Man page - la_gbrcond(3)

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Manual

la_gbrcond

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
real function cla_gbrcond_c (character trans, integer n, integer kl,integer ku, complex, dimension( ldab, * ) ab, integer ldab, complex,dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv,real, dimension( * ) c, logical capply, integer info, complex,dimension( * ) work, real, dimension( * ) rwork)
real function cla_gbrcond_x (character trans, integer n, integer kl,integer ku, complex, dimension( ldab, * ) ab, integer ldab, complex,dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv,complex, dimension( * ) x, integer info, complex, dimension( * ) work,real, dimension( * ) rwork)
double precision function dla_gbrcond (character trans, integer n, integerkl, integer ku, double precision, dimension( ldab, * ) ab, integerldab, double precision, dimension( ldafb, * ) afb, integer ldafb,integer, dimension( * ) ipiv, integer cmode, double precision,dimension( * ) c, integer info, double precision, dimension( * ) work,integer, dimension( * ) iwork)
real function sla_gbrcond (character trans, integer n, integer kl, integerku, real, dimension( ldab, * ) ab, integer ldab, real, dimension(ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, integercmode, real, dimension( * ) c, integer info, real, dimension( * ) work,integer, dimension( * ) iwork)
double precision function zla_gbrcond_c (character trans, integer n,integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integerldab, complex*16, dimension( ldafb, * ) afb, integer ldafb, integer,dimension( * ) ipiv, double precision, dimension( * ) c, logicalcapply, integer info, complex*16, dimension( * ) work, doubleprecision, dimension( * ) rwork)
double precision function zla_gbrcond_x (character trans, integer n,integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integerldab, complex*16, dimension( ldafb, * ) afb, integer ldafb, integer,dimension( * ) ipiv, complex*16, dimension( * ) x, integer info,complex*16, dimension( * ) work, double precision, dimension( * )rwork)
Author

NAME

la_gbrcond - la_gbrcond: Skeel condition number estimate

SYNOPSIS

Functions

real function cla_gbrcond_c (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, c, capply, info, work, rwork)
CLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices.
real function cla_gbrcond_x (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, x, info, work, rwork)
CLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices.
double precision function dla_gbrcond (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, cmode, c, info, work, iwork)
DLA_GBRCOND estimates the Skeel condition number for a general banded matrix.
real function sla_gbrcond (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, cmode, c, info, work, iwork)
SLA_GBRCOND estimates the Skeel condition number for a general banded matrix.
double precision function zla_gbrcond_c (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, c, capply, info, work, rwork)
ZLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices.
double precision function zla_gbrcond_x (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, x, info, work, rwork)
ZLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices.

Detailed Description

Function Documentation

real function cla_gbrcond_c (character trans, integer n, integer kl,integer ku, complex, dimension( ldab, * ) ab, integer ldab, complex,dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv,real, dimension( * ) c, logical capply, integer info, complex,dimension( * ) work, real, dimension( * ) rwork)

CLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices.

Purpose:

CLA_GBRCOND_C Computes the infinity norm condition number of
op(A) * inv(diag(C)) where C is a REAL vector.

Parameters

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate Transpose = Transpose)

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.

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.

IPIV

IPIV is INTEGER array, dimension (N)
The pivot indices from the factorization A = P*L*U
as computed by CGBTRF; row i of the matrix was interchanged
with row IPIV(i).

C

C is REAL array, dimension (N)
The vector C in the formula op(A) * inv(diag(C)).

CAPPLY

CAPPLY is LOGICAL
If .TRUE. then access the vector C in the formula above.

INFO

INFO is INTEGER
= 0: Successful exit.
i > 0: The ith argument is invalid.

WORK

WORK is COMPLEX array, dimension (2*N).
Workspace.

RWORK

RWORK is REAL array, dimension (N).
Workspace.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

real function cla_gbrcond_x (character trans, integer n, integer kl,integer ku, complex, dimension( ldab, * ) ab, integer ldab, complex,dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv,complex, dimension( * ) x, integer info, complex, dimension( * ) work,real, dimension( * ) rwork)

CLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices.

Purpose:

CLA_GBRCOND_X Computes the infinity norm condition number of
op(A) * diag(X) where X is a COMPLEX vector.

Parameters

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate Transpose = Transpose)

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.

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.

IPIV

IPIV is INTEGER array, dimension (N)
The pivot indices from the factorization A = P*L*U
as computed by CGBTRF; row i of the matrix was interchanged
with row IPIV(i).

X

X is COMPLEX array, dimension (N)
The vector X in the formula op(A) * diag(X).

INFO

INFO is INTEGER
= 0: Successful exit.
i > 0: The ith argument is invalid.

WORK

WORK is COMPLEX array, dimension (2*N).
Workspace.

RWORK

RWORK is REAL array, dimension (N).
Workspace.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

double precision function dla_gbrcond (character trans, integer n, integerkl, integer ku, double precision, dimension( ldab, * ) ab, integerldab, double precision, dimension( ldafb, * ) afb, integer ldafb,integer, dimension( * ) ipiv, integer cmode, double precision,dimension( * ) c, integer info, double precision, dimension( * ) work,integer, dimension( * ) iwork)

DLA_GBRCOND estimates the Skeel condition number for a general banded matrix.

Purpose:

DLA_GBRCOND Estimates the Skeel condition number of op(A) * op2(C)
where op2 is determined by CMODE as follows
CMODE = 1 op2(C) = C
CMODE = 0 op2(C) = I
CMODE = -1 op2(C) = inv(C)
The Skeel condition number cond(A) = norminf( |inv(A)||A| )
is computed by computing scaling factors R such that
diag(R)*A*op2(C) is row equilibrated and computing the standard
infinity-norm condition number.

Parameters

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate Transpose = Transpose)

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.

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.

IPIV

IPIV is INTEGER array, dimension (N)
The pivot indices from the factorization A = P*L*U
as computed by DGBTRF; row i of the matrix was interchanged
with row IPIV(i).

CMODE

CMODE is INTEGER
Determines op2(C) in the formula op(A) * op2(C) as follows:
CMODE = 1 op2(C) = C
CMODE = 0 op2(C) = I
CMODE = -1 op2(C) = inv(C)

C

C is DOUBLE PRECISION array, dimension (N)
The vector C in the formula op(A) * op2(C).

INFO

INFO is INTEGER
= 0: Successful exit.
i > 0: The ith argument is invalid.

WORK

WORK is DOUBLE PRECISION array, dimension (5*N).
Workspace.

IWORK

IWORK is INTEGER array, dimension (N).
Workspace.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

real function sla_gbrcond (character trans, integer n, integer kl, integerku, real, dimension( ldab, * ) ab, integer ldab, real, dimension(ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, integercmode, real, dimension( * ) c, integer info, real, dimension( * ) work,integer, dimension( * ) iwork)

SLA_GBRCOND estimates the Skeel condition number for a general banded matrix.

Purpose:

SLA_GBRCOND Estimates the Skeel condition number of op(A) * op2(C)
where op2 is determined by CMODE as follows
CMODE = 1 op2(C) = C
CMODE = 0 op2(C) = I
CMODE = -1 op2(C) = inv(C)
The Skeel condition number cond(A) = norminf( |inv(A)||A| )
is computed by computing scaling factors R such that
diag(R)*A*op2(C) is row equilibrated and computing the standard
infinity-norm condition number.

Parameters

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate Transpose = Transpose)

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.

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.

IPIV

IPIV is INTEGER array, dimension (N)
The pivot indices from the factorization A = P*L*U
as computed by SGBTRF; row i of the matrix was interchanged
with row IPIV(i).

CMODE

CMODE is INTEGER
Determines op2(C) in the formula op(A) * op2(C) as follows:
CMODE = 1 op2(C) = C
CMODE = 0 op2(C) = I
CMODE = -1 op2(C) = inv(C)

C

C is REAL array, dimension (N)
The vector C in the formula op(A) * op2(C).

INFO

INFO is INTEGER
= 0: Successful exit.
i > 0: The ith argument is invalid.

WORK

WORK is REAL array, dimension (5*N).
Workspace.

IWORK

IWORK is INTEGER array, dimension (N).
Workspace.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

double precision function zla_gbrcond_c (character trans, integer n,integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integerldab, complex*16, dimension( ldafb, * ) afb, integer ldafb, integer,dimension( * ) ipiv, double precision, dimension( * ) c, logicalcapply, integer info, complex*16, dimension( * ) work, doubleprecision, dimension( * ) rwork)

ZLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices.

Purpose:

ZLA_GBRCOND_C Computes the infinity norm condition number of
op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.

Parameters

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate Transpose = Transpose)

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.

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.

IPIV

IPIV is INTEGER array, dimension (N)
The pivot indices from the factorization A = P*L*U
as computed by ZGBTRF; row i of the matrix was interchanged
with row IPIV(i).

C

C is DOUBLE PRECISION array, dimension (N)
The vector C in the formula op(A) * inv(diag(C)).

CAPPLY

CAPPLY is LOGICAL
If .TRUE. then access the vector C in the formula above.

INFO

INFO is INTEGER
= 0: Successful exit.
i > 0: The ith argument is invalid.

WORK

WORK is COMPLEX*16 array, dimension (2*N).
Workspace.

RWORK

RWORK is DOUBLE PRECISION array, dimension (N).
Workspace.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

double precision function zla_gbrcond_x (character trans, integer n,integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integerldab, complex*16, dimension( ldafb, * ) afb, integer ldafb, integer,dimension( * ) ipiv, complex*16, dimension( * ) x, integer info,complex*16, dimension( * ) work, double precision, dimension( * )rwork)

ZLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices.

Purpose:

ZLA_GBRCOND_X Computes the infinity norm condition number of
op(A) * diag(X) where X is a COMPLEX*16 vector.

Parameters

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate Transpose = Transpose)

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.

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.

IPIV

IPIV is INTEGER array, dimension (N)
The pivot indices from the factorization A = P*L*U
as computed by ZGBTRF; row i of the matrix was interchanged
with row IPIV(i).

X

X is COMPLEX*16 array, dimension (N)
The vector X in the formula op(A) * diag(X).

INFO

INFO is INTEGER
= 0: Successful exit.
i > 0: The ith argument is invalid.

WORK

WORK is COMPLEX*16 array, dimension (2*N).
Workspace.

RWORK

RWORK is DOUBLE PRECISION array, dimension (N).
Workspace.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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