1245 lines
34 KiB
C
1245 lines
34 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#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]);}
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#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]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#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++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#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]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} 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 doublecomplex c_b1 = {0.,0.};
|
|
static doublecomplex c_b2 = {1.,0.};
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief \b ZGBBRD */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZGBBRD + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgbbrd.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgbbrd.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgbbrd.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, */
|
|
/* LDQ, PT, LDPT, C, LDC, WORK, RWORK, INFO ) */
|
|
|
|
/* CHARACTER VECT */
|
|
/* INTEGER INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC */
|
|
/* DOUBLE PRECISION D( * ), E( * ), RWORK( * ) */
|
|
/* COMPLEX*16 AB( LDAB, * ), C( LDC, * ), PT( LDPT, * ), */
|
|
/* $ Q( LDQ, * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZGBBRD reduces a complex general m-by-n band matrix A to real upper */
|
|
/* > bidiagonal form B by a unitary transformation: Q**H * A * P = B. */
|
|
/* > */
|
|
/* > The routine computes B, and optionally forms Q or P**H, or computes */
|
|
/* > Q**H*C for a given matrix C. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] VECT */
|
|
/* > \verbatim */
|
|
/* > VECT is CHARACTER*1 */
|
|
/* > Specifies whether or not the matrices Q and P**H are to be */
|
|
/* > formed. */
|
|
/* > = 'N': do not form Q or P**H; */
|
|
/* > = 'Q': form Q only; */
|
|
/* > = 'P': form P**H only; */
|
|
/* > = 'B': form both. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of rows of the matrix A. M >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The number of columns of the matrix A. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NCC */
|
|
/* > \verbatim */
|
|
/* > NCC is INTEGER */
|
|
/* > The number of columns of the matrix C. NCC >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] KL */
|
|
/* > \verbatim */
|
|
/* > KL is INTEGER */
|
|
/* > The number of subdiagonals of the matrix A. KL >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] KU */
|
|
/* > \verbatim */
|
|
/* > KU is INTEGER */
|
|
/* > The number of superdiagonals of the matrix A. KU >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] AB */
|
|
/* > \verbatim */
|
|
/* > AB is COMPLEX*16 array, dimension (LDAB,N) */
|
|
/* > On entry, the m-by-n band matrix A, stored in rows 1 to */
|
|
/* > KL+KU+1. The j-th column of A is stored in the j-th column of */
|
|
/* > the array AB as follows: */
|
|
/* > AB(ku+1+i-j,j) = A(i,j) for f2cmax(1,j-ku)<=i<=f2cmin(m,j+kl). */
|
|
/* > On exit, A is overwritten by values generated during the */
|
|
/* > reduction. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDAB */
|
|
/* > \verbatim */
|
|
/* > LDAB is INTEGER */
|
|
/* > The leading dimension of the array A. LDAB >= KL+KU+1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] D */
|
|
/* > \verbatim */
|
|
/* > D is DOUBLE PRECISION array, dimension (f2cmin(M,N)) */
|
|
/* > The diagonal elements of the bidiagonal matrix B. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] E */
|
|
/* > \verbatim */
|
|
/* > E is DOUBLE PRECISION array, dimension (f2cmin(M,N)-1) */
|
|
/* > The superdiagonal elements of the bidiagonal matrix B. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] Q */
|
|
/* > \verbatim */
|
|
/* > Q is COMPLEX*16 array, dimension (LDQ,M) */
|
|
/* > If VECT = 'Q' or 'B', the m-by-m unitary matrix Q. */
|
|
/* > If VECT = 'N' or 'P', the array Q is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDQ */
|
|
/* > \verbatim */
|
|
/* > LDQ is INTEGER */
|
|
/* > The leading dimension of the array Q. */
|
|
/* > LDQ >= f2cmax(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] PT */
|
|
/* > \verbatim */
|
|
/* > PT is COMPLEX*16 array, dimension (LDPT,N) */
|
|
/* > If VECT = 'P' or 'B', the n-by-n unitary matrix P'. */
|
|
/* > If VECT = 'N' or 'Q', the array PT is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDPT */
|
|
/* > \verbatim */
|
|
/* > LDPT is INTEGER */
|
|
/* > The leading dimension of the array PT. */
|
|
/* > LDPT >= f2cmax(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] C */
|
|
/* > \verbatim */
|
|
/* > C is COMPLEX*16 array, dimension (LDC,NCC) */
|
|
/* > On entry, an m-by-ncc matrix C. */
|
|
/* > On exit, C is overwritten by Q**H*C. */
|
|
/* > C is not referenced if NCC = 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDC */
|
|
/* > \verbatim */
|
|
/* > LDC is INTEGER */
|
|
/* > The leading dimension of the array C. */
|
|
/* > LDC >= f2cmax(1,M) if NCC > 0; LDC >= 1 if NCC = 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX*16 array, dimension (f2cmax(M,N)) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RWORK */
|
|
/* > \verbatim */
|
|
/* > RWORK is DOUBLE PRECISION array, dimension (f2cmax(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. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup complex16GBcomputational */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void zgbbrd_(char *vect, integer *m, integer *n, integer *ncc,
|
|
integer *kl, integer *ku, doublecomplex *ab, integer *ldab,
|
|
doublereal *d__, doublereal *e, doublecomplex *q, integer *ldq,
|
|
doublecomplex *pt, integer *ldpt, doublecomplex *c__, integer *ldc,
|
|
doublecomplex *work, doublereal *rwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer ab_dim1, ab_offset, c_dim1, c_offset, pt_dim1, pt_offset, q_dim1,
|
|
q_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7;
|
|
doublecomplex z__1, z__2, z__3;
|
|
|
|
/* Local variables */
|
|
integer inca;
|
|
doublereal abst;
|
|
extern /* Subroutine */ void zrot_(integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublereal *, doublecomplex *);
|
|
integer i__, j, l;
|
|
doublecomplex t;
|
|
extern logical lsame_(char *, char *);
|
|
logical wantb, wantc;
|
|
extern /* Subroutine */ void zscal_(integer *, doublecomplex *,
|
|
doublecomplex *, integer *);
|
|
integer minmn;
|
|
logical wantq;
|
|
integer j1, j2, kb;
|
|
doublecomplex ra, rb;
|
|
doublereal rc;
|
|
integer kk, ml, nr, mu;
|
|
doublecomplex rs;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
integer kb1;
|
|
extern /* Subroutine */ void zlaset_(char *, integer *, integer *,
|
|
doublecomplex *, doublecomplex *, doublecomplex *, integer *), zlartg_(doublecomplex *, doublecomplex *, doublereal *,
|
|
doublecomplex *, doublecomplex *), zlargv_(integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *,
|
|
doublereal *, integer *);
|
|
integer ml0;
|
|
logical wantpt;
|
|
integer mu0;
|
|
extern /* Subroutine */ void zlartv_(integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublereal *, doublecomplex *,
|
|
integer *);
|
|
integer klm, kun, nrt, klu1;
|
|
|
|
|
|
/* -- LAPACK computational 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..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input parameters */
|
|
|
|
/* Parameter adjustments */
|
|
ab_dim1 = *ldab;
|
|
ab_offset = 1 + ab_dim1 * 1;
|
|
ab -= ab_offset;
|
|
--d__;
|
|
--e;
|
|
q_dim1 = *ldq;
|
|
q_offset = 1 + q_dim1 * 1;
|
|
q -= q_offset;
|
|
pt_dim1 = *ldpt;
|
|
pt_offset = 1 + pt_dim1 * 1;
|
|
pt -= pt_offset;
|
|
c_dim1 = *ldc;
|
|
c_offset = 1 + c_dim1 * 1;
|
|
c__ -= c_offset;
|
|
--work;
|
|
--rwork;
|
|
|
|
/* Function Body */
|
|
wantb = lsame_(vect, "B");
|
|
wantq = lsame_(vect, "Q") || wantb;
|
|
wantpt = lsame_(vect, "P") || wantb;
|
|
wantc = *ncc > 0;
|
|
klu1 = *kl + *ku + 1;
|
|
*info = 0;
|
|
if (! wantq && ! wantpt && ! lsame_(vect, "N")) {
|
|
*info = -1;
|
|
} else if (*m < 0) {
|
|
*info = -2;
|
|
} else if (*n < 0) {
|
|
*info = -3;
|
|
} else if (*ncc < 0) {
|
|
*info = -4;
|
|
} else if (*kl < 0) {
|
|
*info = -5;
|
|
} else if (*ku < 0) {
|
|
*info = -6;
|
|
} else if (*ldab < klu1) {
|
|
*info = -8;
|
|
} else if (*ldq < 1 || wantq && *ldq < f2cmax(1,*m)) {
|
|
*info = -12;
|
|
} else if (*ldpt < 1 || wantpt && *ldpt < f2cmax(1,*n)) {
|
|
*info = -14;
|
|
} else if (*ldc < 1 || wantc && *ldc < f2cmax(1,*m)) {
|
|
*info = -16;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("ZGBBRD", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Initialize Q and P**H to the unit matrix, if needed */
|
|
|
|
if (wantq) {
|
|
zlaset_("Full", m, m, &c_b1, &c_b2, &q[q_offset], ldq);
|
|
}
|
|
if (wantpt) {
|
|
zlaset_("Full", n, n, &c_b1, &c_b2, &pt[pt_offset], ldpt);
|
|
}
|
|
|
|
/* Quick return if possible. */
|
|
|
|
if (*m == 0 || *n == 0) {
|
|
return;
|
|
}
|
|
|
|
minmn = f2cmin(*m,*n);
|
|
|
|
if (*kl + *ku > 1) {
|
|
|
|
/* Reduce to upper bidiagonal form if KU > 0; if KU = 0, reduce */
|
|
/* first to lower bidiagonal form and then transform to upper */
|
|
/* bidiagonal */
|
|
|
|
if (*ku > 0) {
|
|
ml0 = 1;
|
|
mu0 = 2;
|
|
} else {
|
|
ml0 = 2;
|
|
mu0 = 1;
|
|
}
|
|
|
|
/* Wherever possible, plane rotations are generated and applied in */
|
|
/* vector operations of length NR over the index set J1:J2:KLU1. */
|
|
|
|
/* The complex sines of the plane rotations are stored in WORK, */
|
|
/* and the real cosines in RWORK. */
|
|
|
|
/* Computing MIN */
|
|
i__1 = *m - 1;
|
|
klm = f2cmin(i__1,*kl);
|
|
/* Computing MIN */
|
|
i__1 = *n - 1;
|
|
kun = f2cmin(i__1,*ku);
|
|
kb = klm + kun;
|
|
kb1 = kb + 1;
|
|
inca = kb1 * *ldab;
|
|
nr = 0;
|
|
j1 = klm + 2;
|
|
j2 = 1 - kun;
|
|
|
|
i__1 = minmn;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
|
|
/* Reduce i-th column and i-th row of matrix to bidiagonal form */
|
|
|
|
ml = klm + 1;
|
|
mu = kun + 1;
|
|
i__2 = kb;
|
|
for (kk = 1; kk <= i__2; ++kk) {
|
|
j1 += kb;
|
|
j2 += kb;
|
|
|
|
/* generate plane rotations to annihilate nonzero elements */
|
|
/* which have been created below the band */
|
|
|
|
if (nr > 0) {
|
|
zlargv_(&nr, &ab[klu1 + (j1 - klm - 1) * ab_dim1], &inca,
|
|
&work[j1], &kb1, &rwork[j1], &kb1);
|
|
}
|
|
|
|
/* apply plane rotations from the left */
|
|
|
|
i__3 = kb;
|
|
for (l = 1; l <= i__3; ++l) {
|
|
if (j2 - klm + l - 1 > *n) {
|
|
nrt = nr - 1;
|
|
} else {
|
|
nrt = nr;
|
|
}
|
|
if (nrt > 0) {
|
|
zlartv_(&nrt, &ab[klu1 - l + (j1 - klm + l - 1) *
|
|
ab_dim1], &inca, &ab[klu1 - l + 1 + (j1 - klm
|
|
+ l - 1) * ab_dim1], &inca, &rwork[j1], &work[
|
|
j1], &kb1);
|
|
}
|
|
/* L10: */
|
|
}
|
|
|
|
if (ml > ml0) {
|
|
if (ml <= *m - i__ + 1) {
|
|
|
|
/* generate plane rotation to annihilate a(i+ml-1,i) */
|
|
/* within the band, and apply rotation from the left */
|
|
|
|
zlartg_(&ab[*ku + ml - 1 + i__ * ab_dim1], &ab[*ku +
|
|
ml + i__ * ab_dim1], &rwork[i__ + ml - 1], &
|
|
work[i__ + ml - 1], &ra);
|
|
i__3 = *ku + ml - 1 + i__ * ab_dim1;
|
|
ab[i__3].r = ra.r, ab[i__3].i = ra.i;
|
|
if (i__ < *n) {
|
|
/* Computing MIN */
|
|
i__4 = *ku + ml - 2, i__5 = *n - i__;
|
|
i__3 = f2cmin(i__4,i__5);
|
|
i__6 = *ldab - 1;
|
|
i__7 = *ldab - 1;
|
|
zrot_(&i__3, &ab[*ku + ml - 2 + (i__ + 1) *
|
|
ab_dim1], &i__6, &ab[*ku + ml - 1 + (i__
|
|
+ 1) * ab_dim1], &i__7, &rwork[i__ + ml -
|
|
1], &work[i__ + ml - 1]);
|
|
}
|
|
}
|
|
++nr;
|
|
j1 -= kb1;
|
|
}
|
|
|
|
if (wantq) {
|
|
|
|
/* accumulate product of plane rotations in Q */
|
|
|
|
i__3 = j2;
|
|
i__4 = kb1;
|
|
for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4)
|
|
{
|
|
d_cnjg(&z__1, &work[j]);
|
|
zrot_(m, &q[(j - 1) * q_dim1 + 1], &c__1, &q[j *
|
|
q_dim1 + 1], &c__1, &rwork[j], &z__1);
|
|
/* L20: */
|
|
}
|
|
}
|
|
|
|
if (wantc) {
|
|
|
|
/* apply plane rotations to C */
|
|
|
|
i__4 = j2;
|
|
i__3 = kb1;
|
|
for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3)
|
|
{
|
|
zrot_(ncc, &c__[j - 1 + c_dim1], ldc, &c__[j + c_dim1]
|
|
, ldc, &rwork[j], &work[j]);
|
|
/* L30: */
|
|
}
|
|
}
|
|
|
|
if (j2 + kun > *n) {
|
|
|
|
/* adjust J2 to keep within the bounds of the matrix */
|
|
|
|
--nr;
|
|
j2 -= kb1;
|
|
}
|
|
|
|
i__3 = j2;
|
|
i__4 = kb1;
|
|
for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
|
|
|
|
/* create nonzero element a(j-1,j+ku) above the band */
|
|
/* and store it in WORK(n+1:2*n) */
|
|
|
|
i__5 = j + kun;
|
|
i__6 = j;
|
|
i__7 = (j + kun) * ab_dim1 + 1;
|
|
z__1.r = work[i__6].r * ab[i__7].r - work[i__6].i * ab[
|
|
i__7].i, z__1.i = work[i__6].r * ab[i__7].i +
|
|
work[i__6].i * ab[i__7].r;
|
|
work[i__5].r = z__1.r, work[i__5].i = z__1.i;
|
|
i__5 = (j + kun) * ab_dim1 + 1;
|
|
i__6 = j;
|
|
i__7 = (j + kun) * ab_dim1 + 1;
|
|
z__1.r = rwork[i__6] * ab[i__7].r, z__1.i = rwork[i__6] *
|
|
ab[i__7].i;
|
|
ab[i__5].r = z__1.r, ab[i__5].i = z__1.i;
|
|
/* L40: */
|
|
}
|
|
|
|
/* generate plane rotations to annihilate nonzero elements */
|
|
/* which have been generated above the band */
|
|
|
|
if (nr > 0) {
|
|
zlargv_(&nr, &ab[(j1 + kun - 1) * ab_dim1 + 1], &inca, &
|
|
work[j1 + kun], &kb1, &rwork[j1 + kun], &kb1);
|
|
}
|
|
|
|
/* apply plane rotations from the right */
|
|
|
|
i__4 = kb;
|
|
for (l = 1; l <= i__4; ++l) {
|
|
if (j2 + l - 1 > *m) {
|
|
nrt = nr - 1;
|
|
} else {
|
|
nrt = nr;
|
|
}
|
|
if (nrt > 0) {
|
|
zlartv_(&nrt, &ab[l + 1 + (j1 + kun - 1) * ab_dim1], &
|
|
inca, &ab[l + (j1 + kun) * ab_dim1], &inca, &
|
|
rwork[j1 + kun], &work[j1 + kun], &kb1);
|
|
}
|
|
/* L50: */
|
|
}
|
|
|
|
if (ml == ml0 && mu > mu0) {
|
|
if (mu <= *n - i__ + 1) {
|
|
|
|
/* generate plane rotation to annihilate a(i,i+mu-1) */
|
|
/* within the band, and apply rotation from the right */
|
|
|
|
zlartg_(&ab[*ku - mu + 3 + (i__ + mu - 2) * ab_dim1],
|
|
&ab[*ku - mu + 2 + (i__ + mu - 1) * ab_dim1],
|
|
&rwork[i__ + mu - 1], &work[i__ + mu - 1], &
|
|
ra);
|
|
i__4 = *ku - mu + 3 + (i__ + mu - 2) * ab_dim1;
|
|
ab[i__4].r = ra.r, ab[i__4].i = ra.i;
|
|
/* Computing MIN */
|
|
i__3 = *kl + mu - 2, i__5 = *m - i__;
|
|
i__4 = f2cmin(i__3,i__5);
|
|
zrot_(&i__4, &ab[*ku - mu + 4 + (i__ + mu - 2) *
|
|
ab_dim1], &c__1, &ab[*ku - mu + 3 + (i__ + mu
|
|
- 1) * ab_dim1], &c__1, &rwork[i__ + mu - 1],
|
|
&work[i__ + mu - 1]);
|
|
}
|
|
++nr;
|
|
j1 -= kb1;
|
|
}
|
|
|
|
if (wantpt) {
|
|
|
|
/* accumulate product of plane rotations in P**H */
|
|
|
|
i__4 = j2;
|
|
i__3 = kb1;
|
|
for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3)
|
|
{
|
|
d_cnjg(&z__1, &work[j + kun]);
|
|
zrot_(n, &pt[j + kun - 1 + pt_dim1], ldpt, &pt[j +
|
|
kun + pt_dim1], ldpt, &rwork[j + kun], &z__1);
|
|
/* L60: */
|
|
}
|
|
}
|
|
|
|
if (j2 + kb > *m) {
|
|
|
|
/* adjust J2 to keep within the bounds of the matrix */
|
|
|
|
--nr;
|
|
j2 -= kb1;
|
|
}
|
|
|
|
i__3 = j2;
|
|
i__4 = kb1;
|
|
for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
|
|
|
|
/* create nonzero element a(j+kl+ku,j+ku-1) below the */
|
|
/* band and store it in WORK(1:n) */
|
|
|
|
i__5 = j + kb;
|
|
i__6 = j + kun;
|
|
i__7 = klu1 + (j + kun) * ab_dim1;
|
|
z__1.r = work[i__6].r * ab[i__7].r - work[i__6].i * ab[
|
|
i__7].i, z__1.i = work[i__6].r * ab[i__7].i +
|
|
work[i__6].i * ab[i__7].r;
|
|
work[i__5].r = z__1.r, work[i__5].i = z__1.i;
|
|
i__5 = klu1 + (j + kun) * ab_dim1;
|
|
i__6 = j + kun;
|
|
i__7 = klu1 + (j + kun) * ab_dim1;
|
|
z__1.r = rwork[i__6] * ab[i__7].r, z__1.i = rwork[i__6] *
|
|
ab[i__7].i;
|
|
ab[i__5].r = z__1.r, ab[i__5].i = z__1.i;
|
|
/* L70: */
|
|
}
|
|
|
|
if (ml > ml0) {
|
|
--ml;
|
|
} else {
|
|
--mu;
|
|
}
|
|
/* L80: */
|
|
}
|
|
/* L90: */
|
|
}
|
|
}
|
|
|
|
if (*ku == 0 && *kl > 0) {
|
|
|
|
/* A has been reduced to complex lower bidiagonal form */
|
|
|
|
/* Transform lower bidiagonal form to upper bidiagonal by applying */
|
|
/* plane rotations from the left, overwriting superdiagonal */
|
|
/* elements on subdiagonal elements */
|
|
|
|
/* Computing MIN */
|
|
i__2 = *m - 1;
|
|
i__1 = f2cmin(i__2,*n);
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
zlartg_(&ab[i__ * ab_dim1 + 1], &ab[i__ * ab_dim1 + 2], &rc, &rs,
|
|
&ra);
|
|
i__2 = i__ * ab_dim1 + 1;
|
|
ab[i__2].r = ra.r, ab[i__2].i = ra.i;
|
|
if (i__ < *n) {
|
|
i__2 = i__ * ab_dim1 + 2;
|
|
i__4 = (i__ + 1) * ab_dim1 + 1;
|
|
z__1.r = rs.r * ab[i__4].r - rs.i * ab[i__4].i, z__1.i = rs.r
|
|
* ab[i__4].i + rs.i * ab[i__4].r;
|
|
ab[i__2].r = z__1.r, ab[i__2].i = z__1.i;
|
|
i__2 = (i__ + 1) * ab_dim1 + 1;
|
|
i__4 = (i__ + 1) * ab_dim1 + 1;
|
|
z__1.r = rc * ab[i__4].r, z__1.i = rc * ab[i__4].i;
|
|
ab[i__2].r = z__1.r, ab[i__2].i = z__1.i;
|
|
}
|
|
if (wantq) {
|
|
d_cnjg(&z__1, &rs);
|
|
zrot_(m, &q[i__ * q_dim1 + 1], &c__1, &q[(i__ + 1) * q_dim1 +
|
|
1], &c__1, &rc, &z__1);
|
|
}
|
|
if (wantc) {
|
|
zrot_(ncc, &c__[i__ + c_dim1], ldc, &c__[i__ + 1 + c_dim1],
|
|
ldc, &rc, &rs);
|
|
}
|
|
/* L100: */
|
|
}
|
|
} else {
|
|
|
|
/* A has been reduced to complex upper bidiagonal form or is */
|
|
/* diagonal */
|
|
|
|
if (*ku > 0 && *m < *n) {
|
|
|
|
/* Annihilate a(m,m+1) by applying plane rotations from the */
|
|
/* right */
|
|
|
|
i__1 = *ku + (*m + 1) * ab_dim1;
|
|
rb.r = ab[i__1].r, rb.i = ab[i__1].i;
|
|
for (i__ = *m; i__ >= 1; --i__) {
|
|
zlartg_(&ab[*ku + 1 + i__ * ab_dim1], &rb, &rc, &rs, &ra);
|
|
i__1 = *ku + 1 + i__ * ab_dim1;
|
|
ab[i__1].r = ra.r, ab[i__1].i = ra.i;
|
|
if (i__ > 1) {
|
|
d_cnjg(&z__3, &rs);
|
|
z__2.r = -z__3.r, z__2.i = -z__3.i;
|
|
i__1 = *ku + i__ * ab_dim1;
|
|
z__1.r = z__2.r * ab[i__1].r - z__2.i * ab[i__1].i,
|
|
z__1.i = z__2.r * ab[i__1].i + z__2.i * ab[i__1]
|
|
.r;
|
|
rb.r = z__1.r, rb.i = z__1.i;
|
|
i__1 = *ku + i__ * ab_dim1;
|
|
i__2 = *ku + i__ * ab_dim1;
|
|
z__1.r = rc * ab[i__2].r, z__1.i = rc * ab[i__2].i;
|
|
ab[i__1].r = z__1.r, ab[i__1].i = z__1.i;
|
|
}
|
|
if (wantpt) {
|
|
d_cnjg(&z__1, &rs);
|
|
zrot_(n, &pt[i__ + pt_dim1], ldpt, &pt[*m + 1 + pt_dim1],
|
|
ldpt, &rc, &z__1);
|
|
}
|
|
/* L110: */
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Make diagonal and superdiagonal elements real, storing them in D */
|
|
/* and E */
|
|
|
|
i__1 = *ku + 1 + ab_dim1;
|
|
t.r = ab[i__1].r, t.i = ab[i__1].i;
|
|
i__1 = minmn;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
abst = z_abs(&t);
|
|
d__[i__] = abst;
|
|
if (abst != 0.) {
|
|
z__1.r = t.r / abst, z__1.i = t.i / abst;
|
|
t.r = z__1.r, t.i = z__1.i;
|
|
} else {
|
|
t.r = 1., t.i = 0.;
|
|
}
|
|
if (wantq) {
|
|
zscal_(m, &t, &q[i__ * q_dim1 + 1], &c__1);
|
|
}
|
|
if (wantc) {
|
|
d_cnjg(&z__1, &t);
|
|
zscal_(ncc, &z__1, &c__[i__ + c_dim1], ldc);
|
|
}
|
|
if (i__ < minmn) {
|
|
if (*ku == 0 && *kl == 0) {
|
|
e[i__] = 0.;
|
|
i__2 = (i__ + 1) * ab_dim1 + 1;
|
|
t.r = ab[i__2].r, t.i = ab[i__2].i;
|
|
} else {
|
|
if (*ku == 0) {
|
|
i__2 = i__ * ab_dim1 + 2;
|
|
d_cnjg(&z__2, &t);
|
|
z__1.r = ab[i__2].r * z__2.r - ab[i__2].i * z__2.i,
|
|
z__1.i = ab[i__2].r * z__2.i + ab[i__2].i *
|
|
z__2.r;
|
|
t.r = z__1.r, t.i = z__1.i;
|
|
} else {
|
|
i__2 = *ku + (i__ + 1) * ab_dim1;
|
|
d_cnjg(&z__2, &t);
|
|
z__1.r = ab[i__2].r * z__2.r - ab[i__2].i * z__2.i,
|
|
z__1.i = ab[i__2].r * z__2.i + ab[i__2].i *
|
|
z__2.r;
|
|
t.r = z__1.r, t.i = z__1.i;
|
|
}
|
|
abst = z_abs(&t);
|
|
e[i__] = abst;
|
|
if (abst != 0.) {
|
|
z__1.r = t.r / abst, z__1.i = t.i / abst;
|
|
t.r = z__1.r, t.i = z__1.i;
|
|
} else {
|
|
t.r = 1., t.i = 0.;
|
|
}
|
|
if (wantpt) {
|
|
zscal_(n, &t, &pt[i__ + 1 + pt_dim1], ldpt);
|
|
}
|
|
i__2 = *ku + 1 + (i__ + 1) * ab_dim1;
|
|
d_cnjg(&z__2, &t);
|
|
z__1.r = ab[i__2].r * z__2.r - ab[i__2].i * z__2.i, z__1.i =
|
|
ab[i__2].r * z__2.i + ab[i__2].i * z__2.r;
|
|
t.r = z__1.r, t.i = z__1.i;
|
|
}
|
|
}
|
|
/* L120: */
|
|
}
|
|
return;
|
|
|
|
/* End of ZGBBRD */
|
|
|
|
} /* zgbbrd_ */
|
|
|