LAPACK
3.4.2
LAPACK: Linear Algebra PACKage
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Go to the source code of this file.
Functions/Subroutines | |
subroutine | chbtrd (VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO) |
CHBTRD |
subroutine chbtrd | ( | character | VECT, |
character | UPLO, | ||
integer | N, | ||
integer | KD, | ||
complex, dimension( ldab, * ) | AB, | ||
integer | LDAB, | ||
real, dimension( * ) | D, | ||
real, dimension( * ) | E, | ||
complex, dimension( ldq, * ) | Q, | ||
integer | LDQ, | ||
complex, dimension( * ) | WORK, | ||
integer | INFO | ||
) |
CHBTRD
Download CHBTRD + dependencies [TGZ] [ZIP] [TXT]CHBTRD reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation: Q**H * A * Q = T.
[in] | VECT | VECT is CHARACTER*1 = 'N': do not form Q; = 'V': form Q; = 'U': update a matrix X, by forming X*Q. |
[in] | UPLO | UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. |
[in] | N | N is INTEGER The order of the matrix A. N >= 0. |
[in] | KD | KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. |
[in,out] | AB | AB is COMPLEX array, dimension (LDAB,N) On entry, the upper or lower triangle of the Hermitian 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,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). On exit, the diagonal elements of AB are overwritten by the diagonal elements of the tridiagonal matrix T; if KD > 0, the elements on the first superdiagonal (if UPLO = 'U') or the first subdiagonal (if UPLO = 'L') are overwritten by the off-diagonal elements of T; the rest of AB is overwritten by values generated during the reduction. |
[in] | LDAB | LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1. |
[out] | D | D is REAL array, dimension (N) The diagonal elements of the tridiagonal matrix T. |
[out] | E | E is REAL array, dimension (N-1) The off-diagonal elements of the tridiagonal matrix T: E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'. |
[in,out] | Q | Q is COMPLEX array, dimension (LDQ,N) On entry, if VECT = 'U', then Q must contain an N-by-N matrix X; if VECT = 'N' or 'V', then Q need not be set. On exit: if VECT = 'V', Q contains the N-by-N unitary matrix Q; if VECT = 'U', Q contains the product X*Q; if VECT = 'N', the array Q is not referenced. |
[in] | LDQ | LDQ is INTEGER The leading dimension of the array Q. LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'. |
[out] | WORK | WORK is COMPLEX array, dimension (N) |
[out] | INFO | INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value |
Modified by Linda Kaufman, Bell Labs.
Definition at line 163 of file chbtrd.f.