trcon(3) Library Functions Manual trcon(3) NAME trcon - trcon: condition number estimate SYNOPSIS Functions subroutine ctrcon (norm, uplo, diag, n, a, lda, rcond, work, rwork, info) CTRCON subroutine dtrcon (norm, uplo, diag, n, a, lda, rcond, work, iwork, info) DTRCON subroutine strcon (norm, uplo, diag, n, a, lda, rcond, work, iwork, info) STRCON subroutine ztrcon (norm, uplo, diag, n, a, lda, rcond, work, rwork, info) ZTRCON Detailed Description Function Documentation subroutine ctrcon (character norm, character uplo, character diag, integer n, complex, dimension( lda, * ) a, integer lda, real rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer info) CTRCON Purpose: CTRCON estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). Parameters NORM NORM is CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm. UPLO UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular. DIAG DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular. N N is INTEGER The order of the matrix A. N >= 0. A A is COMPLEX array, dimension (LDA,N) The triangular matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). RCOND RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). WORK WORK is COMPLEX array, dimension (2*N) RWORK RWORK is REAL 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. Definition at line 135 of file ctrcon.f. subroutine dtrcon (character norm, character uplo, character diag, integer n, double precision, dimension( lda, * ) a, integer lda, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info) DTRCON Purpose: DTRCON estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). Parameters NORM NORM is CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm. UPLO UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular. DIAG DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular. N N is INTEGER The order of the matrix A. N >= 0. A A is DOUBLE PRECISION array, dimension (LDA,N) The triangular matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). RCOND RCOND is DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). WORK WORK is DOUBLE PRECISION array, dimension (3*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. Definition at line 135 of file dtrcon.f. subroutine strcon (character norm, character uplo, character diag, integer n, real, dimension( lda, * ) a, integer lda, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info) STRCON Purpose: STRCON estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). Parameters NORM NORM is CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm. UPLO UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular. DIAG DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular. N N is INTEGER The order of the matrix A. N >= 0. A A is REAL array, dimension (LDA,N) The triangular matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). RCOND RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). WORK WORK is REAL array, dimension (3*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. Definition at line 135 of file strcon.f. subroutine ztrcon (character norm, character uplo, character diag, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision rcond, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info) ZTRCON Purpose: ZTRCON estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). Parameters NORM NORM is CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm. UPLO UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular. DIAG DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular. N N is INTEGER The order of the matrix A. N >= 0. A A is COMPLEX*16 array, dimension (LDA,N) The triangular matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). RCOND RCOND is DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). WORK WORK is COMPLEX*16 array, dimension (2*N) RWORK RWORK is DOUBLE PRECISION 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. Definition at line 135 of file ztrcon.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 trcon(3)