gecon - gecon: condition number estimate

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subroutinecgecon(characternorm,integern,complex,dimension(lda,*)a,integerlda,realanorm,realrcond,complex,dimension(*)work,real,dimension(*)rwork,integerinfo)CGECONPurpose: CGECON estimates the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by CGETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). ParametersNORM 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. N N is INTEGER The order of the matrix A. N >= 0. A A is COMPLEX array, dimension (LDA,N) The factors L and U from the factorization A = P*L*U as computed by CGETRF. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). ANORM ANORM is REAL If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A. 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 (2*N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. NaNs are illegal values for ANORM, and they propagate to the output parameter RCOND. Infinity is illegal for ANORM, and it propagates to the output parameter RCOND as 0. = 1: if RCOND = NaN, or RCOND = Inf, or the computed norm of the inverse of A is 0. In the latter, RCOND = 0 is returned. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinedgecon(characternorm,integern,doubleprecision,dimension(lda,*)a,integerlda,doubleprecisionanorm,doubleprecisionrcond,doubleprecision,dimension(*)work,integer,dimension(*)iwork,integerinfo)DGECONPurpose: DGECON estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by DGETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). ParametersNORM 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. N N is INTEGER The order of the matrix A. N >= 0. A A is DOUBLE PRECISION array, dimension (LDA,N) The factors L and U from the factorization A = P*L*U as computed by DGETRF. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). ANORM ANORM is DOUBLE PRECISION If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-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/(norm(A) * norm(inv(A))). WORK WORK is DOUBLE PRECISION array, dimension (4*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. NaNs are illegal values for ANORM, and they propagate to the output parameter RCOND. Infinity is illegal for ANORM, and it propagates to the output parameter RCOND as 0. = 1: if RCOND = NaN, or RCOND = Inf, or the computed norm of the inverse of A is 0. In the latter, RCOND = 0 is returned. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinesgecon(characternorm,integern,real,dimension(lda,*)a,integerlda,realanorm,realrcond,real,dimension(*)work,integer,dimension(*)iwork,integerinfo)SGECONPurpose: SGECON estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). ParametersNORM 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. N N is INTEGER The order of the matrix A. N >= 0. A A is REAL array, dimension (LDA,N) The factors L and U from the factorization A = P*L*U as computed by SGETRF. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). ANORM ANORM is REAL If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A. 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 (4*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. NaNs are illegal values for ANORM, and they propagate to the output parameter RCOND. Infinity is illegal for ANORM, and it propagates to the output parameter RCOND as 0. = 1: if RCOND = NaN, or RCOND = Inf, or the computed norm of the inverse of A is 0. In the latter, RCOND = 0 is returned. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinezgecon(characternorm,integern,complex*16,dimension(lda,*)a,integerlda,doubleprecisionanorm,doubleprecisionrcond,complex*16,dimension(*)work,doubleprecision,dimension(*)rwork,integerinfo)ZGECONPurpose: ZGECON estimates the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). ParametersNORM 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. N N is INTEGER The order of the matrix A. N >= 0. A A is COMPLEX*16 array, dimension (LDA,N) The factors L and U from the factorization A = P*L*U as computed by ZGETRF. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). ANORM ANORM is DOUBLE PRECISION If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-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/(norm(A) * norm(inv(A))). WORK WORK is COMPLEX*16 array, dimension (2*N) RWORK RWORK is DOUBLE PRECISION array, dimension (2*N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. NaNs are illegal values for ANORM, and they propagate to the output parameter RCOND. Infinity is illegal for ANORM, and it propagates to the output parameter RCOND as 0. = 1: if RCOND = NaN, or RCOND = Inf, or the computed norm of the inverse of A is 0. In the latter, RCOND = 0 is returned. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.

gecon - gecon: condition number estimate

Functions subroutine cgecon (norm, n, a, lda, anorm, rcond, work, rwork, info) CGECON subroutine dgecon (norm, n, a, lda, anorm, rcond, work, iwork, info) DGECON subroutine sgecon (norm, n, a, lda, anorm, rcond, work, iwork, info) SGECON subroutine zgecon (norm, n, a, lda, anorm, rcond, work, rwork, info) ZGECON