# dpbcon.f(3) [centos man page]

dpbcon.f(3) LAPACK dpbcon.f(3)NAME

dpbcon.f-SYNOPSIS

Functions/Subroutines subroutine dpbcon (UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, IWORK, INFO) DPBCONFunction/Subroutine Documentation subroutine dpbcon (characterUPLO, integerN, integerKD, double precision, dimension( ldab, * )AB, integerLDAB, double precisionANORM, double precisionRCOND, double precision, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO) DPBCON 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))). Parameters: UPLO UPLO is CHARACTER*1 = 'U': Upper triangular factor stored in AB; = 'L': Lower triangular factor stored in AB. N N is INTEGER The order of the matrix A. N >= 0. KD KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. AB AB is 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 LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1. ANORM ANORM is DOUBLE PRECISION The 1-norm (or infinity-norm) of the symmetric band matrix A. RCOND RCOND is 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 WORK is DOUBLE PRECISION array, dimension (3*N) IWORK IWORK is INTEGER array, dimension (N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 Definition at line 132 of file dpbcon.f.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 dpbcon.f(3)

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dpbcon.f(3) LAPACK dpbcon.f(3)NAME

dpbcon.f-SYNOPSIS

Functions/Subroutines subroutine dpbcon (UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, IWORK, INFO) DPBCONFunction/Subroutine Documentation subroutine dpbcon (characterUPLO, integerN, integerKD, double precision, dimension( ldab, * )AB, integerLDAB, double precisionANORM, double precisionRCOND, double precision, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO) DPBCON 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))). Parameters: UPLO UPLO is CHARACTER*1 = 'U': Upper triangular factor stored in AB; = 'L': Lower triangular factor stored in AB. N N is INTEGER The order of the matrix A. N >= 0. KD KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. AB AB is 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 LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1. ANORM ANORM is DOUBLE PRECISION The 1-norm (or infinity-norm) of the symmetric band matrix A. RCOND RCOND is 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 WORK is DOUBLE PRECISION array, dimension (3*N) IWORK IWORK is INTEGER array, dimension (N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 Definition at line 132 of file dpbcon.f.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.1Sun May 26 2013 dpbcon.f(3)