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la_gercond(3) Library Functions Manual la_gercond(3)

NAME

la_gercond - la_gercond: Skeel condition number estimate

SYNOPSIS

Functions


real function CLA_GERCOND_C (trans, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)
CLA_GERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices. real function CLA_GERCOND_X (trans, n, a, lda, af, ldaf, ipiv, x, info, work, rwork)
CLA_GERCOND_X computes the infinity norm condition number of op(A)*diag(x) for general matrices. double precision function DLA_GERCOND (trans, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork)
DLA_GERCOND estimates the Skeel condition number for a general matrix. real function SLA_GERCOND (trans, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork)
SLA_GERCOND estimates the Skeel condition number for a general matrix. double precision function ZLA_GERCOND_C (trans, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)
ZLA_GERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices. double precision function ZLA_GERCOND_X (trans, n, a, lda, af, ldaf, ipiv, x, info, work, rwork)
ZLA_GERCOND_X computes the infinity norm condition number of op(A)*diag(x) for general matrices.

Detailed Description

Function Documentation

real function CLA_GERCOND_C (character trans, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, real, dimension( * ) c, logical capply, integer info, complex, dimension( * ) work, real, dimension( * ) rwork)

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

Purpose:

!>
!>
!>    CLA_GERCOND_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.
!>

A

!>          A is COMPLEX array, dimension (LDA,N)
!>     On entry, the N-by-N matrix A
!>

LDA

!>          LDA is INTEGER
!>     The leading dimension of the array A.  LDA >= max(1,N).
!>

AF

!>          AF is COMPLEX array, dimension (LDAF,N)
!>     The factors L and U from the factorization
!>     A = P*L*U as computed by CGETRF.
!>

LDAF

!>          LDAF is INTEGER
!>     The leading dimension of the array AF.  LDAF >= max(1,N).
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>     The pivot indices from the factorization A = P*L*U
!>     as computed by CGETRF; 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 140 of file cla_gercond_c.f.

real function CLA_GERCOND_X (character trans, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, complex, dimension( * ) x, integer info, complex, dimension( * ) work, real, dimension( * ) rwork)

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

Purpose:

!>
!>
!>    CLA_GERCOND_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.
!>

A

!>          A is COMPLEX array, dimension (LDA,N)
!>     On entry, the N-by-N matrix A.
!>

LDA

!>          LDA is INTEGER
!>     The leading dimension of the array A.  LDA >= max(1,N).
!>

AF

!>          AF is COMPLEX array, dimension (LDAF,N)
!>     The factors L and U from the factorization
!>     A = P*L*U as computed by CGETRF.
!>

LDAF

!>          LDAF is INTEGER
!>     The leading dimension of the array AF.  LDAF >= max(1,N).
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>     The pivot indices from the factorization A = P*L*U
!>     as computed by CGETRF; 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 133 of file cla_gercond_x.f.

double precision function DLA_GERCOND (character trans, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, integer cmode, double precision, dimension( * ) c, integer info, double precision, dimension( * ) work, integer, dimension( * ) iwork)

DLA_GERCOND estimates the Skeel condition number for a general matrix.

Purpose:

!>
!>    DLA_GERCOND 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.
!>

A

!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>     On entry, the N-by-N matrix A.
!>

LDA

!>          LDA is INTEGER
!>     The leading dimension of the array A.  LDA >= max(1,N).
!>

AF

!>          AF is DOUBLE PRECISION array, dimension (LDAF,N)
!>     The factors L and U from the factorization
!>     A = P*L*U as computed by DGETRF.
!>

LDAF

!>          LDAF is INTEGER
!>     The leading dimension of the array AF.  LDAF >= max(1,N).
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>     The pivot indices from the factorization A = P*L*U
!>     as computed by DGETRF; 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 (3*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 149 of file dla_gercond.f.

real function SLA_GERCOND (character trans, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, integer cmode, real, dimension( * ) c, integer info, real, dimension( * ) work, integer, dimension( * ) iwork)

SLA_GERCOND estimates the Skeel condition number for a general matrix.

Purpose:

!>
!>    SLA_GERCOND 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.
!>

A

!>          A is REAL array, dimension (LDA,N)
!>     On entry, the N-by-N matrix A.
!>

LDA

!>          LDA is INTEGER
!>     The leading dimension of the array A.  LDA >= max(1,N).
!>

AF

!>          AF is REAL array, dimension (LDAF,N)
!>     The factors L and U from the factorization
!>     A = P*L*U as computed by SGETRF.
!>

LDAF

!>          LDAF is INTEGER
!>     The leading dimension of the array AF.  LDAF >= max(1,N).
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>     The pivot indices from the factorization A = P*L*U
!>     as computed by SGETRF; 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 (3*N).
!>     Workspace.
!>

IWORK

!>          IWORK is INTEGER array, dimension (N).
!>     Workspace.2
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 148 of file sla_gercond.f.

double precision function ZLA_GERCOND_C (character trans, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, double precision, dimension( * ) c, logical capply, integer info, complex*16, dimension( * ) work, double precision, dimension( * ) rwork)

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

Purpose:

!>
!>    ZLA_GERCOND_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.
!>

A

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>     On entry, the N-by-N matrix A
!>

LDA

!>          LDA is INTEGER
!>     The leading dimension of the array A.  LDA >= max(1,N).
!>

AF

!>          AF is COMPLEX*16 array, dimension (LDAF,N)
!>     The factors L and U from the factorization
!>     A = P*L*U as computed by ZGETRF.
!>

LDAF

!>          LDAF is INTEGER
!>     The leading dimension of the array AF.  LDAF >= max(1,N).
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>     The pivot indices from the factorization A = P*L*U
!>     as computed by ZGETRF; 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 140 of file zla_gercond_c.f.

double precision function ZLA_GERCOND_X (character trans, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, complex*16, dimension( * ) x, integer info, complex*16, dimension( * ) work, double precision, dimension( * ) rwork)

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

Purpose:

!>
!>    ZLA_GERCOND_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.
!>

A

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>     On entry, the N-by-N matrix A.
!>

LDA

!>          LDA is INTEGER
!>     The leading dimension of the array A.  LDA >= max(1,N).
!>

AF

!>          AF is COMPLEX*16 array, dimension (LDAF,N)
!>     The factors L and U from the factorization
!>     A = P*L*U as computed by ZGETRF.
!>

LDAF

!>          LDAF is INTEGER
!>     The leading dimension of the array AF.  LDAF >= max(1,N).
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>     The pivot indices from the factorization A = P*L*U
!>     as computed by ZGETRF; 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 133 of file zla_gercond_x.f.

Author

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