1141 lines
34 KiB
C
1141 lines
34 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 integer c__1 = 1;
|
|
static doublereal c_b9 = 1.;
|
|
static doublereal c_b21 = -1.;
|
|
|
|
/* > \brief \b DLARFB_GETT */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DLARFB_GETT + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarfb_
|
|
gett.f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarfb_
|
|
gett.f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarfb_
|
|
gett.f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLARFB_GETT( IDENT, M, N, K, T, LDT, A, LDA, B, LDB, */
|
|
/* $ WORK, LDWORK ) */
|
|
/* IMPLICIT NONE */
|
|
|
|
/* CHARACTER IDENT */
|
|
/* INTEGER K, LDA, LDB, LDT, LDWORK, M, N */
|
|
/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), T( LDT, * ), */
|
|
/* $ WORK( LDWORK, * ) */
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DLARFB_GETT applies a real Householder block reflector H from the */
|
|
/* > left to a real (K+M)-by-N "triangular-pentagonal" matrix */
|
|
/* > composed of two block matrices: an upper trapezoidal K-by-N matrix A */
|
|
/* > stored in the array A, and a rectangular M-by-(N-K) matrix B, stored */
|
|
/* > in the array B. The block reflector H is stored in a compact */
|
|
/* > WY-representation, where the elementary reflectors are in the */
|
|
/* > arrays A, B and T. See Further Details section. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] IDENT */
|
|
/* > \verbatim */
|
|
/* > IDENT is CHARACTER*1 */
|
|
/* > If IDENT = not 'I', or not 'i', then V1 is unit */
|
|
/* > lower-triangular and stored in the left K-by-K block of */
|
|
/* > the input matrix A, */
|
|
/* > If IDENT = 'I' or 'i', then V1 is an identity matrix and */
|
|
/* > not stored. */
|
|
/* > See Further Details section. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of rows of the matrix B. */
|
|
/* > M >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The number of columns of the matrices A and B. */
|
|
/* > N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] K */
|
|
/* > \verbatim */
|
|
/* > K is INTEGER */
|
|
/* > The number or rows of the matrix A. */
|
|
/* > K is also order of the matrix T, i.e. the number of */
|
|
/* > elementary reflectors whose product defines the block */
|
|
/* > reflector. 0 <= K <= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] T */
|
|
/* > \verbatim */
|
|
/* > T is DOUBLE PRECISION array, dimension (LDT,K) */
|
|
/* > The upper-triangular K-by-K matrix T in the representation */
|
|
/* > of the block reflector. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDT */
|
|
/* > \verbatim */
|
|
/* > LDT is INTEGER */
|
|
/* > The leading dimension of the array T. LDT >= K. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is DOUBLE PRECISION array, dimension (LDA,N) */
|
|
/* > */
|
|
/* > On entry: */
|
|
/* > a) In the K-by-N upper-trapezoidal part A: input matrix A. */
|
|
/* > b) In the columns below the diagonal: columns of V1 */
|
|
/* > (ones are not stored on the diagonal). */
|
|
/* > */
|
|
/* > On exit: */
|
|
/* > A is overwritten by rectangular K-by-N product H*A. */
|
|
/* > */
|
|
/* > See Further Details section. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,K). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] B */
|
|
/* > \verbatim */
|
|
/* > B is DOUBLE PRECISION array, dimension (LDB,N) */
|
|
/* > */
|
|
/* > On entry: */
|
|
/* > a) In the M-by-(N-K) right block: input matrix B. */
|
|
/* > b) In the M-by-N left block: columns of V2. */
|
|
/* > */
|
|
/* > On exit: */
|
|
/* > B is overwritten by rectangular M-by-N product H*B. */
|
|
/* > */
|
|
/* > See Further Details section. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of the array B. LDB >= f2cmax(1,M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is DOUBLE PRECISION array, */
|
|
/* > dimension (LDWORK,f2cmax(K,N-K)) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDWORK */
|
|
/* > \verbatim */
|
|
/* > LDWORK is INTEGER */
|
|
/* > The leading dimension of the array WORK. LDWORK>=f2cmax(1,K). */
|
|
/* > */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \ingroup doubleOTHERauxiliary */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > November 2020, Igor Kozachenko, */
|
|
/* > Computer Science Division, */
|
|
/* > University of California, Berkeley */
|
|
/* > */
|
|
/* > \endverbatim */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > (1) Description of the Algebraic Operation. */
|
|
/* > */
|
|
/* > The matrix A is a K-by-N matrix composed of two column block */
|
|
/* > matrices, A1, which is K-by-K, and A2, which is K-by-(N-K): */
|
|
/* > A = ( A1, A2 ). */
|
|
/* > The matrix B is an M-by-N matrix composed of two column block */
|
|
/* > matrices, B1, which is M-by-K, and B2, which is M-by-(N-K): */
|
|
/* > B = ( B1, B2 ). */
|
|
/* > */
|
|
/* > Perform the operation: */
|
|
/* > */
|
|
/* > ( A_out ) := H * ( A_in ) = ( I - V * T * V**T ) * ( A_in ) = */
|
|
/* > ( B_out ) ( B_in ) ( B_in ) */
|
|
/* > = ( I - ( V1 ) * T * ( V1**T, V2**T ) ) * ( A_in ) */
|
|
/* > ( V2 ) ( B_in ) */
|
|
/* > On input: */
|
|
/* > */
|
|
/* > a) ( A_in ) consists of two block columns: */
|
|
/* > ( B_in ) */
|
|
/* > */
|
|
/* > ( A_in ) = (( A1_in ) ( A2_in )) = (( A1_in ) ( A2_in )) */
|
|
/* > ( B_in ) (( B1_in ) ( B2_in )) (( 0 ) ( B2_in )), */
|
|
/* > */
|
|
/* > where the column blocks are: */
|
|
/* > */
|
|
/* > ( A1_in ) is a K-by-K upper-triangular matrix stored in the */
|
|
/* > upper triangular part of the array A(1:K,1:K). */
|
|
/* > ( B1_in ) is an M-by-K rectangular ZERO matrix and not stored. */
|
|
/* > */
|
|
/* > ( A2_in ) is a K-by-(N-K) rectangular matrix stored */
|
|
/* > in the array A(1:K,K+1:N). */
|
|
/* > ( B2_in ) is an M-by-(N-K) rectangular matrix stored */
|
|
/* > in the array B(1:M,K+1:N). */
|
|
/* > */
|
|
/* > b) V = ( V1 ) */
|
|
/* > ( V2 ) */
|
|
/* > */
|
|
/* > where: */
|
|
/* > 1) if IDENT == 'I',V1 is a K-by-K identity matrix, not stored; */
|
|
/* > 2) if IDENT != 'I',V1 is a K-by-K unit lower-triangular matrix, */
|
|
/* > stored in the lower-triangular part of the array */
|
|
/* > A(1:K,1:K) (ones are not stored), */
|
|
/* > and V2 is an M-by-K rectangular stored the array B(1:M,1:K), */
|
|
/* > (because on input B1_in is a rectangular zero */
|
|
/* > matrix that is not stored and the space is */
|
|
/* > used to store V2). */
|
|
/* > */
|
|
/* > c) T is a K-by-K upper-triangular matrix stored */
|
|
/* > in the array T(1:K,1:K). */
|
|
/* > */
|
|
/* > On output: */
|
|
/* > */
|
|
/* > a) ( A_out ) consists of two block columns: */
|
|
/* > ( B_out ) */
|
|
/* > */
|
|
/* > ( A_out ) = (( A1_out ) ( A2_out )) */
|
|
/* > ( B_out ) (( B1_out ) ( B2_out )), */
|
|
/* > */
|
|
/* > where the column blocks are: */
|
|
/* > */
|
|
/* > ( A1_out ) is a K-by-K square matrix, or a K-by-K */
|
|
/* > upper-triangular matrix, if V1 is an */
|
|
/* > identity matrix. AiOut is stored in */
|
|
/* > the array A(1:K,1:K). */
|
|
/* > ( B1_out ) is an M-by-K rectangular matrix stored */
|
|
/* > in the array B(1:M,K:N). */
|
|
/* > */
|
|
/* > ( A2_out ) is a K-by-(N-K) rectangular matrix stored */
|
|
/* > in the array A(1:K,K+1:N). */
|
|
/* > ( B2_out ) is an M-by-(N-K) rectangular matrix stored */
|
|
/* > in the array B(1:M,K+1:N). */
|
|
/* > */
|
|
/* > */
|
|
/* > The operation above can be represented as the same operation */
|
|
/* > on each block column: */
|
|
/* > */
|
|
/* > ( A1_out ) := H * ( A1_in ) = ( I - V * T * V**T ) * ( A1_in ) */
|
|
/* > ( B1_out ) ( 0 ) ( 0 ) */
|
|
/* > */
|
|
/* > ( A2_out ) := H * ( A2_in ) = ( I - V * T * V**T ) * ( A2_in ) */
|
|
/* > ( B2_out ) ( B2_in ) ( B2_in ) */
|
|
/* > */
|
|
/* > If IDENT != 'I': */
|
|
/* > */
|
|
/* > The computation for column block 1: */
|
|
/* > */
|
|
/* > A1_out: = A1_in - V1*T*(V1**T)*A1_in */
|
|
/* > */
|
|
/* > B1_out: = - V2*T*(V1**T)*A1_in */
|
|
/* > */
|
|
/* > The computation for column block 2, which exists if N > K: */
|
|
/* > */
|
|
/* > A2_out: = A2_in - V1*T*( (V1**T)*A2_in + (V2**T)*B2_in ) */
|
|
/* > */
|
|
/* > B2_out: = B2_in - V2*T*( (V1**T)*A2_in + (V2**T)*B2_in ) */
|
|
/* > */
|
|
/* > If IDENT == 'I': */
|
|
/* > */
|
|
/* > The operation for column block 1: */
|
|
/* > */
|
|
/* > A1_out: = A1_in - V1*T**A1_in */
|
|
/* > */
|
|
/* > B1_out: = - V2*T**A1_in */
|
|
/* > */
|
|
/* > The computation for column block 2, which exists if N > K: */
|
|
/* > */
|
|
/* > A2_out: = A2_in - T*( A2_in + (V2**T)*B2_in ) */
|
|
/* > */
|
|
/* > B2_out: = B2_in - V2*T*( A2_in + (V2**T)*B2_in ) */
|
|
/* > */
|
|
/* > (2) Description of the Algorithmic Computation. */
|
|
/* > */
|
|
/* > In the first step, we compute column block 2, i.e. A2 and B2. */
|
|
/* > Here, we need to use the K-by-(N-K) rectangular workspace */
|
|
/* > matrix W2 that is of the same size as the matrix A2. */
|
|
/* > W2 is stored in the array WORK(1:K,1:(N-K)). */
|
|
/* > */
|
|
/* > In the second step, we compute column block 1, i.e. A1 and B1. */
|
|
/* > Here, we need to use the K-by-K square workspace matrix W1 */
|
|
/* > that is of the same size as the as the matrix A1. */
|
|
/* > W1 is stored in the array WORK(1:K,1:K). */
|
|
/* > */
|
|
/* > NOTE: Hence, in this routine, we need the workspace array WORK */
|
|
/* > only of size WORK(1:K,1:f2cmax(K,N-K)) so it can hold both W2 from */
|
|
/* > the first step and W1 from the second step. */
|
|
/* > */
|
|
/* > Case (A), when V1 is unit lower-triangular, i.e. IDENT != 'I', */
|
|
/* > more computations than in the Case (B). */
|
|
/* > */
|
|
/* > if( IDENT != 'I' ) then */
|
|
/* > if ( N > K ) then */
|
|
/* > (First Step - column block 2) */
|
|
/* > col2_(1) W2: = A2 */
|
|
/* > col2_(2) W2: = (V1**T) * W2 = (unit_lower_tr_of_(A1)**T) * W2 */
|
|
/* > col2_(3) W2: = W2 + (V2**T) * B2 = W2 + (B1**T) * B2 */
|
|
/* > col2_(4) W2: = T * W2 */
|
|
/* > col2_(5) B2: = B2 - V2 * W2 = B2 - B1 * W2 */
|
|
/* > col2_(6) W2: = V1 * W2 = unit_lower_tr_of_(A1) * W2 */
|
|
/* > col2_(7) A2: = A2 - W2 */
|
|
/* > else */
|
|
/* > (Second Step - column block 1) */
|
|
/* > col1_(1) W1: = A1 */
|
|
/* > col1_(2) W1: = (V1**T) * W1 = (unit_lower_tr_of_(A1)**T) * W1 */
|
|
/* > col1_(3) W1: = T * W1 */
|
|
/* > col1_(4) B1: = - V2 * W1 = - B1 * W1 */
|
|
/* > col1_(5) square W1: = V1 * W1 = unit_lower_tr_of_(A1) * W1 */
|
|
/* > col1_(6) square A1: = A1 - W1 */
|
|
/* > end if */
|
|
/* > end if */
|
|
/* > */
|
|
/* > Case (B), when V1 is an identity matrix, i.e. IDENT == 'I', */
|
|
/* > less computations than in the Case (A) */
|
|
/* > */
|
|
/* > if( IDENT == 'I' ) then */
|
|
/* > if ( N > K ) then */
|
|
/* > (First Step - column block 2) */
|
|
/* > col2_(1) W2: = A2 */
|
|
/* > col2_(3) W2: = W2 + (V2**T) * B2 = W2 + (B1**T) * B2 */
|
|
/* > col2_(4) W2: = T * W2 */
|
|
/* > col2_(5) B2: = B2 - V2 * W2 = B2 - B1 * W2 */
|
|
/* > col2_(7) A2: = A2 - W2 */
|
|
/* > else */
|
|
/* > (Second Step - column block 1) */
|
|
/* > col1_(1) W1: = A1 */
|
|
/* > col1_(3) W1: = T * W1 */
|
|
/* > col1_(4) B1: = - V2 * W1 = - B1 * W1 */
|
|
/* > col1_(6) upper-triangular_of_(A1): = A1 - W1 */
|
|
/* > end if */
|
|
/* > end if */
|
|
/* > */
|
|
/* > Combine these cases (A) and (B) together, this is the resulting */
|
|
/* > algorithm: */
|
|
/* > */
|
|
/* > if ( N > K ) then */
|
|
/* > */
|
|
/* > (First Step - column block 2) */
|
|
/* > */
|
|
/* > col2_(1) W2: = A2 */
|
|
/* > if( IDENT != 'I' ) then */
|
|
/* > col2_(2) W2: = (V1**T) * W2 */
|
|
/* > = (unit_lower_tr_of_(A1)**T) * W2 */
|
|
/* > end if */
|
|
/* > col2_(3) W2: = W2 + (V2**T) * B2 = W2 + (B1**T) * B2] */
|
|
/* > col2_(4) W2: = T * W2 */
|
|
/* > col2_(5) B2: = B2 - V2 * W2 = B2 - B1 * W2 */
|
|
/* > if( IDENT != 'I' ) then */
|
|
/* > col2_(6) W2: = V1 * W2 = unit_lower_tr_of_(A1) * W2 */
|
|
/* > end if */
|
|
/* > col2_(7) A2: = A2 - W2 */
|
|
/* > */
|
|
/* > else */
|
|
/* > */
|
|
/* > (Second Step - column block 1) */
|
|
/* > */
|
|
/* > col1_(1) W1: = A1 */
|
|
/* > if( IDENT != 'I' ) then */
|
|
/* > col1_(2) W1: = (V1**T) * W1 */
|
|
/* > = (unit_lower_tr_of_(A1)**T) * W1 */
|
|
/* > end if */
|
|
/* > col1_(3) W1: = T * W1 */
|
|
/* > col1_(4) B1: = - V2 * W1 = - B1 * W1 */
|
|
/* > if( IDENT != 'I' ) then */
|
|
/* > col1_(5) square W1: = V1 * W1 = unit_lower_tr_of_(A1) * W1 */
|
|
/* > col1_(6_a) below_diag_of_(A1): = - below_diag_of_(W1) */
|
|
/* > end if */
|
|
/* > col1_(6_b) up_tr_of_(A1): = up_tr_of_(A1) - up_tr_of_(W1) */
|
|
/* > */
|
|
/* > end if */
|
|
/* > */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dlarfb_gett_(char *ident, integer *m, integer *n,
|
|
integer *k, doublereal *t, integer *ldt, doublereal *a, integer *lda,
|
|
doublereal *b, integer *ldb, doublereal *work, integer *ldwork)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, b_dim1, b_offset, t_dim1, t_offset, work_dim1,
|
|
work_offset, i__1, i__2;
|
|
|
|
/* Local variables */
|
|
integer i__, j;
|
|
extern /* Subroutine */ void dgemm_(char *, char *, integer *, integer *,
|
|
integer *, doublereal *, doublereal *, integer *, doublereal *,
|
|
integer *, doublereal *, doublereal *, integer *);
|
|
extern logical lsame_(char *, char *);
|
|
extern /* Subroutine */ void dcopy_(integer *, doublereal *, integer *,
|
|
doublereal *, integer *), dtrmm_(char *, char *, char *, char *,
|
|
integer *, integer *, doublereal *, doublereal *, integer *,
|
|
doublereal *, integer *);
|
|
logical lnotident;
|
|
|
|
|
|
/* -- LAPACK auxiliary routine -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Quick return if possible */
|
|
|
|
/* Parameter adjustments */
|
|
t_dim1 = *ldt;
|
|
t_offset = 1 + t_dim1 * 1;
|
|
t -= t_offset;
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
b_dim1 = *ldb;
|
|
b_offset = 1 + b_dim1 * 1;
|
|
b -= b_offset;
|
|
work_dim1 = *ldwork;
|
|
work_offset = 1 + work_dim1 * 1;
|
|
work -= work_offset;
|
|
|
|
/* Function Body */
|
|
if (*m < 0 || *n <= 0 || *k == 0 || *k > *n) {
|
|
return;
|
|
}
|
|
|
|
lnotident = ! lsame_(ident, "I");
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
|
|
/* First Step. Computation of the Column Block 2: */
|
|
|
|
/* ( A2 ) := H * ( A2 ) */
|
|
/* ( B2 ) ( B2 ) */
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
|
|
if (*n > *k) {
|
|
|
|
/* col2_(1) Compute W2: = A2. Therefore, copy A2 = A(1:K, K+1:N) */
|
|
/* into W2=WORK(1:K, 1:N-K) column-by-column. */
|
|
|
|
i__1 = *n - *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
dcopy_(k, &a[(*k + j) * a_dim1 + 1], &c__1, &work[j * work_dim1 +
|
|
1], &c__1);
|
|
}
|
|
if (lnotident) {
|
|
|
|
/* col2_(2) Compute W2: = (V1**T) * W2 = (A1**T) * W2, */
|
|
/* V1 is not an identy matrix, but unit lower-triangular */
|
|
/* V1 stored in A1 (diagonal ones are not stored). */
|
|
|
|
|
|
i__1 = *n - *k;
|
|
dtrmm_("L", "L", "T", "U", k, &i__1, &c_b9, &a[a_offset], lda, &
|
|
work[work_offset], ldwork);
|
|
}
|
|
|
|
/* col2_(3) Compute W2: = W2 + (V2**T) * B2 = W2 + (B1**T) * B2 */
|
|
/* V2 stored in B1. */
|
|
|
|
if (*m > 0) {
|
|
i__1 = *n - *k;
|
|
dgemm_("T", "N", k, &i__1, m, &c_b9, &b[b_offset], ldb, &b[(*k +
|
|
1) * b_dim1 + 1], ldb, &c_b9, &work[work_offset], ldwork);
|
|
}
|
|
|
|
/* col2_(4) Compute W2: = T * W2, */
|
|
/* T is upper-triangular. */
|
|
|
|
i__1 = *n - *k;
|
|
dtrmm_("L", "U", "N", "N", k, &i__1, &c_b9, &t[t_offset], ldt, &work[
|
|
work_offset], ldwork);
|
|
|
|
/* col2_(5) Compute B2: = B2 - V2 * W2 = B2 - B1 * W2, */
|
|
/* V2 stored in B1. */
|
|
|
|
if (*m > 0) {
|
|
i__1 = *n - *k;
|
|
dgemm_("N", "N", m, &i__1, k, &c_b21, &b[b_offset], ldb, &work[
|
|
work_offset], ldwork, &c_b9, &b[(*k + 1) * b_dim1 + 1],
|
|
ldb);
|
|
}
|
|
|
|
if (lnotident) {
|
|
|
|
/* col2_(6) Compute W2: = V1 * W2 = A1 * W2, */
|
|
/* V1 is not an identity matrix, but unit lower-triangular, */
|
|
/* V1 stored in A1 (diagonal ones are not stored). */
|
|
|
|
i__1 = *n - *k;
|
|
dtrmm_("L", "L", "N", "U", k, &i__1, &c_b9, &a[a_offset], lda, &
|
|
work[work_offset], ldwork);
|
|
}
|
|
|
|
/* col2_(7) Compute A2: = A2 - W2 = */
|
|
/* = A(1:K, K+1:N-K) - WORK(1:K, 1:N-K), */
|
|
/* column-by-column. */
|
|
|
|
i__1 = *n - *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *k;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
a[i__ + (*k + j) * a_dim1] -= work[i__ + j * work_dim1];
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
|
|
/* Second Step. Computation of the Column Block 1: */
|
|
|
|
/* ( A1 ) := H * ( A1 ) */
|
|
/* ( B1 ) ( 0 ) */
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
|
|
/* col1_(1) Compute W1: = A1. Copy the upper-triangular */
|
|
/* A1 = A(1:K, 1:K) into the upper-triangular */
|
|
/* W1 = WORK(1:K, 1:K) column-by-column. */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
dcopy_(&j, &a[j * a_dim1 + 1], &c__1, &work[j * work_dim1 + 1], &c__1)
|
|
;
|
|
}
|
|
|
|
/* Set the subdiagonal elements of W1 to zero column-by-column. */
|
|
|
|
i__1 = *k - 1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *k;
|
|
for (i__ = j + 1; i__ <= i__2; ++i__) {
|
|
work[i__ + j * work_dim1] = 0.;
|
|
}
|
|
}
|
|
|
|
if (lnotident) {
|
|
|
|
/* col1_(2) Compute W1: = (V1**T) * W1 = (A1**T) * W1, */
|
|
/* V1 is not an identity matrix, but unit lower-triangular */
|
|
/* V1 stored in A1 (diagonal ones are not stored), */
|
|
/* W1 is upper-triangular with zeroes below the diagonal. */
|
|
|
|
dtrmm_("L", "L", "T", "U", k, k, &c_b9, &a[a_offset], lda, &work[
|
|
work_offset], ldwork);
|
|
}
|
|
|
|
/* col1_(3) Compute W1: = T * W1, */
|
|
/* T is upper-triangular, */
|
|
/* W1 is upper-triangular with zeroes below the diagonal. */
|
|
|
|
dtrmm_("L", "U", "N", "N", k, k, &c_b9, &t[t_offset], ldt, &work[
|
|
work_offset], ldwork);
|
|
|
|
/* col1_(4) Compute B1: = - V2 * W1 = - B1 * W1, */
|
|
/* V2 = B1, W1 is upper-triangular with zeroes below the diagonal. */
|
|
|
|
if (*m > 0) {
|
|
dtrmm_("R", "U", "N", "N", m, k, &c_b21, &work[work_offset], ldwork, &
|
|
b[b_offset], ldb);
|
|
}
|
|
|
|
if (lnotident) {
|
|
|
|
/* col1_(5) Compute W1: = V1 * W1 = A1 * W1, */
|
|
/* V1 is not an identity matrix, but unit lower-triangular */
|
|
/* V1 stored in A1 (diagonal ones are not stored), */
|
|
/* W1 is upper-triangular on input with zeroes below the diagonal, */
|
|
/* and square on output. */
|
|
|
|
dtrmm_("L", "L", "N", "U", k, k, &c_b9, &a[a_offset], lda, &work[
|
|
work_offset], ldwork);
|
|
|
|
/* col1_(6) Compute A1: = A1 - W1 = A(1:K, 1:K) - WORK(1:K, 1:K) */
|
|
/* column-by-column. A1 is upper-triangular on input. */
|
|
/* If IDENT, A1 is square on output, and W1 is square, */
|
|
/* if NOT IDENT, A1 is upper-triangular on output, */
|
|
/* W1 is upper-triangular. */
|
|
|
|
/* col1_(6)_a Compute elements of A1 below the diagonal. */
|
|
|
|
i__1 = *k - 1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *k;
|
|
for (i__ = j + 1; i__ <= i__2; ++i__) {
|
|
a[i__ + j * a_dim1] = -work[i__ + j * work_dim1];
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
/* col1_(6)_b Compute elements of A1 on and above the diagonal. */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = j;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
a[i__ + j * a_dim1] -= work[i__ + j * work_dim1];
|
|
}
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of DLARFB_GETT */
|
|
|
|
} /* dlarfb_gett__ */
|
|
|