.TH "hbev" 3 "Tue Jan 28 2025 00:54:31" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
hbev \- {hb,sb}ev: eig, QR iteration
.SH SYNOPSIS
.br
.PP
.SS "Functions"
.in +1c
.ti -1c
.RI "subroutine \fBchbev\fP (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, rwork, info)"
.br
.RI "\fB CHBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP "
.ti -1c
.RI "subroutine \fBdsbev\fP (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, info)"
.br
.RI "\fB DSBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP "
.ti -1c
.RI "subroutine \fBssbev\fP (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, info)"
.br
.RI "\fB SSBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP "
.ti -1c
.RI "subroutine \fBzhbev\fP (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, rwork, info)"
.br
.RI "\fB ZHBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP "
.in -1c
.SH "Detailed Description"
.PP
.SH "Function Documentation"
.PP
.SS "subroutine chbev (character jobz, character uplo, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) w, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)"
.PP
\fB CHBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP
.PP
\fBPurpose:\fP
.RS 4
.PP
.nf
CHBEV computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian band matrix A\&.
.fi
.PP
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBZ\fP
.PP
.nf
JOBZ is CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors\&.
.fi
.PP
.br
\fIUPLO\fP
.PP
.nf
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored\&.
.fi
.PP
.br
\fIN\fP
.PP
.nf
N is INTEGER
The order of the matrix A\&. N >= 0\&.
.fi
.PP
.br
\fIKD\fP
.PP
.nf
KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'\&. KD >= 0\&.
.fi
.PP
.br
\fIAB\fP
.PP
.nf
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, AB is overwritten by values generated during the
reduction to tridiagonal form\&. If UPLO = 'U', the first
superdiagonal and the diagonal of the tridiagonal matrix T
are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
the diagonal and first subdiagonal of T are returned in the
first two rows of AB\&.
.fi
.PP
.br
\fILDAB\fP
.PP
.nf
LDAB is INTEGER
The leading dimension of the array AB\&. LDAB >= KD + 1\&.
.fi
.PP
.br
\fIW\fP
.PP
.nf
W is REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order\&.
.fi
.PP
.br
\fIZ\fP
.PP
.nf
Z is COMPLEX array, dimension (LDZ, N)
If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
eigenvectors of the matrix A, with the i-th column of Z
holding the eigenvector associated with W(i)\&.
If JOBZ = 'N', then Z is not referenced\&.
.fi
.PP
.br
\fILDZ\fP
.PP
.nf
LDZ is INTEGER
The leading dimension of the array Z\&. LDZ >= 1, and if
JOBZ = 'V', LDZ >= max(1,N)\&.
.fi
.PP
.br
\fIWORK\fP
.PP
.nf
WORK is COMPLEX array, dimension (N)
.fi
.PP
.br
\fIRWORK\fP
.PP
.nf
RWORK is REAL array, dimension (max(1,3*N-2))
.fi
.PP
.br
\fIINFO\fP
.PP
.nf
INFO is INTEGER
= 0: successful exit\&.
< 0: if INFO = -i, the i-th argument had an illegal value\&.
> 0: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero\&.
.fi
.PP
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee
.PP
Univ\&. of California Berkeley
.PP
Univ\&. of Colorado Denver
.PP
NAG Ltd\&.
.RE
.PP
.SS "subroutine dsbev (character jobz, character uplo, integer n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) w, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer info)"
.PP
\fB DSBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP
.PP
\fBPurpose:\fP
.RS 4
.PP
.nf
DSBEV computes all the eigenvalues and, optionally, eigenvectors of
a real symmetric band matrix A\&.
.fi
.PP
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBZ\fP
.PP
.nf
JOBZ is CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors\&.
.fi
.PP
.br
\fIUPLO\fP
.PP
.nf
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored\&.
.fi
.PP
.br
\fIN\fP
.PP
.nf
N is INTEGER
The order of the matrix A\&. N >= 0\&.
.fi
.PP
.br
\fIKD\fP
.PP
.nf
KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'\&. KD >= 0\&.
.fi
.PP
.br
\fIAB\fP
.PP
.nf
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, AB is overwritten by values generated during the
reduction to tridiagonal form\&. If UPLO = 'U', the first
superdiagonal and the diagonal of the tridiagonal matrix T
are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
the diagonal and first subdiagonal of T are returned in the
first two rows of AB\&.
.fi
.PP
.br
\fILDAB\fP
.PP
.nf
LDAB is INTEGER
The leading dimension of the array AB\&. LDAB >= KD + 1\&.
.fi
.PP
.br
\fIW\fP
.PP
.nf
W is DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order\&.
.fi
.PP
.br
\fIZ\fP
.PP
.nf
Z is DOUBLE PRECISION array, dimension (LDZ, N)
If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
eigenvectors of the matrix A, with the i-th column of Z
holding the eigenvector associated with W(i)\&.
If JOBZ = 'N', then Z is not referenced\&.
.fi
.PP
.br
\fILDZ\fP
.PP
.nf
LDZ is INTEGER
The leading dimension of the array Z\&. LDZ >= 1, and if
JOBZ = 'V', LDZ >= max(1,N)\&.
.fi
.PP
.br
\fIWORK\fP
.PP
.nf
WORK is DOUBLE PRECISION array, dimension (max(1,3*N-2))
.fi
.PP
.br
\fIINFO\fP
.PP
.nf
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero\&.
.fi
.PP
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee
.PP
Univ\&. of California Berkeley
.PP
Univ\&. of Colorado Denver
.PP
NAG Ltd\&.
.RE
.PP
.SS "subroutine ssbev (character jobz, character uplo, integer n, integer kd, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer info)"
.PP
\fB SSBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP
.PP
\fBPurpose:\fP
.RS 4
.PP
.nf
SSBEV computes all the eigenvalues and, optionally, eigenvectors of
a real symmetric band matrix A\&.
.fi
.PP
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBZ\fP
.PP
.nf
JOBZ is CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors\&.
.fi
.PP
.br
\fIUPLO\fP
.PP
.nf
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored\&.
.fi
.PP
.br
\fIN\fP
.PP
.nf
N is INTEGER
The order of the matrix A\&. N >= 0\&.
.fi
.PP
.br
\fIKD\fP
.PP
.nf
KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'\&. KD >= 0\&.
.fi
.PP
.br
\fIAB\fP
.PP
.nf
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, AB is overwritten by values generated during the
reduction to tridiagonal form\&. If UPLO = 'U', the first
superdiagonal and the diagonal of the tridiagonal matrix T
are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
the diagonal and first subdiagonal of T are returned in the
first two rows of AB\&.
.fi
.PP
.br
\fILDAB\fP
.PP
.nf
LDAB is INTEGER
The leading dimension of the array AB\&. LDAB >= KD + 1\&.
.fi
.PP
.br
\fIW\fP
.PP
.nf
W is REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order\&.
.fi
.PP
.br
\fIZ\fP
.PP
.nf
Z is REAL array, dimension (LDZ, N)
If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
eigenvectors of the matrix A, with the i-th column of Z
holding the eigenvector associated with W(i)\&.
If JOBZ = 'N', then Z is not referenced\&.
.fi
.PP
.br
\fILDZ\fP
.PP
.nf
LDZ is INTEGER
The leading dimension of the array Z\&. LDZ >= 1, and if
JOBZ = 'V', LDZ >= max(1,N)\&.
.fi
.PP
.br
\fIWORK\fP
.PP
.nf
WORK is REAL array, dimension (max(1,3*N-2))
.fi
.PP
.br
\fIINFO\fP
.PP
.nf
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero\&.
.fi
.PP
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee
.PP
Univ\&. of California Berkeley
.PP
Univ\&. of Colorado Denver
.PP
NAG Ltd\&.
.RE
.PP
.SS "subroutine zhbev (character jobz, character uplo, integer n, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)"
.PP
\fB ZHBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP
.PP
\fBPurpose:\fP
.RS 4
.PP
.nf
ZHBEV computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian band matrix A\&.
.fi
.PP
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBZ\fP
.PP
.nf
JOBZ is CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors\&.
.fi
.PP
.br
\fIUPLO\fP
.PP
.nf
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored\&.
.fi
.PP
.br
\fIN\fP
.PP
.nf
N is INTEGER
The order of the matrix A\&. N >= 0\&.
.fi
.PP
.br
\fIKD\fP
.PP
.nf
KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'\&. KD >= 0\&.
.fi
.PP
.br
\fIAB\fP
.PP
.nf
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, AB is overwritten by values generated during the
reduction to tridiagonal form\&. If UPLO = 'U', the first
superdiagonal and the diagonal of the tridiagonal matrix T
are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
the diagonal and first subdiagonal of T are returned in the
first two rows of AB\&.
.fi
.PP
.br
\fILDAB\fP
.PP
.nf
LDAB is INTEGER
The leading dimension of the array AB\&. LDAB >= KD + 1\&.
.fi
.PP
.br
\fIW\fP
.PP
.nf
W is DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order\&.
.fi
.PP
.br
\fIZ\fP
.PP
.nf
Z is COMPLEX*16 array, dimension (LDZ, N)
If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
eigenvectors of the matrix A, with the i-th column of Z
holding the eigenvector associated with W(i)\&.
If JOBZ = 'N', then Z is not referenced\&.
.fi
.PP
.br
\fILDZ\fP
.PP
.nf
LDZ is INTEGER
The leading dimension of the array Z\&. LDZ >= 1, and if
JOBZ = 'V', LDZ >= max(1,N)\&.
.fi
.PP
.br
\fIWORK\fP
.PP
.nf
WORK is COMPLEX*16 array, dimension (N)
.fi
.PP
.br
\fIRWORK\fP
.PP
.nf
RWORK is DOUBLE PRECISION array, dimension (max(1,3*N-2))
.fi
.PP
.br
\fIINFO\fP
.PP
.nf
INFO is INTEGER
= 0: successful exit\&.
< 0: if INFO = -i, the i-th argument had an illegal value\&.
> 0: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero\&.
.fi
.PP
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee
.PP
Univ\&. of California Berkeley
.PP
Univ\&. of Colorado Denver
.PP
NAG Ltd\&.
.RE
.PP
.SH "Author"
.PP
Generated automatically by Doxygen for LAPACK from the source code\&.