986 lines
30 KiB
C
986 lines
30 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 blasint logical;
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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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#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 {
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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 = {1.f,0.f};
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief \b CUNHR_COL */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download CUNHR_COL + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cunhr_c
|
|
ol.f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cunhr_c
|
|
ol.f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cunhr_c
|
|
ol.f"> */
|
|
/* > [TXT]</a> */
|
|
/* > */
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE CUNHR_COL( M, N, NB, A, LDA, T, LDT, D, INFO ) */
|
|
|
|
/* INTEGER INFO, LDA, LDT, M, N, NB */
|
|
/* COMPLEX A( LDA, * ), D( * ), T( LDT, * ) */
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > CUNHR_COL takes an M-by-N complex matrix Q_in with orthonormal columns */
|
|
/* > as input, stored in A, and performs Householder Reconstruction (HR), */
|
|
/* > i.e. reconstructs Householder vectors V(i) implicitly representing */
|
|
/* > another M-by-N matrix Q_out, with the property that Q_in = Q_out*S, */
|
|
/* > where S is an N-by-N diagonal matrix with diagonal entries */
|
|
/* > equal to +1 or -1. The Householder vectors (columns V(i) of V) are */
|
|
/* > stored in A on output, and the diagonal entries of S are stored in D. */
|
|
/* > Block reflectors are also returned in T */
|
|
/* > (same output format as CGEQRT). */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of rows of the matrix A. M >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The number of columns of the matrix A. M >= N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NB */
|
|
/* > \verbatim */
|
|
/* > NB is INTEGER */
|
|
/* > The column block size to be used in the reconstruction */
|
|
/* > of Householder column vector blocks in the array A and */
|
|
/* > corresponding block reflectors in the array T. NB >= 1. */
|
|
/* > (Note that if NB > N, then N is used instead of NB */
|
|
/* > as the column block size.) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is COMPLEX array, dimension (LDA,N) */
|
|
/* > */
|
|
/* > On entry: */
|
|
/* > */
|
|
/* > The array A contains an M-by-N orthonormal matrix Q_in, */
|
|
/* > i.e the columns of A are orthogonal unit vectors. */
|
|
/* > */
|
|
/* > On exit: */
|
|
/* > */
|
|
/* > The elements below the diagonal of A represent the unit */
|
|
/* > lower-trapezoidal matrix V of Householder column vectors */
|
|
/* > V(i). The unit diagonal entries of V are not stored */
|
|
/* > (same format as the output below the diagonal in A from */
|
|
/* > CGEQRT). The matrix T and the matrix V stored on output */
|
|
/* > in A implicitly define Q_out. */
|
|
/* > */
|
|
/* > The elements above the diagonal contain the factor U */
|
|
/* > of the "modified" LU-decomposition: */
|
|
/* > Q_in - ( S ) = V * U */
|
|
/* > ( 0 ) */
|
|
/* > where 0 is a (M-N)-by-(M-N) zero matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] T */
|
|
/* > \verbatim */
|
|
/* > T is COMPLEX array, */
|
|
/* > dimension (LDT, N) */
|
|
/* > */
|
|
/* > Let NOCB = Number_of_output_col_blocks */
|
|
/* > = CEIL(N/NB) */
|
|
/* > */
|
|
/* > On exit, T(1:NB, 1:N) contains NOCB upper-triangular */
|
|
/* > block reflectors used to define Q_out stored in compact */
|
|
/* > form as a sequence of upper-triangular NB-by-NB column */
|
|
/* > blocks (same format as the output T in CGEQRT). */
|
|
/* > The matrix T and the matrix V stored on output in A */
|
|
/* > implicitly define Q_out. NOTE: The lower triangles */
|
|
/* > below the upper-triangular blcoks will be filled with */
|
|
/* > zeros. See Further Details. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDT */
|
|
/* > \verbatim */
|
|
/* > LDT is INTEGER */
|
|
/* > The leading dimension of the array T. */
|
|
/* > LDT >= f2cmax(1,f2cmin(NB,N)). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] D */
|
|
/* > \verbatim */
|
|
/* > D is COMPLEX array, dimension f2cmin(M,N). */
|
|
/* > The elements can be only plus or minus one. */
|
|
/* > */
|
|
/* > D(i) is constructed as D(i) = -SIGN(Q_in_i(i,i)), where */
|
|
/* > 1 <= i <= f2cmin(M,N), and Q_in_i is Q_in after performing */
|
|
/* > i-1 steps of “modified” Gaussian elimination. */
|
|
/* > See Further Details. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > The computed M-by-M unitary factor Q_out is defined implicitly as */
|
|
/* > a product of unitary matrices Q_out(i). Each Q_out(i) is stored in */
|
|
/* > the compact WY-representation format in the corresponding blocks of */
|
|
/* > matrices V (stored in A) and T. */
|
|
/* > */
|
|
/* > The M-by-N unit lower-trapezoidal matrix V stored in the M-by-N */
|
|
/* > matrix A contains the column vectors V(i) in NB-size column */
|
|
/* > blocks VB(j). For example, VB(1) contains the columns */
|
|
/* > V(1), V(2), ... V(NB). NOTE: The unit entries on */
|
|
/* > the diagonal of Y are not stored in A. */
|
|
/* > */
|
|
/* > The number of column blocks is */
|
|
/* > */
|
|
/* > NOCB = Number_of_output_col_blocks = CEIL(N/NB) */
|
|
/* > */
|
|
/* > where each block is of order NB except for the last block, which */
|
|
/* > is of order LAST_NB = N - (NOCB-1)*NB. */
|
|
/* > */
|
|
/* > For example, if M=6, N=5 and NB=2, the matrix V is */
|
|
/* > */
|
|
/* > */
|
|
/* > V = ( VB(1), VB(2), VB(3) ) = */
|
|
/* > */
|
|
/* > = ( 1 ) */
|
|
/* > ( v21 1 ) */
|
|
/* > ( v31 v32 1 ) */
|
|
/* > ( v41 v42 v43 1 ) */
|
|
/* > ( v51 v52 v53 v54 1 ) */
|
|
/* > ( v61 v62 v63 v54 v65 ) */
|
|
/* > */
|
|
/* > */
|
|
/* > For each of the column blocks VB(i), an upper-triangular block */
|
|
/* > reflector TB(i) is computed. These blocks are stored as */
|
|
/* > a sequence of upper-triangular column blocks in the NB-by-N */
|
|
/* > matrix T. The size of each TB(i) block is NB-by-NB, except */
|
|
/* > for the last block, whose size is LAST_NB-by-LAST_NB. */
|
|
/* > */
|
|
/* > For example, if M=6, N=5 and NB=2, the matrix T is */
|
|
/* > */
|
|
/* > T = ( TB(1), TB(2), TB(3) ) = */
|
|
/* > */
|
|
/* > = ( t11 t12 t13 t14 t15 ) */
|
|
/* > ( t22 t24 ) */
|
|
/* > */
|
|
/* > */
|
|
/* > The M-by-M factor Q_out is given as a product of NOCB */
|
|
/* > unitary M-by-M matrices Q_out(i). */
|
|
/* > */
|
|
/* > Q_out = Q_out(1) * Q_out(2) * ... * Q_out(NOCB), */
|
|
/* > */
|
|
/* > where each matrix Q_out(i) is given by the WY-representation */
|
|
/* > using corresponding blocks from the matrices V and T: */
|
|
/* > */
|
|
/* > Q_out(i) = I - VB(i) * TB(i) * (VB(i))**T, */
|
|
/* > */
|
|
/* > where I is the identity matrix. Here is the formula with matrix */
|
|
/* > dimensions: */
|
|
/* > */
|
|
/* > Q(i){M-by-M} = I{M-by-M} - */
|
|
/* > VB(i){M-by-INB} * TB(i){INB-by-INB} * (VB(i))**T {INB-by-M}, */
|
|
/* > */
|
|
/* > where INB = NB, except for the last block NOCB */
|
|
/* > for which INB=LAST_NB. */
|
|
/* > */
|
|
/* > ===== */
|
|
/* > NOTE: */
|
|
/* > ===== */
|
|
/* > */
|
|
/* > If Q_in is the result of doing a QR factorization */
|
|
/* > B = Q_in * R_in, then: */
|
|
/* > */
|
|
/* > B = (Q_out*S) * R_in = Q_out * (S * R_in) = O_out * R_out. */
|
|
/* > */
|
|
/* > So if one wants to interpret Q_out as the result */
|
|
/* > of the QR factorization of B, then corresponding R_out */
|
|
/* > should be obtained by R_out = S * R_in, i.e. some rows of R_in */
|
|
/* > should be multiplied by -1. */
|
|
/* > */
|
|
/* > For the details of the algorithm, see [1]. */
|
|
/* > */
|
|
/* > [1] "Reconstructing Householder vectors from tall-skinny QR", */
|
|
/* > G. Ballard, J. Demmel, L. Grigori, M. Jacquelin, H.D. Nguyen, */
|
|
/* > E. Solomonik, J. Parallel Distrib. Comput., */
|
|
/* > vol. 85, pp. 3-31, 2015. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date November 2019 */
|
|
|
|
/* > \ingroup complexOTHERcomputational */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > November 2019, Igor Kozachenko, */
|
|
/* > Computer Science Division, */
|
|
/* > University of California, Berkeley */
|
|
/* > */
|
|
/* > \endverbatim */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void cunhr_col_(integer *m, integer *n, integer *nb, complex
|
|
*a, integer *lda, complex *t, integer *ldt, complex *d__, integer *
|
|
info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, t_dim1, t_offset, i__1, i__2, i__3, i__4, i__5;
|
|
complex q__1;
|
|
|
|
/* Local variables */
|
|
extern /* Subroutine */ void claunhr_col_getrfnp_(integer *, integer *,
|
|
complex *, integer *, complex *, integer *);
|
|
integer nplusone, i__, j;
|
|
extern /* Subroutine */ void cscal_(integer *, complex *, complex *,
|
|
integer *);
|
|
integer iinfo;
|
|
extern /* Subroutine */ void ccopy_(integer *, complex *, integer *,
|
|
complex *, integer *), ctrsm_(char *, char *, char *, char *,
|
|
integer *, integer *, complex *, complex *, integer *, complex *,
|
|
integer *);
|
|
integer jb;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
integer jbtemp1, jbtemp2, jnb;
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.9.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* November 2019 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input parameters */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
t_dim1 = *ldt;
|
|
t_offset = 1 + t_dim1 * 1;
|
|
t -= t_offset;
|
|
--d__;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
if (*m < 0) {
|
|
*info = -1;
|
|
} else if (*n < 0 || *n > *m) {
|
|
*info = -2;
|
|
} else if (*nb < 1) {
|
|
*info = -3;
|
|
} else if (*lda < f2cmax(1,*m)) {
|
|
*info = -5;
|
|
} else /* if(complicated condition) */ {
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = f2cmin(*nb,*n);
|
|
if (*ldt < f2cmax(i__1,i__2)) {
|
|
*info = -7;
|
|
}
|
|
}
|
|
|
|
/* Handle error in the input parameters. */
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("CUNHR_COL", &i__1, (ftnlen)9);
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (f2cmin(*m,*n) == 0) {
|
|
return;
|
|
}
|
|
|
|
/* On input, the M-by-N matrix A contains the unitary */
|
|
/* M-by-N matrix Q_in. */
|
|
|
|
/* (1) Compute the unit lower-trapezoidal V (ones on the diagonal */
|
|
/* are not stored) by performing the "modified" LU-decomposition. */
|
|
|
|
/* Q_in - ( S ) = V * U = ( V1 ) * U, */
|
|
/* ( 0 ) ( V2 ) */
|
|
|
|
/* where 0 is an (M-N)-by-N zero matrix. */
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|
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/* (1-1) Factor V1 and U. */
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claunhr_col_getrfnp_(n, n, &a[a_offset], lda, &d__[1], &iinfo);
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|
|
|
/* (1-2) Solve for V2. */
|
|
|
|
if (*m > *n) {
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|
i__1 = *m - *n;
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|
ctrsm_("R", "U", "N", "N", &i__1, n, &c_b1, &a[a_offset], lda, &a[*n
|
|
+ 1 + a_dim1], lda);
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|
}
|
|
|
|
/* (2) Reconstruct the block reflector T stored in T(1:NB, 1:N) */
|
|
/* as a sequence of upper-triangular blocks with NB-size column */
|
|
/* blocking. */
|
|
|
|
/* Loop over the column blocks of size NB of the array A(1:M,1:N) */
|
|
/* and the array T(1:NB,1:N), JB is the column index of a column */
|
|
/* block, JNB is the column block size at each step JB. */
|
|
|
|
nplusone = *n + 1;
|
|
i__1 = *n;
|
|
i__2 = *nb;
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|
for (jb = 1; i__2 < 0 ? jb >= i__1 : jb <= i__1; jb += i__2) {
|
|
|
|
/* (2-0) Determine the column block size JNB. */
|
|
|
|
/* Computing MIN */
|
|
i__3 = nplusone - jb;
|
|
jnb = f2cmin(i__3,*nb);
|
|
|
|
/* (2-1) Copy the upper-triangular part of the current JNB-by-JNB */
|
|
/* diagonal block U(JB) (of the N-by-N matrix U) stored */
|
|
/* in A(JB:JB+JNB-1,JB:JB+JNB-1) into the upper-triangular part */
|
|
/* of the current JNB-by-JNB block T(1:JNB,JB:JB+JNB-1) */
|
|
/* column-by-column, total JNB*(JNB+1)/2 elements. */
|
|
|
|
jbtemp1 = jb - 1;
|
|
i__3 = jb + jnb - 1;
|
|
for (j = jb; j <= i__3; ++j) {
|
|
i__4 = j - jbtemp1;
|
|
ccopy_(&i__4, &a[jb + j * a_dim1], &c__1, &t[j * t_dim1 + 1], &
|
|
c__1);
|
|
}
|
|
|
|
/* (2-2) Perform on the upper-triangular part of the current */
|
|
/* JNB-by-JNB diagonal block U(JB) (of the N-by-N matrix U) stored */
|
|
/* in T(1:JNB,JB:JB+JNB-1) the following operation in place: */
|
|
/* (-1)*U(JB)*S(JB), i.e the result will be stored in the upper- */
|
|
/* triangular part of T(1:JNB,JB:JB+JNB-1). This multiplication */
|
|
/* of the JNB-by-JNB diagonal block U(JB) by the JNB-by-JNB */
|
|
/* diagonal block S(JB) of the N-by-N sign matrix S from the */
|
|
/* right means changing the sign of each J-th column of the block */
|
|
/* U(JB) according to the sign of the diagonal element of the block */
|
|
/* S(JB), i.e. S(J,J) that is stored in the array element D(J). */
|
|
|
|
i__3 = jb + jnb - 1;
|
|
for (j = jb; j <= i__3; ++j) {
|
|
i__4 = j;
|
|
if (d__[i__4].r == 1.f && d__[i__4].i == 0.f) {
|
|
i__4 = j - jbtemp1;
|
|
q__1.r = -1.f, q__1.i = 0.f;
|
|
cscal_(&i__4, &q__1, &t[j * t_dim1 + 1], &c__1);
|
|
}
|
|
}
|
|
|
|
/* (2-3) Perform the triangular solve for the current block */
|
|
/* matrix X(JB): */
|
|
|
|
/* X(JB) * (A(JB)**T) = B(JB), where: */
|
|
|
|
/* A(JB)**T is a JNB-by-JNB unit upper-triangular */
|
|
/* coefficient block, and A(JB)=V1(JB), which */
|
|
/* is a JNB-by-JNB unit lower-triangular block */
|
|
/* stored in A(JB:JB+JNB-1,JB:JB+JNB-1). */
|
|
/* The N-by-N matrix V1 is the upper part */
|
|
/* of the M-by-N lower-trapezoidal matrix V */
|
|
/* stored in A(1:M,1:N); */
|
|
|
|
/* B(JB) is a JNB-by-JNB upper-triangular right-hand */
|
|
/* side block, B(JB) = (-1)*U(JB)*S(JB), and */
|
|
/* B(JB) is stored in T(1:JNB,JB:JB+JNB-1); */
|
|
|
|
/* X(JB) is a JNB-by-JNB upper-triangular solution */
|
|
/* block, X(JB) is the upper-triangular block */
|
|
/* reflector T(JB), and X(JB) is stored */
|
|
/* in T(1:JNB,JB:JB+JNB-1). */
|
|
|
|
/* In other words, we perform the triangular solve for the */
|
|
/* upper-triangular block T(JB): */
|
|
|
|
/* T(JB) * (V1(JB)**T) = (-1)*U(JB)*S(JB). */
|
|
|
|
/* Even though the blocks X(JB) and B(JB) are upper- */
|
|
/* triangular, the routine CTRSM will access all JNB**2 */
|
|
/* elements of the square T(1:JNB,JB:JB+JNB-1). Therefore, */
|
|
/* we need to set to zero the elements of the block */
|
|
/* T(1:JNB,JB:JB+JNB-1) below the diagonal before the call */
|
|
/* to CTRSM. */
|
|
|
|
/* (2-3a) Set the elements to zero. */
|
|
|
|
jbtemp2 = jb - 2;
|
|
i__3 = jb + jnb - 2;
|
|
for (j = jb; j <= i__3; ++j) {
|
|
i__4 = *nb;
|
|
for (i__ = j - jbtemp2; i__ <= i__4; ++i__) {
|
|
i__5 = i__ + j * t_dim1;
|
|
t[i__5].r = 0.f, t[i__5].i = 0.f;
|
|
}
|
|
}
|
|
|
|
/* (2-3b) Perform the triangular solve. */
|
|
|
|
ctrsm_("R", "L", "C", "U", &jnb, &jnb, &c_b1, &a[jb + jb * a_dim1],
|
|
lda, &t[jb * t_dim1 + 1], ldt);
|
|
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of CUNHR_COL */
|
|
|
|
} /* cunhr_col__ */
|
|
|