1047 lines
29 KiB
C
1047 lines
29 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef blasint logical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static complex c_b1 = {1.f,0.f};
|
|
static integer c__1 = 1;
|
|
static integer c_n1 = -1;
|
|
static real c_b21 = -1.f;
|
|
static real c_b22 = 1.f;
|
|
static integer c__33 = 33;
|
|
|
|
/* > \brief \b CPBTRF */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download CPBTRF + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cpbtrf.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cpbtrf.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cpbtrf.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE CPBTRF( UPLO, N, KD, AB, LDAB, INFO ) */
|
|
|
|
/* CHARACTER UPLO */
|
|
/* INTEGER INFO, KD, LDAB, N */
|
|
/* COMPLEX AB( LDAB, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > CPBTRF computes the Cholesky factorization of a complex Hermitian */
|
|
/* > positive definite band matrix A. */
|
|
/* > */
|
|
/* > The factorization has the form */
|
|
/* > 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 lower triangular. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \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 order of the matrix A. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] KD */
|
|
/* > \verbatim */
|
|
/* > KD is INTEGER */
|
|
/* > The number of superdiagonals of the matrix A if UPLO = 'U', */
|
|
/* > or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] AB */
|
|
/* > \verbatim */
|
|
/* > AB is COMPLEX array, dimension (LDAB,N) */
|
|
/* > On entry, the upper or lower triangle of the Hermitian band */
|
|
/* > matrix A, stored in the first KD+1 rows of the array. The */
|
|
/* > j-th column of A is stored in the j-th column of the array AB */
|
|
/* > as follows: */
|
|
/* > if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for f2cmax(1,j-kd)<=i<=j; */
|
|
/* > if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=f2cmin(n,j+kd). */
|
|
/* > */
|
|
/* > On exit, if INFO = 0, the triangular factor U or L from the */
|
|
/* > Cholesky factorization A = U**H*U or A = L*L**H of the band */
|
|
/* > matrix A, in the same storage format as A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDAB */
|
|
/* > \verbatim */
|
|
/* > LDAB is INTEGER */
|
|
/* > The leading dimension of the array AB. LDAB >= KD+1. */
|
|
/* > \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, the leading minor of order i is not */
|
|
/* > positive definite, and the factorization could not be */
|
|
/* > completed. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup complexOTHERcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > The band storage scheme is illustrated by the following example, when */
|
|
/* > N = 6, KD = 2, and UPLO = 'U': */
|
|
/* > */
|
|
/* > On entry: On exit: */
|
|
/* > */
|
|
/* > * * a13 a24 a35 a46 * * u13 u24 u35 u46 */
|
|
/* > * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 */
|
|
/* > a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 */
|
|
/* > */
|
|
/* > Similarly, if UPLO = 'L' the format of A is as follows: */
|
|
/* > */
|
|
/* > On entry: On exit: */
|
|
/* > */
|
|
/* > a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66 */
|
|
/* > a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 * */
|
|
/* > a31 a42 a53 a64 * * l31 l42 l53 l64 * * */
|
|
/* > */
|
|
/* > Array elements marked * are not used by the routine. */
|
|
/* > \endverbatim */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989 */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void cpbtrf_(char *uplo, integer *n, integer *kd, complex *ab,
|
|
integer *ldab, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4, i__5, i__6;
|
|
complex q__1;
|
|
|
|
/* Local variables */
|
|
complex work[1056] /* was [33][32] */;
|
|
integer i__, j;
|
|
extern /* Subroutine */ void cgemm_(char *, char *, integer *, integer *,
|
|
integer *, complex *, complex *, integer *, complex *, integer *,
|
|
complex *, complex *, integer *), cherk_(char *,
|
|
char *, integer *, integer *, real *, complex *, integer *, real *
|
|
, complex *, integer *);
|
|
extern logical lsame_(char *, char *);
|
|
extern /* Subroutine */ void ctrsm_(char *, char *, char *, char *,
|
|
integer *, integer *, complex *, complex *, integer *, complex *,
|
|
integer *);
|
|
integer i2, i3;
|
|
extern /* Subroutine */ void cpbtf2_(char *, integer *, integer *, complex
|
|
*, integer *, integer *);
|
|
extern int cpotf2_(char *, integer *,
|
|
complex *, integer *, integer *);
|
|
integer ib, nb, ii, jj;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
integer *, integer *, ftnlen, ftnlen);
|
|
|
|
|
|
/* -- LAPACK computational 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 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input parameters. */
|
|
|
|
/* Parameter adjustments */
|
|
ab_dim1 = *ldab;
|
|
ab_offset = 1 + ab_dim1 * 1;
|
|
ab -= ab_offset;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
|
|
*info = -1;
|
|
} else if (*n < 0) {
|
|
*info = -2;
|
|
} else if (*kd < 0) {
|
|
*info = -3;
|
|
} else if (*ldab < *kd + 1) {
|
|
*info = -5;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("CPBTRF", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n == 0) {
|
|
return;
|
|
}
|
|
|
|
/* Determine the block size for this environment */
|
|
|
|
nb = ilaenv_(&c__1, "CPBTRF", uplo, n, kd, &c_n1, &c_n1, (ftnlen)6, (
|
|
ftnlen)1);
|
|
|
|
/* The block size must not exceed the semi-bandwidth KD, and must not */
|
|
/* exceed the limit set by the size of the local array WORK. */
|
|
|
|
nb = f2cmin(nb,32);
|
|
|
|
if (nb <= 1 || nb > *kd) {
|
|
|
|
/* Use unblocked code */
|
|
|
|
cpbtf2_(uplo, n, kd, &ab[ab_offset], ldab, info);
|
|
} else {
|
|
|
|
/* Use blocked code */
|
|
|
|
if (lsame_(uplo, "U")) {
|
|
|
|
/* Compute the Cholesky factorization of a Hermitian band */
|
|
/* matrix, given the upper triangle of the matrix in band */
|
|
/* storage. */
|
|
|
|
/* Zero the upper triangle of the work array. */
|
|
|
|
i__1 = nb;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = j - 1;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = i__ + j * 33 - 34;
|
|
work[i__3].r = 0.f, work[i__3].i = 0.f;
|
|
/* L10: */
|
|
}
|
|
/* L20: */
|
|
}
|
|
|
|
/* Process the band matrix one diagonal block at a time. */
|
|
|
|
i__1 = *n;
|
|
i__2 = nb;
|
|
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
|
|
/* Computing MIN */
|
|
i__3 = nb, i__4 = *n - i__ + 1;
|
|
ib = f2cmin(i__3,i__4);
|
|
|
|
/* Factorize the diagonal block */
|
|
|
|
i__3 = *ldab - 1;
|
|
cpotf2_(uplo, &ib, &ab[*kd + 1 + i__ * ab_dim1], &i__3, &ii);
|
|
if (ii != 0) {
|
|
*info = i__ + ii - 1;
|
|
goto L150;
|
|
}
|
|
if (i__ + ib <= *n) {
|
|
|
|
/* Update the relevant part of the trailing submatrix. */
|
|
/* If A11 denotes the diagonal block which has just been */
|
|
/* factorized, then we need to update the remaining */
|
|
/* blocks in the diagram: */
|
|
|
|
/* A11 A12 A13 */
|
|
/* A22 A23 */
|
|
/* A33 */
|
|
|
|
/* The numbers of rows and columns in the partitioning */
|
|
/* are IB, I2, I3 respectively. The blocks A12, A22 and */
|
|
/* A23 are empty if IB = KD. The upper triangle of A13 */
|
|
/* lies outside the band. */
|
|
|
|
/* Computing MIN */
|
|
i__3 = *kd - ib, i__4 = *n - i__ - ib + 1;
|
|
i2 = f2cmin(i__3,i__4);
|
|
/* Computing MIN */
|
|
i__3 = ib, i__4 = *n - i__ - *kd + 1;
|
|
i3 = f2cmin(i__3,i__4);
|
|
|
|
if (i2 > 0) {
|
|
|
|
/* Update A12 */
|
|
|
|
i__3 = *ldab - 1;
|
|
i__4 = *ldab - 1;
|
|
ctrsm_("Left", "Upper", "Conjugate transpose", "Non-"
|
|
"unit", &ib, &i2, &c_b1, &ab[*kd + 1 + i__ *
|
|
ab_dim1], &i__3, &ab[*kd + 1 - ib + (i__ + ib)
|
|
* ab_dim1], &i__4);
|
|
|
|
/* Update A22 */
|
|
|
|
i__3 = *ldab - 1;
|
|
i__4 = *ldab - 1;
|
|
cherk_("Upper", "Conjugate transpose", &i2, &ib, &
|
|
c_b21, &ab[*kd + 1 - ib + (i__ + ib) *
|
|
ab_dim1], &i__3, &c_b22, &ab[*kd + 1 + (i__ +
|
|
ib) * ab_dim1], &i__4);
|
|
}
|
|
|
|
if (i3 > 0) {
|
|
|
|
/* Copy the lower triangle of A13 into the work array. */
|
|
|
|
i__3 = i3;
|
|
for (jj = 1; jj <= i__3; ++jj) {
|
|
i__4 = ib;
|
|
for (ii = jj; ii <= i__4; ++ii) {
|
|
i__5 = ii + jj * 33 - 34;
|
|
i__6 = ii - jj + 1 + (jj + i__ + *kd - 1) *
|
|
ab_dim1;
|
|
work[i__5].r = ab[i__6].r, work[i__5].i = ab[
|
|
i__6].i;
|
|
/* L30: */
|
|
}
|
|
/* L40: */
|
|
}
|
|
|
|
/* Update A13 (in the work array). */
|
|
|
|
i__3 = *ldab - 1;
|
|
ctrsm_("Left", "Upper", "Conjugate transpose", "Non-"
|
|
"unit", &ib, &i3, &c_b1, &ab[*kd + 1 + i__ *
|
|
ab_dim1], &i__3, work, &c__33);
|
|
|
|
/* Update A23 */
|
|
|
|
if (i2 > 0) {
|
|
q__1.r = -1.f, q__1.i = 0.f;
|
|
i__3 = *ldab - 1;
|
|
i__4 = *ldab - 1;
|
|
cgemm_("Conjugate transpose", "No transpose", &i2,
|
|
&i3, &ib, &q__1, &ab[*kd + 1 - ib + (i__
|
|
+ ib) * ab_dim1], &i__3, work, &c__33, &
|
|
c_b1, &ab[ib + 1 + (i__ + *kd) * ab_dim1],
|
|
&i__4);
|
|
}
|
|
|
|
/* Update A33 */
|
|
|
|
i__3 = *ldab - 1;
|
|
cherk_("Upper", "Conjugate transpose", &i3, &ib, &
|
|
c_b21, work, &c__33, &c_b22, &ab[*kd + 1 + (
|
|
i__ + *kd) * ab_dim1], &i__3);
|
|
|
|
/* Copy the lower triangle of A13 back into place. */
|
|
|
|
i__3 = i3;
|
|
for (jj = 1; jj <= i__3; ++jj) {
|
|
i__4 = ib;
|
|
for (ii = jj; ii <= i__4; ++ii) {
|
|
i__5 = ii - jj + 1 + (jj + i__ + *kd - 1) *
|
|
ab_dim1;
|
|
i__6 = ii + jj * 33 - 34;
|
|
ab[i__5].r = work[i__6].r, ab[i__5].i = work[
|
|
i__6].i;
|
|
/* L50: */
|
|
}
|
|
/* L60: */
|
|
}
|
|
}
|
|
}
|
|
/* L70: */
|
|
}
|
|
} else {
|
|
|
|
/* Compute the Cholesky factorization of a Hermitian band */
|
|
/* matrix, given the lower triangle of the matrix in band */
|
|
/* storage. */
|
|
|
|
/* Zero the lower triangle of the work array. */
|
|
|
|
i__2 = nb;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
i__1 = nb;
|
|
for (i__ = j + 1; i__ <= i__1; ++i__) {
|
|
i__3 = i__ + j * 33 - 34;
|
|
work[i__3].r = 0.f, work[i__3].i = 0.f;
|
|
/* L80: */
|
|
}
|
|
/* L90: */
|
|
}
|
|
|
|
/* Process the band matrix one diagonal block at a time. */
|
|
|
|
i__2 = *n;
|
|
i__1 = nb;
|
|
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {
|
|
/* Computing MIN */
|
|
i__3 = nb, i__4 = *n - i__ + 1;
|
|
ib = f2cmin(i__3,i__4);
|
|
|
|
/* Factorize the diagonal block */
|
|
|
|
i__3 = *ldab - 1;
|
|
cpotf2_(uplo, &ib, &ab[i__ * ab_dim1 + 1], &i__3, &ii);
|
|
if (ii != 0) {
|
|
*info = i__ + ii - 1;
|
|
goto L150;
|
|
}
|
|
if (i__ + ib <= *n) {
|
|
|
|
/* Update the relevant part of the trailing submatrix. */
|
|
/* If A11 denotes the diagonal block which has just been */
|
|
/* factorized, then we need to update the remaining */
|
|
/* blocks in the diagram: */
|
|
|
|
/* A11 */
|
|
/* A21 A22 */
|
|
/* A31 A32 A33 */
|
|
|
|
/* The numbers of rows and columns in the partitioning */
|
|
/* are IB, I2, I3 respectively. The blocks A21, A22 and */
|
|
/* A32 are empty if IB = KD. The lower triangle of A31 */
|
|
/* lies outside the band. */
|
|
|
|
/* Computing MIN */
|
|
i__3 = *kd - ib, i__4 = *n - i__ - ib + 1;
|
|
i2 = f2cmin(i__3,i__4);
|
|
/* Computing MIN */
|
|
i__3 = ib, i__4 = *n - i__ - *kd + 1;
|
|
i3 = f2cmin(i__3,i__4);
|
|
|
|
if (i2 > 0) {
|
|
|
|
/* Update A21 */
|
|
|
|
i__3 = *ldab - 1;
|
|
i__4 = *ldab - 1;
|
|
ctrsm_("Right", "Lower", "Conjugate transpose", "Non"
|
|
"-unit", &i2, &ib, &c_b1, &ab[i__ * ab_dim1 +
|
|
1], &i__3, &ab[ib + 1 + i__ * ab_dim1], &i__4);
|
|
|
|
/* Update A22 */
|
|
|
|
i__3 = *ldab - 1;
|
|
i__4 = *ldab - 1;
|
|
cherk_("Lower", "No transpose", &i2, &ib, &c_b21, &ab[
|
|
ib + 1 + i__ * ab_dim1], &i__3, &c_b22, &ab[(
|
|
i__ + ib) * ab_dim1 + 1], &i__4);
|
|
}
|
|
|
|
if (i3 > 0) {
|
|
|
|
/* Copy the upper triangle of A31 into the work array. */
|
|
|
|
i__3 = ib;
|
|
for (jj = 1; jj <= i__3; ++jj) {
|
|
i__4 = f2cmin(jj,i3);
|
|
for (ii = 1; ii <= i__4; ++ii) {
|
|
i__5 = ii + jj * 33 - 34;
|
|
i__6 = *kd + 1 - jj + ii + (jj + i__ - 1) *
|
|
ab_dim1;
|
|
work[i__5].r = ab[i__6].r, work[i__5].i = ab[
|
|
i__6].i;
|
|
/* L100: */
|
|
}
|
|
/* L110: */
|
|
}
|
|
|
|
/* Update A31 (in the work array). */
|
|
|
|
i__3 = *ldab - 1;
|
|
ctrsm_("Right", "Lower", "Conjugate transpose", "Non"
|
|
"-unit", &i3, &ib, &c_b1, &ab[i__ * ab_dim1 +
|
|
1], &i__3, work, &c__33);
|
|
|
|
/* Update A32 */
|
|
|
|
if (i2 > 0) {
|
|
q__1.r = -1.f, q__1.i = 0.f;
|
|
i__3 = *ldab - 1;
|
|
i__4 = *ldab - 1;
|
|
cgemm_("No transpose", "Conjugate transpose", &i3,
|
|
&i2, &ib, &q__1, work, &c__33, &ab[ib +
|
|
1 + i__ * ab_dim1], &i__3, &c_b1, &ab[*kd
|
|
+ 1 - ib + (i__ + ib) * ab_dim1], &i__4);
|
|
}
|
|
|
|
/* Update A33 */
|
|
|
|
i__3 = *ldab - 1;
|
|
cherk_("Lower", "No transpose", &i3, &ib, &c_b21,
|
|
work, &c__33, &c_b22, &ab[(i__ + *kd) *
|
|
ab_dim1 + 1], &i__3);
|
|
|
|
/* Copy the upper triangle of A31 back into place. */
|
|
|
|
i__3 = ib;
|
|
for (jj = 1; jj <= i__3; ++jj) {
|
|
i__4 = f2cmin(jj,i3);
|
|
for (ii = 1; ii <= i__4; ++ii) {
|
|
i__5 = *kd + 1 - jj + ii + (jj + i__ - 1) *
|
|
ab_dim1;
|
|
i__6 = ii + jj * 33 - 34;
|
|
ab[i__5].r = work[i__6].r, ab[i__5].i = work[
|
|
i__6].i;
|
|
/* L120: */
|
|
}
|
|
/* L130: */
|
|
}
|
|
}
|
|
}
|
|
/* L140: */
|
|
}
|
|
}
|
|
}
|
|
return;
|
|
|
|
L150:
|
|
return;
|
|
|
|
/* End of CPBTRF */
|
|
|
|
} /* cpbtrf_ */
|
|
|