/* Subroutine */ int dsysvx_(char *fact, char *uplo, integer *n, integer * nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf, integer *ipiv, doublereal *b, integer *ldb, doublereal *x, integer * ldx, doublereal *rcond, doublereal *ferr, doublereal *berr, doublereal *work, integer *lwork, integer *iwork, 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 dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *), xerbla_(char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *); extern doublereal dlansy_(char *, char *, integer *, doublereal *, integer *, doublereal *); extern /* Subroutine */ int dsycon_(char *, integer *, doublereal *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *), dsyrfs_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *), dsytrf_(char *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *); integer lwkopt; logical lquery; extern /* Subroutine */ int dsytrs_(char *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *); /* -- LAPACK driver routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* DSYSVX uses the diagonal pivoting factorization to compute the */ /* solution to a real system of linear equations A * X = B, */ /* where A is an N-by-N symmetric 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**T, if UPLO = 'U', or */ /* A = L * D * L**T, if UPLO = 'L', */ /* where U (or L) is a product of permutation and unit upper (lower) */ /* triangular matrices, and D is symmetric 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. 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) DOUBLE PRECISION 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 or output) DOUBLE PRECISION 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**T or A = L*D*L**T as computed by DSYTRF. */ /* 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**T or A = L*D*L**T. */ /* 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 DSYTRF. */ /* 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 DSYTRF. */ /* B (input) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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(1,3*N), and for best */ /* performance, when FACT = 'N', LWORK >= max(1,3*N,N*NB), where */ /* NB is the optimal blocksize for DSYTRF. */ /* 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. */ /* IWORK (workspace) INTEGER 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; --iwork; /* 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 * 3; if (*lwork < max(i__1,i__2) && ! lquery) { *info = -18; } } if (*info == 0) { /* Computing MAX */ i__1 = 1, i__2 = *n * 3; lwkopt = max(i__1,i__2); if (nofact) { nb = ilaenv_(&c__1, "DSYTRF", 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] = (doublereal) lwkopt; } if (*info != 0) { i__1 = -(*info); xerbla_("DSYSVX", &i__1); return 0; } else if (lquery) { return 0; } if (nofact) { /* Compute the factorization A = U*D*U' or A = L*D*L'. */ dlacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf); dsytrf_(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 = dlansy_("I", uplo, n, &a[a_offset], lda, &work[1]); /* Compute the reciprocal of the condition number of A. */ dsycon_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &anorm, rcond, &work[1], &iwork[1], info); /* Compute the solution vectors X. */ dlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx); dsytrs_(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. */ dsyrfs_(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] , &iwork[1], info); /* Set INFO = N+1 if the matrix is singular to working precision. */ if (*rcond < dlamch_("Epsilon")) { *info = *n + 1; } work[1] = (doublereal) lwkopt; return 0; /* End of DSYSVX */ } /* dsysvx_ */
/* Subroutine */ int dchksy_(logical *dotype, integer *nn, integer *nval, integer *nnb, integer *nbval, integer *nns, integer *nsval, doublereal *thresh, logical *tsterr, integer *nmax, doublereal *a, doublereal *afac, doublereal *ainv, doublereal *b, doublereal *x, doublereal *xact, doublereal *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; /* Builtin functions Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void); /* Local variables */ static integer ioff, mode, imat, info; static char path[3], dist[1]; static integer irhs, nrhs; static char uplo[1], type__[1]; static integer nrun, i__, j, k; extern /* Subroutine */ int alahd_(integer *, char *); static integer n; extern /* Subroutine */ int dget04_(integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *); static integer nfail, iseed[4]; extern doublereal dget06_(doublereal *, doublereal *); static doublereal rcond; static integer nimat; extern /* Subroutine */ int dpot02_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *), dpot03_(char *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *), dpot05_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *); static doublereal anorm; extern /* Subroutine */ int dsyt01_(char *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *); static integer iuplo, izero, i1, i2, nerrs, lwork; static logical zerot; static char xtype[1]; extern /* Subroutine */ int dlatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, doublereal *, integer *, doublereal *, char *); static integer nb, in, kl; extern /* Subroutine */ int alaerh_(char *, char *, integer *, integer *, char *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *); static integer ku, nt; static doublereal rcondc; extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *), dlarhs_(char *, char *, char *, char *, integer *, integer *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, integer *), alasum_(char *, integer *, integer *, integer *, integer *); static doublereal cndnum; extern /* Subroutine */ int dlatms_(integer *, integer *, char *, integer *, char *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *, char *, doublereal *, integer *, doublereal *, integer *); extern doublereal dlansy_(char *, char *, integer *, doublereal *, integer *, doublereal *); static logical trfcon; extern /* Subroutine */ int xlaenv_(integer *, integer *), dsycon_(char *, integer *, doublereal *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *), derrsy_(char *, integer *), dsyrfs_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *), dsytrf_(char *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *); static doublereal result[8]; extern /* Subroutine */ int dsytri_(char *, integer *, doublereal *, integer *, integer *, doublereal *, integer *), dsytrs_( char *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *); static integer lda, inb; /* 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 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University December 7, 1999 Purpose ======= DCHKSY tests DSYTRF, -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) DOUBLE PRECISION array, dimension (NMAX*NMAX) AFAC (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) AINV (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) B (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL. X (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX) XACT (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX) WORK (workspace) DOUBLE PRECISION array, dimension (NMAX*max(3,NSMAX)) RWORK (workspace) DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX)) IWORK (workspace) INTEGER array, dimension (2*NMAX) NOUT (input) INTEGER The unit number for output. ===================================================================== Parameter adjustments */ --iwork; --rwork; --work; --xact; --x; --b; --ainv; --afac; --a; --nsval; --nbval; --nval; --dotype; /* Function Body Initialize constants and the random number seed. */ s_copy(path, "Double precision", (ftnlen)1, (ftnlen)16); s_copy(path + 1, "SY", (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) { derrsy_(path, nout); } infoc_1.infot = 0; xlaenv_(&c__2, &c__2); /* 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 DLATB4 and generate a test matrix with DLATMS. */ dlatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, &cndnum, dist); s_copy(srnamc_1.srnamt, "DLATMS", (ftnlen)6, (ftnlen)6); dlatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, & cndnum, &anorm, &kl, &ku, uplo, &a[1], &lda, &work[1], &info); /* Check error code from DLATMS. */ if (info != 0) { alaerh_(path, "DLATMS", &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__) { a[ioff + i__] = 0.; /* L20: */ } ioff += izero; i__3 = n; for (i__ = izero; i__ <= i__3; ++i__) { a[ioff] = 0.; ioff += lda; /* L30: */ } } else { ioff = izero; i__3 = izero - 1; for (i__ = 1; i__ <= i__3; ++i__) { a[ioff] = 0.; ioff += lda; /* L40: */ } ioff -= izero; i__3 = n; for (i__ = izero; i__ <= i__3; ++i__) { a[ioff + 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__) { a[ioff + 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__) { a[ioff + i__] = 0.; /* L80: */ } ioff += lda; /* L90: */ } } } } else { izero = 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. */ dlacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda); lwork = max(2,nb) * lda; s_copy(srnamc_1.srnamt, "DSYTRF", (ftnlen)6, (ftnlen)6); dsytrf_(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 DSYTRF. */ if (info != k) { alaerh_(path, "DSYTRF", &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. */ dsyt01_(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) { dlacpy_(uplo, &n, &n, &afac[1], &lda, &ainv[1], &lda); s_copy(srnamc_1.srnamt, "DSYTRI", (ftnlen)6, (ftnlen) 6); dsytri_(uplo, &n, &ainv[1], &lda, &iwork[1], &work[1], &info); /* Check error code from DSYTRI. */ if (info != 0) { alaerh_(path, "DSYTRI", &info, &c_n1, uplo, &n, & n, &c_n1, &c_n1, &c_n1, &imat, &nfail, & nerrs, nout); } dpot03_(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, "DLARHS", (ftnlen)6, (ftnlen) 6); dlarhs_(path, xtype, uplo, " ", &n, &n, &kl, &ku, & nrhs, &a[1], &lda, &xact[1], &lda, &b[1], & lda, iseed, &info); dlacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &lda); s_copy(srnamc_1.srnamt, "DSYTRS", (ftnlen)6, (ftnlen) 6); dsytrs_(uplo, &n, &nrhs, &afac[1], &lda, &iwork[1], & x[1], &lda, &info); /* Check error code from DSYTRS. */ if (info != 0) { alaerh_(path, "DSYTRS", &info, &c__0, uplo, &n, & n, &c_n1, &c_n1, &nrhs, &imat, &nfail, & nerrs, nout); } dlacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], & lda); dpot02_(uplo, &n, &nrhs, &a[1], &lda, &x[1], &lda, & work[1], &lda, &rwork[1], &result[2]); /* + TEST 4 Check solution from generated exact solution. */ dget04_(&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, "DSYRFS", (ftnlen)6, (ftnlen) 6); dsyrfs_(uplo, &n, &nrhs, &a[1], &lda, &afac[1], &lda, &iwork[1], &b[1], &lda, &x[1], &lda, &rwork[1] , &rwork[nrhs + 1], &work[1], &iwork[n + 1], & info); /* Check error code from DSYRFS. */ if (info != 0) { alaerh_(path, "DSYRFS", &info, &c__0, uplo, &n, & n, &c_n1, &c_n1, &nrhs, &imat, &nfail, & nerrs, nout); } dget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[4]); dpot05_(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 = dlansy_("1", uplo, &n, &a[1], &lda, &rwork[1]); s_copy(srnamc_1.srnamt, "DSYCON", (ftnlen)6, (ftnlen)6); dsycon_(uplo, &n, &afac[1], &lda, &iwork[1], &anorm, & rcond, &work[1], &iwork[n + 1], &info); /* Check error code from DSYCON. */ if (info != 0) { alaerh_(path, "DSYCON", &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 DCHKSY */ } /* dchksy_ */
/* Subroutine */ int derrsy_(char *path, integer *nunit) { /* Builtin functions */ integer s_wsle(cilist *), e_wsle(void); /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); /* Local variables */ static integer info; static doublereal anrm, a[16] /* was [4][4] */, b[4]; static integer i__, j; static doublereal w[12], x[4], rcond; static char c2[2]; static doublereal r1[4], r2[4], af[16] /* was [4][4] */; extern /* Subroutine */ int dsytf2_(char *, integer *, doublereal *, integer *, integer *, integer *); static integer ip[4], iw[4]; extern /* Subroutine */ int alaesm_(char *, logical *, integer *); extern logical lsamen_(integer *, char *, char *); extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical *, logical *), dspcon_(char *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *), dsycon_(char *, integer *, doublereal *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *), dsprfs_(char *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal * , integer *, integer *), dsptrf_(char *, integer *, doublereal *, integer *, integer *), dsptri_(char *, integer *, doublereal *, integer *, doublereal *, integer *), dsyrfs_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *), dsytrf_(char *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *), dsytri_(char *, integer *, doublereal *, integer *, integer *, doublereal *, integer *), dsptrs_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *), dsytrs_( char *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *); /* Fortran I/O blocks */ static cilist io___1 = { 0, 0, 0, 0, 0 }; #define a_ref(a_1,a_2) a[(a_2)*4 + a_1 - 5] #define af_ref(a_1,a_2) af[(a_2)*4 + a_1 - 5] /* -- LAPACK test routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University February 29, 1992 Purpose ======= DERRSY tests the error exits for the DOUBLE PRECISION routines for symmetric indefinite matrices. Arguments ========= PATH (input) CHARACTER*3 The LAPACK path name for the routines to be tested. NUNIT (input) INTEGER The unit number for output. ===================================================================== */ infoc_1.nout = *nunit; io___1.ciunit = infoc_1.nout; s_wsle(&io___1); e_wsle(); s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2); /* Set the variables to innocuous values. */ for (j = 1; j <= 4; ++j) { for (i__ = 1; i__ <= 4; ++i__) { a_ref(i__, j) = 1. / (doublereal) (i__ + j); af_ref(i__, j) = 1. / (doublereal) (i__ + j); /* L10: */ } b[j - 1] = 0.; r1[j - 1] = 0.; r2[j - 1] = 0.; w[j - 1] = 0.; x[j - 1] = 0.; ip[j - 1] = j; iw[j - 1] = j; /* L20: */ } anrm = 1.; rcond = 1.; infoc_1.ok = TRUE_; if (lsamen_(&c__2, c2, "SY")) { /* Test error exits of the routines that use the Bunch-Kaufman factorization of a symmetric indefinite matrix. DSYTRF */ s_copy(srnamc_1.srnamt, "DSYTRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dsytrf_("/", &c__0, a, &c__1, ip, w, &c__1, &info); chkxer_("DSYTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dsytrf_("U", &c_n1, a, &c__1, ip, w, &c__1, &info); chkxer_("DSYTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dsytrf_("U", &c__2, a, &c__1, ip, w, &c__4, &info); chkxer_("DSYTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DSYTF2 */ s_copy(srnamc_1.srnamt, "DSYTF2", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dsytf2_("/", &c__0, a, &c__1, ip, &info); chkxer_("DSYTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dsytf2_("U", &c_n1, a, &c__1, ip, &info); chkxer_("DSYTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dsytf2_("U", &c__2, a, &c__1, ip, &info); chkxer_("DSYTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DSYTRI */ s_copy(srnamc_1.srnamt, "DSYTRI", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dsytri_("/", &c__0, a, &c__1, ip, w, &info); chkxer_("DSYTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dsytri_("U", &c_n1, a, &c__1, ip, w, &info); chkxer_("DSYTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dsytri_("U", &c__2, a, &c__1, ip, w, &info); chkxer_("DSYTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DSYTRS */ s_copy(srnamc_1.srnamt, "DSYTRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dsytrs_("/", &c__0, &c__0, a, &c__1, ip, b, &c__1, &info); chkxer_("DSYTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dsytrs_("U", &c_n1, &c__0, a, &c__1, ip, b, &c__1, &info); chkxer_("DSYTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dsytrs_("U", &c__0, &c_n1, a, &c__1, ip, b, &c__1, &info); chkxer_("DSYTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; dsytrs_("U", &c__2, &c__1, a, &c__1, ip, b, &c__2, &info); chkxer_("DSYTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 8; dsytrs_("U", &c__2, &c__1, a, &c__2, ip, b, &c__1, &info); chkxer_("DSYTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DSYRFS */ s_copy(srnamc_1.srnamt, "DSYRFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dsyrfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, & c__1, r1, r2, w, iw, &info); chkxer_("DSYRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dsyrfs_("U", &c_n1, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, & c__1, r1, r2, w, iw, &info); chkxer_("DSYRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dsyrfs_("U", &c__0, &c_n1, a, &c__1, af, &c__1, ip, b, &c__1, x, & c__1, r1, r2, w, iw, &info); chkxer_("DSYRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; dsyrfs_("U", &c__2, &c__1, a, &c__1, af, &c__2, ip, b, &c__2, x, & c__2, r1, r2, w, iw, &info); chkxer_("DSYRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; dsyrfs_("U", &c__2, &c__1, a, &c__2, af, &c__1, ip, b, &c__2, x, & c__2, r1, r2, w, iw, &info); chkxer_("DSYRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 10; dsyrfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__1, x, & c__2, r1, r2, w, iw, &info); chkxer_("DSYRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 12; dsyrfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__2, x, & c__1, r1, r2, w, iw, &info); chkxer_("DSYRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DSYCON */ s_copy(srnamc_1.srnamt, "DSYCON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dsycon_("/", &c__0, a, &c__1, ip, &anrm, &rcond, w, iw, &info); chkxer_("DSYCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dsycon_("U", &c_n1, a, &c__1, ip, &anrm, &rcond, w, iw, &info); chkxer_("DSYCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dsycon_("U", &c__2, a, &c__1, ip, &anrm, &rcond, w, iw, &info); chkxer_("DSYCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; dsycon_("U", &c__1, a, &c__1, ip, &c_b152, &rcond, w, iw, &info); chkxer_("DSYCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); } else if (lsamen_(&c__2, c2, "SP")) { /* Test error exits of the routines that use the Bunch-Kaufman factorization of a symmetric indefinite packed matrix. DSPTRF */ s_copy(srnamc_1.srnamt, "DSPTRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dsptrf_("/", &c__0, a, ip, &info); chkxer_("DSPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dsptrf_("U", &c_n1, a, ip, &info); chkxer_("DSPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DSPTRI */ s_copy(srnamc_1.srnamt, "DSPTRI", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dsptri_("/", &c__0, a, ip, w, &info); chkxer_("DSPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dsptri_("U", &c_n1, a, ip, w, &info); chkxer_("DSPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DSPTRS */ s_copy(srnamc_1.srnamt, "DSPTRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dsptrs_("/", &c__0, &c__0, a, ip, b, &c__1, &info); chkxer_("DSPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dsptrs_("U", &c_n1, &c__0, a, ip, b, &c__1, &info); chkxer_("DSPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dsptrs_("U", &c__0, &c_n1, a, ip, b, &c__1, &info); chkxer_("DSPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; dsptrs_("U", &c__2, &c__1, a, ip, b, &c__1, &info); chkxer_("DSPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DSPRFS */ s_copy(srnamc_1.srnamt, "DSPRFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dsprfs_("/", &c__0, &c__0, a, af, ip, b, &c__1, x, &c__1, r1, r2, w, iw, &info); chkxer_("DSPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dsprfs_("U", &c_n1, &c__0, a, af, ip, b, &c__1, x, &c__1, r1, r2, w, iw, &info); chkxer_("DSPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dsprfs_("U", &c__0, &c_n1, a, af, ip, b, &c__1, x, &c__1, r1, r2, w, iw, &info); chkxer_("DSPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 8; dsprfs_("U", &c__2, &c__1, a, af, ip, b, &c__1, x, &c__2, r1, r2, w, iw, &info); chkxer_("DSPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 10; dsprfs_("U", &c__2, &c__1, a, af, ip, b, &c__2, x, &c__1, r1, r2, w, iw, &info); chkxer_("DSPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DSPCON */ s_copy(srnamc_1.srnamt, "DSPCON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dspcon_("/", &c__0, a, ip, &anrm, &rcond, w, iw, &info); chkxer_("DSPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dspcon_("U", &c_n1, a, ip, &anrm, &rcond, w, iw, &info); chkxer_("DSPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; dspcon_("U", &c__1, a, ip, &c_b152, &rcond, w, iw, &info); chkxer_("DSPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); } /* Print a summary line. */ alaesm_(path, &infoc_1.ok, &infoc_1.nout); return 0; /* End of DERRSY */ } /* derrsy_ */