1124 lines
32 KiB
C
1124 lines
32 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static complex c_b1 = {0.f,0.f};
|
|
static integer c__2 = 2;
|
|
static integer c_n1 = -1;
|
|
static integer c__3 = 3;
|
|
static integer c__4 = 4;
|
|
|
|
/* > \brief \b CHBTRD_HB2ST reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download CHBTRD_HB2ST + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chbtrd_
|
|
hb2st.f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chbtrd_
|
|
hb2st.f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chbtrd_
|
|
hb2st.f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE CHETRD_HB2ST( STAGE1, VECT, UPLO, N, KD, AB, LDAB, */
|
|
/* D, E, HOUS, LHOUS, WORK, LWORK, INFO ) */
|
|
|
|
/* #if defined(_OPENMP) */
|
|
/* use omp_lib */
|
|
/* #endif */
|
|
|
|
/* IMPLICIT NONE */
|
|
|
|
/* CHARACTER STAGE1, UPLO, VECT */
|
|
/* INTEGER N, KD, IB, LDAB, LHOUS, LWORK, INFO */
|
|
/* REAL D( * ), E( * ) */
|
|
/* COMPLEX AB( LDAB, * ), HOUS( * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > CHETRD_HB2ST reduces a complex Hermitian band matrix A to real symmetric */
|
|
/* > tridiagonal form T by a unitary similarity transformation: */
|
|
/* > Q**H * A * Q = T. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] STAGE1 */
|
|
/* > \verbatim */
|
|
/* > STAGE1 is CHARACTER*1 */
|
|
/* > = 'N': "No": to mention that the stage 1 of the reduction */
|
|
/* > from dense to band using the chetrd_he2hb routine */
|
|
/* > was not called before this routine to reproduce AB. */
|
|
/* > In other term this routine is called as standalone. */
|
|
/* > = 'Y': "Yes": to mention that the stage 1 of the */
|
|
/* > reduction from dense to band using the chetrd_he2hb */
|
|
/* > routine has been called to produce AB (e.g., AB is */
|
|
/* > the output of chetrd_he2hb. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] VECT */
|
|
/* > \verbatim */
|
|
/* > VECT is CHARACTER*1 */
|
|
/* > = 'N': No need for the Housholder representation, */
|
|
/* > and thus LHOUS is of size f2cmax(1, 4*N); */
|
|
/* > = 'V': the Householder representation is needed to */
|
|
/* > either generate or to apply Q later on, */
|
|
/* > then LHOUS is to be queried and computed. */
|
|
/* > (NOT AVAILABLE IN THIS RELEASE). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] UPLO */
|
|
/* > \verbatim */
|
|
/* > UPLO is CHARACTER*1 */
|
|
/* > = 'U': Upper triangle of A is stored; */
|
|
/* > = 'L': Lower triangle of A is stored. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix A. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] KD */
|
|
/* > \verbatim */
|
|
/* > KD is INTEGER */
|
|
/* > The number of superdiagonals of the matrix A if UPLO = 'U', */
|
|
/* > or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] AB */
|
|
/* > \verbatim */
|
|
/* > AB is COMPLEX array, dimension (LDAB,N) */
|
|
/* > On entry, the upper or lower triangle of the Hermitian band */
|
|
/* > matrix A, stored in the first KD+1 rows of the array. The */
|
|
/* > j-th column of A is stored in the j-th column of the array AB */
|
|
/* > as follows: */
|
|
/* > if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for f2cmax(1,j-kd)<=i<=j; */
|
|
/* > if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=f2cmin(n,j+kd). */
|
|
/* > On exit, the diagonal elements of AB are overwritten by the */
|
|
/* > diagonal elements of the tridiagonal matrix T; if KD > 0, the */
|
|
/* > elements on the first superdiagonal (if UPLO = 'U') or the */
|
|
/* > first subdiagonal (if UPLO = 'L') are overwritten by the */
|
|
/* > off-diagonal elements of T; the rest of AB is overwritten by */
|
|
/* > values generated during the reduction. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDAB */
|
|
/* > \verbatim */
|
|
/* > LDAB is INTEGER */
|
|
/* > The leading dimension of the array AB. LDAB >= KD+1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] D */
|
|
/* > \verbatim */
|
|
/* > D is REAL array, dimension (N) */
|
|
/* > The diagonal elements of the tridiagonal matrix T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] E */
|
|
/* > \verbatim */
|
|
/* > E is REAL array, dimension (N-1) */
|
|
/* > The off-diagonal elements of the tridiagonal matrix T: */
|
|
/* > E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] HOUS */
|
|
/* > \verbatim */
|
|
/* > HOUS is COMPLEX array, dimension LHOUS, that */
|
|
/* > store the Householder representation. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LHOUS */
|
|
/* > \verbatim */
|
|
/* > LHOUS is INTEGER */
|
|
/* > The dimension of the array HOUS. LHOUS = MAX(1, dimension) */
|
|
/* > If LWORK = -1, or LHOUS=-1, */
|
|
/* > then a query is assumed; the routine */
|
|
/* > only calculates the optimal size of the HOUS array, returns */
|
|
/* > this value as the first entry of the HOUS array, and no error */
|
|
/* > message related to LHOUS is issued by XERBLA. */
|
|
/* > LHOUS = MAX(1, dimension) where */
|
|
/* > dimension = 4*N if VECT='N' */
|
|
/* > not available now if VECT='H' */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX array, dimension LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. LWORK = MAX(1, dimension) */
|
|
/* > If LWORK = -1, or LHOUS=-1, */
|
|
/* > then a workspace query is assumed; the routine */
|
|
/* > only calculates the optimal size of the WORK array, returns */
|
|
/* > this value as the first entry of the WORK array, and no error */
|
|
/* > message related to LWORK is issued by XERBLA. */
|
|
/* > LWORK = MAX(1, dimension) where */
|
|
/* > dimension = (2KD+1)*N + KD*NTHREADS */
|
|
/* > where KD is the blocking size of the reduction, */
|
|
/* > FACTOPTNB is the blocking used by the QR or LQ */
|
|
/* > algorithm, usually FACTOPTNB=128 is a good choice */
|
|
/* > NTHREADS is the number of threads used when */
|
|
/* > openMP compilation is enabled, otherwise =1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date November 2017 */
|
|
|
|
/* > \ingroup complexOTHERcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > Implemented by Azzam Haidar. */
|
|
/* > */
|
|
/* > All details are available on technical report, SC11, SC13 papers. */
|
|
/* > */
|
|
/* > Azzam Haidar, Hatem Ltaief, and Jack Dongarra. */
|
|
/* > Parallel reduction to condensed forms for symmetric eigenvalue problems */
|
|
/* > using aggregated fine-grained and memory-aware kernels. In Proceedings */
|
|
/* > of 2011 International Conference for High Performance Computing, */
|
|
/* > Networking, Storage and Analysis (SC '11), New York, NY, USA, */
|
|
/* > Article 8 , 11 pages. */
|
|
/* > http://doi.acm.org/10.1145/2063384.2063394 */
|
|
/* > */
|
|
/* > A. Haidar, J. Kurzak, P. Luszczek, 2013. */
|
|
/* > An improved parallel singular value algorithm and its implementation */
|
|
/* > for multicore hardware, In Proceedings of 2013 International Conference */
|
|
/* > for High Performance Computing, Networking, Storage and Analysis (SC '13). */
|
|
/* > Denver, Colorado, USA, 2013. */
|
|
/* > Article 90, 12 pages. */
|
|
/* > http://doi.acm.org/10.1145/2503210.2503292 */
|
|
/* > */
|
|
/* > A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra. */
|
|
/* > A novel hybrid CPU-GPU generalized eigensolver for electronic structure */
|
|
/* > calculations based on fine-grained memory aware tasks. */
|
|
/* > International Journal of High Performance Computing Applications. */
|
|
/* > Volume 28 Issue 2, Pages 196-209, May 2014. */
|
|
/* > http://hpc.sagepub.com/content/28/2/196 */
|
|
/* > */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void chetrd_hb2st_(char *stage1, char *vect, char *uplo,
|
|
integer *n, integer *kd, complex *ab, integer *ldab, real *d__, real *
|
|
e, complex *hous, integer *lhous, complex *work, integer *lwork,
|
|
integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4, i__5;
|
|
real r__1;
|
|
complex q__1;
|
|
|
|
/* Local variables */
|
|
integer inda;
|
|
extern integer ilaenv2stage_(integer *, char *, char *, integer *,
|
|
integer *, integer *, integer *);
|
|
integer thed, indv, myid, indw, apos, dpos, abofdpos, nthreads, i__, k, m,
|
|
edind, debug;
|
|
extern logical lsame_(char *, char *);
|
|
integer lhmin, sicev, sizea, shift, stind, colpt, lwmin, awpos;
|
|
logical wantq, upper;
|
|
integer grsiz, ttype, stepercol, ed, ib;
|
|
extern /* Subroutine */ void chb2st_kernels_(char *, logical *, integer *,
|
|
integer *, integer *, integer *, integer *, integer *, integer *,
|
|
complex *, integer *, complex *, complex *, integer *, complex *);
|
|
integer st, abdpos;
|
|
extern /* Subroutine */ void clacpy_(char *, integer *, integer *, complex
|
|
*, integer *, complex *, integer *), claset_(char *,
|
|
integer *, integer *, complex *, complex *, complex *, integer *);
|
|
extern int xerbla_(char *, integer *, ftnlen);
|
|
integer thgrid, thgrnb, indtau;
|
|
real abstmp;
|
|
integer ofdpos, blklastind;
|
|
extern /* Subroutine */ void mecago_();
|
|
logical lquery, afters1;
|
|
integer lda, tid, ldv;
|
|
complex tmp;
|
|
integer stt, sweepid, nbtiles, sizetau, thgrsiz;
|
|
|
|
|
|
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.8.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* November 2017 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Determine the minimal workspace size required. */
|
|
/* Test the input parameters */
|
|
|
|
/* Parameter adjustments */
|
|
ab_dim1 = *ldab;
|
|
ab_offset = 1 + ab_dim1 * 1;
|
|
ab -= ab_offset;
|
|
--d__;
|
|
--e;
|
|
--hous;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
debug = 0;
|
|
*info = 0;
|
|
afters1 = lsame_(stage1, "Y");
|
|
wantq = lsame_(vect, "V");
|
|
upper = lsame_(uplo, "U");
|
|
lquery = *lwork == -1 || *lhous == -1;
|
|
|
|
/* Determine the block size, the workspace size and the hous size. */
|
|
|
|
ib = ilaenv2stage_(&c__2, "CHETRD_HB2ST", vect, n, kd, &c_n1, &c_n1);
|
|
lhmin = ilaenv2stage_(&c__3, "CHETRD_HB2ST", vect, n, kd, &ib, &c_n1);
|
|
lwmin = ilaenv2stage_(&c__4, "CHETRD_HB2ST", vect, n, kd, &ib, &c_n1);
|
|
|
|
if (! afters1 && ! lsame_(stage1, "N")) {
|
|
*info = -1;
|
|
} else if (! lsame_(vect, "N")) {
|
|
*info = -2;
|
|
} else if (! upper && ! lsame_(uplo, "L")) {
|
|
*info = -3;
|
|
} else if (*n < 0) {
|
|
*info = -4;
|
|
} else if (*kd < 0) {
|
|
*info = -5;
|
|
} else if (*ldab < *kd + 1) {
|
|
*info = -7;
|
|
} else if (*lhous < lhmin && ! lquery) {
|
|
*info = -11;
|
|
} else if (*lwork < lwmin && ! lquery) {
|
|
*info = -13;
|
|
}
|
|
|
|
if (*info == 0) {
|
|
hous[1].r = (real) lhmin, hous[1].i = 0.f;
|
|
work[1].r = (real) lwmin, work[1].i = 0.f;
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("CHETRD_HB2ST", &i__1, (ftnlen)12);
|
|
return;
|
|
} else if (lquery) {
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n == 0) {
|
|
hous[1].r = 1.f, hous[1].i = 0.f;
|
|
work[1].r = 1.f, work[1].i = 0.f;
|
|
return;
|
|
}
|
|
|
|
/* Determine pointer position */
|
|
|
|
ldv = *kd + ib;
|
|
sizetau = *n << 1;
|
|
sicev = *n << 1;
|
|
indtau = 1;
|
|
indv = indtau + sizetau;
|
|
lda = (*kd << 1) + 1;
|
|
sizea = lda * *n;
|
|
inda = 1;
|
|
indw = inda + sizea;
|
|
nthreads = 1;
|
|
tid = 0;
|
|
|
|
if (upper) {
|
|
apos = inda + *kd;
|
|
awpos = inda;
|
|
dpos = apos + *kd;
|
|
ofdpos = dpos - 1;
|
|
abdpos = *kd + 1;
|
|
abofdpos = *kd;
|
|
} else {
|
|
apos = inda;
|
|
awpos = inda + *kd + 1;
|
|
dpos = apos;
|
|
ofdpos = dpos + 1;
|
|
abdpos = 1;
|
|
abofdpos = 2;
|
|
}
|
|
|
|
/* Case KD=0: */
|
|
/* The matrix is diagonal. We just copy it (convert to "real" for */
|
|
/* complex because D is double and the imaginary part should be 0) */
|
|
/* and store it in D. A sequential code here is better or */
|
|
/* in a parallel environment it might need two cores for D and E */
|
|
|
|
if (*kd == 0) {
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = abdpos + i__ * ab_dim1;
|
|
d__[i__] = ab[i__2].r;
|
|
/* L30: */
|
|
}
|
|
i__1 = *n - 1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
e[i__] = 0.f;
|
|
/* L40: */
|
|
}
|
|
|
|
hous[1].r = 1.f, hous[1].i = 0.f;
|
|
work[1].r = 1.f, work[1].i = 0.f;
|
|
return;
|
|
}
|
|
|
|
/* Case KD=1: */
|
|
/* The matrix is already Tridiagonal. We have to make diagonal */
|
|
/* and offdiagonal elements real, and store them in D and E. */
|
|
/* For that, for real precision just copy the diag and offdiag */
|
|
/* to D and E while for the COMPLEX case the bulge chasing is */
|
|
/* performed to convert the hermetian tridiagonal to symmetric */
|
|
/* tridiagonal. A simpler coversion formula might be used, but then */
|
|
/* updating the Q matrix will be required and based if Q is generated */
|
|
/* or not this might complicate the story. */
|
|
|
|
if (*kd == 1) {
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = abdpos + i__ * ab_dim1;
|
|
d__[i__] = ab[i__2].r;
|
|
/* L50: */
|
|
}
|
|
|
|
/* make off-diagonal elements real and copy them to E */
|
|
|
|
if (upper) {
|
|
i__1 = *n - 1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = abofdpos + (i__ + 1) * ab_dim1;
|
|
tmp.r = ab[i__2].r, tmp.i = ab[i__2].i;
|
|
abstmp = c_abs(&tmp);
|
|
i__2 = abofdpos + (i__ + 1) * ab_dim1;
|
|
ab[i__2].r = abstmp, ab[i__2].i = 0.f;
|
|
e[i__] = abstmp;
|
|
if (abstmp != 0.f) {
|
|
q__1.r = tmp.r / abstmp, q__1.i = tmp.i / abstmp;
|
|
tmp.r = q__1.r, tmp.i = q__1.i;
|
|
} else {
|
|
tmp.r = 1.f, tmp.i = 0.f;
|
|
}
|
|
if (i__ < *n - 1) {
|
|
i__2 = abofdpos + (i__ + 2) * ab_dim1;
|
|
i__3 = abofdpos + (i__ + 2) * ab_dim1;
|
|
q__1.r = ab[i__3].r * tmp.r - ab[i__3].i * tmp.i, q__1.i =
|
|
ab[i__3].r * tmp.i + ab[i__3].i * tmp.r;
|
|
ab[i__2].r = q__1.r, ab[i__2].i = q__1.i;
|
|
}
|
|
/* IF( WANTZ ) THEN */
|
|
/* CALL CSCAL( N, CONJG( TMP ), Q( 1, I+1 ), 1 ) */
|
|
/* END IF */
|
|
/* L60: */
|
|
}
|
|
} else {
|
|
i__1 = *n - 1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = abofdpos + i__ * ab_dim1;
|
|
tmp.r = ab[i__2].r, tmp.i = ab[i__2].i;
|
|
abstmp = c_abs(&tmp);
|
|
i__2 = abofdpos + i__ * ab_dim1;
|
|
ab[i__2].r = abstmp, ab[i__2].i = 0.f;
|
|
e[i__] = abstmp;
|
|
if (abstmp != 0.f) {
|
|
q__1.r = tmp.r / abstmp, q__1.i = tmp.i / abstmp;
|
|
tmp.r = q__1.r, tmp.i = q__1.i;
|
|
} else {
|
|
tmp.r = 1.f, tmp.i = 0.f;
|
|
}
|
|
if (i__ < *n - 1) {
|
|
i__2 = abofdpos + (i__ + 1) * ab_dim1;
|
|
i__3 = abofdpos + (i__ + 1) * ab_dim1;
|
|
q__1.r = ab[i__3].r * tmp.r - ab[i__3].i * tmp.i, q__1.i =
|
|
ab[i__3].r * tmp.i + ab[i__3].i * tmp.r;
|
|
ab[i__2].r = q__1.r, ab[i__2].i = q__1.i;
|
|
}
|
|
/* IF( WANTQ ) THEN */
|
|
/* CALL CSCAL( N, TMP, Q( 1, I+1 ), 1 ) */
|
|
/* END IF */
|
|
/* L70: */
|
|
}
|
|
}
|
|
|
|
hous[1].r = 1.f, hous[1].i = 0.f;
|
|
work[1].r = 1.f, work[1].i = 0.f;
|
|
return;
|
|
}
|
|
|
|
/* Main code start here. */
|
|
/* Reduce the hermitian band of A to a tridiagonal matrix. */
|
|
|
|
thgrsiz = *n;
|
|
grsiz = 1;
|
|
shift = 3;
|
|
r__1 = (real) (*n) / (real) (*kd) + .5f;
|
|
nbtiles = r_int(&r__1);
|
|
r__1 = (real) shift / (real) grsiz + .5f;
|
|
stepercol = r_int(&r__1);
|
|
r__1 = (real) (*n - 1) / (real) thgrsiz + .5f;
|
|
thgrnb = r_int(&r__1);
|
|
|
|
i__1 = *kd + 1;
|
|
clacpy_("A", &i__1, n, &ab[ab_offset], ldab, &work[apos], &lda)
|
|
;
|
|
claset_("A", kd, n, &c_b1, &c_b1, &work[awpos], &lda);
|
|
|
|
|
|
/* openMP parallelisation start here */
|
|
|
|
|
|
/* main bulge chasing loop */
|
|
|
|
i__1 = thgrnb;
|
|
for (thgrid = 1; thgrid <= i__1; ++thgrid) {
|
|
stt = (thgrid - 1) * thgrsiz + 1;
|
|
/* Computing MIN */
|
|
i__2 = stt + thgrsiz - 1, i__3 = *n - 1;
|
|
thed = f2cmin(i__2,i__3);
|
|
i__2 = *n - 1;
|
|
for (i__ = stt; i__ <= i__2; ++i__) {
|
|
ed = f2cmin(i__,thed);
|
|
if (stt > ed) {
|
|
myexit_();
|
|
}
|
|
i__3 = stepercol;
|
|
for (m = 1; m <= i__3; ++m) {
|
|
st = stt;
|
|
i__4 = ed;
|
|
for (sweepid = st; sweepid <= i__4; ++sweepid) {
|
|
i__5 = grsiz;
|
|
for (k = 1; k <= i__5; ++k) {
|
|
myid = (i__ - sweepid) * (stepercol * grsiz) + (m - 1)
|
|
* grsiz + k;
|
|
if (myid == 1) {
|
|
ttype = 1;
|
|
} else {
|
|
ttype = myid % 2 + 2;
|
|
}
|
|
if (ttype == 2) {
|
|
colpt = myid / 2 * *kd + sweepid;
|
|
stind = colpt - *kd + 1;
|
|
edind = f2cmin(colpt,*n);
|
|
blklastind = colpt;
|
|
} else {
|
|
colpt = (myid + 1) / 2 * *kd + sweepid;
|
|
stind = colpt - *kd + 1;
|
|
edind = f2cmin(colpt,*n);
|
|
if (stind >= edind - 1 && edind == *n) {
|
|
blklastind = *n;
|
|
} else {
|
|
blklastind = 0;
|
|
}
|
|
}
|
|
|
|
/* Call the kernel */
|
|
|
|
chb2st_kernels_(uplo, &wantq, &ttype, &stind, &edind,
|
|
&sweepid, n, kd, &ib, &work[inda], &lda, &
|
|
hous[indv], &hous[indtau], &ldv, &work[indw +
|
|
tid * *kd]);
|
|
if (blklastind >= *n - 1) {
|
|
++stt;
|
|
myexit_();
|
|
}
|
|
/* L140: */
|
|
}
|
|
/* L130: */
|
|
}
|
|
/* L120: */
|
|
}
|
|
/* L110: */
|
|
}
|
|
/* L100: */
|
|
}
|
|
|
|
|
|
/* Copy the diagonal from A to D. Note that D is REAL thus only */
|
|
/* the Real part is needed, the imaginary part should be zero. */
|
|
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = dpos + (i__ - 1) * lda;
|
|
d__[i__] = work[i__2].r;
|
|
/* L150: */
|
|
}
|
|
|
|
/* Copy the off diagonal from A to E. Note that E is REAL thus only */
|
|
/* the Real part is needed, the imaginary part should be zero. */
|
|
|
|
if (upper) {
|
|
i__1 = *n - 1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = ofdpos + i__ * lda;
|
|
e[i__] = work[i__2].r;
|
|
/* L160: */
|
|
}
|
|
} else {
|
|
i__1 = *n - 1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = ofdpos + (i__ - 1) * lda;
|
|
e[i__] = work[i__2].r;
|
|
/* L170: */
|
|
}
|
|
}
|
|
|
|
hous[1].r = (real) lhmin, hous[1].i = 0.f;
|
|
work[1].r = (real) lwmin, work[1].i = 0.f;
|
|
return;
|
|
|
|
/* End of CHETRD_HB2ST */
|
|
|
|
} /* chetrd_hb2st__ */
|
|
|