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 '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 is INTEGER


     The number of linear equations, i.e., the order of the


     matrix A.  N >= 0.



          KL is INTEGER


     The number of subdiagonals within the band of A.  KL >= 0.



          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 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 is INTEGER


     The number of linear equations, i.e., the order of the


     matrix A.  N >= 0.



          KL is INTEGER


     The number of subdiagonals within the band of A.  KL >= 0.



          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 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 is INTEGER


     The number of linear equations, i.e., the order of the


     matrix A.  N >= 0.



          KL is INTEGER


     The number of subdiagonals within the band of A.  KL >= 0.



          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 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, complex16, dimension( ldab, ) ab, integer ldab, complex16, 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 is INTEGER


     The number of linear equations, i.e., the order of the


     matrix A.  N >= 0.



          KL is INTEGER


     The number of subdiagonals within the band of A.  KL >= 0.



          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 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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