la_gbrpvgrw(3) Library Functions Manual la_gbrpvgrw(3) NAME la_gbrpvgrw - la_gbrpvgrw: reciprocal pivot growth SYNOPSIS Functions real function cla_gbrpvgrw (n, kl, ku, ncols, ab, ldab, afb, ldafb) CLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix. double precision function dla_gbrpvgrw (n, kl, ku, ncols, ab, ldab, afb, ldafb) DLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix. real function sla_gbrpvgrw (n, kl, ku, ncols, ab, ldab, afb, ldafb) SLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix. double precision function zla_gbrpvgrw (n, kl, ku, ncols, ab, ldab, afb, ldafb) ZLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix. Detailed Description Function Documentation real function cla_gbrpvgrw (integer n, integer kl, integer ku, integer ncols, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldafb, * ) afb, integer ldafb) CLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix. Purpose: !> !> CLA_GBRPVGRW computes the reciprocal pivot growth factor !> norm(A)/norm(U). The norm is used. If this is !> much less than 1, the stability of the LU factorization of the !> (equilibrated) matrix A could be poor. This also means that the !> solution X, estimated condition numbers, and error bounds could be !> unreliable. !> Parameters N !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> KL !> KL is INTEGER !> The number of subdiagonals within the band of A. KL >= 0. !> KU !> KU is INTEGER !> The number of superdiagonals within the band of A. KU >= 0. !> NCOLS !> NCOLS is INTEGER !> The number of columns of the matrix A. NCOLS >= 0. !> AB !> AB is COMPLEX array, dimension (LDAB,N) !> On entry, the matrix A in band storage, in rows 1 to KL+KU+1. !> The j-th column of A is stored in the j-th column of the !> array AB as follows: !> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) !> LDAB !> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KL+KU+1. !> AFB !> AFB is COMPLEX array, dimension (LDAFB,N) !> Details of the LU factorization of the band matrix A, as !> computed by CGBTRF. U is stored as an upper triangular !> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, !> and the multipliers used during the factorization are stored !> in rows KL+KU+2 to 2*KL+KU+1. !> LDAFB !> LDAFB is INTEGER !> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 115 of file cla_gbrpvgrw.f. double precision function dla_gbrpvgrw (integer n, integer kl, integer ku, integer ncols, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( ldafb, * ) afb, integer ldafb) DLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix. Purpose: !> !> DLA_GBRPVGRW computes the reciprocal pivot growth factor !> norm(A)/norm(U). The norm is used. If this is !> much less than 1, the stability of the LU factorization of the !> (equilibrated) matrix A could be poor. This also means that the !> solution X, estimated condition numbers, and error bounds could be !> unreliable. !> Parameters N !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> KL !> KL is INTEGER !> The number of subdiagonals within the band of A. KL >= 0. !> KU !> KU is INTEGER !> The number of superdiagonals within the band of A. KU >= 0. !> NCOLS !> NCOLS is INTEGER !> The number of columns of the matrix A. NCOLS >= 0. !> AB !> AB is DOUBLE PRECISION array, dimension (LDAB,N) !> On entry, the matrix A in band storage, in rows 1 to KL+KU+1. !> The j-th column of A is stored in the j-th column of the !> array AB as follows: !> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) !> LDAB !> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KL+KU+1. !> AFB !> AFB is DOUBLE PRECISION array, dimension (LDAFB,N) !> Details of the LU factorization of the band matrix A, as !> computed by DGBTRF. U is stored as an upper triangular !> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, !> and the multipliers used during the factorization are stored !> in rows KL+KU+2 to 2*KL+KU+1. !> LDAFB !> LDAFB is INTEGER !> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 115 of file dla_gbrpvgrw.f. real function sla_gbrpvgrw (integer n, integer kl, integer ku, integer ncols, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldafb, * ) afb, integer ldafb) SLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix. Purpose: !> !> SLA_GBRPVGRW computes the reciprocal pivot growth factor !> norm(A)/norm(U). The norm is used. If this is !> much less than 1, the stability of the LU factorization of the !> (equilibrated) matrix A could be poor. This also means that the !> solution X, estimated condition numbers, and error bounds could be !> unreliable. !> Parameters N !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> KL !> KL is INTEGER !> The number of subdiagonals within the band of A. KL >= 0. !> KU !> KU is INTEGER !> The number of superdiagonals within the band of A. KU >= 0. !> NCOLS !> NCOLS is INTEGER !> The number of columns of the matrix A. NCOLS >= 0. !> AB !> AB is REAL array, dimension (LDAB,N) !> On entry, the matrix A in band storage, in rows 1 to KL+KU+1. !> The j-th column of A is stored in the j-th column of the !> array AB as follows: !> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) !> LDAB !> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KL+KU+1. !> AFB !> AFB is REAL array, dimension (LDAFB,N) !> Details of the LU factorization of the band matrix A, as !> computed by SGBTRF. U is stored as an upper triangular !> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, !> and the multipliers used during the factorization are stored !> in rows KL+KU+2 to 2*KL+KU+1. !> LDAFB !> LDAFB is INTEGER !> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 115 of file sla_gbrpvgrw.f. double precision function zla_gbrpvgrw (integer n, integer kl, integer ku, integer ncols, complex*16, dimension( ldab, * ) ab, integer ldab, complex*16, dimension( ldafb, * ) afb, integer ldafb) ZLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix. Purpose: !> !> ZLA_GBRPVGRW computes the reciprocal pivot growth factor !> norm(A)/norm(U). The norm is used. If this is !> much less than 1, the stability of the LU factorization of the !> (equilibrated) matrix A could be poor. This also means that the !> solution X, estimated condition numbers, and error bounds could be !> unreliable. !> Parameters N !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> KL !> KL is INTEGER !> The number of subdiagonals within the band of A. KL >= 0. !> KU !> KU is INTEGER !> The number of superdiagonals within the band of A. KU >= 0. !> NCOLS !> NCOLS is INTEGER !> The number of columns of the matrix A. NCOLS >= 0. !> AB !> AB is COMPLEX*16 array, dimension (LDAB,N) !> On entry, the matrix A in band storage, in rows 1 to KL+KU+1. !> The j-th column of A is stored in the j-th column of the !> array AB as follows: !> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) !> LDAB !> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KL+KU+1. !> AFB !> AFB is COMPLEX*16 array, dimension (LDAFB,N) !> Details of the LU factorization of the band matrix A, as !> computed by ZGBTRF. U is stored as an upper triangular !> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, !> and the multipliers used during the factorization are stored !> in rows KL+KU+2 to 2*KL+KU+1. !> LDAFB !> LDAFB is INTEGER !> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 115 of file zla_gbrpvgrw.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 la_gbrpvgrw(3)