Library Functions Manual

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 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.
!>

!>          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 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.

Definition at line 158 of file cla_gbrcond_c.f.

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 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.
!>

!>          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 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.

Definition at line 151 of file cla_gbrcond_x.f.

double precision function DLA_GBRCOND (character trans, integer n, integer kl, integer ku, double precision, dimension( ldab, * ) ab, integer ldab, 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 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.
!>

!>          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 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.

Definition at line 167 of file dla_gbrcond.f.

real function SLA_GBRCOND (character trans, integer n, integer kl, integer ku, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, integer cmode, 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 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.
!>

!>          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 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.

Definition at line 166 of file sla_gbrcond.f.

double precision function ZLA_GBRCOND_C (character trans, integer n, integer kl, integer ku, complex16, dimension( ldab, ) ab, integer ldab, complex16, dimension( ldafb, ) afb, integer ldafb, integer, dimension( * ) ipiv, double precision, dimension( * ) c, logical capply, integer info, complex16, dimension( ) work, double precision, 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 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.
!>

!>          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 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.

Definition at line 159 of file zla_gbrcond_c.f.

double precision function ZLA_GBRCOND_X (character trans, integer n, integer kl, integer ku, complex16, dimension( ldab, ) ab, integer ldab, complex16, dimension( ldafb, ) afb, integer ldafb, integer, dimension( * ) ipiv, complex16, dimension( ) x, integer info, complex16, 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 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.
!>

!>          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 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.

Definition at line 152 of file zla_gbrcond_x.f.

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Source file:	la_gbrcond.3.en.gz (from lapack-man 3.12.0-160000.1.3)
Source last updated:	2024-11-04T16:48:43Z
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