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ssycon_3.f(3) | LAPACK | ssycon_3.f(3) |
NAME¶
ssycon_3.f -SYNOPSIS¶
Functions/Subroutines¶
subroutine ssycon_3 (UPLO, N, A, LDA, E, IPIV, ANORM, RCOND, WORK, IWORK, INFO)
Function/Subroutine Documentation¶
subroutine ssycon_3 (characterUPLO, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )E, integer, dimension( * )IPIV, realANORM, realRCOND, real, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)¶
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.
UPLO
Author:
UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix: = 'U': Upper triangular, form is A = P*U*D*(U**T)*(P**T); = 'L': 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 = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': 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 = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; If UPLO = 'L': 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 = 'U' or UPLO = 'L' 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
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
December 2016
Contributors:
Author¶
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