Man page - hecon_3(3)

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Manual

hecon_3

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine checon_3 (character uplo, integer n, complex, dimension( lda, *) a, integer lda, complex, dimension( * ) e, integer, dimension( * )ipiv, real anorm, real rcond, complex, dimension( * ) work, integerinfo)
subroutine csycon_3 (character uplo, integer n, complex, dimension( lda, *) a, integer lda, complex, dimension( * ) e, integer, dimension( * )ipiv, real anorm, real rcond, complex, dimension( * ) work, integerinfo)
subroutine dsycon_3 (character uplo, integer n, double precision,dimension( lda, * ) a, integer lda, double precision, dimension( * ) e,integer, dimension( * ) ipiv, double precision anorm, double precisionrcond, double precision, dimension( * ) work, integer, dimension( * )iwork, integer info)
subroutine ssycon_3 (character uplo, integer n, real, dimension( lda, * )a, integer lda, real, dimension( * ) e, integer, dimension( * ) ipiv,real anorm, real rcond, real, dimension( * ) work, integer, dimension(* ) iwork, integer info)
subroutine zhecon_3 (character uplo, integer n, complex*16, dimension( lda,* ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( *) ipiv, double precision anorm, double precision rcond, complex*16,dimension( * ) work, integer info)
subroutine zsycon_3 (character uplo, integer n, complex*16, dimension( lda,* ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( *) ipiv, double precision anorm, double precision rcond, complex*16,dimension( * ) work, integer info)
Author

NAME

hecon_3 - {he,sy}con_3: condition number estimate

SYNOPSIS

Functions

subroutine checon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)
CHECON_3
subroutine csycon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)
CSYCON_3
subroutine dsycon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, iwork, info)
DSYCON_3
subroutine ssycon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, iwork, info)
SSYCON_3
subroutine zhecon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)
ZHECON_3
subroutine zsycon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)
ZSYCON_3

Detailed Description

Function Documentation

subroutine checon_3 (character uplo, integer n, complex, dimension( lda, *) a, integer lda, complex, dimension( * ) e, integer, dimension( * )ipiv, real anorm, real rcond, complex, dimension( * ) work, integerinfo)

CHECON_3

Purpose:

CHECON_3 estimates the reciprocal of the condition number (in the
1-norm) of a complex Hermitian matrix A using the factorization
computed by CHETRF_RK or CHETRF_BK:

A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix,
U**H (or L**H) is the conjugate of U (or L), P is a permutation
matrix, P**T is the transpose of P, and D is Hermitian and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
This routine uses BLAS3 solver CHETRS_3.

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are
stored as an upper or lower triangular matrix:
= ā€™Uā€™: Upper triangular, form is A = P*U*D*(U**H)*(P**T);
= ā€™Lā€™: Lower triangular, form is A = P*L*D*(L**H)*(P**T).

N

N is INTEGER
The order of the matrix A. N >= 0.

A

A is COMPLEX array, dimension (LDA,N)
Diagonal of the block diagonal matrix D and factors U or L
as computed by CHETRF_RK and CHETRF_BK:
a) ONLY diagonal elements of the Hermitian block diagonal
matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
(superdiagonal (or subdiagonal) elements of D
should be provided on entry in array E), and
b) If UPLO = ā€™Uā€™: factor U in the superdiagonal part of A.
If UPLO = ā€™Lā€™: factor L in the subdiagonal part of A.

LDA

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

E

E is COMPLEX array, dimension (N)
On entry, contains the superdiagonal (or subdiagonal)
elements of the Hermitian block diagonal matrix D
with 1-by-1 or 2-by-2 diagonal blocks, where
If UPLO = ā€™Uā€™: E(i) = D(i-1,i),i=2:N, E(1) not referenced;
If UPLO = ā€™Lā€™: E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

NOTE: For 1-by-1 diagonal block D(k), where
1 <= k <= N, the element E(k) is not referenced in both
UPLO = ā€™Uā€™ or UPLO = ā€™Lā€™ cases.

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CHETRF_RK or CHETRF_BK.

ANORM

ANORM is REAL
The 1-norm of the original matrix A.

RCOND

RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.

WORK

WORK is COMPLEX array, dimension (2*N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

June 2017, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

subroutine csycon_3 (character uplo, integer n, complex, dimension( lda, *) a, integer lda, complex, dimension( * ) e, integer, dimension( * )ipiv, real anorm, real rcond, complex, dimension( * ) work, integerinfo)

CSYCON_3

Purpose:

CSYCON_3 estimates the reciprocal of the condition number (in the
1-norm) of a complex symmetric matrix A using the factorization
computed by CSYTRF_RK or CSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix,
U**T (or L**T) is the transpose of U (or L), P is a permutation
matrix, P**T is the transpose of P, and D is symmetric and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
This routine uses BLAS3 solver CSYTRS_3.

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are
stored as an upper or lower triangular matrix:
= ā€™Uā€™: Upper triangular, form is A = P*U*D*(U**T)*(P**T);
= ā€™Lā€™: Lower triangular, form is A = P*L*D*(L**T)*(P**T).

N

N is INTEGER
The order of the matrix A. N >= 0.

A

A is COMPLEX array, dimension (LDA,N)
Diagonal of the block diagonal matrix D and factors U or L
as computed by CSYTRF_RK and CSYTRF_BK:
a) ONLY diagonal elements of the symmetric block diagonal
matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
(superdiagonal (or subdiagonal) elements of D
should be provided on entry in array E), and
b) If UPLO = ā€™Uā€™: factor U in the superdiagonal part of A.
If UPLO = ā€™Lā€™: factor L in the subdiagonal part of A.

LDA

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

E

E is COMPLEX array, dimension (N)
On entry, contains the superdiagonal (or subdiagonal)
elements of the symmetric block diagonal matrix D
with 1-by-1 or 2-by-2 diagonal blocks, where
If UPLO = ā€™Uā€™: E(i) = D(i-1,i),i=2:N, E(1) not referenced;
If UPLO = ā€™Lā€™: E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

NOTE: For 1-by-1 diagonal block D(k), where
1 <= k <= N, the element E(k) is not referenced in both
UPLO = ā€™Uā€™ or UPLO = ā€™Lā€™ cases.

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CSYTRF_RK or CSYTRF_BK.

ANORM

ANORM is REAL
The 1-norm of the original matrix A.

RCOND

RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.

WORK

WORK is COMPLEX array, dimension (2*N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

June 2017, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

subroutine dsycon_3 (character uplo, integer n, double precision,dimension( lda, * ) a, integer lda, double precision, dimension( * ) e,integer, dimension( * ) ipiv, double precision anorm, double precisionrcond, double precision, dimension( * ) work, integer, dimension( * )iwork, integer info)

DSYCON_3

Purpose:

DSYCON_3 estimates the reciprocal of the condition number (in the
1-norm) of a real symmetric matrix A using the factorization
computed by DSYTRF_RK or DSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix,
U**T (or L**T) is the transpose of U (or L), P is a permutation
matrix, P**T is the transpose of P, and D is symmetric and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
This routine uses BLAS3 solver DSYTRS_3.

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are
stored as an upper or lower triangular matrix:
= ā€™Uā€™: Upper triangular, form is A = P*U*D*(U**T)*(P**T);
= ā€™Lā€™: Lower triangular, form is A = P*L*D*(L**T)*(P**T).

N

N is INTEGER
The order of the matrix A. N >= 0.

A

A is DOUBLE PRECISION array, dimension (LDA,N)
Diagonal of the block diagonal matrix D and factors U or L
as computed by DSYTRF_RK and DSYTRF_BK:
a) ONLY diagonal elements of the symmetric block diagonal
matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
(superdiagonal (or subdiagonal) elements of D
should be provided on entry in array E), and
b) If UPLO = ā€™Uā€™: factor U in the superdiagonal part of A.
If UPLO = ā€™Lā€™: factor L in the subdiagonal part of A.

LDA

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

E

E is DOUBLE PRECISION array, dimension (N)
On entry, contains the superdiagonal (or subdiagonal)
elements of the symmetric block diagonal matrix D
with 1-by-1 or 2-by-2 diagonal blocks, where
If UPLO = ā€™Uā€™: E(i) = D(i-1,i),i=2:N, E(1) not referenced;
If UPLO = ā€™Lā€™: E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

NOTE: For 1-by-1 diagonal block D(k), where
1 <= k <= N, the element E(k) is not referenced in both
UPLO = ā€™Uā€™ or UPLO = ā€™Lā€™ cases.

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by DSYTRF_RK or DSYTRF_BK.

ANORM

ANORM is DOUBLE PRECISION
The 1-norm of the original matrix A.

RCOND

RCOND is DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.

WORK

WORK is DOUBLE PRECISION array, dimension (2*N)

IWORK

IWORK is INTEGER array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

June 2017, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

subroutine ssycon_3 (character uplo, integer n, real, dimension( lda, * )a, integer lda, real, dimension( * ) e, integer, dimension( * ) ipiv,real anorm, real rcond, real, dimension( * ) work, integer, dimension(* ) iwork, integer info)

SSYCON_3

Purpose:

SSYCON_3 estimates the reciprocal of the condition number (in the
1-norm) of a real symmetric matrix A using the factorization
computed by DSYTRF_RK or DSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix,
U**T (or L**T) is the transpose of U (or L), P is a permutation
matrix, P**T is the transpose of P, and D is symmetric and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
This routine uses BLAS3 solver SSYTRS_3.

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are
stored as an upper or lower triangular matrix:
= ā€™Uā€™: Upper triangular, form is A = P*U*D*(U**T)*(P**T);
= ā€™Lā€™: Lower triangular, form is A = P*L*D*(L**T)*(P**T).

N

N is INTEGER
The order of the matrix A. N >= 0.

A

A is REAL array, dimension (LDA,N)
Diagonal of the block diagonal matrix D and factors U or L
as computed by SSYTRF_RK and SSYTRF_BK:
a) ONLY diagonal elements of the symmetric block diagonal
matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
(superdiagonal (or subdiagonal) elements of D
should be provided on entry in array E), and
b) If UPLO = ā€™Uā€™: factor U in the superdiagonal part of A.
If UPLO = ā€™Lā€™: factor L in the subdiagonal part of A.

LDA

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

E

E is REAL array, dimension (N)
On entry, contains the superdiagonal (or subdiagonal)
elements of the symmetric block diagonal matrix D
with 1-by-1 or 2-by-2 diagonal blocks, where
If UPLO = ā€™Uā€™: E(i) = D(i-1,i),i=2:N, E(1) not referenced;
If UPLO = ā€™Lā€™: E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

NOTE: For 1-by-1 diagonal block D(k), where
1 <= k <= N, the element E(k) is not referenced in both
UPLO = ā€™Uā€™ or UPLO = ā€™Lā€™ cases.

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by SSYTRF_RK or SSYTRF_BK.

ANORM

ANORM is REAL
The 1-norm of the original matrix A.

RCOND

RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.

WORK

WORK is REAL array, dimension (2*N)

IWORK

IWORK is INTEGER array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

June 2017, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

subroutine zhecon_3 (character uplo, integer n, complex*16, dimension( lda,* ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( *) ipiv, double precision anorm, double precision rcond, complex*16,dimension( * ) work, integer info)

ZHECON_3

Purpose:

ZHECON_3 estimates the reciprocal of the condition number (in the
1-norm) of a complex Hermitian matrix A using the factorization
computed by ZHETRF_RK or ZHETRF_BK:

A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix,
U**H (or L**H) is the conjugate of U (or L), P is a permutation
matrix, P**T is the transpose of P, and D is Hermitian and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
This routine uses BLAS3 solver ZHETRS_3.

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are
stored as an upper or lower triangular matrix:
= ā€™Uā€™: Upper triangular, form is A = P*U*D*(U**H)*(P**T);
= ā€™Lā€™: Lower triangular, form is A = P*L*D*(L**H)*(P**T).

N

N is INTEGER
The order of the matrix A. N >= 0.

A

A is COMPLEX*16 array, dimension (LDA,N)
Diagonal of the block diagonal matrix D and factors U or L
as computed by ZHETRF_RK and ZHETRF_BK:
a) ONLY diagonal elements of the Hermitian block diagonal
matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
(superdiagonal (or subdiagonal) elements of D
should be provided on entry in array E), and
b) If UPLO = ā€™Uā€™: factor U in the superdiagonal part of A.
If UPLO = ā€™Lā€™: factor L in the subdiagonal part of A.

LDA

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

E

E is COMPLEX*16 array, dimension (N)
On entry, contains the superdiagonal (or subdiagonal)
elements of the Hermitian block diagonal matrix D
with 1-by-1 or 2-by-2 diagonal blocks, where
If UPLO = ā€™Uā€™: E(i) = D(i-1,i),i=2:N, E(1) not referenced;
If UPLO = ā€™Lā€™: E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

NOTE: For 1-by-1 diagonal block D(k), where
1 <= k <= N, the element E(k) is not referenced in both
UPLO = ā€™Uā€™ or UPLO = ā€™Lā€™ cases.

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by ZHETRF_RK or ZHETRF_BK.

ANORM

ANORM is DOUBLE PRECISION
The 1-norm of the original matrix A.

RCOND

RCOND is DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.

WORK

WORK is COMPLEX*16 array, dimension (2*N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

June 2017, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

subroutine zsycon_3 (character uplo, integer n, complex*16, dimension( lda,* ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( *) ipiv, double precision anorm, double precision rcond, complex*16,dimension( * ) work, integer info)

ZSYCON_3

Purpose:

ZSYCON_3 estimates the reciprocal of the condition number (in the
1-norm) of a complex symmetric matrix A using the factorization
computed by ZSYTRF_RK or ZSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix,
U**T (or L**T) is the transpose of U (or L), P is a permutation
matrix, P**T is the transpose of P, and D is symmetric and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
This routine uses BLAS3 solver ZSYTRS_3.

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are
stored as an upper or lower triangular matrix:
= ā€™Uā€™: Upper triangular, form is A = P*U*D*(U**T)*(P**T);
= ā€™Lā€™: Lower triangular, form is A = P*L*D*(L**T)*(P**T).

N

N is INTEGER
The order of the matrix A. N >= 0.

A

A is COMPLEX*16 array, dimension (LDA,N)
Diagonal of the block diagonal matrix D and factors U or L
as computed by ZSYTRF_RK and ZSYTRF_BK:
a) ONLY diagonal elements of the symmetric block diagonal
matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
(superdiagonal (or subdiagonal) elements of D
should be provided on entry in array E), and
b) If UPLO = ā€™Uā€™: factor U in the superdiagonal part of A.
If UPLO = ā€™Lā€™: factor L in the subdiagonal part of A.

LDA

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

E

E is COMPLEX*16 array, dimension (N)
On entry, contains the superdiagonal (or subdiagonal)
elements of the symmetric block diagonal matrix D
with 1-by-1 or 2-by-2 diagonal blocks, where
If UPLO = ā€™Uā€™: E(i) = D(i-1,i),i=2:N, E(1) not referenced;
If UPLO = ā€™Lā€™: E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

NOTE: For 1-by-1 diagonal block D(k), where
1 <= k <= N, the element E(k) is not referenced in both
UPLO = ā€™Uā€™ or UPLO = ā€™Lā€™ cases.

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by ZSYTRF_RK or ZSYTRF_BK.

ANORM

ANORM is DOUBLE PRECISION
The 1-norm of the original matrix A.

RCOND

RCOND is DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.

WORK

WORK is COMPLEX*16 array, dimension (2*N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

June 2017, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

Author

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