3 /* Table of constant values */
5 static integer c__1 = 1;
6 static integer c_n1 = -1;
7 static doublereal c_b16 = 1.;
8 static doublereal c_b19 = -1.;
10 /* Subroutine */ int dgetrf_(integer *m, integer *n, doublereal *a, integer *
11 lda, integer *ipiv, integer *info)
13 /* System generated locals */
14 integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
17 integer i__, j, jb, nb;
18 extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
19 integer *, doublereal *, doublereal *, integer *, doublereal *,
20 integer *, doublereal *, doublereal *, integer *);
22 extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *,
23 integer *, integer *, doublereal *, doublereal *, integer *,
24 doublereal *, integer *), dgetf2_(
25 integer *, integer *, doublereal *, integer *, integer *, integer
26 *), xerbla_(char *, integer *);
27 extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
28 integer *, integer *);
29 extern /* Subroutine */ int dlaswp_(integer *, doublereal *, integer *,
30 integer *, integer *, integer *, integer *);
33 /* -- LAPACK routine (version 3.1) -- */
34 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
37 /* .. Scalar Arguments .. */
39 /* .. Array Arguments .. */
45 /* DGETRF computes an LU factorization of a general M-by-N matrix A */
46 /* using partial pivoting with row interchanges. */
48 /* The factorization has the form */
50 /* where P is a permutation matrix, L is lower triangular with unit */
51 /* diagonal elements (lower trapezoidal if m > n), and U is upper */
52 /* triangular (upper trapezoidal if m < n). */
54 /* This is the right-looking Level 3 BLAS version of the algorithm. */
59 /* M (input) INTEGER */
60 /* The number of rows of the matrix A. M >= 0. */
62 /* N (input) INTEGER */
63 /* The number of columns of the matrix A. N >= 0. */
65 /* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
66 /* On entry, the M-by-N matrix to be factored. */
67 /* On exit, the factors L and U from the factorization */
68 /* A = P*L*U; the unit diagonal elements of L are not stored. */
70 /* LDA (input) INTEGER */
71 /* The leading dimension of the array A. LDA >= max(1,M). */
73 /* IPIV (output) INTEGER array, dimension (min(M,N)) */
74 /* The pivot indices; for 1 <= i <= min(M,N), row i of the */
75 /* matrix was interchanged with row IPIV(i). */
77 /* INFO (output) INTEGER */
78 /* = 0: successful exit */
79 /* < 0: if INFO = -i, the i-th argument had an illegal value */
80 /* > 0: if INFO = i, U(i,i) is exactly zero. The factorization */
81 /* has been completed, but the factor U is exactly */
82 /* singular, and division by zero will occur if it is used */
83 /* to solve a system of equations. */
85 /* ===================================================================== */
87 /* .. Parameters .. */
89 /* .. Local Scalars .. */
91 /* .. External Subroutines .. */
93 /* .. External Functions .. */
95 /* .. Intrinsic Functions .. */
97 /* .. Executable Statements .. */
99 /* Test the input parameters. */
101 /* Parameter adjustments */
103 a_offset = 1 + a_dim1;
113 } else if (*lda < max(1,*m)) {
118 xerbla_("DGETRF", &i__1);
122 /* Quick return if possible */
124 if (*m == 0 || *n == 0) {
128 /* Determine the block size for this environment. */
130 nb = ilaenv_(&c__1, "DGETRF", " ", m, n, &c_n1, &c_n1);
131 if (nb <= 1 || nb >= min(*m,*n)) {
133 /* Use unblocked code. */
135 dgetf2_(m, n, &a[a_offset], lda, &ipiv[1], info);
138 /* Use blocked code. */
142 for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
144 i__3 = min(*m,*n) - j + 1;
147 /* Factor diagonal and subdiagonal blocks and test for exact */
151 dgetf2_(&i__3, &jb, &a[j + j * a_dim1], lda, &ipiv[j], &iinfo);
153 /* Adjust INFO and the pivot indices. */
155 if (*info == 0 && iinfo > 0) {
156 *info = iinfo + j - 1;
159 i__4 = *m, i__5 = j + jb - 1;
160 i__3 = min(i__4,i__5);
161 for (i__ = j; i__ <= i__3; ++i__) {
162 ipiv[i__] = j - 1 + ipiv[i__];
166 /* Apply interchanges to columns 1:J-1. */
170 dlaswp_(&i__3, &a[a_offset], lda, &j, &i__4, &ipiv[1], &c__1);
174 /* Apply interchanges to columns J+JB:N. */
176 i__3 = *n - j - jb + 1;
178 dlaswp_(&i__3, &a[(j + jb) * a_dim1 + 1], lda, &j, &i__4, &
181 /* Compute block row of U. */
183 i__3 = *n - j - jb + 1;
184 dtrsm_("Left", "Lower", "No transpose", "Unit", &jb, &i__3, &
185 c_b16, &a[j + j * a_dim1], lda, &a[j + (j + jb) *
189 /* Update trailing submatrix. */
191 i__3 = *m - j - jb + 1;
192 i__4 = *n - j - jb + 1;
193 dgemm_("No transpose", "No transpose", &i__3, &i__4, &jb,
194 &c_b19, &a[j + jb + j * a_dim1], lda, &a[j + (j +
195 jb) * a_dim1], lda, &c_b16, &a[j + jb + (j + jb) *