ZLAQHB(3F) ZLAQHB(3F)
ZLAQHB - equilibrate a symmetric band matrix A using the scaling factors
in the vector S
SUBROUTINE ZLAQHB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
CHARACTER EQUED, UPLO
INTEGER KD, LDAB, N
DOUBLE PRECISION AMAX, SCOND
DOUBLE PRECISION S( * )
COMPLEX*16 AB( LDAB, * )
ZLAQHB 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) COMPLEX*16 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.
Page 1
ZLAQHB(3F) ZLAQHB(3F)
S (output) DOUBLE PRECISION array, dimension (N)
The scale factors for A.
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= 'Y': Equilibration was done, i.e., A has been replaced by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.
ZLAQHB(3F) ZLAQHB(3F)
ZLAQHB - equilibrate a symmetric band matrix A using the scaling factors
in the vector S
SUBROUTINE ZLAQHB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
CHARACTER EQUED, UPLO
INTEGER KD, LDAB, N
DOUBLE PRECISION AMAX, SCOND
DOUBLE PRECISION S( * )
COMPLEX*16 AB( LDAB, * )
ZLAQHB 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) COMPLEX*16 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.
Page 1
ZLAQHB(3F) ZLAQHB(3F)
S (output) DOUBLE PRECISION array, dimension (N)
The scale factors for A.
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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