la_gercond - Man Page

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