897 lines
27 KiB
C
897 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 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]/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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#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 {
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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 integer c__4 = 4;
|
|
static integer c__8 = 8;
|
|
|
|
/* > \brief \b ZLAROT */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZLAROT( LROWS, LLEFT, LRIGHT, NL, C, S, A, LDA, XLEFT, */
|
|
/* XRIGHT ) */
|
|
|
|
/* LOGICAL LLEFT, LRIGHT, LROWS */
|
|
/* INTEGER LDA, NL */
|
|
/* COMPLEX*16 C, S, XLEFT, XRIGHT */
|
|
/* COMPLEX*16 A( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZLAROT applies a (Givens) rotation to two adjacent rows or */
|
|
/* > columns, where one element of the first and/or last column/row */
|
|
/* > for use on matrices stored in some format other than GE, so */
|
|
/* > that elements of the matrix may be used or modified for which */
|
|
/* > no array element is provided. */
|
|
/* > */
|
|
/* > One example is a symmetric matrix in SB format (bandwidth=4), for */
|
|
/* > which UPLO='L': Two adjacent rows will have the format: */
|
|
/* > */
|
|
/* > row j: C> C> C> C> C> . . . . */
|
|
/* > row j+1: C> C> C> C> C> . . . . */
|
|
/* > */
|
|
/* > '*' indicates elements for which storage is provided, */
|
|
/* > '.' indicates elements for which no storage is provided, but */
|
|
/* > are not necessarily zero; their values are determined by */
|
|
/* > symmetry. ' ' indicates elements which are necessarily zero, */
|
|
/* > and have no storage provided. */
|
|
/* > */
|
|
/* > Those columns which have two '*'s can be handled by DROT. */
|
|
/* > Those columns which have no '*'s can be ignored, since as long */
|
|
/* > as the Givens rotations are carefully applied to preserve */
|
|
/* > symmetry, their values are determined. */
|
|
/* > Those columns which have one '*' have to be handled separately, */
|
|
/* > by using separate variables "p" and "q": */
|
|
/* > */
|
|
/* > row j: C> C> C> C> C> p . . . */
|
|
/* > row j+1: q C> C> C> C> C> . . . . */
|
|
/* > */
|
|
/* > The element p would have to be set correctly, then that column */
|
|
/* > is rotated, setting p to its new value. The next call to */
|
|
/* > ZLAROT would rotate columns j and j+1, using p, and restore */
|
|
/* > symmetry. The element q would start out being zero, and be */
|
|
/* > made non-zero by the rotation. Later, rotations would presumably */
|
|
/* > be chosen to zero q out. */
|
|
/* > */
|
|
/* > Typical Calling Sequences: rotating the i-th and (i+1)-st rows. */
|
|
/* > ------- ------- --------- */
|
|
/* > */
|
|
/* > General dense matrix: */
|
|
/* > */
|
|
/* > CALL ZLAROT(.TRUE.,.FALSE.,.FALSE., N, C,S, */
|
|
/* > A(i,1),LDA, DUMMY, DUMMY) */
|
|
/* > */
|
|
/* > General banded matrix in GB format: */
|
|
/* > */
|
|
/* > j = MAX(1, i-KL ) */
|
|
/* > NL = MIN( N, i+KU+1 ) + 1-j */
|
|
/* > CALL ZLAROT( .TRUE., i-KL.GE.1, i+KU.LT.N, NL, C,S, */
|
|
/* > A(KU+i+1-j,j),LDA-1, XLEFT, XRIGHT ) */
|
|
/* > */
|
|
/* > [ note that i+1-j is just MIN(i,KL+1) ] */
|
|
/* > */
|
|
/* > Symmetric banded matrix in SY format, bandwidth K, */
|
|
/* > lower triangle only: */
|
|
/* > */
|
|
/* > j = MAX(1, i-K ) */
|
|
/* > NL = MIN( K+1, i ) + 1 */
|
|
/* > CALL ZLAROT( .TRUE., i-K.GE.1, .TRUE., NL, C,S, */
|
|
/* > A(i,j), LDA, XLEFT, XRIGHT ) */
|
|
/* > */
|
|
/* > Same, but upper triangle only: */
|
|
/* > */
|
|
/* > NL = MIN( K+1, N-i ) + 1 */
|
|
/* > CALL ZLAROT( .TRUE., .TRUE., i+K.LT.N, NL, C,S, */
|
|
/* > A(i,i), LDA, XLEFT, XRIGHT ) */
|
|
/* > */
|
|
/* > Symmetric banded matrix in SB format, bandwidth K, */
|
|
/* > lower triangle only: */
|
|
/* > */
|
|
/* > [ same as for SY, except:] */
|
|
/* > . . . . */
|
|
/* > A(i+1-j,j), LDA-1, XLEFT, XRIGHT ) */
|
|
/* > */
|
|
/* > [ note that i+1-j is just MIN(i,K+1) ] */
|
|
/* > */
|
|
/* > Same, but upper triangle only: */
|
|
/* > . . . */
|
|
/* > A(K+1,i), LDA-1, XLEFT, XRIGHT ) */
|
|
/* > */
|
|
/* > Rotating columns is just the transpose of rotating rows, except */
|
|
/* > for GB and SB: (rotating columns i and i+1) */
|
|
/* > */
|
|
/* > GB: */
|
|
/* > j = MAX(1, i-KU ) */
|
|
/* > NL = MIN( N, i+KL+1 ) + 1-j */
|
|
/* > CALL ZLAROT( .TRUE., i-KU.GE.1, i+KL.LT.N, NL, C,S, */
|
|
/* > A(KU+j+1-i,i),LDA-1, XTOP, XBOTTM ) */
|
|
/* > */
|
|
/* > [note that KU+j+1-i is just MAX(1,KU+2-i)] */
|
|
/* > */
|
|
/* > SB: (upper triangle) */
|
|
/* > */
|
|
/* > . . . . . . */
|
|
/* > A(K+j+1-i,i),LDA-1, XTOP, XBOTTM ) */
|
|
/* > */
|
|
/* > SB: (lower triangle) */
|
|
/* > */
|
|
/* > . . . . . . */
|
|
/* > A(1,i),LDA-1, XTOP, XBOTTM ) */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \verbatim */
|
|
/* > LROWS - LOGICAL */
|
|
/* > If .TRUE., then ZLAROT will rotate two rows. If .FALSE., */
|
|
/* > then it will rotate two columns. */
|
|
/* > Not modified. */
|
|
/* > */
|
|
/* > LLEFT - LOGICAL */
|
|
/* > If .TRUE., then XLEFT will be used instead of the */
|
|
/* > corresponding element of A for the first element in the */
|
|
/* > second row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) */
|
|
/* > If .FALSE., then the corresponding element of A will be */
|
|
/* > used. */
|
|
/* > Not modified. */
|
|
/* > */
|
|
/* > LRIGHT - LOGICAL */
|
|
/* > If .TRUE., then XRIGHT will be used instead of the */
|
|
/* > corresponding element of A for the last element in the */
|
|
/* > first row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) If */
|
|
/* > .FALSE., then the corresponding element of A will be used. */
|
|
/* > Not modified. */
|
|
/* > */
|
|
/* > NL - INTEGER */
|
|
/* > The length of the rows (if LROWS=.TRUE.) or columns (if */
|
|
/* > LROWS=.FALSE.) to be rotated. If XLEFT and/or XRIGHT are */
|
|
/* > used, the columns/rows they are in should be included in */
|
|
/* > NL, e.g., if LLEFT = LRIGHT = .TRUE., then NL must be at */
|
|
/* > least 2. The number of rows/columns to be rotated */
|
|
/* > exclusive of those involving XLEFT and/or XRIGHT may */
|
|
/* > not be negative, i.e., NL minus how many of LLEFT and */
|
|
/* > LRIGHT are .TRUE. must be at least zero; if not, XERBLA */
|
|
/* > will be called. */
|
|
/* > Not modified. */
|
|
/* > */
|
|
/* > C, S - COMPLEX*16 */
|
|
/* > Specify the Givens rotation to be applied. If LROWS is */
|
|
/* > true, then the matrix ( c s ) */
|
|
/* > ( _ _ ) */
|
|
/* > (-s c ) is applied from the left; */
|
|
/* > if false, then the transpose (not conjugated) thereof is */
|
|
/* > applied from the right. Note that in contrast to the */
|
|
/* > output of ZROTG or to most versions of ZROT, both C and S */
|
|
/* > are complex. For a Givens rotation, |C|**2 + |S|**2 should */
|
|
/* > be 1, but this is not checked. */
|
|
/* > Not modified. */
|
|
/* > */
|
|
/* > A - COMPLEX*16 array. */
|
|
/* > The array containing the rows/columns to be rotated. The */
|
|
/* > first element of A should be the upper left element to */
|
|
/* > be rotated. */
|
|
/* > Read and modified. */
|
|
/* > */
|
|
/* > LDA - INTEGER */
|
|
/* > The "effective" leading dimension of A. If A contains */
|
|
/* > a matrix stored in GE, HE, or SY format, then this is just */
|
|
/* > the leading dimension of A as dimensioned in the calling */
|
|
/* > routine. If A contains a matrix stored in band (GB, HB, or */
|
|
/* > SB) format, then this should be *one less* than the leading */
|
|
/* > dimension used in the calling routine. Thus, if A were */
|
|
/* > dimensioned A(LDA,*) in ZLAROT, then A(1,j) would be the */
|
|
/* > j-th element in the first of the two rows to be rotated, */
|
|
/* > and A(2,j) would be the j-th in the second, regardless of */
|
|
/* > how the array may be stored in the calling routine. [A */
|
|
/* > cannot, however, actually be dimensioned thus, since for */
|
|
/* > band format, the row number may exceed LDA, which is not */
|
|
/* > legal FORTRAN.] */
|
|
/* > If LROWS=.TRUE., then LDA must be at least 1, otherwise */
|
|
/* > it must be at least NL minus the number of .TRUE. values */
|
|
/* > in XLEFT and XRIGHT. */
|
|
/* > Not modified. */
|
|
/* > */
|
|
/* > XLEFT - COMPLEX*16 */
|
|
/* > If LLEFT is .TRUE., then XLEFT will be used and modified */
|
|
/* > instead of A(2,1) (if LROWS=.TRUE.) or A(1,2) */
|
|
/* > (if LROWS=.FALSE.). */
|
|
/* > Read and modified. */
|
|
/* > */
|
|
/* > XRIGHT - COMPLEX*16 */
|
|
/* > If LRIGHT is .TRUE., then XRIGHT will be used and modified */
|
|
/* > instead of A(1,NL) (if LROWS=.TRUE.) or A(NL,1) */
|
|
/* > (if LROWS=.FALSE.). */
|
|
/* > Read and modified. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup complex16_matgen */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void zlarot_(logical *lrows, logical *lleft, logical *lright,
|
|
integer *nl, doublecomplex *c__, doublecomplex *s, doublecomplex *a,
|
|
integer *lda, doublecomplex *xleft, doublecomplex *xright)
|
|
{
|
|
/* System generated locals */
|
|
integer i__1, i__2, i__3, i__4;
|
|
doublecomplex z__1, z__2, z__3, z__4, z__5, z__6;
|
|
|
|
/* Local variables */
|
|
integer iinc, j, inext;
|
|
doublecomplex tempx;
|
|
integer ix, iy, nt;
|
|
doublecomplex xt[2], yt[2];
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
integer iyt;
|
|
|
|
|
|
/* -- LAPACK auxiliary routine (version 3.7.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Set up indices, arrays for ends */
|
|
|
|
/* Parameter adjustments */
|
|
--a;
|
|
|
|
/* Function Body */
|
|
if (*lrows) {
|
|
iinc = *lda;
|
|
inext = 1;
|
|
} else {
|
|
iinc = 1;
|
|
inext = *lda;
|
|
}
|
|
|
|
if (*lleft) {
|
|
nt = 1;
|
|
ix = iinc + 1;
|
|
iy = *lda + 2;
|
|
xt[0].r = a[1].r, xt[0].i = a[1].i;
|
|
yt[0].r = xleft->r, yt[0].i = xleft->i;
|
|
} else {
|
|
nt = 0;
|
|
ix = 1;
|
|
iy = inext + 1;
|
|
}
|
|
|
|
if (*lright) {
|
|
iyt = inext + 1 + (*nl - 1) * iinc;
|
|
++nt;
|
|
i__1 = nt - 1;
|
|
xt[i__1].r = xright->r, xt[i__1].i = xright->i;
|
|
i__1 = nt - 1;
|
|
i__2 = iyt;
|
|
yt[i__1].r = a[i__2].r, yt[i__1].i = a[i__2].i;
|
|
}
|
|
|
|
/* Check for errors */
|
|
|
|
if (*nl < nt) {
|
|
xerbla_("ZLAROT", &c__4, 6);
|
|
return;
|
|
}
|
|
if (*lda <= 0 || ! (*lrows) && *lda < *nl - nt) {
|
|
xerbla_("ZLAROT", &c__8, 6);
|
|
return;
|
|
}
|
|
|
|
/* Rotate */
|
|
|
|
/* ZROT( NL-NT, A(IX),IINC, A(IY),IINC, C, S ) with complex C, S */
|
|
|
|
i__1 = *nl - nt - 1;
|
|
for (j = 0; j <= i__1; ++j) {
|
|
i__2 = ix + j * iinc;
|
|
z__2.r = c__->r * a[i__2].r - c__->i * a[i__2].i, z__2.i = c__->r * a[
|
|
i__2].i + c__->i * a[i__2].r;
|
|
i__3 = iy + j * iinc;
|
|
z__3.r = s->r * a[i__3].r - s->i * a[i__3].i, z__3.i = s->r * a[i__3]
|
|
.i + s->i * a[i__3].r;
|
|
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
|
|
tempx.r = z__1.r, tempx.i = z__1.i;
|
|
i__2 = iy + j * iinc;
|
|
d_cnjg(&z__4, s);
|
|
z__3.r = -z__4.r, z__3.i = -z__4.i;
|
|
i__3 = ix + j * iinc;
|
|
z__2.r = z__3.r * a[i__3].r - z__3.i * a[i__3].i, z__2.i = z__3.r * a[
|
|
i__3].i + z__3.i * a[i__3].r;
|
|
d_cnjg(&z__6, c__);
|
|
i__4 = iy + j * iinc;
|
|
z__5.r = z__6.r * a[i__4].r - z__6.i * a[i__4].i, z__5.i = z__6.r * a[
|
|
i__4].i + z__6.i * a[i__4].r;
|
|
z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i;
|
|
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
|
|
i__2 = ix + j * iinc;
|
|
a[i__2].r = tempx.r, a[i__2].i = tempx.i;
|
|
/* L10: */
|
|
}
|
|
|
|
/* ZROT( NT, XT,1, YT,1, C, S ) with complex C, S */
|
|
|
|
i__1 = nt;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = j - 1;
|
|
z__2.r = c__->r * xt[i__2].r - c__->i * xt[i__2].i, z__2.i = c__->r *
|
|
xt[i__2].i + c__->i * xt[i__2].r;
|
|
i__3 = j - 1;
|
|
z__3.r = s->r * yt[i__3].r - s->i * yt[i__3].i, z__3.i = s->r * yt[
|
|
i__3].i + s->i * yt[i__3].r;
|
|
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
|
|
tempx.r = z__1.r, tempx.i = z__1.i;
|
|
i__2 = j - 1;
|
|
d_cnjg(&z__4, s);
|
|
z__3.r = -z__4.r, z__3.i = -z__4.i;
|
|
i__3 = j - 1;
|
|
z__2.r = z__3.r * xt[i__3].r - z__3.i * xt[i__3].i, z__2.i = z__3.r *
|
|
xt[i__3].i + z__3.i * xt[i__3].r;
|
|
d_cnjg(&z__6, c__);
|
|
i__4 = j - 1;
|
|
z__5.r = z__6.r * yt[i__4].r - z__6.i * yt[i__4].i, z__5.i = z__6.r *
|
|
yt[i__4].i + z__6.i * yt[i__4].r;
|
|
z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i;
|
|
yt[i__2].r = z__1.r, yt[i__2].i = z__1.i;
|
|
i__2 = j - 1;
|
|
xt[i__2].r = tempx.r, xt[i__2].i = tempx.i;
|
|
/* L20: */
|
|
}
|
|
|
|
/* Stuff values back into XLEFT, XRIGHT, etc. */
|
|
|
|
if (*lleft) {
|
|
a[1].r = xt[0].r, a[1].i = xt[0].i;
|
|
xleft->r = yt[0].r, xleft->i = yt[0].i;
|
|
}
|
|
|
|
if (*lright) {
|
|
i__1 = nt - 1;
|
|
xright->r = xt[i__1].r, xright->i = xt[i__1].i;
|
|
i__1 = iyt;
|
|
i__2 = nt - 1;
|
|
a[i__1].r = yt[i__2].r, a[i__1].i = yt[i__2].i;
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of ZLAROT */
|
|
|
|
} /* zlarot_ */
|
|
|