1062 lines
33 KiB
C
1062 lines
33 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 {
|
|
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)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* > \brief <b> ZPOSVX computes the solution to system of linear equations A * X = B for PO matrices</b> */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZPOSVX + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zposvx.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zposvx.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zposvx.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZPOSVX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, EQUED, */
|
|
/* S, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, */
|
|
/* RWORK, INFO ) */
|
|
|
|
/* CHARACTER EQUED, FACT, UPLO */
|
|
/* INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS */
|
|
/* DOUBLE PRECISION RCOND */
|
|
/* DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * ), S( * ) */
|
|
/* COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ), */
|
|
/* $ WORK( * ), X( LDX, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZPOSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to */
|
|
/* > compute the solution to a complex system of linear equations */
|
|
/* > A * X = B, */
|
|
/* > where A is an N-by-N Hermitian positive definite matrix and X and B */
|
|
/* > are N-by-NRHS matrices. */
|
|
/* > */
|
|
/* > Error bounds on the solution and a condition estimate are also */
|
|
/* > provided. */
|
|
/* > \endverbatim */
|
|
|
|
/* > \par Description: */
|
|
/* ================= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > The following steps are performed: */
|
|
/* > */
|
|
/* > 1. If FACT = 'E', real scaling factors are computed to equilibrate */
|
|
/* > the system: */
|
|
/* > diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B */
|
|
/* > Whether or not the system will be equilibrated depends on the */
|
|
/* > scaling of the matrix A, but if equilibration is used, A is */
|
|
/* > overwritten by diag(S)*A*diag(S) and B by diag(S)*B. */
|
|
/* > */
|
|
/* > 2. If FACT = 'N' or 'E', the Cholesky decomposition is used to */
|
|
/* > factor the matrix A (after equilibration if FACT = 'E') as */
|
|
/* > A = U**H* U, if UPLO = 'U', or */
|
|
/* > A = L * L**H, if UPLO = 'L', */
|
|
/* > where U is an upper triangular matrix and L is a lower triangular */
|
|
/* > matrix. */
|
|
/* > */
|
|
/* > 3. If the leading i-by-i principal minor is not positive definite, */
|
|
/* > then the routine returns with INFO = i. Otherwise, the factored */
|
|
/* > form of A is used to estimate the condition number of the matrix */
|
|
/* > A. If the reciprocal of the condition number is less than machine */
|
|
/* > precision, INFO = N+1 is returned as a warning, but the routine */
|
|
/* > still goes on to solve for X and compute error bounds as */
|
|
/* > described below. */
|
|
/* > */
|
|
/* > 4. The system of equations is solved for X using the factored form */
|
|
/* > of A. */
|
|
/* > */
|
|
/* > 5. Iterative refinement is applied to improve the computed solution */
|
|
/* > matrix and calculate error bounds and backward error estimates */
|
|
/* > for it. */
|
|
/* > */
|
|
/* > 6. If equilibration was used, the matrix X is premultiplied by */
|
|
/* > diag(S) so that it solves the original system before */
|
|
/* > equilibration. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] FACT */
|
|
/* > \verbatim */
|
|
/* > FACT is CHARACTER*1 */
|
|
/* > Specifies whether or not the factored form of the matrix A is */
|
|
/* > supplied on entry, and if not, whether the matrix A should be */
|
|
/* > equilibrated before it is factored. */
|
|
/* > = 'F': On entry, AF contains the factored form of A. */
|
|
/* > If EQUED = 'Y', the matrix A has been equilibrated */
|
|
/* > with scaling factors given by S. A and AF will not */
|
|
/* > be modified. */
|
|
/* > = 'N': The matrix A will be copied to AF and factored. */
|
|
/* > = 'E': The matrix A will be equilibrated if necessary, then */
|
|
/* > copied to AF and factored. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] UPLO */
|
|
/* > \verbatim */
|
|
/* > UPLO is CHARACTER*1 */
|
|
/* > = 'U': Upper triangle of A is stored; */
|
|
/* > = 'L': Lower triangle of A is stored. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The number of linear equations, i.e., the order of the */
|
|
/* > matrix A. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NRHS */
|
|
/* > \verbatim */
|
|
/* > NRHS is INTEGER */
|
|
/* > The number of right hand sides, i.e., the number of columns */
|
|
/* > of the matrices B and X. NRHS >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is COMPLEX*16 array, dimension (LDA,N) */
|
|
/* > On entry, the Hermitian matrix A, except if FACT = 'F' and */
|
|
/* > EQUED = 'Y', then A must contain the equilibrated matrix */
|
|
/* > diag(S)*A*diag(S). If UPLO = 'U', the leading */
|
|
/* > N-by-N upper triangular part of A contains the upper */
|
|
/* > triangular part of the matrix A, and the strictly lower */
|
|
/* > triangular part of A is not referenced. If UPLO = 'L', the */
|
|
/* > leading N-by-N lower triangular part of A contains the lower */
|
|
/* > triangular part of the matrix A, and the strictly upper */
|
|
/* > triangular part of A is not referenced. A is not modified if */
|
|
/* > FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit. */
|
|
/* > */
|
|
/* > On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by */
|
|
/* > diag(S)*A*diag(S). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] AF */
|
|
/* > \verbatim */
|
|
/* > AF is COMPLEX*16 array, dimension (LDAF,N) */
|
|
/* > If FACT = 'F', then AF is an input argument and on entry */
|
|
/* > contains the triangular factor U or L from the Cholesky */
|
|
/* > factorization A = U**H *U or A = L*L**H, in the same storage */
|
|
/* > format as A. If EQUED .ne. 'N', then AF is the factored form */
|
|
/* > of the equilibrated matrix diag(S)*A*diag(S). */
|
|
/* > */
|
|
/* > If FACT = 'N', then AF is an output argument and on exit */
|
|
/* > returns the triangular factor U or L from the Cholesky */
|
|
/* > factorization A = U**H *U or A = L*L**H of the original */
|
|
/* > matrix A. */
|
|
/* > */
|
|
/* > If FACT = 'E', then AF is an output argument and on exit */
|
|
/* > returns the triangular factor U or L from the Cholesky */
|
|
/* > factorization A = U**H *U or A = L*L**H of the equilibrated */
|
|
/* > matrix A (see the description of A for the form of the */
|
|
/* > equilibrated matrix). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDAF */
|
|
/* > \verbatim */
|
|
/* > LDAF is INTEGER */
|
|
/* > The leading dimension of the array AF. LDAF >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] EQUED */
|
|
/* > \verbatim */
|
|
/* > EQUED is CHARACTER*1 */
|
|
/* > Specifies the form of equilibration that was done. */
|
|
/* > = 'N': No equilibration (always true if FACT = 'N'). */
|
|
/* > = 'Y': Equilibration was done, i.e., A has been replaced by */
|
|
/* > diag(S) * A * diag(S). */
|
|
/* > EQUED is an input argument if FACT = 'F'; otherwise, it is an */
|
|
/* > output argument. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] S */
|
|
/* > \verbatim */
|
|
/* > S is DOUBLE PRECISION array, dimension (N) */
|
|
/* > The scale factors for A; not accessed if EQUED = 'N'. S is */
|
|
/* > an input argument if FACT = 'F'; otherwise, S is an output */
|
|
/* > argument. If FACT = 'F' and EQUED = 'Y', each element of S */
|
|
/* > must be positive. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] B */
|
|
/* > \verbatim */
|
|
/* > B is COMPLEX*16 array, dimension (LDB,NRHS) */
|
|
/* > On entry, the N-by-NRHS righthand side matrix B. */
|
|
/* > On exit, if EQUED = 'N', B is not modified; if EQUED = 'Y', */
|
|
/* > B is overwritten by diag(S) * B. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] X */
|
|
/* > \verbatim */
|
|
/* > X is COMPLEX*16 array, dimension (LDX,NRHS) */
|
|
/* > If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X to */
|
|
/* > the original system of equations. Note that if EQUED = 'Y', */
|
|
/* > A and B are modified on exit, and the solution to the */
|
|
/* > equilibrated system is inv(diag(S))*X. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDX */
|
|
/* > \verbatim */
|
|
/* > LDX is INTEGER */
|
|
/* > The leading dimension of the array X. LDX >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RCOND */
|
|
/* > \verbatim */
|
|
/* > RCOND is DOUBLE PRECISION */
|
|
/* > The estimate of the reciprocal condition number of the matrix */
|
|
/* > A after equilibration (if done). If RCOND is less than the */
|
|
/* > machine precision (in particular, if RCOND = 0), the matrix */
|
|
/* > is singular to working precision. This condition is */
|
|
/* > indicated by a return code of INFO > 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] FERR */
|
|
/* > \verbatim */
|
|
/* > FERR is DOUBLE PRECISION array, dimension (NRHS) */
|
|
/* > The estimated forward error bound for each solution vector */
|
|
/* > X(j) (the j-th column of the solution matrix X). */
|
|
/* > If XTRUE is the true solution corresponding to X(j), FERR(j) */
|
|
/* > is an estimated upper bound for the magnitude of the largest */
|
|
/* > element in (X(j) - XTRUE) divided by the magnitude of the */
|
|
/* > largest element in X(j). The estimate is as reliable as */
|
|
/* > the estimate for RCOND, and is almost always a slight */
|
|
/* > overestimate of the true error. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] BERR */
|
|
/* > \verbatim */
|
|
/* > BERR is DOUBLE PRECISION array, dimension (NRHS) */
|
|
/* > The componentwise relative backward error of each solution */
|
|
/* > vector X(j) (i.e., the smallest relative change in */
|
|
/* > any element of A or B that makes X(j) an exact solution). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX*16 array, dimension (2*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RWORK */
|
|
/* > \verbatim */
|
|
/* > RWORK is DOUBLE PRECISION array, dimension (N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
|
|
/* > > 0: if INFO = i, and i is */
|
|
/* > <= N: the leading minor of order i of A is */
|
|
/* > not positive definite, so the factorization */
|
|
/* > could not be completed, and the solution has not */
|
|
/* > been computed. RCOND = 0 is returned. */
|
|
/* > = N+1: U is nonsingular, but RCOND is less than machine */
|
|
/* > precision, meaning that the matrix is singular */
|
|
/* > to working precision. Nevertheless, the */
|
|
/* > solution and error bounds are computed because */
|
|
/* > there are a number of situations where the */
|
|
/* > computed solution can be more accurate than the */
|
|
/* > value of RCOND would suggest. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date April 2012 */
|
|
|
|
/* > \ingroup complex16POsolve */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void zposvx_(char *fact, char *uplo, integer *n, integer *
|
|
nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer *
|
|
ldaf, char *equed, doublereal *s, doublecomplex *b, integer *ldb,
|
|
doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *ferr,
|
|
doublereal *berr, doublecomplex *work, doublereal *rwork, integer *
|
|
info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
|
|
x_offset, i__1, i__2, i__3, i__4, i__5;
|
|
doublereal d__1, d__2;
|
|
doublecomplex z__1;
|
|
|
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/* Local variables */
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doublereal amax, smin, smax;
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integer i__, j;
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extern logical lsame_(char *, char *);
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doublereal scond, anorm;
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logical equil, rcequ;
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extern doublereal dlamch_(char *);
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logical nofact;
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
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doublereal bignum;
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extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *,
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integer *, doublereal *);
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extern /* Subroutine */ void zlaqhe_(char *, integer *, doublecomplex *,
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integer *, doublereal *, doublereal *, doublereal *, char *);
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integer infequ;
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extern /* Subroutine */ void zlacpy_(char *, integer *, integer *,
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doublecomplex *, integer *, doublecomplex *, integer *),
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zpocon_(char *, integer *, doublecomplex *, integer *, doublereal
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*, doublereal *, doublecomplex *, doublereal *, integer *)
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;
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doublereal smlnum;
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extern /* Subroutine */ void zpoequ_(integer *, doublecomplex *, integer *,
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doublereal *, doublereal *, doublereal *, integer *), zporfs_(
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char *, integer *, integer *, doublecomplex *, integer *,
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doublecomplex *, integer *, doublecomplex *, integer *,
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doublecomplex *, integer *, doublereal *, doublereal *,
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doublecomplex *, doublereal *, integer *);
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extern int zpotrf_(char *,
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integer *, doublecomplex *, integer *, integer *);
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extern void zpotrs_(char *, integer *, integer *, doublecomplex *, integer *,
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doublecomplex *, integer *, integer *);
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/* -- LAPACK driver routine (version 3.7.0) -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* April 2012 */
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/* ===================================================================== */
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1 * 1;
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a -= a_offset;
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af_dim1 = *ldaf;
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af_offset = 1 + af_dim1 * 1;
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af -= af_offset;
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--s;
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b_dim1 = *ldb;
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b_offset = 1 + b_dim1 * 1;
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b -= b_offset;
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x_dim1 = *ldx;
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x_offset = 1 + x_dim1 * 1;
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x -= x_offset;
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--ferr;
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--berr;
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--work;
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--rwork;
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/* Function Body */
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*info = 0;
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nofact = lsame_(fact, "N");
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equil = lsame_(fact, "E");
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if (nofact || equil) {
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*(unsigned char *)equed = 'N';
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rcequ = FALSE_;
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} else {
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rcequ = lsame_(equed, "Y");
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smlnum = dlamch_("Safe minimum");
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bignum = 1. / smlnum;
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}
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/* Test the input parameters. */
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if (! nofact && ! equil && ! lsame_(fact, "F")) {
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*info = -1;
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} else if (! lsame_(uplo, "U") && ! lsame_(uplo,
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"L")) {
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*info = -2;
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} else if (*n < 0) {
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*info = -3;
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} else if (*nrhs < 0) {
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*info = -4;
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} else if (*lda < f2cmax(1,*n)) {
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*info = -6;
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} else if (*ldaf < f2cmax(1,*n)) {
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*info = -8;
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} else if (lsame_(fact, "F") && ! (rcequ || lsame_(
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equed, "N"))) {
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*info = -9;
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} else {
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if (rcequ) {
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smin = bignum;
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smax = 0.;
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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/* Computing MIN */
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d__1 = smin, d__2 = s[j];
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smin = f2cmin(d__1,d__2);
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/* Computing MAX */
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d__1 = smax, d__2 = s[j];
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smax = f2cmax(d__1,d__2);
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/* L10: */
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}
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if (smin <= 0.) {
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*info = -10;
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} else if (*n > 0) {
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scond = f2cmax(smin,smlnum) / f2cmin(smax,bignum);
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} else {
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scond = 1.;
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}
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}
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if (*info == 0) {
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if (*ldb < f2cmax(1,*n)) {
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*info = -12;
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} else if (*ldx < f2cmax(1,*n)) {
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*info = -14;
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}
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}
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("ZPOSVX", &i__1, (ftnlen)6);
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return;
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}
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if (equil) {
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/* Compute row and column scalings to equilibrate the matrix A. */
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zpoequ_(n, &a[a_offset], lda, &s[1], &scond, &amax, &infequ);
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if (infequ == 0) {
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/* Equilibrate the matrix. */
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zlaqhe_(uplo, n, &a[a_offset], lda, &s[1], &scond, &amax, equed);
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rcequ = lsame_(equed, "Y");
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}
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}
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/* Scale the right hand side. */
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if (rcequ) {
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i__1 = *nrhs;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *n;
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for (i__ = 1; i__ <= i__2; ++i__) {
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i__3 = i__ + j * b_dim1;
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i__4 = i__;
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i__5 = i__ + j * b_dim1;
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z__1.r = s[i__4] * b[i__5].r, z__1.i = s[i__4] * b[i__5].i;
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b[i__3].r = z__1.r, b[i__3].i = z__1.i;
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/* L20: */
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}
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/* L30: */
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}
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}
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if (nofact || equil) {
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/* Compute the Cholesky factorization A = U**H *U or A = L*L**H. */
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zlacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf);
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zpotrf_(uplo, n, &af[af_offset], ldaf, info);
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/* Return if INFO is non-zero. */
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if (*info > 0) {
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*rcond = 0.;
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return;
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}
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}
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/* Compute the norm of the matrix A. */
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anorm = zlanhe_("1", uplo, n, &a[a_offset], lda, &rwork[1]);
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/* Compute the reciprocal of the condition number of A. */
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zpocon_(uplo, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &rwork[1],
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info);
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/* Compute the solution matrix X. */
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zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
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zpotrs_(uplo, n, nrhs, &af[af_offset], ldaf, &x[x_offset], ldx, info);
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/* Use iterative refinement to improve the computed solution and */
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/* compute error bounds and backward error estimates for it. */
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zporfs_(uplo, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &b[
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b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[1], &
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rwork[1], info);
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/* Transform the solution matrix X to a solution of the original */
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/* system. */
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if (rcequ) {
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i__1 = *nrhs;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *n;
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for (i__ = 1; i__ <= i__2; ++i__) {
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i__3 = i__ + j * x_dim1;
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i__4 = i__;
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i__5 = i__ + j * x_dim1;
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z__1.r = s[i__4] * x[i__5].r, z__1.i = s[i__4] * x[i__5].i;
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x[i__3].r = z__1.r, x[i__3].i = z__1.i;
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/* L40: */
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}
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/* L50: */
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}
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i__1 = *nrhs;
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for (j = 1; j <= i__1; ++j) {
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ferr[j] /= scond;
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/* L60: */
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}
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}
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/* Set INFO = N+1 if the matrix is singular to working precision. */
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if (*rcond < dlamch_("Epsilon")) {
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*info = *n + 1;
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}
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return;
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/* End of ZPOSVX */
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} /* zposvx_ */
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