Provided by: liblapack-doc_3.3.1-1_all

**NAME**

LAPACK-3 - 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 SPBTRF

**SYNOPSIS**

SUBROUTINE SPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, IWORK, INFO ) CHARACTER UPLO INTEGER INFO, KD, LDAB, N REAL ANORM, RCOND INTEGER IWORK( * ) REAL AB( LDAB, * ), WORK( * )

**PURPOSE**

SPBCON 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 SPBTRF. 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) REAL 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) REAL The 1-norm (or infinity-norm) of the symmetric band matrix A. RCOND (output) REAL 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) REAL 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 LAPACK routine (version 3.3.1) April 2011 SPBCON(3lapack)