Example #1
0
INT16 dlm_cholfC(COMPLEX64* Z, const COMPLEX64* A, INT32 nXD) {
  integer info = 0;
  integer n = (integer) nXD;
  char uplo[1] = { 'U' };
#ifdef __MAX_TYPE_32BIT
  extern int clacpy_(char*,integer*,integer*,complex*,integer*,complex*,integer *ldb);
  extern int cpotrf_(char*,integer*,complex*,integer*,integer*);
#else
  extern int zlacpy_(char*,integer*,integer*,doublecomplex*,integer*,doublecomplex*,integer *ldb);
  extern int zpotrf_(char*,integer*,doublecomplex*,integer*,integer*);
#endif

  /* Declare variables */
  DLPASSERT(Z != A);                                                            /* Assert input is not output        */
  DLPASSERT(dlp_size(Z) >= nXD * nXD * sizeof(FLOAT64));                        /* Check size of output buffer       */
  DLPASSERT(dlp_size(A) >= nXD * nXD * sizeof(FLOAT64));                        /* Check size of input buffer        */

  /* ... computation ... *//* --------------------------------- */
#ifdef __MAX_TYPE_32BIT
  cpotrf_(uplo, &n, (complex*)A, &n, &info);
  clacpy_(uplo, &n, &n, (complex*)A, &n, (complex*)Z, &n);
#else
  zpotrf_(uplo, &n, (doublecomplex*)A, &n, &info);
  zlacpy_(uplo, &n, &n, (doublecomplex*)A, &n, (doublecomplex*)Z, &n);
#endif
  return (info == 0) ? O_K : NOT_EXEC; /* All done successfully             */
}
Example #2
0
	DLLEXPORT MKL_INT z_cholesky_factor(MKL_INT n, MKL_Complex16 a[]){
		char uplo = 'L';
		MKL_INT info = 0;
		MKL_Complex16 zero = {0.0, 0.0};
		zpotrf_(&uplo, &n, a, &n, &info);
		for (MKL_INT i = 0; i < n; ++i)
		{
			MKL_INT index = i * n;
			for (MKL_INT j = 0; j < n && i > j; ++j)
			{
				a[index + j] = zero;
			}
		}
		return info;
	}
Example #3
0
	DLLEXPORT int z_cholesky_factor(int n, doublecomplex a[]){
		char uplo = 'L';
		int info = 0;
		doublecomplex zero = {0.0, 0.0};
		zpotrf_(&uplo, &n, a, &n, &info);
		for (int i = 0; i < n; ++i)
		{
			int index = i * n;
			for (int j = 0; j < n && i > j; ++j)
			{
				a[index + j] = zero;
			}
		}
		return info;
	}
Example #4
0
	DLLEXPORT int z_cholesky_solve(int n, int nrhs, doublecomplex a[], doublecomplex b[])
	{
		doublecomplex* clone = new doublecomplex[n*n];
		memcpy(clone, a, n*n*sizeof(doublecomplex));
		char uplo = 'L';
		int info = 0;
		zpotrf_(&uplo, &n, clone, &n, &info);

		if (info != 0){
			delete[] clone;
			return info;
		}

		zpotrs_(&uplo, &n, &nrhs, clone, &n, b, &n, &info);
		return info;
	}
Example #5
0
	DLLEXPORT MKL_INT z_cholesky_solve(MKL_INT n, MKL_INT nrhs, MKL_Complex16 a[], MKL_Complex16 b[])
	{
		MKL_Complex16* clone = new MKL_Complex16[n*n];
		std::memcpy(clone, a, n*n*sizeof(MKL_Complex16));
		char uplo = 'L';
		MKL_INT info = 0;
		zpotrf_(&uplo, &n, clone, &n, &info);

		if (info != 0){
			delete[] clone;
			return info;
		}

		zpotrs_(&uplo, &n, &nrhs, clone, &n, b, &n, &info);
		delete[] clone;
		return info;
	}
Example #6
0
/* Subroutine */ int zchkpo_(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 *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;

    /* Local variables */
    integer i__, k, n, nb, in, kl, ku, lda, inb, ioff, mode, imat, info;
    char path[3], dist[1];
    integer irhs, nrhs;
    char uplo[1], type__[1];
    integer nrun;
    integer nfail, iseed[4];
    doublereal rcond;
    integer nimat;
    doublereal anorm;
    integer iuplo, izero, nerrs;
    logical zerot;
    char xtype[1];
    doublereal rcondc;
    doublereal cndnum;
    doublereal result[8];

    /* Fortran I/O blocks */
    static cilist io___33 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___36 = { 0, 0, 0, fmt_9998, 0 };
    static cilist io___38 = { 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 */
/*  ======= */

/*  ZCHKPO tests ZPOTRF, -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 */
/*                      (NMAX+2*NSMAX) */

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

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Local Arrays .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Scalars in Common .. */
/*     .. */
/*     .. Common blocks .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Data statements .. */
    /* Parameter adjustments */
    --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, "PO", (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) {
	zerrpo_(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 = 9;
	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 L110;
	    }

/*           Skip types 3, 4, or 5 if the matrix size is too small. */

	    zerot = imat >= 3 && imat <= 5;
	    if (zerot && n < imat - 2) {
		goto L110;
	    }

/*           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)32, (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 L100;
		}

/*              For types 3-5, zero one row and column 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;
		    }
		    ioff = (izero - 1) * lda;

/*                 Set row and column IZERO of A to 0. */

		    if (iuplo == 1) {
			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 {
		    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*L' or U'*U factorization of the matrix. */

		    zlacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda);
		    s_copy(srnamc_1.srnamt, "ZPOTRF", (ftnlen)32, (ftnlen)6);
		    zpotrf_(uplo, &n, &afac[1], &lda, &info);

/*                 Check error code from ZPOTRF. */

		    if (info != izero) {
			alaerh_(path, "ZPOTRF", &info, &izero, uplo, &n, &n, &
				c_n1, &c_n1, &nb, &imat, &nfail, &nerrs, nout);
			goto L90;
		    }

/*                 Skip the tests if INFO is not 0. */

		    if (info != 0) {
			goto L90;
		    }

/* +    TEST 1 */
/*                 Reconstruct matrix from factors and compute residual. */

		    zlacpy_(uplo, &n, &n, &afac[1], &lda, &ainv[1], &lda);
		    zpot01_(uplo, &n, &a[1], &lda, &ainv[1], &lda, &rwork[1], 
			    result);

/* +    TEST 2 */
/*                 Form the inverse and compute the residual. */

		    zlacpy_(uplo, &n, &n, &afac[1], &lda, &ainv[1], &lda);
		    s_copy(srnamc_1.srnamt, "ZPOTRI", (ftnlen)32, (ftnlen)6);
		    zpotri_(uplo, &n, &ainv[1], &lda, &info);

/*                 Check error code from ZPOTRI. */

		    if (info != 0) {
			alaerh_(path, "ZPOTRI", &info, &c__0, 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]);

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

		    for (k = 1; k <= 2; ++k) {
			if (result[k - 1] >= *thresh) {
			    if (nfail == 0 && nerrs == 0) {
				alahd_(nout, path);
			    }
			    io___33.ciunit = *nout;
			    s_wsfe(&io___33);
			    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;
			}
/* L60: */
		    }
		    nrun += 2;

/*                 Skip the rest of the tests unless this is the first */
/*                 blocksize. */

		    if (inb != 1) {
			goto L90;
		    }

		    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)32, (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, "ZPOTRS", (ftnlen)32, (ftnlen)
				6);
			zpotrs_(uplo, &n, &nrhs, &afac[1], &lda, &x[1], &lda, 
				&info);

/*                 Check error code from ZPOTRS. */

			if (info != 0) {
			    alaerh_(path, "ZPOTRS", &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, "ZPORFS", (ftnlen)32, (ftnlen)
				6);
			zporfs_(uplo, &n, &nrhs, &a[1], &lda, &afac[1], &lda, 
				&b[1], &lda, &x[1], &lda, &rwork[1], &rwork[
				nrhs + 1], &work[1], &rwork[(nrhs << 1) + 1], 
				&info);

/*                 Check error code from ZPORFS. */

			if (info != 0) {
			    alaerh_(path, "ZPORFS", &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___36.ciunit = *nout;
				s_wsfe(&io___36);
				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;
			    }
/* L70: */
			}
			nrun += 5;
/* L80: */
		    }

/* +    TEST 8 */
/*                 Get an estimate of RCOND = 1/CNDNUM. */

		    anorm = zlanhe_("1", uplo, &n, &a[1], &lda, &rwork[1]);
		    s_copy(srnamc_1.srnamt, "ZPOCON", (ftnlen)32, (ftnlen)6);
		    zpocon_(uplo, &n, &afac[1], &lda, &anorm, &rcond, &work[1]
, &rwork[1], &info);

/*                 Check error code from ZPOCON. */

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

		    result[7] = dget06_(&rcond, &rcondc);

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

		    if (result[7] >= *thresh) {
			if (nfail == 0 && nerrs == 0) {
			    alahd_(nout, path);
			}
			io___38.ciunit = *nout;
			s_wsfe(&io___38);
			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;
L90:
		    ;
		}
L100:
		;
	    }
L110:
	    ;
	}
/* L120: */
    }

/*     Print a summary of the results. */

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

    return 0;

/*     End of ZCHKPO */

} /* zchkpo_ */
Example #7
0
/* Subroutine */
int zposvxx_(char *fact, char *uplo, integer *n, integer * nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * ldaf, char *equed, doublereal *s, doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *rpvgrw, 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;
    /* Local variables */
    integer j;
    doublereal amax, smin, smax;
    extern doublereal zla_porpvgrw_(char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *);
    extern logical lsame_(char *, char *);
    doublereal scond;
    logical equil, rcequ;
    extern doublereal dlamch_(char *);
    logical nofact;
    extern /* Subroutine */
    int xerbla_(char *, integer *);
    doublereal bignum;
    extern /* Subroutine */
    int zlaqhe_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, char *);
    integer infequ;
    extern /* Subroutine */
    int zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *);
    doublereal smlnum;
    extern /* Subroutine */
    int zpotrf_(char *, integer *, doublecomplex *, integer *, integer *), zpotrs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *), zlascl2_(integer *, integer *, doublereal *, doublecomplex *, integer *), zpoequb_(integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, integer *), zporfsx_(char *, char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, doublecomplex *, doublereal *, integer * );
    /* -- LAPACK driver routine (version 3.4.1) -- */
    /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
    /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
    /* April 2012 */
    /* .. Scalar Arguments .. */
    /* .. */
    /* .. Array Arguments .. */
    /* .. */
    /* ================================================================== */
    /* .. Parameters .. */
    /* .. */
    /* .. Local Scalars .. */
    /* .. */
    /* .. External Functions .. */
    /* .. */
    /* .. External Subroutines .. */
    /* .. */
    /* .. Intrinsic Functions .. */
    /* .. */
    /* .. Executable Statements .. */
    /* 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;
    --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;
    nofact = lsame_(fact, "N");
    equil = lsame_(fact, "E");
    smlnum = dlamch_("Safe minimum");
    bignum = 1. / smlnum;
    if (nofact || equil)
    {
        *(unsigned char *)equed = 'N';
        rcequ = FALSE_;
    }
    else
    {
        rcequ = lsame_(equed, "Y");
    }
    /* Default is failure. If an input parameter is wrong or */
    /* factorization fails, make everything look horrible. Only the */
    /* pivot growth is set here, the rest is initialized in ZPORFSX. */
    *rpvgrw = 0.;
    /* Test the input parameters. PARAMS is not tested until ZPORFSX. */
    if (! nofact && ! equil && ! 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 (lsame_(fact, "F") && ! (rcequ || lsame_( equed, "N")))
    {
        *info = -9;
    }
    else
    {
        if (rcequ)
        {
            smin = bignum;
            smax = 0.;
            i__1 = *n;
            for (j = 1;
                    j <= i__1;
                    ++j)
            {
                /* Computing MIN */
                d__1 = smin;
                d__2 = s[j]; // , expr subst
                smin = min(d__1,d__2);
                /* Computing MAX */
                d__1 = smax;
                d__2 = s[j]; // , expr subst
                smax = max(d__1,d__2);
                /* L10: */
            }
            if (smin <= 0.)
            {
                *info = -10;
            }
            else if (*n > 0)
            {
                scond = max(smin,smlnum) / min(smax,bignum);
            }
            else
            {
                scond = 1.;
            }
        }
        if (*info == 0)
        {
            if (*ldb < max(1,*n))
            {
                *info = -12;
            }
            else if (*ldx < max(1,*n))
            {
                *info = -14;
            }
        }
    }
    if (*info != 0)
    {
        i__1 = -(*info);
        xerbla_("ZPOSVXX", &i__1);
        return 0;
    }
    if (equil)
    {
        /* Compute row and column scalings to equilibrate the matrix A. */
        zpoequb_(n, &a[a_offset], lda, &s[1], &scond, &amax, &infequ);
        if (infequ == 0)
        {
            /* Equilibrate the matrix. */
            zlaqhe_(uplo, n, &a[a_offset], lda, &s[1], &scond, &amax, equed);
            rcequ = lsame_(equed, "Y");
        }
    }
    /* Scale the right-hand side. */
    if (rcequ)
    {
        zlascl2_(n, nrhs, &s[1], &b[b_offset], ldb);
    }
    if (nofact || equil)
    {
        /* Compute the Cholesky factorization of A. */
        zlacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf);
        zpotrf_(uplo, n, &af[af_offset], ldaf, info);
        /* Return if INFO is non-zero. */
        if (*info > 0)
        {
            /* Pivot in column INFO is exactly 0 */
            /* Compute the reciprocal pivot growth factor of the */
            /* leading rank-deficient INFO columns of A. */
            *rpvgrw = zla_porpvgrw_(uplo, n, &a[a_offset], lda, &af[ af_offset], ldaf, &rwork[1]);
            return 0;
        }
    }
    /* Compute the reciprocal pivot growth factor RPVGRW. */
    *rpvgrw = zla_porpvgrw_(uplo, n, &a[a_offset], lda, &af[af_offset], ldaf, &rwork[1]);
    /* Compute the solution matrix X. */
    zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
    zpotrs_(uplo, n, nrhs, &af[af_offset], ldaf, &x[x_offset], ldx, info);
    /* Use iterative refinement to improve the computed solution and */
    /* compute error bounds and backward error estimates for it. */
    zporfsx_(uplo, equed, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, & s[1], &b[b_offset], ldb, &x[x_offset], ldx, rcond, &berr[1], n_err_bnds__, &err_bnds_norm__[err_bnds_norm_offset], & err_bnds_comp__[err_bnds_comp_offset], nparams, &params[1], &work[ 1], &rwork[1], info);
    /* Scale solutions. */
    if (rcequ)
    {
        zlascl2_(n, nrhs, &s[1], &x[x_offset], ldx);
    }
    return 0;
    /* End of ZPOSVXX */
}
Example #8
0
/* Subroutine */ int zdrvpo_(logical *dotype, integer *nn, integer *nval, 
	integer *nrhs, doublereal *thresh, logical *tsterr, integer *nmax, 
	doublecomplex *a, doublecomplex *afac, doublecomplex *asav, 
	doublecomplex *b, doublecomplex *bsav, doublecomplex *x, 
	doublecomplex *xact, doublereal *s, doublecomplex *work, doublereal *
	rwork, integer *nout)
{
    /* Initialized data */

    static integer iseedy[4] = { 1988,1989,1990,1991 };
    static char uplos[1*2] = "U" "L";
    static char facts[1*3] = "F" "N" "E";
    static char equeds[1*2] = "N" "Y";

    /* Format strings */
    static char fmt_9999[] = "(1x,a6,\002, UPLO='\002,a1,\002', N =\002,i5"
	    ",\002, type \002,i1,\002, test(\002,i1,\002)=\002,g12.5)";
    static char fmt_9997[] = "(1x,a6,\002, FACT='\002,a1,\002', UPLO='\002,a"
	    "1,\002', N=\002,i5,\002, EQUED='\002,a1,\002', type \002,i1,\002"
	    ", test(\002,i1,\002) =\002,g12.5)";
    static char fmt_9998[] = "(1x,a6,\002, FACT='\002,a1,\002', UPLO='\002,a"
	    "1,\002', N=\002,i5,\002, type \002,i1,\002, test(\002,i1,\002)"
	    "=\002,g12.5)";

    /* System generated locals */
    address a__1[2];
    integer i__1, i__2, i__3, i__4, i__5[2];
    char ch__1[2];

    /* Builtin functions   
       Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
    integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
    /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);

    /* Local variables */
    static char fact[1];
    static integer ioff, mode;
    static doublereal amax;
    static char path[3];
    static integer imat, info;
    static char dist[1], uplo[1], type__[1];
    static integer nrun, i__, k, n, ifact, nfail, iseed[4], nfact;
    extern doublereal dget06_(doublereal *, doublereal *);
    extern logical lsame_(char *, char *);
    static char equed[1];
    static integer nbmin;
    static doublereal rcond, roldc, scond;
    static integer nimat;
    static doublereal anorm;
    extern /* Subroutine */ int zget04_(integer *, integer *, doublecomplex *,
	     integer *, doublecomplex *, integer *, doublereal *, doublereal *
	    );
    static logical equil;
    static integer iuplo, izero, nerrs, k1;
    extern /* Subroutine */ int zpot01_(char *, integer *, doublecomplex *, 
	    integer *, doublecomplex *, integer *, doublereal *, doublereal *), zpot02_(char *, integer *, integer *, doublecomplex *, 
	    integer *, doublecomplex *, integer *, doublecomplex *, integer *,
	     doublereal *, doublereal *), zpot05_(char *, integer *, 
	    integer *, doublecomplex *, integer *, doublecomplex *, integer *,
	     doublecomplex *, integer *, doublecomplex *, integer *, 
	    doublereal *, doublereal *, doublereal *);
    static logical zerot;
    static char xtype[1];
    extern /* Subroutine */ int zposv_(char *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, integer *), zlatb4_(char *, integer *, integer *, integer *, char *,
	     integer *, integer *, doublereal *, integer *, doublereal *, 
	    char *), aladhd_(integer *, 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 logical prefac;
    static integer ku, nt;
    static doublereal rcondc;
    static logical nofact;
    static integer iequed;
    extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, 
	    integer *, doublereal *);
    extern /* Subroutine */ int alasvm_(char *, integer *, integer *, integer 
	    *, integer *);
    static doublereal cndnum;
    extern /* Subroutine */ int zlaipd_(integer *, doublecomplex *, integer *,
	     integer *), zlaqhe_(char *, integer *, doublecomplex *, integer *
	    , doublereal *, doublereal *, doublereal *, char *);
    static doublereal ainvnm;
    extern /* Subroutine */ int xlaenv_(integer *, integer *), zlacpy_(char *,
	     integer *, integer *, doublecomplex *, integer *, doublecomplex *
	    , integer *), zlarhs_(char *, char *, char *, char *, 
	    integer *, integer *, integer *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, integer *, integer *), zlaset_(char *, integer *, integer *, 
	    doublecomplex *, doublecomplex *, doublecomplex *, integer *), zlatms_(integer *, integer *, char *, integer *, char *, 
	    doublereal *, integer *, doublereal *, doublereal *, integer *, 
	    integer *, char *, doublecomplex *, integer *, doublecomplex *, 
	    integer *);
    static doublereal result[6];
    extern /* Subroutine */ int zpoequ_(integer *, doublecomplex *, integer *,
	     doublereal *, doublereal *, doublereal *, integer *), zpotrf_(
	    char *, integer *, doublecomplex *, integer *, integer *),
	     zpotri_(char *, integer *, doublecomplex *, integer *, integer *), zerrvx_(char *, integer *), zposvx_(char *, 
	    char *, integer *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, char *, doublereal *, doublecomplex *,
	     integer *, doublecomplex *, integer *, doublereal *, doublereal *
	    , doublereal *, doublecomplex *, doublereal *, integer *);
    static integer lda;

    /* Fortran I/O blocks */
    static cilist io___48 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___51 = { 0, 0, 0, fmt_9997, 0 };
    static cilist io___52 = { 0, 0, 0, fmt_9998, 0 };



/*  -- LAPACK test routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       June 30, 1999   


    Purpose   
    =======   

    ZDRVPO tests the driver routines ZPOSV and -SVX.   

    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.   

    NRHS    (input) INTEGER   
            The number of right hand side vectors to be generated for   
            each linear system.   

    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)   

    ASAV    (workspace) COMPLEX*16 array, dimension (NMAX*NMAX)   

    B       (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)   

    BSAV    (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)   

    X       (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)   

    XACT    (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)   

    S       (workspace) DOUBLE PRECISION array, dimension (NMAX)   

    WORK    (workspace) COMPLEX*16 array, dimension   
                        (NMAX*max(3,NRHS))   

    RWORK   (workspace) DOUBLE PRECISION array, dimension (NMAX+2*NRHS)   

    NOUT    (input) INTEGER   
            The unit number for output.   

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

       Parameter adjustments */
    --rwork;
    --work;
    --s;
    --xact;
    --x;
    --bsav;
    --b;
    --asav;
    --afac;
    --a;
    --nval;
    --dotype;

    /* Function Body   

       Initialize constants and the random number seed. */

    s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17);
    s_copy(path + 1, "PO", (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) {
	zerrvx_(path, nout);
    }
    infoc_1.infot = 0;

/*     Set the block size and minimum block size for testing. */

    nb = 1;
    nbmin = 2;
    xlaenv_(&c__1, &nb);
    xlaenv_(&c__2, &nbmin);

/*     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 = 9;
	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 L120;
	    }

/*           Skip types 3, 4, or 5 if the matrix size is too small. */

	    zerot = imat >= 3 && imat <= 5;
	    if (zerot && n < imat - 2) {
		goto L120;
	    }

/*           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 L110;
		}

/*              For types 3-5, zero one row and column 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;
		    }
		    ioff = (izero - 1) * lda;

/*                 Set row and column IZERO of A to 0. */

		    if (iuplo == 1) {
			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 {
		    izero = 0;
		}

/*              Set the imaginary part of the diagonals. */

		i__3 = lda + 1;
		zlaipd_(&n, &a[1], &i__3, &c__0);

/*              Save a copy of the matrix A in ASAV. */

		zlacpy_(uplo, &n, &n, &a[1], &lda, &asav[1], &lda);

		for (iequed = 1; iequed <= 2; ++iequed) {
		    *(unsigned char *)equed = *(unsigned char *)&equeds[
			    iequed - 1];
		    if (iequed == 1) {
			nfact = 3;
		    } else {
			nfact = 1;
		    }

		    i__3 = nfact;
		    for (ifact = 1; ifact <= i__3; ++ifact) {
			*(unsigned char *)fact = *(unsigned char *)&facts[
				ifact - 1];
			prefac = lsame_(fact, "F");
			nofact = lsame_(fact, "N");
			equil = lsame_(fact, "E");

			if (zerot) {
			    if (prefac) {
				goto L90;
			    }
			    rcondc = 0.;

			} else if (! lsame_(fact, "N")) 
				{

/*                       Compute the condition number for comparison with   
                         the value returned by ZPOSVX (FACT = 'N' reuses   
                         the condition number from the previous iteration   
                         with FACT = 'F'). */

			    zlacpy_(uplo, &n, &n, &asav[1], &lda, &afac[1], &
				    lda);
			    if (equil || iequed > 1) {

/*                          Compute row and column scale factors to   
                            equilibrate the matrix A. */

				zpoequ_(&n, &afac[1], &lda, &s[1], &scond, &
					amax, &info);
				if (info == 0 && n > 0) {
				    if (iequed > 1) {
					scond = 0.;
				    }

/*                             Equilibrate the matrix. */

				    zlaqhe_(uplo, &n, &afac[1], &lda, &s[1], &
					    scond, &amax, equed);
				}
			    }

/*                       Save the condition number of the   
                         non-equilibrated system for use in ZGET04. */

			    if (equil) {
				roldc = rcondc;
			    }

/*                       Compute the 1-norm of A. */

			    anorm = zlanhe_("1", uplo, &n, &afac[1], &lda, &
				    rwork[1]);

/*                       Factor the matrix A. */

			    zpotrf_(uplo, &n, &afac[1], &lda, &info);

/*                       Form the inverse of A. */

			    zlacpy_(uplo, &n, &n, &afac[1], &lda, &a[1], &lda);
			    zpotri_(uplo, &n, &a[1], &lda, &info);

/*                       Compute the 1-norm condition number of A. */

			    ainvnm = zlanhe_("1", uplo, &n, &a[1], &lda, &
				    rwork[1]);
			    if (anorm <= 0. || ainvnm <= 0.) {
				rcondc = 1.;
			    } else {
				rcondc = 1. / anorm / ainvnm;
			    }
			}

/*                    Restore the matrix A. */

			zlacpy_(uplo, &n, &n, &asav[1], &lda, &a[1], &lda);

/*                    Form an exact solution and set the right hand side. */

			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);
			*(unsigned char *)xtype = 'C';
			zlacpy_("Full", &n, nrhs, &b[1], &lda, &bsav[1], &lda);

			if (nofact) {

/*                       --- Test ZPOSV  ---   

                         Compute the L*L' or U'*U factorization of the   
                         matrix and solve the system. */

			    zlacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda);
			    zlacpy_("Full", &n, nrhs, &b[1], &lda, &x[1], &
				    lda);

			    s_copy(srnamc_1.srnamt, "ZPOSV ", (ftnlen)6, (
				    ftnlen)6);
			    zposv_(uplo, &n, nrhs, &afac[1], &lda, &x[1], &
				    lda, &info);

/*                       Check error code from ZPOSV . */

			    if (info != izero) {
				alaerh_(path, "ZPOSV ", &info, &izero, uplo, &
					n, &n, &c_n1, &c_n1, nrhs, &imat, &
					nfail, &nerrs, nout);
				goto L70;
			    } else if (info != 0) {
				goto L70;
			    }

/*                       Reconstruct matrix from factors and compute   
                         residual. */

			    zpot01_(uplo, &n, &a[1], &lda, &afac[1], &lda, &
				    rwork[1], result);

/*                       Compute residual of the computed solution. */

			    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[1]);

/*                       Check solution from generated exact solution. */

			    zget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, &
				    rcondc, &result[2]);
			    nt = 3;

/*                       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) {
					aladhd_(nout, path);
				    }
				    io___48.ciunit = *nout;
				    s_wsfe(&io___48);
				    do_fio(&c__1, "ZPOSV ", (ftnlen)6);
				    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 *)&k, (ftnlen)sizeof(
					    integer));
				    do_fio(&c__1, (char *)&result[k - 1], (
					    ftnlen)sizeof(doublereal));
				    e_wsfe();
				    ++nfail;
				}
/* L60: */
			    }
			    nrun += nt;
L70:
			    ;
			}

/*                    --- Test ZPOSVX --- */

			if (! prefac) {
			    zlaset_(uplo, &n, &n, &c_b51, &c_b51, &afac[1], &
				    lda);
			}
			zlaset_("Full", &n, nrhs, &c_b51, &c_b51, &x[1], &lda);
			if (iequed > 1 && n > 0) {

/*                       Equilibrate the matrix if FACT='F' and   
                         EQUED='Y'. */

			    zlaqhe_(uplo, &n, &a[1], &lda, &s[1], &scond, &
				    amax, equed);
			}

/*                    Solve the system and compute the condition number   
                      and error bounds using ZPOSVX. */

			s_copy(srnamc_1.srnamt, "ZPOSVX", (ftnlen)6, (ftnlen)
				6);
			zposvx_(fact, uplo, &n, nrhs, &a[1], &lda, &afac[1], &
				lda, equed, &s[1], &b[1], &lda, &x[1], &lda, &
				rcond, &rwork[1], &rwork[*nrhs + 1], &work[1],
				 &rwork[(*nrhs << 1) + 1], &info);

/*                    Check the error code from ZPOSVX. */

			if (info != izero) {
/* Writing concatenation */
			    i__5[0] = 1, a__1[0] = fact;
			    i__5[1] = 1, a__1[1] = uplo;
			    s_cat(ch__1, a__1, i__5, &c__2, (ftnlen)2);
			    alaerh_(path, "ZPOSVX", &info, &izero, ch__1, &n, 
				    &n, &c_n1, &c_n1, nrhs, &imat, &nfail, &
				    nerrs, nout);
			    goto L90;
			}

			if (info == 0) {
			    if (! prefac) {

/*                          Reconstruct matrix from factors and compute   
                            residual. */

				zpot01_(uplo, &n, &a[1], &lda, &afac[1], &lda,
					 &rwork[(*nrhs << 1) + 1], result);
				k1 = 1;
			    } else {
				k1 = 2;
			    }

/*                       Compute residual of the computed solution. */

			    zlacpy_("Full", &n, nrhs, &bsav[1], &lda, &work[1]
				    , &lda);
			    zpot02_(uplo, &n, nrhs, &asav[1], &lda, &x[1], &
				    lda, &work[1], &lda, &rwork[(*nrhs << 1) 
				    + 1], &result[1]);

/*                       Check solution from generated exact solution. */

			    if (nofact || prefac && lsame_(equed, "N")) {
				zget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda,
					 &rcondc, &result[2]);
			    } else {
				zget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda,
					 &roldc, &result[2]);
			    }

/*                       Check the error bounds from iterative   
                         refinement. */

			    zpot05_(uplo, &n, nrhs, &asav[1], &lda, &b[1], &
				    lda, &x[1], &lda, &xact[1], &lda, &rwork[
				    1], &rwork[*nrhs + 1], &result[3]);
			} else {
			    k1 = 6;
			}

/*                    Compare RCOND from ZPOSVX with the computed value   
                      in RCONDC. */

			result[5] = dget06_(&rcond, &rcondc);

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

			for (k = k1; k <= 6; ++k) {
			    if (result[k - 1] >= *thresh) {
				if (nfail == 0 && nerrs == 0) {
				    aladhd_(nout, path);
				}
				if (prefac) {
				    io___51.ciunit = *nout;
				    s_wsfe(&io___51);
				    do_fio(&c__1, "ZPOSVX", (ftnlen)6);
				    do_fio(&c__1, fact, (ftnlen)1);
				    do_fio(&c__1, uplo, (ftnlen)1);
				    do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
					    integer));
				    do_fio(&c__1, equed, (ftnlen)1);
				    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();
				} else {
				    io___52.ciunit = *nout;
				    s_wsfe(&io___52);
				    do_fio(&c__1, "ZPOSVX", (ftnlen)6);
				    do_fio(&c__1, fact, (ftnlen)1);
				    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 *)&k, (ftnlen)sizeof(
					    integer));
				    do_fio(&c__1, (char *)&result[k - 1], (
					    ftnlen)sizeof(doublereal));
				    e_wsfe();
				}
				++nfail;
			    }
/* L80: */
			}
			nrun = nrun + 7 - k1;
L90:
			;
		    }
/* L100: */
		}
L110:
		;
	    }
L120:
	    ;
	}
/* L130: */
    }

/*     Print a summary of the results. */

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

    return 0;

/*     End of ZDRVPO */

} /* zdrvpo_ */
Example #9
0
/* Subroutine */
int zhegv_(integer *itype, char *jobz, char *uplo, integer * n, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, doublereal *w, doublecomplex *work, integer *lwork, doublereal *rwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
    /* Local variables */
    integer nb, neig;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */
    int zheev_(char *, char *, integer *, doublecomplex *, integer *, doublereal *, doublecomplex *, integer *, doublereal *, integer *);
    char trans[1];
    logical upper, wantz;
    extern /* Subroutine */
    int ztrmm_(char *, char *, char *, char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *), ztrsm_(char *, char *, char *, char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *), xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
    extern /* Subroutine */
    int zhegst_(integer *, char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *);
    integer lwkopt;
    logical lquery;
    extern /* Subroutine */
    int zpotrf_(char *, integer *, doublecomplex *, integer *, integer *);
    /* -- LAPACK driver routine (version 3.4.0) -- */
    /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
    /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
    /* November 2011 */
    /* .. Scalar Arguments .. */
    /* .. */
    /* .. Array Arguments .. */
    /* .. */
    /* ===================================================================== */
    /* .. 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;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    --w;
    --work;
    --rwork;
    /* Function Body */
    wantz = lsame_(jobz, "V");
    upper = lsame_(uplo, "U");
    lquery = *lwork == -1;
    *info = 0;
    if (*itype < 1 || *itype > 3)
    {
        *info = -1;
    }
    else if (! (wantz || lsame_(jobz, "N")))
    {
        *info = -2;
    }
    else if (! (upper || lsame_(uplo, "L")))
    {
        *info = -3;
    }
    else if (*n < 0)
    {
        *info = -4;
    }
    else if (*lda < max(1,*n))
    {
        *info = -6;
    }
    else if (*ldb < max(1,*n))
    {
        *info = -8;
    }
    if (*info == 0)
    {
        nb = ilaenv_(&c__1, "ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1);
        /* Computing MAX */
        i__1 = 1;
        i__2 = (nb + 1) * *n; // , expr subst
        lwkopt = max(i__1,i__2);
        work[1].r = (doublereal) lwkopt;
        work[1].i = 0.; // , expr subst
        /* Computing MAX */
        i__1 = 1;
        i__2 = (*n << 1) - 1; // , expr subst
        if (*lwork < max(i__1,i__2) && ! lquery)
        {
            *info = -11;
        }
    }
    if (*info != 0)
    {
        i__1 = -(*info);
        xerbla_("ZHEGV ", &i__1);
        return 0;
    }
    else if (lquery)
    {
        return 0;
    }
    /* Quick return if possible */
    if (*n == 0)
    {
        return 0;
    }
    /* Form a Cholesky factorization of B. */
    zpotrf_(uplo, n, &b[b_offset], ldb, info);
    if (*info != 0)
    {
        *info = *n + *info;
        return 0;
    }
    /* Transform problem to standard eigenvalue problem and solve. */
    zhegst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info);
    zheev_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, &rwork[1] , info);
    if (wantz)
    {
        /* Backtransform eigenvectors to the original problem. */
        neig = *n;
        if (*info > 0)
        {
            neig = *info - 1;
        }
        if (*itype == 1 || *itype == 2)
        {
            /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
            */
            /* backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y */
            if (upper)
            {
                *(unsigned char *)trans = 'N';
            }
            else
            {
                *(unsigned char *)trans = 'C';
            }
            ztrsm_("Left", uplo, trans, "Non-unit", n, &neig, &c_b1, &b[ b_offset], ldb, &a[a_offset], lda);
        }
        else if (*itype == 3)
        {
            /* For B*A*x=(lambda)*x;
            */
            /* backtransform eigenvectors: x = L*y or U**H *y */
            if (upper)
            {
                *(unsigned char *)trans = 'C';
            }
            else
            {
                *(unsigned char *)trans = 'N';
            }
            ztrmm_("Left", uplo, trans, "Non-unit", n, &neig, &c_b1, &b[ b_offset], ldb, &a[a_offset], lda);
        }
    }
    work[1].r = (doublereal) lwkopt;
    work[1].i = 0.; // , expr subst
    return 0;
    /* End of ZHEGV */
}
Example #10
0
/* Subroutine */ int zposv_(char *uplo, integer *n, integer *nrhs, 
	doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
	integer *info, ftnlen uplo_len)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1;

    /* Local variables */
    extern logical lsame_(char *, char *, ftnlen, ftnlen);
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), zpotrf_(
	    char *, integer *, doublecomplex *, integer *, integer *, ftnlen),
	     zpotrs_(char *, integer *, integer *, doublecomplex *, integer *,
	     doublecomplex *, integer *, integer *, ftnlen);


/*  -- LAPACK driver routine (version 3.0) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/*     Courant Institute, Argonne National Lab, and Rice University */
/*     March 31, 1993 */

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

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

/*  ZPOSV computes the solution to a complex system of linear equations */
/*     A * X = B, */
/*  where A is an N-by-N Hermitian positive definite matrix and X and B */
/*  are N-by-NRHS matrices. */

/*  The Cholesky decomposition is used to factor A as */
/*     A = U**H* U,  if UPLO = 'U', or */
/*     A = L * L**H,  if UPLO = 'L', */
/*  where U is an upper triangular matrix and  L is a lower triangular */
/*  matrix.  The factored form of A is then used to solve the system of */
/*  equations A * X = B. */

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

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

/*  A       (input/output) COMPLEX*16 array, dimension (LDA,N) */
/*          On entry, 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. */

/*          On exit, if INFO = 0, the factor U or L from the Cholesky */
/*          factorization A = U**H*U or A = L*L**H. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A.  LDA >= max(1,N). */

/*  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS) */
/*          On entry, the N-by-NRHS right hand side matrix B. */
/*          On exit, if INFO = 0, the N-by-NRHS solution matrix X. */

/*  LDB     (input) INTEGER */
/*          The leading dimension of the array B.  LDB >= max(1,N). */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
/*          > 0:  if INFO = i, the leading minor of order i of A is not */
/*                positive definite, so the factorization could not be */
/*                completed, and the solution has not been computed. */

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

/*     .. 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;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;

    /* Function Body */
    *info = 0;
    if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, "L", (
	    ftnlen)1, (ftnlen)1)) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*nrhs < 0) {
	*info = -3;
    } else if (*lda < max(1,*n)) {
	*info = -5;
    } else if (*ldb < max(1,*n)) {
	*info = -7;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZPOSV ", &i__1, (ftnlen)6);
	return 0;
    }

/*     Compute the Cholesky factorization A = U'*U or A = L*L'. */

    zpotrf_(uplo, n, &a[a_offset], lda, info, (ftnlen)1);
    if (*info == 0) {

/*        Solve the system A*X = B, overwriting B with X. */

	zpotrs_(uplo, n, nrhs, &a[a_offset], lda, &b[b_offset], ldb, info, (
		ftnlen)1);

    }
    return 0;

/*     End of ZPOSV */

} /* zposv_ */
Example #11
0
/* Subroutine */ int zpftrf_(char *transr, char *uplo, integer *n, 
	doublecomplex *a, integer *info)
{
    /* System generated locals */
    integer i__1, i__2;

    /* Local variables */
    integer k, n1, n2;
    logical normaltransr;
    logical lower;
    logical nisodd;

/*  -- LAPACK routine (version 3.2)                                    -- */

/*  -- Contributed by Fred Gustavson of the IBM Watson Research Center -- */
/*  -- November 2008                                                   -- */

/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */

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

/*  ZPFTRF computes the Cholesky factorization of a complex Hermitian */
/*  positive definite matrix A. */

/*  The factorization has the form */
/*     A = U**H * U,  if UPLO = 'U', or */
/*     A = L  * L**H,  if UPLO = 'L', */
/*  where U is an upper triangular matrix and L is lower triangular. */

/*  This is the block version of the algorithm, calling Level 3 BLAS. */

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

/*  TRANSR    (input) CHARACTER */
/*          = 'N':  The Normal TRANSR of RFP A is stored; */
/*          = 'C':  The Conjugate-transpose TRANSR of RFP A is stored. */

/*  UPLO    (input) CHARACTER */
/*          = 'U':  Upper triangle of RFP A is stored; */
/*          = 'L':  Lower triangle of RFP A is stored. */

/*  N       (input) INTEGER */
/*          The order of the matrix A.  N >= 0. */

/*  A       (input/output) COMPLEX array, dimension ( N*(N+1)/2 ); */
/*          On entry, the Hermitian matrix A in RFP format. RFP format is */
/*          described by TRANSR, UPLO, and N as follows: If TRANSR = 'N' */
/*          then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is */
/*          (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'C' then RFP is */
/*          the Conjugate-transpose of RFP A as defined when */
/*          TRANSR = 'N'. The contents of RFP A are defined by UPLO as */
/*          follows: If UPLO = 'U' the RFP A contains the nt elements of */
/*          upper packed A. If UPLO = 'L' the RFP A contains the elements */
/*          of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = */
/*          'C'. When TRANSR is 'N' the LDA is N+1 when N is even and N */
/*          is odd. See the Note below for more details. */

/*          On exit, if INFO = 0, the factor U or L from the Cholesky */
/*          factorization RFP A = U**H*U or RFP A = L*L**H. */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
/*          > 0:  if INFO = i, the leading minor of order i is not */
/*                positive definite, and the factorization could not be */
/*                completed. */

/*  Further Notes on RFP Format: */
/*  ============================ */

/*  We first consider Standard Packed Format when N is even. */
/*  We give an example where N = 6. */

/*     AP is Upper             AP is Lower */

/*   00 01 02 03 04 05       00 */
/*      11 12 13 14 15       10 11 */
/*         22 23 24 25       20 21 22 */
/*            33 34 35       30 31 32 33 */
/*               44 45       40 41 42 43 44 */
/*                  55       50 51 52 53 54 55 */

/*  Let TRANSR = 'N'. RFP holds AP as follows: */
/*  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last */
/*  three columns of AP upper. The lower triangle A(4:6,0:2) consists of */
/*  conjugate-transpose of the first three columns of AP upper. */
/*  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first */
/*  three columns of AP lower. The upper triangle A(0:2,0:2) consists of */
/*  conjugate-transpose of the last three columns of AP lower. */
/*  To denote conjugate we place -- above the element. This covers the */
/*  case N even and TRANSR = 'N'. */

/*         RFP A                   RFP A */

/*                                -- -- -- */
/*        03 04 05                33 43 53 */
/*                                   -- -- */
/*        13 14 15                00 44 54 */
/*                                      -- */
/*        23 24 25                10 11 55 */

/*        33 34 35                20 21 22 */
/*        -- */
/*        00 44 45                30 31 32 */
/*        -- -- */
/*        01 11 55                40 41 42 */
/*        -- -- -- */
/*        02 12 22                50 51 52 */

/*  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- */
/*  transpose of RFP A above. One therefore gets: */

/*           RFP A                   RFP A */

/*     -- -- -- --                -- -- -- -- -- -- */
/*     03 13 23 33 00 01 02    33 00 10 20 30 40 50 */
/*     -- -- -- -- --                -- -- -- -- -- */
/*     04 14 24 34 44 11 12    43 44 11 21 31 41 51 */
/*     -- -- -- -- -- --                -- -- -- -- */
/*     05 15 25 35 45 55 22    53 54 55 22 32 42 52 */

/*  We next  consider Standard Packed Format when N is odd. */
/*  We give an example where N = 5. */

/*     AP is Upper                 AP is Lower */

/*   00 01 02 03 04              00 */
/*      11 12 13 14              10 11 */
/*         22 23 24              20 21 22 */
/*            33 34              30 31 32 33 */
/*               44              40 41 42 43 44 */

/*  Let TRANSR = 'N'. RFP holds AP as follows: */
/*  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last */
/*  three columns of AP upper. The lower triangle A(3:4,0:1) consists of */
/*  conjugate-transpose of the first two   columns of AP upper. */
/*  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first */
/*  three columns of AP lower. The upper triangle A(0:1,1:2) consists of */
/*  conjugate-transpose of the last two   columns of AP lower. */
/*  To denote conjugate we place -- above the element. This covers the */
/*  case N odd  and TRANSR = 'N'. */

/*         RFP A                   RFP A */

/*                                   -- -- */
/*        02 03 04                00 33 43 */
/*                                      -- */
/*        12 13 14                10 11 44 */

/*        22 23 24                20 21 22 */
/*        -- */
/*        00 33 34                30 31 32 */
/*        -- -- */
/*        01 11 44                40 41 42 */

/*  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- */
/*  transpose of RFP A above. One therefore gets: */

/*           RFP A                   RFP A */

/*     -- -- --                   -- -- -- -- -- -- */
/*     02 12 22 00 01             00 10 20 30 40 50 */
/*     -- -- -- --                   -- -- -- -- -- */
/*     03 13 23 33 11             33 11 21 31 41 51 */
/*     -- -- -- -- --                   -- -- -- -- */
/*     04 14 24 34 44             43 44 22 32 42 52 */

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

/*     Test the input parameters. */

    *info = 0;
    normaltransr = lsame_(transr, "N");
    lower = lsame_(uplo, "L");
    if (! normaltransr && ! lsame_(transr, "C")) {
	*info = -1;
    } else if (! lower && ! lsame_(uplo, "U")) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZPFTRF", &i__1);
	return 0;
    }

/*     Quick return if possible */

    if (*n == 0) {
	return 0;
    }

/*     If N is odd, set NISODD = .TRUE. */
/*     If N is even, set K = N/2 and NISODD = .FALSE. */

    if (*n % 2 == 0) {
	k = *n / 2;
	nisodd = FALSE_;
    } else {
	nisodd = TRUE_;
    }

/*     Set N1 and N2 depending on LOWER */

    if (lower) {
	n2 = *n / 2;
	n1 = *n - n2;
    } else {
	n1 = *n / 2;
	n2 = *n - n1;
    }

/*     start execution: there are eight cases */

    if (nisodd) {

/*        N is odd */

	if (normaltransr) {

/*           N is odd and TRANSR = 'N' */

	    if (lower) {

/*             SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) ) */
/*             T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0) */
/*             T1 -> a(0), T2 -> a(n), S -> a(n1) */

		zpotrf_("L", &n1, a, n, info);
		if (*info > 0) {
		    return 0;
		}
		ztrsm_("R", "L", "C", "N", &n2, &n1, &c_b1, a, n, &a[n1], n);
		zherk_("U", "N", &n2, &n1, &c_b15, &a[n1], n, &c_b16, &a[*n], 
			n);
		zpotrf_("U", &n2, &a[*n], n, info);
		if (*info > 0) {
		    *info += n1;
		}

	    } else {

/*             SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1) */
/*             T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0) */
/*             T1 -> a(n2), T2 -> a(n1), S -> a(0) */

		zpotrf_("L", &n1, &a[n2], n, info);
		if (*info > 0) {
		    return 0;
		}
		ztrsm_("L", "L", "N", "N", &n1, &n2, &c_b1, &a[n2], n, a, n);
		zherk_("U", "C", &n2, &n1, &c_b15, a, n, &c_b16, &a[n1], n);
		zpotrf_("U", &n2, &a[n1], n, info);
		if (*info > 0) {
		    *info += n1;
		}

	    }

	} else {

/*           N is odd and TRANSR = 'C' */

	    if (lower) {

/*              SRPA for LOWER, TRANSPOSE and N is odd */
/*              T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1) */
/*              T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1 */

		zpotrf_("U", &n1, a, &n1, info);
		if (*info > 0) {
		    return 0;
		}
		ztrsm_("L", "U", "C", "N", &n1, &n2, &c_b1, a, &n1, &a[n1 * 
			n1], &n1);
		zherk_("L", "C", &n2, &n1, &c_b15, &a[n1 * n1], &n1, &c_b16, &
			a[1], &n1);
		zpotrf_("L", &n2, &a[1], &n1, info);
		if (*info > 0) {
		    *info += n1;
		}

	    } else {

/*              SRPA for UPPER, TRANSPOSE and N is odd */
/*              T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0) */
/*              T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2 */

		zpotrf_("U", &n1, &a[n2 * n2], &n2, info);
		if (*info > 0) {
		    return 0;
		}
		ztrsm_("R", "U", "N", "N", &n2, &n1, &c_b1, &a[n2 * n2], &n2, 
			a, &n2);
		zherk_("L", "N", &n2, &n1, &c_b15, a, &n2, &c_b16, &a[n1 * n2]
, &n2);
		zpotrf_("L", &n2, &a[n1 * n2], &n2, info);
		if (*info > 0) {
		    *info += n1;
		}

	    }

	}

    } else {

/*        N is even */

	if (normaltransr) {

/*           N is even and TRANSR = 'N' */

	    if (lower) {

/*              SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) ) */
/*              T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0) */
/*              T1 -> a(1), T2 -> a(0), S -> a(k+1) */

		i__1 = *n + 1;
		zpotrf_("L", &k, &a[1], &i__1, info);
		if (*info > 0) {
		    return 0;
		}
		i__1 = *n + 1;
		i__2 = *n + 1;
		ztrsm_("R", "L", "C", "N", &k, &k, &c_b1, &a[1], &i__1, &a[k 
			+ 1], &i__2);
		i__1 = *n + 1;
		i__2 = *n + 1;
		zherk_("U", "N", &k, &k, &c_b15, &a[k + 1], &i__1, &c_b16, a, 
			&i__2);
		i__1 = *n + 1;
		zpotrf_("U", &k, a, &i__1, info);
		if (*info > 0) {
		    *info += k;
		}

	    } else {

/*              SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) ) */
/*              T1 -> a(k+1,0) ,  T2 -> a(k,0),   S -> a(0,0) */
/*              T1 -> a(k+1), T2 -> a(k), S -> a(0) */

		i__1 = *n + 1;
		zpotrf_("L", &k, &a[k + 1], &i__1, info);
		if (*info > 0) {
		    return 0;
		}
		i__1 = *n + 1;
		i__2 = *n + 1;
		ztrsm_("L", "L", "N", "N", &k, &k, &c_b1, &a[k + 1], &i__1, a, 
			 &i__2);
		i__1 = *n + 1;
		i__2 = *n + 1;
		zherk_("U", "C", &k, &k, &c_b15, a, &i__1, &c_b16, &a[k], &
			i__2);
		i__1 = *n + 1;
		zpotrf_("U", &k, &a[k], &i__1, info);
		if (*info > 0) {
		    *info += k;
		}

	    }

	} else {

/*           N is even and TRANSR = 'C' */

	    if (lower) {

/*              SRPA for LOWER, TRANSPOSE and N is even (see paper) */
/*              T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1) */
/*              T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k */

		zpotrf_("U", &k, &a[k], &k, info);
		if (*info > 0) {
		    return 0;
		}
		ztrsm_("L", "U", "C", "N", &k, &k, &c_b1, &a[k], &n1, &a[k * (
			k + 1)], &k);
		zherk_("L", "C", &k, &k, &c_b15, &a[k * (k + 1)], &k, &c_b16, 
			a, &k);
		zpotrf_("L", &k, a, &k, info);
		if (*info > 0) {
		    *info += k;
		}

	    } else {

/*              SRPA for UPPER, TRANSPOSE and N is even (see paper) */
/*              T1 -> B(0,k+1),     T2 -> B(0,k),   S -> B(0,0) */
/*              T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k */

		zpotrf_("U", &k, &a[k * (k + 1)], &k, info);
		if (*info > 0) {
		    return 0;
		}
		ztrsm_("R", "U", "N", "N", &k, &k, &c_b1, &a[k * (k + 1)], &k, 
			 a, &k);
		zherk_("L", "N", &k, &k, &c_b15, a, &k, &c_b16, &a[k * k], &k);
		zpotrf_("L", &k, &a[k * k], &k, info);
		if (*info > 0) {
		    *info += k;
		}

	    }

	}

    }

    return 0;

/*     End of ZPFTRF */

} /* zpftrf_ */
Example #12
0
/* Subroutine */
int zposvx_(char *fact, char *uplo, integer *n, integer * nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * ldaf, char *equed, doublereal *s, doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *ferr, doublereal *berr, 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, i__1, i__2, i__3, i__4, i__5;
    doublereal d__1, d__2;
    doublecomplex z__1;
    /* Local variables */
    integer i__, j;
    doublereal amax, smin, smax;
    extern logical lsame_(char *, char *);
    doublereal scond, anorm;
    logical equil, rcequ;
    extern doublereal dlamch_(char *);
    logical nofact;
    extern /* Subroutine */
    int xerbla_(char *, integer *);
    doublereal bignum;
    extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, integer *, doublereal *);
    extern /* Subroutine */
    int zlaqhe_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, char *);
    integer infequ;
    extern /* Subroutine */
    int zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zpocon_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *) ;
    doublereal smlnum;
    extern /* Subroutine */
    int zpoequ_(integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, integer *), zporfs_( char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpotrf_(char *, integer *, doublecomplex *, integer *, integer *), zpotrs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *);
    /* -- LAPACK driver routine (version 3.4.1) -- */
    /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
    /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
    /* April 2012 */
    /* .. Scalar Arguments .. */
    /* .. */
    /* .. Array Arguments .. */
    /* .. */
    /* ===================================================================== */
    /* .. Parameters .. */
    /* .. */
    /* .. Local Scalars .. */
    /* .. */
    /* .. External Functions .. */
    /* .. */
    /* .. External Subroutines .. */
    /* .. */
    /* .. Intrinsic Functions .. */
    /* .. */
    /* .. Executable Statements .. */
    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    af_dim1 = *ldaf;
    af_offset = 1 + af_dim1;
    af -= af_offset;
    --s;
    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");
    equil = lsame_(fact, "E");
    if (nofact || equil)
    {
        *(unsigned char *)equed = 'N';
        rcequ = FALSE_;
    }
    else
    {
        rcequ = lsame_(equed, "Y");
        smlnum = dlamch_("Safe minimum");
        bignum = 1. / smlnum;
    }
    /* Test the input parameters. */
    if (! nofact && ! equil && ! 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 (lsame_(fact, "F") && ! (rcequ || lsame_( equed, "N")))
    {
        *info = -9;
    }
    else
    {
        if (rcequ)
        {
            smin = bignum;
            smax = 0.;
            i__1 = *n;
            for (j = 1;
                    j <= i__1;
                    ++j)
            {
                /* Computing MIN */
                d__1 = smin;
                d__2 = s[j]; // , expr subst
                smin = min(d__1,d__2);
                /* Computing MAX */
                d__1 = smax;
                d__2 = s[j]; // , expr subst
                smax = max(d__1,d__2);
                /* L10: */
            }
            if (smin <= 0.)
            {
                *info = -10;
            }
            else if (*n > 0)
            {
                scond = max(smin,smlnum) / min(smax,bignum);
            }
            else
            {
                scond = 1.;
            }
        }
        if (*info == 0)
        {
            if (*ldb < max(1,*n))
            {
                *info = -12;
            }
            else if (*ldx < max(1,*n))
            {
                *info = -14;
            }
        }
    }
    if (*info != 0)
    {
        i__1 = -(*info);
        xerbla_("ZPOSVX", &i__1);
        return 0;
    }
    if (equil)
    {
        /* Compute row and column scalings to equilibrate the matrix A. */
        zpoequ_(n, &a[a_offset], lda, &s[1], &scond, &amax, &infequ);
        if (infequ == 0)
        {
            /* Equilibrate the matrix. */
            zlaqhe_(uplo, n, &a[a_offset], lda, &s[1], &scond, &amax, equed);
            rcequ = lsame_(equed, "Y");
        }
    }
    /* Scale the right hand side. */
    if (rcequ)
    {
        i__1 = *nrhs;
        for (j = 1;
                j <= i__1;
                ++j)
        {
            i__2 = *n;
            for (i__ = 1;
                    i__ <= i__2;
                    ++i__)
            {
                i__3 = i__ + j * b_dim1;
                i__4 = i__;
                i__5 = i__ + j * b_dim1;
                z__1.r = s[i__4] * b[i__5].r;
                z__1.i = s[i__4] * b[i__5].i; // , expr subst
                b[i__3].r = z__1.r;
                b[i__3].i = z__1.i; // , expr subst
                /* L20: */
            }
            /* L30: */
        }
    }
    if (nofact || equil)
    {
        /* Compute the Cholesky factorization A = U**H *U or A = L*L**H. */
        zlacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf);
        zpotrf_(uplo, n, &af[af_offset], ldaf, info);
        /* Return if INFO is non-zero. */
        if (*info > 0)
        {
            *rcond = 0.;
            return 0;
        }
    }
    /* Compute the norm of the matrix A. */
    anorm = zlanhe_("1", uplo, n, &a[a_offset], lda, &rwork[1]);
    /* Compute the reciprocal of the condition number of A. */
    zpocon_(uplo, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &rwork[1], info);
    /* Compute the solution matrix X. */
    zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
    zpotrs_(uplo, n, nrhs, &af[af_offset], ldaf, &x[x_offset], ldx, info);
    /* Use iterative refinement to improve the computed solution and */
    /* compute error bounds and backward error estimates for it. */
    zporfs_(uplo, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &b[ b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[1], & rwork[1], info);
    /* Transform the solution matrix X to a solution of the original */
    /* system. */
    if (rcequ)
    {
        i__1 = *nrhs;
        for (j = 1;
                j <= i__1;
                ++j)
        {
            i__2 = *n;
            for (i__ = 1;
                    i__ <= i__2;
                    ++i__)
            {
                i__3 = i__ + j * x_dim1;
                i__4 = i__;
                i__5 = i__ + j * x_dim1;
                z__1.r = s[i__4] * x[i__5].r;
                z__1.i = s[i__4] * x[i__5].i; // , expr subst
                x[i__3].r = z__1.r;
                x[i__3].i = z__1.i; // , expr subst
                /* L40: */
            }
            /* L50: */
        }
        i__1 = *nrhs;
        for (j = 1;
                j <= i__1;
                ++j)
        {
            ferr[j] /= scond;
            /* L60: */
        }
    }
    /* Set INFO = N+1 if the matrix is singular to working precision. */
    if (*rcond < dlamch_("Epsilon"))
    {
        *info = *n + 1;
    }
    return 0;
    /* End of ZPOSVX */
}
Example #13
0
/* Subroutine */ int zerrpo_(char *path, integer *nunit)
{
    /* System generated locals */
    integer i__1;
    doublereal d__1, d__2;
    doublecomplex z__1;

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

    /* Local variables */
    doublecomplex a[16]	/* was [4][4] */, b[4];
    integer i__, j;
    doublereal r__[4];
    doublecomplex w[8], x[4];
    char c2[2];
    doublereal r1[4], r2[4];
    doublecomplex af[16]	/* was [4][4] */;
    integer info;
    doublereal anrm, rcond;
    extern /* Subroutine */ int zpbtf2_(char *, integer *, integer *, 
	    doublecomplex *, integer *, integer *), zpotf2_(char *, 
	    integer *, doublecomplex *, integer *, integer *), 
	    alaesm_(char *, logical *, integer *);
    extern logical lsamen_(integer *, char *, char *);
    extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical 
	    *, logical *), zpbcon_(char *, integer *, integer *, 
	    doublecomplex *, integer *, doublereal *, doublereal *, 
	    doublecomplex *, doublereal *, integer *), zpbequ_(char *, 
	     integer *, integer *, doublecomplex *, integer *, doublereal *, 
	    doublereal *, doublereal *, integer *), zpbrfs_(char *, 
	    integer *, integer *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, doublereal *, doublereal *, 
	    doublecomplex *, doublereal *, integer *), zpbtrf_(char *, 
	     integer *, integer *, doublecomplex *, integer *, integer *), zpocon_(char *, integer *, doublecomplex *, integer *, 
	    doublereal *, doublereal *, doublecomplex *, doublereal *, 
	    integer *), zppcon_(char *, integer *, doublecomplex *, 
	    doublereal *, doublereal *, doublecomplex *, doublereal *, 
	    integer *), zpoequ_(integer *, doublecomplex *, integer *, 
	     doublereal *, doublereal *, doublereal *, integer *), zpbtrs_(
	    char *, integer *, integer *, integer *, doublecomplex *, integer 
	    *, doublecomplex *, integer *, integer *), zporfs_(char *, 
	     integer *, integer *, doublecomplex *, integer *, doublecomplex *
, integer *, doublecomplex *, integer *, doublecomplex *, integer 
	    *, doublereal *, doublereal *, doublecomplex *, doublereal *, 
	    integer *), zpotrf_(char *, integer *, doublecomplex *, 
	    integer *, integer *), zpotri_(char *, integer *, 
	    doublecomplex *, integer *, integer *), zppequ_(char *, 
	    integer *, doublecomplex *, doublereal *, doublereal *, 
	    doublereal *, integer *), zpprfs_(char *, integer *, 
	    integer *, doublecomplex *, doublecomplex *, doublecomplex *, 
	    integer *, doublecomplex *, integer *, doublereal *, doublereal *, 
	     doublecomplex *, doublereal *, integer *), zpptrf_(char *
, integer *, doublecomplex *, integer *), zpptri_(char *, 
	    integer *, doublecomplex *, integer *), zpotrs_(char *, 
	    integer *, integer *, doublecomplex *, integer *, doublecomplex *, 
	     integer *, integer *), zpptrs_(char *, integer *, 
	    integer *, doublecomplex *, doublecomplex *, 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 */
/*  ======= */

/*  ZERRPO tests the error exits for the COMPLEX*16 routines */
/*  for Hermitian positive definite matrices. */

/*  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 .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. 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);

/*     Set the variables to innocuous values. */

    for (j = 1; j <= 4; ++j) {
	for (i__ = 1; i__ <= 4; ++i__) {
	    i__1 = i__ + (j << 2) - 5;
	    d__1 = 1. / (doublereal) (i__ + j);
	    d__2 = -1. / (doublereal) (i__ + j);
	    z__1.r = d__1, z__1.i = d__2;
	    a[i__1].r = z__1.r, a[i__1].i = z__1.i;
	    i__1 = i__ + (j << 2) - 5;
	    d__1 = 1. / (doublereal) (i__ + j);
	    d__2 = -1. / (doublereal) (i__ + j);
	    z__1.r = d__1, z__1.i = d__2;
	    af[i__1].r = z__1.r, af[i__1].i = z__1.i;
/* L10: */
	}
	i__1 = j - 1;
	b[i__1].r = 0., b[i__1].i = 0.;
	r1[j - 1] = 0.;
	r2[j - 1] = 0.;
	i__1 = j - 1;
	w[i__1].r = 0., w[i__1].i = 0.;
	i__1 = j - 1;
	x[i__1].r = 0., x[i__1].i = 0.;
/* L20: */
    }
    anrm = 1.;
    infoc_1.ok = TRUE_;

/*     Test error exits of the routines that use the Cholesky */
/*     decomposition of a Hermitian positive definite matrix. */

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

/*        ZPOTRF */

	s_copy(srnamc_1.srnamt, "ZPOTRF", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpotrf_("/", &c__0, a, &c__1, &info);
	chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpotrf_("U", &c_n1, a, &c__1, &info);
	chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	zpotrf_("U", &c__2, a, &c__1, &info);
	chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPOTF2 */

	s_copy(srnamc_1.srnamt, "ZPOTF2", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpotf2_("/", &c__0, a, &c__1, &info);
	chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpotf2_("U", &c_n1, a, &c__1, &info);
	chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	zpotf2_("U", &c__2, a, &c__1, &info);
	chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPOTRI */

	s_copy(srnamc_1.srnamt, "ZPOTRI", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpotri_("/", &c__0, a, &c__1, &info);
	chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpotri_("U", &c_n1, a, &c__1, &info);
	chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	zpotri_("U", &c__2, a, &c__1, &info);
	chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPOTRS */

	s_copy(srnamc_1.srnamt, "ZPOTRS", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpotrs_("/", &c__0, &c__0, a, &c__1, b, &c__1, &info);
	chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpotrs_("U", &c_n1, &c__0, a, &c__1, b, &c__1, &info);
	chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zpotrs_("U", &c__0, &c_n1, a, &c__1, b, &c__1, &info);
	chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zpotrs_("U", &c__2, &c__1, a, &c__1, b, &c__2, &info);
	chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 7;
	zpotrs_("U", &c__2, &c__1, a, &c__2, b, &c__1, &info);
	chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPORFS */

	s_copy(srnamc_1.srnamt, "ZPORFS", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zporfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1, 
		r1, r2, w, r__, &info);
	chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zporfs_("U", &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1, 
		r1, r2, w, r__, &info);
	chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zporfs_("U", &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, &c__1, 
		r1, r2, w, r__, &info);
	chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zporfs_("U", &c__2, &c__1, a, &c__1, af, &c__2, b, &c__2, x, &c__2, 
		r1, r2, w, r__, &info);
	chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 7;
	zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__1, b, &c__2, x, &c__2, 
		r1, r2, w, r__, &info);
	chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 9;
	zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__1, x, &c__2, 
		r1, r2, w, r__, &info);
	chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 11;
	zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__2, x, &c__1, 
		r1, r2, w, r__, &info);
	chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPOCON */

	s_copy(srnamc_1.srnamt, "ZPOCON", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpocon_("/", &c__0, a, &c__1, &anrm, &rcond, w, r__, &info)
		;
	chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpocon_("U", &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info)
		;
	chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	zpocon_("U", &c__2, a, &c__1, &anrm, &rcond, w, r__, &info)
		;
	chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	d__1 = -anrm;
	zpocon_("U", &c__1, a, &c__1, &d__1, &rcond, w, r__, &info)
		;
	chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPOEQU */

	s_copy(srnamc_1.srnamt, "ZPOEQU", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpoequ_(&c_n1, a, &c__1, r1, &rcond, &anrm, &info);
	chkxer_("ZPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zpoequ_(&c__2, a, &c__1, r1, &rcond, &anrm, &info);
	chkxer_("ZPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*     Test error exits of the routines that use the Cholesky */
/*     decomposition of a Hermitian positive definite packed matrix. */

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

/*        ZPPTRF */

	s_copy(srnamc_1.srnamt, "ZPPTRF", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpptrf_("/", &c__0, a, &info);
	chkxer_("ZPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpptrf_("U", &c_n1, a, &info);
	chkxer_("ZPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPPTRI */

	s_copy(srnamc_1.srnamt, "ZPPTRI", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpptri_("/", &c__0, a, &info);
	chkxer_("ZPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpptri_("U", &c_n1, a, &info);
	chkxer_("ZPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPPTRS */

	s_copy(srnamc_1.srnamt, "ZPPTRS", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpptrs_("/", &c__0, &c__0, a, b, &c__1, &info);
	chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpptrs_("U", &c_n1, &c__0, a, b, &c__1, &info);
	chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zpptrs_("U", &c__0, &c_n1, a, b, &c__1, &info);
	chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 6;
	zpptrs_("U", &c__2, &c__1, a, b, &c__1, &info);
	chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPPRFS */

	s_copy(srnamc_1.srnamt, "ZPPRFS", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpprfs_("/", &c__0, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, r__, 
		&info);
	chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpprfs_("U", &c_n1, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, r__, 
		&info);
	chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zpprfs_("U", &c__0, &c_n1, a, af, b, &c__1, x, &c__1, r1, r2, w, r__, 
		&info);
	chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 7;
	zpprfs_("U", &c__2, &c__1, a, af, b, &c__1, x, &c__2, r1, r2, w, r__, 
		&info);
	chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 9;
	zpprfs_("U", &c__2, &c__1, a, af, b, &c__2, x, &c__1, r1, r2, w, r__, 
		&info);
	chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPPCON */

	s_copy(srnamc_1.srnamt, "ZPPCON", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zppcon_("/", &c__0, a, &anrm, &rcond, w, r__, &info);
	chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zppcon_("U", &c_n1, a, &anrm, &rcond, w, r__, &info);
	chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	d__1 = -anrm;
	zppcon_("U", &c__1, a, &d__1, &rcond, w, r__, &info);
	chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPPEQU */

	s_copy(srnamc_1.srnamt, "ZPPEQU", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zppequ_("/", &c__0, a, r1, &rcond, &anrm, &info);
	chkxer_("ZPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zppequ_("U", &c_n1, a, r1, &rcond, &anrm, &info);
	chkxer_("ZPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*     Test error exits of the routines that use the Cholesky */
/*     decomposition of a Hermitian positive definite band matrix. */

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

/*        ZPBTRF */

	s_copy(srnamc_1.srnamt, "ZPBTRF", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpbtrf_("/", &c__0, &c__0, a, &c__1, &info);
	chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpbtrf_("U", &c_n1, &c__0, a, &c__1, &info);
	chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zpbtrf_("U", &c__1, &c_n1, a, &c__1, &info);
	chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zpbtrf_("U", &c__2, &c__1, a, &c__1, &info);
	chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPBTF2 */

	s_copy(srnamc_1.srnamt, "ZPBTF2", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpbtf2_("/", &c__0, &c__0, a, &c__1, &info);
	chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpbtf2_("U", &c_n1, &c__0, a, &c__1, &info);
	chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zpbtf2_("U", &c__1, &c_n1, a, &c__1, &info);
	chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zpbtf2_("U", &c__2, &c__1, a, &c__1, &info);
	chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPBTRS */

	s_copy(srnamc_1.srnamt, "ZPBTRS", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpbtrs_("/", &c__0, &c__0, &c__0, a, &c__1, b, &c__1, &info);
	chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpbtrs_("U", &c_n1, &c__0, &c__0, a, &c__1, b, &c__1, &info);
	chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zpbtrs_("U", &c__1, &c_n1, &c__0, a, &c__1, b, &c__1, &info);
	chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	zpbtrs_("U", &c__0, &c__0, &c_n1, a, &c__1, b, &c__1, &info);
	chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 6;
	zpbtrs_("U", &c__2, &c__1, &c__1, a, &c__1, b, &c__1, &info);
	chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 8;
	zpbtrs_("U", &c__2, &c__0, &c__1, a, &c__1, b, &c__1, &info);
	chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPBRFS */

	s_copy(srnamc_1.srnamt, "ZPBRFS", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpbrfs_("/", &c__0, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &
		c__1, r1, r2, w, r__, &info);
	chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpbrfs_("U", &c_n1, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &
		c__1, r1, r2, w, r__, &info);
	chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zpbrfs_("U", &c__1, &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &
		c__1, r1, r2, w, r__, &info);
	chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	zpbrfs_("U", &c__0, &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, &
		c__1, r1, r2, w, r__, &info);
	chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 6;
	zpbrfs_("U", &c__2, &c__1, &c__1, a, &c__1, af, &c__2, b, &c__2, x, &
		c__2, r1, r2, w, r__, &info);
	chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 8;
	zpbrfs_("U", &c__2, &c__1, &c__1, a, &c__2, af, &c__1, b, &c__2, x, &
		c__2, r1, r2, w, r__, &info);
	chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 10;
	zpbrfs_("U", &c__2, &c__0, &c__1, a, &c__1, af, &c__1, b, &c__1, x, &
		c__2, r1, r2, w, r__, &info);
	chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 12;
	zpbrfs_("U", &c__2, &c__0, &c__1, a, &c__1, af, &c__1, b, &c__2, x, &
		c__1, r1, r2, w, r__, &info);
	chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPBCON */

	s_copy(srnamc_1.srnamt, "ZPBCON", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpbcon_("/", &c__0, &c__0, a, &c__1, &anrm, &rcond, w, r__, &info);
	chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpbcon_("U", &c_n1, &c__0, a, &c__1, &anrm, &rcond, w, r__, &info);
	chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zpbcon_("U", &c__1, &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info);
	chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zpbcon_("U", &c__2, &c__1, a, &c__1, &anrm, &rcond, w, r__, &info);
	chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 6;
	d__1 = -anrm;
	zpbcon_("U", &c__1, &c__0, a, &c__1, &d__1, &rcond, w, r__, &info);
	chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPBEQU */

	s_copy(srnamc_1.srnamt, "ZPBEQU", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpbequ_("/", &c__0, &c__0, a, &c__1, r1, &rcond, &anrm, &info);
	chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpbequ_("U", &c_n1, &c__0, a, &c__1, r1, &rcond, &anrm, &info);
	chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zpbequ_("U", &c__1, &c_n1, a, &c__1, r1, &rcond, &anrm, &info);
	chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zpbequ_("U", &c__2, &c__1, a, &c__1, r1, &rcond, &anrm, &info);
	chkxer_("ZPBEQU", &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 ZERRPO */

} /* zerrpo_ */
Example #14
0
/* Subroutine */ int zhegv_(integer *itype, char *jobz, char *uplo, integer *
	n, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
	doublereal *w, doublecomplex *work, integer *lwork, doublereal *rwork,
	 integer *info)
{
/*  -- LAPACK driver routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       June 30, 1999   


    Purpose   
    =======   

    ZHEGV computes all the eigenvalues, and optionally, the eigenvectors   
    of a complex generalized Hermitian-definite eigenproblem, of the form   
    A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.   
    Here A and B are assumed to be Hermitian and B is also   
    positive definite.   

    Arguments   
    =========   

    ITYPE   (input) INTEGER   
            Specifies the problem type to be solved:   
            = 1:  A*x = (lambda)*B*x   
            = 2:  A*B*x = (lambda)*x   
            = 3:  B*A*x = (lambda)*x   

    JOBZ    (input) CHARACTER*1   
            = 'N':  Compute eigenvalues only;   
            = 'V':  Compute eigenvalues and eigenvectors.   

    UPLO    (input) CHARACTER*1   
            = 'U':  Upper triangles of A and B are stored;   
            = 'L':  Lower triangles of A and B are stored.   

    N       (input) INTEGER   
            The order of the matrices A and B.  N >= 0.   

    A       (input/output) COMPLEX*16 array, dimension (LDA, N)   
            On entry, 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.  If UPLO = 'L',   
            the leading N-by-N lower triangular part of A contains   
            the lower triangular part of the matrix A.   

            On exit, if JOBZ = 'V', then if INFO = 0, A contains the   
            matrix Z of eigenvectors.  The eigenvectors are normalized   
            as follows:   
            if ITYPE = 1 or 2, Z**H*B*Z = I;   
            if ITYPE = 3, Z**H*inv(B)*Z = I.   
            If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')   
            or the lower triangle (if UPLO='L') of A, including the   
            diagonal, is destroyed.   

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

    B       (input/output) COMPLEX*16 array, dimension (LDB, N)   
            On entry, the Hermitian positive definite matrix B.   
            If UPLO = 'U', the leading N-by-N upper triangular part of B   
            contains the upper triangular part of the matrix B.   
            If UPLO = 'L', the leading N-by-N lower triangular part of B   
            contains the lower triangular part of the matrix B.   

            On exit, if INFO <= N, the part of B containing the matrix is   
            overwritten by the triangular factor U or L from the Cholesky   
            factorization B = U**H*U or B = L*L**H.   

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

    W       (output) DOUBLE PRECISION array, dimension (N)   
            If INFO = 0, the eigenvalues in ascending order.   

    WORK    (workspace/output) COMPLEX*16 array, dimension (LWORK)   
            On exit, if INFO = 0, WORK(1) returns the optimal LWORK.   

    LWORK   (input) INTEGER   
            The length of the array WORK.  LWORK >= max(1,2*N-1).   
            For optimal efficiency, LWORK >= (NB+1)*N,   
            where NB is the blocksize for ZHETRD returned by ILAENV.   

            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 (max(1, 3*N-2))   

    INFO    (output) INTEGER   
            = 0:  successful exit   
            < 0:  if INFO = -i, the i-th argument had an illegal value   
            > 0:  ZPOTRF or ZHEEV returned an error code:   
               <= N:  if INFO = i, ZHEEV failed to converge;   
                      i off-diagonal elements of an intermediate   
                      tridiagonal form did not converge to zero;   
               > N:   if INFO = N + i, for 1 <= i <= N, then the leading   
                      minor of order i of B is not positive definite.   
                      The factorization of B could not be completed and   
                      no eigenvalues or eigenvectors were computed.   

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


       Test the input parameters.   

       Parameter adjustments */
    /* Table of constant values */
    static doublecomplex c_b1 = {1.,0.};
    static integer c__1 = 1;
    static integer c_n1 = -1;
    
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
    /* Local variables */
    static integer neig;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int zheev_(char *, char *, integer *, 
	    doublecomplex *, integer *, doublereal *, doublecomplex *, 
	    integer *, doublereal *, integer *);
    static char trans[1];
    static logical upper, wantz;
    extern /* Subroutine */ int ztrmm_(char *, char *, char *, char *, 
	    integer *, integer *, doublecomplex *, doublecomplex *, integer *,
	     doublecomplex *, integer *), 
	    ztrsm_(char *, char *, char *, char *, integer *, integer *, 
	    doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
	    integer *);
    static integer nb;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    extern /* Subroutine */ int zhegst_(integer *, char *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, integer *);
    static integer lwkopt;
    static logical lquery;
    extern /* Subroutine */ int zpotrf_(char *, integer *, doublecomplex *, 
	    integer *, integer *);


    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    --w;
    --work;
    --rwork;

    /* Function Body */
    wantz = lsame_(jobz, "V");
    upper = lsame_(uplo, "U");
    lquery = *lwork == -1;

    *info = 0;
    if (*itype < 1 || *itype > 3) {
	*info = -1;
    } else if (! (wantz || lsame_(jobz, "N"))) {
	*info = -2;
    } else if (! (upper || lsame_(uplo, "L"))) {
	*info = -3;
    } else if (*n < 0) {
	*info = -4;
    } else if (*lda < max(1,*n)) {
	*info = -6;
    } else if (*ldb < max(1,*n)) {
	*info = -8;
    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__1 = 1, i__2 = (*n << 1) - 1;
	if (*lwork < max(i__1,i__2) && ! lquery) {
	    *info = -11;
	}
    }

    if (*info == 0) {
	nb = ilaenv_(&c__1, "ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6,
		 (ftnlen)1);
	lwkopt = (nb + 1) * *n;
	work[1].r = (doublereal) lwkopt, work[1].i = 0.;
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZHEGV ", &i__1);
	return 0;
    }

/*     Quick return if possible */

    if (*n == 0) {
	return 0;
    }

/*     Form a Cholesky factorization of B. */

    zpotrf_(uplo, n, &b[b_offset], ldb, info);
    if (*info != 0) {
	*info = *n + *info;
	return 0;
    }

/*     Transform problem to standard eigenvalue problem and solve. */

    zhegst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info);
    zheev_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, &rwork[1]
	    , info);

    if (wantz) {

/*        Backtransform eigenvectors to the original problem. */

	neig = *n;
	if (*info > 0) {
	    neig = *info - 1;
	}
	if (*itype == 1 || *itype == 2) {

/*           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;   
             backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */

	    if (upper) {
		*(unsigned char *)trans = 'N';
	    } else {
		*(unsigned char *)trans = 'C';
	    }

	    ztrsm_("Left", uplo, trans, "Non-unit", n, &neig, &c_b1, &b[
		    b_offset], ldb, &a[a_offset], lda);

	} else if (*itype == 3) {

/*           For B*A*x=(lambda)*x;   
             backtransform eigenvectors: x = L*y or U'*y */

	    if (upper) {
		*(unsigned char *)trans = 'C';
	    } else {
		*(unsigned char *)trans = 'N';
	    }

	    ztrmm_("Left", uplo, trans, "Non-unit", n, &neig, &c_b1, &b[
		    b_offset], ldb, &a[a_offset], lda);
	}
    }

    work[1].r = (doublereal) lwkopt, work[1].i = 0.;

    return 0;

/*     End of ZHEGV */

} /* zhegv_ */
Example #15
0
/* Subroutine */ int zposvx_(char *fact, char *uplo, integer *n, integer *
	nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer *
	ldaf, char *equed, doublereal *s, doublecomplex *b, integer *ldb, 
	doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *ferr, 
	doublereal *berr, doublecomplex *work, doublereal *rwork, integer *
	info, ftnlen fact_len, ftnlen uplo_len, ftnlen equed_len)
{
    /* System generated locals */
    integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, 
	    x_offset, i__1, i__2, i__3, i__4, i__5;
    doublereal d__1, d__2;
    doublecomplex z__1;

    /* Local variables */
    static integer i__, j;
    static doublereal amax, smin, smax;
    extern logical lsame_(char *, char *, ftnlen, ftnlen);
    static doublereal scond, anorm;
    static logical equil, rcequ;
    extern doublereal dlamch_(char *, ftnlen);
    static logical nofact;
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    static doublereal bignum;
    extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, 
	    integer *, doublereal *, ftnlen, ftnlen);
    extern /* Subroutine */ int zlaqhe_(char *, integer *, doublecomplex *, 
	    integer *, doublereal *, doublereal *, doublereal *, char *, 
	    ftnlen, ftnlen);
    static integer infequ;
    extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, ftnlen), 
	    zpocon_(char *, integer *, doublecomplex *, integer *, doublereal 
	    *, doublereal *, doublecomplex *, doublereal *, integer *, ftnlen)
	    ;
    static doublereal smlnum;
    extern /* Subroutine */ int zpoequ_(integer *, doublecomplex *, integer *,
	     doublereal *, doublereal *, doublereal *, integer *), zporfs_(
	    char *, integer *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, doublereal *, doublereal *, 
	    doublecomplex *, doublereal *, integer *, ftnlen), zpotrf_(char *,
	     integer *, doublecomplex *, integer *, integer *, ftnlen), 
	    zpotrs_(char *, integer *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, integer *, ftnlen);


/*  -- LAPACK driver routine (version 3.0) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/*     Courant Institute, Argonne National Lab, and Rice University */
/*     June 30, 1999 */

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

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

/*  ZPOSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to */
/*  compute the solution to a complex system of linear equations */
/*     A * X = B, */
/*  where A is an N-by-N Hermitian positive definite 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 = 'E', real scaling factors are computed to equilibrate */
/*     the system: */
/*        diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B */
/*     Whether or not the system will be equilibrated depends on the */
/*     scaling of the matrix A, but if equilibration is used, A is */
/*     overwritten by diag(S)*A*diag(S) and B by diag(S)*B. */

/*  2. If FACT = 'N' or 'E', the Cholesky decomposition is used to */
/*     factor the matrix A (after equilibration if FACT = 'E') as */
/*        A = U**H* U,  if UPLO = 'U', or */
/*        A = L * L**H,  if UPLO = 'L', */
/*     where U is an upper triangular matrix and L is a lower triangular */
/*     matrix. */

/*  3. If the leading i-by-i principal minor is not positive definite, */
/*     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. */

/*  4. The system of equations is solved for X using the factored form */
/*     of A. */

/*  5. Iterative refinement is applied to improve the computed solution */
/*     matrix and calculate error bounds and backward error estimates */
/*     for it. */

/*  6. If equilibration was used, the matrix X is premultiplied by */
/*     diag(S) so that it solves the original system before */
/*     equilibration. */

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

/*  FACT    (input) CHARACTER*1 */
/*          Specifies whether or not the factored form of the matrix A is */
/*          supplied on entry, and if not, whether the matrix A should be */
/*          equilibrated before it is factored. */
/*          = 'F':  On entry, AF contains the factored form of A. */
/*                  If EQUED = 'Y', the matrix A has been equilibrated */
/*                  with scaling factors given by S.  A and AF will not */
/*                  be modified. */
/*          = 'N':  The matrix A will be copied to AF and factored. */
/*          = 'E':  The matrix A will be equilibrated if necessary, then */
/*                  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/output) COMPLEX*16 array, dimension (LDA,N) */
/*          On entry, the Hermitian matrix A, except if FACT = 'F' and */
/*          EQUED = 'Y', then A must contain the equilibrated matrix */
/*          diag(S)*A*diag(S).  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.  A is not modified if */
/*          FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit. */

/*          On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by */
/*          diag(S)*A*diag(S). */

/*  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 triangular factor U or L from the Cholesky */
/*          factorization A = U**H*U or A = L*L**H, in the same storage */
/*          format as A.  If EQUED .ne. 'N', then AF is the factored form */
/*          of the equilibrated matrix diag(S)*A*diag(S). */

/*          If FACT = 'N', then AF is an output argument and on exit */
/*          returns the triangular factor U or L from the Cholesky */
/*          factorization A = U**H*U or A = L*L**H of the original */
/*          matrix A. */

/*          If FACT = 'E', then AF is an output argument and on exit */
/*          returns the triangular factor U or L from the Cholesky */
/*          factorization A = U**H*U or A = L*L**H of the equilibrated */
/*          matrix A (see the description of A for the form of the */
/*          equilibrated matrix). */

/*  LDAF    (input) INTEGER */
/*          The leading dimension of the array AF.  LDAF >= max(1,N). */

/*  EQUED   (input or output) CHARACTER*1 */
/*          Specifies the form of equilibration that was done. */
/*          = 'N':  No equilibration (always true if FACT = 'N'). */
/*          = 'Y':  Equilibration was done, i.e., A has been replaced by */
/*                  diag(S) * A * diag(S). */
/*          EQUED is an input argument if FACT = 'F'; otherwise, it is an */
/*          output argument. */

/*  S       (input or output) DOUBLE PRECISION array, dimension (N) */
/*          The scale factors for A; not accessed if EQUED = 'N'.  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. */

/*  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS) */
/*          On entry, the N-by-NRHS righthand side matrix B. */
/*          On exit, if EQUED = 'N', B is not modified; if EQUED = 'Y', */
/*          B is overwritten by diag(S) * 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 to */
/*          the original system of equations.  Note that if EQUED = 'Y', */
/*          A and B are modified on exit, and the solution to the */
/*          equilibrated system is inv(diag(S))*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 after equilibration (if done).  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) COMPLEX*16 array, dimension (2*N) */

/*  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:  the leading minor of order i of A is */
/*                       not positive definite, so the factorization */
/*                       could not be completed, and the solution has not */
/*                       been 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 */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    af_dim1 = *ldaf;
    af_offset = 1 + af_dim1;
    af -= af_offset;
    --s;
    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", (ftnlen)1, (ftnlen)1);
    equil = lsame_(fact, "E", (ftnlen)1, (ftnlen)1);
    if (nofact || equil) {
	*(unsigned char *)equed = 'N';
	rcequ = FALSE_;
    } else {
	rcequ = lsame_(equed, "Y", (ftnlen)1, (ftnlen)1);
	smlnum = dlamch_("Safe minimum", (ftnlen)12);
	bignum = 1. / smlnum;
    }

/*     Test the input parameters. */

    if (! nofact && ! equil && ! lsame_(fact, "F", (ftnlen)1, (ftnlen)1)) {
	*info = -1;
    } else if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, 
	    "L", (ftnlen)1, (ftnlen)1)) {
	*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 (lsame_(fact, "F", (ftnlen)1, (ftnlen)1) && ! (rcequ || lsame_(
	    equed, "N", (ftnlen)1, (ftnlen)1))) {
	*info = -9;
    } else {
	if (rcequ) {
	    smin = bignum;
	    smax = 0.;
	    i__1 = *n;
	    for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
		d__1 = smin, d__2 = s[j];
		smin = min(d__1,d__2);
/* Computing MAX */
		d__1 = smax, d__2 = s[j];
		smax = max(d__1,d__2);
/* L10: */
	    }
	    if (smin <= 0.) {
		*info = -10;
	    } else if (*n > 0) {
		scond = max(smin,smlnum) / min(smax,bignum);
	    } else {
		scond = 1.;
	    }
	}
	if (*info == 0) {
	    if (*ldb < max(1,*n)) {
		*info = -12;
	    } else if (*ldx < max(1,*n)) {
		*info = -14;
	    }
	}
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZPOSVX", &i__1, (ftnlen)6);
	return 0;
    }

    if (equil) {

/*        Compute row and column scalings to equilibrate the matrix A. */

	zpoequ_(n, &a[a_offset], lda, &s[1], &scond, &amax, &infequ);
	if (infequ == 0) {

/*           Equilibrate the matrix. */

	    zlaqhe_(uplo, n, &a[a_offset], lda, &s[1], &scond, &amax, equed, (
		    ftnlen)1, (ftnlen)1);
	    rcequ = lsame_(equed, "Y", (ftnlen)1, (ftnlen)1);
	}
    }

/*     Scale the right hand side. */

    if (rcequ) {
	i__1 = *nrhs;
	for (j = 1; j <= i__1; ++j) {
	    i__2 = *n;
	    for (i__ = 1; i__ <= i__2; ++i__) {
		i__3 = i__ + j * b_dim1;
		i__4 = i__;
		i__5 = i__ + j * b_dim1;
		z__1.r = s[i__4] * b[i__5].r, z__1.i = s[i__4] * b[i__5].i;
		b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L20: */
	    }
/* L30: */
	}
    }

    if (nofact || equil) {

/*        Compute the Cholesky factorization A = U'*U or A = L*L'. */

	zlacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf, (ftnlen)
		1);
	zpotrf_(uplo, n, &af[af_offset], ldaf, info, (ftnlen)1);

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

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

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

    anorm = zlanhe_("1", uplo, n, &a[a_offset], lda, &rwork[1], (ftnlen)1, (
	    ftnlen)1);

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

    zpocon_(uplo, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &rwork[1],
	     info, (ftnlen)1);

/*     Set INFO = N+1 if the matrix is singular to working precision. */

    if (*rcond < dlamch_("Epsilon", (ftnlen)7)) {
	*info = *n + 1;
    }

/*     Compute the solution matrix X. */

    zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx, (ftnlen)4);
    zpotrs_(uplo, n, nrhs, &af[af_offset], ldaf, &x[x_offset], ldx, info, (
	    ftnlen)1);

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

    zporfs_(uplo, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &b[
	    b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[1], &
	    rwork[1], info, (ftnlen)1);

/*     Transform the solution matrix X to a solution of the original */
/*     system. */

    if (rcequ) {
	i__1 = *nrhs;
	for (j = 1; j <= i__1; ++j) {
	    i__2 = *n;
	    for (i__ = 1; i__ <= i__2; ++i__) {
		i__3 = i__ + j * x_dim1;
		i__4 = i__;
		i__5 = i__ + j * x_dim1;
		z__1.r = s[i__4] * x[i__5].r, z__1.i = s[i__4] * x[i__5].i;
		x[i__3].r = z__1.r, x[i__3].i = z__1.i;
/* L40: */
	    }
/* L50: */
	}
	i__1 = *nrhs;
	for (j = 1; j <= i__1; ++j) {
	    ferr[j] /= scond;
/* L60: */
	}
    }

    return 0;

/*     End of ZPOSVX */

} /* zposvx_ */
Example #16
0
/* Subroutine */ int zhegvd_(integer *itype, char *jobz, char *uplo, integer *
	n, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
	doublereal *w, doublecomplex *work, integer *lwork, doublereal *rwork, 
	 integer *lrwork, integer *iwork, integer *liwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1;
    doublereal d__1, d__2;

    /* Local variables */
    integer lopt;
    extern logical lsame_(char *, char *);
    integer lwmin;
    char trans[1];
    integer liopt;
    logical upper;
    integer lropt;
    logical wantz;
    extern /* Subroutine */ int ztrmm_(char *, char *, char *, char *, 
	    integer *, integer *, doublecomplex *, doublecomplex *, integer *, 
	     doublecomplex *, integer *), 
	    ztrsm_(char *, char *, char *, char *, integer *, integer *, 
	    doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
	    integer *), xerbla_(char *, 
	    integer *), zheevd_(char *, char *, integer *, 
	    doublecomplex *, integer *, doublereal *, doublecomplex *, 
	    integer *, doublereal *, integer *, integer *, integer *, integer 
	    *);
    integer liwmin;
    extern /* Subroutine */ int zhegst_(integer *, char *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, integer *);
    integer lrwmin;
    logical lquery;
    extern /* Subroutine */ int zpotrf_(char *, integer *, doublecomplex *, 
	    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 */
/*  ======= */

/*  ZHEGVD computes all the eigenvalues, and optionally, the eigenvectors */
/*  of a complex generalized Hermitian-definite eigenproblem, of the form */
/*  A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.  Here A and */
/*  B are assumed to be Hermitian and B is also positive definite. */
/*  If eigenvectors are desired, it uses a divide and conquer algorithm. */

/*  The divide and conquer algorithm makes very mild assumptions about */
/*  floating point arithmetic. It will work on machines with a guard */
/*  digit in add/subtract, or on those binary machines without guard */
/*  digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
/*  Cray-2. It could conceivably fail on hexadecimal or decimal machines */
/*  without guard digits, but we know of none. */

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

/*  ITYPE   (input) INTEGER */
/*          Specifies the problem type to be solved: */
/*          = 1:  A*x = (lambda)*B*x */
/*          = 2:  A*B*x = (lambda)*x */
/*          = 3:  B*A*x = (lambda)*x */

/*  JOBZ    (input) CHARACTER*1 */
/*          = 'N':  Compute eigenvalues only; */
/*          = 'V':  Compute eigenvalues and eigenvectors. */

/*  UPLO    (input) CHARACTER*1 */
/*          = 'U':  Upper triangles of A and B are stored; */
/*          = 'L':  Lower triangles of A and B are stored. */

/*  N       (input) INTEGER */
/*          The order of the matrices A and B.  N >= 0. */

/*  A       (input/output) COMPLEX*16 array, dimension (LDA, N) */
/*          On entry, 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.  If UPLO = 'L', */
/*          the leading N-by-N lower triangular part of A contains */
/*          the lower triangular part of the matrix A. */

/*          On exit, if JOBZ = 'V', then if INFO = 0, A contains the */
/*          matrix Z of eigenvectors.  The eigenvectors are normalized */
/*          as follows: */
/*          if ITYPE = 1 or 2, Z**H*B*Z = I; */
/*          if ITYPE = 3, Z**H*inv(B)*Z = I. */
/*          If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') */
/*          or the lower triangle (if UPLO='L') of A, including the */
/*          diagonal, is destroyed. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A.  LDA >= max(1,N). */

/*  B       (input/output) COMPLEX*16 array, dimension (LDB, N) */
/*          On entry, the Hermitian matrix B.  If UPLO = 'U', the */
/*          leading N-by-N upper triangular part of B contains the */
/*          upper triangular part of the matrix B.  If UPLO = 'L', */
/*          the leading N-by-N lower triangular part of B contains */
/*          the lower triangular part of the matrix B. */

/*          On exit, if INFO <= N, the part of B containing the matrix is */
/*          overwritten by the triangular factor U or L from the Cholesky */
/*          factorization B = U**H*U or B = L*L**H. */

/*  LDB     (input) INTEGER */
/*          The leading dimension of the array B.  LDB >= max(1,N). */

/*  W       (output) DOUBLE PRECISION array, dimension (N) */
/*          If INFO = 0, the eigenvalues in ascending order. */

/*  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 the array WORK. */
/*          If N <= 1,                LWORK >= 1. */
/*          If JOBZ  = 'N' and N > 1, LWORK >= N + 1. */
/*          If JOBZ  = 'V' and N > 1, LWORK >= 2*N + N**2. */

/*          If LWORK = -1, then a workspace query is assumed; the routine */
/*          only calculates the optimal sizes of the WORK, RWORK and */
/*          IWORK arrays, returns these values as the first entries of */
/*          the WORK, RWORK and IWORK arrays, and no error message */
/*          related to LWORK or LRWORK or LIWORK is issued by XERBLA. */

/*  RWORK   (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) */
/*          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. */

/*  LRWORK  (input) INTEGER */
/*          The dimension of the array RWORK. */
/*          If N <= 1,                LRWORK >= 1. */
/*          If JOBZ  = 'N' and N > 1, LRWORK >= N. */
/*          If JOBZ  = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. */

/*          If LRWORK = -1, then a workspace query is assumed; the */
/*          routine only calculates the optimal sizes of the WORK, RWORK */
/*          and IWORK arrays, returns these values as the first entries */
/*          of the WORK, RWORK and IWORK arrays, and no error message */
/*          related to LWORK or LRWORK or LIWORK is issued by XERBLA. */

/*  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */
/*          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */

/*  LIWORK  (input) INTEGER */
/*          The dimension of the array IWORK. */
/*          If N <= 1,                LIWORK >= 1. */
/*          If JOBZ  = 'N' and N > 1, LIWORK >= 1. */
/*          If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N. */

/*          If LIWORK = -1, then a workspace query is assumed; the */
/*          routine only calculates the optimal sizes of the WORK, RWORK */
/*          and IWORK arrays, returns these values as the first entries */
/*          of the WORK, RWORK and IWORK arrays, and no error message */
/*          related to LWORK or LRWORK or LIWORK is issued by XERBLA. */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
/*          > 0:  ZPOTRF or ZHEEVD returned an error code: */
/*             <= N:  if INFO = i and JOBZ = 'N', then the algorithm */
/*                    failed to converge; i off-diagonal elements of an */
/*                    intermediate tridiagonal form did not converge to */
/*                    zero; */
/*                    if INFO = i and JOBZ = 'V', then the algorithm */
/*                    failed to compute an eigenvalue while working on */
/*                    the submatrix lying in rows and columns INFO/(N+1) */
/*                    through mod(INFO,N+1); */
/*             > N:   if INFO = N + i, for 1 <= i <= N, then the leading */
/*                    minor of order i of B is not positive definite. */
/*                    The factorization of B could not be completed and */
/*                    no eigenvalues or eigenvectors were computed. */

/*  Further Details */
/*  =============== */

/*  Based on contributions by */
/*     Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */

/*  Modified so that no backsubstitution is performed if ZHEEVD fails to */
/*  converge (NEIG in old code could be greater than N causing out of */
/*  bounds reference to A - reported by Ralf Meyer).  Also corrected the */
/*  description of INFO and the test on ITYPE. Sven, 16 Feb 05. */
/*  ===================================================================== */

/*     .. 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;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    --w;
    --work;
    --rwork;
    --iwork;

    /* Function Body */
    wantz = lsame_(jobz, "V");
    upper = lsame_(uplo, "U");
    lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1;

    *info = 0;
    if (*n <= 1) {
	lwmin = 1;
	lrwmin = 1;
	liwmin = 1;
    } else if (wantz) {
	lwmin = (*n << 1) + *n * *n;
	lrwmin = *n * 5 + 1 + (*n << 1) * *n;
	liwmin = *n * 5 + 3;
    } else {
	lwmin = *n + 1;
	lrwmin = *n;
	liwmin = 1;
    }
    lopt = lwmin;
    lropt = lrwmin;
    liopt = liwmin;
    if (*itype < 1 || *itype > 3) {
	*info = -1;
    } else if (! (wantz || lsame_(jobz, "N"))) {
	*info = -2;
    } else if (! (upper || lsame_(uplo, "L"))) {
	*info = -3;
    } else if (*n < 0) {
	*info = -4;
    } else if (*lda < max(1,*n)) {
	*info = -6;
    } else if (*ldb < max(1,*n)) {
	*info = -8;
    }

    if (*info == 0) {
	work[1].r = (doublereal) lopt, work[1].i = 0.;
	rwork[1] = (doublereal) lropt;
	iwork[1] = liopt;

	if (*lwork < lwmin && ! lquery) {
	    *info = -11;
	} else if (*lrwork < lrwmin && ! lquery) {
	    *info = -13;
	} else if (*liwork < liwmin && ! lquery) {
	    *info = -15;
	}
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZHEGVD", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

    if (*n == 0) {
	return 0;
    }

/*     Form a Cholesky factorization of B. */

    zpotrf_(uplo, n, &b[b_offset], ldb, info);
    if (*info != 0) {
	*info = *n + *info;
	return 0;
    }

/*     Transform problem to standard eigenvalue problem and solve. */

    zhegst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info);
    zheevd_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, &rwork[
	    1], lrwork, &iwork[1], liwork, info);
/* Computing MAX */
    d__1 = (doublereal) lopt, d__2 = work[1].r;
    lopt = (integer) max(d__1,d__2);
/* Computing MAX */
    d__1 = (doublereal) lropt;
    lropt = (integer) max(d__1,rwork[1]);
/* Computing MAX */
    d__1 = (doublereal) liopt, d__2 = (doublereal) iwork[1];
    liopt = (integer) max(d__1,d__2);

    if (wantz && *info == 0) {

/*        Backtransform eigenvectors to the original problem. */

	if (*itype == 1 || *itype == 2) {

/*           For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */
/*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */

	    if (upper) {
		*(unsigned char *)trans = 'N';
	    } else {
		*(unsigned char *)trans = 'C';
	    }

	    ztrsm_("Left", uplo, trans, "Non-unit", n, n, &c_b1, &b[b_offset], 
		     ldb, &a[a_offset], lda);

	} else if (*itype == 3) {

/*           For B*A*x=(lambda)*x; */
/*           backtransform eigenvectors: x = L*y or U'*y */

	    if (upper) {
		*(unsigned char *)trans = 'C';
	    } else {
		*(unsigned char *)trans = 'N';
	    }

	    ztrmm_("Left", uplo, trans, "Non-unit", n, n, &c_b1, &b[b_offset], 
		     ldb, &a[a_offset], lda);
	}
    }

    work[1].r = (doublereal) lopt, work[1].i = 0.;
    rwork[1] = (doublereal) lropt;
    iwork[1] = liopt;

    return 0;

/*     End of ZHEGVD */

} /* zhegvd_ */
Example #17
0
/* dest <- dest + sum_i eigVec[i]*H^{-1}*eigVec[i].resid, 
   resid = src - (-Dslash^2 + 4*mass^2)*dest
*/
static void initCG(su3_vector *src, su3_vector *dest, int Nvecs_curr, int Nvecs_max,
		   su3_vector **eigVec, double_complex *H, Real mass, int parity,
		   imp_ferm_links_t *fn){

  /* Constants */
  int ione = 1;
  int otherparity = (parity == EVEN) ? ODD : EVEN;
  Real msq_x4 = 4.0*mass*mass;
  double dzero = (double)0.0;
  double_complex zzero = dcmplx(dzero, dzero);

  register int i;
  int j, info;
  double_complex cc;
  double_complex *c, *H2;
  su3_vector *resid;

  c = (double_complex *)malloc(Nvecs_curr*sizeof(double_complex));
  resid = (su3_vector *)malloc(sites_on_node*sizeof(su3_vector));

  /* resid <- src - (-Dslash^2 + 4*mass^2)*dest */
  dslash_fn_field(dest, resid, otherparity, fn);
  dslash_fn_field(resid, resid, parity, fn);
  FORSOMEFIELDPARITY_OMP(i, parity, default(shared)){
    scalar_mult_sum_su3_vector(resid+i, dest+i, -msq_x4);
    add_su3_vector(resid+i, src+i, resid+i);
  } END_LOOP_OMP

  /* c[i] = eigVec[i].resid */
  for(j = 0; j < Nvecs_curr; j++){
//    c[j] = zzero;
//    FORSOMEFIELDPARITY_OMP(i, parity, private(cc) reduction(+:c[j])){
//      cc = su3_dot(eigVec[j]+i, resid+i);
//      CSUM(c[j], cc);
//    } END_LOOP_OMP

    double cctotr=0., cctoti=0.;
    FORSOMEFIELDPARITY_OMP(i, parity, private(cc) reduction(+:cctotr,cctoti)){
      cc = su3_dot(eigVec[j]+i, resid+i);
      cctotr += cc.real;
      cctoti += cc.imag;
    } END_LOOP_OMP;
    c[j].real = cctotr;
    c[j].imag = cctoti;

  }
  g_vecdcomplexsum(c, Nvecs_curr);

  free(resid);

  H2 = (double_complex *)malloc(Nvecs_curr*Nvecs_curr*sizeof(double_complex));

  /* H2 = H + 4*mass^2*I */
  for(j = 0; j < Nvecs_curr; j++){
    zcopy_(&Nvecs_curr, H+Nvecs_max*j, &ione, H2+Nvecs_curr*j, &ione);
    CSUM(H2[(Nvecs_curr+1)*j], dcmplx(msq_x4, dzero));
  }

  /* Compute H^{-1}*c = H^{-1}*eigVec.resid with Cholesky decomposition */
  zpotrf_("U", &Nvecs_curr, H2, &Nvecs_curr, &info);
  zpotrs_("U", &Nvecs_curr, &ione, H2, &Nvecs_curr, c, &Nvecs_curr, &info);

  free(H2);

  /* dest <- dest + sum_j c[i]*eigVec[i] = dest + sum_i eigVec[i]*H^{-1}*eigVec[i].resid */ 
  for(j = 0; j < Nvecs_curr; j++){
    FORSOMEFIELDPARITY_OMP(i, parity, default(shared)){
      c_scalar_mult_add_su3vec(dest+i, c+j, eigVec[j]+i);
    } END_LOOP_OMP
  }

  free(c);
}
Example #18
0
/* Subroutine */ int zhegv_(integer *itype, char *jobz, char *uplo, integer *
	n, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
	doublereal *w, doublecomplex *work, integer *lwork, doublereal *rwork, 
	 integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;

    /* Local variables */
    integer nb, neig;
    char trans[1];
    logical upper, wantz;
    integer lwkopt;
    logical lquery;

/*  -- LAPACK driver routine (version 3.2) -- */
/*     November 2006 */

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

/*  ZHEGV computes all the eigenvalues, and optionally, the eigenvectors */
/*  of a complex generalized Hermitian-definite eigenproblem, of the form */
/*  A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x. */
/*  Here A and B are assumed to be Hermitian and B is also */
/*  positive definite. */

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

/*  ITYPE   (input) INTEGER */
/*          Specifies the problem type to be solved: */
/*          = 1:  A*x = (lambda)*B*x */
/*          = 2:  A*B*x = (lambda)*x */
/*          = 3:  B*A*x = (lambda)*x */

/*  JOBZ    (input) CHARACTER*1 */
/*          = 'N':  Compute eigenvalues only; */
/*          = 'V':  Compute eigenvalues and eigenvectors. */

/*  UPLO    (input) CHARACTER*1 */
/*          = 'U':  Upper triangles of A and B are stored; */
/*          = 'L':  Lower triangles of A and B are stored. */

/*  N       (input) INTEGER */
/*          The order of the matrices A and B.  N >= 0. */

/*  A       (input/output) COMPLEX*16 array, dimension (LDA, N) */
/*          On entry, 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.  If UPLO = 'L', */
/*          the leading N-by-N lower triangular part of A contains */
/*          the lower triangular part of the matrix A. */

/*          On exit, if JOBZ = 'V', then if INFO = 0, A contains the */
/*          matrix Z of eigenvectors.  The eigenvectors are normalized */
/*          as follows: */
/*          if ITYPE = 1 or 2, Z**H*B*Z = I; */
/*          if ITYPE = 3, Z**H*inv(B)*Z = I. */
/*          If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') */
/*          or the lower triangle (if UPLO='L') of A, including the */
/*          diagonal, is destroyed. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A.  LDA >= max(1,N). */

/*  B       (input/output) COMPLEX*16 array, dimension (LDB, N) */
/*          On entry, the Hermitian positive definite matrix B. */
/*          If UPLO = 'U', the leading N-by-N upper triangular part of B */
/*          contains the upper triangular part of the matrix B. */
/*          If UPLO = 'L', the leading N-by-N lower triangular part of B */
/*          contains the lower triangular part of the matrix B. */

/*          On exit, if INFO <= N, the part of B containing the matrix is */
/*          overwritten by the triangular factor U or L from the Cholesky */
/*          factorization B = U**H*U or B = L*L**H. */

/*  LDB     (input) INTEGER */
/*          The leading dimension of the array B.  LDB >= max(1,N). */

/*  W       (output) DOUBLE PRECISION array, dimension (N) */
/*          If INFO = 0, the eigenvalues in ascending order. */

/*  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 the array WORK.  LWORK >= max(1,2*N-1). */
/*          For optimal efficiency, LWORK >= (NB+1)*N, */
/*          where NB is the blocksize for ZHETRD returned by ILAENV. */

/*          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 (max(1, 3*N-2)) */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
/*          > 0:  ZPOTRF or ZHEEV returned an error code: */
/*             <= N:  if INFO = i, ZHEEV failed to converge; */
/*                    i off-diagonal elements of an intermediate */
/*                    tridiagonal form did not converge to zero; */
/*             > N:   if INFO = N + i, for 1 <= i <= N, then the leading */
/*                    minor of order i of B is not positive definite. */
/*                    The factorization of B could not be completed and */
/*                    no eigenvalues or eigenvectors were computed. */

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

/*     Test the input parameters. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    --w;
    --work;
    --rwork;

    /* Function Body */
    wantz = lsame_(jobz, "V");
    upper = lsame_(uplo, "U");
    lquery = *lwork == -1;

    *info = 0;
    if (*itype < 1 || *itype > 3) {
	*info = -1;
    } else if (! (wantz || lsame_(jobz, "N"))) {
	*info = -2;
    } else if (! (upper || lsame_(uplo, "L"))) {
	*info = -3;
    } else if (*n < 0) {
	*info = -4;
    } else if (*lda < max(1,*n)) {
	*info = -6;
    } else if (*ldb < max(1,*n)) {
	*info = -8;
    }

    if (*info == 0) {
	nb = ilaenv_(&c__1, "ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1);
/* Computing MAX */
	i__1 = 1, i__2 = (nb + 1) * *n;
	lwkopt = max(i__1,i__2);
	work[1].r = (doublereal) lwkopt, work[1].i = 0.;

/* Computing MAX */
	i__1 = 1, i__2 = (*n << 1) - 1;
	if (*lwork < max(i__1,i__2) && ! lquery) {
	    *info = -11;
	}
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZHEGV ", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

    if (*n == 0) {
	return 0;
    }

/*     Form a Cholesky factorization of B. */

    zpotrf_(uplo, n, &b[b_offset], ldb, info);
    if (*info != 0) {
	*info = *n + *info;
	return 0;
    }

/*     Transform problem to standard eigenvalue problem and solve. */

    zhegst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info);
    zheev_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, &rwork[1]
, info);

    if (wantz) {

/*        Backtransform eigenvectors to the original problem. */

	neig = *n;
	if (*info > 0) {
	    neig = *info - 1;
	}
	if (*itype == 1 || *itype == 2) {

/*           For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */
/*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */

	    if (upper) {
		*(unsigned char *)trans = 'N';
	    } else {
		*(unsigned char *)trans = 'C';
	    }

	    ztrsm_("Left", uplo, trans, "Non-unit", n, &neig, &c_b1, &b[
		    b_offset], ldb, &a[a_offset], lda);

	} else if (*itype == 3) {

/*           For B*A*x=(lambda)*x; */
/*           backtransform eigenvectors: x = L*y or U'*y */

	    if (upper) {
		*(unsigned char *)trans = 'C';
	    } else {
		*(unsigned char *)trans = 'N';
	    }

	    ztrmm_("Left", uplo, trans, "Non-unit", n, &neig, &c_b1, &b[
		    b_offset], ldb, &a[a_offset], lda);
	}
    }

    work[1].r = (doublereal) lwkopt, work[1].i = 0.;

    return 0;

/*     End of ZHEGV */

} /* zhegv_ */
Example #19
0
/* Subroutine */ int zerrpo_(char *path, integer *nunit)
{
    /* System generated locals */
    integer i__1;
    doublereal d__1, d__2;
    doublecomplex z__1;

    /* 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;
    static doublecomplex a[16]	/* was [4][4] */, b[4];
    static integer i__, j;
    static doublereal r__[4];
    static doublecomplex w[8], x[4];
    static doublereal rcond;
    static char c2[2];
    static doublereal r1[4], r2[4];
    static doublecomplex af[16]	/* was [4][4] */;
    extern /* Subroutine */ int zpbtf2_(char *, integer *, integer *, 
	    doublecomplex *, integer *, integer *), zpotf2_(char *, 
	    integer *, doublecomplex *, integer *, integer *), 
	    alaesm_(char *, logical *, integer *);
    extern logical lsamen_(integer *, char *, char *);
    extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical 
	    *, logical *), zpbcon_(char *, integer *, integer *, 
	    doublecomplex *, integer *, doublereal *, doublereal *, 
	    doublecomplex *, doublereal *, integer *), zpbequ_(char *,
	     integer *, integer *, doublecomplex *, integer *, doublereal *, 
	    doublereal *, doublereal *, integer *), zpbrfs_(char *, 
	    integer *, integer *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, doublereal *, doublereal *, 
	    doublecomplex *, doublereal *, integer *), zpbtrf_(char *,
	     integer *, integer *, doublecomplex *, integer *, integer *), zpocon_(char *, integer *, doublecomplex *, integer *, 
	    doublereal *, doublereal *, doublecomplex *, doublereal *, 
	    integer *), zppcon_(char *, integer *, doublecomplex *, 
	    doublereal *, doublereal *, doublecomplex *, doublereal *, 
	    integer *), zpoequ_(integer *, doublecomplex *, integer *,
	     doublereal *, doublereal *, doublereal *, integer *), zpbtrs_(
	    char *, integer *, integer *, integer *, doublecomplex *, integer 
	    *, doublecomplex *, integer *, integer *), zporfs_(char *,
	     integer *, integer *, doublecomplex *, integer *, doublecomplex *
	    , integer *, doublecomplex *, integer *, doublecomplex *, integer 
	    *, doublereal *, doublereal *, doublecomplex *, doublereal *, 
	    integer *), zpotrf_(char *, integer *, doublecomplex *, 
	    integer *, integer *), zpotri_(char *, integer *, 
	    doublecomplex *, integer *, integer *), zppequ_(char *, 
	    integer *, doublecomplex *, doublereal *, doublereal *, 
	    doublereal *, integer *), zpprfs_(char *, integer *, 
	    integer *, doublecomplex *, doublecomplex *, doublecomplex *, 
	    integer *, doublecomplex *, integer *, doublereal *, doublereal *,
	     doublecomplex *, doublereal *, integer *), zpptrf_(char *
	    , integer *, doublecomplex *, integer *), zpptri_(char *, 
	    integer *, doublecomplex *, integer *), zpotrs_(char *, 
	    integer *, integer *, doublecomplex *, integer *, doublecomplex *,
	     integer *, integer *), zpptrs_(char *, integer *, 
	    integer *, doublecomplex *, doublecomplex *, integer *, integer *);

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



#define a_subscr(a_1,a_2) (a_2)*4 + a_1 - 5
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
#define af_subscr(a_1,a_2) (a_2)*4 + a_1 - 5
#define af_ref(a_1,a_2) af[af_subscr(a_1,a_2)]


/*  -- 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   
    =======   

    ZERRPO tests the error exits for the COMPLEX*16 routines   
    for Hermitian positive definite 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__) {
	    i__1 = a_subscr(i__, j);
	    d__1 = 1. / (doublereal) (i__ + j);
	    d__2 = -1. / (doublereal) (i__ + j);
	    z__1.r = d__1, z__1.i = d__2;
	    a[i__1].r = z__1.r, a[i__1].i = z__1.i;
	    i__1 = af_subscr(i__, j);
	    d__1 = 1. / (doublereal) (i__ + j);
	    d__2 = -1. / (doublereal) (i__ + j);
	    z__1.r = d__1, z__1.i = d__2;
	    af[i__1].r = z__1.r, af[i__1].i = z__1.i;
/* L10: */
	}
	i__1 = j - 1;
	b[i__1].r = 0., b[i__1].i = 0.;
	r1[j - 1] = 0.;
	r2[j - 1] = 0.;
	i__1 = j - 1;
	w[i__1].r = 0., w[i__1].i = 0.;
	i__1 = j - 1;
	x[i__1].r = 0., x[i__1].i = 0.;
/* L20: */
    }
    anrm = 1.;
    infoc_1.ok = TRUE_;

/*     Test error exits of the routines that use the Cholesky   
       decomposition of a Hermitian positive definite matrix. */

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

/*        ZPOTRF */

	s_copy(srnamc_1.srnamt, "ZPOTRF", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpotrf_("/", &c__0, a, &c__1, &info);
	chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpotrf_("U", &c_n1, a, &c__1, &info);
	chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	zpotrf_("U", &c__2, a, &c__1, &info);
	chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPOTF2 */

	s_copy(srnamc_1.srnamt, "ZPOTF2", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpotf2_("/", &c__0, a, &c__1, &info);
	chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpotf2_("U", &c_n1, a, &c__1, &info);
	chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	zpotf2_("U", &c__2, a, &c__1, &info);
	chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPOTRI */

	s_copy(srnamc_1.srnamt, "ZPOTRI", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpotri_("/", &c__0, a, &c__1, &info);
	chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpotri_("U", &c_n1, a, &c__1, &info);
	chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	zpotri_("U", &c__2, a, &c__1, &info);
	chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPOTRS */

	s_copy(srnamc_1.srnamt, "ZPOTRS", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpotrs_("/", &c__0, &c__0, a, &c__1, b, &c__1, &info);
	chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpotrs_("U", &c_n1, &c__0, a, &c__1, b, &c__1, &info);
	chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zpotrs_("U", &c__0, &c_n1, a, &c__1, b, &c__1, &info);
	chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zpotrs_("U", &c__2, &c__1, a, &c__1, b, &c__2, &info);
	chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 7;
	zpotrs_("U", &c__2, &c__1, a, &c__2, b, &c__1, &info);
	chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPORFS */

	s_copy(srnamc_1.srnamt, "ZPORFS", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zporfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1, 
		r1, r2, w, r__, &info);
	chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zporfs_("U", &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1, 
		r1, r2, w, r__, &info);
	chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zporfs_("U", &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, &c__1, 
		r1, r2, w, r__, &info);
	chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zporfs_("U", &c__2, &c__1, a, &c__1, af, &c__2, b, &c__2, x, &c__2, 
		r1, r2, w, r__, &info);
	chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 7;
	zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__1, b, &c__2, x, &c__2, 
		r1, r2, w, r__, &info);
	chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 9;
	zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__1, x, &c__2, 
		r1, r2, w, r__, &info);
	chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 11;
	zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__2, x, &c__1, 
		r1, r2, w, r__, &info);
	chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPOCON */

	s_copy(srnamc_1.srnamt, "ZPOCON", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpocon_("/", &c__0, a, &c__1, &anrm, &rcond, w, r__, &info)
		;
	chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpocon_("U", &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info)
		;
	chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	zpocon_("U", &c__2, a, &c__1, &anrm, &rcond, w, r__, &info)
		;
	chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	d__1 = -anrm;
	zpocon_("U", &c__1, a, &c__1, &d__1, &rcond, w, r__, &info)
		;
	chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPOEQU */

	s_copy(srnamc_1.srnamt, "ZPOEQU", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpoequ_(&c_n1, a, &c__1, r1, &rcond, &anrm, &info);
	chkxer_("ZPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zpoequ_(&c__2, a, &c__1, r1, &rcond, &anrm, &info);
	chkxer_("ZPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*     Test error exits of the routines that use the Cholesky   
       decomposition of a Hermitian positive definite packed matrix. */

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

/*        ZPPTRF */

	s_copy(srnamc_1.srnamt, "ZPPTRF", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpptrf_("/", &c__0, a, &info);
	chkxer_("ZPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpptrf_("U", &c_n1, a, &info);
	chkxer_("ZPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPPTRI */

	s_copy(srnamc_1.srnamt, "ZPPTRI", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpptri_("/", &c__0, a, &info);
	chkxer_("ZPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpptri_("U", &c_n1, a, &info);
	chkxer_("ZPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPPTRS */

	s_copy(srnamc_1.srnamt, "ZPPTRS", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpptrs_("/", &c__0, &c__0, a, b, &c__1, &info);
	chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpptrs_("U", &c_n1, &c__0, a, b, &c__1, &info);
	chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zpptrs_("U", &c__0, &c_n1, a, b, &c__1, &info);
	chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 6;
	zpptrs_("U", &c__2, &c__1, a, b, &c__1, &info);
	chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPPRFS */

	s_copy(srnamc_1.srnamt, "ZPPRFS", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpprfs_("/", &c__0, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, r__, 
		&info);
	chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpprfs_("U", &c_n1, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, r__, 
		&info);
	chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zpprfs_("U", &c__0, &c_n1, a, af, b, &c__1, x, &c__1, r1, r2, w, r__, 
		&info);
	chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 7;
	zpprfs_("U", &c__2, &c__1, a, af, b, &c__1, x, &c__2, r1, r2, w, r__, 
		&info);
	chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 9;
	zpprfs_("U", &c__2, &c__1, a, af, b, &c__2, x, &c__1, r1, r2, w, r__, 
		&info);
	chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPPCON */

	s_copy(srnamc_1.srnamt, "ZPPCON", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zppcon_("/", &c__0, a, &anrm, &rcond, w, r__, &info);
	chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zppcon_("U", &c_n1, a, &anrm, &rcond, w, r__, &info);
	chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	d__1 = -anrm;
	zppcon_("U", &c__1, a, &d__1, &rcond, w, r__, &info);
	chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPPEQU */

	s_copy(srnamc_1.srnamt, "ZPPEQU", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zppequ_("/", &c__0, a, r1, &rcond, &anrm, &info);
	chkxer_("ZPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zppequ_("U", &c_n1, a, r1, &rcond, &anrm, &info);
	chkxer_("ZPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*     Test error exits of the routines that use the Cholesky   
       decomposition of a Hermitian positive definite band matrix. */

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

/*        ZPBTRF */

	s_copy(srnamc_1.srnamt, "ZPBTRF", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpbtrf_("/", &c__0, &c__0, a, &c__1, &info);
	chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpbtrf_("U", &c_n1, &c__0, a, &c__1, &info);
	chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zpbtrf_("U", &c__1, &c_n1, a, &c__1, &info);
	chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zpbtrf_("U", &c__2, &c__1, a, &c__1, &info);
	chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPBTF2 */

	s_copy(srnamc_1.srnamt, "ZPBTF2", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpbtf2_("/", &c__0, &c__0, a, &c__1, &info);
	chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpbtf2_("U", &c_n1, &c__0, a, &c__1, &info);
	chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zpbtf2_("U", &c__1, &c_n1, a, &c__1, &info);
	chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zpbtf2_("U", &c__2, &c__1, a, &c__1, &info);
	chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPBTRS */

	s_copy(srnamc_1.srnamt, "ZPBTRS", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpbtrs_("/", &c__0, &c__0, &c__0, a, &c__1, b, &c__1, &info);
	chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpbtrs_("U", &c_n1, &c__0, &c__0, a, &c__1, b, &c__1, &info);
	chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zpbtrs_("U", &c__1, &c_n1, &c__0, a, &c__1, b, &c__1, &info);
	chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	zpbtrs_("U", &c__0, &c__0, &c_n1, a, &c__1, b, &c__1, &info);
	chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 6;
	zpbtrs_("U", &c__2, &c__1, &c__1, a, &c__1, b, &c__1, &info);
	chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 8;
	zpbtrs_("U", &c__2, &c__0, &c__1, a, &c__1, b, &c__1, &info);
	chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPBRFS */

	s_copy(srnamc_1.srnamt, "ZPBRFS", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpbrfs_("/", &c__0, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &
		c__1, r1, r2, w, r__, &info);
	chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpbrfs_("U", &c_n1, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &
		c__1, r1, r2, w, r__, &info);
	chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zpbrfs_("U", &c__1, &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &
		c__1, r1, r2, w, r__, &info);
	chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	zpbrfs_("U", &c__0, &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, &
		c__1, r1, r2, w, r__, &info);
	chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 6;
	zpbrfs_("U", &c__2, &c__1, &c__1, a, &c__1, af, &c__2, b, &c__2, x, &
		c__2, r1, r2, w, r__, &info);
	chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 8;
	zpbrfs_("U", &c__2, &c__1, &c__1, a, &c__2, af, &c__1, b, &c__2, x, &
		c__2, r1, r2, w, r__, &info);
	chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 10;
	zpbrfs_("U", &c__2, &c__0, &c__1, a, &c__1, af, &c__1, b, &c__1, x, &
		c__2, r1, r2, w, r__, &info);
	chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 12;
	zpbrfs_("U", &c__2, &c__0, &c__1, a, &c__1, af, &c__1, b, &c__2, x, &
		c__1, r1, r2, w, r__, &info);
	chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPBCON */

	s_copy(srnamc_1.srnamt, "ZPBCON", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpbcon_("/", &c__0, &c__0, a, &c__1, &anrm, &rcond, w, r__, &info);
	chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpbcon_("U", &c_n1, &c__0, a, &c__1, &anrm, &rcond, w, r__, &info);
	chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zpbcon_("U", &c__1, &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info);
	chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zpbcon_("U", &c__2, &c__1, a, &c__1, &anrm, &rcond, w, r__, &info);
	chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 6;
	d__1 = -anrm;
	zpbcon_("U", &c__1, &c__0, a, &c__1, &d__1, &rcond, w, r__, &info);
	chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);

/*        ZPBEQU */

	s_copy(srnamc_1.srnamt, "ZPBEQU", (ftnlen)6, (ftnlen)6);
	infoc_1.infot = 1;
	zpbequ_("/", &c__0, &c__0, a, &c__1, r1, &rcond, &anrm, &info);
	chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zpbequ_("U", &c_n1, &c__0, a, &c__1, r1, &rcond, &anrm, &info);
	chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zpbequ_("U", &c__1, &c_n1, a, &c__1, r1, &rcond, &anrm, &info);
	chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zpbequ_("U", &c__2, &c__1, a, &c__1, r1, &rcond, &anrm, &info);
	chkxer_("ZPBEQU", &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 ZERRPO */

} /* zerrpo_ */
Example #20
0
/* Subroutine */ int ztimpo_(char *line, integer *nn, integer *nval, integer *
	nns, integer *nsval, integer *nnb, integer *nbval, integer *nlda, 
	integer *ldaval, doublereal *timmin, doublecomplex *a, doublecomplex *
	b, integer *iwork, doublereal *reslts, integer *ldr1, integer *ldr2, 
	integer *ldr3, integer *nout, ftnlen line_len)
{
    /* Initialized data */

    static char uplos[1*2] = "U" "L";
    static char subnam[6*3] = "ZPOTRF" "ZPOTRS" "ZPOTRI";

    /* Format strings */
    static char fmt_9999[] = "(1x,a6,\002 timing run not attempted\002,/)";
    static char fmt_9998[] = "(/\002 *** Speed of \002,a6,\002 in megaflops "
	    "***\002)";
    static char fmt_9997[] = "(5x,\002line \002,i2,\002 with LDA = \002,i5)";
    static char fmt_9996[] = "(5x,a6,\002 with UPLO = '\002,a1,\002'\002,/)";

    /* System generated locals */
    integer reslts_dim1, reslts_dim2, reslts_dim3, reslts_offset, i__1, i__2, 
	    i__3;

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

    /* Local variables */
    static integer ilda, info;
    static char path[3];
    static doublereal time;
    static integer isub, nrhs;
    static char uplo[1];
    static integer i__, n;
    static char cname[6];
    extern doublereal dopla_(char *, integer *, integer *, integer *, integer 
	    *, integer *);
    extern logical lsame_(char *, char *);
    static integer iuplo, i3;
    static doublereal s1, s2;
    static integer ic, nb, in;
    extern doublereal dsecnd_(void);
    extern /* Subroutine */ int atimck_(integer *, char *, integer *, integer 
	    *, integer *, integer *, integer *, integer *, ftnlen);
    extern doublereal dmflop_(doublereal *, doublereal *, integer *);
    extern /* Subroutine */ int atimin_(char *, char *, integer *, char *, 
	    logical *, integer *, integer *, ftnlen, ftnlen, ftnlen), dprtbl_(
	    char *, char *, integer *, integer *, integer *, integer *, 
	    integer *, doublereal *, integer *, integer *, integer *, ftnlen, 
	    ftnlen), xlaenv_(integer *, integer *);
    static doublereal untime;
    extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *);
    static logical timsub[3];
    extern /* Subroutine */ int ztimmg_(integer *, integer *, integer *, 
	    doublecomplex *, integer *, integer *, integer *), zpotrf_(char *,
	     integer *, doublecomplex *, integer *, integer *), 
	    zpotri_(char *, integer *, doublecomplex *, integer *, integer *), zpotrs_(char *, integer *, integer *, doublecomplex *, 
	    integer *, doublecomplex *, integer *, integer *);
    static integer lda, ldb, icl, inb, mat;
    static doublereal ops;

    /* Fortran I/O blocks */
    static cilist io___7 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___29 = { 0, 0, 0, fmt_9998, 0 };
    static cilist io___30 = { 0, 0, 0, fmt_9997, 0 };
    static cilist io___31 = { 0, 0, 0, 0, 0 };
    static cilist io___32 = { 0, 0, 0, fmt_9996, 0 };



#define subnam_ref(a_0,a_1) &subnam[(a_1)*6 + a_0 - 6]
#define reslts_ref(a_1,a_2,a_3,a_4) reslts[(((a_4)*reslts_dim3 + (a_3))*\
reslts_dim2 + (a_2))*reslts_dim1 + a_1]


/*  -- LAPACK timing routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       March 31, 1993   


    Purpose   
    =======   

    ZTIMPO times ZPOTRF, -TRS, and -TRI.   

    Arguments   
    =========   

    LINE    (input) CHARACTER*80   
            The input line that requested this routine.  The first six   
            characters contain either the name of a subroutine or a   
            generic path name.  The remaining characters may be used to   
            specify the individual routines to be timed.  See ATIMIN for   
            a full description of the format of the input line.   

    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 size 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.   

    NNB     (input) INTEGER   
            The number of values of NB contained in the vector NBVAL.   

    NBVAL   (input) INTEGER array, dimension (NNB)   
            The values of the blocksize NB.   

    NLDA    (input) INTEGER   
            The number of values of LDA contained in the vector LDAVAL.   

    LDAVAL  (input) INTEGER array, dimension (NLDA)   
            The values of the leading dimension of the array A.   

    TIMMIN  (input) DOUBLE PRECISION   
            The minimum time a subroutine will be timed.   

    A       (workspace) COMPLEX*16 array, dimension (LDAMAX*NMAX)   
            where LDAMAX and NMAX are the maximum values permitted   
            for LDA and N.   

    B       (workspace) COMPLEX*16 array, dimension (LDAMAX*NMAX)   

    IWORK   (workspace) INTEGER array, dimension (NMAX)   

    RESLTS  (output) DOUBLE PRECISION array, dimension   
                     (LDR1,LDR2,LDR3,NSUBS)   
            The timing results for each subroutine over the relevant   
            values of N, NB, and LDA.   

    LDR1    (input) INTEGER   
            The first dimension of RESLTS.  LDR1 >= max(4,NNB).   

    LDR2    (input) INTEGER   
            The second dimension of RESLTS.  LDR2 >= max(1,NN).   

    LDR3    (input) INTEGER   
            The third dimension of RESLTS.  LDR3 >= max(1,2*NLDA).   

    NOUT    (input) INTEGER   
            The unit number for output.   

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

       Parameter adjustments */
    --nval;
    --nsval;
    --nbval;
    --ldaval;
    --a;
    --b;
    --iwork;
    reslts_dim1 = *ldr1;
    reslts_dim2 = *ldr2;
    reslts_dim3 = *ldr3;
    reslts_offset = 1 + reslts_dim1 * (1 + reslts_dim2 * (1 + reslts_dim3 * 1)
	    );
    reslts -= reslts_offset;

    /* Function Body   

       Extract the timing request from the input line. */

    s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17);
    s_copy(path + 1, "PO", (ftnlen)2, (ftnlen)2);
    atimin_(path, line, &c__3, subnam, timsub, nout, &info, (ftnlen)3, (
	    ftnlen)80, (ftnlen)6);
    if (info != 0) {
	goto L150;
    }

/*     Check that N <= LDA for the input values. */

    s_copy(cname, line, (ftnlen)6, (ftnlen)6);
    atimck_(&c__2, cname, nn, &nval[1], nlda, &ldaval[1], nout, &info, (
	    ftnlen)6);
    if (info > 0) {
	io___7.ciunit = *nout;
	s_wsfe(&io___7);
	do_fio(&c__1, cname, (ftnlen)6);
	e_wsfe();
	goto L150;
    }

/*     Do first for UPLO = 'U', then for UPLO = 'L' */

    for (iuplo = 1; iuplo <= 2; ++iuplo) {
	*(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1];
	if (lsame_(uplo, "U")) {
	    mat = 3;
	} else {
	    mat = -3;
	}

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

	i__1 = *nn;
	for (in = 1; in <= i__1; ++in) {
	    n = nval[in];

/*           Do for each value of LDA: */

	    i__2 = *nlda;
	    for (ilda = 1; ilda <= i__2; ++ilda) {
		lda = ldaval[ilda];
		i3 = (iuplo - 1) * *nlda + ilda;

/*              Do for each value of NB in NBVAL.  Only the blocked   
                routines are timed in this loop since the other routines   
                are independent of NB. */

		i__3 = *nnb;
		for (inb = 1; inb <= i__3; ++inb) {
		    nb = nbval[inb];
		    xlaenv_(&c__1, &nb);

/*                 Time ZPOTRF */

		    if (timsub[0]) {
			ztimmg_(&mat, &n, &n, &a[1], &lda, &c__0, &c__0);
			ic = 0;
			s1 = dsecnd_();
L10:
			zpotrf_(uplo, &n, &a[1], &lda, &info);
			s2 = dsecnd_();
			time = s2 - s1;
			++ic;
			if (time < *timmin) {
			    ztimmg_(&mat, &n, &n, &a[1], &lda, &c__0, &c__0);
			    goto L10;
			}

/*                    Subtract the time used in ZTIMMG. */

			icl = 1;
			s1 = dsecnd_();
L20:
			s2 = dsecnd_();
			untime = s2 - s1;
			++icl;
			if (icl <= ic) {
			    ztimmg_(&mat, &n, &n, &a[1], &lda, &c__0, &c__0);
			    goto L20;
			}

			time = (time - untime) / (doublereal) ic;
			ops = dopla_("ZPOTRF", &n, &n, &c__0, &c__0, &nb);
			reslts_ref(inb, in, i3, 1) = dmflop_(&ops, &time, &
				info);

		    } else {
			ic = 0;
			ztimmg_(&mat, &n, &n, &a[1], &lda, &c__0, &c__0);
		    }

/*                 Generate another matrix and factor it using ZPOTRF so   
                   that the factored form can be used in timing the other   
                   routines. */

		    if (ic != 1) {
			zpotrf_(uplo, &n, &a[1], &lda, &info);
		    }

/*                 Time ZPOTRI */

		    if (timsub[2]) {
			zlacpy_(uplo, &n, &n, &a[1], &lda, &b[1], &lda);
			ic = 0;
			s1 = dsecnd_();
L30:
			zpotri_(uplo, &n, &b[1], &lda, &info);
			s2 = dsecnd_();
			time = s2 - s1;
			++ic;
			if (time < *timmin) {
			    zlacpy_(uplo, &n, &n, &a[1], &lda, &b[1], &lda);
			    goto L30;
			}

/*                    Subtract the time used in ZLACPY. */

			icl = 1;
			s1 = dsecnd_();
L40:
			s2 = dsecnd_();
			untime = s2 - s1;
			++icl;
			if (icl <= ic) {
			    zlacpy_(uplo, &n, &n, &a[1], &lda, &b[1], &lda);
			    goto L40;
			}

			time = (time - untime) / (doublereal) ic;
			ops = dopla_("ZPOTRI", &n, &n, &c__0, &c__0, &nb);
			reslts_ref(inb, in, i3, 3) = dmflop_(&ops, &time, &
				info);
		    }
/* L50: */
		}

/*              Time ZPOTRS */

		if (timsub[1]) {
		    i__3 = *nns;
		    for (i__ = 1; i__ <= i__3; ++i__) {
			nrhs = nsval[i__];
			ldb = lda;
			ztimmg_(&c__0, &n, &nrhs, &b[1], &ldb, &c__0, &c__0);
			ic = 0;
			s1 = dsecnd_();
L60:
			zpotrs_(uplo, &n, &nrhs, &a[1], &lda, &b[1], &ldb, &
				info);
			s2 = dsecnd_();
			time = s2 - s1;
			++ic;
			if (time < *timmin) {
			    ztimmg_(&c__0, &n, &nrhs, &b[1], &ldb, &c__0, &
				    c__0);
			    goto L60;
			}

/*                    Subtract the time used in ZTIMMG. */

			icl = 1;
			s1 = dsecnd_();
L70:
			s2 = dsecnd_();
			untime = s2 - s1;
			++icl;
			if (icl <= ic) {
			    ztimmg_(&c__0, &n, &nrhs, &b[1], &ldb, &c__0, &
				    c__0);
			    goto L70;
			}

			time = (time - untime) / (doublereal) ic;
			ops = dopla_("ZPOTRS", &n, &nrhs, &c__0, &c__0, &c__0);
			reslts_ref(i__, in, i3, 2) = dmflop_(&ops, &time, &
				info);
/* L80: */
		    }
		}
/* L90: */
	    }
/* L100: */
	}
/* L110: */
    }

/*     Print tables of results for each timed routine. */

    for (isub = 1; isub <= 3; ++isub) {
	if (! timsub[isub - 1]) {
	    goto L140;
	}
	io___29.ciunit = *nout;
	s_wsfe(&io___29);
	do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
	e_wsfe();
	if (*nlda > 1) {
	    i__1 = *nlda;
	    for (i__ = 1; i__ <= i__1; ++i__) {
		io___30.ciunit = *nout;
		s_wsfe(&io___30);
		do_fio(&c__1, (char *)&i__, (ftnlen)sizeof(integer));
		do_fio(&c__1, (char *)&ldaval[i__], (ftnlen)sizeof(integer));
		e_wsfe();
/* L120: */
	    }
	}
	io___31.ciunit = *nout;
	s_wsle(&io___31);
	e_wsle();
	for (iuplo = 1; iuplo <= 2; ++iuplo) {
	    io___32.ciunit = *nout;
	    s_wsfe(&io___32);
	    do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
	    do_fio(&c__1, uplos + (iuplo - 1), (ftnlen)1);
	    e_wsfe();
	    i3 = (iuplo - 1) * *nlda + 1;
	    if (isub == 1) {
		dprtbl_("NB", "N", nnb, &nbval[1], nn, &nval[1], nlda, &
			reslts_ref(1, 1, i3, 1), ldr1, ldr2, nout, (ftnlen)2, 
			(ftnlen)1);
	    } else if (isub == 2) {
		dprtbl_("NRHS", "N", nns, &nsval[1], nn, &nval[1], nlda, &
			reslts_ref(1, 1, i3, 2), ldr1, ldr2, nout, (ftnlen)4, 
			(ftnlen)1);
	    } else if (isub == 3) {
		dprtbl_("NB", "N", nnb, &nbval[1], nn, &nval[1], nlda, &
			reslts_ref(1, 1, i3, 3), ldr1, ldr2, nout, (ftnlen)2, 
			(ftnlen)1);
	    }
/* L130: */
	}
L140:
	;
    }

L150:
    return 0;

/*     End of ZTIMPO */

} /* ztimpo_ */