#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int dtptri_(char *uplo, char *diag, integer *n, doublereal * ap, integer *info) { /* -- LAPACK routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University September 30, 1994 Purpose ======= DTPTRI computes the inverse of a real upper or lower triangular matrix A stored in packed format. Arguments ========= UPLO (input) CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular. DIAG (input) CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular. N (input) INTEGER The order of the matrix A. N >= 0. AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) On entry, the upper or lower triangular matrix A, stored columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n. See below for further details. On exit, the (triangular) inverse of the original matrix, in the same packed storage format. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, A(i,i) is exactly zero. The triangular matrix is singular and its inverse can not be computed. Further Details =============== A triangular matrix A can be transferred to packed storage using one of the following program segments: UPLO = 'U': UPLO = 'L': JC = 1 JC = 1 DO 2 J = 1, N DO 2 J = 1, N DO 1 I = 1, J DO 1 I = J, N AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J) 1 CONTINUE 1 CONTINUE JC = JC + J JC = JC + N - J + 1 2 CONTINUE 2 CONTINUE ===================================================================== Test the input parameters. Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; /* System generated locals */ integer i__1, i__2; /* Local variables */ static integer j; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); extern logical lsame_(char *, char *); extern /* Subroutine */ int dtpmv_(char *, char *, char *, integer *, doublereal *, doublereal *, integer *); static logical upper; static integer jc, jj; extern /* Subroutine */ int xerbla_(char *, integer *); static integer jclast; static logical nounit; static doublereal ajj; --ap; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); nounit = lsame_(diag, "N"); if (! upper && ! lsame_(uplo, "L")) { *info = -1; } else if (! nounit && ! lsame_(diag, "U")) { *info = -2; } else if (*n < 0) { *info = -3; } if (*info != 0) { i__1 = -(*info); xerbla_("DTPTRI", &i__1); return 0; } /* Check for singularity if non-unit. */ if (nounit) { if (upper) { jj = 0; i__1 = *n; for (*info = 1; *info <= i__1; ++(*info)) { jj += *info; if (ap[jj] == 0.) { return 0; } /* L10: */ } } else { jj = 1; i__1 = *n; for (*info = 1; *info <= i__1; ++(*info)) { if (ap[jj] == 0.) { return 0; } jj = jj + *n - *info + 1; /* L20: */ } } *info = 0; } if (upper) { /* Compute inverse of upper triangular matrix. */ jc = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { if (nounit) { ap[jc + j - 1] = 1. / ap[jc + j - 1]; ajj = -ap[jc + j - 1]; } else { ajj = -1.; } /* Compute elements 1:j-1 of j-th column. */ i__2 = j - 1; dtpmv_("Upper", "No transpose", diag, &i__2, &ap[1], &ap[jc], & c__1); i__2 = j - 1; dscal_(&i__2, &ajj, &ap[jc], &c__1); jc += j; /* L30: */ } } else { /* Compute inverse of lower triangular matrix. */ jc = *n * (*n + 1) / 2; for (j = *n; j >= 1; --j) { if (nounit) { ap[jc] = 1. / ap[jc]; ajj = -ap[jc]; } else { ajj = -1.; } if (j < *n) { /* Compute elements j+1:n of j-th column. */ i__1 = *n - j; dtpmv_("Lower", "No transpose", diag, &i__1, &ap[jclast], &ap[ jc + 1], &c__1); i__1 = *n - j; dscal_(&i__1, &ajj, &ap[jc + 1], &c__1); } jclast = jc; jc = jc - *n + j - 2; /* L40: */ } } return 0; /* End of DTPTRI */ } /* dtptri_ */