1041 lines
31 KiB
C
1041 lines
31 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]/Cd(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)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* > \brief \b ZLAGS2 */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZLAGS2 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlags2.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlags2.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlags2.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, */
|
|
/* SNV, CSQ, SNQ ) */
|
|
|
|
/* LOGICAL UPPER */
|
|
/* DOUBLE PRECISION A1, A3, B1, B3, CSQ, CSU, CSV */
|
|
/* COMPLEX*16 A2, B2, SNQ, SNU, SNV */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZLAGS2 computes 2-by-2 unitary matrices U, V and Q, such */
|
|
/* > that if ( UPPER ) then */
|
|
/* > */
|
|
/* > U**H *A*Q = U**H *( A1 A2 )*Q = ( x 0 ) */
|
|
/* > ( 0 A3 ) ( x x ) */
|
|
/* > and */
|
|
/* > V**H*B*Q = V**H *( B1 B2 )*Q = ( x 0 ) */
|
|
/* > ( 0 B3 ) ( x x ) */
|
|
/* > */
|
|
/* > or if ( .NOT.UPPER ) then */
|
|
/* > */
|
|
/* > U**H *A*Q = U**H *( A1 0 )*Q = ( x x ) */
|
|
/* > ( A2 A3 ) ( 0 x ) */
|
|
/* > and */
|
|
/* > V**H *B*Q = V**H *( B1 0 )*Q = ( x x ) */
|
|
/* > ( B2 B3 ) ( 0 x ) */
|
|
/* > where */
|
|
/* > */
|
|
/* > U = ( CSU SNU ), V = ( CSV SNV ), */
|
|
/* > ( -SNU**H CSU ) ( -SNV**H CSV ) */
|
|
/* > */
|
|
/* > Q = ( CSQ SNQ ) */
|
|
/* > ( -SNQ**H CSQ ) */
|
|
/* > */
|
|
/* > The rows of the transformed A and B are parallel. Moreover, if the */
|
|
/* > input 2-by-2 matrix A is not zero, then the transformed (1,1) entry */
|
|
/* > of A is not zero. If the input matrices A and B are both not zero, */
|
|
/* > then the transformed (2,2) element of B is not zero, except when the */
|
|
/* > first rows of input A and B are parallel and the second rows are */
|
|
/* > zero. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] UPPER */
|
|
/* > \verbatim */
|
|
/* > UPPER is LOGICAL */
|
|
/* > = .TRUE.: the input matrices A and B are upper triangular. */
|
|
/* > = .FALSE.: the input matrices A and B are lower triangular. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] A1 */
|
|
/* > \verbatim */
|
|
/* > A1 is DOUBLE PRECISION */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] A2 */
|
|
/* > \verbatim */
|
|
/* > A2 is COMPLEX*16 */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] A3 */
|
|
/* > \verbatim */
|
|
/* > A3 is DOUBLE PRECISION */
|
|
/* > On entry, A1, A2 and A3 are elements of the input 2-by-2 */
|
|
/* > upper (lower) triangular matrix A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] B1 */
|
|
/* > \verbatim */
|
|
/* > B1 is DOUBLE PRECISION */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] B2 */
|
|
/* > \verbatim */
|
|
/* > B2 is COMPLEX*16 */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] B3 */
|
|
/* > \verbatim */
|
|
/* > B3 is DOUBLE PRECISION */
|
|
/* > On entry, B1, B2 and B3 are elements of the input 2-by-2 */
|
|
/* > upper (lower) triangular matrix B. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] CSU */
|
|
/* > \verbatim */
|
|
/* > CSU is DOUBLE PRECISION */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] SNU */
|
|
/* > \verbatim */
|
|
/* > SNU is COMPLEX*16 */
|
|
/* > The desired unitary matrix U. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] CSV */
|
|
/* > \verbatim */
|
|
/* > CSV is DOUBLE PRECISION */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] SNV */
|
|
/* > \verbatim */
|
|
/* > SNV is COMPLEX*16 */
|
|
/* > The desired unitary matrix V. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] CSQ */
|
|
/* > \verbatim */
|
|
/* > CSQ is DOUBLE PRECISION */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] SNQ */
|
|
/* > \verbatim */
|
|
/* > SNQ is COMPLEX*16 */
|
|
/* > The desired unitary matrix Q. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup complex16OTHERauxiliary */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void zlags2_(logical *upper, doublereal *a1, doublecomplex *
|
|
a2, doublereal *a3, doublereal *b1, doublecomplex *b2, doublereal *b3,
|
|
doublereal *csu, doublecomplex *snu, doublereal *csv, doublecomplex *
|
|
snv, doublereal *csq, doublecomplex *snq)
|
|
{
|
|
/* System generated locals */
|
|
doublereal d__1, d__2, d__3, d__4, d__5, d__6, d__7, d__8;
|
|
doublecomplex z__1, z__2, z__3, z__4, z__5;
|
|
|
|
/* Local variables */
|
|
doublereal aua11, aua12, aua21, aua22, avb12, avb11, avb21, avb22, ua11r,
|
|
ua22r, vb11r, vb22r, a;
|
|
doublecomplex b, c__;
|
|
doublereal d__;
|
|
doublecomplex r__, d1;
|
|
doublereal s1, s2;
|
|
extern /* Subroutine */ void dlasv2_(doublereal *, doublereal *,
|
|
doublereal *, doublereal *, doublereal *, doublereal *,
|
|
doublereal *, doublereal *, doublereal *);
|
|
doublereal fb, fc;
|
|
extern /* Subroutine */ void zlartg_(doublecomplex *, doublecomplex *,
|
|
doublereal *, doublecomplex *, doublecomplex *);
|
|
doublecomplex ua11, ua12, ua21, ua22, vb11, vb12, vb21, vb22;
|
|
doublereal csl, csr, snl, snr;
|
|
|
|
|
|
/* -- LAPACK auxiliary 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 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
if (*upper) {
|
|
|
|
/* Input matrices A and B are upper triangular matrices */
|
|
|
|
/* Form matrix C = A*adj(B) = ( a b ) */
|
|
/* ( 0 d ) */
|
|
|
|
a = *a1 * *b3;
|
|
d__ = *a3 * *b1;
|
|
z__2.r = *b1 * a2->r, z__2.i = *b1 * a2->i;
|
|
z__3.r = *a1 * b2->r, z__3.i = *a1 * b2->i;
|
|
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
|
|
b.r = z__1.r, b.i = z__1.i;
|
|
fb = z_abs(&b);
|
|
|
|
/* Transform complex 2-by-2 matrix C to real matrix by unitary */
|
|
/* diagonal matrix diag(1,D1). */
|
|
|
|
d1.r = 1., d1.i = 0.;
|
|
if (fb != 0.) {
|
|
z__1.r = b.r / fb, z__1.i = b.i / fb;
|
|
d1.r = z__1.r, d1.i = z__1.i;
|
|
}
|
|
|
|
/* The SVD of real 2 by 2 triangular C */
|
|
|
|
/* ( CSL -SNL )*( A B )*( CSR SNR ) = ( R 0 ) */
|
|
/* ( SNL CSL ) ( 0 D ) ( -SNR CSR ) ( 0 T ) */
|
|
|
|
dlasv2_(&a, &fb, &d__, &s1, &s2, &snr, &csr, &snl, &csl);
|
|
|
|
if (abs(csl) >= abs(snl) || abs(csr) >= abs(snr)) {
|
|
|
|
/* Compute the (1,1) and (1,2) elements of U**H *A and V**H *B, */
|
|
/* and (1,2) element of |U|**H *|A| and |V|**H *|B|. */
|
|
|
|
ua11r = csl * *a1;
|
|
z__2.r = csl * a2->r, z__2.i = csl * a2->i;
|
|
z__4.r = snl * d1.r, z__4.i = snl * d1.i;
|
|
z__3.r = *a3 * z__4.r, z__3.i = *a3 * z__4.i;
|
|
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
|
|
ua12.r = z__1.r, ua12.i = z__1.i;
|
|
|
|
vb11r = csr * *b1;
|
|
z__2.r = csr * b2->r, z__2.i = csr * b2->i;
|
|
z__4.r = snr * d1.r, z__4.i = snr * d1.i;
|
|
z__3.r = *b3 * z__4.r, z__3.i = *b3 * z__4.i;
|
|
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
|
|
vb12.r = z__1.r, vb12.i = z__1.i;
|
|
|
|
aua12 = abs(csl) * ((d__1 = a2->r, abs(d__1)) + (d__2 = d_imag(a2)
|
|
, abs(d__2))) + abs(snl) * abs(*a3);
|
|
avb12 = abs(csr) * ((d__1 = b2->r, abs(d__1)) + (d__2 = d_imag(b2)
|
|
, abs(d__2))) + abs(snr) * abs(*b3);
|
|
|
|
/* zero (1,2) elements of U**H *A and V**H *B */
|
|
|
|
if (abs(ua11r) + ((d__1 = ua12.r, abs(d__1)) + (d__2 = d_imag(&
|
|
ua12), abs(d__2))) == 0.) {
|
|
z__2.r = vb11r, z__2.i = 0.;
|
|
z__1.r = -z__2.r, z__1.i = -z__2.i;
|
|
d_cnjg(&z__3, &vb12);
|
|
zlartg_(&z__1, &z__3, csq, snq, &r__);
|
|
} else if (abs(vb11r) + ((d__1 = vb12.r, abs(d__1)) + (d__2 =
|
|
d_imag(&vb12), abs(d__2))) == 0.) {
|
|
z__2.r = ua11r, z__2.i = 0.;
|
|
z__1.r = -z__2.r, z__1.i = -z__2.i;
|
|
d_cnjg(&z__3, &ua12);
|
|
zlartg_(&z__1, &z__3, csq, snq, &r__);
|
|
} else if (aua12 / (abs(ua11r) + ((d__1 = ua12.r, abs(d__1)) + (
|
|
d__2 = d_imag(&ua12), abs(d__2)))) <= avb12 / (abs(vb11r)
|
|
+ ((d__3 = vb12.r, abs(d__3)) + (d__4 = d_imag(&vb12),
|
|
abs(d__4))))) {
|
|
z__2.r = ua11r, z__2.i = 0.;
|
|
z__1.r = -z__2.r, z__1.i = -z__2.i;
|
|
d_cnjg(&z__3, &ua12);
|
|
zlartg_(&z__1, &z__3, csq, snq, &r__);
|
|
} else {
|
|
z__2.r = vb11r, z__2.i = 0.;
|
|
z__1.r = -z__2.r, z__1.i = -z__2.i;
|
|
d_cnjg(&z__3, &vb12);
|
|
zlartg_(&z__1, &z__3, csq, snq, &r__);
|
|
}
|
|
|
|
*csu = csl;
|
|
z__2.r = -d1.r, z__2.i = -d1.i;
|
|
z__1.r = snl * z__2.r, z__1.i = snl * z__2.i;
|
|
snu->r = z__1.r, snu->i = z__1.i;
|
|
*csv = csr;
|
|
z__2.r = -d1.r, z__2.i = -d1.i;
|
|
z__1.r = snr * z__2.r, z__1.i = snr * z__2.i;
|
|
snv->r = z__1.r, snv->i = z__1.i;
|
|
|
|
} else {
|
|
|
|
/* Compute the (2,1) and (2,2) elements of U**H *A and V**H *B, */
|
|
/* and (2,2) element of |U|**H *|A| and |V|**H *|B|. */
|
|
|
|
d_cnjg(&z__4, &d1);
|
|
z__3.r = -z__4.r, z__3.i = -z__4.i;
|
|
z__2.r = snl * z__3.r, z__2.i = snl * z__3.i;
|
|
z__1.r = *a1 * z__2.r, z__1.i = *a1 * z__2.i;
|
|
ua21.r = z__1.r, ua21.i = z__1.i;
|
|
d_cnjg(&z__5, &d1);
|
|
z__4.r = -z__5.r, z__4.i = -z__5.i;
|
|
z__3.r = snl * z__4.r, z__3.i = snl * z__4.i;
|
|
z__2.r = z__3.r * a2->r - z__3.i * a2->i, z__2.i = z__3.r * a2->i
|
|
+ z__3.i * a2->r;
|
|
d__1 = csl * *a3;
|
|
z__1.r = z__2.r + d__1, z__1.i = z__2.i;
|
|
ua22.r = z__1.r, ua22.i = z__1.i;
|
|
|
|
d_cnjg(&z__4, &d1);
|
|
z__3.r = -z__4.r, z__3.i = -z__4.i;
|
|
z__2.r = snr * z__3.r, z__2.i = snr * z__3.i;
|
|
z__1.r = *b1 * z__2.r, z__1.i = *b1 * z__2.i;
|
|
vb21.r = z__1.r, vb21.i = z__1.i;
|
|
d_cnjg(&z__5, &d1);
|
|
z__4.r = -z__5.r, z__4.i = -z__5.i;
|
|
z__3.r = snr * z__4.r, z__3.i = snr * z__4.i;
|
|
z__2.r = z__3.r * b2->r - z__3.i * b2->i, z__2.i = z__3.r * b2->i
|
|
+ z__3.i * b2->r;
|
|
d__1 = csr * *b3;
|
|
z__1.r = z__2.r + d__1, z__1.i = z__2.i;
|
|
vb22.r = z__1.r, vb22.i = z__1.i;
|
|
|
|
aua22 = abs(snl) * ((d__1 = a2->r, abs(d__1)) + (d__2 = d_imag(a2)
|
|
, abs(d__2))) + abs(csl) * abs(*a3);
|
|
avb22 = abs(snr) * ((d__1 = b2->r, abs(d__1)) + (d__2 = d_imag(b2)
|
|
, abs(d__2))) + abs(csr) * abs(*b3);
|
|
|
|
/* zero (2,2) elements of U**H *A and V**H *B, and then swap. */
|
|
|
|
if ((d__1 = ua21.r, abs(d__1)) + (d__2 = d_imag(&ua21), abs(d__2))
|
|
+ ((d__3 = ua22.r, abs(d__3)) + (d__4 = d_imag(&ua22),
|
|
abs(d__4))) == 0.) {
|
|
d_cnjg(&z__2, &vb21);
|
|
z__1.r = -z__2.r, z__1.i = -z__2.i;
|
|
d_cnjg(&z__3, &vb22);
|
|
zlartg_(&z__1, &z__3, csq, snq, &r__);
|
|
} else if ((d__1 = vb21.r, abs(d__1)) + (d__2 = d_imag(&vb21),
|
|
abs(d__2)) + z_abs(&vb22) == 0.) {
|
|
d_cnjg(&z__2, &ua21);
|
|
z__1.r = -z__2.r, z__1.i = -z__2.i;
|
|
d_cnjg(&z__3, &ua22);
|
|
zlartg_(&z__1, &z__3, csq, snq, &r__);
|
|
} else if (aua22 / ((d__1 = ua21.r, abs(d__1)) + (d__2 = d_imag(&
|
|
ua21), abs(d__2)) + ((d__3 = ua22.r, abs(d__3)) + (d__4 =
|
|
d_imag(&ua22), abs(d__4)))) <= avb22 / ((d__5 = vb21.r,
|
|
abs(d__5)) + (d__6 = d_imag(&vb21), abs(d__6)) + ((d__7 =
|
|
vb22.r, abs(d__7)) + (d__8 = d_imag(&vb22), abs(d__8)))))
|
|
{
|
|
d_cnjg(&z__2, &ua21);
|
|
z__1.r = -z__2.r, z__1.i = -z__2.i;
|
|
d_cnjg(&z__3, &ua22);
|
|
zlartg_(&z__1, &z__3, csq, snq, &r__);
|
|
} else {
|
|
d_cnjg(&z__2, &vb21);
|
|
z__1.r = -z__2.r, z__1.i = -z__2.i;
|
|
d_cnjg(&z__3, &vb22);
|
|
zlartg_(&z__1, &z__3, csq, snq, &r__);
|
|
}
|
|
|
|
*csu = snl;
|
|
z__1.r = csl * d1.r, z__1.i = csl * d1.i;
|
|
snu->r = z__1.r, snu->i = z__1.i;
|
|
*csv = snr;
|
|
z__1.r = csr * d1.r, z__1.i = csr * d1.i;
|
|
snv->r = z__1.r, snv->i = z__1.i;
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* Input matrices A and B are lower triangular matrices */
|
|
|
|
/* Form matrix C = A*adj(B) = ( a 0 ) */
|
|
/* ( c d ) */
|
|
|
|
a = *a1 * *b3;
|
|
d__ = *a3 * *b1;
|
|
z__2.r = *b3 * a2->r, z__2.i = *b3 * a2->i;
|
|
z__3.r = *a3 * b2->r, z__3.i = *a3 * b2->i;
|
|
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
|
|
c__.r = z__1.r, c__.i = z__1.i;
|
|
fc = z_abs(&c__);
|
|
|
|
/* Transform complex 2-by-2 matrix C to real matrix by unitary */
|
|
/* diagonal matrix diag(d1,1). */
|
|
|
|
d1.r = 1., d1.i = 0.;
|
|
if (fc != 0.) {
|
|
z__1.r = c__.r / fc, z__1.i = c__.i / fc;
|
|
d1.r = z__1.r, d1.i = z__1.i;
|
|
}
|
|
|
|
/* The SVD of real 2 by 2 triangular C */
|
|
|
|
/* ( CSL -SNL )*( A 0 )*( CSR SNR ) = ( R 0 ) */
|
|
/* ( SNL CSL ) ( C D ) ( -SNR CSR ) ( 0 T ) */
|
|
|
|
dlasv2_(&a, &fc, &d__, &s1, &s2, &snr, &csr, &snl, &csl);
|
|
|
|
if (abs(csr) >= abs(snr) || abs(csl) >= abs(snl)) {
|
|
|
|
/* Compute the (2,1) and (2,2) elements of U**H *A and V**H *B, */
|
|
/* and (2,1) element of |U|**H *|A| and |V|**H *|B|. */
|
|
|
|
z__4.r = -d1.r, z__4.i = -d1.i;
|
|
z__3.r = snr * z__4.r, z__3.i = snr * z__4.i;
|
|
z__2.r = *a1 * z__3.r, z__2.i = *a1 * z__3.i;
|
|
z__5.r = csr * a2->r, z__5.i = csr * a2->i;
|
|
z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i;
|
|
ua21.r = z__1.r, ua21.i = z__1.i;
|
|
ua22r = csr * *a3;
|
|
|
|
z__4.r = -d1.r, z__4.i = -d1.i;
|
|
z__3.r = snl * z__4.r, z__3.i = snl * z__4.i;
|
|
z__2.r = *b1 * z__3.r, z__2.i = *b1 * z__3.i;
|
|
z__5.r = csl * b2->r, z__5.i = csl * b2->i;
|
|
z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i;
|
|
vb21.r = z__1.r, vb21.i = z__1.i;
|
|
vb22r = csl * *b3;
|
|
|
|
aua21 = abs(snr) * abs(*a1) + abs(csr) * ((d__1 = a2->r, abs(d__1)
|
|
) + (d__2 = d_imag(a2), abs(d__2)));
|
|
avb21 = abs(snl) * abs(*b1) + abs(csl) * ((d__1 = b2->r, abs(d__1)
|
|
) + (d__2 = d_imag(b2), abs(d__2)));
|
|
|
|
/* zero (2,1) elements of U**H *A and V**H *B. */
|
|
|
|
if ((d__1 = ua21.r, abs(d__1)) + (d__2 = d_imag(&ua21), abs(d__2))
|
|
+ abs(ua22r) == 0.) {
|
|
z__1.r = vb22r, z__1.i = 0.;
|
|
zlartg_(&z__1, &vb21, csq, snq, &r__);
|
|
} else if ((d__1 = vb21.r, abs(d__1)) + (d__2 = d_imag(&vb21),
|
|
abs(d__2)) + abs(vb22r) == 0.) {
|
|
z__1.r = ua22r, z__1.i = 0.;
|
|
zlartg_(&z__1, &ua21, csq, snq, &r__);
|
|
} else if (aua21 / ((d__1 = ua21.r, abs(d__1)) + (d__2 = d_imag(&
|
|
ua21), abs(d__2)) + abs(ua22r)) <= avb21 / ((d__3 =
|
|
vb21.r, abs(d__3)) + (d__4 = d_imag(&vb21), abs(d__4)) +
|
|
abs(vb22r))) {
|
|
z__1.r = ua22r, z__1.i = 0.;
|
|
zlartg_(&z__1, &ua21, csq, snq, &r__);
|
|
} else {
|
|
z__1.r = vb22r, z__1.i = 0.;
|
|
zlartg_(&z__1, &vb21, csq, snq, &r__);
|
|
}
|
|
|
|
*csu = csr;
|
|
d_cnjg(&z__3, &d1);
|
|
z__2.r = -z__3.r, z__2.i = -z__3.i;
|
|
z__1.r = snr * z__2.r, z__1.i = snr * z__2.i;
|
|
snu->r = z__1.r, snu->i = z__1.i;
|
|
*csv = csl;
|
|
d_cnjg(&z__3, &d1);
|
|
z__2.r = -z__3.r, z__2.i = -z__3.i;
|
|
z__1.r = snl * z__2.r, z__1.i = snl * z__2.i;
|
|
snv->r = z__1.r, snv->i = z__1.i;
|
|
|
|
} else {
|
|
|
|
/* Compute the (1,1) and (1,2) elements of U**H *A and V**H *B, */
|
|
/* and (1,1) element of |U|**H *|A| and |V|**H *|B|. */
|
|
|
|
d__1 = csr * *a1;
|
|
d_cnjg(&z__4, &d1);
|
|
z__3.r = snr * z__4.r, z__3.i = snr * z__4.i;
|
|
z__2.r = z__3.r * a2->r - z__3.i * a2->i, z__2.i = z__3.r * a2->i
|
|
+ z__3.i * a2->r;
|
|
z__1.r = d__1 + z__2.r, z__1.i = z__2.i;
|
|
ua11.r = z__1.r, ua11.i = z__1.i;
|
|
d_cnjg(&z__3, &d1);
|
|
z__2.r = snr * z__3.r, z__2.i = snr * z__3.i;
|
|
z__1.r = *a3 * z__2.r, z__1.i = *a3 * z__2.i;
|
|
ua12.r = z__1.r, ua12.i = z__1.i;
|
|
|
|
d__1 = csl * *b1;
|
|
d_cnjg(&z__4, &d1);
|
|
z__3.r = snl * z__4.r, z__3.i = snl * z__4.i;
|
|
z__2.r = z__3.r * b2->r - z__3.i * b2->i, z__2.i = z__3.r * b2->i
|
|
+ z__3.i * b2->r;
|
|
z__1.r = d__1 + z__2.r, z__1.i = z__2.i;
|
|
vb11.r = z__1.r, vb11.i = z__1.i;
|
|
d_cnjg(&z__3, &d1);
|
|
z__2.r = snl * z__3.r, z__2.i = snl * z__3.i;
|
|
z__1.r = *b3 * z__2.r, z__1.i = *b3 * z__2.i;
|
|
vb12.r = z__1.r, vb12.i = z__1.i;
|
|
|
|
aua11 = abs(csr) * abs(*a1) + abs(snr) * ((d__1 = a2->r, abs(d__1)
|
|
) + (d__2 = d_imag(a2), abs(d__2)));
|
|
avb11 = abs(csl) * abs(*b1) + abs(snl) * ((d__1 = b2->r, abs(d__1)
|
|
) + (d__2 = d_imag(b2), abs(d__2)));
|
|
|
|
/* zero (1,1) elements of U**H *A and V**H *B, and then swap. */
|
|
|
|
if ((d__1 = ua11.r, abs(d__1)) + (d__2 = d_imag(&ua11), abs(d__2))
|
|
+ ((d__3 = ua12.r, abs(d__3)) + (d__4 = d_imag(&ua12),
|
|
abs(d__4))) == 0.) {
|
|
zlartg_(&vb12, &vb11, csq, snq, &r__);
|
|
} else if ((d__1 = vb11.r, abs(d__1)) + (d__2 = d_imag(&vb11),
|
|
abs(d__2)) + ((d__3 = vb12.r, abs(d__3)) + (d__4 = d_imag(
|
|
&vb12), abs(d__4))) == 0.) {
|
|
zlartg_(&ua12, &ua11, csq, snq, &r__);
|
|
} else if (aua11 / ((d__1 = ua11.r, abs(d__1)) + (d__2 = d_imag(&
|
|
ua11), abs(d__2)) + ((d__3 = ua12.r, abs(d__3)) + (d__4 =
|
|
d_imag(&ua12), abs(d__4)))) <= avb11 / ((d__5 = vb11.r,
|
|
abs(d__5)) + (d__6 = d_imag(&vb11), abs(d__6)) + ((d__7 =
|
|
vb12.r, abs(d__7)) + (d__8 = d_imag(&vb12), abs(d__8)))))
|
|
{
|
|
zlartg_(&ua12, &ua11, csq, snq, &r__);
|
|
} else {
|
|
zlartg_(&vb12, &vb11, csq, snq, &r__);
|
|
}
|
|
|
|
*csu = snr;
|
|
d_cnjg(&z__2, &d1);
|
|
z__1.r = csr * z__2.r, z__1.i = csr * z__2.i;
|
|
snu->r = z__1.r, snu->i = z__1.i;
|
|
*csv = snl;
|
|
d_cnjg(&z__2, &d1);
|
|
z__1.r = csl * z__2.r, z__1.i = csl * z__2.i;
|
|
snv->r = z__1.r, snv->i = z__1.i;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of ZLAGS2 */
|
|
|
|
} /* zlags2_ */
|
|
|