sgetri.c

#include "clapack.h"

/* Table of constant values */

static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__2 = 2;
static real c_b20 = -1.f;
static real c_b22 = 1.f;

/* Subroutine */ int sgetri_(integer *n, real *a, integer *lda, integer *ipiv, 
	 real *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, nbmin;
    extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, 
	    integer *, real *, real *, integer *, real *, integer *, real *, 
	    real *, integer *), sgemv_(char *, integer *, 
	    integer *, real *, real *, integer *, real *, integer *, real *, 
	    real *, integer *), sswap_(integer *, real *, integer *, 
	    real *, integer *), strsm_(char *, char *, char *, char *, 
	    integer *, integer *, real *, real *, integer *, real *, integer *
), xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *);
    integer ldwork, lwkopt;
    logical lquery;
    extern /* Subroutine */ int strtri_(char *, char *, integer *, real *, 
	    integer *, integer *);


/*  -- LAPACK routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  SGETRI computes the inverse of a matrix using the LU factorization */
/*  computed by SGETRF. */

/*  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) REAL array, dimension (LDA,N) */
/*          On entry, the factors L and U from the factorization */
/*          A = P*L*U as computed by SGETRF. */
/*          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 SGETRF; for 1<=i<=N, row i of the */
/*          matrix was interchanged with row IPIV(i). */

/*  WORK    (workspace/output) REAL 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, "SGETRI", " ", n, &c_n1, &c_n1, &c_n1);
    lwkopt = *n * nb;
    work[1] = (real) 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_("SGETRI", &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 STRTRI, then U is singular, */
/*     and the inverse is not computed. */

    strtri_("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, "SGETRI", " ", 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.f;
/* L10: */
	    }

/*           Compute current column of inv(A). */

	    if (j < *n) {
		i__1 = *n - j;
		sgemv_("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.f;
/* L30: */
		}
/* L40: */
	    }

/*           Compute current block column of inv(A). */

	    if (j + jb <= *n) {
		i__2 = *n - j - jb + 1;
		sgemm_("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);
	    }
	    strsm_("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) {
	    sswap_(n, &a[j * a_dim1 + 1], &c__1, &a[jp * a_dim1 + 1], &c__1);
	}
/* L60: */
    }

    work[1] = (real) iws;
    return 0;

/*     End of SGETRI */

} /* sgetri_ */