la_gbrpvgrw - la_gbrpvgrw: reciprocal pivot growth

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Sun Jul 20 2025 01:40:05 la_gbrpvgrw(3)

realfunctioncla_gbrpvgrw(integern,integerkl,integerku,integerncols,complex,dimension(ldab,*)ab,integerldab,complex,dimension(ldafb,*)afb,integerldafb)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 'max absolute element' 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. ParametersN 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. doubleprecisionfunctiondla_gbrpvgrw(integern,integerkl,integerku,integerncols,doubleprecision,dimension(ldab,*)ab,integerldab,doubleprecision,dimension(ldafb,*)afb,integerldafb)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 'max absolute element' 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. ParametersN 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. realfunctionsla_gbrpvgrw(integern,integerkl,integerku,integerncols,real,dimension(ldab,*)ab,integerldab,real,dimension(ldafb,*)afb,integerldafb)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 'max absolute element' 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. ParametersN 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. doubleprecisionfunctionzla_gbrpvgrw(integern,integerkl,integerku,integerncols,complex*16,dimension(ldab,*)ab,integerldab,complex*16,dimension(ldafb,*)afb,integerldafb)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 'max absolute element' 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. ParametersN 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.

la_gbrpvgrw - la_gbrpvgrw: reciprocal pivot growth

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.