la_gbrcond - Man Page

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.

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

          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.

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

          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.

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

          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.

Definition at line 166 of file sla_gbrcond.f.

double precision function zla_gbrcond_c (character trans, integer n, integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, complex*16, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, double precision, dimension( * ) c, logical capply, integer info, complex*16, 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

          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.

Definition at line 159 of file zla_gbrcond_c.f.

double precision function zla_gbrcond_x (character trans, integer n, integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, 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.

Definition at line 152 of file zla_gbrcond_x.f.

Author

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Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK