + 1], &
- ldwrkr);
-
- /* Generate Q in A */
- /* CWorkspace: need N*N [U] + N*N [R] + N [tau] + N [work] */
- /* CWorkspace: prefer N*N [U] + N*N [R] + N [tau] + N*NB [work] */
- /* RWorkspace: need 0 */
-
- i__1 = *lwork - nwork + 1;
- cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork],
- &i__1, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *n;
- nwork = itaup + *n;
-
- /* Bidiagonalize R in WORK(IR) */
- /* CWorkspace: need N*N [U] + N*N [R] + 2*N [tauq, taup] + N [work] */
- /* CWorkspace: prefer N*N [U] + N*N [R] + 2*N [tauq, taup] + 2*N*NB [work] */
- /* RWorkspace: need N [e] */
-
- i__1 = *lwork - nwork + 1;
- cgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &work[
- itauq], &work[itaup], &work[nwork], &i__1, &ierr);
-
- /* Perform bidiagonal SVD, computing left singular vectors */
- /* of R in WORK(IRU) and computing right singular vectors */
- /* of R in WORK(IRVT) */
- /* CWorkspace: need 0 */
- /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
-
- iru = ie + *n;
- irvt = iru + *n * *n;
- nrwork = irvt + *n * *n;
- sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
- rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
- info);
-
- /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */
- /* Overwrite WORK(IU) by the left singular vectors of R */
- /* CWorkspace: need N*N [U] + N*N [R] + 2*N [tauq, taup] + N [work] */
- /* CWorkspace: prefer N*N [U] + N*N [R] + 2*N [tauq, taup] + N*NB [work] */
- /* RWorkspace: need 0 */
-
- clacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku);
- i__1 = *lwork - nwork + 1;
- cunmbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[
- itauq], &work[iu], &ldwrku, &work[nwork], &i__1, &
- ierr);
-
- /* Copy real matrix RWORK(IRVT) to complex matrix VT */
- /* Overwrite VT by the right singular vectors of R */
- /* CWorkspace: need N*N [U] + N*N [R] + 2*N [tauq, taup] + N [work] */
- /* CWorkspace: prefer N*N [U] + N*N [R] + 2*N [tauq, taup] + N*NB [work] */
- /* RWorkspace: need 0 */
-
- clacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
- i__1 = *lwork - nwork + 1;
- cunmbr_("P", "R", "C", n, n, n, &work[ir], &ldwrkr, &work[
- itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
- ierr);
-
- /* Multiply Q in A by left singular vectors of R in */
- /* WORK(IU), storing result in WORK(IR) and copying to A */
- /* CWorkspace: need N*N [U] + N*N [R] */
- /* CWorkspace: prefer N*N [U] + M*N [R] */
- /* RWorkspace: need 0 */
-
- i__1 = *m;
- i__2 = ldwrkr;
- for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
- i__2) {
- /* Computing MIN */
- i__3 = *m - i__ + 1;
- chunk = f2cmin(i__3,ldwrkr);
- cgemm_("N", "N", &chunk, n, n, &c_b2, &a[i__ + a_dim1],
- lda, &work[iu], &ldwrku, &c_b1, &work[ir], &
- ldwrkr);
- clacpy_("F", &chunk, n, &work[ir], &ldwrkr, &a[i__ +
- a_dim1], lda);
- /* L10: */
- }
-
- } else if (wntqs) {
-
- /* Path 3 (M >> N, JOBZ='S') */
- /* N left singular vectors to be computed in U and */
- /* N right singular vectors to be computed in VT */
-
- ir = 1;
-
- /* WORK(IR) is N by N */
-
- ldwrkr = *n;
- itau = ir + ldwrkr * *n;
- nwork = itau + *n;
-
- /* Compute A=Q*R */
- /* CWorkspace: need N*N [R] + N [tau] + N [work] */
- /* CWorkspace: prefer N*N [R] + N [tau] + N*NB [work] */
- /* RWorkspace: need 0 */
-
- i__2 = *lwork - nwork + 1;
- cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
- 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__1 = *n - 1;
- claset_("L", &i__2, &i__1, &c_b1, &c_b1, &work[ir + 1], &
- ldwrkr);
-
- /* Generate Q in A */
- /* CWorkspace: need N*N [R] + N [tau] + N [work] */
- /* CWorkspace: prefer N*N [R] + N [tau] + N*NB [work] */
- /* RWorkspace: need 0 */
-
- i__2 = *lwork - nwork + 1;
- cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork],
- &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *n;
- nwork = itaup + *n;
-
- /* Bidiagonalize R in WORK(IR) */
- /* CWorkspace: need N*N [R] + 2*N [tauq, taup] + N [work] */
- /* CWorkspace: prefer N*N [R] + 2*N [tauq, taup] + 2*N*NB [work] */
- /* RWorkspace: need N [e] */
-
- i__2 = *lwork - nwork + 1;
- cgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &work[
- itauq], &work[itaup], &work[nwork], &i__2, &ierr);
-
- /* Perform bidiagonal SVD, computing left singular vectors */
- /* of bidiagonal matrix in RWORK(IRU) and computing right */
- /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
- /* CWorkspace: need 0 */
- /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
-
- iru = ie + *n;
- irvt = iru + *n * *n;
- nrwork = irvt + *n * *n;
- sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
- rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
- info);
-
- /* Copy real matrix RWORK(IRU) to complex matrix U */
- /* Overwrite U by left singular vectors of R */
- /* CWorkspace: need N*N [R] + 2*N [tauq, taup] + N [work] */
- /* CWorkspace: prefer N*N [R] + 2*N [tauq, taup] + N*NB [work] */
- /* RWorkspace: need 0 */
-
- clacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu);
- i__2 = *lwork - nwork + 1;
- cunmbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[
- itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
-
- /* Copy real matrix RWORK(IRVT) to complex matrix VT */
- /* Overwrite VT by right singular vectors of R */
- /* CWorkspace: need N*N [R] + 2*N [tauq, taup] + N [work] */
- /* CWorkspace: prefer N*N [R] + 2*N [tauq, taup] + N*NB [work] */
- /* RWorkspace: need 0 */
-
- clacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
- i__2 = *lwork - nwork + 1;
- cunmbr_("P", "R", "C", n, n, n, &work[ir], &ldwrkr, &work[
- itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
- ierr);
-
- /* Multiply Q in A by left singular vectors of R in */
- /* WORK(IR), storing result in U */
- /* CWorkspace: need N*N [R] */
- /* RWorkspace: need 0 */
-
- clacpy_("F", n, n, &u[u_offset], ldu, &work[ir], &ldwrkr);
- cgemm_("N", "N", m, n, n, &c_b2, &a[a_offset], lda, &work[ir],
- &ldwrkr, &c_b1, &u[u_offset], ldu);
-
- } else if (wntqa) {
-
- /* Path 4 (M >> N, JOBZ='A') */
- /* M left singular vectors to be computed in U and */
- /* N right singular vectors to be computed in VT */
-
- iu = 1;
-
- /* WORK(IU) is N by N */
-
- ldwrku = *n;
- itau = iu + ldwrku * *n;
- nwork = itau + *n;
-
- /* Compute A=Q*R, copying result to U */
- /* CWorkspace: need N*N [U] + N [tau] + N [work] */
- /* CWorkspace: prefer N*N [U] + N [tau] + N*NB [work] */
- /* RWorkspace: need 0 */
-
- i__2 = *lwork - nwork + 1;
- cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
- i__2, &ierr);
- clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
-
- /* Generate Q in U */
- /* CWorkspace: need N*N [U] + N [tau] + M [work] */
- /* CWorkspace: prefer N*N [U] + N [tau] + M*NB [work] */
- /* RWorkspace: need 0 */
-
- i__2 = *lwork - nwork + 1;
- cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &work[nwork],
- &i__2, &ierr);
-
- /* Produce R in A, zeroing out below it */
-
- i__2 = *n - 1;
- i__1 = *n - 1;
- claset_("L", &i__2, &i__1, &c_b1, &c_b1, &a[a_dim1 + 2], lda);
- ie = 1;
- itauq = itau;
- itaup = itauq + *n;
- nwork = itaup + *n;
-
- /* Bidiagonalize R in A */
- /* CWorkspace: need N*N [U] + 2*N [tauq, taup] + N [work] */
- /* CWorkspace: prefer N*N [U] + 2*N [tauq, taup] + 2*N*NB [work] */
- /* RWorkspace: need N [e] */
-
- i__2 = *lwork - nwork + 1;
- cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
- itauq], &work[itaup], &work[nwork], &i__2, &ierr);
- iru = ie + *n;
- irvt = iru + *n * *n;
- nrwork = irvt + *n * *n;
-
- /* Perform bidiagonal SVD, computing left singular vectors */
- /* of bidiagonal matrix in RWORK(IRU) and computing right */
- /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
- /* CWorkspace: need 0 */
- /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
-
- sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
- rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
- info);
-
- /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */
- /* Overwrite WORK(IU) by left singular vectors of R */
- /* CWorkspace: need N*N [U] + 2*N [tauq, taup] + N [work] */
- /* CWorkspace: prefer N*N [U] + 2*N [tauq, taup] + N*NB [work] */
- /* RWorkspace: need 0 */
-
- clacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku);
- i__2 = *lwork - nwork + 1;
- cunmbr_("Q", "L", "N", n, n, n, &a[a_offset], lda, &work[
- itauq], &work[iu], &ldwrku, &work[nwork], &i__2, &
- ierr);
-
- /* Copy real matrix RWORK(IRVT) to complex matrix VT */
- /* Overwrite VT by right singular vectors of R */
- /* CWorkspace: need N*N [U] + 2*N [tauq, taup] + N [work] */
- /* CWorkspace: prefer N*N [U] + 2*N [tauq, taup] + N*NB [work] */
- /* RWorkspace: need 0 */
-
- clacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
- i__2 = *lwork - nwork + 1;
- cunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
- itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
- ierr);
-
- /* Multiply Q in U by left singular vectors of R in */
- /* WORK(IU), storing result in A */
- /* CWorkspace: need N*N [U] */
- /* RWorkspace: need 0 */
-
- 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 if (*m >= mnthr2) {
-
- /* MNTHR2 <= M < MNTHR1 */
-
- /* Path 5 (M >> N, but not as much as MNTHR1) */
- /* Reduce to bidiagonal form without QR decomposition, use */
- /* CUNGBR and matrix multiplication to compute singular vectors */
-
- ie = 1;
- nrwork = ie + *n;
- itauq = 1;
- itaup = itauq + *n;
- nwork = itaup + *n;
-
- /* Bidiagonalize A */
- /* CWorkspace: need 2*N [tauq, taup] + M [work] */
- /* CWorkspace: prefer 2*N [tauq, taup] + (M+N)*NB [work] */
- /* RWorkspace: need N [e] */
-
- i__2 = *lwork - nwork + 1;
- cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
- &work[itaup], &work[nwork], &i__2, &ierr);
- if (wntqn) {
-
- /* Path 5n (M >> N, JOBZ='N') */
- /* Compute singular values only */
- /* CWorkspace: need 0 */
- /* RWorkspace: need N [e] + BDSPAC */
-
- sbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, &
- c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
- } else if (wntqo) {
- iu = nwork;
- iru = nrwork;
- irvt = iru + *n * *n;
- nrwork = irvt + *n * *n;
-
- /* Path 5o (M >> N, JOBZ='O') */
- /* Copy A to VT, generate P**H */
- /* CWorkspace: need 2*N [tauq, taup] + N [work] */
- /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
- /* RWorkspace: need 0 */
-
- clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
- i__2 = *lwork - nwork + 1;
- cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
- work[nwork], &i__2, &ierr);
-
- /* Generate Q in A */
- /* CWorkspace: need 2*N [tauq, taup] + N [work] */
- /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
- /* RWorkspace: need 0 */
-
- i__2 = *lwork - nwork + 1;
- cungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[
- nwork], &i__2, &ierr);
-
- if (*lwork >= *m * *n + *n * 3) {
-
- /* WORK( IU ) is M by N */
-
- ldwrku = *m;
- } else {
-
- /* WORK(IU) is LDWRKU by N */
-
- ldwrku = (*lwork - *n * 3) / *n;
- }
- nwork = iu + ldwrku * *n;
-
- /* Perform bidiagonal SVD, computing left singular vectors */
- /* of bidiagonal matrix in RWORK(IRU) and computing right */
- /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
- /* CWorkspace: need 0 */
- /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
-
- sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
- rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
- info);
-
- /* Multiply real matrix RWORK(IRVT) by P**H in VT, */
- /* storing the result in WORK(IU), copying to VT */
- /* CWorkspace: need 2*N [tauq, taup] + N*N [U] */
- /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + 2*N*N [rwork] */
-
- clarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &work[iu]
- , &ldwrku, &rwork[nrwork]);
- clacpy_("F", n, n, &work[iu], &ldwrku, &vt[vt_offset], ldvt);
-
- /* Multiply Q in A by real matrix RWORK(IRU), storing the */
- /* result in WORK(IU), copying to A */
- /* CWorkspace: need 2*N [tauq, taup] + N*N [U] */
- /* CWorkspace: prefer 2*N [tauq, taup] + M*N [U] */
- /* RWorkspace: need N [e] + N*N [RU] + 2*N*N [rwork] */
- /* RWorkspace: prefer N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */
-
- nrwork = irvt;
- i__2 = *m;
- i__1 = ldwrku;
- for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
- i__1) {
- /* Computing MIN */
- i__3 = *m - i__ + 1;
- chunk = f2cmin(i__3,ldwrku);
- clacrm_(&chunk, n, &a[i__ + a_dim1], lda, &rwork[iru], n,
- &work[iu], &ldwrku, &rwork[nrwork]);
- clacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
- a_dim1], lda);
- /* L20: */
- }
-
- } else if (wntqs) {
-
- /* Path 5s (M >> N, JOBZ='S') */
- /* Copy A to VT, generate P**H */
- /* CWorkspace: need 2*N [tauq, taup] + N [work] */
- /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
- /* RWorkspace: need 0 */
-
- clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
- i__1 = *lwork - nwork + 1;
- cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
- work[nwork], &i__1, &ierr);
-
- /* Copy A to U, generate Q */
- /* CWorkspace: need 2*N [tauq, taup] + N [work] */
- /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
- /* RWorkspace: need 0 */
-
- clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
- i__1 = *lwork - nwork + 1;
- cungbr_("Q", m, n, n, &u[u_offset], ldu, &work[itauq], &work[
- nwork], &i__1, &ierr);
-
- /* Perform bidiagonal SVD, computing left singular vectors */
- /* of bidiagonal matrix in RWORK(IRU) and computing right */
- /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
- /* CWorkspace: need 0 */
- /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
-
- iru = nrwork;
- irvt = iru + *n * *n;
- nrwork = irvt + *n * *n;
- sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
- rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
- info);
-
- /* Multiply real matrix RWORK(IRVT) by P**H in VT, */
- /* storing the result in A, copying to VT */
- /* CWorkspace: need 0 */
- /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + 2*N*N [rwork] */
-
- clarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &a[
- a_offset], lda, &rwork[nrwork]);
- clacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
-
- /* Multiply Q in U by real matrix RWORK(IRU), storing the */
- /* result in A, copying to U */
- /* CWorkspace: need 0 */
- /* RWorkspace: need N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */
-
- nrwork = irvt;
- clacrm_(m, n, &u[u_offset], ldu, &rwork[iru], n, &a[a_offset],
- lda, &rwork[nrwork]);
- clacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);
- } else {
-
- /* Path 5a (M >> N, JOBZ='A') */
- /* Copy A to VT, generate P**H */
- /* CWorkspace: need 2*N [tauq, taup] + N [work] */
- /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
- /* RWorkspace: need 0 */
-
- clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
- i__1 = *lwork - nwork + 1;
- cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
- work[nwork], &i__1, &ierr);
-
- /* Copy A to U, generate Q */
- /* CWorkspace: need 2*N [tauq, taup] + M [work] */
- /* CWorkspace: prefer 2*N [tauq, taup] + M*NB [work] */
- /* RWorkspace: need 0 */
-
- clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
- i__1 = *lwork - nwork + 1;
- cungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
- nwork], &i__1, &ierr);
-
- /* Perform bidiagonal SVD, computing left singular vectors */
- /* of bidiagonal matrix in RWORK(IRU) and computing right */
- /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
- /* CWorkspace: need 0 */
- /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
-
- iru = nrwork;
- irvt = iru + *n * *n;
- nrwork = irvt + *n * *n;
- sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
- rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
- info);
-
- /* Multiply real matrix RWORK(IRVT) by P**H in VT, */
- /* storing the result in A, copying to VT */
- /* CWorkspace: need 0 */
- /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + 2*N*N [rwork] */
-
- clarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &a[
- a_offset], lda, &rwork[nrwork]);
- clacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
-
- /* Multiply Q in U by real matrix RWORK(IRU), storing the */
- /* result in A, copying to U */
- /* CWorkspace: need 0 */
- /* RWorkspace: need N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */
-
- nrwork = irvt;
- clacrm_(m, n, &u[u_offset], ldu, &rwork[iru], n, &a[a_offset],
- lda, &rwork[nrwork]);
- clacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);
- }
-
- } else {
-
- /* M .LT. MNTHR2 */
-
- /* Path 6 (M >= N, but not much larger) */
- /* Reduce to bidiagonal form without QR decomposition */
- /* Use CUNMBR to compute singular vectors */
-
- ie = 1;
- nrwork = ie + *n;
- itauq = 1;
- itaup = itauq + *n;
- nwork = itaup + *n;
-
- /* Bidiagonalize A */
- /* CWorkspace: need 2*N [tauq, taup] + M [work] */
- /* CWorkspace: prefer 2*N [tauq, taup] + (M+N)*NB [work] */
- /* RWorkspace: need N [e] */
-
- i__1 = *lwork - nwork + 1;
- cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
- &work[itaup], &work[nwork], &i__1, &ierr);
- if (wntqn) {
-
- /* Path 6n (M >= N, JOBZ='N') */
- /* Compute singular values only */
- /* CWorkspace: need 0 */
- /* RWorkspace: need N [e] + BDSPAC */
-
- sbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, &
- c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
- } else if (wntqo) {
- iu = nwork;
- iru = nrwork;
- irvt = iru + *n * *n;
- nrwork = irvt + *n * *n;
- if (*lwork >= *m * *n + *n * 3) {
-
- /* WORK( IU ) is M by N */
-
- ldwrku = *m;
- } else {
-
- /* WORK( IU ) is LDWRKU by N */
-
- ldwrku = (*lwork - *n * 3) / *n;
- }
- nwork = iu + ldwrku * *n;
-
- /* Path 6o (M >= N, JOBZ='O') */
- /* Perform bidiagonal SVD, computing left singular vectors */
- /* of bidiagonal matrix in RWORK(IRU) and computing right */
- /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
- /* CWorkspace: need 0 */
- /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
-
- sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
- rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
- info);
-
- /* Copy real matrix RWORK(IRVT) to complex matrix VT */
- /* Overwrite VT by right singular vectors of A */
- /* CWorkspace: need 2*N [tauq, taup] + N*N [U] + N [work] */
- /* CWorkspace: prefer 2*N [tauq, taup] + N*N [U] + N*NB [work] */
- /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
-
- clacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
- i__1 = *lwork - nwork + 1;
- cunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
- itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
- ierr);
-
- if (*lwork >= *m * *n + *n * 3) {
-
- /* Path 6o-fast */
- /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */
- /* Overwrite WORK(IU) by left singular vectors of A, copying */
- /* to A */
- /* CWorkspace: need 2*N [tauq, taup] + M*N [U] + N [work] */
- /* CWorkspace: prefer 2*N [tauq, taup] + M*N [U] + N*NB [work] */
- /* RWorkspace: need N [e] + N*N [RU] */
-
- claset_("F", m, n, &c_b1, &c_b1, &work[iu], &ldwrku);
- clacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku);
- i__1 = *lwork - nwork + 1;
- cunmbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[
- itauq], &work[iu], &ldwrku, &work[nwork], &i__1, &
- ierr);
- clacpy_("F", m, n, &work[iu], &ldwrku, &a[a_offset], lda);
- } else {
-
- /* Path 6o-slow */
- /* Generate Q in A */
- /* CWorkspace: need 2*N [tauq, taup] + N*N [U] + N [work] */
- /* CWorkspace: prefer 2*N [tauq, taup] + N*N [U] + N*NB [work] */
- /* RWorkspace: need 0 */
-
- i__1 = *lwork - nwork + 1;
- cungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &
- work[nwork], &i__1, &ierr);
-
- /* Multiply Q in A by real matrix RWORK(IRU), storing the */
- /* result in WORK(IU), copying to A */
- /* CWorkspace: need 2*N [tauq, taup] + N*N [U] */
- /* CWorkspace: prefer 2*N [tauq, taup] + M*N [U] */
- /* RWorkspace: need N [e] + N*N [RU] + 2*N*N [rwork] */
- /* RWorkspace: prefer N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */
-
- nrwork = irvt;
- i__1 = *m;
- i__2 = ldwrku;
- for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
- i__2) {
- /* Computing MIN */
- i__3 = *m - i__ + 1;
- chunk = f2cmin(i__3,ldwrku);
- clacrm_(&chunk, n, &a[i__ + a_dim1], lda, &rwork[iru],
- n, &work[iu], &ldwrku, &rwork[nrwork]);
- clacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
- a_dim1], lda);
- /* L30: */
- }
- }
-
- } else if (wntqs) {
-
- /* Path 6s (M >= N, JOBZ='S') */
- /* Perform bidiagonal SVD, computing left singular vectors */
- /* of bidiagonal matrix in RWORK(IRU) and computing right */
- /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
- /* CWorkspace: need 0 */
- /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
-
- iru = nrwork;
- irvt = iru + *n * *n;
- nrwork = irvt + *n * *n;
- sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
- rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
- info);
-
- /* Copy real matrix RWORK(IRU) to complex matrix U */
- /* Overwrite U by left singular vectors of A */
- /* CWorkspace: need 2*N [tauq, taup] + N [work] */
- /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
- /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
-
- claset_("F", m, n, &c_b1, &c_b1, &u[u_offset], ldu)
- ;
- clacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu);
- i__2 = *lwork - nwork + 1;
- cunmbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[
- itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
-
- /* Copy real matrix RWORK(IRVT) to complex matrix VT */
- /* Overwrite VT by right singular vectors of A */
- /* CWorkspace: need 2*N [tauq, taup] + N [work] */
- /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
- /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
-
- clacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
- i__2 = *lwork - nwork + 1;
- cunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
- itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
- ierr);
- } else {
-
- /* Path 6a (M >= N, JOBZ='A') */
- /* Perform bidiagonal SVD, computing left singular vectors */
- /* of bidiagonal matrix in RWORK(IRU) and computing right */
- /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
- /* CWorkspace: need 0 */
- /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
-
- iru = nrwork;
- irvt = iru + *n * *n;
- nrwork = irvt + *n * *n;
- sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
- rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
- info);
-
- /* Set the right corner of U to identity matrix */
-
- claset_("F", m, m, &c_b1, &c_b1, &u[u_offset], ldu)
- ;
- if (*m > *n) {
- i__2 = *m - *n;
- i__1 = *m - *n;
- claset_("F", &i__2, &i__1, &c_b1, &c_b2, &u[*n + 1 + (*n
- + 1) * u_dim1], ldu);
- }
-
- /* Copy real matrix RWORK(IRU) to complex matrix U */
- /* Overwrite U by left singular vectors of A */
- /* CWorkspace: need 2*N [tauq, taup] + M [work] */
- /* CWorkspace: prefer 2*N [tauq, taup] + M*NB [work] */
- /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
-
- clacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu);
- i__2 = *lwork - nwork + 1;
- cunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
- itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
-
- /* Copy real matrix RWORK(IRVT) to complex matrix VT */
- /* Overwrite VT by right singular vectors of A */
- /* CWorkspace: need 2*N [tauq, taup] + N [work] */
- /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
- /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
-
- clacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
- i__2 = *lwork - nwork + 1;
- cunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
- itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
- ierr);
- }
-
- }
-
- } else {
-
- /* A has more columns than rows. If A has sufficiently more */
- /* columns than rows, first reduce using the LQ decomposition (if */
- /* sufficient workspace available) */
-
- if (*n >= mnthr1) {
-
- if (wntqn) {
-
- /* Path 1t (N >> M, JOBZ='N') */
- /* No singular vectors to be computed */
-
- itau = 1;
- nwork = itau + *m;
-
- /* Compute A=L*Q */
- /* CWorkspace: need M [tau] + M [work] */
- /* CWorkspace: prefer M [tau] + M*NB [work] */
- /* RWorkspace: need 0 */
-
- i__2 = *lwork - nwork + 1;
- cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
- i__2, &ierr);
-
- /* Zero out above L */
-
- i__2 = *m - 1;
- i__1 = *m - 1;
- claset_("U", &i__2, &i__1, &c_b1, &c_b1, &a[(a_dim1 << 1) + 1]
- , lda);
- ie = 1;
- itauq = 1;
- itaup = itauq + *m;
- nwork = itaup + *m;
-
- /* Bidiagonalize L in A */
- /* CWorkspace: need 2*M [tauq, taup] + M [work] */
- /* CWorkspace: prefer 2*M [tauq, taup] + 2*M*NB [work] */
- /* RWorkspace: need M [e] */
-
- i__2 = *lwork - nwork + 1;
- cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &work[
- itauq], &work[itaup], &work[nwork], &i__2, &ierr);
- nrwork = ie + *m;
-
- /* Perform bidiagonal SVD, compute singular values only */
- /* CWorkspace: need 0 */
- /* RWorkspace: need M [e] + BDSPAC */
-
- sbdsdc_("U", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, &
- c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
-
- } else if (wntqo) {
-
- /* Path 2t (N >> M, JOBZ='O') */
- /* M right singular vectors to be overwritten on A and */
- /* M left singular vectors to be computed in U */
-
- ivt = 1;
- ldwkvt = *m;
-
- /* WORK(IVT) is M by M */
-
- il = ivt + ldwkvt * *m;
- if (*lwork >= *m * *n + *m * *m + *m * 3) {
-
- /* WORK(IL) M by N */
-
- ldwrkl = *m;
- chunk = *n;
- } else {
-
- /* WORK(IL) is M by CHUNK */
-
- ldwrkl = *m;
- chunk = (*lwork - *m * *m - *m * 3) / *m;
- }
- itau = il + ldwrkl * chunk;
- nwork = itau + *m;
-
- /* Compute A=L*Q */
- /* CWorkspace: need M*M [VT] + M*M [L] + M [tau] + M [work] */
- /* CWorkspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work] */
- /* RWorkspace: need 0 */
-
- i__2 = *lwork - nwork + 1;
- cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
- i__2, &ierr);
-
- /* Copy L to WORK(IL), zeroing about above it */
-
- clacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl);
- i__2 = *m - 1;
- i__1 = *m - 1;
- claset_("U", &i__2, &i__1, &c_b1, &c_b1, &work[il + ldwrkl], &
- ldwrkl);
-
- /* Generate Q in A */
- /* CWorkspace: need M*M [VT] + M*M [L] + M [tau] + M [work] */
- /* CWorkspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work] */
- /* RWorkspace: need 0 */
-
- i__2 = *lwork - nwork + 1;
- cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork],
- &i__2, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *m;
- nwork = itaup + *m;
-
- /* Bidiagonalize L in WORK(IL) */
- /* CWorkspace: need M*M [VT] + M*M [L] + 2*M [tauq, taup] + M [work] */
- /* CWorkspace: prefer M*M [VT] + M*M [L] + 2*M [tauq, taup] + 2*M*NB [work] */
- /* RWorkspace: need M [e] */
-
- i__2 = *lwork - nwork + 1;
- cgebrd_(m, m, &work[il], &ldwrkl, &s[1], &rwork[ie], &work[
- itauq], &work[itaup], &work[nwork], &i__2, &ierr);
-
- /* Perform bidiagonal SVD, computing left singular vectors */
- /* of bidiagonal matrix in RWORK(IRU) and computing right */
- /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
- /* CWorkspace: need 0 */
- /* RWorkspace: need M [e] + M*M [RU] + M*M [RVT] + BDSPAC */
-
- iru = ie + *m;
- irvt = iru + *m * *m;
- nrwork = irvt + *m * *m;
- sbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
- rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
- info);
-
- /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */
- /* Overwrite WORK(IU) by the left singular vectors of L */
- /* CWorkspace: need M*M [VT] + M*M [L] + 2*M [tauq, taup] + M [work] */
- /* CWorkspace: prefer M*M [VT] + M*M [L] + 2*M [tauq, taup] + M*NB [work] */
- /* RWorkspace: need 0 */
-
- clacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
- i__2 = *lwork - nwork + 1;
- cunmbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[
- itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
-
- /* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) */
- /* Overwrite WORK(IVT) by the right singular vectors of L */
- /* CWorkspace: need M*M [VT] + M*M [L] + 2*M [tauq, taup] + M [work] */
- /* CWorkspace: prefer M*M [VT] + M*M [L] + 2*M [tauq, taup] + M*NB [work] */
- /* RWorkspace: need 0 */
-
- clacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt);
- i__2 = *lwork - nwork + 1;
- cunmbr_("P", "R", "C", m, m, m, &work[il], &ldwrkl, &work[
- itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2, &
- ierr);
-
- /* Multiply right singular vectors of L in WORK(IL) by Q */
- /* in A, storing result in WORK(IL) and copying to A */
- /* CWorkspace: need M*M [VT] + M*M [L] */
- /* CWorkspace: prefer M*M [VT] + M*N [L] */
- /* RWorkspace: need 0 */
-
- i__2 = *n;
- i__1 = chunk;
- for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
- i__1) {
- /* Computing MIN */
- i__3 = *n - i__ + 1;
- blk = f2cmin(i__3,chunk);
- cgemm_("N", "N", m, &blk, m, &c_b2, &work[ivt], m, &a[i__
- * a_dim1 + 1], lda, &c_b1, &work[il], &ldwrkl);
- clacpy_("F", m, &blk, &work[il], &ldwrkl, &a[i__ * a_dim1
- + 1], lda);
- /* L40: */
- }
-
- } else if (wntqs) {
-
- /* Path 3t (N >> M, JOBZ='S') */
- /* M right singular vectors to be computed in VT and */
- /* M left singular vectors to be computed in U */
-
- il = 1;
-
- /* WORK(IL) is M by M */
-
- ldwrkl = *m;
- itau = il + ldwrkl * *m;
- nwork = itau + *m;
-
- /* Compute A=L*Q */
- /* CWorkspace: need M*M [L] + M [tau] + M [work] */
- /* CWorkspace: prefer M*M [L] + M [tau] + M*NB [work] */
- /* RWorkspace: need 0 */
-
- i__1 = *lwork - nwork + 1;
- cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
- i__1, &ierr);
-
- /* Copy L to WORK(IL), zeroing out above it */
-
- clacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl);
- i__1 = *m - 1;
- i__2 = *m - 1;
- claset_("U", &i__1, &i__2, &c_b1, &c_b1, &work[il + ldwrkl], &
- ldwrkl);
-
- /* Generate Q in A */
- /* CWorkspace: need M*M [L] + M [tau] + M [work] */
- /* CWorkspace: prefer M*M [L] + M [tau] + M*NB [work] */
- /* RWorkspace: need 0 */
-
- i__1 = *lwork - nwork + 1;
- cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork],
- &i__1, &ierr);
- ie = 1;
- itauq = itau;
- itaup = itauq + *m;
- nwork = itaup + *m;
-
- /* Bidiagonalize L in WORK(IL) */
- /* CWorkspace: need M*M [L] + 2*M [tauq, taup] + M [work] */
- /* CWorkspace: prefer M*M [L] + 2*M [tauq, taup] + 2*M*NB [work] */
- /* RWorkspace: need M [e] */
-
- i__1 = *lwork - nwork + 1;
- cgebrd_(m, m, &work[il], &ldwrkl, &s[1], &rwork[ie], &work[
- itauq], &work[itaup], &work[nwork], &i__1, &ierr);
-
- /* Perform bidiagonal SVD, computing left singular vectors */
- /* of bidiagonal matrix in RWORK(IRU) and computing right */
- /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
- /* CWorkspace: need 0 */
- /* RWorkspace: need M [e] + M*M [RU] + M*M [RVT] + BDSPAC */
-
- iru = ie + *m;
- irvt = iru + *m * *m;
- nrwork = irvt + *m * *m;
- sbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
- rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
- info);
-
- /* Copy real matrix RWORK(IRU) to complex matrix U */
- /* Overwrite U by left singular vectors of L */
- /* CWorkspace: need M*M [L] + 2*M [tauq, taup] + M [work] */
- /* CWorkspace: prefer M*M [L] + 2*M [tauq, taup] + M*NB [work] */
- /* RWorkspace: need 0 */
-
- clacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
- i__1 = *lwork - nwork + 1;
- cunmbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[
- itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
-
- /* Copy real matrix RWORK(IRVT) to complex matrix VT */
- /* Overwrite VT by left singular vectors of L */
- /* CWorkspace: need M*M [L] + 2*M [tauq, taup] + M [work] */
- /* CWorkspace: prefer M*M [L] + 2*M [tauq, taup] + M*NB [work] */
- /* RWorkspace: need 0 */
-
- clacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt);
- i__1 = *lwork - nwork + 1;
- cunmbr_("P", "R", "C", m, m, m, &work[il], &ldwrkl, &work[
- itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
- ierr);
-
- /* Copy VT to WORK(IL), multiply right singular vectors of L */
- /* in WORK(IL) by Q in A, storing result in VT */
- /* CWorkspace: need M*M [L] */
- /* RWorkspace: need 0 */
-
- clacpy_("F", m, m, &vt[vt_offset], ldvt, &work[il], &ldwrkl);
- cgemm_("N", "N", m, n, m, &c_b2, &work[il], &ldwrkl, &a[
- a_offset], lda, &c_b1, &vt[vt_offset], ldvt);
-
- } else if (wntqa) {
-
- /* Path 4t (N >> M, JOBZ='A') */
- /* N right singular vectors to be computed in VT and */
- /* M left singular vectors to be computed in U */
-
- ivt = 1;
-
- /* WORK(IVT) is M by M */
-
- ldwkvt = *m;
- itau = ivt + ldwkvt * *m;
- nwork = itau + *m;
-
- /* Compute A=L*Q, copying result to VT */
- /* CWorkspace: need M*M [VT] + M [tau] + M [work] */
- /* CWorkspace: prefer M*M [VT] + M [tau] + M*NB [work] */
- /* RWorkspace: need 0 */
-
- i__1 = *lwork - nwork + 1;
- cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
- i__1, &ierr);
- clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
-
- /* Generate Q in VT */
- /* CWorkspace: need M*M [VT] + M [tau] + N [work] */
- /* CWorkspace: prefer M*M [VT] + M [tau] + N*NB [work] */
- /* RWorkspace: need 0 */
-
- i__1 = *lwork - nwork + 1;
- cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &work[
- nwork], &i__1, &ierr);
-
- /* Produce L in A, zeroing out above it */
-
- i__1 = *m - 1;
- i__2 = *m - 1;
- claset_("U", &i__1, &i__2, &c_b1, &c_b1, &a[(a_dim1 << 1) + 1]
- , lda);
- ie = 1;
- itauq = itau;
- itaup = itauq + *m;
- nwork = itaup + *m;
-
- /* Bidiagonalize L in A */
- /* CWorkspace: need M*M [VT] + 2*M [tauq, taup] + M [work] */
- /* CWorkspace: prefer M*M [VT] + 2*M [tauq, taup] + 2*M*NB [work] */
- /* RWorkspace: need M [e] */
-
- i__1 = *lwork - nwork + 1;
- cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &work[
- itauq], &work[itaup], &work[nwork], &i__1, &ierr);
-
- /* Perform bidiagonal SVD, computing left singular vectors */
- /* of bidiagonal matrix in RWORK(IRU) and computing right */
- /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
- /* CWorkspace: need 0 */
- /* RWorkspace: need M [e] + M*M [RU] + M*M [RVT] + BDSPAC */
-
- iru = ie + *m;
- irvt = iru + *m * *m;
- nrwork = irvt + *m * *m;
- sbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
- rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
- info);
-
- /* Copy real matrix RWORK(IRU) to complex matrix U */
- /* Overwrite U by left singular vectors of L */
- /* CWorkspace: need M*M [VT] + 2*M [tauq, taup] + M [work] */
- /* CWorkspace: prefer M*M [VT] + 2*M [tauq, taup] + M*NB [work] */
- /* RWorkspace: need 0 */
-
- clacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
- i__1 = *lwork - nwork + 1;
- cunmbr_("Q", "L", "N", m, m, m, &a[a_offset], lda, &work[
- itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
-
- /* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) */
- /* Overwrite WORK(IVT) by right singular vectors of L */
- /* CWorkspace: need M*M [VT] + 2*M [tauq, taup] + M [work] */
- /* CWorkspace: prefer M*M [VT] + 2*M [tauq, taup] + M*NB [work] */
- /* RWorkspace: need 0 */
-
- clacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt);
- i__1 = *lwork - nwork + 1;
- cunmbr_("P", "R", "C", m, m, m, &a[a_offset], lda, &work[
- itaup], &work[ivt], &ldwkvt, &work[nwork], &i__1, &
- ierr);
-
- /* Multiply right singular vectors of L in WORK(IVT) by */
- /* Q in VT, storing result in A */
- /* CWorkspace: need M*M [VT] */
- /* RWorkspace: need 0 */
-
- cgemm_("N", "N", m, n, m, &c_b2, &work[ivt], &ldwkvt, &vt[
- vt_offset], ldvt, &c_b1, &a[a_offset], lda);
-
- /* Copy right singular vectors of A from A to VT */
-
- clacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
-
- }
-
- } else if (*n >= mnthr2) {
-
- /* MNTHR2 <= N < MNTHR1 */
-
- /* Path 5t (N >> M, but not as much as MNTHR1) */
- /* Reduce to bidiagonal form without QR decomposition, use */
- /* CUNGBR and matrix multiplication to compute singular vectors */
-
- ie = 1;
- nrwork = ie + *m;
- itauq = 1;
- itaup = itauq + *m;
- nwork = itaup + *m;
-
- /* Bidiagonalize A */
- /* CWorkspace: need 2*M [tauq, taup] + N [work] */
- /* CWorkspace: prefer 2*M [tauq, taup] + (M+N)*NB [work] */
- /* RWorkspace: need M [e] */
-
- i__1 = *lwork - nwork + 1;
- cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
- &work[itaup], &work[nwork], &i__1, &ierr);
-
- if (wntqn) {
-
- /* Path 5tn (N >> M, JOBZ='N') */
- /* Compute singular values only */
- /* CWorkspace: need 0 */
- /* RWorkspace: need M [e] + BDSPAC */
-
- sbdsdc_("L", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, &
- c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
- } else if (wntqo) {
- irvt = nrwork;
- iru = irvt + *m * *m;
- nrwork = iru + *m * *m;
- ivt = nwork;
-
- /* Path 5to (N >> M, JOBZ='O') */
- /* Copy A to U, generate Q */
- /* CWorkspace: need 2*M [tauq, taup] + M [work] */
- /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
- /* RWorkspace: need 0 */
-
- clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
- i__1 = *lwork - nwork + 1;
- cungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
- nwork], &i__1, &ierr);
-
- /* Generate P**H in A */
- /* CWorkspace: need 2*M [tauq, taup] + M [work] */
- /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
- /* RWorkspace: need 0 */
-
- i__1 = *lwork - nwork + 1;
- cungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[
- nwork], &i__1, &ierr);
-
- ldwkvt = *m;
- if (*lwork >= *m * *n + *m * 3) {
-
- /* WORK( IVT ) is M by N */
-
- nwork = ivt + ldwkvt * *n;
- chunk = *n;
- } else {
-
- /* WORK( IVT ) is M by CHUNK */
-
- chunk = (*lwork - *m * 3) / *m;
- nwork = ivt + ldwkvt * chunk;
- }
-
- /* Perform bidiagonal SVD, computing left singular vectors */
- /* of bidiagonal matrix in RWORK(IRU) and computing right */
- /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
- /* CWorkspace: need 0 */
- /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
-
- sbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
- rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
- info);
-
- /* Multiply Q in U by real matrix RWORK(IRVT) */
- /* storing the result in WORK(IVT), copying to U */
- /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] */
- /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + 2*M*M [rwork] */
-
- clacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &work[ivt], &
- ldwkvt, &rwork[nrwork]);
- clacpy_("F", m, m, &work[ivt], &ldwkvt, &u[u_offset], ldu);
-
- /* Multiply RWORK(IRVT) by P**H in A, storing the */
- /* result in WORK(IVT), copying to A */
- /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] */
- /* CWorkspace: prefer 2*M [tauq, taup] + M*N [VT] */
- /* RWorkspace: need M [e] + M*M [RVT] + 2*M*M [rwork] */
- /* RWorkspace: prefer M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */
-
- nrwork = iru;
- i__1 = *n;
- i__2 = chunk;
- for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
- i__2) {
- /* Computing MIN */
- i__3 = *n - i__ + 1;
- blk = f2cmin(i__3,chunk);
- clarcm_(m, &blk, &rwork[irvt], m, &a[i__ * a_dim1 + 1],
- lda, &work[ivt], &ldwkvt, &rwork[nrwork]);
- clacpy_("F", m, &blk, &work[ivt], &ldwkvt, &a[i__ *
- a_dim1 + 1], lda);
- /* L50: */
- }
- } else if (wntqs) {
-
- /* Path 5ts (N >> M, JOBZ='S') */
- /* Copy A to U, generate Q */
- /* CWorkspace: need 2*M [tauq, taup] + M [work] */
- /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
- /* RWorkspace: need 0 */
-
- clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
- i__2 = *lwork - nwork + 1;
- cungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
- nwork], &i__2, &ierr);
-
- /* Copy A to VT, generate P**H */
- /* CWorkspace: need 2*M [tauq, taup] + M [work] */
- /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
- /* RWorkspace: need 0 */
-
- clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
- i__2 = *lwork - nwork + 1;
- cungbr_("P", m, n, m, &vt[vt_offset], ldvt, &work[itaup], &
- work[nwork], &i__2, &ierr);
-
- /* Perform bidiagonal SVD, computing left singular vectors */
- /* of bidiagonal matrix in RWORK(IRU) and computing right */
- /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
- /* CWorkspace: need 0 */
- /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
-
- irvt = nrwork;
- iru = irvt + *m * *m;
- nrwork = iru + *m * *m;
- sbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
- rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
- info);
-
- /* Multiply Q in U by real matrix RWORK(IRU), storing the */
- /* result in A, copying to U */
- /* CWorkspace: need 0 */
- /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + 2*M*M [rwork] */
-
- clacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &a[a_offset],
- lda, &rwork[nrwork]);
- clacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu);
-
- /* Multiply real matrix RWORK(IRVT) by P**H in VT, */
- /* storing the result in A, copying to VT */
- /* CWorkspace: need 0 */
- /* RWorkspace: need M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */
-
- nrwork = iru;
- clarcm_(m, n, &rwork[irvt], m, &vt[vt_offset], ldvt, &a[
- a_offset], lda, &rwork[nrwork]);
- clacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
- } else {
-
- /* Path 5ta (N >> M, JOBZ='A') */
- /* Copy A to U, generate Q */
- /* CWorkspace: need 2*M [tauq, taup] + M [work] */
- /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
- /* RWorkspace: need 0 */
-
- clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
- i__2 = *lwork - nwork + 1;
- cungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
- nwork], &i__2, &ierr);
-
- /* Copy A to VT, generate P**H */
- /* CWorkspace: need 2*M [tauq, taup] + N [work] */
- /* CWorkspace: prefer 2*M [tauq, taup] + N*NB [work] */
- /* RWorkspace: need 0 */
-
- clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
- i__2 = *lwork - nwork + 1;
- cungbr_("P", n, n, m, &vt[vt_offset], ldvt, &work[itaup], &
- work[nwork], &i__2, &ierr);
-
- /* Perform bidiagonal SVD, computing left singular vectors */
- /* of bidiagonal matrix in RWORK(IRU) and computing right */
- /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
- /* CWorkspace: need 0 */
- /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
-
- irvt = nrwork;
- iru = irvt + *m * *m;
- nrwork = iru + *m * *m;
- sbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
- rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
- info);
-
- /* Multiply Q in U by real matrix RWORK(IRU), storing the */
- /* result in A, copying to U */
- /* CWorkspace: need 0 */
- /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + 2*M*M [rwork] */
-
- clacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &a[a_offset],
- lda, &rwork[nrwork]);
- clacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu);
-
- /* Multiply real matrix RWORK(IRVT) by P**H in VT, */
- /* storing the result in A, copying to VT */
- /* CWorkspace: need 0 */
- /* RWorkspace: need M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */
-
- nrwork = iru;
- clarcm_(m, n, &rwork[irvt], m, &vt[vt_offset], ldvt, &a[
- a_offset], lda, &rwork[nrwork]);
- clacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
- }
-
- } else {
-
- /* N .LT. MNTHR2 */
-
- /* Path 6t (N > M, but not much larger) */
- /* Reduce to bidiagonal form without LQ decomposition */
- /* Use CUNMBR to compute singular vectors */
-
- ie = 1;
- nrwork = ie + *m;
- itauq = 1;
- itaup = itauq + *m;
- nwork = itaup + *m;
-
- /* Bidiagonalize A */
- /* CWorkspace: need 2*M [tauq, taup] + N [work] */
- /* CWorkspace: prefer 2*M [tauq, taup] + (M+N)*NB [work] */
- /* RWorkspace: need M [e] */
-
- i__2 = *lwork - nwork + 1;
- cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
- &work[itaup], &work[nwork], &i__2, &ierr);
- if (wntqn) {
-
- /* Path 6tn (N > M, JOBZ='N') */
- /* Compute singular values only */
- /* CWorkspace: need 0 */
- /* RWorkspace: need M [e] + BDSPAC */
-
- sbdsdc_("L", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, &
- c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
- } else if (wntqo) {
- /* Path 6to (N > M, JOBZ='O') */
- ldwkvt = *m;
- ivt = nwork;
- if (*lwork >= *m * *n + *m * 3) {
-
- /* WORK( IVT ) is M by N */
-
- claset_("F", m, n, &c_b1, &c_b1, &work[ivt], &ldwkvt);
- nwork = ivt + ldwkvt * *n;
- } else {
-
- /* WORK( IVT ) is M by CHUNK */
-
- chunk = (*lwork - *m * 3) / *m;
- nwork = ivt + ldwkvt * chunk;
- }
-
- /* Perform bidiagonal SVD, computing left singular vectors */
- /* of bidiagonal matrix in RWORK(IRU) and computing right */
- /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
- /* CWorkspace: need 0 */
- /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
-
- irvt = nrwork;
- iru = irvt + *m * *m;
- nrwork = iru + *m * *m;
- sbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
- rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
- info);
-
- /* Copy real matrix RWORK(IRU) to complex matrix U */
- /* Overwrite U by left singular vectors of A */
- /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] + M [work] */
- /* CWorkspace: prefer 2*M [tauq, taup] + M*M [VT] + M*NB [work] */
- /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] */
-
- clacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
- i__2 = *lwork - nwork + 1;
- cunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
- itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
-
- if (*lwork >= *m * *n + *m * 3) {
-
- /* Path 6to-fast */
- /* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) */
- /* Overwrite WORK(IVT) by right singular vectors of A, */
- /* copying to A */
- /* CWorkspace: need 2*M [tauq, taup] + M*N [VT] + M [work] */
- /* CWorkspace: prefer 2*M [tauq, taup] + M*N [VT] + M*NB [work] */
- /* RWorkspace: need M [e] + M*M [RVT] */
-
- clacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt);
- i__2 = *lwork - nwork + 1;
- cunmbr_("P", "R", "C", m, n, m, &a[a_offset], lda, &work[
- itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2,
- &ierr);
- clacpy_("F", m, n, &work[ivt], &ldwkvt, &a[a_offset], lda);
- } else {
-
- /* Path 6to-slow */
- /* Generate P**H in A */
- /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] + M [work] */
- /* CWorkspace: prefer 2*M [tauq, taup] + M*M [VT] + M*NB [work] */
- /* RWorkspace: need 0 */
-
- i__2 = *lwork - nwork + 1;
- cungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &
- work[nwork], &i__2, &ierr);
-
- /* Multiply Q in A by real matrix RWORK(IRU), storing the */
- /* result in WORK(IU), copying to A */
- /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] */
- /* CWorkspace: prefer 2*M [tauq, taup] + M*N [VT] */
- /* RWorkspace: need M [e] + M*M [RVT] + 2*M*M [rwork] */
- /* RWorkspace: prefer M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */
-
- nrwork = iru;
- i__2 = *n;
- i__1 = chunk;
- for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
- i__1) {
- /* Computing MIN */
- i__3 = *n - i__ + 1;
- blk = f2cmin(i__3,chunk);
- clarcm_(m, &blk, &rwork[irvt], m, &a[i__ * a_dim1 + 1]
- , lda, &work[ivt], &ldwkvt, &rwork[nrwork]);
- clacpy_("F", m, &blk, &work[ivt], &ldwkvt, &a[i__ *
- a_dim1 + 1], lda);
- /* L60: */
- }
- }
- } else if (wntqs) {
-
- /* Path 6ts (N > M, JOBZ='S') */
- /* Perform bidiagonal SVD, computing left singular vectors */
- /* of bidiagonal matrix in RWORK(IRU) and computing right */
- /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
- /* CWorkspace: need 0 */
- /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
-
- irvt = nrwork;
- iru = irvt + *m * *m;
- nrwork = iru + *m * *m;
- sbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
- rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
- info);
-
- /* Copy real matrix RWORK(IRU) to complex matrix U */
- /* Overwrite U by left singular vectors of A */
- /* CWorkspace: need 2*M [tauq, taup] + M [work] */
- /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
- /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] */
-
- clacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
- i__1 = *lwork - nwork + 1;
- cunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
- itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
-
- /* Copy real matrix RWORK(IRVT) to complex matrix VT */
- /* Overwrite VT by right singular vectors of A */
- /* CWorkspace: need 2*M [tauq, taup] + M [work] */
- /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
- /* RWorkspace: need M [e] + M*M [RVT] */
-
- claset_("F", m, n, &c_b1, &c_b1, &vt[vt_offset], ldvt);
- clacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt);
- i__1 = *lwork - nwork + 1;
- cunmbr_("P", "R", "C", m, n, m, &a[a_offset], lda, &work[
- itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
- ierr);
- } else {
-
- /* Path 6ta (N > M, JOBZ='A') */
- /* Perform bidiagonal SVD, computing left singular vectors */
- /* of bidiagonal matrix in RWORK(IRU) and computing right */
- /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
- /* CWorkspace: need 0 */
- /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
-
- irvt = nrwork;
- iru = irvt + *m * *m;
- nrwork = iru + *m * *m;
-
- sbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
- rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
- info);
-
- /* Copy real matrix RWORK(IRU) to complex matrix U */
- /* Overwrite U by left singular vectors of A */
- /* CWorkspace: need 2*M [tauq, taup] + M [work] */
- /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
- /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] */
-
- clacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
- i__1 = *lwork - nwork + 1;
- cunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
- itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
-
- /* Set all of VT to identity matrix */
-
- claset_("F", n, n, &c_b1, &c_b2, &vt[vt_offset], ldvt);
-
- /* Copy real matrix RWORK(IRVT) to complex matrix VT */
- /* Overwrite VT by right singular vectors of A */
- /* CWorkspace: need 2*M [tauq, taup] + N [work] */
- /* CWorkspace: prefer 2*M [tauq, taup] + N*NB [work] */
- /* RWorkspace: need M [e] + M*M [RVT] */
-
- clacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt);
- i__1 = *lwork - nwork + 1;
- cunmbr_("P", "R", "C", n, n, m, &a[a_offset], lda, &work[
- itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
- ierr);
- }
-
- }
-
- }
-
- /* Undo scaling if necessary */
-
- if (iscl == 1) {
- if (anrm > bignum) {
- slascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
- minmn, &ierr);
- }
- if (*info != 0 && anrm > bignum) {
- i__1 = minmn - 1;
- slascl_("G", &c__0, &c__0, &bignum, &anrm, &i__1, &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__1 = minmn - 1;
- slascl_("G", &c__0, &c__0, &smlnum, &anrm, &i__1, &c__1, &rwork[
- ie], &minmn, &ierr);
- }
- }
-
- /* Return optimal workspace in WORK(1) */
-
- work[1].r = (real) maxwrk, work[1].i = 0.f;
-
- return;
-
- /* End of CGESDD */
-
- } /* cgesdd_ */
-
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