table of contents
- testing 3.12.0-4
- unstable 3.12.1-2
- experimental 3.12.1-1
| la_hercond(3) | LAPACK | la_hercond(3) |
NAME¶
la_hercond - la_hercond: Skeel condition number estimate
SYNOPSIS¶
Functions¶
real function cla_hercond_c (uplo, n, a, lda, af, ldaf,
ipiv, c, capply, info, work, rwork)
CLA_HERCOND_C computes the infinity norm condition number of
op(A)*inv(diag(c)) for Hermitian indefinite matrices. real function
cla_hercond_x (uplo, n, a, lda, af, ldaf, ipiv, x, info, work, rwork)
CLA_HERCOND_X computes the infinity norm condition number of
op(A)*diag(x) for Hermitian indefinite matrices. real function
cla_syrcond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info,
work, rwork)
CLA_SYRCOND_C computes the infinity norm condition number of
op(A)*inv(diag(c)) for symmetric indefinite matrices. real function
cla_syrcond_x (uplo, n, a, lda, af, ldaf, ipiv, x, info, work, rwork)
CLA_SYRCOND_X computes the infinity norm condition number of
op(A)*diag(x) for symmetric indefinite matrices. double precision function
dla_syrcond (uplo, n, a, lda, af, ldaf, ipiv, cmode, c, info, work,
iwork)
DLA_SYRCOND estimates the Skeel condition number for a symmetric
indefinite matrix. real function sla_syrcond (uplo, n, a, lda, af,
ldaf, ipiv, cmode, c, info, work, iwork)
SLA_SYRCOND estimates the Skeel condition number for a symmetric
indefinite matrix. double precision function zla_hercond_c (uplo, n,
a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)
ZLA_HERCOND_C computes the infinity norm condition number of
op(A)*inv(diag(c)) for Hermitian indefinite matrices. double precision
function zla_hercond_x (uplo, n, a, lda, af, ldaf, ipiv, x, info,
work, rwork)
ZLA_HERCOND_X computes the infinity norm condition number of
op(A)*diag(x) for Hermitian indefinite matrices. double precision function
zla_syrcond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info,
work, rwork)
ZLA_SYRCOND_C computes the infinity norm condition number of
op(A)*inv(diag(c)) for symmetric indefinite matrices. double precision
function zla_syrcond_x (uplo, n, a, lda, af, ldaf, ipiv, x, info,
work, rwork)
ZLA_SYRCOND_X computes the infinity norm condition number of
op(A)*diag(x) for symmetric indefinite matrices.
Detailed Description¶
Function Documentation¶
real function cla_hercond_c (character uplo, 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_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefinite matrices.
Purpose:
CLA_HERCOND_C computes the infinity norm condition number of
op(A) * inv(diag(C)) where C is a REAL vector.
Parameters
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
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 block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by CHETRF.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CHETRF.
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
real function cla_hercond_x (character uplo, 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_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite matrices.
Purpose:
CLA_HERCOND_X computes the infinity norm condition number of
op(A) * diag(X) where X is a COMPLEX vector.
Parameters
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
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 block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by CHETRF.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CHETRF.
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
real function cla_syrcond_c (character uplo, 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_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefinite matrices.
Purpose:
CLA_SYRCOND_C Computes the infinity norm condition number of
op(A) * inv(diag(C)) where C is a REAL vector.
Parameters
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
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 block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by CSYTRF.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CSYTRF.
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
real function cla_syrcond_x (character uplo, 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_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices.
Purpose:
CLA_SYRCOND_X Computes the infinity norm condition number of
op(A) * diag(X) where X is a COMPLEX vector.
Parameters
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
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 block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by CSYTRF.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CSYTRF.
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
double precision function dla_syrcond (character uplo, 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_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix.
Purpose:
DLA_SYRCOND 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
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
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 block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by DSYTRF.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by DSYTRF.
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
real function sla_syrcond (character uplo, 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_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix.
Purpose:
SLA_SYRCOND 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
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
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 block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by SSYTRF.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by SSYTRF.
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.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
double precision function zla_hercond_c (character uplo, 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_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefinite matrices.
Purpose:
ZLA_HERCOND_C computes the infinity norm condition number of
op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
Parameters
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
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 block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by ZHETRF.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CHETRF.
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
double precision function zla_hercond_x (character uplo, 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_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite matrices.
Purpose:
ZLA_HERCOND_X computes the infinity norm condition number of
op(A) * diag(X) where X is a COMPLEX*16 vector.
Parameters
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
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 block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by ZHETRF.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CHETRF.
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
double precision function zla_syrcond_c (character uplo, 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_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefinite matrices.
Purpose:
ZLA_SYRCOND_C Computes the infinity norm condition number of
op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
Parameters
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
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 block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by ZSYTRF.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by ZSYTRF.
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
double precision function zla_syrcond_x (character uplo, 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_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices.
Purpose:
ZLA_SYRCOND_X Computes the infinity norm condition number of
op(A) * diag(X) where X is a COMPLEX*16 vector.
Parameters
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
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 block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by ZSYTRF.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by ZSYTRF.
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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| Tue Jan 14 2025 16:19:47 | Version 3.12.0 |