606 lines
18 KiB
C
606 lines
18 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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#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 doublereal c_b4 = -1.;
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static doublereal c_b5 = 1.;
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static integer c__1 = 1;
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static doublereal c_b38 = 0.;
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/* > \brief \b DLAHRD reduces the first nb columns of a general rectangular matrix A so that elements below th
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e k-th subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformati
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on to the unreduced part of A. */
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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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/* > \htmlonly */
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/* > Download DLAHRD + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlahrd.
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f"> */
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/* > [TGZ]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlahrd.
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f"> */
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/* > [ZIP]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlahrd.
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f"> */
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/* > [TXT]</a> */
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/* > \endhtmlonly */
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/* Definition: */
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/* =========== */
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/* SUBROUTINE DLAHRD( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY ) */
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/* INTEGER K, LDA, LDT, LDY, N, NB */
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/* DOUBLE PRECISION A( LDA, * ), T( LDT, NB ), TAU( NB ), */
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/* $ Y( LDY, NB ) */
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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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/* > This routine is deprecated and has been replaced by routine DLAHR2. */
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/* > */
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/* > DLAHRD reduces the first NB columns of a real general n-by-(n-k+1) */
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/* > matrix A so that elements below the k-th subdiagonal are zero. The */
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/* > reduction is performed by an orthogonal similarity transformation */
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/* > Q**T * A * Q. The routine returns the matrices V and T which determine */
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/* > Q as a block reflector I - V*T*V**T, and also the matrix Y = A * V * T. */
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/* > \endverbatim */
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/* Arguments: */
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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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/* > The order of the matrix A. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] K */
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/* > \verbatim */
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/* > K is INTEGER */
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/* > The offset for the reduction. Elements below the k-th */
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/* > subdiagonal in the first NB columns are reduced to zero. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] NB */
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/* > \verbatim */
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/* > NB is INTEGER */
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/* > The number of columns to be reduced. */
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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 DOUBLE PRECISION array, dimension (LDA,N-K+1) */
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/* > On entry, the n-by-(n-k+1) general matrix A. */
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/* > On exit, the elements on and above the k-th subdiagonal in */
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/* > the first NB columns are overwritten with the corresponding */
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/* > elements of the reduced matrix; the elements below the k-th */
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/* > subdiagonal, with the array TAU, represent the matrix Q as a */
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/* > product of elementary reflectors. The other columns of A are */
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/* > unchanged. See Further Details. */
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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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/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] TAU */
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/* > \verbatim */
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/* > TAU is DOUBLE PRECISION array, dimension (NB) */
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/* > The scalar factors of the elementary reflectors. See Further */
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/* > Details. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] T */
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/* > \verbatim */
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/* > T is DOUBLE PRECISION array, dimension (LDT,NB) */
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/* > The upper triangular matrix T. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDT */
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/* > \verbatim */
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/* > LDT is INTEGER */
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/* > The leading dimension of the array T. LDT >= NB. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] Y */
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/* > \verbatim */
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/* > Y is DOUBLE PRECISION array, dimension (LDY,NB) */
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/* > The n-by-nb matrix Y. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDY */
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/* > \verbatim */
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/* > LDY is INTEGER */
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/* > The leading dimension of the array Y. LDY >= N. */
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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 doubleOTHERauxiliary */
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/* > \par Further Details: */
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/* ===================== */
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/* > */
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/* > \verbatim */
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/* > */
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/* > The matrix Q is represented as a product of nb elementary reflectors */
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/* > */
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/* > Q = H(1) H(2) . . . H(nb). */
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/* > */
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/* > Each H(i) has the form */
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/* > */
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/* > H(i) = I - tau * v * v**T */
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/* > */
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/* > where tau is a real scalar, and v is a real vector with */
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/* > v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in */
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/* > A(i+k+1:n,i), and tau in TAU(i). */
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/* > */
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/* > The elements of the vectors v together form the (n-k+1)-by-nb matrix */
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/* > V which is needed, with T and Y, to apply the transformation to the */
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/* > unreduced part of the matrix, using an update of the form: */
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/* > A := (I - V*T*V**T) * (A - Y*V**T). */
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/* > */
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/* > The contents of A on exit are illustrated by the following example */
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/* > with n = 7, k = 3 and nb = 2: */
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/* > */
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/* > ( a h a a a ) */
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/* > ( a h a a a ) */
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/* > ( a h a a a ) */
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/* > ( h h a a a ) */
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/* > ( v1 h a a a ) */
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/* > ( v1 v2 a a a ) */
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/* > ( v1 v2 a a a ) */
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/* > */
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/* > where a denotes an element of the original matrix A, h denotes a */
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/* > modified element of the upper Hessenberg matrix H, and vi denotes an */
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/* > element of the vector defining H(i). */
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/* > \endverbatim */
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/* > */
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/* ===================================================================== */
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/* Subroutine */ void dlahrd_(integer *n, integer *k, integer *nb, doublereal *
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a, integer *lda, doublereal *tau, doublereal *t, integer *ldt,
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doublereal *y, integer *ldy)
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{
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/* System generated locals */
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integer a_dim1, a_offset, t_dim1, t_offset, y_dim1, y_offset, i__1, i__2,
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i__3;
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doublereal d__1;
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/* Local variables */
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integer i__;
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extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *,
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integer *), dgemv_(char *, integer *, integer *, doublereal *,
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doublereal *, integer *, doublereal *, integer *, doublereal *,
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doublereal *, integer *), dcopy_(integer *, doublereal *,
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integer *, doublereal *, integer *), daxpy_(integer *, doublereal
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*, doublereal *, integer *, doublereal *, integer *), dtrmv_(char
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*, char *, char *, integer *, doublereal *, integer *, doublereal
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*, integer *);
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doublereal ei;
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extern /* Subroutine */ void dlarfg_(integer *, doublereal *, doublereal *,
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integer *, doublereal *);
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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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/* Quick return if possible */
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/* Parameter adjustments */
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--tau;
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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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t_dim1 = *ldt;
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t_offset = 1 + t_dim1 * 1;
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t -= t_offset;
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y_dim1 = *ldy;
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y_offset = 1 + y_dim1 * 1;
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y -= y_offset;
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/* Function Body */
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if (*n <= 1) {
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return;
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}
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i__1 = *nb;
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for (i__ = 1; i__ <= i__1; ++i__) {
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if (i__ > 1) {
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/* Update A(1:n,i) */
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/* Compute i-th column of A - Y * V**T */
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i__2 = i__ - 1;
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dgemv_("No transpose", n, &i__2, &c_b4, &y[y_offset], ldy, &a[*k
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+ i__ - 1 + a_dim1], lda, &c_b5, &a[i__ * a_dim1 + 1], &
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c__1);
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/* Apply I - V * T**T * V**T to this column (call it b) from the */
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/* left, using the last column of T as workspace */
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/* Let V = ( V1 ) and b = ( b1 ) (first I-1 rows) */
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/* ( V2 ) ( b2 ) */
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/* where V1 is unit lower triangular */
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/* w := V1**T * b1 */
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i__2 = i__ - 1;
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dcopy_(&i__2, &a[*k + 1 + i__ * a_dim1], &c__1, &t[*nb * t_dim1 +
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1], &c__1);
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i__2 = i__ - 1;
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dtrmv_("Lower", "Transpose", "Unit", &i__2, &a[*k + 1 + a_dim1],
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lda, &t[*nb * t_dim1 + 1], &c__1);
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/* w := w + V2**T *b2 */
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i__2 = *n - *k - i__ + 1;
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i__3 = i__ - 1;
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dgemv_("Transpose", &i__2, &i__3, &c_b5, &a[*k + i__ + a_dim1],
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lda, &a[*k + i__ + i__ * a_dim1], &c__1, &c_b5, &t[*nb *
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t_dim1 + 1], &c__1);
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/* w := T**T *w */
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i__2 = i__ - 1;
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dtrmv_("Upper", "Transpose", "Non-unit", &i__2, &t[t_offset], ldt,
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&t[*nb * t_dim1 + 1], &c__1);
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/* b2 := b2 - V2*w */
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i__2 = *n - *k - i__ + 1;
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i__3 = i__ - 1;
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dgemv_("No transpose", &i__2, &i__3, &c_b4, &a[*k + i__ + a_dim1],
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lda, &t[*nb * t_dim1 + 1], &c__1, &c_b5, &a[*k + i__ +
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i__ * a_dim1], &c__1);
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/* b1 := b1 - V1*w */
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i__2 = i__ - 1;
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dtrmv_("Lower", "No transpose", "Unit", &i__2, &a[*k + 1 + a_dim1]
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, lda, &t[*nb * t_dim1 + 1], &c__1);
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i__2 = i__ - 1;
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daxpy_(&i__2, &c_b4, &t[*nb * t_dim1 + 1], &c__1, &a[*k + 1 + i__
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* a_dim1], &c__1);
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a[*k + i__ - 1 + (i__ - 1) * a_dim1] = ei;
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}
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/* Generate the elementary reflector H(i) to annihilate */
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/* A(k+i+1:n,i) */
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i__2 = *n - *k - i__ + 1;
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/* Computing MIN */
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i__3 = *k + i__ + 1;
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dlarfg_(&i__2, &a[*k + i__ + i__ * a_dim1], &a[f2cmin(i__3,*n) + i__ *
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a_dim1], &c__1, &tau[i__]);
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ei = a[*k + i__ + i__ * a_dim1];
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a[*k + i__ + i__ * a_dim1] = 1.;
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/* Compute Y(1:n,i) */
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i__2 = *n - *k - i__ + 1;
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dgemv_("No transpose", n, &i__2, &c_b5, &a[(i__ + 1) * a_dim1 + 1],
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lda, &a[*k + i__ + i__ * a_dim1], &c__1, &c_b38, &y[i__ *
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y_dim1 + 1], &c__1);
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i__2 = *n - *k - i__ + 1;
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i__3 = i__ - 1;
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dgemv_("Transpose", &i__2, &i__3, &c_b5, &a[*k + i__ + a_dim1], lda, &
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a[*k + i__ + i__ * a_dim1], &c__1, &c_b38, &t[i__ * t_dim1 +
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1], &c__1);
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i__2 = i__ - 1;
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dgemv_("No transpose", n, &i__2, &c_b4, &y[y_offset], ldy, &t[i__ *
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t_dim1 + 1], &c__1, &c_b5, &y[i__ * y_dim1 + 1], &c__1);
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dscal_(n, &tau[i__], &y[i__ * y_dim1 + 1], &c__1);
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/* Compute T(1:i,i) */
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i__2 = i__ - 1;
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d__1 = -tau[i__];
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dscal_(&i__2, &d__1, &t[i__ * t_dim1 + 1], &c__1);
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i__2 = i__ - 1;
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dtrmv_("Upper", "No transpose", "Non-unit", &i__2, &t[t_offset], ldt,
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&t[i__ * t_dim1 + 1], &c__1)
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;
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t[i__ + i__ * t_dim1] = tau[i__];
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/* L10: */
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}
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a[*k + *nb + *nb * a_dim1] = ei;
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return;
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/* End of DLAHRD */
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} /* dlahrd_ */
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