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/* dgetri.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_n1 = -1;
static integer c__2 = 2;
static doublereal c_b20 = -1.;
static doublereal c_b22 = 1.;
/* Subroutine */ int dgetri_(integer *n, doublereal *a, integer *lda, integer
*ipiv, doublereal *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
/* Local variables */
integer i__, j, jb, nb, jj, jp, nn, iws;
extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *),
dgemv_(char *, integer *, integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *);
integer nbmin;
extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *,
doublereal *, integer *), dtrsm_(char *, char *, char *, char *,
integer *, integer *, doublereal *, doublereal *, integer *,
doublereal *, integer *), xerbla_(
char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
integer ldwork;
extern /* Subroutine */ int dtrtri_(char *, char *, integer *, doublereal
*, integer *, integer *);
integer lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DGETRI computes the inverse of a matrix using the LU factorization */
/* computed by DGETRF. */
/* This method inverts U and then computes inv(A) by solving the system */
/* inv(A)*L = inv(U) for inv(A). */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/* On entry, the factors L and U from the factorization */
/* A = P*L*U as computed by DGETRF. */
/* On exit, if INFO = 0, the inverse of the original matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* IPIV (input) INTEGER array, dimension (N) */
/* The pivot indices from DGETRF; for 1<=i<=N, row i of the */
/* matrix was interchanged with row IPIV(i). */
/* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO=0, then WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= max(1,N). */
/* For optimal performance LWORK >= N*NB, where NB is */
/* the optimal blocksize returned by ILAENV. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* 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 matrix is */
/* singular and its inverse could not be computed. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--ipiv;
--work;
/* Function Body */
*info = 0;
nb = ilaenv_(&c__1, "DGETRI", " ", n, &c_n1, &c_n1, &c_n1);
lwkopt = *n * nb;
work[1] = (doublereal) lwkopt;
lquery = *lwork == -1;
if (*n < 0) {
*info = -1;
} else if (*lda < max(1,*n)) {
*info = -3;
} else if (*lwork < max(1,*n) && ! lquery) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGETRI", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Form inv(U). If INFO > 0 from DTRTRI, then U is singular, */
/* and the inverse is not computed. */
dtrtri_("Upper", "Non-unit", n, &a[a_offset], lda, info);
if (*info > 0) {
return 0;
}
nbmin = 2;
ldwork = *n;
if (nb > 1 && nb < *n) {
/* Computing MAX */
i__1 = ldwork * nb;
iws = max(i__1,1);
if (*lwork < iws) {
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "DGETRI", " ", n, &c_n1, &c_n1, &
c_n1);
nbmin = max(i__1,i__2);
}
} else {
iws = *n;
}
/* Solve the equation inv(A)*L = inv(U) for inv(A). */
if (nb < nbmin || nb >= *n) {
/* Use unblocked code. */
for (j = *n; j >= 1; --j) {
/* Copy current column of L to WORK and replace with zeros. */
i__1 = *n;
for (i__ = j + 1; i__ <= i__1; ++i__) {
work[i__] = a[i__ + j * a_dim1];
a[i__ + j * a_dim1] = 0.;
/* L10: */
}
/* Compute current column of inv(A). */
if (j < *n) {
i__1 = *n - j;
dgemv_("No transpose", n, &i__1, &c_b20, &a[(j + 1) * a_dim1
+ 1], lda, &work[j + 1], &c__1, &c_b22, &a[j * a_dim1
+ 1], &c__1);
}
/* L20: */
}
} else {
/* Use blocked code. */
nn = (*n - 1) / nb * nb + 1;
i__1 = -nb;
for (j = nn; i__1 < 0 ? j >= 1 : j <= 1; j += i__1) {
/* Computing MIN */
i__2 = nb, i__3 = *n - j + 1;
jb = min(i__2,i__3);
/* Copy current block column of L to WORK and replace with */
/* zeros. */
i__2 = j + jb - 1;
for (jj = j; jj <= i__2; ++jj) {
i__3 = *n;
for (i__ = jj + 1; i__ <= i__3; ++i__) {
work[i__ + (jj - j) * ldwork] = a[i__ + jj * a_dim1];
a[i__ + jj * a_dim1] = 0.;
/* L30: */
}
/* L40: */
}
/* Compute current block column of inv(A). */
if (j + jb <= *n) {
i__2 = *n - j - jb + 1;
dgemm_("No transpose", "No transpose", n, &jb, &i__2, &c_b20,
&a[(j + jb) * a_dim1 + 1], lda, &work[j + jb], &
ldwork, &c_b22, &a[j * a_dim1 + 1], lda);
}
dtrsm_("Right", "Lower", "No transpose", "Unit", n, &jb, &c_b22, &
work[j], &ldwork, &a[j * a_dim1 + 1], lda);
/* L50: */
}
}
/* Apply column interchanges. */
for (j = *n - 1; j >= 1; --j) {
jp = ipiv[j];
if (jp != j) {
dswap_(n, &a[j * a_dim1 + 1], &c__1, &a[jp * a_dim1 + 1], &c__1);
}
/* L60: */
}
work[1] = (doublereal) iws;
return 0;
/* End of DGETRI */
} /* dgetri_ */
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