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hbtrd

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
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)
subroutine dsbtrd (character vect, character uplo, integer n, integer kd,double precision, dimension( ldab, * ) ab, integer ldab, doubleprecision, dimension( * ) d, double precision, dimension( * ) e, doubleprecision, dimension( ldq, * ) q, integer ldq, double precision,dimension( * ) work, integer info)
subroutine ssbtrd (character vect, character uplo, integer n, integer kd,real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) d,real, dimension( * ) e, real, dimension( ldq, * ) q, integer ldq, real,dimension( * ) work, integer info)
subroutine zhbtrd (character vect, character uplo, integer n, integer kd,complex*16, dimension( ldab, * ) ab, integer ldab, double precision,dimension( * ) d, double precision, dimension( * ) e, complex*16,dimension( ldq, * ) q, integer ldq, complex*16, dimension( * ) work,integer info)
Author

NAME

hbtrd - {hb,sb}trd: reduction to tridiagonal

SYNOPSIS

Functions

subroutine chbtrd (vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work, info)
CHBTRD
subroutine dsbtrd (vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work, info)
DSBTRD
subroutine ssbtrd (vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work, info)
SSBTRD
subroutine zhbtrd (vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work, info)
ZHBTRD

Detailed Description

Function Documentation

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

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.

Parameters

VECT

VECT is CHARACTER*1
= ’N’: do not form Q;
= ’V’: form Q;
= ’U’: update a matrix X, by forming X*Q.

UPLO

UPLO is CHARACTER*1
= ’U’: Upper triangle of A is stored;
= ’L’: Lower triangle of A is stored.

N is INTEGER
The order of the matrix A. N >= 0.

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ’U’,
or the number of subdiagonals if UPLO = ’L’. KD >= 0.

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.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

D is REAL array, dimension (N)
The diagonal elements of the tridiagonal matrix T.

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’.

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.

LDQ

LDQ is INTEGER
The leading dimension of the array Q.
LDQ >= 1, and LDQ >= N if VECT = ’V’ or ’U’.

WORK

WORK is COMPLEX array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Modified by Linda Kaufman, Bell Labs.

subroutine dsbtrd (character vect, character uplo, integer n, integer kd,double precision, dimension( ldab, * ) ab, integer ldab, doubleprecision, dimension( * ) d, double precision, dimension( * ) e, doubleprecision, dimension( ldq, * ) q, integer ldq, double precision,dimension( * ) work, integer info)

DSBTRD

Purpose:

DSBTRD reduces a real symmetric band matrix A to symmetric
tridiagonal form T by an orthogonal similarity transformation:
Q**T * A * Q = T.

Parameters

VECT

VECT is CHARACTER*1
= ’N’: do not form Q;
= ’V’: form Q;
= ’U’: update a matrix X, by forming X*Q.

UPLO

UPLO is CHARACTER*1
= ’U’: Upper triangle of A is stored;
= ’L’: Lower triangle of A is stored.

N is INTEGER
The order of the matrix A. N >= 0.

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ’U’,
or the number of subdiagonals if UPLO = ’L’. KD >= 0.

AB is 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,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.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

D is DOUBLE PRECISION array, dimension (N)
The diagonal elements of the tridiagonal matrix T.

E is DOUBLE PRECISION 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’.

Q is DOUBLE PRECISION 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 orthogonal matrix Q;
if VECT = ’U’, Q contains the product X*Q;
if VECT = ’N’, the array Q is not referenced.

LDQ

LDQ is INTEGER
The leading dimension of the array Q.
LDQ >= 1, and LDQ >= N if VECT = ’V’ or ’U’.

WORK

WORK is DOUBLE PRECISION array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Modified by Linda Kaufman, Bell Labs.

subroutine ssbtrd (character vect, character uplo, integer n, integer kd,real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) d,real, dimension( * ) e, real, dimension( ldq, * ) q, integer ldq, real,dimension( * ) work, integer info)

SSBTRD

Purpose:

SSBTRD reduces a real symmetric band matrix A to symmetric
tridiagonal form T by an orthogonal similarity transformation:
Q**T * A * Q = T.

Parameters

VECT

VECT is CHARACTER*1
= ’N’: do not form Q;
= ’V’: form Q;
= ’U’: update a matrix X, by forming X*Q.

UPLO

UPLO is CHARACTER*1
= ’U’: Upper triangle of A is stored;
= ’L’: Lower triangle of A is stored.

N is INTEGER
The order of the matrix A. N >= 0.

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ’U’,
or the number of subdiagonals if UPLO = ’L’. KD >= 0.

AB is REAL 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,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.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

D is REAL array, dimension (N)
The diagonal elements of the tridiagonal matrix T.

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’.

Q is REAL 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 orthogonal matrix Q;
if VECT = ’U’, Q contains the product X*Q;
if VECT = ’N’, the array Q is not referenced.

LDQ

LDQ is INTEGER
The leading dimension of the array Q.
LDQ >= 1, and LDQ >= N if VECT = ’V’ or ’U’.

WORK

WORK is REAL array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Modified by Linda Kaufman, Bell Labs.

subroutine zhbtrd (character vect, character uplo, integer n, integer kd,complex16, dimension( ldab, ) ab, integer ldab, double precision,dimension( * ) d, double precision, dimension( * ) e, complex16,dimension( ldq, ) q, integer ldq, complex16, dimension( ) work,integer info)

ZHBTRD

Purpose:

ZHBTRD reduces a complex Hermitian band matrix A to real symmetric
tridiagonal form T by a unitary similarity transformation:
Q**H * A * Q = T.

Parameters

VECT

VECT is CHARACTER*1
= ’N’: do not form Q;
= ’V’: form Q;
= ’U’: update a matrix X, by forming X*Q.

UPLO

UPLO is CHARACTER*1
= ’U’: Upper triangle of A is stored;
= ’L’: Lower triangle of A is stored.

N is INTEGER
The order of the matrix A. N >= 0.

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ’U’,
or the number of subdiagonals if UPLO = ’L’. KD >= 0.

AB is COMPLEX*16 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.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

D is DOUBLE PRECISION array, dimension (N)
The diagonal elements of the tridiagonal matrix T.

E is DOUBLE PRECISION 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’.

Q is COMPLEX*16 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.

LDQ

LDQ is INTEGER
The leading dimension of the array Q.
LDQ >= 1, and LDQ >= N if VECT = ’V’ or ’U’.

WORK

WORK is COMPLEX*16 array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Modified by Linda Kaufman, Bell Labs.

Author

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