zgbt01.c

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/* zgbt01.f -- translated by f2c (version 20061008).
   You must link the resulting object file with libf2c:
        on Microsoft Windows system, link with libf2c.lib;
        on Linux or Unix systems, link with .../path/to/libf2c.a -lm
        or, if you install libf2c.a in a standard place, with -lf2c -lm
        -- in that order, at the end of the command line, as in
                cc *.o -lf2c -lm
        Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

                http://www.netlib.org/f2c/libf2c.zip
*/

#include "f2c.h"
#include "blaswrap.h"

/* Table of constant values */

static integer c__1 = 1;
static doublecomplex c_b12 = {-1.,-0.};

/* Subroutine */ int zgbt01_(integer *m, integer *n, integer *kl, integer *ku, 
         doublecomplex *a, integer *lda, doublecomplex *afac, integer *ldafac, 
         integer *ipiv, doublecomplex *work, doublereal *resid)
{
    /* System generated locals */
    integer a_dim1, a_offset, afac_dim1, afac_offset, i__1, i__2, i__3, i__4;
    doublereal d__1, d__2;

    /* Local variables */
    integer i__, j;
    doublecomplex t;
    integer i1, i2, kd, il, jl, ip, ju, iw, jua;
    doublereal eps;
    integer lenj;
    doublereal anorm;
    extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *, 
            doublecomplex *, integer *, doublecomplex *, integer *);
    extern doublereal dlamch_(char *), dzasum_(integer *, 
            doublecomplex *, integer *);


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

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

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

/*  ZGBT01 reconstructs a band matrix  A  from its L*U factorization and */
/*  computes the residual: */
/*     norm(L*U - A) / ( N * norm(A) * EPS ), */
/*  where EPS is the machine epsilon. */

/*  The expression L*U - A is computed one column at a time, so A and */
/*  AFAC are not modified. */

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

/*  M       (input) INTEGER */
/*          The number of rows of the matrix A.  M >= 0. */

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

/*  KL      (input) INTEGER */
/*          The number of subdiagonals within the band of A.  KL >= 0. */

/*  KU      (input) INTEGER */
/*          The number of superdiagonals within the band of A.  KU >= 0. */

/*  A       (input/output) COMPLEX*16 array, dimension (LDA,N) */
/*          The original matrix A in band storage, stored in rows 1 to */
/*          KL+KU+1. */

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

/*  AFAC    (input) COMPLEX*16 array, dimension (LDAFAC,N) */
/*          The factored form of the matrix A.  AFAC contains the banded */
/*          factors L and U from the L*U factorization, as computed by */
/*          ZGBTRF.  U is stored as an upper triangular band matrix with */
/*          KL+KU superdiagonals in rows 1 to KL+KU+1, and the */
/*          multipliers used during the factorization are stored in rows */
/*          KL+KU+2 to 2*KL+KU+1.  See ZGBTRF for further details. */

/*  LDAFAC  (input) INTEGER */
/*          The leading dimension of the array AFAC. */
/*          LDAFAC >= max(1,2*KL*KU+1). */

/*  IPIV    (input) INTEGER array, dimension (min(M,N)) */
/*          The pivot indices from ZGBTRF. */

/*  WORK    (workspace) COMPLEX*16 array, dimension (2*KL+KU+1) */

/*  RESID   (output) DOUBLE PRECISION */
/*          norm(L*U - A) / ( N * norm(A) * EPS ) */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Quick exit if M = 0 or N = 0. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    afac_dim1 = *ldafac;
    afac_offset = 1 + afac_dim1;
    afac -= afac_offset;
    --ipiv;
    --work;

    /* Function Body */
    *resid = 0.;
    if (*m <= 0 || *n <= 0) {
        return 0;
    }

/*     Determine EPS and the norm of A. */

    eps = dlamch_("Epsilon");
    kd = *ku + 1;
    anorm = 0.;
    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
        i__2 = kd + 1 - j;
        i1 = max(i__2,1);
/* Computing MIN */
        i__2 = kd + *m - j, i__3 = *kl + kd;
        i2 = min(i__2,i__3);
        if (i2 >= i1) {
/* Computing MAX */
            i__2 = i2 - i1 + 1;
            d__1 = anorm, d__2 = dzasum_(&i__2, &a[i1 + j * a_dim1], &c__1);
            anorm = max(d__1,d__2);
        }
/* L10: */
    }

/*     Compute one column at a time of L*U - A. */

    kd = *kl + *ku + 1;
    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {

/*        Copy the J-th column of U to WORK. */

/* Computing MIN */
        i__2 = *kl + *ku, i__3 = j - 1;
        ju = min(i__2,i__3);
/* Computing MIN */
        i__2 = *kl, i__3 = *m - j;
        jl = min(i__2,i__3);
        lenj = min(*m,j) - j + ju + 1;
        if (lenj > 0) {
            zcopy_(&lenj, &afac[kd - ju + j * afac_dim1], &c__1, &work[1], &
                    c__1);
            i__2 = ju + jl + 1;
            for (i__ = lenj + 1; i__ <= i__2; ++i__) {
                i__3 = i__;
                work[i__3].r = 0., work[i__3].i = 0.;
/* L20: */
            }

/*           Multiply by the unit lower triangular matrix L.  Note that L */
/*           is stored as a product of transformations and permutations. */

/* Computing MIN */
            i__2 = *m - 1;
            i__3 = j - ju;
            for (i__ = min(i__2,j); i__ >= i__3; --i__) {
/* Computing MIN */
                i__2 = *kl, i__4 = *m - i__;
                il = min(i__2,i__4);
                if (il > 0) {
                    iw = i__ - j + ju + 1;
                    i__2 = iw;
                    t.r = work[i__2].r, t.i = work[i__2].i;
                    zaxpy_(&il, &t, &afac[kd + 1 + i__ * afac_dim1], &c__1, &
                            work[iw + 1], &c__1);
                    ip = ipiv[i__];
                    if (i__ != ip) {
                        ip = ip - j + ju + 1;
                        i__2 = iw;
                        i__4 = ip;
                        work[i__2].r = work[i__4].r, work[i__2].i = work[i__4]
                                .i;
                        i__2 = ip;
                        work[i__2].r = t.r, work[i__2].i = t.i;
                    }
                }
/* L30: */
            }

/*           Subtract the corresponding column of A. */

            jua = min(ju,*ku);
            if (jua + jl + 1 > 0) {
                i__3 = jua + jl + 1;
                zaxpy_(&i__3, &c_b12, &a[*ku + 1 - jua + j * a_dim1], &c__1, &
                        work[ju + 1 - jua], &c__1);
            }

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

/* Computing MAX */
            i__3 = ju + jl + 1;
            d__1 = *resid, d__2 = dzasum_(&i__3, &work[1], &c__1);
            *resid = max(d__1,d__2);
        }
/* L40: */
    }

/*     Compute norm( L*U - A ) / ( N * norm(A) * EPS ) */

    if (anorm <= 0.) {
        if (*resid != 0.) {
            *resid = 1. / eps;
        }
    } else {
        *resid = *resid / (doublereal) (*n) / anorm / eps;
    }

    return 0;

/*     End of ZGBT01 */

} /* zgbt01_ */