926 lines
27 KiB
C
926 lines
27 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]/Cd(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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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 doublecomplex c_b1 = {1.,0.};
|
|
static doublecomplex c_b2 = {0.,0.};
|
|
static integer c__0 = 0;
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief \b ZUNGTSQR_ROW */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZUNGTSQR_ROW + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zunrgts
|
|
qr_row.f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zunrgts
|
|
qr_row.f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zunrgts
|
|
qr_row.f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZUNGTSQR_ROW( M, N, MB, NB, A, LDA, T, LDT, WORK, */
|
|
/* $ LWORK, INFO ) */
|
|
/* IMPLICIT NONE */
|
|
|
|
/* INTEGER INFO, LDA, LDT, LWORK, M, N, MB, NB */
|
|
/* COMPLEX*16 A( LDA, * ), T( LDT, * ), WORK( * ) */
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZUNGTSQR_ROW generates an M-by-N complex matrix Q_out with */
|
|
/* > orthonormal columns from the output of ZLATSQR. These N orthonormal */
|
|
/* > columns are the first N columns of a product of complex unitary */
|
|
/* > matrices Q(k)_in of order M, which are returned by ZLATSQR in */
|
|
/* > a special format. */
|
|
/* > */
|
|
/* > Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ). */
|
|
/* > */
|
|
/* > The input matrices Q(k)_in are stored in row and column blocks in A. */
|
|
/* > See the documentation of ZLATSQR for more details on the format of */
|
|
/* > Q(k)_in, where each Q(k)_in is represented by block Householder */
|
|
/* > transformations. This routine calls an auxiliary routine ZLARFB_GETT, */
|
|
/* > where the computation is performed on each individual block. The */
|
|
/* > algorithm first sweeps NB-sized column blocks from the right to left */
|
|
/* > starting in the bottom row block and continues to the top row block */
|
|
/* > (hence _ROW in the routine name). This sweep is in reverse order of */
|
|
/* > the order in which ZLATSQR generates the output blocks. */
|
|
/* > \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] MB */
|
|
/* > \verbatim */
|
|
/* > MB is INTEGER */
|
|
/* > The row block size used by ZLATSQR to return */
|
|
/* > arrays A and T. MB > N. */
|
|
/* > (Note that if MB > M, then M is used instead of MB */
|
|
/* > as the row block size). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NB */
|
|
/* > \verbatim */
|
|
/* > NB is INTEGER */
|
|
/* > The column block size used by ZLATSQR to return */
|
|
/* > arrays A and 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*16 array, dimension (LDA,N) */
|
|
/* > */
|
|
/* > On entry: */
|
|
/* > */
|
|
/* > The elements on and above the diagonal are not used as */
|
|
/* > input. The elements below the diagonal represent the unit */
|
|
/* > lower-trapezoidal blocked matrix V computed by ZLATSQR */
|
|
/* > that defines the input matrices Q_in(k) (ones on the */
|
|
/* > diagonal are not stored). See ZLATSQR for more details. */
|
|
/* > */
|
|
/* > On exit: */
|
|
/* > */
|
|
/* > The array A contains an M-by-N orthonormal matrix Q_out, */
|
|
/* > i.e the columns of A are orthogonal unit vectors. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] T */
|
|
/* > \verbatim */
|
|
/* > T is COMPLEX*16 array, */
|
|
/* > dimension (LDT, N * NIRB) */
|
|
/* > where NIRB = Number_of_input_row_blocks */
|
|
/* > = MAX( 1, CEIL((M-N)/(MB-N)) ) */
|
|
/* > Let NICB = Number_of_input_col_blocks */
|
|
/* > = CEIL(N/NB) */
|
|
/* > */
|
|
/* > The upper-triangular block reflectors used to define the */
|
|
/* > input matrices Q_in(k), k=(1:NIRB*NICB). The block */
|
|
/* > reflectors are stored in compact form in NIRB block */
|
|
/* > reflector sequences. Each of the NIRB block reflector */
|
|
/* > sequences is stored in a larger NB-by-N column block of T */
|
|
/* > and consists of NICB smaller NB-by-NB upper-triangular */
|
|
/* > column blocks. See ZLATSQR for more details on the format */
|
|
/* > of T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDT */
|
|
/* > \verbatim */
|
|
/* > LDT is INTEGER */
|
|
/* > The leading dimension of the array T. */
|
|
/* > LDT >= f2cmax(1,f2cmin(NB,N)). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) */
|
|
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > The dimension of the array WORK. */
|
|
/* > LWORK >= NBLOCAL * MAX(NBLOCAL,(N-NBLOCAL)), */
|
|
/* > where NBLOCAL=MIN(NB,N). */
|
|
/* > If LWORK = -1, then a workspace query is assumed. */
|
|
/* > The routine only calculates the optimal size of the WORK */
|
|
/* > array, returns this value as the first entry of the WORK */
|
|
/* > array, and no error message related to LWORK is issued */
|
|
/* > by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \ingroup complex16OTHERcomputational */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > November 2020, Igor Kozachenko, */
|
|
/* > Computer Science Division, */
|
|
/* > University of California, Berkeley */
|
|
/* > */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void zungtsqr_row_(integer *m, integer *n, integer *mb,
|
|
integer *nb, doublecomplex *a, integer *lda, doublecomplex *t,
|
|
integer *ldt, doublecomplex *work, integer *lwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, t_dim1, t_offset, i__1, i__2, i__3, i__4, i__5;
|
|
doublecomplex z__1;
|
|
|
|
/* Local variables */
|
|
integer jb_t__, itmp, lworkopt;
|
|
doublecomplex dummy[1] /* was [1][1] */;
|
|
integer ib_bottom__, ib, kb;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
integer mb1, mb2;
|
|
extern /* Subroutine */ void zlaset_(char *, integer *, integer *,
|
|
doublecomplex *, doublecomplex *, doublecomplex *, integer *);
|
|
integer m_plus_one__;
|
|
logical lquery;
|
|
integer num_all_row_blocks__, imb, knb, nblocal, kb_last__;
|
|
extern /* Subroutine */ void zlarfb_gett_(char *, integer *, integer *,
|
|
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *);
|
|
|
|
|
|
/* -- LAPACK computational routine -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* 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;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
lquery = *lwork == -1;
|
|
if (*m < 0) {
|
|
*info = -1;
|
|
} else if (*n < 0 || *m < *n) {
|
|
*info = -2;
|
|
} else if (*mb <= *n) {
|
|
*info = -3;
|
|
} else if (*nb < 1) {
|
|
*info = -4;
|
|
} else if (*lda < f2cmax(1,*m)) {
|
|
*info = -6;
|
|
} else /* if(complicated condition) */ {
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = f2cmin(*nb,*n);
|
|
if (*ldt < f2cmax(i__1,i__2)) {
|
|
*info = -8;
|
|
} else if (*lwork < 1 && ! lquery) {
|
|
*info = -10;
|
|
}
|
|
}
|
|
|
|
nblocal = f2cmin(*nb,*n);
|
|
|
|
/* Determine the workspace size. */
|
|
|
|
if (*info == 0) {
|
|
/* Computing MAX */
|
|
i__1 = nblocal, i__2 = *n - nblocal;
|
|
lworkopt = nblocal * f2cmax(i__1,i__2);
|
|
}
|
|
|
|
/* Handle error in the input parameters and handle the workspace query. */
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("ZUNGTSQR_ROW", &i__1, (ftnlen)12);
|
|
return;
|
|
} else if (lquery) {
|
|
z__1.r = (doublereal) lworkopt, z__1.i = 0.;
|
|
work[1].r = z__1.r, work[1].i = z__1.i;
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (f2cmin(*m,*n) == 0) {
|
|
z__1.r = (doublereal) lworkopt, z__1.i = 0.;
|
|
work[1].r = z__1.r, work[1].i = z__1.i;
|
|
return;
|
|
}
|
|
|
|
/* (0) Set the upper-triangular part of the matrix A to zero and */
|
|
/* its diagonal elements to one. */
|
|
|
|
zlaset_("U", m, n, &c_b2, &c_b1, &a[a_offset], lda);
|
|
|
|
/* KB_LAST is the column index of the last column block reflector */
|
|
/* in the matrices T and V. */
|
|
|
|
kb_last__ = (*n - 1) / nblocal * nblocal + 1;
|
|
|
|
|
|
/* (1) Bottom-up loop over row blocks of A, except the top row block. */
|
|
/* NOTE: If MB>=M, then the loop is never executed. */
|
|
|
|
if (*mb < *m) {
|
|
|
|
/* MB2 is the row blocking size for the row blocks before the */
|
|
/* first top row block in the matrix A. IB is the row index for */
|
|
/* the row blocks in the matrix A before the first top row block. */
|
|
/* IB_BOTTOM is the row index for the last bottom row block */
|
|
/* in the matrix A. JB_T is the column index of the corresponding */
|
|
/* column block in the matrix T. */
|
|
|
|
/* Initialize variables. */
|
|
|
|
/* NUM_ALL_ROW_BLOCKS is the number of row blocks in the matrix A */
|
|
/* including the first row block. */
|
|
|
|
mb2 = *mb - *n;
|
|
m_plus_one__ = *m + 1;
|
|
itmp = (*m - *mb - 1) / mb2;
|
|
ib_bottom__ = itmp * mb2 + *mb + 1;
|
|
num_all_row_blocks__ = itmp + 2;
|
|
jb_t__ = num_all_row_blocks__ * *n + 1;
|
|
|
|
i__1 = *mb + 1;
|
|
i__2 = -mb2;
|
|
for (ib = ib_bottom__; i__2 < 0 ? ib >= i__1 : ib <= i__1; ib += i__2)
|
|
{
|
|
|
|
/* Determine the block size IMB for the current row block */
|
|
/* in the matrix A. */
|
|
|
|
/* Computing MIN */
|
|
i__3 = m_plus_one__ - ib;
|
|
imb = f2cmin(i__3,mb2);
|
|
|
|
/* Determine the column index JB_T for the current column block */
|
|
/* in the matrix T. */
|
|
|
|
jb_t__ -= *n;
|
|
|
|
/* Apply column blocks of H in the row block from right to left. */
|
|
|
|
/* KB is the column index of the current column block reflector */
|
|
/* in the matrices T and V. */
|
|
|
|
i__3 = -nblocal;
|
|
for (kb = kb_last__; i__3 < 0 ? kb >= 1 : kb <= 1; kb += i__3) {
|
|
|
|
/* Determine the size of the current column block KNB in */
|
|
/* the matrices T and V. */
|
|
|
|
/* Computing MIN */
|
|
i__4 = nblocal, i__5 = *n - kb + 1;
|
|
knb = f2cmin(i__4,i__5);
|
|
|
|
i__4 = *n - kb + 1;
|
|
zlarfb_gett_("I", &imb, &i__4, &knb, &t[(jb_t__ + kb - 1) *
|
|
t_dim1 + 1], ldt, &a[kb + kb * a_dim1], lda, &a[ib +
|
|
kb * a_dim1], lda, &work[1], &knb);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
/* (2) Top row block of A. */
|
|
/* NOTE: If MB>=M, then we have only one row block of A of size M */
|
|
/* and we work on the entire matrix A. */
|
|
|
|
mb1 = f2cmin(*mb,*m);
|
|
|
|
/* Apply column blocks of H in the top row block from right to left. */
|
|
|
|
/* KB is the column index of the current block reflector in */
|
|
/* the matrices T and V. */
|
|
|
|
i__2 = -nblocal;
|
|
for (kb = kb_last__; i__2 < 0 ? kb >= 1 : kb <= 1; kb += i__2) {
|
|
|
|
/* Determine the size of the current column block KNB in */
|
|
/* the matrices T and V. */
|
|
|
|
/* Computing MIN */
|
|
i__1 = nblocal, i__3 = *n - kb + 1;
|
|
knb = f2cmin(i__1,i__3);
|
|
|
|
if (mb1 - kb - knb + 1 == 0) {
|
|
|
|
/* In SLARFB_GETT parameters, when M=0, then the matrix B */
|
|
/* does not exist, hence we need to pass a dummy array */
|
|
/* reference DUMMY(1,1) to B with LDDUMMY=1. */
|
|
|
|
i__1 = *n - kb + 1;
|
|
zlarfb_gett_("N", &c__0, &i__1, &knb, &t[kb * t_dim1 + 1], ldt, &
|
|
a[kb + kb * a_dim1], lda, dummy, &c__1, &work[1], &knb);
|
|
} else {
|
|
i__1 = mb1 - kb - knb + 1;
|
|
i__3 = *n - kb + 1;
|
|
zlarfb_gett_("N", &i__1, &i__3, &knb, &t[kb * t_dim1 + 1], ldt, &
|
|
a[kb + kb * a_dim1], lda, &a[kb + knb + kb * a_dim1], lda,
|
|
&work[1], &knb);
|
|
}
|
|
|
|
}
|
|
|
|
z__1.r = (doublereal) lworkopt, z__1.i = 0.;
|
|
work[1].r = z__1.r, work[1].i = z__1.i;
|
|
return;
|
|
|
|
/* End of ZUNGTSQR_ROW */
|
|
|
|
} /* zungtsqr_row__ */
|
|
|