DPBCON(3F) DPBCON(3F)
DPBCON - estimate the reciprocal of the condition number (in the 1-norm)
of a real symmetric positive definite band matrix using the Cholesky
factorization A = U**T*U or A = L*L**T computed by DPBTRF
SUBROUTINE DPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, IWORK, INFO
)
CHARACTER UPLO
INTEGER INFO, KD, LDAB, N
DOUBLE PRECISION ANORM, RCOND
INTEGER IWORK( * )
DOUBLE PRECISION AB( LDAB, * ), WORK( * )
DPBCON estimates the reciprocal of the condition number (in the 1-norm)
of a real symmetric positive definite band matrix using the Cholesky
factorization A = U**T*U or A = L*L**T computed by DPBTRF.
An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
UPLO (input) CHARACTER*1
= 'U': Upper triangular factor stored in AB;
= 'L': Lower triangular factor stored in AB.
N (input) INTEGER
The order of the matrix A. N >= 0.
KD (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U', or
the number of subdiagonals if UPLO = 'L'. KD >= 0.
AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
The triangular factor U or L from the Cholesky factorization A =
U**T*U or A = L*L**T of the band matrix A, stored in the first
KD+1 rows of the array. The j-th column of U or L is stored in
the j-th column of the array AB as follows: if UPLO ='U',
AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L',
AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
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DPBCON(3F) DPBCON(3F)
ANORM (input) DOUBLE PRECISION
The 1-norm (or infinity-norm) of the symmetric band matrix A.
RCOND (output) 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 (workspace) DOUBLE PRECISION array, dimension (3*N)
IWORK (workspace) INTEGER array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
DPBCON(3F) DPBCON(3F)
DPBCON - estimate the reciprocal of the condition number (in the 1-norm)
of a real symmetric positive definite band matrix using the Cholesky
factorization A = U**T*U or A = L*L**T computed by DPBTRF
SUBROUTINE DPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, IWORK, INFO
)
CHARACTER UPLO
INTEGER INFO, KD, LDAB, N
DOUBLE PRECISION ANORM, RCOND
INTEGER IWORK( * )
DOUBLE PRECISION AB( LDAB, * ), WORK( * )
DPBCON estimates the reciprocal of the condition number (in the 1-norm)
of a real symmetric positive definite band matrix using the Cholesky
factorization A = U**T*U or A = L*L**T computed by DPBTRF.
An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
UPLO (input) CHARACTER*1
= 'U': Upper triangular factor stored in AB;
= 'L': Lower triangular factor stored in AB.
N (input) INTEGER
The order of the matrix A. N >= 0.
KD (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U', or
the number of subdiagonals if UPLO = 'L'. KD >= 0.
AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
The triangular factor U or L from the Cholesky factorization A =
U**T*U or A = L*L**T of the band matrix A, stored in the first
KD+1 rows of the array. The j-th column of U or L is stored in
the j-th column of the array AB as follows: if UPLO ='U',
AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L',
AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
Page 1
DPBCON(3F) DPBCON(3F)
ANORM (input) DOUBLE PRECISION
The 1-norm (or infinity-norm) of the symmetric band matrix A.
RCOND (output) 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 (workspace) DOUBLE PRECISION array, dimension (3*N)
IWORK (workspace) INTEGER array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
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