665 lines
19 KiB
C
665 lines
19 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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#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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/* Table of constant values */
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static doublecomplex c_b1 = {0.,0.};
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static doublecomplex c_b2 = {1.,0.};
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static integer c__3 = 3;
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static integer c__1 = 1;
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/* > \brief \b ZLAROR */
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/* =========== DOCUMENTATION =========== */
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/* Online html documentation available at */
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/* http://www.netlib.org/lapack/explore-html/ */
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/* Definition: */
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/* =========== */
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/* SUBROUTINE ZLAROR( SIDE, INIT, M, N, A, LDA, ISEED, X, INFO ) */
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/* CHARACTER INIT, SIDE */
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/* INTEGER INFO, LDA, M, N */
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/* INTEGER ISEED( 4 ) */
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/* COMPLEX*16 A( LDA, * ), X( * ) */
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/* > \par Purpose: */
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/* ============= */
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/* > */
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/* > \verbatim */
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/* > */
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/* > ZLAROR pre- or post-multiplies an M by N matrix A by a random */
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/* > unitary matrix U, overwriting A. A may optionally be */
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/* > initialized to the identity matrix before multiplying by U. */
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/* > U is generated using the method of G.W. Stewart */
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/* > ( SIAM J. Numer. Anal. 17, 1980, pp. 403-409 ). */
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/* > (BLAS-2 version) */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] SIDE */
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/* > \verbatim */
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/* > SIDE is CHARACTER*1 */
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/* > SIDE specifies whether A is multiplied on the left or right */
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/* > by U. */
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/* > SIDE = 'L' Multiply A on the left (premultiply) by U */
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/* > SIDE = 'R' Multiply A on the right (postmultiply) by UC> SIDE = 'C' Multiply A on the lef
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t by U and the right by UC> SIDE = 'T' Multiply A on the left by U and the right by U' */
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/* > Not modified. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] INIT */
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/* > \verbatim */
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/* > INIT is CHARACTER*1 */
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/* > INIT specifies whether or not A should be initialized to */
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/* > the identity matrix. */
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/* > INIT = 'I' Initialize A to (a section of) the */
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/* > identity matrix before applying U. */
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/* > INIT = 'N' No initialization. Apply U to the */
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/* > input matrix A. */
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/* > */
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/* > INIT = 'I' may be used to generate square (i.e., unitary) */
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/* > or rectangular orthogonal matrices (orthogonality being */
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/* > in the sense of ZDOTC): */
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/* > */
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/* > For square matrices, M=N, and SIDE many be either 'L' or */
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/* > 'R'; the rows will be orthogonal to each other, as will the */
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/* > columns. */
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/* > For rectangular matrices where M < N, SIDE = 'R' will */
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/* > produce a dense matrix whose rows will be orthogonal and */
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/* > whose columns will not, while SIDE = 'L' will produce a */
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/* > matrix whose rows will be orthogonal, and whose first M */
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/* > columns will be orthogonal, the remaining columns being */
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/* > zero. */
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/* > For matrices where M > N, just use the previous */
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/* > explanation, interchanging 'L' and 'R' and "rows" and */
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/* > "columns". */
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/* > */
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/* > Not modified. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] M */
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/* > \verbatim */
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/* > M is INTEGER */
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/* > Number of rows of A. Not modified. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] N */
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/* > \verbatim */
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/* > N is INTEGER */
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/* > Number of columns of A. Not modified. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] A */
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/* > \verbatim */
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/* > A is COMPLEX*16 array, dimension ( LDA, N ) */
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/* > Input and output array. Overwritten by U A ( if SIDE = 'L' ) */
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/* > or by A U ( if SIDE = 'R' ) */
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/* > or by U A U* ( if SIDE = 'C') */
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/* > or by U A U' ( if SIDE = 'T') on exit. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDA */
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/* > \verbatim */
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/* > LDA is INTEGER */
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/* > Leading dimension of A. Must be at least MAX ( 1, M ). */
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/* > Not modified. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] ISEED */
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/* > \verbatim */
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/* > ISEED is INTEGER array, dimension ( 4 ) */
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/* > On entry ISEED specifies the seed of the random number */
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/* > generator. The array elements should be between 0 and 4095; */
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/* > if not they will be reduced mod 4096. Also, ISEED(4) must */
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/* > be odd. The random number generator uses a linear */
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/* > congruential sequence limited to small integers, and so */
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/* > should produce machine independent random numbers. The */
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/* > values of ISEED are changed on exit, and can be used in the */
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/* > next call to ZLAROR to continue the same random number */
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/* > sequence. */
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/* > Modified. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] X */
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/* > \verbatim */
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/* > X is COMPLEX*16 array, dimension ( 3*MAX( M, N ) ) */
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/* > Workspace. Of length: */
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/* > 2*M + N if SIDE = 'L', */
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/* > 2*N + M if SIDE = 'R', */
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/* > 3*N if SIDE = 'C' or 'T'. */
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/* > Modified. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] INFO */
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/* > \verbatim */
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/* > INFO is INTEGER */
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/* > An error flag. It is set to: */
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/* > 0 if no error. */
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/* > 1 if ZLARND returned a bad random number (installation */
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/* > problem) */
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/* > -1 if SIDE is not L, R, C, or T. */
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/* > -3 if M is negative. */
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/* > -4 if N is negative or if SIDE is C or T and N is not equal */
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/* > to M. */
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/* > -6 if LDA is less than M. */
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/* > \endverbatim */
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/* Authors: */
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/* ======== */
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/* > \author Univ. of Tennessee */
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/* > \author Univ. of California Berkeley */
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/* > \author Univ. of Colorado Denver */
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/* > \author NAG Ltd. */
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/* > \date December 2016 */
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/* > \ingroup complex16_matgen */
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/* ===================================================================== */
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/* Subroutine */ void zlaror_(char *side, char *init, integer *m, integer *n,
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doublecomplex *a, integer *lda, integer *iseed, doublecomplex *x,
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integer *info)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2, i__3;
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doublecomplex z__1, z__2;
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/* Local variables */
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integer kbeg, jcol;
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doublereal xabs;
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integer irow, j;
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extern logical lsame_(char *, char *);
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doublecomplex csign;
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extern /* Subroutine */ void zgerc_(integer *, integer *, doublecomplex *,
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doublecomplex *, integer *, doublecomplex *, integer *,
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doublecomplex *, integer *), zscal_(integer *, doublecomplex *,
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doublecomplex *, integer *);
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integer ixfrm;
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extern /* Subroutine */ void zgemv_(char *, integer *, integer *,
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doublecomplex *, doublecomplex *, integer *, doublecomplex *,
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integer *, doublecomplex *, doublecomplex *, integer *);
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integer itype, nxfrm;
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doublereal xnorm;
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extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
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doublereal factor;
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extern /* Subroutine */ void zlacgv_(integer *, doublecomplex *, integer *)
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;
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//extern /* Double Complex */ VOID zlarnd_(doublecomplex *, integer *,
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extern doublecomplex zlarnd_(integer *,
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integer *);
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extern /* Subroutine */ void zlaset_(char *, integer *, integer *,
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doublecomplex *, doublecomplex *, doublecomplex *, integer *);
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doublecomplex xnorms;
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/* -- LAPACK auxiliary routine (version 3.7.0) -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* December 2016 */
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/* ===================================================================== */
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1 * 1;
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a -= a_offset;
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--iseed;
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--x;
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/* Function Body */
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*info = 0;
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if (*n == 0 || *m == 0) {
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return;
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}
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itype = 0;
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if (lsame_(side, "L")) {
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itype = 1;
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} else if (lsame_(side, "R")) {
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itype = 2;
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} else if (lsame_(side, "C")) {
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itype = 3;
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} else if (lsame_(side, "T")) {
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itype = 4;
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}
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/* Check for argument errors. */
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if (itype == 0) {
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*info = -1;
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} else if (*m < 0) {
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*info = -3;
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} else if (*n < 0 || itype == 3 && *n != *m) {
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*info = -4;
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} else if (*lda < *m) {
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*info = -6;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("ZLAROR", &i__1, 6);
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return;
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}
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if (itype == 1) {
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nxfrm = *m;
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} else {
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nxfrm = *n;
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}
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/* Initialize A to the identity matrix if desired */
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if (lsame_(init, "I")) {
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zlaset_("Full", m, n, &c_b1, &c_b2, &a[a_offset], lda);
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}
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/* If no rotation possible, still multiply by */
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/* a random complex number from the circle |x| = 1 */
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/* 2) Compute Rotation by computing Householder */
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/* Transformations H(2), H(3), ..., H(n). Note that the */
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/* order in which they are computed is irrelevant. */
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i__1 = nxfrm;
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for (j = 1; j <= i__1; ++j) {
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i__2 = j;
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x[i__2].r = 0., x[i__2].i = 0.;
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/* L10: */
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}
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i__1 = nxfrm;
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for (ixfrm = 2; ixfrm <= i__1; ++ixfrm) {
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kbeg = nxfrm - ixfrm + 1;
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/* Generate independent normal( 0, 1 ) random numbers */
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i__2 = nxfrm;
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for (j = kbeg; j <= i__2; ++j) {
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i__3 = j;
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//zlarnd_(&z__1, &c__3, &iseed[1]);
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z__1=zlarnd_(&c__3, &iseed[1]);
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x[i__3].r = z__1.r, x[i__3].i = z__1.i;
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/* L20: */
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}
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/* Generate a Householder transformation from the random vector X */
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xnorm = dznrm2_(&ixfrm, &x[kbeg], &c__1);
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xabs = z_abs(&x[kbeg]);
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if (xabs != 0.) {
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i__2 = kbeg;
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z__1.r = x[i__2].r / xabs, z__1.i = x[i__2].i / xabs;
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csign.r = z__1.r, csign.i = z__1.i;
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} else {
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csign.r = 1., csign.i = 0.;
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}
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z__1.r = xnorm * csign.r, z__1.i = xnorm * csign.i;
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xnorms.r = z__1.r, xnorms.i = z__1.i;
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i__2 = nxfrm + kbeg;
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z__1.r = -csign.r, z__1.i = -csign.i;
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x[i__2].r = z__1.r, x[i__2].i = z__1.i;
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factor = xnorm * (xnorm + xabs);
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if (abs(factor) < 1e-20) {
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*info = 1;
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i__2 = -(*info);
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xerbla_("ZLAROR", &i__2, 6);
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return;
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} else {
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factor = 1. / factor;
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}
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i__2 = kbeg;
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i__3 = kbeg;
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z__1.r = x[i__3].r + xnorms.r, z__1.i = x[i__3].i + xnorms.i;
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x[i__2].r = z__1.r, x[i__2].i = z__1.i;
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/* Apply Householder transformation to A */
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if (itype == 1 || itype == 3 || itype == 4) {
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/* Apply H(k) on the left of A */
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zgemv_("C", &ixfrm, n, &c_b2, &a[kbeg + a_dim1], lda, &x[kbeg], &
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c__1, &c_b1, &x[(nxfrm << 1) + 1], &c__1);
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z__2.r = factor, z__2.i = 0.;
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z__1.r = -z__2.r, z__1.i = -z__2.i;
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zgerc_(&ixfrm, n, &z__1, &x[kbeg], &c__1, &x[(nxfrm << 1) + 1], &
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c__1, &a[kbeg + a_dim1], lda);
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}
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if (itype >= 2 && itype <= 4) {
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/* Apply H(k)* (or H(k)') on the right of A */
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if (itype == 4) {
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zlacgv_(&ixfrm, &x[kbeg], &c__1);
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}
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zgemv_("N", m, &ixfrm, &c_b2, &a[kbeg * a_dim1 + 1], lda, &x[kbeg]
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, &c__1, &c_b1, &x[(nxfrm << 1) + 1], &c__1);
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z__2.r = factor, z__2.i = 0.;
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z__1.r = -z__2.r, z__1.i = -z__2.i;
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zgerc_(m, &ixfrm, &z__1, &x[(nxfrm << 1) + 1], &c__1, &x[kbeg], &
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c__1, &a[kbeg * a_dim1 + 1], lda);
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}
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/* L30: */
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}
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//zlarnd_(&z__1, &c__3, &iseed[1]);
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z__1=zlarnd_(&c__3, &iseed[1]);
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x[1].r = z__1.r, x[1].i = z__1.i;
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xabs = z_abs(&x[1]);
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if (xabs != 0.) {
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z__1.r = x[1].r / xabs, z__1.i = x[1].i / xabs;
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csign.r = z__1.r, csign.i = z__1.i;
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} else {
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csign.r = 1., csign.i = 0.;
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}
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i__1 = nxfrm << 1;
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x[i__1].r = csign.r, x[i__1].i = csign.i;
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/* Scale the matrix A by D. */
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if (itype == 1 || itype == 3 || itype == 4) {
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i__1 = *m;
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for (irow = 1; irow <= i__1; ++irow) {
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d_cnjg(&z__1, &x[nxfrm + irow]);
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zscal_(n, &z__1, &a[irow + a_dim1], lda);
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/* L40: */
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}
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}
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if (itype == 2 || itype == 3) {
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i__1 = *n;
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for (jcol = 1; jcol <= i__1; ++jcol) {
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zscal_(m, &x[nxfrm + jcol], &a[jcol * a_dim1 + 1], &c__1);
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/* L50: */
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}
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}
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if (itype == 4) {
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i__1 = *n;
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for (jcol = 1; jcol <= i__1; ++jcol) {
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d_cnjg(&z__1, &x[nxfrm + jcol]);
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zscal_(m, &z__1, &a[jcol * a_dim1 + 1], &c__1);
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/* L60: */
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}
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}
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return;
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/* End of ZLAROR */
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} /* zlaror_ */
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