DLAQSB(3F) DLAQSB(3F)
DLAQSB - equilibrate a symmetric band matrix A using the scaling factors
in the vector S
SUBROUTINE DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
CHARACTER EQUED, UPLO
INTEGER KD, LDAB, N
DOUBLE PRECISION AMAX, SCOND
DOUBLE PRECISION AB( LDAB, * ), S( * )
DLAQSB equilibrates a symmetric band matrix A using the scaling factors
in the vector S.
UPLO (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored. = 'U': Upper triangular
= 'L': Lower triangular
N (input) INTEGER
The order of the matrix A. N >= 0.
KD (input) INTEGER
The number of super-diagonals of the matrix A if UPLO = 'U', or
the number of sub-diagonals if UPLO = 'L'. KD >= 0.
AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first KD+1 rows of the array. The j-th
column of A is stored in the j-th column of the array AB as
follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,jkd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for
j<=i<=min(n,j+kd).
On exit, if INFO = 0, the triangular factor U or L from the
Cholesky factorization A = U'*U or A = L*L' of the band matrix A,
in the same storage format as A.
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
S (output) DOUBLE PRECISION array, dimension (N)
The scale factors for A.
Page 1
DLAQSB(3F) DLAQSB(3F)
SCOND (input) DOUBLE PRECISION
Ratio of the smallest S(i) to the largest S(i).
AMAX (input) DOUBLE PRECISION
Absolute value of largest matrix entry.
EQUED (output) CHARACTER*1
Specifies whether or not equilibration was done. = 'N': No
equilibration.
= 'Y': Equilibration was done, i.e., A has been replaced by
diag(S) * A * diag(S).
THRESH is a threshold value used to decide if scaling should be done
based on the ratio of the scaling factors. If SCOND < THRESH, scaling is
done.
LARGE and SMALL are threshold values used to decide if scaling should be
done based on the absolute size of the largest matrix element. If AMAX >
LARGE or AMAX < SMALL, scaling is done.
DLAQSB(3F) DLAQSB(3F)
DLAQSB - equilibrate a symmetric band matrix A using the scaling factors
in the vector S
SUBROUTINE DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
CHARACTER EQUED, UPLO
INTEGER KD, LDAB, N
DOUBLE PRECISION AMAX, SCOND
DOUBLE PRECISION AB( LDAB, * ), S( * )
DLAQSB equilibrates a symmetric band matrix A using the scaling factors
in the vector S.
UPLO (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored. = 'U': Upper triangular
= 'L': Lower triangular
N (input) INTEGER
The order of the matrix A. N >= 0.
KD (input) INTEGER
The number of super-diagonals of the matrix A if UPLO = 'U', or
the number of sub-diagonals if UPLO = 'L'. KD >= 0.
AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first KD+1 rows of the array. The j-th
column of A is stored in the j-th column of the array AB as
follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,jkd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for
j<=i<=min(n,j+kd).
On exit, if INFO = 0, the triangular factor U or L from the
Cholesky factorization A = U'*U or A = L*L' of the band matrix A,
in the same storage format as A.
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
S (output) DOUBLE PRECISION array, dimension (N)
The scale factors for A.
Page 1
DLAQSB(3F) DLAQSB(3F)
SCOND (input) DOUBLE PRECISION
Ratio of the smallest S(i) to the largest S(i).
AMAX (input) DOUBLE PRECISION
Absolute value of largest matrix entry.
EQUED (output) CHARACTER*1
Specifies whether or not equilibration was done. = 'N': No
equilibration.
= 'Y': Equilibration was done, i.e., A has been replaced by
diag(S) * A * diag(S).
THRESH is a threshold value used to decide if scaling should be done
based on the ratio of the scaling factors. If SCOND < THRESH, scaling is
done.
LARGE and SMALL are threshold values used to decide if scaling should be
done based on the absolute size of the largest matrix element. If AMAX >
LARGE or AMAX < SMALL, scaling is done.
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