c@427: /* dgetri.f -- translated by f2c (version 20061008).
c@427:    You must link the resulting object file with libf2c:
c@427: 	on Microsoft Windows system, link with libf2c.lib;
c@427: 	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
c@427: 	or, if you install libf2c.a in a standard place, with -lf2c -lm
c@427: 	-- in that order, at the end of the command line, as in
c@427: 		cc *.o -lf2c -lm
c@427: 	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
c@427: 
c@427: 		http://www.netlib.org/f2c/libf2c.zip
c@427: */
c@427: 
c@427: #include "f2c.h"
c@427: #include "blaswrap.h"
c@427: 
c@427: /* Table of constant values */
c@427: 
c@427: static integer c__1 = 1;
c@427: static integer c_n1 = -1;
c@427: static integer c__2 = 2;
c@427: static doublereal c_b20 = -1.;
c@427: static doublereal c_b22 = 1.;
c@427: 
c@427: /* Subroutine */ int dgetri_(integer *n, doublereal *a, integer *lda, integer 
c@427: 	*ipiv, doublereal *work, integer *lwork, integer *info)
c@427: {
c@427:     /* System generated locals */
c@427:     integer a_dim1, a_offset, i__1, i__2, i__3;
c@427: 
c@427:     /* Local variables */
c@427:     integer i__, j, jb, nb, jj, jp, nn, iws;
c@427:     extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
c@427: 	    integer *, doublereal *, doublereal *, integer *, doublereal *, 
c@427: 	    integer *, doublereal *, doublereal *, integer *),
c@427: 	     dgemv_(char *, integer *, integer *, doublereal *, doublereal *, 
c@427: 	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
c@427: 	    integer *);
c@427:     integer nbmin;
c@427:     extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, 
c@427: 	    doublereal *, integer *), dtrsm_(char *, char *, char *, char *, 
c@427: 	    integer *, integer *, doublereal *, doublereal *, integer *, 
c@427: 	    doublereal *, integer *), xerbla_(
c@427: 	    char *, integer *);
c@427:     extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
c@427: 	    integer *, integer *);
c@427:     integer ldwork;
c@427:     extern /* Subroutine */ int dtrtri_(char *, char *, integer *, doublereal 
c@427: 	    *, integer *, integer *);
c@427:     integer lwkopt;
c@427:     logical lquery;
c@427: 
c@427: 
c@427: /*  -- LAPACK routine (version 3.2) -- */
c@427: /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
c@427: /*     November 2006 */
c@427: 
c@427: /*     .. Scalar Arguments .. */
c@427: /*     .. */
c@427: /*     .. Array Arguments .. */
c@427: /*     .. */
c@427: 
c@427: /*  Purpose */
c@427: /*  ======= */
c@427: 
c@427: /*  DGETRI computes the inverse of a matrix using the LU factorization */
c@427: /*  computed by DGETRF. */
c@427: 
c@427: /*  This method inverts U and then computes inv(A) by solving the system */
c@427: /*  inv(A)*L = inv(U) for inv(A). */
c@427: 
c@427: /*  Arguments */
c@427: /*  ========= */
c@427: 
c@427: /*  N       (input) INTEGER */
c@427: /*          The order of the matrix A.  N >= 0. */
c@427: 
c@427: /*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
c@427: /*          On entry, the factors L and U from the factorization */
c@427: /*          A = P*L*U as computed by DGETRF. */
c@427: /*          On exit, if INFO = 0, the inverse of the original matrix A. */
c@427: 
c@427: /*  LDA     (input) INTEGER */
c@427: /*          The leading dimension of the array A.  LDA >= max(1,N). */
c@427: 
c@427: /*  IPIV    (input) INTEGER array, dimension (N) */
c@427: /*          The pivot indices from DGETRF; for 1<=i<=N, row i of the */
c@427: /*          matrix was interchanged with row IPIV(i). */
c@427: 
c@427: /*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
c@427: /*          On exit, if INFO=0, then WORK(1) returns the optimal LWORK. */
c@427: 
c@427: /*  LWORK   (input) INTEGER */
c@427: /*          The dimension of the array WORK.  LWORK >= max(1,N). */
c@427: /*          For optimal performance LWORK >= N*NB, where NB is */
c@427: /*          the optimal blocksize returned by ILAENV. */
c@427: 
c@427: /*          If LWORK = -1, then a workspace query is assumed; the routine */
c@427: /*          only calculates the optimal size of the WORK array, returns */
c@427: /*          this value as the first entry of the WORK array, and no error */
c@427: /*          message related to LWORK is issued by XERBLA. */
c@427: 
c@427: /*  INFO    (output) INTEGER */
c@427: /*          = 0:  successful exit */
c@427: /*          < 0:  if INFO = -i, the i-th argument had an illegal value */
c@427: /*          > 0:  if INFO = i, U(i,i) is exactly zero; the matrix is */
c@427: /*                singular and its inverse could not be computed. */
c@427: 
c@427: /*  ===================================================================== */
c@427: 
c@427: /*     .. Parameters .. */
c@427: /*     .. */
c@427: /*     .. Local Scalars .. */
c@427: /*     .. */
c@427: /*     .. External Functions .. */
c@427: /*     .. */
c@427: /*     .. External Subroutines .. */
c@427: /*     .. */
c@427: /*     .. Intrinsic Functions .. */
c@427: /*     .. */
c@427: /*     .. Executable Statements .. */
c@427: 
c@427: /*     Test the input parameters. */
c@427: 
c@427:     /* Parameter adjustments */
c@427:     a_dim1 = *lda;
c@427:     a_offset = 1 + a_dim1;
c@427:     a -= a_offset;
c@427:     --ipiv;
c@427:     --work;
c@427: 
c@427:     /* Function Body */
c@427:     *info = 0;
c@427:     nb = ilaenv_(&c__1, "DGETRI", " ", n, &c_n1, &c_n1, &c_n1);
c@427:     lwkopt = *n * nb;
c@427:     work[1] = (doublereal) lwkopt;
c@427:     lquery = *lwork == -1;
c@427:     if (*n < 0) {
c@427: 	*info = -1;
c@427:     } else if (*lda < max(1,*n)) {
c@427: 	*info = -3;
c@427:     } else if (*lwork < max(1,*n) && ! lquery) {
c@427: 	*info = -6;
c@427:     }
c@427:     if (*info != 0) {
c@427: 	i__1 = -(*info);
c@427: 	xerbla_("DGETRI", &i__1);
c@427: 	return 0;
c@427:     } else if (lquery) {
c@427: 	return 0;
c@427:     }
c@427: 
c@427: /*     Quick return if possible */
c@427: 
c@427:     if (*n == 0) {
c@427: 	return 0;
c@427:     }
c@427: 
c@427: /*     Form inv(U).  If INFO > 0 from DTRTRI, then U is singular, */
c@427: /*     and the inverse is not computed. */
c@427: 
c@427:     dtrtri_("Upper", "Non-unit", n, &a[a_offset], lda, info);
c@427:     if (*info > 0) {
c@427: 	return 0;
c@427:     }
c@427: 
c@427:     nbmin = 2;
c@427:     ldwork = *n;
c@427:     if (nb > 1 && nb < *n) {
c@427: /* Computing MAX */
c@427: 	i__1 = ldwork * nb;
c@427: 	iws = max(i__1,1);
c@427: 	if (*lwork < iws) {
c@427: 	    nb = *lwork / ldwork;
c@427: /* Computing MAX */
c@427: 	    i__1 = 2, i__2 = ilaenv_(&c__2, "DGETRI", " ", n, &c_n1, &c_n1, &
c@427: 		    c_n1);
c@427: 	    nbmin = max(i__1,i__2);
c@427: 	}
c@427:     } else {
c@427: 	iws = *n;
c@427:     }
c@427: 
c@427: /*     Solve the equation inv(A)*L = inv(U) for inv(A). */
c@427: 
c@427:     if (nb < nbmin || nb >= *n) {
c@427: 
c@427: /*        Use unblocked code. */
c@427: 
c@427: 	for (j = *n; j >= 1; --j) {
c@427: 
c@427: /*           Copy current column of L to WORK and replace with zeros. */
c@427: 
c@427: 	    i__1 = *n;
c@427: 	    for (i__ = j + 1; i__ <= i__1; ++i__) {
c@427: 		work[i__] = a[i__ + j * a_dim1];
c@427: 		a[i__ + j * a_dim1] = 0.;
c@427: /* L10: */
c@427: 	    }
c@427: 
c@427: /*           Compute current column of inv(A). */
c@427: 
c@427: 	    if (j < *n) {
c@427: 		i__1 = *n - j;
c@427: 		dgemv_("No transpose", n, &i__1, &c_b20, &a[(j + 1) * a_dim1 
c@427: 			+ 1], lda, &work[j + 1], &c__1, &c_b22, &a[j * a_dim1 
c@427: 			+ 1], &c__1);
c@427: 	    }
c@427: /* L20: */
c@427: 	}
c@427:     } else {
c@427: 
c@427: /*        Use blocked code. */
c@427: 
c@427: 	nn = (*n - 1) / nb * nb + 1;
c@427: 	i__1 = -nb;
c@427: 	for (j = nn; i__1 < 0 ? j >= 1 : j <= 1; j += i__1) {
c@427: /* Computing MIN */
c@427: 	    i__2 = nb, i__3 = *n - j + 1;
c@427: 	    jb = min(i__2,i__3);
c@427: 
c@427: /*           Copy current block column of L to WORK and replace with */
c@427: /*           zeros. */
c@427: 
c@427: 	    i__2 = j + jb - 1;
c@427: 	    for (jj = j; jj <= i__2; ++jj) {
c@427: 		i__3 = *n;
c@427: 		for (i__ = jj + 1; i__ <= i__3; ++i__) {
c@427: 		    work[i__ + (jj - j) * ldwork] = a[i__ + jj * a_dim1];
c@427: 		    a[i__ + jj * a_dim1] = 0.;
c@427: /* L30: */
c@427: 		}
c@427: /* L40: */
c@427: 	    }
c@427: 
c@427: /*           Compute current block column of inv(A). */
c@427: 
c@427: 	    if (j + jb <= *n) {
c@427: 		i__2 = *n - j - jb + 1;
c@427: 		dgemm_("No transpose", "No transpose", n, &jb, &i__2, &c_b20, 
c@427: 			&a[(j + jb) * a_dim1 + 1], lda, &work[j + jb], &
c@427: 			ldwork, &c_b22, &a[j * a_dim1 + 1], lda);
c@427: 	    }
c@427: 	    dtrsm_("Right", "Lower", "No transpose", "Unit", n, &jb, &c_b22, &
c@427: 		    work[j], &ldwork, &a[j * a_dim1 + 1], lda);
c@427: /* L50: */
c@427: 	}
c@427:     }
c@427: 
c@427: /*     Apply column interchanges. */
c@427: 
c@427:     for (j = *n - 1; j >= 1; --j) {
c@427: 	jp = ipiv[j];
c@427: 	if (jp != j) {
c@427: 	    dswap_(n, &a[j * a_dim1 + 1], &c__1, &a[jp * a_dim1 + 1], &c__1);
c@427: 	}
c@427: /* L60: */
c@427:     }
c@427: 
c@427:     work[1] = (doublereal) iws;
c@427:     return 0;
c@427: 
c@427: /*     End of DGETRI */
c@427: 
c@427: } /* dgetri_ */