Example #1
0
/* Subroutine */ int cgetrf_(integer *m, integer *n, complex *a, integer *lda, 
	 integer *ipiv, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
    complex q__1;

    /* Local variables */
    integer i__, j, jb, nb;
    extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, 
	    integer *, complex *, complex *, integer *, complex *, integer *, 
	    complex *, complex *, integer *);
    integer iinfo;
    extern /* Subroutine */ int ctrsm_(char *, char *, char *, char *, 
	    integer *, integer *, complex *, complex *, integer *, complex *, 
	    integer *), cgetf2_(integer *, 
	    integer *, complex *, integer *, integer *, integer *), xerbla_(
	    char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *);
    extern /* Subroutine */ int claswp_(integer *, complex *, integer *, 
	    integer *, integer *, integer *, integer *);


/*  -- LAPACK routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     March 2008 */

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

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

/*  CGETRF computes an LU factorization of a general M-by-N matrix A */
/*  using partial pivoting with row interchanges. */

/*  The factorization has the form */
/*     A = P * L * U */
/*  where P is a permutation matrix, L is lower triangular with unit */
/*  diagonal elements (lower trapezoidal if m > n), and U is upper */
/*  triangular (upper trapezoidal if m < n). */

/*  This is the Crout Level 3 BLAS version of the algorithm. */

/*  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. */

/*  A       (input/output) COMPLEX array, dimension (LDA,N) */
/*          On entry, the M-by-N matrix to be factored. */
/*          On exit, the factors L and U from the factorization */
/*          A = P*L*U; the unit diagonal elements of L are not stored. */

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

/*  IPIV    (output) INTEGER array, dimension (min(M,N)) */
/*          The pivot indices; for 1 <= i <= min(M,N), row i of the */
/*          matrix was interchanged with row IPIV(i). */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
/*          > 0:  if INFO = i, U(i,i) is exactly zero. The factorization */
/*                has been completed, but the factor U is exactly */
/*                singular, and division by zero will occur if it is used */
/*                to solve a system of equations. */

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

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

/*     Test the input parameters. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --ipiv;

    /* Function Body */
    *info = 0;
    if (*m < 0) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*lda < max(1,*m)) {
	*info = -4;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("CGETRF", &i__1);
	return 0;
    }

/*     Quick return if possible */

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

/*     Determine the block size for this environment. */

    nb = ilaenv_(&c__1, "CGETRF", " ", m, n, &c_n1, &c_n1);
    if (nb <= 1 || nb >= min(*m,*n)) {

/*        Use unblocked code. */

	cgetf2_(m, n, &a[a_offset], lda, &ipiv[1], info);
    } else {

/*        Use blocked code. */

	i__1 = min(*m,*n);
	i__2 = nb;
	for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/* Computing MIN */
	    i__3 = min(*m,*n) - j + 1;
	    jb = min(i__3,nb);

/*           Update current block. */

	    i__3 = *m - j + 1;
	    i__4 = j - 1;
	    q__1.r = -1.f, q__1.i = -0.f;
	    cgemm_("No transpose", "No transpose", &i__3, &jb, &i__4, &q__1, &
		    a[j + a_dim1], lda, &a[j * a_dim1 + 1], lda, &c_b1, &a[j 
		    + j * a_dim1], lda);

/*           Factor diagonal and subdiagonal blocks and test for exact */
/*           singularity. */

	    i__3 = *m - j + 1;
	    cgetf2_(&i__3, &jb, &a[j + j * a_dim1], lda, &ipiv[j], &iinfo);

/*           Adjust INFO and the pivot indices. */

	    if (*info == 0 && iinfo > 0) {
		*info = iinfo + j - 1;
	    }
/* Computing MIN */
	    i__4 = *m, i__5 = j + jb - 1;
	    i__3 = min(i__4,i__5);
	    for (i__ = j; i__ <= i__3; ++i__) {
		ipiv[i__] = j - 1 + ipiv[i__];
/* L10: */
	    }

/*           Apply interchanges to column 1:J-1 */

	    i__3 = j - 1;
	    i__4 = j + jb - 1;
	    claswp_(&i__3, &a[a_offset], lda, &j, &i__4, &ipiv[1], &c__1);

	    if (j + jb <= *n) {

/*              Apply interchanges to column J+JB:N */

		i__3 = *n - j - jb + 1;
		i__4 = j + jb - 1;
		claswp_(&i__3, &a[(j + jb) * a_dim1 + 1], lda, &j, &i__4, &
			ipiv[1], &c__1);

		i__3 = *n - j - jb + 1;
		i__4 = j - 1;
		q__1.r = -1.f, q__1.i = -0.f;
		cgemm_("No transpose", "No transpose", &jb, &i__3, &i__4, &
			q__1, &a[j + a_dim1], lda, &a[(j + jb) * a_dim1 + 1], 
			lda, &c_b1, &a[j + (j + jb) * a_dim1], lda);

/*              Compute block row of U. */

		i__3 = *n - j - jb + 1;
		ctrsm_("Left", "Lower", "No transpose", "Unit", &jb, &i__3, &
			c_b1, &a[j + j * a_dim1], lda, &a[j + (j + jb) * 
			a_dim1], lda);
	    }
/* L20: */
	}
    }
    return 0;

/*     End of CGETRF */

} /* cgetrf_ */
Example #2
0
/* Subroutine */ int cgesc2_(integer *n, complex *a, integer *lda, complex *
	rhs, integer *ipiv, integer *jpiv, real *scale)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
    real r__1;
    complex q__1, q__2, q__3;

    /* Local variables */
    integer i__, j;
    real eps;
    complex temp;
    real bignum;
    real smlnum;

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

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

/*  CGESC2 solves a system of linear equations */

/*            A * X = scale* RHS */

/*  with a general N-by-N matrix A using the LU factorization with */
/*  complete pivoting computed by CGETC2. */

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

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

/*  A       (input) COMPLEX array, dimension (LDA, N) */
/*          On entry, the  LU part of the factorization of the n-by-n */
/*          matrix A computed by CGETC2:  A = P * L * U * Q */

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

/*  RHS     (input/output) COMPLEX array, dimension N. */
/*          On entry, the right hand side vector b. */
/*          On exit, the solution vector X. */

/*  IPIV    (input) INTEGER array, dimension (N). */
/*          The pivot indices; for 1 <= i <= N, row i of the */
/*          matrix has been interchanged with row IPIV(i). */

/*  JPIV    (input) INTEGER array, dimension (N). */
/*          The pivot indices; for 1 <= j <= N, column j of the */
/*          matrix has been interchanged with column JPIV(j). */

/*  SCALE    (output) REAL */
/*           On exit, SCALE contains the scale factor. SCALE is chosen */
/*           0 <= SCALE <= 1 to prevent owerflow in the solution. */

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

/*  Based on contributions by */
/*     Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/*     Umea University, S-901 87 Umea, Sweden. */

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

/*     Set constant to control overflow */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --rhs;
    --ipiv;
    --jpiv;

    /* Function Body */
    eps = slamch_("P");
    smlnum = slamch_("S") / eps;
    bignum = 1.f / smlnum;
    slabad_(&smlnum, &bignum);

/*     Apply permutations IPIV to RHS */

    i__1 = *n - 1;
    claswp_(&c__1, &rhs[1], lda, &c__1, &i__1, &ipiv[1], &c__1);

/*     Solve for L part */

    i__1 = *n - 1;
    for (i__ = 1; i__ <= i__1; ++i__) {
	i__2 = *n;
	for (j = i__ + 1; j <= i__2; ++j) {
	    i__3 = j;
	    i__4 = j;
	    i__5 = j + i__ * a_dim1;
	    i__6 = i__;
	    q__2.r = a[i__5].r * rhs[i__6].r - a[i__5].i * rhs[i__6].i, 
		    q__2.i = a[i__5].r * rhs[i__6].i + a[i__5].i * rhs[i__6]
		    .r;
	    q__1.r = rhs[i__4].r - q__2.r, q__1.i = rhs[i__4].i - q__2.i;
	    rhs[i__3].r = q__1.r, rhs[i__3].i = q__1.i;
	}
    }

/*     Solve for U part */

    *scale = 1.f;

/*     Check for scaling */

    i__ = icamax_(n, &rhs[1], &c__1);
    if (smlnum * 2.f * c_abs(&rhs[i__]) > c_abs(&a[*n + *n * a_dim1])) {
	r__1 = c_abs(&rhs[i__]);
	q__1.r = .5f / r__1, q__1.i = 0.f / r__1;
	temp.r = q__1.r, temp.i = q__1.i;
	cscal_(n, &temp, &rhs[1], &c__1);
	*scale *= temp.r;
    }
    for (i__ = *n; i__ >= 1; --i__) {
	c_div(&q__1, &c_b13, &a[i__ + i__ * a_dim1]);
	temp.r = q__1.r, temp.i = q__1.i;
	i__1 = i__;
	i__2 = i__;
	q__1.r = rhs[i__2].r * temp.r - rhs[i__2].i * temp.i, q__1.i = rhs[
		i__2].r * temp.i + rhs[i__2].i * temp.r;
	rhs[i__1].r = q__1.r, rhs[i__1].i = q__1.i;
	i__1 = *n;
	for (j = i__ + 1; j <= i__1; ++j) {
	    i__2 = i__;
	    i__3 = i__;
	    i__4 = j;
	    i__5 = i__ + j * a_dim1;
	    q__3.r = a[i__5].r * temp.r - a[i__5].i * temp.i, q__3.i = a[i__5]
		    .r * temp.i + a[i__5].i * temp.r;
	    q__2.r = rhs[i__4].r * q__3.r - rhs[i__4].i * q__3.i, q__2.i = 
		    rhs[i__4].r * q__3.i + rhs[i__4].i * q__3.r;
	    q__1.r = rhs[i__3].r - q__2.r, q__1.i = rhs[i__3].i - q__2.i;
	    rhs[i__2].r = q__1.r, rhs[i__2].i = q__1.i;
	}
    }

/*     Apply permutations JPIV to the solution (RHS) */

    i__1 = *n - 1;
    claswp_(&c__1, &rhs[1], lda, &c__1, &i__1, &jpiv[1], &c_n1);
    return 0;

/*     End of CGESC2 */

} /* cgesc2_ */
Example #3
0
/* Subroutine */ int cgetrs_(char *trans, integer *n, integer *nrhs, complex *
	a, integer *lda, integer *ipiv, complex *b, integer *ldb, integer *
	info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1;

    /* Local variables */
    logical notran;

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

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

/*  CGETRS solves a system of linear equations */
/*     A * X = B,  A**T * X = B,  or  A**H * X = B */
/*  with a general N-by-N matrix A using the LU factorization computed */
/*  by CGETRF. */

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

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

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

/*  NRHS    (input) INTEGER */
/*          The number of right hand sides, i.e., the number of columns */
/*          of the matrix B.  NRHS >= 0. */

/*  A       (input) COMPLEX array, dimension (LDA,N) */
/*          The factors L and U from the factorization A = P*L*U */
/*          as computed by CGETRF. */

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

/*  IPIV    (input) INTEGER array, dimension (N) */
/*          The pivot indices from CGETRF; for 1<=i<=N, row i of the */
/*          matrix was interchanged with row IPIV(i). */

/*  B       (input/output) COMPLEX array, dimension (LDB,NRHS) */
/*          On entry, the right hand side matrix B. */
/*          On exit, the 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 */

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

/*     Test the input parameters. */

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

    /* Function Body */
    *info = 0;
    notran = lsame_(trans, "N");
    if (! notran && ! lsame_(trans, "T") && ! lsame_(
	    trans, "C")) {
	*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 = -8;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("CGETRS", &i__1);
	return 0;
    }

/*     Quick return if possible */

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

    if (notran) {

/*        Solve A * X = B. */

/*        Apply row interchanges to the right hand sides. */

	claswp_(nrhs, &b[b_offset], ldb, &c__1, n, &ipiv[1], &c__1);

/*        Solve L*X = B, overwriting B with X. */

	ctrsm_("Left", "Lower", "No transpose", "Unit", n, nrhs, &c_b1, &a[
		a_offset], lda, &b[b_offset], ldb);

/*        Solve U*X = B, overwriting B with X. */

	ctrsm_("Left", "Upper", "No transpose", "Non-unit", n, nrhs, &c_b1, &
		a[a_offset], lda, &b[b_offset], ldb);
    } else {

/*        Solve A**T * X = B  or A**H * X = B. */

/*        Solve U'*X = B, overwriting B with X. */

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

/*        Solve L'*X = B, overwriting B with X. */

	ctrsm_("Left", "Lower", trans, "Unit", n, nrhs, &c_b1, &a[a_offset], 
		lda, &b[b_offset], ldb);

/*        Apply row interchanges to the solution vectors. */

	claswp_(nrhs, &b[b_offset], ldb, &c__1, n, &ipiv[1], &c_n1);
    }

    return 0;

/*     End of CGETRS */

} /* cgetrs_ */
Example #4
0
/* Subroutine */ int cgbtrf_(integer *m, integer *n, integer *kl, integer *ku, 
	 complex *ab, integer *ldab, integer *ipiv, integer *info)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4, i__5, i__6;
    complex q__1;

    /* Builtin functions */
    void c_div(complex *, complex *, complex *);

    /* Local variables */
    integer i__, j, i2, i3, j2, j3, k2, jb, nb, ii, jj, jm, ip, jp, km, ju, 
	    kv, nw;
    complex temp;
    extern /* Subroutine */ int cscal_(integer *, complex *, complex *, 
	    integer *), cgemm_(char *, char *, integer *, integer *, integer *
, complex *, complex *, integer *, complex *, integer *, complex *
, complex *, integer *), cgeru_(integer *, 
	    integer *, complex *, complex *, integer *, complex *, integer *, 
	    complex *, integer *), ccopy_(integer *, complex *, integer *, 
	    complex *, integer *), cswap_(integer *, complex *, integer *, 
	    complex *, integer *);
	  #ifdef LAPACK_DISABLE_MEMORY_HOGS
		  complex work13[1]	/* was [65][64] */, work31[1]	/* 
		    was [65][64] */;
	    /** This function uses too much memory, so we stopped allocating the memory
	     * above and assert false here. */
	    assert(0 && "cgbtrf_ was called. This function allocates too much"
	                " memory and has been disabled.");
	  #else
	    complex work13[4160]	/* was [65][64] */, work31[4160]	/* 
		    was [65][64] */;
	  #endif
    extern /* Subroutine */ int ctrsm_(char *, char *, char *, char *, 
	    integer *, integer *, complex *, complex *, integer *, complex *, 
	    integer *), cgbtf2_(integer *, 
	    integer *, integer *, integer *, complex *, integer *, integer *, 
	    integer *);
    extern integer icamax_(integer *, complex *, integer *);
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *);
    extern /* Subroutine */ int claswp_(integer *, complex *, integer *, 
	    integer *, integer *, integer *, integer *);


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  CGBTRF computes an LU factorization of a complex m-by-n band matrix A */
/*  using partial pivoting with row interchanges. */

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

/*  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. */

/*  AB      (input/output) COMPLEX array, dimension (LDAB,N) */
/*          On entry, the matrix A in band storage, in rows KL+1 to */
/*          2*KL+KU+1; rows 1 to KL of the array need not be set. */
/*          The j-th column of A is stored in the j-th column of the */
/*          array AB as follows: */
/*          AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) */

/*          On exit, details of the factorization: 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 below for further details. */

/*  LDAB    (input) INTEGER */
/*          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1. */

/*  IPIV    (output) INTEGER array, dimension (min(M,N)) */
/*          The pivot indices; for 1 <= i <= min(M,N), row i of the */
/*          matrix was interchanged with row IPIV(i). */

/*  INFO    (output) INTEGER */
/*          = 0: successful exit */
/*          < 0: if INFO = -i, the i-th argument had an illegal value */
/*          > 0: if INFO = +i, U(i,i) is exactly zero. The factorization */
/*               has been completed, but the factor U is exactly */
/*               singular, and division by zero will occur if it is used */
/*               to solve a system of equations. */

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

/*  The band storage scheme is illustrated by the following example, when */
/*  M = N = 6, KL = 2, KU = 1: */

/*  On entry:                       On exit: */

/*      *    *    *    +    +    +       *    *    *   u14  u25  u36 */
/*      *    *    +    +    +    +       *    *   u13  u24  u35  u46 */
/*      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56 */
/*     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66 */
/*     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   * */
/*     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    * */

/*  Array elements marked * are not used by the routine; elements marked */
/*  + need not be set on entry, but are required by the routine to store */
/*  elements of U because of fill-in resulting from the row interchanges. */

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

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


/*     KV is the number of superdiagonals in the factor U, allowing for */
/*     fill-in */

    /* Parameter adjustments */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1;
    ab -= ab_offset;
    --ipiv;

    /* Function Body */
    kv = *ku + *kl;

/*     Test the input parameters. */

    *info = 0;
    if (*m < 0) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*kl < 0) {
	*info = -3;
    } else if (*ku < 0) {
	*info = -4;
    } else if (*ldab < *kl + kv + 1) {
	*info = -6;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("CGBTRF", &i__1);
	return 0;
    }

/*     Quick return if possible */

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

/*     Determine the block size for this environment */

    nb = ilaenv_(&c__1, "CGBTRF", " ", m, n, kl, ku);

/*     The block size must not exceed the limit set by the size of the */
/*     local arrays WORK13 and WORK31. */

    nb = min(nb,64);

    if (nb <= 1 || nb > *kl) {

/*        Use unblocked code */

	cgbtf2_(m, n, kl, ku, &ab[ab_offset], ldab, &ipiv[1], info);
    } else {

/*        Use blocked code */

/*        Zero the superdiagonal elements of the work array WORK13 */

	i__1 = nb;
	for (j = 1; j <= i__1; ++j) {
	    i__2 = j - 1;
	    for (i__ = 1; i__ <= i__2; ++i__) {
		i__3 = i__ + j * 65 - 66;
		work13[i__3].r = 0.f, work13[i__3].i = 0.f;
/* L10: */
	    }
/* L20: */
	}

/*        Zero the subdiagonal elements of the work array WORK31 */

	i__1 = nb;
	for (j = 1; j <= i__1; ++j) {
	    i__2 = nb;
	    for (i__ = j + 1; i__ <= i__2; ++i__) {
		i__3 = i__ + j * 65 - 66;
		work31[i__3].r = 0.f, work31[i__3].i = 0.f;
/* L30: */
	    }
/* L40: */
	}

/*        Gaussian elimination with partial pivoting */

/*        Set fill-in elements in columns KU+2 to KV to zero */

	i__1 = min(kv,*n);
	for (j = *ku + 2; j <= i__1; ++j) {
	    i__2 = *kl;
	    for (i__ = kv - j + 2; i__ <= i__2; ++i__) {
		i__3 = i__ + j * ab_dim1;
		ab[i__3].r = 0.f, ab[i__3].i = 0.f;
/* L50: */
	    }
/* L60: */
	}

/*        JU is the index of the last column affected by the current */
/*        stage of the factorization */

	ju = 1;

	i__1 = min(*m,*n);
	i__2 = nb;
	for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/* Computing MIN */
	    i__3 = nb, i__4 = min(*m,*n) - j + 1;
	    jb = min(i__3,i__4);

/*           The active part of the matrix is partitioned */

/*              A11   A12   A13 */
/*              A21   A22   A23 */
/*              A31   A32   A33 */

/*           Here A11, A21 and A31 denote the current block of JB columns */
/*           which is about to be factorized. The number of rows in the */
/*           partitioning are JB, I2, I3 respectively, and the numbers */
/*           of columns are JB, J2, J3. The superdiagonal elements of A13 */
/*           and the subdiagonal elements of A31 lie outside the band. */

/* Computing MIN */
	    i__3 = *kl - jb, i__4 = *m - j - jb + 1;
	    i2 = min(i__3,i__4);
/* Computing MIN */
	    i__3 = jb, i__4 = *m - j - *kl + 1;
	    i3 = min(i__3,i__4);

/*           J2 and J3 are computed after JU has been updated. */

/*           Factorize the current block of JB columns */

	    i__3 = j + jb - 1;
	    for (jj = j; jj <= i__3; ++jj) {

/*              Set fill-in elements in column JJ+KV to zero */

		if (jj + kv <= *n) {
		    i__4 = *kl;
		    for (i__ = 1; i__ <= i__4; ++i__) {
			i__5 = i__ + (jj + kv) * ab_dim1;
			ab[i__5].r = 0.f, ab[i__5].i = 0.f;
/* L70: */
		    }
		}

/*              Find pivot and test for singularity. KM is the number of */
/*              subdiagonal elements in the current column. */

/* Computing MIN */
		i__4 = *kl, i__5 = *m - jj;
		km = min(i__4,i__5);
		i__4 = km + 1;
		jp = icamax_(&i__4, &ab[kv + 1 + jj * ab_dim1], &c__1);
		ipiv[jj] = jp + jj - j;
		i__4 = kv + jp + jj * ab_dim1;
		if (ab[i__4].r != 0.f || ab[i__4].i != 0.f) {
/* Computing MAX */
/* Computing MIN */
		    i__6 = jj + *ku + jp - 1;
		    i__4 = ju, i__5 = min(i__6,*n);
		    ju = max(i__4,i__5);
		    if (jp != 1) {

/*                    Apply interchange to columns J to J+JB-1 */

			if (jp + jj - 1 < j + *kl) {

			    i__4 = *ldab - 1;
			    i__5 = *ldab - 1;
			    cswap_(&jb, &ab[kv + 1 + jj - j + j * ab_dim1], &
				    i__4, &ab[kv + jp + jj - j + j * ab_dim1], 
				     &i__5);
			} else {

/*                       The interchange affects columns J to JJ-1 of A31 */
/*                       which are stored in the work array WORK31 */

			    i__4 = jj - j;
			    i__5 = *ldab - 1;
			    cswap_(&i__4, &ab[kv + 1 + jj - j + j * ab_dim1], 
				    &i__5, &work31[jp + jj - j - *kl - 1], &
				    c__65);
			    i__4 = j + jb - jj;
			    i__5 = *ldab - 1;
			    i__6 = *ldab - 1;
			    cswap_(&i__4, &ab[kv + 1 + jj * ab_dim1], &i__5, &
				    ab[kv + jp + jj * ab_dim1], &i__6);
			}
		    }

/*                 Compute multipliers */

		    c_div(&q__1, &c_b1, &ab[kv + 1 + jj * ab_dim1]);
		    cscal_(&km, &q__1, &ab[kv + 2 + jj * ab_dim1], &c__1);

/*                 Update trailing submatrix within the band and within */
/*                 the current block. JM is the index of the last column */
/*                 which needs to be updated. */

/* Computing MIN */
		    i__4 = ju, i__5 = j + jb - 1;
		    jm = min(i__4,i__5);
		    if (jm > jj) {
			i__4 = jm - jj;
			q__1.r = -1.f, q__1.i = -0.f;
			i__5 = *ldab - 1;
			i__6 = *ldab - 1;
			cgeru_(&km, &i__4, &q__1, &ab[kv + 2 + jj * ab_dim1], 
				&c__1, &ab[kv + (jj + 1) * ab_dim1], &i__5, &
				ab[kv + 1 + (jj + 1) * ab_dim1], &i__6);
		    }
		} else {

/*                 If pivot is zero, set INFO to the index of the pivot */
/*                 unless a zero pivot has already been found. */

		    if (*info == 0) {
			*info = jj;
		    }
		}

/*              Copy current column of A31 into the work array WORK31 */

/* Computing MIN */
		i__4 = jj - j + 1;
		nw = min(i__4,i3);
		if (nw > 0) {
		    ccopy_(&nw, &ab[kv + *kl + 1 - jj + j + jj * ab_dim1], &
			    c__1, &work31[(jj - j + 1) * 65 - 65], &c__1);
		}
/* L80: */
	    }
	    if (j + jb <= *n) {

/*              Apply the row interchanges to the other blocks. */

/* Computing MIN */
		i__3 = ju - j + 1;
		j2 = min(i__3,kv) - jb;
/* Computing MAX */
		i__3 = 0, i__4 = ju - j - kv + 1;
		j3 = max(i__3,i__4);

/*              Use CLASWP to apply the row interchanges to A12, A22, and */
/*              A32. */

		i__3 = *ldab - 1;
		claswp_(&j2, &ab[kv + 1 - jb + (j + jb) * ab_dim1], &i__3, &
			c__1, &jb, &ipiv[j], &c__1);

/*              Adjust the pivot indices. */

		i__3 = j + jb - 1;
		for (i__ = j; i__ <= i__3; ++i__) {
		    ipiv[i__] = ipiv[i__] + j - 1;
/* L90: */
		}

/*              Apply the row interchanges to A13, A23, and A33 */
/*              columnwise. */

		k2 = j - 1 + jb + j2;
		i__3 = j3;
		for (i__ = 1; i__ <= i__3; ++i__) {
		    jj = k2 + i__;
		    i__4 = j + jb - 1;
		    for (ii = j + i__ - 1; ii <= i__4; ++ii) {
			ip = ipiv[ii];
			if (ip != ii) {
			    i__5 = kv + 1 + ii - jj + jj * ab_dim1;
			    temp.r = ab[i__5].r, temp.i = ab[i__5].i;
			    i__5 = kv + 1 + ii - jj + jj * ab_dim1;
			    i__6 = kv + 1 + ip - jj + jj * ab_dim1;
			    ab[i__5].r = ab[i__6].r, ab[i__5].i = ab[i__6].i;
			    i__5 = kv + 1 + ip - jj + jj * ab_dim1;
			    ab[i__5].r = temp.r, ab[i__5].i = temp.i;
			}
/* L100: */
		    }
/* L110: */
		}

/*              Update the relevant part of the trailing submatrix */

		if (j2 > 0) {

/*                 Update A12 */

		    i__3 = *ldab - 1;
		    i__4 = *ldab - 1;
		    ctrsm_("Left", "Lower", "No transpose", "Unit", &jb, &j2, 
			    &c_b1, &ab[kv + 1 + j * ab_dim1], &i__3, &ab[kv + 
			    1 - jb + (j + jb) * ab_dim1], &i__4);

		    if (i2 > 0) {

/*                    Update A22 */

			q__1.r = -1.f, q__1.i = -0.f;
			i__3 = *ldab - 1;
			i__4 = *ldab - 1;
			i__5 = *ldab - 1;
			cgemm_("No transpose", "No transpose", &i2, &j2, &jb, 
				&q__1, &ab[kv + 1 + jb + j * ab_dim1], &i__3, 
				&ab[kv + 1 - jb + (j + jb) * ab_dim1], &i__4, 
				&c_b1, &ab[kv + 1 + (j + jb) * ab_dim1], &
				i__5);
		    }

		    if (i3 > 0) {

/*                    Update A32 */

			q__1.r = -1.f, q__1.i = -0.f;
			i__3 = *ldab - 1;
			i__4 = *ldab - 1;
			cgemm_("No transpose", "No transpose", &i3, &j2, &jb, 
				&q__1, work31, &c__65, &ab[kv + 1 - jb + (j + 
				jb) * ab_dim1], &i__3, &c_b1, &ab[kv + *kl + 
				1 - jb + (j + jb) * ab_dim1], &i__4);
		    }
		}

		if (j3 > 0) {

/*                 Copy the lower triangle of A13 into the work array */
/*                 WORK13 */

		    i__3 = j3;
		    for (jj = 1; jj <= i__3; ++jj) {
			i__4 = jb;
			for (ii = jj; ii <= i__4; ++ii) {
			    i__5 = ii + jj * 65 - 66;
			    i__6 = ii - jj + 1 + (jj + j + kv - 1) * ab_dim1;
			    work13[i__5].r = ab[i__6].r, work13[i__5].i = ab[
				    i__6].i;
/* L120: */
			}
/* L130: */
		    }

/*                 Update A13 in the work array */

		    i__3 = *ldab - 1;
		    ctrsm_("Left", "Lower", "No transpose", "Unit", &jb, &j3, 
			    &c_b1, &ab[kv + 1 + j * ab_dim1], &i__3, work13, &
			    c__65);

		    if (i2 > 0) {

/*                    Update A23 */

			q__1.r = -1.f, q__1.i = -0.f;
			i__3 = *ldab - 1;
			i__4 = *ldab - 1;
			cgemm_("No transpose", "No transpose", &i2, &j3, &jb, 
				&q__1, &ab[kv + 1 + jb + j * ab_dim1], &i__3, 
				work13, &c__65, &c_b1, &ab[jb + 1 + (j + kv) *
				 ab_dim1], &i__4);
		    }

		    if (i3 > 0) {

/*                    Update A33 */

			q__1.r = -1.f, q__1.i = -0.f;
			i__3 = *ldab - 1;
			cgemm_("No transpose", "No transpose", &i3, &j3, &jb, 
				&q__1, work31, &c__65, work13, &c__65, &c_b1, 
				&ab[*kl + 1 + (j + kv) * ab_dim1], &i__3);
		    }

/*                 Copy the lower triangle of A13 back into place */

		    i__3 = j3;
		    for (jj = 1; jj <= i__3; ++jj) {
			i__4 = jb;
			for (ii = jj; ii <= i__4; ++ii) {
			    i__5 = ii - jj + 1 + (jj + j + kv - 1) * ab_dim1;
			    i__6 = ii + jj * 65 - 66;
			    ab[i__5].r = work13[i__6].r, ab[i__5].i = work13[
				    i__6].i;
/* L140: */
			}
/* L150: */
		    }
		}
	    } else {

/*              Adjust the pivot indices. */

		i__3 = j + jb - 1;
		for (i__ = j; i__ <= i__3; ++i__) {
		    ipiv[i__] = ipiv[i__] + j - 1;
/* L160: */
		}
	    }

/*           Partially undo the interchanges in the current block to */
/*           restore the upper triangular form of A31 and copy the upper */
/*           triangle of A31 back into place */

	    i__3 = j;
	    for (jj = j + jb - 1; jj >= i__3; --jj) {
		jp = ipiv[jj] - jj + 1;
		if (jp != 1) {

/*                 Apply interchange to columns J to JJ-1 */

		    if (jp + jj - 1 < j + *kl) {

/*                    The interchange does not affect A31 */

			i__4 = jj - j;
			i__5 = *ldab - 1;
			i__6 = *ldab - 1;
			cswap_(&i__4, &ab[kv + 1 + jj - j + j * ab_dim1], &
				i__5, &ab[kv + jp + jj - j + j * ab_dim1], &
				i__6);
		    } else {

/*                    The interchange does affect A31 */

			i__4 = jj - j;
			i__5 = *ldab - 1;
			cswap_(&i__4, &ab[kv + 1 + jj - j + j * ab_dim1], &
				i__5, &work31[jp + jj - j - *kl - 1], &c__65);
		    }
		}

/*              Copy the current column of A31 back into place */

/* Computing MIN */
		i__4 = i3, i__5 = jj - j + 1;
		nw = min(i__4,i__5);
		if (nw > 0) {
		    ccopy_(&nw, &work31[(jj - j + 1) * 65 - 65], &c__1, &ab[
			    kv + *kl + 1 - jj + j + jj * ab_dim1], &c__1);
		}
/* L170: */
	    }
/* L180: */
	}
    }

    return 0;

/*     End of CGBTRF */

} /* cgbtrf_ */
/* Subroutine */ int cgesc2_(integer *n, complex *a, integer *lda, complex *
	rhs, integer *ipiv, integer *jpiv, real *scale)
{
/*  -- LAPACK auxiliary 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   
    =======   

    CGESC2 solves a system of linear equations   

              A * X = scale* RHS   

    with a general N-by-N matrix A using the LU factorization with   
    complete pivoting computed by CGETC2.   


    Arguments   
    =========   

    N       (input) INTEGER   
            The number of columns of the matrix A.   

    A       (input) COMPLEX array, dimension (LDA, N)   
            On entry, the  LU part of the factorization of the n-by-n   
            matrix A computed by CGETC2:  A = P * L * U * Q   

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

    RHS     (input/output) COMPLEX array, dimension N.   
            On entry, the right hand side vector b.   
            On exit, the solution vector X.   

    IPIV    (iput) INTEGER array, dimension (N).   
            The pivot indices; for 1 <= i <= N, row i of the   
            matrix has been interchanged with row IPIV(i).   

    JPIV    (iput) INTEGER array, dimension (N).   
            The pivot indices; for 1 <= j <= N, column j of the   
            matrix has been interchanged with column JPIV(j).   

    SCALE    (output) REAL   
             On exit, SCALE contains the scale factor. SCALE is chosen   
             0 <= SCALE <= 1 to prevent owerflow in the solution.   

    Further Details   
    ===============   

    Based on contributions by   
       Bo Kagstrom and Peter Poromaa, Department of Computing Science,   
       Umea University, S-901 87 Umea, Sweden.   

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


       Set constant to control overflow   

       Parameter adjustments */
    /* Table of constant values */
    static integer c__1 = 1;
    static complex c_b13 = {1.f,0.f};
    static integer c_n1 = -1;
    
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
    real r__1;
    complex q__1, q__2, q__3;
    /* Builtin functions */
    double c_abs(complex *);
    void c_div(complex *, complex *, complex *);
    /* Local variables */
    static complex temp;
    static integer i__, j;
    extern /* Subroutine */ int cscal_(integer *, complex *, complex *, 
	    integer *), slabad_(real *, real *);
    extern integer icamax_(integer *, complex *, integer *);
    extern doublereal slamch_(char *);
    static real bignum;
    extern /* Subroutine */ int claswp_(integer *, complex *, integer *, 
	    integer *, integer *, integer *, integer *);
    static real smlnum, eps;
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]


    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --rhs;
    --ipiv;
    --jpiv;

    /* Function Body */
    eps = slamch_("P");
    smlnum = slamch_("S") / eps;
    bignum = 1.f / smlnum;
    slabad_(&smlnum, &bignum);

/*     Apply permutations IPIV to RHS */

    i__1 = *n - 1;
    claswp_(&c__1, &rhs[1], lda, &c__1, &i__1, &ipiv[1], &c__1);

/*     Solve for L part */

    i__1 = *n - 1;
    for (i__ = 1; i__ <= i__1; ++i__) {
	i__2 = *n;
	for (j = i__ + 1; j <= i__2; ++j) {
	    i__3 = j;
	    i__4 = j;
	    i__5 = a_subscr(j, i__);
	    i__6 = i__;
	    q__2.r = a[i__5].r * rhs[i__6].r - a[i__5].i * rhs[i__6].i, 
		    q__2.i = a[i__5].r * rhs[i__6].i + a[i__5].i * rhs[i__6]
		    .r;
	    q__1.r = rhs[i__4].r - q__2.r, q__1.i = rhs[i__4].i - q__2.i;
	    rhs[i__3].r = q__1.r, rhs[i__3].i = q__1.i;
/* L10: */
	}
/* L20: */
    }

/*     Solve for U part */

    *scale = 1.f;

/*     Check for scaling */

    i__ = icamax_(n, &rhs[1], &c__1);
    if (smlnum * 2.f * c_abs(&rhs[i__]) > c_abs(&a_ref(*n, *n))) {
	r__1 = c_abs(&rhs[i__]);
	q__1.r = .5f / r__1, q__1.i = 0.f / r__1;
	temp.r = q__1.r, temp.i = q__1.i;
	cscal_(n, &temp, &rhs[1], &c__1);
	*scale *= temp.r;
    }
    for (i__ = *n; i__ >= 1; --i__) {
	c_div(&q__1, &c_b13, &a_ref(i__, i__));
	temp.r = q__1.r, temp.i = q__1.i;
	i__1 = i__;
	i__2 = i__;
	q__1.r = rhs[i__2].r * temp.r - rhs[i__2].i * temp.i, q__1.i = rhs[
		i__2].r * temp.i + rhs[i__2].i * temp.r;
	rhs[i__1].r = q__1.r, rhs[i__1].i = q__1.i;
	i__1 = *n;
	for (j = i__ + 1; j <= i__1; ++j) {
	    i__2 = i__;
	    i__3 = i__;
	    i__4 = j;
	    i__5 = a_subscr(i__, j);
	    q__3.r = a[i__5].r * temp.r - a[i__5].i * temp.i, q__3.i = a[i__5]
		    .r * temp.i + a[i__5].i * temp.r;
	    q__2.r = rhs[i__4].r * q__3.r - rhs[i__4].i * q__3.i, q__2.i = 
		    rhs[i__4].r * q__3.i + rhs[i__4].i * q__3.r;
	    q__1.r = rhs[i__3].r - q__2.r, q__1.i = rhs[i__3].i - q__2.i;
	    rhs[i__2].r = q__1.r, rhs[i__2].i = q__1.i;
/* L30: */
	}
/* L40: */
    }

/*     Apply permutations JPIV to the solution (RHS) */

    i__1 = *n - 1;
    claswp_(&c__1, &rhs[1], lda, &c__1, &i__1, &jpiv[1], &c_n1);
    return 0;

/*     End of CGESC2 */

} /* cgesc2_ */