Beispiel #1
0
/* Subroutine */ int serrgt_(char *path, integer *nunit)
{
    /* System generated locals */
    real r__1;

    /* Builtin functions */
    integer s_wsle(cilist *), e_wsle(void);
    /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);

    /* Local variables */
    real b[2], c__[2], d__[2], e[2], f[2], w[2], x[2];
    char c2[2];
    real r1[2], r2[2], cf[2], df[2], ef[2];
    integer ip[2], iw[2], info;
    real rcond, anorm;
    extern /* Subroutine */ int alaesm_(char *, logical *, integer *);
    extern logical lsamen_(integer *, char *, char *);
    extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical 
	    *, logical *), sgtcon_(char *, integer *, real *, real *, 
	    real *, real *, integer *, real *, real *, real *, integer *, 
	    integer *), sptcon_(integer *, real *, real *, real *, 
	    real *, real *, integer *), sgtrfs_(char *, integer *, integer *, 
	    real *, real *, real *, real *, real *, real *, real *, integer *, 
	     real *, integer *, real *, integer *, real *, real *, real *, 
	    integer *, integer *), sgttrf_(integer *, real *, real *, 
	    real *, real *, integer *, integer *), sptrfs_(integer *, integer 
	    *, real *, real *, real *, real *, real *, integer *, real *, 
	    integer *, real *, real *, real *, integer *), spttrf_(integer *, 
	    real *, real *, integer *), sgttrs_(char *, integer *, integer *, 
	    real *, real *, real *, real *, integer *, real *, integer *, 
	    integer *), spttrs_(integer *, integer *, real *, real *, 
	    real *, integer *, integer *);

    /* Fortran I/O blocks */
    static cilist io___1 = { 0, 0, 0, 0, 0 };



/*  -- LAPACK test routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  SERRGT tests the error exits for the REAL tridiagonal */
/*  routines. */

/*  Arguments */
/*  ========= */

/*  PATH    (input) CHARACTER*3 */
/*          The LAPACK path name for the routines to be tested. */

/*  NUNIT   (input) INTEGER */
/*          The unit number for output. */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Local Arrays .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Scalars in Common .. */
/*     .. */
/*     .. Common blocks .. */
/*     .. */
/*     .. Executable Statements .. */

    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);
    d__[0] = 1.f;
    d__[1] = 2.f;
    df[0] = 1.f;
    df[1] = 2.f;
    e[0] = 3.f;
    e[1] = 4.f;
    ef[0] = 3.f;
    ef[1] = 4.f;
    anorm = 1.f;
    infoc_1.ok = TRUE_;

    if (lsamen_(&c__2, c2, "GT")) {

/*        Test error exits for the general tridiagonal routines. */

/*        SGTTRF */

	s_copy(srnamc_1.srnamt, "SGTTRF", (ftnlen)32, (ftnlen)6);
	infoc_1.infot = 1;
	sgttrf_(&c_n1, c__, d__, e, f, ip, &info);
	chkxer_("SGTTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        SGTTRS */

	s_copy(srnamc_1.srnamt, "SGTTRS", (ftnlen)32, (ftnlen)6);
	infoc_1.infot = 1;
	sgttrs_("/", &c__0, &c__0, c__, d__, e, f, ip, x, &c__1, &info);
	chkxer_("SGTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	sgttrs_("N", &c_n1, &c__0, c__, d__, e, f, ip, x, &c__1, &info);
	chkxer_("SGTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	sgttrs_("N", &c__0, &c_n1, c__, d__, e, f, ip, x, &c__1, &info);
	chkxer_("SGTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 10;
	sgttrs_("N", &c__2, &c__1, c__, d__, e, f, ip, x, &c__1, &info);
	chkxer_("SGTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        SGTRFS */

	s_copy(srnamc_1.srnamt, "SGTRFS", (ftnlen)32, (ftnlen)6);
	infoc_1.infot = 1;
	sgtrfs_("/", &c__0, &c__0, c__, d__, e, cf, df, ef, f, ip, b, &c__1, 
		x, &c__1, r1, r2, w, iw, &info);
	chkxer_("SGTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	sgtrfs_("N", &c_n1, &c__0, c__, d__, e, cf, df, ef, f, ip, b, &c__1, 
		x, &c__1, r1, r2, w, iw, &info);
	chkxer_("SGTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	sgtrfs_("N", &c__0, &c_n1, c__, d__, e, cf, df, ef, f, ip, b, &c__1, 
		x, &c__1, r1, r2, w, iw, &info);
	chkxer_("SGTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 13;
	sgtrfs_("N", &c__2, &c__1, c__, d__, e, cf, df, ef, f, ip, b, &c__1, 
		x, &c__2, r1, r2, w, iw, &info);
	chkxer_("SGTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 15;
	sgtrfs_("N", &c__2, &c__1, c__, d__, e, cf, df, ef, f, ip, b, &c__2, 
		x, &c__1, r1, r2, w, iw, &info);
	chkxer_("SGTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        SGTCON */

	s_copy(srnamc_1.srnamt, "SGTCON", (ftnlen)32, (ftnlen)6);
	infoc_1.infot = 1;
	sgtcon_("/", &c__0, c__, d__, e, f, ip, &anorm, &rcond, w, iw, &info);
	chkxer_("SGTCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	sgtcon_("I", &c_n1, c__, d__, e, f, ip, &anorm, &rcond, w, iw, &info);
	chkxer_("SGTCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 8;
	r__1 = -anorm;
	sgtcon_("I", &c__0, c__, d__, e, f, ip, &r__1, &rcond, w, iw, &info);
	chkxer_("SGTCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

    } else if (lsamen_(&c__2, c2, "PT")) {

/*        Test error exits for the positive definite tridiagonal */
/*        routines. */

/*        SPTTRF */

	s_copy(srnamc_1.srnamt, "SPTTRF", (ftnlen)32, (ftnlen)6);
	infoc_1.infot = 1;
	spttrf_(&c_n1, d__, e, &info);
	chkxer_("SPTTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        SPTTRS */

	s_copy(srnamc_1.srnamt, "SPTTRS", (ftnlen)32, (ftnlen)6);
	infoc_1.infot = 1;
	spttrs_(&c_n1, &c__0, d__, e, x, &c__1, &info);
	chkxer_("SPTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	spttrs_(&c__0, &c_n1, d__, e, x, &c__1, &info);
	chkxer_("SPTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 6;
	spttrs_(&c__2, &c__1, d__, e, x, &c__1, &info);
	chkxer_("SPTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        SPTRFS */

	s_copy(srnamc_1.srnamt, "SPTRFS", (ftnlen)32, (ftnlen)6);
	infoc_1.infot = 1;
	sptrfs_(&c_n1, &c__0, d__, e, df, ef, b, &c__1, x, &c__1, r1, r2, w, &
		info);
	chkxer_("SPTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	sptrfs_(&c__0, &c_n1, d__, e, df, ef, b, &c__1, x, &c__1, r1, r2, w, &
		info);
	chkxer_("SPTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 8;
	sptrfs_(&c__2, &c__1, d__, e, df, ef, b, &c__1, x, &c__2, r1, r2, w, &
		info);
	chkxer_("SPTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 10;
	sptrfs_(&c__2, &c__1, d__, e, df, ef, b, &c__2, x, &c__1, r1, r2, w, &
		info);
	chkxer_("SPTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        SPTCON */

	s_copy(srnamc_1.srnamt, "SPTCON", (ftnlen)32, (ftnlen)6);
	infoc_1.infot = 1;
	sptcon_(&c_n1, d__, e, &anorm, &rcond, w, &info);
	chkxer_("SPTCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	r__1 = -anorm;
	sptcon_(&c__0, d__, e, &r__1, &rcond, w, &info);
	chkxer_("SPTCON", &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 SERRGT */

} /* serrgt_ */
Beispiel #2
0
/* Subroutine */ int sgtsvx_(char *fact, char *trans, integer *n, integer *
	nrhs, real *dl, real *d, real *du, real *dlf, real *df, real *duf, 
	real *du2, integer *ipiv, real *b, integer *ldb, real *x, integer *
	ldx, real *rcond, real *ferr, real *berr, real *work, integer *iwork, 
	integer *info)
{
/*  -- LAPACK routine (version 2.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       September 30, 1994   


    Purpose   
    =======   

    SGTSVX uses the LU factorization to compute the solution to a real   
    system of linear equations A * X = B or A**T * X = B,   
    where A is a tridiagonal matrix of order N 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 LU decomposition is used to factor the matrix A 
  
       as A = L * U, where L is a product of permutation and unit lower   
       bidiagonal matrices and U is upper triangular with nonzeros in   
       only the main diagonal and first two superdiagonals.   

    2. 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, steps 3 and 4 are skipped.   

    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':  DLF, DF, DUF, DU2, and IPIV contain the factored   
                    form of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV   
                    will not be modified.   
            = 'N':  The matrix will be copied to DLF, DF, and DUF   
                    and factored.   

    TRANS   (input) CHARACTER*1   
            Specifies the form of the system of equations:   
            = 'N':  A * X = B     (No transpose)   
            = 'T':  A**T * X = B  (Transpose)   
            = 'C':  A**H * X = B  (Conjugate transpose = Transpose)   

    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 matrix B.  NRHS >= 0.   

    DL      (input) REAL array, dimension (N-1)   
            The (n-1) subdiagonal elements of A.   

    D       (input) REAL array, dimension (N)   
            The n diagonal elements of A.   

    DU      (input) REAL array, dimension (N-1)   
            The (n-1) superdiagonal elements of A.   

    DLF     (input or output) REAL array, dimension (N-1)   
            If FACT = 'F', then DLF is an input argument and on entry   
            contains the (n-1) multipliers that define the matrix L from 
  
            the LU factorization of A as computed by SGTTRF.   

            If FACT = 'N', then DLF is an output argument and on exit   
            contains the (n-1) multipliers that define the matrix L from 
  
            the LU factorization of A.   

    DF      (input or output) REAL array, dimension (N)   
            If FACT = 'F', then DF is an input argument and on entry   
            contains the n diagonal elements of the upper triangular   
            matrix U from the LU factorization of A.   

            If FACT = 'N', then DF is an output argument and on exit   
            contains the n diagonal elements of the upper triangular   
            matrix U from the LU factorization of A.   

    DUF     (input or output) REAL array, dimension (N-1)   
            If FACT = 'F', then DUF is an input argument and on entry   
            contains the (n-1) elements of the first superdiagonal of U. 
  

            If FACT = 'N', then DUF is an output argument and on exit   
            contains the (n-1) elements of the first superdiagonal of U. 
  

    DU2     (input or output) REAL array, dimension (N-2)   
            If FACT = 'F', then DU2 is an input argument and on entry   
            contains the (n-2) elements of the second superdiagonal of   
            U.   

            If FACT = 'N', then DU2 is an output argument and on exit   
            contains the (n-2) elements of the second superdiagonal of   
            U.   

    IPIV    (input or output) INTEGER array, dimension (N)   
            If FACT = 'F', then IPIV is an input argument and on entry   
            contains the pivot indices from the LU factorization of A as 
  
            computed by SGTTRF.   

            If FACT = 'N', then IPIV is an output argument and on exit   
            contains the pivot indices from the LU factorization of A;   
            row i of the matrix was interchanged with row IPIV(i).   
            IPIV(i) will always be either i or i+1; IPIV(i) = i indicates 
  
            a row interchange was not required.   

    B       (input) REAL 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) REAL array, dimension (LDX,NRHS)   
            If INFO = 0, the N-by-NRHS solution matrix X.   

    LDX     (input) INTEGER   
            The leading dimension of the array X.  LDX >= max(1,N).   

    RCOND   (output) REAL   
            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, and the solution and error bounds are not computed. 
  

    FERR    (output) 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.   

    BERR    (output) 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).   

    WORK    (workspace) REAL array, dimension (3*N)   

    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:  U(i,i) is exactly zero.  The factorization   
                         has not been completed unless i = N, but the   
                         factor U is exactly singular, so the solution   
                         and error bounds could not be computed.   
                 = N+1:  RCOND is less than machine precision.  The   
                         factorization has been completed, but the   
                         matrix is singular to working precision, and   
                         the solution and error bounds have not been   
                         computed.   

    ===================================================================== 
  


    
   Parameter adjustments   
       Function Body */
    /* Table of constant values */
    static integer c__1 = 1;
    
    /* System generated locals */
    integer b_dim1, b_offset, x_dim1, x_offset, i__1;
    /* Local variables */
    static char norm[1];
    extern logical lsame_(char *, char *);
    static real anorm;
    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
	    integer *);
    extern doublereal slamch_(char *);
    static logical nofact;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern doublereal slangt_(char *, integer *, real *, real *, real *);
    extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, 
	    integer *, real *, integer *), sgtcon_(char *, integer *, 
	    real *, real *, real *, real *, integer *, real *, real *, real *,
	     integer *, integer *);
    static logical notran;
    extern /* Subroutine */ int sgtrfs_(char *, integer *, integer *, real *, 
	    real *, real *, real *, real *, real *, real *, integer *, real *,
	     integer *, real *, integer *, real *, real *, real *, integer *, 
	    integer *), sgttrf_(integer *, real *, real *, real *, 
	    real *, integer *, integer *), sgttrs_(char *, integer *, integer 
	    *, real *, real *, real *, real *, integer *, real *, integer *, 
	    integer *);



#define DL(I) dl[(I)-1]
#define D(I) d[(I)-1]
#define DU(I) du[(I)-1]
#define DLF(I) dlf[(I)-1]
#define DF(I) df[(I)-1]
#define DUF(I) duf[(I)-1]
#define DU2(I) du2[(I)-1]
#define IPIV(I) ipiv[(I)-1]
#define FERR(I) ferr[(I)-1]
#define BERR(I) berr[(I)-1]
#define WORK(I) work[(I)-1]
#define IWORK(I) iwork[(I)-1]

#define B(I,J) b[(I)-1 + ((J)-1)* ( *ldb)]
#define X(I,J) x[(I)-1 + ((J)-1)* ( *ldx)]

    *info = 0;
    nofact = lsame_(fact, "N");
    notran = lsame_(trans, "N");
    if (! nofact && ! lsame_(fact, "F")) {
	*info = -1;
    } else if (! notran && ! lsame_(trans, "T") && ! lsame_(trans, 
	    "C")) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*nrhs < 0) {
	*info = -4;
    } else if (*ldb < max(1,*n)) {
	*info = -14;
    } else if (*ldx < max(1,*n)) {
	*info = -16;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SGTSVX", &i__1);
	return 0;
    }

    if (nofact) {

/*        Compute the LU factorization of A. */

	scopy_(n, &D(1), &c__1, &DF(1), &c__1);
	if (*n > 1) {
	    i__1 = *n - 1;
	    scopy_(&i__1, &DL(1), &c__1, &DLF(1), &c__1);
	    i__1 = *n - 1;
	    scopy_(&i__1, &DU(1), &c__1, &DUF(1), &c__1);
	}
	sgttrf_(n, &DLF(1), &DF(1), &DUF(1), &DU2(1), &IPIV(1), info);

/*        Return if INFO is non-zero. */

	if (*info != 0) {
	    if (*info > 0) {
		*rcond = 0.f;
	    }
	    return 0;
	}
    }

/*     Compute the norm of the matrix A. */

    if (notran) {
	*(unsigned char *)norm = '1';
    } else {
	*(unsigned char *)norm = 'I';
    }
    anorm = slangt_(norm, n, &DL(1), &D(1), &DU(1));

/*     Compute the reciprocal of the condition number of A. */

    sgtcon_(norm, n, &DLF(1), &DF(1), &DUF(1), &DU2(1), &IPIV(1), &anorm, 
	    rcond, &WORK(1), &IWORK(1), info);

/*     Return if the matrix is singular to working precision. */

    if (*rcond < slamch_("Epsilon")) {
	*info = *n + 1;
	return 0;
    }

/*     Compute the solution vectors X. */

    slacpy_("Full", n, nrhs, &B(1,1), ldb, &X(1,1), ldx);
    sgttrs_(trans, n, nrhs, &DLF(1), &DF(1), &DUF(1), &DU2(1), &IPIV(1), &X(1,1), ldx, info);

/*     Use iterative refinement to improve the computed solutions and   
       compute error bounds and backward error estimates for them. */

    sgtrfs_(trans, n, nrhs, &DL(1), &D(1), &DU(1), &DLF(1), &DF(1), &DUF(1), &
	    DU2(1), &IPIV(1), &B(1,1), ldb, &X(1,1), ldx, &FERR(1), 
	    &BERR(1), &WORK(1), &IWORK(1), info);

    return 0;

/*     End of SGTSVX */

} /* sgtsvx_ */
Beispiel #3
0
/* Subroutine */ int schkgt_(logical *dotype, integer *nn, integer *nval, 
	integer *nns, integer *nsval, real *thresh, logical *tsterr, real *a, 
	real *af, real *b, real *x, real *xact, real *work, real *rwork, 
	integer *iwork, integer *nout)
{
    /* Initialized data */

    static integer iseedy[4] = { 0,0,0,1 };
    static char transs[1*3] = "N" "T" "C";

    /* Format strings */
    static char fmt_9999[] = "(12x,\002N =\002,i5,\002,\002,10x,\002 type"
	    " \002,i2,\002, test(\002,i2,\002) = \002,g12.5)";
    static char fmt_9997[] = "(\002 NORM ='\002,a1,\002', N =\002,i5,\002"
	    ",\002,10x,\002 type \002,i2,\002, test(\002,i2,\002) = \002,g12."
	    "5)";
    static char fmt_9998[] = "(\002 TRANS='\002,a1,\002', N =\002,i5,\002, N"
	    "RHS=\002,i3,\002, type \002,i2,\002, test(\002,i2,\002) = \002,g"
	    "12.5)";

    /* System generated locals */
    integer i__1, i__2, i__3, i__4;
    real r__1, r__2;

    /* Local variables */
    integer i__, j, k, m, n;
    real z__[3];
    integer in, kl, ku, ix, lda;
    real cond;
    integer mode, koff, imat, info;
    char path[3], dist[1];
    integer irhs, nrhs;
    char norm[1], type__[1];
    integer nrun;
    integer nfail, iseed[4];
    real rcond;
    integer nimat;
    real anorm;
    integer itran;
    char trans[1];
    integer izero, nerrs;
    logical zerot;
    real rcondc, rcondi, rcondo;
    real ainvnm;
    logical trfcon;
    real result[7];

    /* Fortran I/O blocks */
    static cilist io___29 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___39 = { 0, 0, 0, fmt_9997, 0 };
    static cilist io___44 = { 0, 0, 0, fmt_9998, 0 };



/*  -- LAPACK test routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  SCHKGT tests SGTTRF, -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. */

/*  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) REAL */
/*          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. */

/*  A       (workspace) REAL array, dimension (NMAX*4) */

/*  AF      (workspace) REAL array, dimension (NMAX*4) */

/*  B       (workspace) REAL array, dimension (NMAX*NSMAX) */
/*          where NSMAX is the largest entry in NSVAL. */

/*  X       (workspace) REAL array, dimension (NMAX*NSMAX) */

/*  XACT    (workspace) REAL array, dimension (NMAX*NSMAX) */

/*  WORK    (workspace) REAL array, dimension */
/*                      (NMAX*max(3,NSMAX)) */

/*  RWORK   (workspace) REAL array, dimension */
/*                      (max(NMAX,2*NSMAX)) */

/*  IWORK   (workspace) INTEGER array, dimension (2*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;
    --af;
    --a;
    --nsval;
    --nval;
    --dotype;

    /* Function Body */
/*     .. */
/*     .. Executable Statements .. */

    s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16);
    s_copy(path + 1, "GT", (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) {
	serrge_(path, nout);
    }
    infoc_1.infot = 0;

    i__1 = *nn;
    for (in = 1; in <= i__1; ++in) {

/*        Do for each value of N in NVAL. */

	n = nval[in];
/* Computing MAX */
	i__2 = n - 1;
	m = max(i__2,0);
	lda = max(1,n);
	nimat = 12;
	if (n <= 0) {
	    nimat = 1;
	}

	i__2 = nimat;
	for (imat = 1; imat <= i__2; ++imat) {

/*           Do the tests only if DOTYPE( IMAT ) is true. */

	    if (! dotype[imat]) {
		goto L100;
	    }

/*           Set up parameters with SLATB4. */

	    slatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, &
		    cond, dist);

	    zerot = imat >= 8 && imat <= 10;
	    if (imat <= 6) {

/*              Types 1-6:  generate matrices of known condition number. */

/* Computing MAX */
		i__3 = 2 - ku, i__4 = 3 - max(1,n);
		koff = max(i__3,i__4);
		s_copy(srnamc_1.srnamt, "SLATMS", (ftnlen)32, (ftnlen)6);
		slatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &cond, 
			&anorm, &kl, &ku, "Z", &af[koff], &c__3, &work[1], &
			info);

/*              Check the error code from SLATMS. */

		if (info != 0) {
		    alaerh_(path, "SLATMS", &info, &c__0, " ", &n, &n, &kl, &
			    ku, &c_n1, &imat, &nfail, &nerrs, nout);
		    goto L100;
		}
		izero = 0;

		if (n > 1) {
		    i__3 = n - 1;
		    scopy_(&i__3, &af[4], &c__3, &a[1], &c__1);
		    i__3 = n - 1;
		    scopy_(&i__3, &af[3], &c__3, &a[n + m + 1], &c__1);
		}
		scopy_(&n, &af[2], &c__3, &a[m + 1], &c__1);
	    } else {

/*              Types 7-12:  generate tridiagonal matrices with */
/*              unknown condition numbers. */

		if (! zerot || ! dotype[7]) {

/*                 Generate a matrix with elements from [-1,1]. */

		    i__3 = n + (m << 1);
		    slarnv_(&c__2, iseed, &i__3, &a[1]);
		    if (anorm != 1.f) {
			i__3 = n + (m << 1);
			sscal_(&i__3, &anorm, &a[1], &c__1);
		    }
		} else if (izero > 0) {

/*                 Reuse the last matrix by copying back the zeroed out */
/*                 elements. */

		    if (izero == 1) {
			a[n] = z__[1];
			if (n > 1) {
			    a[1] = z__[2];
			}
		    } else if (izero == n) {
			a[n * 3 - 2] = z__[0];
			a[(n << 1) - 1] = z__[1];
		    } else {
			a[(n << 1) - 2 + izero] = z__[0];
			a[n - 1 + izero] = z__[1];
			a[izero] = z__[2];
		    }
		}

/*              If IMAT > 7, set one column of the matrix to 0. */

		if (! zerot) {
		    izero = 0;
		} else if (imat == 8) {
		    izero = 1;
		    z__[1] = a[n];
		    a[n] = 0.f;
		    if (n > 1) {
			z__[2] = a[1];
			a[1] = 0.f;
		    }
		} else if (imat == 9) {
		    izero = n;
		    z__[0] = a[n * 3 - 2];
		    z__[1] = a[(n << 1) - 1];
		    a[n * 3 - 2] = 0.f;
		    a[(n << 1) - 1] = 0.f;
		} else {
		    izero = (n + 1) / 2;
		    i__3 = n - 1;
		    for (i__ = izero; i__ <= i__3; ++i__) {
			a[(n << 1) - 2 + i__] = 0.f;
			a[n - 1 + i__] = 0.f;
			a[i__] = 0.f;
/* L20: */
		    }
		    a[n * 3 - 2] = 0.f;
		    a[(n << 1) - 1] = 0.f;
		}
	    }

/* +    TEST 1 */
/*           Factor A as L*U and compute the ratio */
/*              norm(L*U - A) / (n * norm(A) * EPS ) */

	    i__3 = n + (m << 1);
	    scopy_(&i__3, &a[1], &c__1, &af[1], &c__1);
	    s_copy(srnamc_1.srnamt, "SGTTRF", (ftnlen)32, (ftnlen)6);
	    sgttrf_(&n, &af[1], &af[m + 1], &af[n + m + 1], &af[n + (m << 1) 
		    + 1], &iwork[1], &info);

/*           Check error code from SGTTRF. */

	    if (info != izero) {
		alaerh_(path, "SGTTRF", &info, &izero, " ", &n, &n, &c__1, &
			c__1, &c_n1, &imat, &nfail, &nerrs, nout);
	    }
	    trfcon = info != 0;

	    sgtt01_(&n, &a[1], &a[m + 1], &a[n + m + 1], &af[1], &af[m + 1], &
		    af[n + m + 1], &af[n + (m << 1) + 1], &iwork[1], &work[1], 
		     &lda, &rwork[1], result);

/*           Print the test ratio if it is .GE. THRESH. */

	    if (result[0] >= *thresh) {
		if (nfail == 0 && nerrs == 0) {
		    alahd_(nout, path);
		}
		io___29.ciunit = *nout;
		s_wsfe(&io___29);
		do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
		do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer));
		do_fio(&c__1, (char *)&c__1, (ftnlen)sizeof(integer));
		do_fio(&c__1, (char *)&result[0], (ftnlen)sizeof(real));
		e_wsfe();
		++nfail;
	    }
	    ++nrun;

	    for (itran = 1; itran <= 2; ++itran) {
		*(unsigned char *)trans = *(unsigned char *)&transs[itran - 1]
			;
		if (itran == 1) {
		    *(unsigned char *)norm = 'O';
		} else {
		    *(unsigned char *)norm = 'I';
		}
		anorm = slangt_(norm, &n, &a[1], &a[m + 1], &a[n + m + 1]);

		if (! trfcon) {

/*                 Use SGTTRS to solve for one column at a time of inv(A) */
/*                 or inv(A^T), computing the maximum column sum as we */
/*                 go. */

		    ainvnm = 0.f;
		    i__3 = n;
		    for (i__ = 1; i__ <= i__3; ++i__) {
			i__4 = n;
			for (j = 1; j <= i__4; ++j) {
			    x[j] = 0.f;
/* L30: */
			}
			x[i__] = 1.f;
			sgttrs_(trans, &n, &c__1, &af[1], &af[m + 1], &af[n + 
				m + 1], &af[n + (m << 1) + 1], &iwork[1], &x[
				1], &lda, &info);
/* Computing MAX */
			r__1 = ainvnm, r__2 = sasum_(&n, &x[1], &c__1);
			ainvnm = dmax(r__1,r__2);
/* L40: */
		    }

/*                 Compute RCONDC = 1 / (norm(A) * norm(inv(A)) */

		    if (anorm <= 0.f || ainvnm <= 0.f) {
			rcondc = 1.f;
		    } else {
			rcondc = 1.f / anorm / ainvnm;
		    }
		    if (itran == 1) {
			rcondo = rcondc;
		    } else {
			rcondi = rcondc;
		    }
		} else {
		    rcondc = 0.f;
		}

/* +    TEST 7 */
/*              Estimate the reciprocal of the condition number of the */
/*              matrix. */

		s_copy(srnamc_1.srnamt, "SGTCON", (ftnlen)32, (ftnlen)6);
		sgtcon_(norm, &n, &af[1], &af[m + 1], &af[n + m + 1], &af[n + 
			(m << 1) + 1], &iwork[1], &anorm, &rcond, &work[1], &
			iwork[n + 1], &info);

/*              Check error code from SGTCON. */

		if (info != 0) {
		    alaerh_(path, "SGTCON", &info, &c__0, norm, &n, &n, &c_n1, 
			     &c_n1, &c_n1, &imat, &nfail, &nerrs, nout);
		}

		result[6] = sget06_(&rcond, &rcondc);

/*              Print the test ratio if it is .GE. THRESH. */

		if (result[6] >= *thresh) {
		    if (nfail == 0 && nerrs == 0) {
			alahd_(nout, path);
		    }
		    io___39.ciunit = *nout;
		    s_wsfe(&io___39);
		    do_fio(&c__1, norm, (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__7, (ftnlen)sizeof(integer));
		    do_fio(&c__1, (char *)&result[6], (ftnlen)sizeof(real));
		    e_wsfe();
		    ++nfail;
		}
		++nrun;
/* L50: */
	    }

/*           Skip the remaining tests if the matrix is singular. */

	    if (trfcon) {
		goto L100;
	    }

	    i__3 = *nns;
	    for (irhs = 1; irhs <= i__3; ++irhs) {
		nrhs = nsval[irhs];

/*              Generate NRHS random solution vectors. */

		ix = 1;
		i__4 = nrhs;
		for (j = 1; j <= i__4; ++j) {
		    slarnv_(&c__2, iseed, &n, &xact[ix]);
		    ix += lda;
/* L60: */
		}

		for (itran = 1; itran <= 3; ++itran) {
		    *(unsigned char *)trans = *(unsigned char *)&transs[itran 
			    - 1];
		    if (itran == 1) {
			rcondc = rcondo;
		    } else {
			rcondc = rcondi;
		    }

/*                 Set the right hand side. */

		    slagtm_(trans, &n, &nrhs, &c_b63, &a[1], &a[m + 1], &a[n 
			    + m + 1], &xact[1], &lda, &c_b64, &b[1], &lda);

/* +    TEST 2 */
/*                 Solve op(A) * X = B and compute the residual. */

		    slacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &lda);
		    s_copy(srnamc_1.srnamt, "SGTTRS", (ftnlen)32, (ftnlen)6);
		    sgttrs_(trans, &n, &nrhs, &af[1], &af[m + 1], &af[n + m + 
			    1], &af[n + (m << 1) + 1], &iwork[1], &x[1], &lda, 
			     &info);

/*                 Check error code from SGTTRS. */

		    if (info != 0) {
			alaerh_(path, "SGTTRS", &info, &c__0, trans, &n, &n, &
				c_n1, &c_n1, &nrhs, &imat, &nfail, &nerrs, 
				nout);
		    }

		    slacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], &lda);
		    sgtt02_(trans, &n, &nrhs, &a[1], &a[m + 1], &a[n + m + 1], 
			     &x[1], &lda, &work[1], &lda, &rwork[1], &result[
			    1]);

/* +    TEST 3 */
/*                 Check solution from generated exact solution. */

		    sget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, &
			    result[2]);

/* +    TESTS 4, 5, and 6 */
/*                 Use iterative refinement to improve the solution. */

		    s_copy(srnamc_1.srnamt, "SGTRFS", (ftnlen)32, (ftnlen)6);
		    sgtrfs_(trans, &n, &nrhs, &a[1], &a[m + 1], &a[n + m + 1], 
			     &af[1], &af[m + 1], &af[n + m + 1], &af[n + (m <<
			     1) + 1], &iwork[1], &b[1], &lda, &x[1], &lda, &
			    rwork[1], &rwork[nrhs + 1], &work[1], &iwork[n + 
			    1], &info);

/*                 Check error code from SGTRFS. */

		    if (info != 0) {
			alaerh_(path, "SGTRFS", &info, &c__0, trans, &n, &n, &
				c_n1, &c_n1, &nrhs, &imat, &nfail, &nerrs, 
				nout);
		    }

		    sget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, &
			    result[3]);
		    sgtt05_(trans, &n, &nrhs, &a[1], &a[m + 1], &a[n + m + 1], 
			     &b[1], &lda, &x[1], &lda, &xact[1], &lda, &rwork[
			    1], &rwork[nrhs + 1], &result[4]);

/*                 Print information about the tests that did not pass */
/*                 the threshold. */

		    for (k = 2; k <= 6; ++k) {
			if (result[k - 1] >= *thresh) {
			    if (nfail == 0 && nerrs == 0) {
				alahd_(nout, path);
			    }
			    io___44.ciunit = *nout;
			    s_wsfe(&io___44);
			    do_fio(&c__1, trans, (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(real));
			    e_wsfe();
			    ++nfail;
			}
/* L70: */
		    }
		    nrun += 5;
/* L80: */
		}
/* L90: */
	    }

L100:
	    ;
	}
/* L110: */
    }

/*     Print a summary of the results. */

    alasum_(path, nout, &nfail, &nrun, &nerrs);

    return 0;

/*     End of SCHKGT */

} /* schkgt_ */
Beispiel #4
0
/* Subroutine */ int sgtsvx_(char *fact, char *trans, integer *n, integer *
	nrhs, real *dl, real *d__, real *du, real *dlf, real *df, real *duf, 
	real *du2, integer *ipiv, real *b, integer *ldb, real *x, integer *
	ldx, real *rcond, real *ferr, real *berr, real *work, integer *iwork, 
	integer *info)
{
    /* System generated locals */
    integer b_dim1, b_offset, x_dim1, x_offset, i__1;

    /* Local variables */
    char norm[1];
    extern logical lsame_(char *, char *);
    real anorm;
    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
	    integer *);
    extern doublereal slamch_(char *);
    logical nofact;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern doublereal slangt_(char *, integer *, real *, real *, real *);
    extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, 
	    integer *, real *, integer *), sgtcon_(char *, integer *, 
	    real *, real *, real *, real *, integer *, real *, real *, real *, 
	     integer *, integer *);
    logical notran;
    extern /* Subroutine */ int sgtrfs_(char *, integer *, integer *, real *, 
	    real *, real *, real *, real *, real *, real *, integer *, real *, 
	     integer *, real *, integer *, real *, real *, real *, integer *, 
	    integer *), sgttrf_(integer *, real *, real *, real *, 
	    real *, integer *, integer *), sgttrs_(char *, integer *, integer 
	    *, real *, real *, real *, real *, integer *, real *, integer *, 
	    integer *);


/*  -- LAPACK routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  SGTSVX uses the LU factorization to compute the solution to a real */
/*  system of linear equations A * X = B or A**T * X = B, */
/*  where A is a tridiagonal matrix of order N 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 LU decomposition is used to factor the matrix A */
/*     as A = L * U, where L is a product of permutation and unit lower */
/*     bidiagonal matrices and U is upper triangular with nonzeros in */
/*     only the main diagonal and first two superdiagonals. */

/*  2. If some U(i,i)=0, so that U 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':  DLF, DF, DUF, DU2, and IPIV contain the factored */
/*                  form of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV */
/*                  will not be modified. */
/*          = 'N':  The matrix will be copied to DLF, DF, and DUF */
/*                  and factored. */

/*  TRANS   (input) CHARACTER*1 */
/*          Specifies the form of the system of equations: */
/*          = 'N':  A * X = B     (No transpose) */
/*          = 'T':  A**T * X = B  (Transpose) */
/*          = 'C':  A**H * X = B  (Conjugate transpose = Transpose) */

/*  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 matrix B.  NRHS >= 0. */

/*  DL      (input) REAL array, dimension (N-1) */
/*          The (n-1) subdiagonal elements of A. */

/*  D       (input) REAL array, dimension (N) */
/*          The n diagonal elements of A. */

/*  DU      (input) REAL array, dimension (N-1) */
/*          The (n-1) superdiagonal elements of A. */

/*  DLF     (input or output) REAL array, dimension (N-1) */
/*          If FACT = 'F', then DLF is an input argument and on entry */
/*          contains the (n-1) multipliers that define the matrix L from */
/*          the LU factorization of A as computed by SGTTRF. */

/*          If FACT = 'N', then DLF is an output argument and on exit */
/*          contains the (n-1) multipliers that define the matrix L from */
/*          the LU factorization of A. */

/*  DF      (input or output) REAL array, dimension (N) */
/*          If FACT = 'F', then DF is an input argument and on entry */
/*          contains the n diagonal elements of the upper triangular */
/*          matrix U from the LU factorization of A. */

/*          If FACT = 'N', then DF is an output argument and on exit */
/*          contains the n diagonal elements of the upper triangular */
/*          matrix U from the LU factorization of A. */

/*  DUF     (input or output) REAL array, dimension (N-1) */
/*          If FACT = 'F', then DUF is an input argument and on entry */
/*          contains the (n-1) elements of the first superdiagonal of U. */

/*          If FACT = 'N', then DUF is an output argument and on exit */
/*          contains the (n-1) elements of the first superdiagonal of U. */

/*  DU2     (input or output) REAL array, dimension (N-2) */
/*          If FACT = 'F', then DU2 is an input argument and on entry */
/*          contains the (n-2) elements of the second superdiagonal of */
/*          U. */

/*          If FACT = 'N', then DU2 is an output argument and on exit */
/*          contains the (n-2) elements of the second superdiagonal of */
/*          U. */

/*  IPIV    (input or output) INTEGER array, dimension (N) */
/*          If FACT = 'F', then IPIV is an input argument and on entry */
/*          contains the pivot indices from the LU factorization of A as */
/*          computed by SGTTRF. */

/*          If FACT = 'N', then IPIV is an output argument and on exit */
/*          contains the pivot indices from the LU factorization of A; */
/*          row i of the matrix was interchanged with row IPIV(i). */
/*          IPIV(i) will always be either i or i+1; IPIV(i) = i indicates */
/*          a row interchange was not required. */

/*  B       (input) REAL 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) REAL 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) REAL */
/*          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) 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. */

/*  BERR    (output) 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). */

/*  WORK    (workspace) REAL array, dimension (3*N) */

/*  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:  U(i,i) is exactly zero.  The factorization */
/*                       has not been completed unless i = N, but the */
/*                       factor U is exactly singular, so the solution */
/*                       and error bounds could not be computed. */
/*                       RCOND = 0 is returned. */
/*                = N+1: U 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 .. */

    /* Parameter adjustments */
    --dl;
    --d__;
    --du;
    --dlf;
    --df;
    --duf;
    --du2;
    --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");
    notran = lsame_(trans, "N");
    if (! nofact && ! lsame_(fact, "F")) {
	*info = -1;
    } else if (! notran && ! lsame_(trans, "T") && ! 
	    lsame_(trans, "C")) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*nrhs < 0) {
	*info = -4;
    } else if (*ldb < max(1,*n)) {
	*info = -14;
    } else if (*ldx < max(1,*n)) {
	*info = -16;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SGTSVX", &i__1);
	return 0;
    }

    if (nofact) {

/*        Compute the LU factorization of A. */

	scopy_(n, &d__[1], &c__1, &df[1], &c__1);
	if (*n > 1) {
	    i__1 = *n - 1;
	    scopy_(&i__1, &dl[1], &c__1, &dlf[1], &c__1);
	    i__1 = *n - 1;
	    scopy_(&i__1, &du[1], &c__1, &duf[1], &c__1);
	}
	sgttrf_(n, &dlf[1], &df[1], &duf[1], &du2[1], &ipiv[1], info);

/*        Return if INFO is non-zero. */

	if (*info > 0) {
	    *rcond = 0.f;
	    return 0;
	}
    }

/*     Compute the norm of the matrix A. */

    if (notran) {
	*(unsigned char *)norm = '1';
    } else {
	*(unsigned char *)norm = 'I';
    }
    anorm = slangt_(norm, n, &dl[1], &d__[1], &du[1]);

/*     Compute the reciprocal of the condition number of A. */

    sgtcon_(norm, n, &dlf[1], &df[1], &duf[1], &du2[1], &ipiv[1], &anorm, 
	    rcond, &work[1], &iwork[1], info);

/*     Compute the solution vectors X. */

    slacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
    sgttrs_(trans, n, nrhs, &dlf[1], &df[1], &duf[1], &du2[1], &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. */

    sgtrfs_(trans, n, nrhs, &dl[1], &d__[1], &du[1], &dlf[1], &df[1], &duf[1], 
	     &du2[1], &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 < slamch_("Epsilon")) {
	*info = *n + 1;
    }

    return 0;

/*     End of SGTSVX */

} /* sgtsvx_ */