#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]/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++ */ #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 CPORFS */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download CPORFS + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE CPORFS( UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, */ /* LDX, FERR, BERR, WORK, RWORK, INFO ) */ /* CHARACTER UPLO */ /* INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS */ /* REAL BERR( * ), FERR( * ), RWORK( * ) */ /* COMPLEX A( LDA, * ), AF( LDAF, * ), B( LDB, * ), */ /* $ WORK( * ), X( LDX, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > CPORFS improves the computed solution to a system of linear */ /* > equations when the coefficient matrix is Hermitian positive definite, */ /* > and provides error bounds and backward error estimates for the */ /* > solution. */ /* > \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] NRHS */ /* > \verbatim */ /* > NRHS is INTEGER */ /* > The number of right hand sides, i.e., the number of columns */ /* > of the matrices B and X. NRHS >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] A */ /* > \verbatim */ /* > A is COMPLEX array, dimension (LDA,N) */ /* > The Hermitian matrix A. If UPLO = 'U', the leading N-by-N */ /* > upper triangular part of A contains the upper triangular part */ /* > of the matrix A, and the strictly lower triangular part of A */ /* > is not referenced. If UPLO = 'L', the leading N-by-N lower */ /* > triangular part of A contains the lower triangular part of */ /* > the matrix A, and the strictly upper triangular part of A is */ /* > not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[in] AF */ /* > \verbatim */ /* > AF is COMPLEX array, dimension (LDAF,N) */ /* > The triangular factor U or L from the Cholesky factorization */ /* > A = U**H*U or A = L*L**H, as computed by CPOTRF. */ /* > \endverbatim */ /* > */ /* > \param[in] LDAF */ /* > \verbatim */ /* > LDAF is INTEGER */ /* > The leading dimension of the array AF. LDAF >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[in] B */ /* > \verbatim */ /* > B is COMPLEX 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 array, dimension (LDX,NRHS) */ /* > On entry, the solution matrix X, as computed by CPOTRS. */ /* > 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 REAL array, dimension (NRHS) */ /* > The estimated forward error bound for each solution vector */ /* > X(j) (the j-th column of the solution matrix X). */ /* > If XTRUE is the true solution corresponding to X(j), FERR(j) */ /* > is an estimated upper bound for the magnitude of the largest */ /* > element in (X(j) - XTRUE) divided by the magnitude of the */ /* > largest element in X(j). The estimate is as reliable as */ /* > the estimate for RCOND, and is almost always a slight */ /* > overestimate of the true error. */ /* > \endverbatim */ /* > */ /* > \param[out] BERR */ /* > \verbatim */ /* > BERR is REAL 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 array, dimension (2*N) */ /* > \endverbatim */ /* > */ /* > \param[out] RWORK */ /* > \verbatim */ /* > RWORK is REAL 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 complexPOcomputational */ /* ===================================================================== */ /* Subroutine */ int cporfs_(char *uplo, integer *n, integer *nrhs, complex * a, integer *lda, complex *af, integer *ldaf, complex *b, integer *ldb, complex *x, integer *ldx, real *ferr, real *berr, complex *work, real *rwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5; real r__1, r__2, r__3, r__4; complex q__1; /* Local variables */ integer kase; real safe1, safe2; integer i__, j, k; real s; extern logical lsame_(char *, char *); extern /* Subroutine */ int chemv_(char *, integer *, complex *, complex * , integer *, complex *, integer *, complex *, complex *, integer * ); integer isave[3]; extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, complex *, integer *), caxpy_(integer *, complex *, complex *, integer *, complex *, integer *); integer count; logical upper; extern /* Subroutine */ int clacn2_(integer *, complex *, complex *, real *, integer *, integer *); real xk; extern real slamch_(char *); integer nz; real safmin; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), cpotrs_( char *, integer *, integer *, complex *, integer *, complex *, integer *, integer *); real lstres, 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 */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; af_dim1 = *ldaf; af_offset = 1 + af_dim1 * 1; af -= af_offset; 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 (*lda < f2cmax(1,*n)) { *info = -5; } else if (*ldaf < f2cmax(1,*n)) { *info = -7; } else if (*ldb < f2cmax(1,*n)) { *info = -9; } else if (*ldx < f2cmax(1,*n)) { *info = -11; } if (*info != 0) { i__1 = -(*info); xerbla_("CPORFS", &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.f; berr[j] = 0.f; /* L10: */ } return 0; } /* NZ = maximum number of nonzero elements in each row of A, plus 1 */ nz = *n + 1; eps = slamch_("Epsilon"); safmin = slamch_("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.f; L20: /* Loop until stopping criterion is satisfied. */ /* Compute residual R = B - A * X */ ccopy_(n, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1); q__1.r = -1.f, q__1.i = 0.f; chemv_(uplo, n, &q__1, &a[a_offset], lda, &x[j * x_dim1 + 1], &c__1, & c_b1, &work[1], &c__1); /* 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. */ i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; rwork[i__] = (r__1 = b[i__3].r, abs(r__1)) + (r__2 = r_imag(&b[ i__ + j * b_dim1]), abs(r__2)); /* L30: */ } /* Compute abs(A)*abs(X) + abs(B). */ if (upper) { i__2 = *n; for (k = 1; k <= i__2; ++k) { s = 0.f; i__3 = k + j * x_dim1; xk = (r__1 = x[i__3].r, abs(r__1)) + (r__2 = r_imag(&x[k + j * x_dim1]), abs(r__2)); i__3 = k - 1; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = i__ + k * a_dim1; rwork[i__] += ((r__1 = a[i__4].r, abs(r__1)) + (r__2 = r_imag(&a[i__ + k * a_dim1]), abs(r__2))) * xk; i__4 = i__ + k * a_dim1; i__5 = i__ + j * x_dim1; s += ((r__1 = a[i__4].r, abs(r__1)) + (r__2 = r_imag(&a[ i__ + k * a_dim1]), abs(r__2))) * ((r__3 = x[i__5] .r, abs(r__3)) + (r__4 = r_imag(&x[i__ + j * x_dim1]), abs(r__4))); /* L40: */ } i__3 = k + k * a_dim1; rwork[k] = rwork[k] + (r__1 = a[i__3].r, abs(r__1)) * xk + s; /* L50: */ } } else { i__2 = *n; for (k = 1; k <= i__2; ++k) { s = 0.f; i__3 = k + j * x_dim1; xk = (r__1 = x[i__3].r, abs(r__1)) + (r__2 = r_imag(&x[k + j * x_dim1]), abs(r__2)); i__3 = k + k * a_dim1; rwork[k] += (r__1 = a[i__3].r, abs(r__1)) * xk; i__3 = *n; for (i__ = k + 1; i__ <= i__3; ++i__) { i__4 = i__ + k * a_dim1; rwork[i__] += ((r__1 = a[i__4].r, abs(r__1)) + (r__2 = r_imag(&a[i__ + k * a_dim1]), abs(r__2))) * xk; i__4 = i__ + k * a_dim1; i__5 = i__ + j * x_dim1; s += ((r__1 = a[i__4].r, abs(r__1)) + (r__2 = r_imag(&a[ i__ + k * a_dim1]), abs(r__2))) * ((r__3 = x[i__5] .r, abs(r__3)) + (r__4 = r_imag(&x[i__ + j * x_dim1]), abs(r__4))); /* L60: */ } rwork[k] += s; /* L70: */ } } s = 0.f; i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { if (rwork[i__] > safe2) { /* Computing MAX */ i__3 = i__; r__3 = s, r__4 = ((r__1 = work[i__3].r, abs(r__1)) + (r__2 = r_imag(&work[i__]), abs(r__2))) / rwork[i__]; s = f2cmax(r__3,r__4); } else { /* Computing MAX */ i__3 = i__; r__3 = s, r__4 = ((r__1 = work[i__3].r, abs(r__1)) + (r__2 = r_imag(&work[i__]), abs(r__2)) + safe1) / (rwork[i__] + safe1); s = f2cmax(r__3,r__4); } /* L80: */ } 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.f <= lstres && count <= 5) { /* Update solution and try again. */ cpotrs_(uplo, n, &c__1, &af[af_offset], ldaf, &work[1], n, info); caxpy_(n, &c_b1, &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. */ /* Use CLACN2 to estimate the infinity-norm of the matrix */ /* inv(A) * diag(W), */ /* where W = abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) */ i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { if (rwork[i__] > safe2) { i__3 = i__; rwork[i__] = (r__1 = work[i__3].r, abs(r__1)) + (r__2 = r_imag(&work[i__]), abs(r__2)) + nz * eps * rwork[i__] ; } else { i__3 = i__; rwork[i__] = (r__1 = work[i__3].r, abs(r__1)) + (r__2 = r_imag(&work[i__]), abs(r__2)) + nz * eps * rwork[i__] + safe1; } /* L90: */ } kase = 0; L100: clacn2_(n, &work[*n + 1], &work[1], &ferr[j], &kase, isave); if (kase != 0) { if (kase == 1) { /* Multiply by diag(W)*inv(A**H). */ cpotrs_(uplo, n, &c__1, &af[af_offset], ldaf, &work[1], n, info); i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__; i__4 = i__; i__5 = i__; q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4] * work[i__5].i; work[i__3].r = q__1.r, work[i__3].i = q__1.i; /* L110: */ } } else if (kase == 2) { /* Multiply by inv(A)*diag(W). */ i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__; i__4 = i__; i__5 = i__; q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4] * work[i__5].i; work[i__3].r = q__1.r, work[i__3].i = q__1.i; /* L120: */ } cpotrs_(uplo, n, &c__1, &af[af_offset], ldaf, &work[1], n, info); } goto L100; } /* Normalize error. */ lstres = 0.f; i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { /* Computing MAX */ i__3 = i__ + j * x_dim1; r__3 = lstres, r__4 = (r__1 = x[i__3].r, abs(r__1)) + (r__2 = r_imag(&x[i__ + j * x_dim1]), abs(r__2)); lstres = f2cmax(r__3,r__4); /* L130: */ } if (lstres != 0.f) { ferr[j] /= lstres; } /* L140: */ } return 0; /* End of CPORFS */ } /* cporfs_ */