gtcon - gtcon: condition number estimate

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subroutinecgtcon(characternorm,integern,complex,dimension(*)dl,complex,dimension(*)d,complex,dimension(*)du,complex,dimension(*)du2,integer,dimension(*)ipiv,realanorm,realrcond,complex,dimension(*)work,integerinfo)CGTCONPurpose: CGTCON estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * 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. DL DL is COMPLEX array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by CGTTRF. D D is COMPLEX array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. DU DU is COMPLEX array, dimension (N-1) The (n-1) elements of the first superdiagonal of U. DU2 DU2 is COMPLEX array, dimension (N-2) The (n-2) elements of the second superdiagonal of U. IPIV IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required. 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/(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. subroutinedgtcon(characternorm,integern,doubleprecision,dimension(*)dl,doubleprecision,dimension(*)d,doubleprecision,dimension(*)du,doubleprecision,dimension(*)du2,integer,dimension(*)ipiv,doubleprecisionanorm,doubleprecisionrcond,doubleprecision,dimension(*)work,integer,dimension(*)iwork,integerinfo)DGTCONPurpose: DGTCON estimates the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by DGTTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * 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. DL DL is DOUBLE PRECISION array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by DGTTRF. D D is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. DU DU is DOUBLE PRECISION array, dimension (N-1) The (n-1) elements of the first superdiagonal of U. DU2 DU2 is DOUBLE PRECISION array, dimension (N-2) The (n-2) elements of the second superdiagonal of U. IPIV IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required. 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/(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. subroutinesgtcon(characternorm,integern,real,dimension(*)dl,real,dimension(*)d,real,dimension(*)du,real,dimension(*)du2,integer,dimension(*)ipiv,realanorm,realrcond,real,dimension(*)work,integer,dimension(*)iwork,integerinfo)SGTCONPurpose: SGTCON estimates the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * 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. DL DL is REAL array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF. D D is REAL array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. DU DU is REAL array, dimension (N-1) The (n-1) elements of the first superdiagonal of U. DU2 DU2 is REAL array, dimension (N-2) The (n-2) elements of the second superdiagonal of U. IPIV IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required. 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/(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. subroutinezgtcon(characternorm,integern,complex*16,dimension(*)dl,complex*16,dimension(*)d,complex*16,dimension(*)du,complex*16,dimension(*)du2,integer,dimension(*)ipiv,doubleprecisionanorm,doubleprecisionrcond,complex*16,dimension(*)work,integerinfo)ZGTCONPurpose: ZGTCON estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * 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. DL DL is COMPLEX*16 array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by ZGTTRF. D D is COMPLEX*16 array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. DU DU is COMPLEX*16 array, dimension (N-1) The (n-1) elements of the first superdiagonal of U. DU2 DU2 is COMPLEX*16 array, dimension (N-2) The (n-2) elements of the second superdiagonal of U. IPIV IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required. 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/(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.

gtcon - gtcon: condition number estimate

Functions subroutine cgtcon (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, info) CGTCON subroutine dgtcon (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, iwork, info) DGTCON subroutine sgtcon (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, iwork, info) SGTCON subroutine zgtcon (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, info) ZGTCON