#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int zgbtf2_(integer *m, integer *n, integer *kl, integer *ku, doublecomplex *ab, integer *ldab, integer *ipiv, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= ZGBTF2 computes an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges. This is the unblocked version of the algorithm, calling Level 2 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*16 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. ===================================================================== KV is the number of superdiagonals in the factor U, allowing for fill-in. Parameter adjustments */ /* Table of constant values */ static doublecomplex c_b1 = {1.,0.}; static integer c__1 = 1; /* System generated locals */ integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4; doublecomplex z__1; /* Builtin functions */ void z_div(doublecomplex *, doublecomplex *, doublecomplex *); /* Local variables */ static integer i__, j, km, jp, ju, kv; extern /* Subroutine */ int zscal_(integer *, doublecomplex *, doublecomplex *, integer *), zgeru_(integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), xerbla_( char *, integer *); extern integer izamax_(integer *, doublecomplex *, integer *); 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_("ZGBTF2", &i__1); return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { return 0; } /* 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., ab[i__3].i = 0.; /* L10: */ } /* L20: */ } /* JU is the index of the last column affected by the current stage of the factorization. */ ju = 1; i__1 = min(*m,*n); for (j = 1; j <= i__1; ++j) { /* Set fill-in elements in column J+KV to zero. */ if (j + kv <= *n) { i__2 = *kl; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + (j + kv) * ab_dim1; ab[i__3].r = 0., ab[i__3].i = 0.; /* L30: */ } } /* Find pivot and test for singularity. KM is the number of subdiagonal elements in the current column. Computing MIN */ i__2 = *kl, i__3 = *m - j; km = min(i__2,i__3); i__2 = km + 1; jp = izamax_(&i__2, &ab[kv + 1 + j * ab_dim1], &c__1); ipiv[j] = jp + j - 1; i__2 = kv + jp + j * ab_dim1; if (ab[i__2].r != 0. || ab[i__2].i != 0.) { /* Computing MAX Computing MIN */ i__4 = j + *ku + jp - 1; i__2 = ju, i__3 = min(i__4,*n); ju = max(i__2,i__3); /* Apply interchange to columns J to JU. */ if (jp != 1) { i__2 = ju - j + 1; i__3 = *ldab - 1; i__4 = *ldab - 1; zswap_(&i__2, &ab[kv + jp + j * ab_dim1], &i__3, &ab[kv + 1 + j * ab_dim1], &i__4); } if (km > 0) { /* Compute multipliers. */ z_div(&z__1, &c_b1, &ab[kv + 1 + j * ab_dim1]); zscal_(&km, &z__1, &ab[kv + 2 + j * ab_dim1], &c__1); /* Update trailing submatrix within the band. */ if (ju > j) { i__2 = ju - j; z__1.r = -1., z__1.i = -0.; i__3 = *ldab - 1; i__4 = *ldab - 1; zgeru_(&km, &i__2, &z__1, &ab[kv + 2 + j * ab_dim1], & c__1, &ab[kv + (j + 1) * ab_dim1], &i__3, &ab[kv + 1 + (j + 1) * ab_dim1], &i__4); } } } 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 = j; } } /* L40: */ } return 0; /* End of ZGBTF2 */ } /* zgbtf2_ */