#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int dpbcon_(char *uplo, integer *n, integer *kd, doublereal * ab, integer *ldab, doublereal *anorm, doublereal *rcond, doublereal * work, integer *iwork, 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 ======= DPBCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). Arguments ========= UPLO (input) CHARACTER*1 = 'U': Upper triangular factor stored in AB; = 'L': Lower triangular factor stored in AB. N (input) INTEGER The order of the matrix A. N >= 0. KD (input) INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. AB (input) DOUBLE PRECISION array, dimension (LDAB,N) The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows: if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd). LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KD+1. ANORM (input) DOUBLE PRECISION The 1-norm (or infinity-norm) of the symmetric band matrix A. RCOND (output) DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine. WORK (workspace) DOUBLE PRECISION array, dimension (3*N) IWORK (workspace) INTEGER array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value ===================================================================== Test the input parameters. Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; /* System generated locals */ integer ab_dim1, ab_offset, i__1; doublereal d__1; /* Local variables */ static integer kase; static doublereal scale; extern logical lsame_(char *, char *); extern /* Subroutine */ int drscl_(integer *, doublereal *, doublereal *, integer *); static logical upper; extern doublereal dlamch_(char *); extern /* Subroutine */ int dlacon_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *); static integer ix; static doublereal scalel; extern integer idamax_(integer *, doublereal *, integer *); extern /* Subroutine */ int dlatbs_(char *, char *, char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *); static doublereal scaleu; extern /* Subroutine */ int xerbla_(char *, integer *); static doublereal ainvnm; static char normin[1]; static doublereal smlnum; ab_dim1 = *ldab; ab_offset = 1 + ab_dim1 * 1; ab -= ab_offset; --work; --iwork; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); if (! upper && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*kd < 0) { *info = -3; } else if (*ldab < *kd + 1) { *info = -5; } else if (*anorm < 0.) { *info = -6; } if (*info != 0) { i__1 = -(*info); xerbla_("DPBCON", &i__1); return 0; } /* Quick return if possible */ *rcond = 0.; if (*n == 0) { *rcond = 1.; return 0; } else if (*anorm == 0.) { return 0; } smlnum = dlamch_("Safe minimum"); /* Estimate the 1-norm of the inverse. */ kase = 0; *(unsigned char *)normin = 'N'; L10: dlacon_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase); if (kase != 0) { if (upper) { /* Multiply by inv(U'). */ dlatbs_("Upper", "Transpose", "Non-unit", normin, n, kd, &ab[ ab_offset], ldab, &work[1], &scalel, &work[(*n << 1) + 1], info); *(unsigned char *)normin = 'Y'; /* Multiply by inv(U). */ dlatbs_("Upper", "No transpose", "Non-unit", normin, n, kd, &ab[ ab_offset], ldab, &work[1], &scaleu, &work[(*n << 1) + 1], info); } else { /* Multiply by inv(L). */ dlatbs_("Lower", "No transpose", "Non-unit", normin, n, kd, &ab[ ab_offset], ldab, &work[1], &scalel, &work[(*n << 1) + 1], info); *(unsigned char *)normin = 'Y'; /* Multiply by inv(L'). */ dlatbs_("Lower", "Transpose", "Non-unit", normin, n, kd, &ab[ ab_offset], ldab, &work[1], &scaleu, &work[(*n << 1) + 1], info); } /* Multiply by 1/SCALE if doing so will not cause overflow. */ scale = scalel * scaleu; if (scale != 1.) { ix = idamax_(n, &work[1], &c__1); if (scale < (d__1 = work[ix], abs(d__1)) * smlnum || scale == 0.) { goto L20; } drscl_(n, &scale, &work[1], &c__1); } goto L10; } /* Compute the estimate of the reciprocal condition number. */ if (ainvnm != 0.) { *rcond = 1. / ainvnm / *anorm; } L20: return 0; /* End of DPBCON */ } /* dpbcon_ */