chbtrd (l) - Linux Manuals
chbtrd: reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
Command to display chbtrd manual in Linux: $ man l chbtrd
NAME
CHBTRD - reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
SYNOPSIS
- SUBROUTINE CHBTRD(
-
VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ,
WORK, INFO )
-
CHARACTER
UPLO, VECT
-
INTEGER
INFO, KD, LDAB, LDQ, N
-
REAL
D( * ), E( * )
-
COMPLEX
AB( LDAB, * ), Q( LDQ, * ), WORK( * )
PURPOSE
CHBTRD reduces a complex Hermitian band matrix A to real symmetric
tridiagonal form T by a unitary similarity transformation:
Q**H * A * Q = T.
ARGUMENTS
- VECT (input) CHARACTER*1
-
= aqNaq: do not form Q;
= aqVaq: form Q;
= aqUaq: update a matrix X, by forming X*Q.
- UPLO (input) CHARACTER*1
-
= aqUaq: Upper triangle of A is stored;
= aqLaq: Lower triangle of A is stored.
- N (input) INTEGER
-
The order of the matrix A. N >= 0.
- KD (input) INTEGER
-
The number of superdiagonals of the matrix A if UPLO = aqUaq,
or the number of subdiagonals if UPLO = aqLaq. KD >= 0.
- AB (input/output) 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 = aqUaq, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = aqLaq, 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 = aqUaq) or the
first subdiagonal (if UPLO = aqLaq) are overwritten by the
off-diagonal elements of T; the rest of AB is overwritten by
values generated during the reduction.
- LDAB (input) INTEGER
-
The leading dimension of the array AB. LDAB >= KD+1.
- D (output) REAL array, dimension (N)
-
The diagonal elements of the tridiagonal matrix T.
- E (output) REAL array, dimension (N-1)
-
The off-diagonal elements of the tridiagonal matrix T:
E(i) = T(i,i+1) if UPLO = aqUaq; E(i) = T(i+1,i) if UPLO = aqLaq.
- Q (input/output) COMPLEX array, dimension (LDQ,N)
-
On entry, if VECT = aqUaq, then Q must contain an N-by-N
matrix X; if VECT = aqNaq or aqVaq, then Q need not be set.
On exit:
if VECT = aqVaq, Q contains the N-by-N unitary matrix Q;
if VECT = aqUaq, Q contains the product X*Q;
if VECT = aqNaq, the array Q is not referenced.
- LDQ (input) INTEGER
-
The leading dimension of the array Q.
LDQ >= 1, and LDQ >= N if VECT = aqVaq or aqUaq.
- WORK (workspace) COMPLEX array, dimension (N)
-
- INFO (output) INTEGER
-
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
FURTHER DETAILS
Modified by Linda Kaufman, Bell Labs.