/* dgbtrf.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 integer c__65 = 65;
static doublereal c_b18 = -1.;
static doublereal c_b31 = 1.;
/* Subroutine */ int dgbtrf_(integer *m, integer *n, integer *kl, integer *ku,
doublereal *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;
doublereal d__1;
/* Local variables */
integer i__, j, i2, i3, j2, j3, k2, jb, nb, ii, jj, jm, ip, jp, km, ju,
kv, nw;
extern /* Subroutine */ int dger_(integer *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *);
doublereal temp;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *), dgemm_(char *, char *, integer *, integer *, integer *
, doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *), dcopy_(
integer *, doublereal *, integer *, doublereal *, integer *),
dswap_(integer *, doublereal *, integer *, doublereal *, integer *
);
doublereal work13[4160] /* was [65][64] */, work31[4160] /*
was [65][64] */;
extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *,
integer *, integer *, doublereal *, doublereal *, integer *,
doublereal *, integer *), dgbtf2_(
integer *, integer *, integer *, integer *, doublereal *, integer
*, integer *, integer *);
extern integer idamax_(integer *, doublereal *, integer *);
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int dlaswp_(integer *, doublereal *, 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 */
/* ======= */
/* DGBTRF computes an LU factorization of a real 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) DOUBLE PRECISION 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_("DGBTRF", &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, "DGBTRF", " ", 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 */
dgbtf2_(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__) {
work13[i__ + j * 65 - 66] = 0.;
/* 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__) {
work31[i__ + j * 65 - 66] = 0.;
/* 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__) {
ab[i__ + j * ab_dim1] = 0.;
/* 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__) {
ab[i__ + (jj + kv) * ab_dim1] = 0.;
/* 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 = idamax_(&i__4, &ab[kv + 1 + jj * ab_dim1], &c__1);
ipiv[jj] = jp + jj - j;
if (ab[kv + jp + jj * ab_dim1] != 0.) {
/* 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;
dswap_(&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;
dswap_(&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;
dswap_(&i__4, &ab[kv + 1 + jj * ab_dim1], &i__5, &
ab[kv + jp + jj * ab_dim1], &i__6);
}
}
/* Compute multipliers */
d__1 = 1. / ab[kv + 1 + jj * ab_dim1];
dscal_(&km, &d__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;
i__5 = *ldab - 1;
i__6 = *ldab - 1;
dger_(&km, &i__4, &c_b18, &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) {
dcopy_(&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 DLASWP to apply the row interchanges to A12, A22, and */
/* A32. */
i__3 = *ldab - 1;
dlaswp_(&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) {
temp = ab[kv + 1 + ii - jj + jj * ab_dim1];
ab[kv + 1 + ii - jj + jj * ab_dim1] = ab[kv + 1 +
ip - jj + jj * ab_dim1];
ab[kv + 1 + ip - jj + jj * ab_dim1] = temp;
}
/* L100: */
}
/* L110: */
}
/* Update the relevant part of the trailing submatrix */
if (j2 > 0) {
/* Update A12 */
i__3 = *ldab - 1;
i__4 = *ldab - 1;
dtrsm_("Left", "Lower", "No transpose", "Unit", &jb, &j2,
&c_b31, &ab[kv + 1 + j * ab_dim1], &i__3, &ab[kv
+ 1 - jb + (j + jb) * ab_dim1], &i__4);
if (i2 > 0) {
/* Update A22 */
i__3 = *ldab - 1;
i__4 = *ldab - 1;
i__5 = *ldab - 1;
dgemm_("No transpose", "No transpose", &i2, &j2, &jb,
&c_b18, &ab[kv + 1 + jb + j * ab_dim1], &i__3,
&ab[kv + 1 - jb + (j + jb) * ab_dim1], &i__4,
&c_b31, &ab[kv + 1 + (j + jb) * ab_dim1], &
i__5);
}
if (i3 > 0) {
/* Update A32 */
i__3 = *ldab - 1;
i__4 = *ldab - 1;
dgemm_("No transpose", "No transpose", &i3, &j2, &jb,
&c_b18, work31, &c__65, &ab[kv + 1 - jb + (j
+ jb) * ab_dim1], &i__3, &c_b31, &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) {
work13[ii + jj * 65 - 66] = ab[ii - jj + 1 + (jj
+ j + kv - 1) * ab_dim1];
/* L120: */
}
/* L130: */
}
/* Update A13 in the work array */
i__3 = *ldab - 1;
dtrsm_("Left", "Lower", "No transpose", "Unit", &jb, &j3,
&c_b31, &ab[kv + 1 + j * ab_dim1], &i__3, work13,
&c__65);
if (i2 > 0) {
/* Update A23 */
i__3 = *ldab - 1;
i__4 = *ldab - 1;
dgemm_("No transpose", "No transpose", &i2, &j3, &jb,
&c_b18, &ab[kv + 1 + jb + j * ab_dim1], &i__3,
work13, &c__65, &c_b31, &ab[jb + 1 + (j + kv)
* ab_dim1], &i__4);
}
if (i3 > 0) {
/* Update A33 */
i__3 = *ldab - 1;
dgemm_("No transpose", "No transpose", &i3, &j3, &jb,
&c_b18, work31, &c__65, work13, &c__65, &
c_b31, &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) {
ab[ii - jj + 1 + (jj + j + kv - 1) * ab_dim1] =
work13[ii + jj * 65 - 66];
/* 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;
dswap_(&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;
dswap_(&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) {
dcopy_(&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 DGBTRF */
} /* dgbtrf_ */