#include #include #include #include #include #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 int logical; typedef short int shortlogical; 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]/Cd(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++ */ #define F2C_proc_par_types 1 #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 \brief \b ZPTRFS */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download ZPTRFS + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE ZPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, */ /* FERR, BERR, WORK, RWORK, INFO ) */ /* CHARACTER UPLO */ /* INTEGER INFO, LDB, LDX, N, NRHS */ /* DOUBLE PRECISION BERR( * ), D( * ), DF( * ), FERR( * ), */ /* $ RWORK( * ) */ /* COMPLEX*16 B( LDB, * ), E( * ), EF( * ), WORK( * ), */ /* $ X( LDX, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZPTRFS improves the computed solution to a system of linear */ /* > equations when the coefficient matrix is Hermitian positive definite */ /* > and tridiagonal, and provides error bounds and backward error */ /* > estimates for the solution. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] UPLO */ /* > \verbatim */ /* > UPLO is CHARACTER*1 */ /* > Specifies whether the superdiagonal or the subdiagonal of the */ /* > tridiagonal matrix A is stored and the form of the */ /* > factorization: */ /* > = 'U': E is the superdiagonal of A, and A = U**H*D*U; */ /* > = 'L': E is the subdiagonal of A, and A = L*D*L**H. */ /* > (The two forms are equivalent if A is real.) */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > 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 matrix B. NRHS >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] D */ /* > \verbatim */ /* > D is DOUBLE PRECISION array, dimension (N) */ /* > The n real diagonal elements of the tridiagonal matrix A. */ /* > \endverbatim */ /* > */ /* > \param[in] E */ /* > \verbatim */ /* > E is COMPLEX*16 array, dimension (N-1) */ /* > The (n-1) off-diagonal elements of the tridiagonal matrix A */ /* > (see UPLO). */ /* > \endverbatim */ /* > */ /* > \param[in] DF */ /* > \verbatim */ /* > DF is DOUBLE PRECISION array, dimension (N) */ /* > The n diagonal elements of the diagonal matrix D from */ /* > the factorization computed by ZPTTRF. */ /* > \endverbatim */ /* > */ /* > \param[in] EF */ /* > \verbatim */ /* > EF is COMPLEX*16 array, dimension (N-1) */ /* > The (n-1) off-diagonal elements of the unit bidiagonal */ /* > factor U or L from the factorization computed by ZPTTRF */ /* > (see UPLO). */ /* > \endverbatim */ /* > */ /* > \param[in] B */ /* > \verbatim */ /* > B is COMPLEX*16 array, dimension (LDB,NRHS) */ /* > The right hand side matrix B. */ /* > \endverbatim */ /* > */ /* > \param[in] LDB */ /* > \verbatim */ /* > LDB is INTEGER */ /* > The leading dimension of the array B. LDB >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[in,out] X */ /* > \verbatim */ /* > X is COMPLEX*16 array, dimension (LDX,NRHS) */ /* > On entry, the solution matrix X, as computed by ZPTTRS. */ /* > On exit, the improved solution matrix X. */ /* > \endverbatim */ /* > */ /* > \param[in] LDX */ /* > \verbatim */ /* > LDX is INTEGER */ /* > The leading dimension of the array X. LDX >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[out] FERR */ /* > \verbatim */ /* > FERR is DOUBLE PRECISION array, dimension (NRHS) */ /* > The 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). */ /* > \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 (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 */ /* > \endverbatim */ /* > \par Internal Parameters: */ /* ========================= */ /* > */ /* > \verbatim */ /* > ITMAX is the maximum number of steps of iterative refinement. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup complex16PTcomputational */ /* ===================================================================== */ /* Subroutine */ int zptrfs_(char *uplo, integer *n, integer *nrhs, doublereal *d__, doublecomplex *e, doublereal *df, doublecomplex *ef, doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, doublereal *ferr, doublereal *berr, doublecomplex *work, doublereal * rwork, integer *info) { /* System generated locals */ integer b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5, i__6; doublereal d__1, d__2, d__3, d__4, d__5, d__6, d__7, d__8, d__9, d__10, d__11, d__12; doublecomplex z__1, z__2, z__3; /* Local variables */ doublereal safe1, safe2; integer i__, j; doublereal s; extern logical lsame_(char *, char *); integer count; logical upper; extern /* Subroutine */ int zaxpy_(integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *); doublecomplex bi; extern doublereal dlamch_(char *); doublecomplex cx, dx, ex; integer ix; extern integer idamax_(integer *, doublereal *, integer *); integer nz; doublereal safmin; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); doublereal lstres; extern /* Subroutine */ int zpttrs_(char *, integer *, integer *, doublereal *, doublecomplex *, doublecomplex *, integer *, integer *); doublereal eps; /* -- 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 */ --d__; --e; --df; --ef; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; x_dim1 = *ldx; x_offset = 1 + x_dim1 * 1; x -= x_offset; --ferr; --berr; --work; --rwork; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); if (! upper && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*nrhs < 0) { *info = -3; } else if (*ldb < f2cmax(1,*n)) { *info = -9; } else if (*ldx < f2cmax(1,*n)) { *info = -11; } if (*info != 0) { i__1 = -(*info); xerbla_("ZPTRFS", &i__1, (ftnlen)6); return 0; } /* Quick return if possible */ if (*n == 0 || *nrhs == 0) { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { ferr[j] = 0.; berr[j] = 0.; /* L10: */ } return 0; } /* NZ = maximum number of nonzero elements in each row of A, plus 1 */ nz = 4; eps = dlamch_("Epsilon"); safmin = dlamch_("Safe minimum"); safe1 = nz * safmin; safe2 = safe1 / eps; /* Do for each right hand side */ i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { count = 1; lstres = 3.; L20: /* Loop until stopping criterion is satisfied. */ /* Compute residual R = B - A * X. Also compute */ /* abs(A)*abs(x) + abs(b) for use in the backward error bound. */ if (upper) { if (*n == 1) { i__2 = j * b_dim1 + 1; bi.r = b[i__2].r, bi.i = b[i__2].i; i__2 = j * x_dim1 + 1; z__1.r = d__[1] * x[i__2].r, z__1.i = d__[1] * x[i__2].i; dx.r = z__1.r, dx.i = z__1.i; z__1.r = bi.r - dx.r, z__1.i = bi.i - dx.i; work[1].r = z__1.r, work[1].i = z__1.i; rwork[1] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&bi), abs(d__2)) + ((d__3 = dx.r, abs(d__3)) + (d__4 = d_imag(&dx), abs(d__4))); } else { i__2 = j * b_dim1 + 1; bi.r = b[i__2].r, bi.i = b[i__2].i; i__2 = j * x_dim1 + 1; z__1.r = d__[1] * x[i__2].r, z__1.i = d__[1] * x[i__2].i; dx.r = z__1.r, dx.i = z__1.i; i__2 = j * x_dim1 + 2; z__1.r = e[1].r * x[i__2].r - e[1].i * x[i__2].i, z__1.i = e[ 1].r * x[i__2].i + e[1].i * x[i__2].r; ex.r = z__1.r, ex.i = z__1.i; z__2.r = bi.r - dx.r, z__2.i = bi.i - dx.i; z__1.r = z__2.r - ex.r, z__1.i = z__2.i - ex.i; work[1].r = z__1.r, work[1].i = z__1.i; i__2 = j * x_dim1 + 2; rwork[1] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&bi), abs(d__2)) + ((d__3 = dx.r, abs(d__3)) + (d__4 = d_imag(&dx), abs(d__4))) + ((d__5 = e[1].r, abs(d__5)) + (d__6 = d_imag(&e[1]), abs(d__6))) * ((d__7 = x[ i__2].r, abs(d__7)) + (d__8 = d_imag(&x[j * x_dim1 + 2]), abs(d__8))); i__2 = *n - 1; for (i__ = 2; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; bi.r = b[i__3].r, bi.i = b[i__3].i; d_cnjg(&z__2, &e[i__ - 1]); i__3 = i__ - 1 + j * x_dim1; z__1.r = z__2.r * x[i__3].r - z__2.i * x[i__3].i, z__1.i = z__2.r * x[i__3].i + z__2.i * x[i__3].r; cx.r = z__1.r, cx.i = z__1.i; i__3 = i__; i__4 = i__ + j * x_dim1; z__1.r = d__[i__3] * x[i__4].r, z__1.i = d__[i__3] * x[ i__4].i; dx.r = z__1.r, dx.i = z__1.i; i__3 = i__; i__4 = i__ + 1 + j * x_dim1; z__1.r = e[i__3].r * x[i__4].r - e[i__3].i * x[i__4].i, z__1.i = e[i__3].r * x[i__4].i + e[i__3].i * x[ i__4].r; ex.r = z__1.r, ex.i = z__1.i; i__3 = i__; z__3.r = bi.r - cx.r, z__3.i = bi.i - cx.i; z__2.r = z__3.r - dx.r, z__2.i = z__3.i - dx.i; z__1.r = z__2.r - ex.r, z__1.i = z__2.i - ex.i; work[i__3].r = z__1.r, work[i__3].i = z__1.i; i__3 = i__ - 1; i__4 = i__ - 1 + j * x_dim1; i__5 = i__; i__6 = i__ + 1 + j * x_dim1; rwork[i__] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(& bi), abs(d__2)) + ((d__3 = e[i__3].r, abs(d__3)) + (d__4 = d_imag(&e[i__ - 1]), abs(d__4))) * (( d__5 = x[i__4].r, abs(d__5)) + (d__6 = d_imag(&x[ i__ - 1 + j * x_dim1]), abs(d__6))) + ((d__7 = dx.r, abs(d__7)) + (d__8 = d_imag(&dx), abs(d__8)) ) + ((d__9 = e[i__5].r, abs(d__9)) + (d__10 = d_imag(&e[i__]), abs(d__10))) * ((d__11 = x[i__6] .r, abs(d__11)) + (d__12 = d_imag(&x[i__ + 1 + j * x_dim1]), abs(d__12))); /* L30: */ } i__2 = *n + j * b_dim1; bi.r = b[i__2].r, bi.i = b[i__2].i; d_cnjg(&z__2, &e[*n - 1]); i__2 = *n - 1 + j * x_dim1; z__1.r = z__2.r * x[i__2].r - z__2.i * x[i__2].i, z__1.i = z__2.r * x[i__2].i + z__2.i * x[i__2].r; cx.r = z__1.r, cx.i = z__1.i; i__2 = *n; i__3 = *n + j * x_dim1; z__1.r = d__[i__2] * x[i__3].r, z__1.i = d__[i__2] * x[i__3] .i; dx.r = z__1.r, dx.i = z__1.i; i__2 = *n; z__2.r = bi.r - cx.r, z__2.i = bi.i - cx.i; z__1.r = z__2.r - dx.r, z__1.i = z__2.i - dx.i; work[i__2].r = z__1.r, work[i__2].i = z__1.i; i__2 = *n - 1; i__3 = *n - 1 + j * x_dim1; rwork[*n] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&bi), abs(d__2)) + ((d__3 = e[i__2].r, abs(d__3)) + (d__4 = d_imag(&e[*n - 1]), abs(d__4))) * ((d__5 = x[i__3].r, abs(d__5)) + (d__6 = d_imag(&x[*n - 1 + j * x_dim1]), abs(d__6))) + ((d__7 = dx.r, abs(d__7)) + (d__8 = d_imag(&dx), abs(d__8))); } } else { if (*n == 1) { i__2 = j * b_dim1 + 1; bi.r = b[i__2].r, bi.i = b[i__2].i; i__2 = j * x_dim1 + 1; z__1.r = d__[1] * x[i__2].r, z__1.i = d__[1] * x[i__2].i; dx.r = z__1.r, dx.i = z__1.i; z__1.r = bi.r - dx.r, z__1.i = bi.i - dx.i; work[1].r = z__1.r, work[1].i = z__1.i; rwork[1] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&bi), abs(d__2)) + ((d__3 = dx.r, abs(d__3)) + (d__4 = d_imag(&dx), abs(d__4))); } else { i__2 = j * b_dim1 + 1; bi.r = b[i__2].r, bi.i = b[i__2].i; i__2 = j * x_dim1 + 1; z__1.r = d__[1] * x[i__2].r, z__1.i = d__[1] * x[i__2].i; dx.r = z__1.r, dx.i = z__1.i; d_cnjg(&z__2, &e[1]); i__2 = j * x_dim1 + 2; z__1.r = z__2.r * x[i__2].r - z__2.i * x[i__2].i, z__1.i = z__2.r * x[i__2].i + z__2.i * x[i__2].r; ex.r = z__1.r, ex.i = z__1.i; z__2.r = bi.r - dx.r, z__2.i = bi.i - dx.i; z__1.r = z__2.r - ex.r, z__1.i = z__2.i - ex.i; work[1].r = z__1.r, work[1].i = z__1.i; i__2 = j * x_dim1 + 2; rwork[1] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&bi), abs(d__2)) + ((d__3 = dx.r, abs(d__3)) + (d__4 = d_imag(&dx), abs(d__4))) + ((d__5 = e[1].r, abs(d__5)) + (d__6 = d_imag(&e[1]), abs(d__6))) * ((d__7 = x[ i__2].r, abs(d__7)) + (d__8 = d_imag(&x[j * x_dim1 + 2]), abs(d__8))); i__2 = *n - 1; for (i__ = 2; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; bi.r = b[i__3].r, bi.i = b[i__3].i; i__3 = i__ - 1; i__4 = i__ - 1 + j * x_dim1; z__1.r = e[i__3].r * x[i__4].r - e[i__3].i * x[i__4].i, z__1.i = e[i__3].r * x[i__4].i + e[i__3].i * x[ i__4].r; cx.r = z__1.r, cx.i = z__1.i; i__3 = i__; i__4 = i__ + j * x_dim1; z__1.r = d__[i__3] * x[i__4].r, z__1.i = d__[i__3] * x[ i__4].i; dx.r = z__1.r, dx.i = z__1.i; d_cnjg(&z__2, &e[i__]); i__3 = i__ + 1 + j * x_dim1; z__1.r = z__2.r * x[i__3].r - z__2.i * x[i__3].i, z__1.i = z__2.r * x[i__3].i + z__2.i * x[i__3].r; ex.r = z__1.r, ex.i = z__1.i; i__3 = i__; z__3.r = bi.r - cx.r, z__3.i = bi.i - cx.i; z__2.r = z__3.r - dx.r, z__2.i = z__3.i - dx.i; z__1.r = z__2.r - ex.r, z__1.i = z__2.i - ex.i; work[i__3].r = z__1.r, work[i__3].i = z__1.i; i__3 = i__ - 1; i__4 = i__ - 1 + j * x_dim1; i__5 = i__; i__6 = i__ + 1 + j * x_dim1; rwork[i__] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(& bi), abs(d__2)) + ((d__3 = e[i__3].r, abs(d__3)) + (d__4 = d_imag(&e[i__ - 1]), abs(d__4))) * (( d__5 = x[i__4].r, abs(d__5)) + (d__6 = d_imag(&x[ i__ - 1 + j * x_dim1]), abs(d__6))) + ((d__7 = dx.r, abs(d__7)) + (d__8 = d_imag(&dx), abs(d__8)) ) + ((d__9 = e[i__5].r, abs(d__9)) + (d__10 = d_imag(&e[i__]), abs(d__10))) * ((d__11 = x[i__6] .r, abs(d__11)) + (d__12 = d_imag(&x[i__ + 1 + j * x_dim1]), abs(d__12))); /* L40: */ } i__2 = *n + j * b_dim1; bi.r = b[i__2].r, bi.i = b[i__2].i; i__2 = *n - 1; i__3 = *n - 1 + j * x_dim1; z__1.r = e[i__2].r * x[i__3].r - e[i__2].i * x[i__3].i, z__1.i = e[i__2].r * x[i__3].i + e[i__2].i * x[i__3] .r; cx.r = z__1.r, cx.i = z__1.i; i__2 = *n; i__3 = *n + j * x_dim1; z__1.r = d__[i__2] * x[i__3].r, z__1.i = d__[i__2] * x[i__3] .i; dx.r = z__1.r, dx.i = z__1.i; i__2 = *n; z__2.r = bi.r - cx.r, z__2.i = bi.i - cx.i; z__1.r = z__2.r - dx.r, z__1.i = z__2.i - dx.i; work[i__2].r = z__1.r, work[i__2].i = z__1.i; i__2 = *n - 1; i__3 = *n - 1 + j * x_dim1; rwork[*n] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&bi), abs(d__2)) + ((d__3 = e[i__2].r, abs(d__3)) + (d__4 = d_imag(&e[*n - 1]), abs(d__4))) * ((d__5 = x[i__3].r, abs(d__5)) + (d__6 = d_imag(&x[*n - 1 + j * x_dim1]), abs(d__6))) + ((d__7 = dx.r, abs(d__7)) + (d__8 = d_imag(&dx), abs(d__8))); } } /* Compute componentwise relative backward error from formula */ /* f2cmax(i) ( abs(R(i)) / ( abs(A)*abs(X) + abs(B) )(i) ) */ /* where abs(Z) is the componentwise absolute value of the matrix */ /* or vector Z. If the i-th component of the denominator is less */ /* than SAFE2, then SAFE1 is added to the i-th components of the */ /* numerator and denominator before dividing. */ s = 0.; i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { if (rwork[i__] > safe2) { /* Computing MAX */ i__3 = i__; d__3 = s, d__4 = ((d__1 = work[i__3].r, abs(d__1)) + (d__2 = d_imag(&work[i__]), abs(d__2))) / rwork[i__]; s = f2cmax(d__3,d__4); } else { /* Computing MAX */ i__3 = i__; d__3 = s, d__4 = ((d__1 = work[i__3].r, abs(d__1)) + (d__2 = d_imag(&work[i__]), abs(d__2)) + safe1) / (rwork[i__] + safe1); s = f2cmax(d__3,d__4); } /* L50: */ } berr[j] = s; /* Test stopping criterion. Continue iterating if */ /* 1) The residual BERR(J) is larger than machine epsilon, and */ /* 2) BERR(J) decreased by at least a factor of 2 during the */ /* last iteration, and */ /* 3) At most ITMAX iterations tried. */ if (berr[j] > eps && berr[j] * 2. <= lstres && count <= 5) { /* Update solution and try again. */ zpttrs_(uplo, n, &c__1, &df[1], &ef[1], &work[1], n, info); zaxpy_(n, &c_b16, &work[1], &c__1, &x[j * x_dim1 + 1], &c__1); lstres = berr[j]; ++count; goto L20; } /* Bound error from formula */ /* norm(X - XTRUE) / norm(X) .le. FERR = */ /* norm( abs(inv(A))* */ /* ( abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) / norm(X) */ /* where */ /* norm(Z) is the magnitude of the largest component of Z */ /* inv(A) is the inverse of A */ /* abs(Z) is the componentwise absolute value of the matrix or */ /* vector Z */ /* NZ is the maximum number of nonzeros in any row of A, plus 1 */ /* EPS is machine epsilon */ /* The i-th component of abs(R)+NZ*EPS*(abs(A)*abs(X)+abs(B)) */ /* is incremented by SAFE1 if the i-th component of */ /* abs(A)*abs(X) + abs(B) is less than SAFE2. */ i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { if (rwork[i__] > safe2) { i__3 = i__; rwork[i__] = (d__1 = work[i__3].r, abs(d__1)) + (d__2 = d_imag(&work[i__]), abs(d__2)) + nz * eps * rwork[i__] ; } else { i__3 = i__; rwork[i__] = (d__1 = work[i__3].r, abs(d__1)) + (d__2 = d_imag(&work[i__]), abs(d__2)) + nz * eps * rwork[i__] + safe1; } /* L60: */ } ix = idamax_(n, &rwork[1], &c__1); ferr[j] = rwork[ix]; /* Estimate the norm of inv(A). */ /* Solve M(A) * x = e, where M(A) = (m(i,j)) is given by */ /* m(i,j) = abs(A(i,j)), i = j, */ /* m(i,j) = -abs(A(i,j)), i .ne. j, */ /* and e = [ 1, 1, ..., 1 ]**T. Note M(A) = M(L)*D*M(L)**H. */ /* Solve M(L) * x = e. */ rwork[1] = 1.; i__2 = *n; for (i__ = 2; i__ <= i__2; ++i__) { rwork[i__] = rwork[i__ - 1] * z_abs(&ef[i__ - 1]) + 1.; /* L70: */ } /* Solve D * M(L)**H * x = b. */ rwork[*n] /= df[*n]; for (i__ = *n - 1; i__ >= 1; --i__) { rwork[i__] = rwork[i__] / df[i__] + rwork[i__ + 1] * z_abs(&ef[ i__]); /* L80: */ } /* Compute norm(inv(A)) = f2cmax(x(i)), 1<=i<=n. */ ix = idamax_(n, &rwork[1], &c__1); ferr[j] *= (d__1 = rwork[ix], abs(d__1)); /* Normalize error. */ lstres = 0.; i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { /* Computing MAX */ d__1 = lstres, d__2 = z_abs(&x[i__ + j * x_dim1]); lstres = f2cmax(d__1,d__2); /* L90: */ } if (lstres != 0.) { ferr[j] /= lstres; } /* L100: */ } return 0; /* End of ZPTRFS */ } /* zptrfs_ */