pocon - pocon: condition number estimate

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subroutinecpocon(characteruplo,integern,complex,dimension(lda,*)a,integerlda,realanorm,realrcond,complex,dimension(*)work,real,dimension(*)rwork,integerinfo)CPOCONPurpose: CPOCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). ParametersUPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrix A. N >= 0. A A is COMPLEX array, dimension (LDA,N) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by CPOTRF. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). ANORM ANORM is REAL The 1-norm (or infinity-norm) of the Hermitian 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) 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. subroutinedpocon(characteruplo,integern,doubleprecision,dimension(lda,*)a,integerlda,doubleprecisionanorm,doubleprecisionrcond,doubleprecision,dimension(*)work,integer,dimension(*)iwork,integerinfo)DPOCONPurpose: DPOCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). ParametersUPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrix A. N >= 0. A A is DOUBLE PRECISION array, dimension (LDA,N) The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by DPOTRF. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). ANORM ANORM is DOUBLE PRECISION The 1-norm (or infinity-norm) of the symmetric 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 (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. subroutinespocon(characteruplo,integern,real,dimension(lda,*)a,integerlda,realanorm,realrcond,real,dimension(*)work,integer,dimension(*)iwork,integerinfo)SPOCONPurpose: SPOCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). ParametersUPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrix A. N >= 0. A A is REAL array, dimension (LDA,N) The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by SPOTRF. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). ANORM ANORM is REAL The 1-norm (or infinity-norm) of the symmetric 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 (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. subroutinezpocon(characteruplo,integern,complex*16,dimension(lda,*)a,integerlda,doubleprecisionanorm,doubleprecisionrcond,complex*16,dimension(*)work,doubleprecision,dimension(*)rwork,integerinfo)ZPOCONPurpose: ZPOCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). ParametersUPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrix A. N >= 0. A A is COMPLEX*16 array, dimension (LDA,N) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by ZPOTRF. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). ANORM ANORM is DOUBLE PRECISION The 1-norm (or infinity-norm) of the Hermitian 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) 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.

pocon - pocon: condition number estimate

Functions subroutine cpocon (uplo, n, a, lda, anorm, rcond, work, rwork, info) CPOCON subroutine dpocon (uplo, n, a, lda, anorm, rcond, work, iwork, info) DPOCON subroutine spocon (uplo, n, a, lda, anorm, rcond, work, iwork, info) SPOCON subroutine zpocon (uplo, n, a, lda, anorm, rcond, work, rwork, info) ZPOCON