la_gbrpvgrw - Man Page
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 '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.
- 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 '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.
- 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 '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.
- 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 '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.
- 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
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