CTPCON(1) LAPACK routine (version 3.2) CTPCON(1)[top]NAMECTPCON - estimates the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-normSYNOPSISSUBROUTINE CTPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, RWORK, INFO ) CHARACTER DIAG, NORM, UPLO INTEGER INFO, N REAL RCOND REAL RWORK( * ) COMPLEX AP( * ), WORK( * )PURPOSECTPCON estimates the reciprocal of the condition number of a packed 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)) ).ARGUMENTSNORM (input) 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 (input) CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular. DIAG (input) CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular. N (input) INTEGER The order of the matrix A. N >= 0. AP (input) COMPLEX array, dimension (N*(N+1)/2) The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1. RCOND (output) REAL The reciprocal of the condition number of the matrix A, com‐ puted as RCOND = 1/(norm(A) * norm(inv(A))). WORK (workspace) COMPLEX array, dimension (2*N) RWORK (workspace) REAL array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value LAPACK routine (version 3.2) November 2008 CTPCON(1)-i

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