#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int dsptri_(char *uplo, integer *n, doublereal *ap, integer * ipiv, doublereal *work, integer *info) { /* -- LAPACK routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University March 31, 1993 Purpose ======= DSPTRI computes the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF. Arguments ========= UPLO (input) CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**T; = 'L': Lower triangular, form is A = L*D*L**T. 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 block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSPTRF, stored as a packed triangular matrix. On exit, if INFO = 0, the (symmetric) inverse of the original matrix, stored as a packed triangular matrix. The j-th column of inv(A) is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n. IPIV (input) INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by DSPTRF. WORK (workspace) DOUBLE PRECISION array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed. ===================================================================== Test the input parameters. Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; static doublereal c_b11 = -1.; static doublereal c_b13 = 0.; /* System generated locals */ integer i__1; doublereal d__1; /* Local variables */ extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, integer *); static doublereal temp, akkp1, d__; static integer j, k; static doublereal t; extern logical lsame_(char *, char *); extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *), dswap_(integer *, doublereal *, integer *, doublereal *, integer *); static integer kstep; extern /* Subroutine */ int dspmv_(char *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, integer *); static logical upper; static doublereal ak; static integer kc, kp, kx; extern /* Subroutine */ int xerbla_(char *, integer *); static integer kcnext, kpc, npp; static doublereal akp1; --work; --ipiv; --ap; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); if (! upper && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } if (*info != 0) { i__1 = -(*info); xerbla_("DSPTRI", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } /* Check that the diagonal matrix D is nonsingular. */ if (upper) { /* Upper triangular storage: examine D from bottom to top */ kp = *n * (*n + 1) / 2; for (*info = *n; *info >= 1; --(*info)) { if (ipiv[*info] > 0 && ap[kp] == 0.) { return 0; } kp -= *info; /* L10: */ } } else { /* Lower triangular storage: examine D from top to bottom. */ kp = 1; i__1 = *n; for (*info = 1; *info <= i__1; ++(*info)) { if (ipiv[*info] > 0 && ap[kp] == 0.) { return 0; } kp = kp + *n - *info + 1; /* L20: */ } } *info = 0; if (upper) { /* Compute inv(A) from the factorization A = U*D*U'. K is the main loop index, increasing from 1 to N in steps of 1 or 2, depending on the size of the diagonal blocks. */ k = 1; kc = 1; L30: /* If K > N, exit from loop. */ if (k > *n) { goto L50; } kcnext = kc + k; if (ipiv[k] > 0) { /* 1 x 1 diagonal block Invert the diagonal block. */ ap[kc + k - 1] = 1. / ap[kc + k - 1]; /* Compute column K of the inverse. */ if (k > 1) { i__1 = k - 1; dcopy_(&i__1, &ap[kc], &c__1, &work[1], &c__1); i__1 = k - 1; dspmv_(uplo, &i__1, &c_b11, &ap[1], &work[1], &c__1, &c_b13, & ap[kc], &c__1); i__1 = k - 1; ap[kc + k - 1] -= ddot_(&i__1, &work[1], &c__1, &ap[kc], & c__1); } kstep = 1; } else { /* 2 x 2 diagonal block Invert the diagonal block. */ t = (d__1 = ap[kcnext + k - 1], abs(d__1)); ak = ap[kc + k - 1] / t; akp1 = ap[kcnext + k] / t; akkp1 = ap[kcnext + k - 1] / t; d__ = t * (ak * akp1 - 1.); ap[kc + k - 1] = akp1 / d__; ap[kcnext + k] = ak / d__; ap[kcnext + k - 1] = -akkp1 / d__; /* Compute columns K and K+1 of the inverse. */ if (k > 1) { i__1 = k - 1; dcopy_(&i__1, &ap[kc], &c__1, &work[1], &c__1); i__1 = k - 1; dspmv_(uplo, &i__1, &c_b11, &ap[1], &work[1], &c__1, &c_b13, & ap[kc], &c__1); i__1 = k - 1; ap[kc + k - 1] -= ddot_(&i__1, &work[1], &c__1, &ap[kc], & c__1); i__1 = k - 1; ap[kcnext + k - 1] -= ddot_(&i__1, &ap[kc], &c__1, &ap[kcnext] , &c__1); i__1 = k - 1; dcopy_(&i__1, &ap[kcnext], &c__1, &work[1], &c__1); i__1 = k - 1; dspmv_(uplo, &i__1, &c_b11, &ap[1], &work[1], &c__1, &c_b13, & ap[kcnext], &c__1); i__1 = k - 1; ap[kcnext + k] -= ddot_(&i__1, &work[1], &c__1, &ap[kcnext], & c__1); } kstep = 2; kcnext = kcnext + k + 1; } kp = (i__1 = ipiv[k], abs(i__1)); if (kp != k) { /* Interchange rows and columns K and KP in the leading submatrix A(1:k+1,1:k+1) */ kpc = (kp - 1) * kp / 2 + 1; i__1 = kp - 1; dswap_(&i__1, &ap[kc], &c__1, &ap[kpc], &c__1); kx = kpc + kp - 1; i__1 = k - 1; for (j = kp + 1; j <= i__1; ++j) { kx = kx + j - 1; temp = ap[kc + j - 1]; ap[kc + j - 1] = ap[kx]; ap[kx] = temp; /* L40: */ } temp = ap[kc + k - 1]; ap[kc + k - 1] = ap[kpc + kp - 1]; ap[kpc + kp - 1] = temp; if (kstep == 2) { temp = ap[kc + k + k - 1]; ap[kc + k + k - 1] = ap[kc + k + kp - 1]; ap[kc + k + kp - 1] = temp; } } k += kstep; kc = kcnext; goto L30; L50: ; } else { /* Compute inv(A) from the factorization A = L*D*L'. K is the main loop index, increasing from 1 to N in steps of 1 or 2, depending on the size of the diagonal blocks. */ npp = *n * (*n + 1) / 2; k = *n; kc = npp; L60: /* If K < 1, exit from loop. */ if (k < 1) { goto L80; } kcnext = kc - (*n - k + 2); if (ipiv[k] > 0) { /* 1 x 1 diagonal block Invert the diagonal block. */ ap[kc] = 1. / ap[kc]; /* Compute column K of the inverse. */ if (k < *n) { i__1 = *n - k; dcopy_(&i__1, &ap[kc + 1], &c__1, &work[1], &c__1); i__1 = *n - k; dspmv_(uplo, &i__1, &c_b11, &ap[kc + *n - k + 1], &work[1], & c__1, &c_b13, &ap[kc + 1], &c__1); i__1 = *n - k; ap[kc] -= ddot_(&i__1, &work[1], &c__1, &ap[kc + 1], &c__1); } kstep = 1; } else { /* 2 x 2 diagonal block Invert the diagonal block. */ t = (d__1 = ap[kcnext + 1], abs(d__1)); ak = ap[kcnext] / t; akp1 = ap[kc] / t; akkp1 = ap[kcnext + 1] / t; d__ = t * (ak * akp1 - 1.); ap[kcnext] = akp1 / d__; ap[kc] = ak / d__; ap[kcnext + 1] = -akkp1 / d__; /* Compute columns K-1 and K of the inverse. */ if (k < *n) { i__1 = *n - k; dcopy_(&i__1, &ap[kc + 1], &c__1, &work[1], &c__1); i__1 = *n - k; dspmv_(uplo, &i__1, &c_b11, &ap[kc + (*n - k + 1)], &work[1], &c__1, &c_b13, &ap[kc + 1], &c__1); i__1 = *n - k; ap[kc] -= ddot_(&i__1, &work[1], &c__1, &ap[kc + 1], &c__1); i__1 = *n - k; ap[kcnext + 1] -= ddot_(&i__1, &ap[kc + 1], &c__1, &ap[kcnext + 2], &c__1); i__1 = *n - k; dcopy_(&i__1, &ap[kcnext + 2], &c__1, &work[1], &c__1); i__1 = *n - k; dspmv_(uplo, &i__1, &c_b11, &ap[kc + (*n - k + 1)], &work[1], &c__1, &c_b13, &ap[kcnext + 2], &c__1); i__1 = *n - k; ap[kcnext] -= ddot_(&i__1, &work[1], &c__1, &ap[kcnext + 2], & c__1); } kstep = 2; kcnext -= *n - k + 3; } kp = (i__1 = ipiv[k], abs(i__1)); if (kp != k) { /* Interchange rows and columns K and KP in the trailing submatrix A(k-1:n,k-1:n) */ kpc = npp - (*n - kp + 1) * (*n - kp + 2) / 2 + 1; if (kp < *n) { i__1 = *n - kp; dswap_(&i__1, &ap[kc + kp - k + 1], &c__1, &ap[kpc + 1], & c__1); } kx = kc + kp - k; i__1 = kp - 1; for (j = k + 1; j <= i__1; ++j) { kx = kx + *n - j + 1; temp = ap[kc + j - k]; ap[kc + j - k] = ap[kx]; ap[kx] = temp; /* L70: */ } temp = ap[kc]; ap[kc] = ap[kpc]; ap[kpc] = temp; if (kstep == 2) { temp = ap[kc - *n + k - 1]; ap[kc - *n + k - 1] = ap[kc - *n + kp - 1]; ap[kc - *n + kp - 1] = temp; } } k -= kstep; kc = kcnext; goto L60; L80: ; } return 0; /* End of DSPTRI */ } /* dsptri_ */