/* Subroutine */ int zherfsx_(char *uplo, char *equed, integer *n, integer * nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * ldaf, integer *ipiv, doublereal *s, doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *berr, integer *n_err_bnds__, doublereal *err_bnds_norm__, doublereal * err_bnds_comp__, integer *nparams, doublereal *params, doublecomplex * work, doublereal *rwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, x_offset, err_bnds_norm_dim1, err_bnds_norm_offset, err_bnds_comp_dim1, err_bnds_comp_offset, i__1; doublereal d__1, d__2; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ doublereal illrcond_thresh__, unstable_thresh__, err_lbnd__; integer ref_type__; integer j; doublereal rcond_tmp__; integer prec_type__; doublereal cwise_wrong__; extern /* Subroutine */ int zla_herfsx_extended__(integer *, char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, logical *, doublereal *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, doublecomplex *, doublecomplex *, doublereal *, integer *, doublereal *, doublereal *, logical *, integer *, ftnlen); char norm[1]; logical ignore_cwise__; extern logical lsame_(char *, char *); doublereal anorm; logical rcequ; extern doublereal zla_hercond_c__(char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublereal *, logical *, integer *, doublecomplex *, doublereal *, ftnlen), zla_hercond_x__(char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublereal *, ftnlen), dlamch_(char *); extern /* Subroutine */ int xerbla_(char *, integer *); extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, integer *, doublereal *); extern /* Subroutine */ int zhecon_(char *, integer *, doublecomplex *, integer *, integer *, doublereal *, doublereal *, doublecomplex *, integer *); extern integer ilaprec_(char *); integer ithresh, n_norms__; doublereal rthresh; /* -- LAPACK routine (version 3.2.1) -- */ /* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */ /* -- Jason Riedy of Univ. of California Berkeley. -- */ /* -- April 2009 -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley and NAG Ltd. -- */ /* .. */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* Purpose */ /* ======= */ /* ZHERFSX improves the computed solution to a system of linear */ /* equations when the coefficient matrix is Hermitian indefinite, and */ /* provides error bounds and backward error estimates for the */ /* solution. In addition to normwise error bound, the code provides */ /* maximum componentwise error bound if possible. See comments for */ /* ERR_BNDS_NORM and ERR_BNDS_COMP for details of the error bounds. */ /* The original system of linear equations may have been equilibrated */ /* before calling this routine, as described by arguments EQUED and S */ /* below. In this case, the solution and error bounds returned are */ /* for the original unequilibrated system. */ /* Arguments */ /* ========= */ /* Some optional parameters are bundled in the PARAMS array. These */ /* settings determine how refinement is performed, but often the */ /* defaults are acceptable. If the defaults are acceptable, users */ /* can pass NPARAMS = 0 which prevents the source code from accessing */ /* the PARAMS argument. */ /* UPLO (input) CHARACTER*1 */ /* = 'U': Upper triangle of A is stored; */ /* = 'L': Lower triangle of A is stored. */ /* EQUED (input) CHARACTER*1 */ /* Specifies the form of equilibration that was done to A */ /* before calling this routine. This is needed to compute */ /* the solution and error bounds correctly. */ /* = 'N': No equilibration */ /* = 'Y': Both row and column equilibration, i.e., A has been */ /* replaced by diag(S) * A * diag(S). */ /* The right hand side B has been changed accordingly. */ /* N (input) INTEGER */ /* The order of the matrix A. N >= 0. */ /* NRHS (input) INTEGER */ /* The number of right hand sides, i.e., the number of columns */ /* of the matrices B and X. NRHS >= 0. */ /* A (input) COMPLEX*16 array, dimension (LDA,N) */ /* The symmetric 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. */ /* LDA (input) INTEGER */ /* The leading dimension of the array A. LDA >= max(1,N). */ /* AF (input) COMPLEX*16 array, dimension (LDAF,N) */ /* The factored form of the matrix A. AF contains the block */ /* diagonal matrix D and the multipliers used to obtain the */ /* factor U or L from the factorization A = U*D*U**T or A = */ /* L*D*L**T as computed by DSYTRF. */ /* LDAF (input) INTEGER */ /* The leading dimension of the array AF. LDAF >= max(1,N). */ /* IPIV (input) INTEGER array, dimension (N) */ /* Details of the interchanges and the block structure of D */ /* as determined by DSYTRF. */ /* S (input or output) DOUBLE PRECISION array, dimension (N) */ /* The scale factors for A. If EQUED = 'Y', A is multiplied on */ /* the left and right by diag(S). S is an input argument if FACT = */ /* 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED */ /* = 'Y', each element of S must be positive. If S is output, each */ /* element of S is a power of the radix. If S is input, each element */ /* of S should be a power of the radix to ensure a reliable solution */ /* and error estimates. Scaling by powers of the radix does not cause */ /* rounding errors unless the result underflows or overflows. */ /* Rounding errors during scaling lead to refining with a matrix that */ /* is not equivalent to the input matrix, producing error estimates */ /* that may not be reliable. */ /* B (input) COMPLEX*16 array, dimension (LDB,NRHS) */ /* The right hand side matrix B. */ /* LDB (input) INTEGER */ /* The leading dimension of the array B. LDB >= max(1,N). */ /* X (input/output) COMPLEX*16 array, dimension (LDX,NRHS) */ /* On entry, the solution matrix X, as computed by DGETRS. */ /* On exit, the improved solution matrix X. */ /* LDX (input) INTEGER */ /* The leading dimension of the array X. LDX >= max(1,N). */ /* RCOND (output) DOUBLE PRECISION */ /* Reciprocal scaled condition number. This is an estimate of the */ /* reciprocal Skeel condition number of the matrix A after */ /* equilibration (if done). If this is less than the machine */ /* precision (in particular, if it is zero), the matrix is singular */ /* to working precision. Note that the error may still be small even */ /* if this number is very small and the matrix appears ill- */ /* conditioned. */ /* BERR (output) DOUBLE PRECISION array, dimension (NRHS) */ /* Componentwise relative backward error. This is 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). */ /* N_ERR_BNDS (input) INTEGER */ /* Number of error bounds to return for each right hand side */ /* and each type (normwise or componentwise). See ERR_BNDS_NORM and */ /* ERR_BNDS_COMP below. */ /* ERR_BNDS_NORM (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */ /* For each right-hand side, this array contains information about */ /* various error bounds and condition numbers corresponding to the */ /* normwise relative error, which is defined as follows: */ /* Normwise relative error in the ith solution vector: */ /* max_j (abs(XTRUE(j,i) - X(j,i))) */ /* ------------------------------ */ /* max_j abs(X(j,i)) */ /* The array is indexed by the type of error information as described */ /* below. There currently are up to three pieces of information */ /* returned. */ /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ /* right-hand side. */ /* The second index in ERR_BNDS_NORM(:,err) contains the following */ /* three fields: */ /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ /* reciprocal condition number is less than the threshold */ /* sqrt(n) * dlamch('Epsilon'). */ /* err = 2 "Guaranteed" error bound: The estimated forward error, */ /* almost certainly within a factor of 10 of the true error */ /* so long as the next entry is greater than the threshold */ /* sqrt(n) * dlamch('Epsilon'). This error bound should only */ /* be trusted if the previous boolean is true. */ /* err = 3 Reciprocal condition number: Estimated normwise */ /* reciprocal condition number. Compared with the threshold */ /* sqrt(n) * dlamch('Epsilon') to determine if the error */ /* estimate is "guaranteed". These reciprocal condition */ /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ /* appropriately scaled matrix Z. */ /* Let Z = S*A, where S scales each row by a power of the */ /* radix so all absolute row sums of Z are approximately 1. */ /* See Lapack Working Note 165 for further details and extra */ /* cautions. */ /* ERR_BNDS_COMP (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */ /* For each right-hand side, this array contains information about */ /* various error bounds and condition numbers corresponding to the */ /* componentwise relative error, which is defined as follows: */ /* Componentwise relative error in the ith solution vector: */ /* abs(XTRUE(j,i) - X(j,i)) */ /* max_j ---------------------- */ /* abs(X(j,i)) */ /* The array is indexed by the right-hand side i (on which the */ /* componentwise relative error depends), and the type of error */ /* information as described below. There currently are up to three */ /* pieces of information returned for each right-hand side. If */ /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ /* the first (:,N_ERR_BNDS) entries are returned. */ /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ /* right-hand side. */ /* The second index in ERR_BNDS_COMP(:,err) contains the following */ /* three fields: */ /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ /* reciprocal condition number is less than the threshold */ /* sqrt(n) * dlamch('Epsilon'). */ /* err = 2 "Guaranteed" error bound: The estimated forward error, */ /* almost certainly within a factor of 10 of the true error */ /* so long as the next entry is greater than the threshold */ /* sqrt(n) * dlamch('Epsilon'). This error bound should only */ /* be trusted if the previous boolean is true. */ /* err = 3 Reciprocal condition number: Estimated componentwise */ /* reciprocal condition number. Compared with the threshold */ /* sqrt(n) * dlamch('Epsilon') to determine if the error */ /* estimate is "guaranteed". These reciprocal condition */ /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ /* appropriately scaled matrix Z. */ /* Let Z = S*(A*diag(x)), where x is the solution for the */ /* current right-hand side and S scales each row of */ /* A*diag(x) by a power of the radix so all absolute row */ /* sums of Z are approximately 1. */ /* See Lapack Working Note 165 for further details and extra */ /* cautions. */ /* NPARAMS (input) INTEGER */ /* Specifies the number of parameters set in PARAMS. If .LE. 0, the */ /* PARAMS array is never referenced and default values are used. */ /* PARAMS (input / output) DOUBLE PRECISION array, dimension NPARAMS */ /* Specifies algorithm parameters. If an entry is .LT. 0.0, then */ /* that entry will be filled with default value used for that */ /* parameter. Only positions up to NPARAMS are accessed; defaults */ /* are used for higher-numbered parameters. */ /* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */ /* refinement or not. */ /* Default: 1.0D+0 */ /* = 0.0 : No refinement is performed, and no error bounds are */ /* computed. */ /* = 1.0 : Use the double-precision refinement algorithm, */ /* possibly with doubled-single computations if the */ /* compilation environment does not support DOUBLE */ /* PRECISION. */ /* (other values are reserved for future use) */ /* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */ /* computations allowed for refinement. */ /* Default: 10 */ /* Aggressive: Set to 100 to permit convergence using approximate */ /* factorizations or factorizations other than LU. If */ /* the factorization uses a technique other than */ /* Gaussian elimination, the guarantees in */ /* err_bnds_norm and err_bnds_comp may no longer be */ /* trustworthy. */ /* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */ /* will attempt to find a solution with small componentwise */ /* relative error in the double-precision algorithm. Positive */ /* is true, 0.0 is false. */ /* Default: 1.0 (attempt componentwise convergence) */ /* WORK (workspace) COMPLEX*16 array, dimension (2*N) */ /* RWORK (workspace) DOUBLE PRECISION array, dimension (2*N) */ /* INFO (output) INTEGER */ /* = 0: Successful exit. The solution to every right-hand side is */ /* guaranteed. */ /* < 0: If INFO = -i, the i-th argument had an illegal value */ /* > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */ /* has been completed, but the factor U is exactly singular, so */ /* the solution and error bounds could not be computed. RCOND = 0 */ /* is returned. */ /* = N+J: The solution corresponding to the Jth right-hand side is */ /* not guaranteed. The solutions corresponding to other right- */ /* hand sides K with K > J may not be guaranteed as well, but */ /* only the first such right-hand side is reported. If a small */ /* componentwise error is not requested (PARAMS(3) = 0.0) then */ /* the Jth right-hand side is the first with a normwise error */ /* bound that is not guaranteed (the smallest J such */ /* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */ /* the Jth right-hand side is the first with either a normwise or */ /* componentwise error bound that is not guaranteed (the smallest */ /* J such that either ERR_BNDS_NORM(J,1) = 0.0 or */ /* ERR_BNDS_COMP(J,1) = 0.0). See the definition of */ /* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */ /* about all of the right-hand sides check ERR_BNDS_NORM or */ /* ERR_BNDS_COMP. */ /* ================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Check the input parameters. */ /* Parameter adjustments */ err_bnds_comp_dim1 = *nrhs; err_bnds_comp_offset = 1 + err_bnds_comp_dim1; err_bnds_comp__ -= err_bnds_comp_offset; err_bnds_norm_dim1 = *nrhs; err_bnds_norm_offset = 1 + err_bnds_norm_dim1; err_bnds_norm__ -= err_bnds_norm_offset; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; af_dim1 = *ldaf; af_offset = 1 + af_dim1; af -= af_offset; --ipiv; --s; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; x_dim1 = *ldx; x_offset = 1 + x_dim1; x -= x_offset; --berr; --params; --work; --rwork; /* Function Body */ *info = 0; ref_type__ = 1; if (*nparams >= 1) { if (params[1] < 0.) { params[1] = 1.; } else { ref_type__ = (integer) params[1]; } } /* Set default parameters. */ illrcond_thresh__ = (doublereal) (*n) * dlamch_("Epsilon"); ithresh = 10; rthresh = .5; unstable_thresh__ = .25; ignore_cwise__ = FALSE_; if (*nparams >= 2) { if (params[2] < 0.) { params[2] = (doublereal) ithresh; } else { ithresh = (integer) params[2]; } } if (*nparams >= 3) { if (params[3] < 0.) { if (ignore_cwise__) { params[3] = 0.; } else { params[3] = 1.; } } else { ignore_cwise__ = params[3] == 0.; } } if (ref_type__ == 0 || *n_err_bnds__ == 0) { n_norms__ = 0; } else if (ignore_cwise__) { n_norms__ = 1; } else { n_norms__ = 2; } rcequ = lsame_(equed, "Y"); /* Test input parameters. */ if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { *info = -1; } else if (! rcequ && ! lsame_(equed, "N")) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*nrhs < 0) { *info = -4; } else if (*lda < max(1,*n)) { *info = -6; } else if (*ldaf < max(1,*n)) { *info = -8; } else if (*ldb < max(1,*n)) { *info = -11; } else if (*ldx < max(1,*n)) { *info = -13; } if (*info != 0) { i__1 = -(*info); xerbla_("ZHERFSX", &i__1); return 0; } /* Quick return if possible. */ if (*n == 0 || *nrhs == 0) { *rcond = 1.; i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { berr[j] = 0.; if (*n_err_bnds__ >= 1) { err_bnds_norm__[j + err_bnds_norm_dim1] = 1.; err_bnds_comp__[j + err_bnds_comp_dim1] = 1.; } else if (*n_err_bnds__ >= 2) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 0.; err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 0.; } else if (*n_err_bnds__ >= 3) { err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 1.; err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 1.; } } return 0; } /* Default to failure. */ *rcond = 0.; i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { berr[j] = 1.; if (*n_err_bnds__ >= 1) { err_bnds_norm__[j + err_bnds_norm_dim1] = 1.; err_bnds_comp__[j + err_bnds_comp_dim1] = 1.; } else if (*n_err_bnds__ >= 2) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.; err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.; } else if (*n_err_bnds__ >= 3) { err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 0.; err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 0.; } } /* Compute the norm of A and the reciprocal of the condition */ /* number of A. */ *(unsigned char *)norm = 'I'; anorm = zlanhe_(norm, uplo, n, &a[a_offset], lda, &rwork[1]); zhecon_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &anorm, rcond, &work[1], info); /* Perform refinement on each right-hand side */ if (ref_type__ != 0) { prec_type__ = ilaprec_("E"); zla_herfsx_extended__(&prec_type__, uplo, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &ipiv[1], &rcequ, &s[1], &b[b_offset], ldb, &x[x_offset], ldx, &berr[1], &n_norms__, & err_bnds_norm__[err_bnds_norm_offset], &err_bnds_comp__[ err_bnds_comp_offset], &work[1], &rwork[1], &work[*n + 1], (doublecomplex *)(&rwork[1]), rcond, &ithresh, &rthresh, &unstable_thresh__, & ignore_cwise__, info, (ftnlen)1); } /* Computing MAX */ d__1 = 10., d__2 = sqrt((doublereal) (*n)); err_lbnd__ = max(d__1,d__2) * dlamch_("Epsilon"); if (*n_err_bnds__ >= 1 && n_norms__ >= 1) { /* Compute scaled normwise condition number cond(A*C). */ if (rcequ) { rcond_tmp__ = zla_hercond_c__(uplo, n, &a[a_offset], lda, &af[ af_offset], ldaf, &ipiv[1], &s[1], &c_true, info, &work[1] , &rwork[1], (ftnlen)1); } else { rcond_tmp__ = zla_hercond_c__(uplo, n, &a[a_offset], lda, &af[ af_offset], ldaf, &ipiv[1], &s[1], &c_false, info, &work[ 1], &rwork[1], (ftnlen)1); } i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { /* Cap the error at 1.0. */ if (*n_err_bnds__ >= 2 && err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] > 1.) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.; } /* Threshold the error (see LAWN). */ if (rcond_tmp__ < illrcond_thresh__) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.; err_bnds_norm__[j + err_bnds_norm_dim1] = 0.; if (*info <= *n) { *info = *n + j; } } else if (err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] < err_lbnd__) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = err_lbnd__; err_bnds_norm__[j + err_bnds_norm_dim1] = 1.; } /* Save the condition number. */ if (*n_err_bnds__ >= 3) { err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = rcond_tmp__; } } } if (*n_err_bnds__ >= 1 && n_norms__ >= 2) { /* Compute componentwise condition number cond(A*diag(Y(:,J))) for */ /* each right-hand side using the current solution as an estimate of */ /* the true solution. If the componentwise error estimate is too */ /* large, then the solution is a lousy estimate of truth and the */ /* estimated RCOND may be too optimistic. To avoid misleading users, */ /* the inverse condition number is set to 0.0 when the estimated */ /* cwise error is at least CWISE_WRONG. */ cwise_wrong__ = sqrt(dlamch_("Epsilon")); i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < cwise_wrong__) { rcond_tmp__ = zla_hercond_x__(uplo, n, &a[a_offset], lda, &af[ af_offset], ldaf, &ipiv[1], &x[j * x_dim1 + 1], info, &work[1], &rwork[1], (ftnlen)1); } else { rcond_tmp__ = 0.; } /* Cap the error at 1.0. */ if (*n_err_bnds__ >= 2 && err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] > 1.) { err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.; } /* Threshold the error (see LAWN). */ if (rcond_tmp__ < illrcond_thresh__) { err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.; err_bnds_comp__[j + err_bnds_comp_dim1] = 0.; if (params[3] == 1. && *info < *n + j) { *info = *n + j; } } else if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < err_lbnd__) { err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = err_lbnd__; err_bnds_comp__[j + err_bnds_comp_dim1] = 1.; } /* Save the condition number. */ if (*n_err_bnds__ >= 3) { err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = rcond_tmp__; } } } return 0; /* End of ZHERFSX */ } /* zherfsx_ */
/* Subroutine */ int zchkhe_(logical *dotype, integer *nn, integer *nval, integer *nnb, integer *nbval, integer *nns, integer *nsval, doublereal *thresh, logical *tsterr, integer *nmax, doublecomplex *a, doublecomplex *afac, doublecomplex *ainv, doublecomplex *b, doublecomplex *x, doublecomplex *xact, doublecomplex *work, doublereal *rwork, integer *iwork, integer *nout) { /* Initialized data */ static integer iseedy[4] = { 1988,1989,1990,1991 }; static char uplos[1*2] = "U" "L"; /* Format strings */ static char fmt_9999[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002, " "NB =\002,i4,\002, type \002,i2,\002, test \002,i2,\002, ratio " "=\002,g12.5)"; static char fmt_9998[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002, " "NRHS=\002,i3,\002, type \002,i2,\002, test(\002,i2,\002) =\002,g" "12.5)"; static char fmt_9997[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002" ",\002,10x,\002 type \002,i2,\002, test(\002,i2,\002) =\002,g12.5)" ; /* System generated locals */ integer i__1, i__2, i__3, i__4, i__5; /* Builtin functions */ /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void); /* Local variables */ integer i__, j, k, n, i1, i2, nb, in, kl, ku, nt, lda, inb, ioff, mode, imat, info; char path[3], dist[1]; integer irhs, nrhs; char uplo[1], type__[1]; integer nrun; extern /* Subroutine */ int alahd_(integer *, char *); integer nfail, iseed[4]; extern doublereal dget06_(doublereal *, doublereal *); doublereal rcond; integer nimat; extern /* Subroutine */ int zhet01_(char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, doublereal *, doublereal *); doublereal anorm; extern /* Subroutine */ int zget04_(integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal * ); integer iuplo, izero, nerrs, lwork; extern /* Subroutine */ int zpot02_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *), zpot03_(char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *), zpot05_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex * , integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *); logical zerot; char xtype[1]; extern /* Subroutine */ int zlatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, doublereal *, integer *, doublereal *, char *), alaerh_(char *, char *, integer *, integer *, char *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *); doublereal rcondc; extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, integer *, doublereal *); extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer *, integer *); doublereal cndnum; extern /* Subroutine */ int zlaipd_(integer *, doublecomplex *, integer *, integer *), zhecon_(char *, integer *, doublecomplex *, integer * , integer *, doublereal *, doublereal *, doublecomplex *, integer *); logical trfcon; extern /* Subroutine */ int xlaenv_(integer *, integer *), zerrhe_(char *, integer *), zherfs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zhetrf_(char *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zhetri_(char *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *), zlarhs_(char *, char *, char *, char *, integer *, integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, integer *), zlatms_(integer *, integer *, char *, integer *, char *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *, char *, doublecomplex *, integer *, doublecomplex *, integer *); doublereal result[8]; extern /* Subroutine */ int zhetrs_(char *, integer *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, integer *); /* Fortran I/O blocks */ static cilist io___39 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___42 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___44 = { 0, 0, 0, fmt_9997, 0 }; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZCHKHE tests ZHETRF, -TRI, -TRS, -RFS, and -CON. */ /* Arguments */ /* ========= */ /* DOTYPE (input) LOGICAL array, dimension (NTYPES) */ /* The matrix types to be used for testing. Matrices of type j */ /* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */ /* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */ /* NN (input) INTEGER */ /* The number of values of N contained in the vector NVAL. */ /* NVAL (input) INTEGER array, dimension (NN) */ /* The values of the matrix dimension N. */ /* NNB (input) INTEGER */ /* The number of values of NB contained in the vector NBVAL. */ /* NBVAL (input) INTEGER array, dimension (NBVAL) */ /* The values of the blocksize NB. */ /* NNS (input) INTEGER */ /* The number of values of NRHS contained in the vector NSVAL. */ /* NSVAL (input) INTEGER array, dimension (NNS) */ /* The values of the number of right hand sides NRHS. */ /* THRESH (input) DOUBLE PRECISION */ /* The threshold value for the test ratios. A result is */ /* included in the output file if RESULT >= THRESH. To have */ /* every test ratio printed, use THRESH = 0. */ /* TSTERR (input) LOGICAL */ /* Flag that indicates whether error exits are to be tested. */ /* NMAX (input) INTEGER */ /* The maximum value permitted for N, used in dimensioning the */ /* work arrays. */ /* A (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) */ /* AFAC (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) */ /* AINV (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) */ /* B (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */ /* where NSMAX is the largest entry in NSVAL. */ /* X (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */ /* XACT (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */ /* WORK (workspace) COMPLEX*16 array, dimension */ /* (NMAX*max(3,NSMAX)) */ /* RWORK (workspace) DOUBLE PRECISION array, dimension */ /* (max(NMAX,2*NSMAX)) */ /* IWORK (workspace) INTEGER array, dimension (NMAX) */ /* NOUT (input) INTEGER */ /* The unit number for output. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Scalars in Common .. */ /* .. */ /* .. Common blocks .. */ /* .. */ /* .. Data statements .. */ /* Parameter adjustments */ --iwork; --rwork; --work; --xact; --x; --b; --ainv; --afac; --a; --nsval; --nbval; --nval; --dotype; /* Function Body */ /* .. */ /* .. Executable Statements .. */ /* Initialize constants and the random number seed. */ s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17); s_copy(path + 1, "HE", (ftnlen)2, (ftnlen)2); nrun = 0; nfail = 0; nerrs = 0; for (i__ = 1; i__ <= 4; ++i__) { iseed[i__ - 1] = iseedy[i__ - 1]; /* L10: */ } /* Test the error exits */ if (*tsterr) { zerrhe_(path, nout); } infoc_1.infot = 0; /* Do for each value of N in NVAL */ i__1 = *nn; for (in = 1; in <= i__1; ++in) { n = nval[in]; lda = max(n,1); *(unsigned char *)xtype = 'N'; nimat = 10; if (n <= 0) { nimat = 1; } izero = 0; i__2 = nimat; for (imat = 1; imat <= i__2; ++imat) { /* Do the tests only if DOTYPE( IMAT ) is true. */ if (! dotype[imat]) { goto L170; } /* Skip types 3, 4, 5, or 6 if the matrix size is too small. */ zerot = imat >= 3 && imat <= 6; if (zerot && n < imat - 2) { goto L170; } /* Do first for UPLO = 'U', then for UPLO = 'L' */ for (iuplo = 1; iuplo <= 2; ++iuplo) { *(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1]; /* Set up parameters with ZLATB4 and generate a test matrix */ /* with ZLATMS. */ zlatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, &cndnum, dist); s_copy(srnamc_1.srnamt, "ZLATMS", (ftnlen)6, (ftnlen)6); zlatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, & cndnum, &anorm, &kl, &ku, uplo, &a[1], &lda, &work[1], &info); /* Check error code from ZLATMS. */ if (info != 0) { alaerh_(path, "ZLATMS", &info, &c__0, uplo, &n, &n, &c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); goto L160; } /* For types 3-6, zero one or more rows and columns of */ /* the matrix to test that INFO is returned correctly. */ if (zerot) { if (imat == 3) { izero = 1; } else if (imat == 4) { izero = n; } else { izero = n / 2 + 1; } if (imat < 6) { /* Set row and column IZERO to zero. */ if (iuplo == 1) { ioff = (izero - 1) * lda; i__3 = izero - 1; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = ioff + i__; a[i__4].r = 0., a[i__4].i = 0.; /* L20: */ } ioff += izero; i__3 = n; for (i__ = izero; i__ <= i__3; ++i__) { i__4 = ioff; a[i__4].r = 0., a[i__4].i = 0.; ioff += lda; /* L30: */ } } else { ioff = izero; i__3 = izero - 1; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = ioff; a[i__4].r = 0., a[i__4].i = 0.; ioff += lda; /* L40: */ } ioff -= izero; i__3 = n; for (i__ = izero; i__ <= i__3; ++i__) { i__4 = ioff + i__; a[i__4].r = 0., a[i__4].i = 0.; /* L50: */ } } } else { ioff = 0; if (iuplo == 1) { /* Set the first IZERO rows and columns to zero. */ i__3 = n; for (j = 1; j <= i__3; ++j) { i2 = min(j,izero); i__4 = i2; for (i__ = 1; i__ <= i__4; ++i__) { i__5 = ioff + i__; a[i__5].r = 0., a[i__5].i = 0.; /* L60: */ } ioff += lda; /* L70: */ } } else { /* Set the last IZERO rows and columns to zero. */ i__3 = n; for (j = 1; j <= i__3; ++j) { i1 = max(j,izero); i__4 = n; for (i__ = i1; i__ <= i__4; ++i__) { i__5 = ioff + i__; a[i__5].r = 0., a[i__5].i = 0.; /* L80: */ } ioff += lda; /* L90: */ } } } } else { izero = 0; } /* Set the imaginary part of the diagonals. */ i__3 = lda + 1; zlaipd_(&n, &a[1], &i__3, &c__0); /* Do for each value of NB in NBVAL */ i__3 = *nnb; for (inb = 1; inb <= i__3; ++inb) { nb = nbval[inb]; xlaenv_(&c__1, &nb); /* Compute the L*D*L' or U*D*U' factorization of the */ /* matrix. */ zlacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda); lwork = max(2,nb) * lda; s_copy(srnamc_1.srnamt, "ZHETRF", (ftnlen)6, (ftnlen)6); zhetrf_(uplo, &n, &afac[1], &lda, &iwork[1], &ainv[1], & lwork, &info); /* Adjust the expected value of INFO to account for */ /* pivoting. */ k = izero; if (k > 0) { L100: if (iwork[k] < 0) { if (iwork[k] != -k) { k = -iwork[k]; goto L100; } } else if (iwork[k] != k) { k = iwork[k]; goto L100; } } /* Check error code from ZHETRF. */ if (info != k) { alaerh_(path, "ZHETRF", &info, &k, uplo, &n, &n, & c_n1, &c_n1, &nb, &imat, &nfail, &nerrs, nout); } if (info != 0) { trfcon = TRUE_; } else { trfcon = FALSE_; } /* + TEST 1 */ /* Reconstruct matrix from factors and compute residual. */ zhet01_(uplo, &n, &a[1], &lda, &afac[1], &lda, &iwork[1], &ainv[1], &lda, &rwork[1], result); nt = 1; /* + TEST 2 */ /* Form the inverse and compute the residual. */ if (inb == 1 && ! trfcon) { zlacpy_(uplo, &n, &n, &afac[1], &lda, &ainv[1], &lda); s_copy(srnamc_1.srnamt, "ZHETRI", (ftnlen)6, (ftnlen) 6); zhetri_(uplo, &n, &ainv[1], &lda, &iwork[1], &work[1], &info); /* Check error code from ZHETRI. */ if (info != 0) { alaerh_(path, "ZHETRI", &info, &c_n1, uplo, &n, & n, &c_n1, &c_n1, &c_n1, &imat, &nfail, & nerrs, nout); } zpot03_(uplo, &n, &a[1], &lda, &ainv[1], &lda, &work[ 1], &lda, &rwork[1], &rcondc, &result[1]); nt = 2; } /* Print information about the tests that did not pass */ /* the threshold. */ i__4 = nt; for (k = 1; k <= i__4; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___39.ciunit = *nout; s_wsfe(&io___39); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&nb, (ftnlen)sizeof(integer) ); do_fio(&c__1, (char *)&imat, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&k, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&result[k - 1], (ftnlen) sizeof(doublereal)); e_wsfe(); ++nfail; } /* L110: */ } nrun += nt; /* Skip the other tests if this is not the first block */ /* size. */ if (inb > 1) { goto L150; } /* Do only the condition estimate if INFO is not 0. */ if (trfcon) { rcondc = 0.; goto L140; } i__4 = *nns; for (irhs = 1; irhs <= i__4; ++irhs) { nrhs = nsval[irhs]; /* + TEST 3 */ /* Solve and compute residual for A * X = B. */ s_copy(srnamc_1.srnamt, "ZLARHS", (ftnlen)6, (ftnlen) 6); zlarhs_(path, xtype, uplo, " ", &n, &n, &kl, &ku, & nrhs, &a[1], &lda, &xact[1], &lda, &b[1], & lda, iseed, &info); zlacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &lda); s_copy(srnamc_1.srnamt, "ZHETRS", (ftnlen)6, (ftnlen) 6); zhetrs_(uplo, &n, &nrhs, &afac[1], &lda, &iwork[1], & x[1], &lda, &info); /* Check error code from ZHETRS. */ if (info != 0) { alaerh_(path, "ZHETRS", &info, &c__0, uplo, &n, & n, &c_n1, &c_n1, &nrhs, &imat, &nfail, & nerrs, nout); } zlacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], & lda); zpot02_(uplo, &n, &nrhs, &a[1], &lda, &x[1], &lda, & work[1], &lda, &rwork[1], &result[2]); /* + TEST 4 */ /* Check solution from generated exact solution. */ zget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[3]); /* + TESTS 5, 6, and 7 */ /* Use iterative refinement to improve the solution. */ s_copy(srnamc_1.srnamt, "ZHERFS", (ftnlen)6, (ftnlen) 6); zherfs_(uplo, &n, &nrhs, &a[1], &lda, &afac[1], &lda, &iwork[1], &b[1], &lda, &x[1], &lda, &rwork[1] , &rwork[nrhs + 1], &work[1], &rwork[(nrhs << 1) + 1], &info); /* Check error code from ZHERFS. */ if (info != 0) { alaerh_(path, "ZHERFS", &info, &c__0, uplo, &n, & n, &c_n1, &c_n1, &nrhs, &imat, &nfail, & nerrs, nout); } zget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[4]); zpot05_(uplo, &n, &nrhs, &a[1], &lda, &b[1], &lda, &x[ 1], &lda, &xact[1], &lda, &rwork[1], &rwork[ nrhs + 1], &result[5]); /* Print information about the tests that did not pass */ /* the threshold. */ for (k = 3; k <= 7; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___42.ciunit = *nout; s_wsfe(&io___42); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&nrhs, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&imat, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&k, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&result[k - 1], (ftnlen) sizeof(doublereal)); e_wsfe(); ++nfail; } /* L120: */ } nrun += 5; /* L130: */ } /* + TEST 8 */ /* Get an estimate of RCOND = 1/CNDNUM. */ L140: anorm = zlanhe_("1", uplo, &n, &a[1], &lda, &rwork[1]); s_copy(srnamc_1.srnamt, "ZHECON", (ftnlen)6, (ftnlen)6); zhecon_(uplo, &n, &afac[1], &lda, &iwork[1], &anorm, & rcond, &work[1], &info); /* Check error code from ZHECON. */ if (info != 0) { alaerh_(path, "ZHECON", &info, &c__0, uplo, &n, &n, & c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); } result[7] = dget06_(&rcond, &rcondc); /* Print information about the tests that did not pass */ /* the threshold. */ if (result[7] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___44.ciunit = *nout; s_wsfe(&io___44); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&c__8, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&result[7], (ftnlen)sizeof( doublereal)); e_wsfe(); ++nfail; } ++nrun; L150: ; } L160: ; } L170: ; } /* L180: */ } /* Print a summary of the results. */ alasum_(path, nout, &nfail, &nrun, &nerrs); return 0; /* End of ZCHKHE */ } /* zchkhe_ */
int main(void) { /* Local scalars */ char uplo, uplo_i; lapack_int n, n_i; lapack_int lda, lda_i; lapack_int lda_r; double anorm, anorm_i; double rcond, rcond_i; lapack_int info, info_i; lapack_int i; int failed; /* Local arrays */ lapack_complex_double *a = NULL, *a_i = NULL; lapack_int *ipiv = NULL, *ipiv_i = NULL; lapack_complex_double *work = NULL, *work_i = NULL; lapack_complex_double *a_r = NULL; /* Iniitialize the scalar parameters */ init_scalars_zhecon( &uplo, &n, &lda, &anorm ); lda_r = n+2; uplo_i = uplo; n_i = n; lda_i = lda; anorm_i = anorm; /* Allocate memory for the LAPACK routine arrays */ a = (lapack_complex_double *) LAPACKE_malloc( lda*n * sizeof(lapack_complex_double) ); ipiv = (lapack_int *)LAPACKE_malloc( n * sizeof(lapack_int) ); work = (lapack_complex_double *) LAPACKE_malloc( 2*n * sizeof(lapack_complex_double) ); /* Allocate memory for the C interface function arrays */ a_i = (lapack_complex_double *) LAPACKE_malloc( lda*n * sizeof(lapack_complex_double) ); ipiv_i = (lapack_int *)LAPACKE_malloc( n * sizeof(lapack_int) ); work_i = (lapack_complex_double *) LAPACKE_malloc( 2*n * sizeof(lapack_complex_double) ); /* Allocate memory for the row-major arrays */ a_r = (lapack_complex_double *) LAPACKE_malloc( n*(n+2) * sizeof(lapack_complex_double) ); /* Initialize input arrays */ init_a( lda*n, a ); init_ipiv( n, ipiv ); init_work( 2*n, work ); /* Call the LAPACK routine */ zhecon_( &uplo, &n, a, &lda, ipiv, &anorm, &rcond, work, &info ); /* Initialize input data, call the column-major middle-level * interface to LAPACK routine and check the results */ for( i = 0; i < lda*n; i++ ) { a_i[i] = a[i]; } for( i = 0; i < n; i++ ) { ipiv_i[i] = ipiv[i]; } for( i = 0; i < 2*n; i++ ) { work_i[i] = work[i]; } info_i = LAPACKE_zhecon_work( LAPACK_COL_MAJOR, uplo_i, n_i, a_i, lda_i, ipiv_i, anorm_i, &rcond_i, work_i ); failed = compare_zhecon( rcond, rcond_i, info, info_i ); if( failed == 0 ) { printf( "PASSED: column-major middle-level interface to zhecon\n" ); } else { printf( "FAILED: column-major middle-level interface to zhecon\n" ); } /* Initialize input data, call the column-major high-level * interface to LAPACK routine and check the results */ for( i = 0; i < lda*n; i++ ) { a_i[i] = a[i]; } for( i = 0; i < n; i++ ) { ipiv_i[i] = ipiv[i]; } for( i = 0; i < 2*n; i++ ) { work_i[i] = work[i]; } info_i = LAPACKE_zhecon( LAPACK_COL_MAJOR, uplo_i, n_i, a_i, lda_i, ipiv_i, anorm_i, &rcond_i ); failed = compare_zhecon( rcond, rcond_i, info, info_i ); if( failed == 0 ) { printf( "PASSED: column-major high-level interface to zhecon\n" ); } else { printf( "FAILED: column-major high-level interface to zhecon\n" ); } /* Initialize input data, call the row-major middle-level * interface to LAPACK routine and check the results */ for( i = 0; i < lda*n; i++ ) { a_i[i] = a[i]; } for( i = 0; i < n; i++ ) { ipiv_i[i] = ipiv[i]; } for( i = 0; i < 2*n; i++ ) { work_i[i] = work[i]; } LAPACKE_zge_trans( LAPACK_COL_MAJOR, n, n, a_i, lda, a_r, n+2 ); info_i = LAPACKE_zhecon_work( LAPACK_ROW_MAJOR, uplo_i, n_i, a_r, lda_r, ipiv_i, anorm_i, &rcond_i, work_i ); failed = compare_zhecon( rcond, rcond_i, info, info_i ); if( failed == 0 ) { printf( "PASSED: row-major middle-level interface to zhecon\n" ); } else { printf( "FAILED: row-major middle-level interface to zhecon\n" ); } /* Initialize input data, call the row-major high-level * interface to LAPACK routine and check the results */ for( i = 0; i < lda*n; i++ ) { a_i[i] = a[i]; } for( i = 0; i < n; i++ ) { ipiv_i[i] = ipiv[i]; } for( i = 0; i < 2*n; i++ ) { work_i[i] = work[i]; } /* Init row_major arrays */ LAPACKE_zge_trans( LAPACK_COL_MAJOR, n, n, a_i, lda, a_r, n+2 ); info_i = LAPACKE_zhecon( LAPACK_ROW_MAJOR, uplo_i, n_i, a_r, lda_r, ipiv_i, anorm_i, &rcond_i ); failed = compare_zhecon( rcond, rcond_i, info, info_i ); if( failed == 0 ) { printf( "PASSED: row-major high-level interface to zhecon\n" ); } else { printf( "FAILED: row-major high-level interface to zhecon\n" ); } /* Release memory */ if( a != NULL ) { LAPACKE_free( a ); } if( a_i != NULL ) { LAPACKE_free( a_i ); } if( a_r != NULL ) { LAPACKE_free( a_r ); } if( ipiv != NULL ) { LAPACKE_free( ipiv ); } if( ipiv_i != NULL ) { LAPACKE_free( ipiv_i ); } if( work != NULL ) { LAPACKE_free( work ); } if( work_i != NULL ) { LAPACKE_free( work_i ); } return 0; }
/* Subroutine */ int zhesvx_(char *fact, char *uplo, integer *n, integer * nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * ldaf, integer *ipiv, doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *ferr, doublereal *berr, doublecomplex *work, integer *lwork, doublereal *rwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, x_offset, i__1, i__2; /* Local variables */ integer nb; extern logical lsame_(char *, char *); doublereal anorm; extern doublereal dlamch_(char *); logical nofact; extern /* Subroutine */ int xerbla_(char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *); extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, integer *, doublereal *); extern /* Subroutine */ int zhecon_(char *, integer *, doublecomplex *, integer *, integer *, doublereal *, doublereal *, doublecomplex *, integer *), zherfs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zhetrf_(char *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zhetrs_(char *, integer *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, integer *); integer lwkopt; logical lquery; /* -- LAPACK driver routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZHESVX uses the diagonal pivoting factorization to compute the */ /* solution to a complex system of linear equations A * X = B, */ /* where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS */ /* matrices. */ /* Error bounds on the solution and a condition estimate are also */ /* provided. */ /* Description */ /* =========== */ /* The following steps are performed: */ /* 1. If FACT = 'N', the diagonal pivoting method is used to factor A. */ /* The form of the factorization is */ /* A = U * D * U**H, if UPLO = 'U', or */ /* A = L * D * L**H, if UPLO = 'L', */ /* where U (or L) is a product of permutation and unit upper (lower) */ /* triangular matrices, and D is Hermitian and block diagonal with */ /* 1-by-1 and 2-by-2 diagonal blocks. */ /* 2. If some D(i,i)=0, so that D is exactly singular, then the routine */ /* returns with INFO = i. Otherwise, the factored form of A is used */ /* to estimate the condition number of the matrix A. If the */ /* reciprocal of the condition number is less than machine precision, */ /* INFO = N+1 is returned as a warning, but the routine still goes on */ /* to solve for X and compute error bounds as described below. */ /* 3. The system of equations is solved for X using the factored form */ /* of A. */ /* 4. Iterative refinement is applied to improve the computed solution */ /* matrix and calculate error bounds and backward error estimates */ /* for it. */ /* Arguments */ /* ========= */ /* FACT (input) CHARACTER*1 */ /* Specifies whether or not the factored form of A has been */ /* supplied on entry. */ /* = 'F': On entry, AF and IPIV contain the factored form */ /* of A. A, AF and IPIV will not be modified. */ /* = 'N': The matrix A will be copied to AF and factored. */ /* UPLO (input) CHARACTER*1 */ /* = 'U': Upper triangle of A is stored; */ /* = 'L': Lower triangle of A is stored. */ /* N (input) INTEGER */ /* The number of linear equations, i.e., the order of the */ /* matrix A. N >= 0. */ /* NRHS (input) INTEGER */ /* The number of right hand sides, i.e., the number of columns */ /* of the matrices B and X. NRHS >= 0. */ /* A (input) COMPLEX*16 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. */ /* LDA (input) INTEGER */ /* The leading dimension of the array A. LDA >= max(1,N). */ /* AF (input or output) COMPLEX*16 array, dimension (LDAF,N) */ /* If FACT = 'F', then AF is an input argument and on entry */ /* contains the block diagonal matrix D and the multipliers used */ /* to obtain the factor U or L from the factorization */ /* A = U*D*U**H or A = L*D*L**H as computed by ZHETRF. */ /* If FACT = 'N', then AF is an output argument and on exit */ /* returns the block diagonal matrix D and the multipliers used */ /* to obtain the factor U or L from the factorization */ /* A = U*D*U**H or A = L*D*L**H. */ /* LDAF (input) INTEGER */ /* The leading dimension of the array AF. LDAF >= max(1,N). */ /* IPIV (input or output) INTEGER array, dimension (N) */ /* If FACT = 'F', then IPIV is an input argument and on entry */ /* contains details of the interchanges and the block structure */ /* of D, as determined by ZHETRF. */ /* If IPIV(k) > 0, then rows and columns k and IPIV(k) were */ /* interchanged and D(k,k) is a 1-by-1 diagonal block. */ /* If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and */ /* columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) */ /* is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = */ /* IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were */ /* interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. */ /* If FACT = 'N', then IPIV is an output argument and on exit */ /* contains details of the interchanges and the block structure */ /* of D, as determined by ZHETRF. */ /* B (input) COMPLEX*16 array, dimension (LDB,NRHS) */ /* The N-by-NRHS right hand side matrix B. */ /* LDB (input) INTEGER */ /* The leading dimension of the array B. LDB >= max(1,N). */ /* X (output) COMPLEX*16 array, dimension (LDX,NRHS) */ /* If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X. */ /* LDX (input) INTEGER */ /* The leading dimension of the array X. LDX >= max(1,N). */ /* RCOND (output) DOUBLE PRECISION */ /* The estimate of the reciprocal condition number of the matrix */ /* A. If RCOND is less than the machine precision (in */ /* particular, if RCOND = 0), the matrix is singular to working */ /* precision. This condition is indicated by a return code of */ /* INFO > 0. */ /* FERR (output) DOUBLE PRECISION array, dimension (NRHS) */ /* The estimated forward error bound for each solution vector */ /* X(j) (the j-th column of the solution matrix X). */ /* If XTRUE is the true solution corresponding to X(j), FERR(j) */ /* is an estimated upper bound for the magnitude of the largest */ /* element in (X(j) - XTRUE) divided by the magnitude of the */ /* largest element in X(j). The estimate is as reliable as */ /* the estimate for RCOND, and is almost always a slight */ /* overestimate of the true error. */ /* BERR (output) 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). */ /* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) */ /* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ /* LWORK (input) INTEGER */ /* The length of WORK. LWORK >= max(1,2*N), and for best */ /* performance, when FACT = 'N', LWORK >= max(1,2*N,N*NB), where */ /* NB is the optimal blocksize for ZHETRF. */ /* If LWORK = -1, then a workspace query is assumed; the routine */ /* only calculates the optimal size of the WORK array, returns */ /* this value as the first entry of the WORK array, and no error */ /* message related to LWORK is issued by XERBLA. */ /* RWORK (workspace) DOUBLE PRECISION array, dimension (N) */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value */ /* > 0: if INFO = i, and i is */ /* <= N: D(i,i) is exactly zero. The factorization */ /* has been completed but the factor D is exactly */ /* singular, so the solution and error bounds could */ /* not be computed. RCOND = 0 is returned. */ /* = N+1: D is nonsingular, but RCOND is less than machine */ /* precision, meaning that the matrix is singular */ /* to working precision. Nevertheless, the */ /* solution and error bounds are computed because */ /* there are a number of situations where the */ /* computed solution can be more accurate than the */ /* value of RCOND would suggest. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; af_dim1 = *ldaf; af_offset = 1 + af_dim1; af -= af_offset; --ipiv; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; x_dim1 = *ldx; x_offset = 1 + x_dim1; x -= x_offset; --ferr; --berr; --work; --rwork; /* Function Body */ *info = 0; nofact = lsame_(fact, "N"); lquery = *lwork == -1; if (! nofact && ! lsame_(fact, "F")) { *info = -1; } else if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*nrhs < 0) { *info = -4; } else if (*lda < max(1,*n)) { *info = -6; } else if (*ldaf < max(1,*n)) { *info = -8; } else if (*ldb < max(1,*n)) { *info = -11; } else if (*ldx < max(1,*n)) { *info = -13; } else /* if(complicated condition) */ { /* Computing MAX */ i__1 = 1, i__2 = *n << 1; if (*lwork < max(i__1,i__2) && ! lquery) { *info = -18; } } if (*info == 0) { /* Computing MAX */ i__1 = 1, i__2 = *n << 1; lwkopt = max(i__1,i__2); if (nofact) { nb = ilaenv_(&c__1, "ZHETRF", uplo, n, &c_n1, &c_n1, &c_n1); /* Computing MAX */ i__1 = lwkopt, i__2 = *n * nb; lwkopt = max(i__1,i__2); } work[1].r = (doublereal) lwkopt, work[1].i = 0.; } if (*info != 0) { i__1 = -(*info); xerbla_("ZHESVX", &i__1); return 0; } else if (lquery) { return 0; } if (nofact) { /* Compute the factorization A = U*D*U' or A = L*D*L'. */ zlacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf); zhetrf_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &work[1], lwork, info); /* Return if INFO is non-zero. */ if (*info > 0) { *rcond = 0.; return 0; } } /* Compute the norm of the matrix A. */ anorm = zlanhe_("I", uplo, n, &a[a_offset], lda, &rwork[1]); /* Compute the reciprocal of the condition number of A. */ zhecon_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &anorm, rcond, &work[1], info); /* Compute the solution vectors X. */ zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx); zhetrs_(uplo, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &x[x_offset], ldx, info); /* Use iterative refinement to improve the computed solutions and */ /* compute error bounds and backward error estimates for them. */ zherfs_(uplo, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &ipiv[1], &b[b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[1] , &rwork[1], info); /* Set INFO = N+1 if the matrix is singular to working precision. */ if (*rcond < dlamch_("Epsilon")) { *info = *n + 1; } work[1].r = (doublereal) lwkopt, work[1].i = 0.; return 0; /* End of ZHESVX */ } /* zhesvx_ */