table of contents
la_porcond(3) | Library Functions Manual | la_porcond(3) |
NAME¶
la_porcond - la_porcond: Skeel condition number estimate
SYNOPSIS¶
Functions¶
real function CLA_PORCOND_C (uplo, n, a, lda, af, ldaf, c,
capply, info, work, rwork)
CLA_PORCOND_C computes the infinity norm condition number of
op(A)*inv(diag(c)) for Hermitian positive-definite matrices. real function
CLA_PORCOND_X (uplo, n, a, lda, af, ldaf, x, info, work, rwork)
CLA_PORCOND_X computes the infinity norm condition number of
op(A)*diag(x) for Hermitian positive-definite matrices. double precision
function DLA_PORCOND (uplo, n, a, lda, af, ldaf, cmode, c, info,
work, iwork)
DLA_PORCOND estimates the Skeel condition number for a symmetric
positive-definite matrix. real function SLA_PORCOND (uplo, n, a, lda,
af, ldaf, cmode, c, info, work, iwork)
SLA_PORCOND estimates the Skeel condition number for a symmetric
positive-definite matrix. double precision function ZLA_PORCOND_C
(uplo, n, a, lda, af, ldaf, c, capply, info, work, rwork)
ZLA_PORCOND_C computes the infinity norm condition number of
op(A)*inv(diag(c)) for Hermitian positive-definite matrices. double
precision function ZLA_PORCOND_X (uplo, n, a, lda, af, ldaf, x, info,
work, rwork)
ZLA_PORCOND_X computes the infinity norm condition number of
op(A)*diag(x) for Hermitian positive-definite matrices.
Detailed Description¶
Function Documentation¶
real function CLA_PORCOND_C (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf, real, dimension( * ) c, logical capply, integer info, complex, dimension( * ) work, real, dimension( * ) rwork)¶
CLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices.
Purpose:
!> !> CLA_PORCOND_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 triangular factor U or L from the Cholesky factorization !> A = U**H*U or A = L*L**H, as computed by CPOTRF. !>
LDAF
!> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !>
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.
Definition at line 128 of file cla_porcond_c.f.
real function CLA_PORCOND_X (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf, complex, dimension( * ) x, integer info, complex, dimension( * ) work, real, dimension( * ) rwork)¶
CLA_PORCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-definite matrices.
Purpose:
!> !> CLA_PORCOND_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 triangular factor U or L from the Cholesky factorization !> A = U**H*U or A = L*L**H, as computed by CPOTRF. !>
LDAF
!> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !>
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.
Definition at line 121 of file cla_porcond_x.f.
double precision function DLA_PORCOND (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldaf, * ) af, integer ldaf, integer cmode, double precision, dimension( * ) c, integer info, double precision, dimension( * ) work, integer, dimension( * ) iwork)¶
DLA_PORCOND estimates the Skeel condition number for a symmetric positive-definite matrix.
Purpose:
!> !> DLA_PORCOND 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 triangular factor U or L from the Cholesky factorization !> A = U**T*U or A = L*L**T, as computed by DPOTRF. !>
LDAF
!> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !>
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.
Definition at line 139 of file dla_porcond.f.
real function SLA_PORCOND (character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldaf, * ) af, integer ldaf, integer cmode, real, dimension( * ) c, integer info, real, dimension( * ) work, integer, dimension( * ) iwork)¶
SLA_PORCOND estimates the Skeel condition number for a symmetric positive-definite matrix.
Purpose:
!> !> SLA_PORCOND 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 triangular factor U or L from the Cholesky factorization !> A = U**T*U or A = L*L**T, as computed by SPOTRF. !>
LDAF
!> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !>
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.
Definition at line 138 of file sla_porcond.f.
double precision function ZLA_PORCOND_C (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, double precision, dimension( * ) c, logical capply, integer info, complex*16, dimension( * ) work, double precision, dimension( * ) rwork)¶
ZLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices.
Purpose:
!> !> ZLA_PORCOND_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 triangular factor U or L from the Cholesky factorization !> A = U**H*U or A = L*L**H, as computed by ZPOTRF. !>
LDAF
!> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !>
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.
Definition at line 129 of file zla_porcond_c.f.
double precision function ZLA_PORCOND_X (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, complex*16, dimension( * ) x, integer info, complex*16, dimension( * ) work, double precision, dimension( * ) rwork)¶
ZLA_PORCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-definite matrices.
Purpose:
!> !> ZLA_PORCOND_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 triangular factor U or L from the Cholesky factorization !> A = U**H*U or A = L*L**H, as computed by ZPOTRF. !>
LDAF
!> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !>
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.
Definition at line 122 of file zla_porcond_x.f.
Author¶
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