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OpenBLAS/lapack-netlib/SRC/dsytri_3x.c

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#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <complex.h>
#ifdef complex
#undef complex
#endif
#ifdef I
#undef I
#endif
#if defined(_WIN64)
typedef long long BLASLONG;
typedef unsigned long long BLASULONG;
#else
typedef long BLASLONG;
typedef unsigned long BLASULONG;
#endif
#ifdef LAPACK_ILP64
typedef BLASLONG blasint;
#if defined(_WIN64)
#define blasabs(x) llabs(x)
#else
#define blasabs(x) labs(x)
#endif
#else
typedef int blasint;
#define blasabs(x) abs(x)
#endif
typedef blasint integer;
typedef unsigned int uinteger;
typedef char *address;
typedef short int shortint;
typedef float real;
typedef double doublereal;
typedef struct { real r, i; } complex;
typedef struct { doublereal r, i; } doublecomplex;
#ifdef _MSC_VER
static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
#else
static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
#endif
#define pCf(z) (*_pCf(z))
#define pCd(z) (*_pCd(z))
typedef blasint logical;
typedef char logical1;
typedef char integer1;
#define TRUE_ (1)
#define FALSE_ (0)
/* Extern is for use with -E */
#ifndef Extern
#define Extern extern
#endif
/* I/O stuff */
typedef int flag;
typedef int ftnlen;
typedef int ftnint;
/*external read, write*/
typedef struct
{ flag cierr;
ftnint ciunit;
flag ciend;
char *cifmt;
ftnint cirec;
} cilist;
/*internal read, write*/
typedef struct
{ flag icierr;
char *iciunit;
flag iciend;
char *icifmt;
ftnint icirlen;
ftnint icirnum;
} icilist;
/*open*/
typedef struct
{ flag oerr;
ftnint ounit;
char *ofnm;
ftnlen ofnmlen;
char *osta;
char *oacc;
char *ofm;
ftnint orl;
char *oblnk;
} olist;
/*close*/
typedef struct
{ flag cerr;
ftnint cunit;
char *csta;
} cllist;
/*rewind, backspace, endfile*/
typedef struct
{ flag aerr;
ftnint aunit;
} alist;
/* inquire */
typedef struct
{ flag inerr;
ftnint inunit;
char *infile;
ftnlen infilen;
ftnint *inex; /*parameters in standard's order*/
ftnint *inopen;
ftnint *innum;
ftnint *innamed;
char *inname;
ftnlen innamlen;
char *inacc;
ftnlen inacclen;
char *inseq;
ftnlen inseqlen;
char *indir;
ftnlen indirlen;
char *infmt;
ftnlen infmtlen;
char *inform;
ftnint informlen;
char *inunf;
ftnlen inunflen;
ftnint *inrecl;
ftnint *innrec;
char *inblank;
ftnlen inblanklen;
} inlist;
#define VOID void
union Multitype { /* for multiple entry points */
integer1 g;
shortint h;
integer i;
/* longint j; */
real r;
doublereal d;
complex c;
doublecomplex z;
};
typedef union Multitype Multitype;
struct Vardesc { /* for Namelist */
char *name;
char *addr;
ftnlen *dims;
int type;
};
typedef struct Vardesc Vardesc;
struct Namelist {
char *name;
Vardesc **vars;
int nvars;
};
typedef struct Namelist Namelist;
#define abs(x) ((x) >= 0 ? (x) : -(x))
#define dabs(x) (fabs(x))
#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
#define dmin(a,b) (f2cmin(a,b))
#define dmax(a,b) (f2cmax(a,b))
#define bit_test(a,b) ((a) >> (b) & 1)
#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
#define abort_() { sig_die("Fortran abort routine called", 1); }
#define c_abs(z) (cabsf(Cf(z)))
#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
#ifdef _MSC_VER
#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]);}
#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]);}
#else
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#endif
#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
#define d_abs(x) (fabs(*(x)))
#define d_acos(x) (acos(*(x)))
#define d_asin(x) (asin(*(x)))
#define d_atan(x) (atan(*(x)))
#define d_atn2(x, y) (atan2(*(x),*(y)))
#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
#define d_cos(x) (cos(*(x)))
#define d_cosh(x) (cosh(*(x)))
#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
#define d_exp(x) (exp(*(x)))
#define d_imag(z) (cimag(Cd(z)))
#define r_imag(z) (cimagf(Cf(z)))
#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define d_log(x) (log(*(x)))
#define d_mod(x, y) (fmod(*(x), *(y)))
#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
#define d_nint(x) u_nint(*(x))
#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
#define d_sign(a,b) u_sign(*(a),*(b))
#define r_sign(a,b) u_sign(*(a),*(b))
#define d_sin(x) (sin(*(x)))
#define d_sinh(x) (sinh(*(x)))
#define d_sqrt(x) (sqrt(*(x)))
#define d_tan(x) (tan(*(x)))
#define d_tanh(x) (tanh(*(x)))
#define i_abs(x) abs(*(x))
#define i_dnnt(x) ((integer)u_nint(*(x)))
#define i_len(s, n) (n)
#define i_nint(x) ((integer)u_nint(*(x)))
#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
#define pow_si(B,E) spow_ui(*(B),*(E))
#define pow_ri(B,E) spow_ui(*(B),*(E))
#define pow_di(B,E) dpow_ui(*(B),*(E))
#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
#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++ = ' '; }
#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
#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]; }
#define sig_die(s, kill) { exit(1); }
#define s_stop(s, n) {exit(0);}
static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
#define z_abs(z) (cabs(Cd(z)))
#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
#define myexit_() break;
#define mycycle() continue;
#define myceiling(w) {ceil(w)}
#define myhuge(w) {HUGE_VAL}
//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
/* procedure parameter types for -A and -C++ */
#ifdef __cplusplus
typedef logical (*L_fp)(...);
#else
typedef logical (*L_fp)();
#endif
static float spow_ui(float x, integer n) {
float pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static double dpow_ui(double x, integer n) {
double pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#ifdef _MSC_VER
static _Fcomplex cpow_ui(complex x, integer n) {
complex pow={1.0,0.0}; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
for(u = n; ; ) {
if(u & 01) pow.r *= x.r, pow.i *= x.i;
if(u >>= 1) x.r *= x.r, x.i *= x.i;
else break;
}
}
_Fcomplex p={pow.r, pow.i};
return p;
}
#else
static _Complex float cpow_ui(_Complex float x, integer n) {
_Complex float pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#endif
#ifdef _MSC_VER
static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
_Dcomplex pow={1.0,0.0}; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
for(u = n; ; ) {
if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
else break;
}
}
_Dcomplex p = {pow._Val[0], pow._Val[1]};
return p;
}
#else
static _Complex double zpow_ui(_Complex double x, integer n) {
_Complex double pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#endif
static integer pow_ii(integer x, integer n) {
integer pow; unsigned long int u;
if (n <= 0) {
if (n == 0 || x == 1) pow = 1;
else if (x != -1) pow = x == 0 ? 1/x : 0;
else n = -n;
}
if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
u = n;
for(pow = 1; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static integer dmaxloc_(double *w, integer s, integer e, integer *n)
{
double m; integer i, mi;
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
if (w[i-1]>m) mi=i ,m=w[i-1];
return mi-s+1;
}
static integer smaxloc_(float *w, integer s, integer e, integer *n)
{
float m; integer i, mi;
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
if (w[i-1]>m) mi=i ,m=w[i-1];
return mi-s+1;
}
static inline void cdotc_(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] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
zdotc._Val[1] += conjf(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] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
zdotc._Val[1] += conjf(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 += conjf(Cf(&x[i])) * Cf(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
}
}
pCf(z) = zdotc;
}
#endif
static inline void zdotc_(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] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
zdotc._Val[1] += conj(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] += 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 doublereal c_b10 = 1.;
static doublereal c_b14 = 0.;
/* > \brief \b DSYTRI_3X */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DSYTRI_3X + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytri_
3x.f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytri_
3x.f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytri_
3x.f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE DSYTRI_3X( UPLO, N, A, LDA, E, IPIV, WORK, NB, INFO ) */
/* CHARACTER UPLO */
/* INTEGER INFO, LDA, N, NB */
/* INTEGER IPIV( * ) */
/* DOUBLE PRECISION A( LDA, * ), E( * ), WORK( N+NB+1, * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > DSYTRI_3X computes the inverse of a real symmetric indefinite */
/* > matrix A using the factorization computed by DSYTRF_RK or DSYTRF_BK: */
/* > */
/* > A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T), */
/* > */
/* > where U (or L) is unit upper (or lower) triangular matrix, */
/* > U**T (or L**T) is the transpose of U (or L), P is a permutation */
/* > matrix, P**T is the transpose of P, and D is symmetric and block */
/* > diagonal with 1-by-1 and 2-by-2 diagonal blocks. */
/* > */
/* > This is the blocked version of the algorithm, calling Level 3 BLAS. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] UPLO */
/* > \verbatim */
/* > UPLO is CHARACTER*1 */
/* > Specifies whether the details of the factorization are */
/* > stored as an upper or lower triangular matrix. */
/* > = '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,out] A */
/* > \verbatim */
/* > A is DOUBLE PRECISION array, dimension (LDA,N) */
/* > On entry, diagonal of the block diagonal matrix D and */
/* > factors U or L as computed by DSYTRF_RK and DSYTRF_BK: */
/* > a) ONLY diagonal elements of the symmetric block diagonal */
/* > matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); */
/* > (superdiagonal (or subdiagonal) elements of D */
/* > should be provided on entry in array E), and */
/* > b) If UPLO = 'U': factor U in the superdiagonal part of A. */
/* > If UPLO = 'L': factor L in the subdiagonal part of A. */
/* > */
/* > On exit, if INFO = 0, the symmetric inverse of the original */
/* > matrix. */
/* > If UPLO = 'U': the upper triangular part of the inverse */
/* > is formed and the part of A below the diagonal is not */
/* > referenced; */
/* > If UPLO = 'L': the lower triangular part of the inverse */
/* > is formed and the part of A above the diagonal is not */
/* > referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in] E */
/* > \verbatim */
/* > E is DOUBLE PRECISION array, dimension (N) */
/* > On entry, contains the superdiagonal (or subdiagonal) */
/* > elements of the symmetric block diagonal matrix D */
/* > with 1-by-1 or 2-by-2 diagonal blocks, where */
/* > If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) not referenced; */
/* > If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) not referenced. */
/* > */
/* > NOTE: For 1-by-1 diagonal block D(k), where */
/* > 1 <= k <= N, the element E(k) is not referenced in both */
/* > UPLO = 'U' or UPLO = 'L' cases. */
/* > \endverbatim */
/* > */
/* > \param[in] IPIV */
/* > \verbatim */
/* > IPIV is INTEGER array, dimension (N) */
/* > Details of the interchanges and the block structure of D */
/* > as determined by DSYTRF_RK or DSYTRF_BK. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is DOUBLE PRECISION array, dimension (N+NB+1,NB+3). */
/* > \endverbatim */
/* > */
/* > \param[in] NB */
/* > \verbatim */
/* > NB is INTEGER */
/* > Block size. */
/* > \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, D(i,i) = 0; the matrix is singular and its */
/* > inverse could not be computed. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date June 2017 */
/* > \ingroup doubleSYcomputational */
/* > \par Contributors: */
/* ================== */
/* > \verbatim */
/* > */
/* > June 2017, Igor Kozachenko, */
/* > Computer Science Division, */
/* > University of California, Berkeley */
/* > */
/* > \endverbatim */
/* ===================================================================== */
/* Subroutine */ void dsytri_3x_(char *uplo, integer *n, doublereal *a,
integer *lda, doublereal *e, integer *ipiv, doublereal *work, integer
*nb, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, work_dim1, work_offset, i__1, i__2, i__3;
/* Local variables */
integer invd;
doublereal akkp1;
extern /* Subroutine */ void dsyswapr_(char *, integer *, doublereal *,
integer *, integer *, integer *);
doublereal d__;
integer i__, j, k;
doublereal t;
extern /* Subroutine */ void dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ void dtrmm_(char *, char *, char *, char *,
integer *, integer *, doublereal *, doublereal *, integer *,
doublereal *, integer *);
logical upper;
doublereal ak, u01_i_j__;
integer u11;
doublereal u11_i_j__;
integer ip;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
integer icount;
extern /* Subroutine */ int dtrtri_(char *, char *, integer *, doublereal
*, integer *, integer *);
integer nnb, cut;
doublereal akp1, u01_ip1_j__, u11_ip1_j__;
/* -- LAPACK computational routine (version 3.7.1) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* June 2017 */
/* ===================================================================== */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--e;
--ipiv;
work_dim1 = *n + *nb + 1;
work_offset = 1 + work_dim1 * 1;
work -= work_offset;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < f2cmax(1,*n)) {
*info = -4;
}
/* Quick return if possible */
if (*info != 0) {
i__1 = -(*info);
xerbla_("DSYTRI_3X", &i__1, (ftnlen)9);
return;
}
if (*n == 0) {
return;
}
/* Workspace got Non-diag elements of D */
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
work[k + work_dim1] = e[k];
}
/* Check that the diagonal matrix D is nonsingular. */
if (upper) {
/* Upper triangular storage: examine D from bottom to top */
for (*info = *n; *info >= 1; --(*info)) {
if (ipiv[*info] > 0 && a[*info + *info * a_dim1] == 0.) {
return;
}
}
} else {
/* Lower triangular storage: examine D from top to bottom. */
i__1 = *n;
for (*info = 1; *info <= i__1; ++(*info)) {
if (ipiv[*info] > 0 && a[*info + *info * a_dim1] == 0.) {
return;
}
}
}
*info = 0;
/* Splitting Workspace */
/* U01 is a block ( N, NB+1 ) */
/* The first element of U01 is in WORK( 1, 1 ) */
/* U11 is a block ( NB+1, NB+1 ) */
/* The first element of U11 is in WORK( N+1, 1 ) */
u11 = *n;
/* INVD is a block ( N, 2 ) */
/* The first element of INVD is in WORK( 1, INVD ) */
invd = *nb + 2;
if (upper) {
/* Begin Upper */
/* invA = P * inv(U**T) * inv(D) * inv(U) * P**T. */
dtrtri_(uplo, "U", n, &a[a_offset], lda, info);
/* inv(D) and inv(D) * inv(U) */
k = 1;
while(k <= *n) {
if (ipiv[k] > 0) {
/* 1 x 1 diagonal NNB */
work[k + invd * work_dim1] = 1. / a[k + k * a_dim1];
work[k + (invd + 1) * work_dim1] = 0.;
} else {
/* 2 x 2 diagonal NNB */
t = work[k + 1 + work_dim1];
ak = a[k + k * a_dim1] / t;
akp1 = a[k + 1 + (k + 1) * a_dim1] / t;
akkp1 = work[k + 1 + work_dim1] / t;
d__ = t * (ak * akp1 - 1.);
work[k + invd * work_dim1] = akp1 / d__;
work[k + 1 + (invd + 1) * work_dim1] = ak / d__;
work[k + (invd + 1) * work_dim1] = -akkp1 / d__;
work[k + 1 + invd * work_dim1] = work[k + (invd + 1) *
work_dim1];
++k;
}
++k;
}
/* inv(U**T) = (inv(U))**T */
/* inv(U**T) * inv(D) * inv(U) */
cut = *n;
while(cut > 0) {
nnb = *nb;
if (cut <= nnb) {
nnb = cut;
} else {
icount = 0;
/* count negative elements, */
i__1 = cut;
for (i__ = cut + 1 - nnb; i__ <= i__1; ++i__) {
if (ipiv[i__] < 0) {
++icount;
}
}
/* need a even number for a clear cut */
if (icount % 2 == 1) {
++nnb;
}
}
cut -= nnb;
/* U01 Block */
i__1 = cut;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = nnb;
for (j = 1; j <= i__2; ++j) {
work[i__ + j * work_dim1] = a[i__ + (cut + j) * a_dim1];
}
}
/* U11 Block */
i__1 = nnb;
for (i__ = 1; i__ <= i__1; ++i__) {
work[u11 + i__ + i__ * work_dim1] = 1.;
i__2 = i__ - 1;
for (j = 1; j <= i__2; ++j) {
work[u11 + i__ + j * work_dim1] = 0.;
}
i__2 = nnb;
for (j = i__ + 1; j <= i__2; ++j) {
work[u11 + i__ + j * work_dim1] = a[cut + i__ + (cut + j)
* a_dim1];
}
}
/* invD * U01 */
i__ = 1;
while(i__ <= cut) {
if (ipiv[i__] > 0) {
i__1 = nnb;
for (j = 1; j <= i__1; ++j) {
work[i__ + j * work_dim1] = work[i__ + invd *
work_dim1] * work[i__ + j * work_dim1];
}
} else {
i__1 = nnb;
for (j = 1; j <= i__1; ++j) {
u01_i_j__ = work[i__ + j * work_dim1];
u01_ip1_j__ = work[i__ + 1 + j * work_dim1];
work[i__ + j * work_dim1] = work[i__ + invd *
work_dim1] * u01_i_j__ + work[i__ + (invd + 1)
* work_dim1] * u01_ip1_j__;
work[i__ + 1 + j * work_dim1] = work[i__ + 1 + invd *
work_dim1] * u01_i_j__ + work[i__ + 1 + (invd
+ 1) * work_dim1] * u01_ip1_j__;
}
++i__;
}
++i__;
}
/* invD1 * U11 */
i__ = 1;
while(i__ <= nnb) {
if (ipiv[cut + i__] > 0) {
i__1 = nnb;
for (j = i__; j <= i__1; ++j) {
work[u11 + i__ + j * work_dim1] = work[cut + i__ +
invd * work_dim1] * work[u11 + i__ + j *
work_dim1];
}
} else {
i__1 = nnb;
for (j = i__; j <= i__1; ++j) {
u11_i_j__ = work[u11 + i__ + j * work_dim1];
u11_ip1_j__ = work[u11 + i__ + 1 + j * work_dim1];
work[u11 + i__ + j * work_dim1] = work[cut + i__ +
invd * work_dim1] * work[u11 + i__ + j *
work_dim1] + work[cut + i__ + (invd + 1) *
work_dim1] * work[u11 + i__ + 1 + j *
work_dim1];
work[u11 + i__ + 1 + j * work_dim1] = work[cut + i__
+ 1 + invd * work_dim1] * u11_i_j__ + work[
cut + i__ + 1 + (invd + 1) * work_dim1] *
u11_ip1_j__;
}
++i__;
}
++i__;
}
/* U11**T * invD1 * U11 -> U11 */
i__1 = *n + *nb + 1;
dtrmm_("L", "U", "T", "U", &nnb, &nnb, &c_b10, &a[cut + 1 + (cut
+ 1) * a_dim1], lda, &work[u11 + 1 + work_dim1], &i__1);
i__1 = nnb;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = nnb;
for (j = i__; j <= i__2; ++j) {
a[cut + i__ + (cut + j) * a_dim1] = work[u11 + i__ + j *
work_dim1];
}
}
/* U01**T * invD * U01 -> A( CUT+I, CUT+J ) */
i__1 = *n + *nb + 1;
i__2 = *n + *nb + 1;
dgemm_("T", "N", &nnb, &nnb, &cut, &c_b10, &a[(cut + 1) * a_dim1
+ 1], lda, &work[work_offset], &i__1, &c_b14, &work[u11 +
1 + work_dim1], &i__2);
/* U11 = U11**T * invD1 * U11 + U01**T * invD * U01 */
i__1 = nnb;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = nnb;
for (j = i__; j <= i__2; ++j) {
a[cut + i__ + (cut + j) * a_dim1] += work[u11 + i__ + j *
work_dim1];
}
}
/* U01 = U00**T * invD0 * U01 */
i__1 = *n + *nb + 1;
dtrmm_("L", uplo, "T", "U", &cut, &nnb, &c_b10, &a[a_offset], lda,
&work[work_offset], &i__1);
/* Update U01 */
i__1 = cut;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = nnb;
for (j = 1; j <= i__2; ++j) {
a[i__ + (cut + j) * a_dim1] = work[i__ + j * work_dim1];
}
}
/* Next Block */
}
/* Apply PERMUTATIONS P and P**T: */
/* P * inv(U**T) * inv(D) * inv(U) * P**T. */
/* Interchange rows and columns I and IPIV(I) in reverse order */
/* from the formation order of IPIV vector for Upper case. */
/* ( We can use a loop over IPIV with increment 1, */
/* since the ABS value of IPIV(I) represents the row (column) */
/* index of the interchange with row (column) i in both 1x1 */
/* and 2x2 pivot cases, i.e. we don't need separate code branches */
/* for 1x1 and 2x2 pivot cases ) */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
ip = (i__2 = ipiv[i__], abs(i__2));
if (ip != i__) {
if (i__ < ip) {
dsyswapr_(uplo, n, &a[a_offset], lda, &i__, &ip);
}
if (i__ > ip) {
dsyswapr_(uplo, n, &a[a_offset], lda, &ip, &i__);
}
}
}
} else {
/* Begin Lower */
/* inv A = P * inv(L**T) * inv(D) * inv(L) * P**T. */
dtrtri_(uplo, "U", n, &a[a_offset], lda, info);
/* inv(D) and inv(D) * inv(L) */
k = *n;
while(k >= 1) {
if (ipiv[k] > 0) {
/* 1 x 1 diagonal NNB */
work[k + invd * work_dim1] = 1. / a[k + k * a_dim1];
work[k + (invd + 1) * work_dim1] = 0.;
} else {
/* 2 x 2 diagonal NNB */
t = work[k - 1 + work_dim1];
ak = a[k - 1 + (k - 1) * a_dim1] / t;
akp1 = a[k + k * a_dim1] / t;
akkp1 = work[k - 1 + work_dim1] / t;
d__ = t * (ak * akp1 - 1.);
work[k - 1 + invd * work_dim1] = akp1 / d__;
work[k + invd * work_dim1] = ak / d__;
work[k + (invd + 1) * work_dim1] = -akkp1 / d__;
work[k - 1 + (invd + 1) * work_dim1] = work[k + (invd + 1) *
work_dim1];
--k;
}
--k;
}
/* inv(L**T) = (inv(L))**T */
/* inv(L**T) * inv(D) * inv(L) */
cut = 0;
while(cut < *n) {
nnb = *nb;
if (cut + nnb > *n) {
nnb = *n - cut;
} else {
icount = 0;
/* count negative elements, */
i__1 = cut + nnb;
for (i__ = cut + 1; i__ <= i__1; ++i__) {
if (ipiv[i__] < 0) {
++icount;
}
}
/* need a even number for a clear cut */
if (icount % 2 == 1) {
++nnb;
}
}
/* L21 Block */
i__1 = *n - cut - nnb;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = nnb;
for (j = 1; j <= i__2; ++j) {
work[i__ + j * work_dim1] = a[cut + nnb + i__ + (cut + j)
* a_dim1];
}
}
/* L11 Block */
i__1 = nnb;
for (i__ = 1; i__ <= i__1; ++i__) {
work[u11 + i__ + i__ * work_dim1] = 1.;
i__2 = nnb;
for (j = i__ + 1; j <= i__2; ++j) {
work[u11 + i__ + j * work_dim1] = 0.;
}
i__2 = i__ - 1;
for (j = 1; j <= i__2; ++j) {
work[u11 + i__ + j * work_dim1] = a[cut + i__ + (cut + j)
* a_dim1];
}
}
/* invD*L21 */
i__ = *n - cut - nnb;
while(i__ >= 1) {
if (ipiv[cut + nnb + i__] > 0) {
i__1 = nnb;
for (j = 1; j <= i__1; ++j) {
work[i__ + j * work_dim1] = work[cut + nnb + i__ +
invd * work_dim1] * work[i__ + j * work_dim1];
}
} else {
i__1 = nnb;
for (j = 1; j <= i__1; ++j) {
u01_i_j__ = work[i__ + j * work_dim1];
u01_ip1_j__ = work[i__ - 1 + j * work_dim1];
work[i__ + j * work_dim1] = work[cut + nnb + i__ +
invd * work_dim1] * u01_i_j__ + work[cut +
nnb + i__ + (invd + 1) * work_dim1] *
u01_ip1_j__;
work[i__ - 1 + j * work_dim1] = work[cut + nnb + i__
- 1 + (invd + 1) * work_dim1] * u01_i_j__ +
work[cut + nnb + i__ - 1 + invd * work_dim1] *
u01_ip1_j__;
}
--i__;
}
--i__;
}
/* invD1*L11 */
i__ = nnb;
while(i__ >= 1) {
if (ipiv[cut + i__] > 0) {
i__1 = nnb;
for (j = 1; j <= i__1; ++j) {
work[u11 + i__ + j * work_dim1] = work[cut + i__ +
invd * work_dim1] * work[u11 + i__ + j *
work_dim1];
}
} else {
i__1 = nnb;
for (j = 1; j <= i__1; ++j) {
u11_i_j__ = work[u11 + i__ + j * work_dim1];
u11_ip1_j__ = work[u11 + i__ - 1 + j * work_dim1];
work[u11 + i__ + j * work_dim1] = work[cut + i__ +
invd * work_dim1] * work[u11 + i__ + j *
work_dim1] + work[cut + i__ + (invd + 1) *
work_dim1] * u11_ip1_j__;
work[u11 + i__ - 1 + j * work_dim1] = work[cut + i__
- 1 + (invd + 1) * work_dim1] * u11_i_j__ +
work[cut + i__ - 1 + invd * work_dim1] *
u11_ip1_j__;
}
--i__;
}
--i__;
}
/* L11**T * invD1 * L11 -> L11 */
i__1 = *n + *nb + 1;
dtrmm_("L", uplo, "T", "U", &nnb, &nnb, &c_b10, &a[cut + 1 + (cut
+ 1) * a_dim1], lda, &work[u11 + 1 + work_dim1], &i__1);
i__1 = nnb;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
for (j = 1; j <= i__2; ++j) {
a[cut + i__ + (cut + j) * a_dim1] = work[u11 + i__ + j *
work_dim1];
}
}
if (cut + nnb < *n) {
/* L21**T * invD2*L21 -> A( CUT+I, CUT+J ) */
i__1 = *n - nnb - cut;
i__2 = *n + *nb + 1;
i__3 = *n + *nb + 1;
dgemm_("T", "N", &nnb, &nnb, &i__1, &c_b10, &a[cut + nnb + 1
+ (cut + 1) * a_dim1], lda, &work[work_offset], &i__2,
&c_b14, &work[u11 + 1 + work_dim1], &i__3);
/* L11 = L11**T * invD1 * L11 + U01**T * invD * U01 */
i__1 = nnb;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
for (j = 1; j <= i__2; ++j) {
a[cut + i__ + (cut + j) * a_dim1] += work[u11 + i__ +
j * work_dim1];
}
}
/* L01 = L22**T * invD2 * L21 */
i__1 = *n - nnb - cut;
i__2 = *n + *nb + 1;
dtrmm_("L", uplo, "T", "U", &i__1, &nnb, &c_b10, &a[cut + nnb
+ 1 + (cut + nnb + 1) * a_dim1], lda, &work[
work_offset], &i__2);
/* Update L21 */
i__1 = *n - cut - nnb;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = nnb;
for (j = 1; j <= i__2; ++j) {
a[cut + nnb + i__ + (cut + j) * a_dim1] = work[i__ +
j * work_dim1];
}
}
} else {
/* L11 = L11**T * invD1 * L11 */
i__1 = nnb;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
for (j = 1; j <= i__2; ++j) {
a[cut + i__ + (cut + j) * a_dim1] = work[u11 + i__ +
j * work_dim1];
}
}
}
/* Next Block */
cut += nnb;
}
/* Apply PERMUTATIONS P and P**T: */
/* P * inv(L**T) * inv(D) * inv(L) * P**T. */
/* Interchange rows and columns I and IPIV(I) in reverse order */
/* from the formation order of IPIV vector for Lower case. */
/* ( We can use a loop over IPIV with increment -1, */
/* since the ABS value of IPIV(I) represents the row (column) */
/* index of the interchange with row (column) i in both 1x1 */
/* and 2x2 pivot cases, i.e. we don't need separate code branches */
/* for 1x1 and 2x2 pivot cases ) */
for (i__ = *n; i__ >= 1; --i__) {
ip = (i__1 = ipiv[i__], abs(i__1));
if (ip != i__) {
if (i__ < ip) {
dsyswapr_(uplo, n, &a[a_offset], lda, &i__, &ip);
}
if (i__ > ip) {
dsyswapr_(uplo, n, &a[a_offset], lda, &ip, &i__);
}
}
}
}
return;
/* End of DSYTRI_3X */
} /* dsytri_3x__ */
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