.TH "hbgvd" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
hbgvd \- {hb,sb}gvd: eig, divide and conquer
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBchbgvd\fP (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)"
.br
.RI "\fBCHBGVD\fP "
.ti -1c
.RI "subroutine \fBdsbgvd\fP (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, lwork, iwork, liwork, info)"
.br
.RI "\fBDSBGVD\fP "
.ti -1c
.RI "subroutine \fBssbgvd\fP (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, lwork, iwork, liwork, info)"
.br
.RI "\fBSSBGVD\fP "
.ti -1c
.RI "subroutine \fBzhbgvd\fP (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)"
.br
.RI "\fBZHBGVD\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine chbgvd (character jobz, character uplo, integer n, integer ka, integer kb, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldbb, * ) bb, integer ldbb, real, dimension( * ) w, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info)"

.PP
\fBCHBGVD\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CHBGVD computes all the eigenvalues, and optionally, the eigenvectors
 of a complex generalized Hermitian-definite banded eigenproblem, of
 the form A*x=(lambda)*B*x\&. Here A and B are assumed to be Hermitian
 and banded, and B is also positive definite\&.  If eigenvectors are
 desired, it uses a divide and conquer algorithm\&.
.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 triangles of A and B are stored;
          = 'L':  Lower triangles of A and B are stored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrices A and B\&.  N >= 0\&.
.fi
.PP
.br
\fIKA\fP 
.PP
.nf
          KA is INTEGER
          The number of superdiagonals of the matrix A if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'\&. KA >= 0\&.
.fi
.PP
.br
\fIKB\fP 
.PP
.nf
          KB is INTEGER
          The number of superdiagonals of the matrix B if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'\&. KB >= 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 ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka)\&.

          On exit, the contents of AB are destroyed\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array AB\&.  LDAB >= KA+1\&.
.fi
.PP
.br
\fIBB\fP 
.PP
.nf
          BB is COMPLEX array, dimension (LDBB, N)
          On entry, the upper or lower triangle of the Hermitian band
          matrix B, stored in the first kb+1 rows of the array\&.  The
          j-th column of B is stored in the j-th column of the array BB
          as follows:
          if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
          if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb)\&.

          On exit, the factor S from the split Cholesky factorization
          B = S**H*S, as returned by CPBSTF\&.
.fi
.PP
.br
\fILDBB\fP 
.PP
.nf
          LDBB is INTEGER
          The leading dimension of the array BB\&.  LDBB >= KB+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 matrix Z of
          eigenvectors, with the i-th column of Z holding the
          eigenvector associated with W(i)\&. The eigenvectors are
          normalized so that Z**H*B*Z = 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 >= N\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX array, dimension (MAX(1,LWORK))
          On exit, if INFO=0, WORK(1) returns the optimal LWORK\&.
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          LWORK is INTEGER
          The dimension of the array WORK\&.
          If N <= 1,               LWORK >= 1\&.
          If JOBZ = 'N' and N > 1, LWORK >= N\&.
          If JOBZ = 'V' and N > 1, LWORK >= 2*N**2\&.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal sizes of the WORK, RWORK and
          IWORK arrays, returns these values as the first entries of
          the WORK, RWORK and IWORK arrays, and no error message
          related to LWORK or LRWORK or LIWORK is issued by XERBLA\&.
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
          RWORK is REAL array, dimension (MAX(1,LRWORK))
          On exit, if INFO=0, RWORK(1) returns the optimal LRWORK\&.
.fi
.PP
.br
\fILRWORK\fP 
.PP
.nf
          LRWORK is INTEGER
          The dimension of array RWORK\&.
          If N <= 1,               LRWORK >= 1\&.
          If JOBZ = 'N' and N > 1, LRWORK >= N\&.
          If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2\&.

          If LRWORK = -1, then a workspace query is assumed; the
          routine only calculates the optimal sizes of the WORK, RWORK
          and IWORK arrays, returns these values as the first entries
          of the WORK, RWORK and IWORK arrays, and no error message
          related to LWORK or LRWORK or LIWORK is issued by XERBLA\&.
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
          On exit, if INFO=0, IWORK(1) returns the optimal LIWORK\&.
.fi
.PP
.br
\fILIWORK\fP 
.PP
.nf
          LIWORK is INTEGER
          The dimension of array IWORK\&.
          If JOBZ = 'N' or N <= 1, LIWORK >= 1\&.
          If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N\&.

          If LIWORK = -1, then a workspace query is assumed; the
          routine only calculates the optimal sizes of the WORK, RWORK
          and IWORK arrays, returns these values as the first entries
          of the WORK, RWORK and IWORK arrays, and no error message
          related to LWORK or LRWORK or LIWORK is issued by XERBLA\&.
.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, and i is:
             <= N:  the algorithm failed to converge:
                    i off-diagonal elements of an intermediate
                    tridiagonal form did not converge to zero;
             > N:   if INFO = N + i, for 1 <= i <= N, then CPBSTF
                    returned INFO = i: B is not positive definite\&.
                    The factorization of B could not be completed and
                    no eigenvalues or eigenvectors were computed\&.
.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
\fBContributors:\fP
.RS 4
Mark Fahey, Department of Mathematics, Univ\&. of Kentucky, USA 
.RE
.PP

.SS "subroutine dsbgvd (character jobz, character uplo, integer n, integer ka, integer kb, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( ldbb, * ) bb, integer ldbb, double precision, dimension( * ) w, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)"

.PP
\fBDSBGVD\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DSBGVD computes all the eigenvalues, and optionally, the eigenvectors
 of a real generalized symmetric-definite banded eigenproblem, of the
 form A*x=(lambda)*B*x\&.  Here A and B are assumed to be symmetric and
 banded, and B is also positive definite\&.  If eigenvectors are
 desired, it uses a divide and conquer algorithm\&.
.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 triangles of A and B are stored;
          = 'L':  Lower triangles of A and B are stored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrices A and B\&.  N >= 0\&.
.fi
.PP
.br
\fIKA\fP 
.PP
.nf
          KA is INTEGER
          The number of superdiagonals of the matrix A if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'\&.  KA >= 0\&.
.fi
.PP
.br
\fIKB\fP 
.PP
.nf
          KB is INTEGER
          The number of superdiagonals of the matrix B if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'\&.  KB >= 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 ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka)\&.

          On exit, the contents of AB are destroyed\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array AB\&.  LDAB >= KA+1\&.
.fi
.PP
.br
\fIBB\fP 
.PP
.nf
          BB is DOUBLE PRECISION array, dimension (LDBB, N)
          On entry, the upper or lower triangle of the symmetric band
          matrix B, stored in the first kb+1 rows of the array\&.  The
          j-th column of B is stored in the j-th column of the array BB
          as follows:
          if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
          if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb)\&.

          On exit, the factor S from the split Cholesky factorization
          B = S**T*S, as returned by DPBSTF\&.
.fi
.PP
.br
\fILDBB\fP 
.PP
.nf
          LDBB is INTEGER
          The leading dimension of the array BB\&.  LDBB >= KB+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 matrix Z of
          eigenvectors, with the i-th column of Z holding the
          eigenvector associated with W(i)\&.  The eigenvectors are
          normalized so Z**T*B*Z = 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,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          LWORK is INTEGER
          The dimension of the array WORK\&.
          If N <= 1,               LWORK >= 1\&.
          If JOBZ = 'N' and N > 1, LWORK >= 2*N\&.
          If JOBZ = 'V' and N > 1, LWORK >= 1 + 5*N + 2*N**2\&.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal sizes of the WORK and IWORK
          arrays, returns these values as the first entries of the WORK
          and IWORK arrays, and no error message related to LWORK or
          LIWORK is issued by XERBLA\&.
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
          On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK\&.
.fi
.PP
.br
\fILIWORK\fP 
.PP
.nf
          LIWORK is INTEGER
          The dimension of the array IWORK\&.
          If JOBZ  = 'N' or N <= 1, LIWORK >= 1\&.
          If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N\&.

          If LIWORK = -1, then a workspace query is assumed; the
          routine only calculates the optimal sizes of the WORK and
          IWORK arrays, returns these values as the first entries of
          the WORK and IWORK arrays, and no error message related to
          LWORK or LIWORK is issued by XERBLA\&.
.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, and i is:
             <= N:  the algorithm failed to converge:
                    i off-diagonal elements of an intermediate
                    tridiagonal form did not converge to zero;
             > N:   if INFO = N + i, for 1 <= i <= N, then DPBSTF
                    returned INFO = i: B is not positive definite\&.
                    The factorization of B could not be completed and
                    no eigenvalues or eigenvectors were computed\&.
.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
\fBContributors:\fP
.RS 4
Mark Fahey, Department of Mathematics, Univ\&. of Kentucky, USA 
.RE
.PP

.SS "subroutine ssbgvd (character jobz, character uplo, integer n, integer ka, integer kb, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldbb, * ) bb, integer ldbb, real, dimension( * ) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)"

.PP
\fBSSBGVD\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SSBGVD computes all the eigenvalues, and optionally, the eigenvectors
 of a real generalized symmetric-definite banded eigenproblem, of the
 form A*x=(lambda)*B*x\&.  Here A and B are assumed to be symmetric and
 banded, and B is also positive definite\&.  If eigenvectors are
 desired, it uses a divide and conquer algorithm\&.
.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 triangles of A and B are stored;
          = 'L':  Lower triangles of A and B are stored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrices A and B\&.  N >= 0\&.
.fi
.PP
.br
\fIKA\fP 
.PP
.nf
          KA is INTEGER
          The number of superdiagonals of the matrix A if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'\&.  KA >= 0\&.
.fi
.PP
.br
\fIKB\fP 
.PP
.nf
          KB is INTEGER
          The number of superdiagonals of the matrix B if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'\&.  KB >= 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 ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka)\&.

          On exit, the contents of AB are destroyed\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array AB\&.  LDAB >= KA+1\&.
.fi
.PP
.br
\fIBB\fP 
.PP
.nf
          BB is REAL array, dimension (LDBB, N)
          On entry, the upper or lower triangle of the symmetric band
          matrix B, stored in the first kb+1 rows of the array\&.  The
          j-th column of B is stored in the j-th column of the array BB
          as follows:
          if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
          if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb)\&.

          On exit, the factor S from the split Cholesky factorization
          B = S**T*S, as returned by SPBSTF\&.
.fi
.PP
.br
\fILDBB\fP 
.PP
.nf
          LDBB is INTEGER
          The leading dimension of the array BB\&.  LDBB >= KB+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 matrix Z of
          eigenvectors, with the i-th column of Z holding the
          eigenvector associated with W(i)\&.  The eigenvectors are
          normalized so Z**T*B*Z = 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,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          LWORK is INTEGER
          The dimension of the array WORK\&.
          If N <= 1,               LWORK >= 1\&.
          If JOBZ = 'N' and N > 1, LWORK >= 3*N\&.
          If JOBZ = 'V' and N > 1, LWORK >= 1 + 5*N + 2*N**2\&.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal sizes of the WORK and IWORK
          arrays, returns these values as the first entries of the WORK
          and IWORK arrays, and no error message related to LWORK or
          LIWORK is issued by XERBLA\&.
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
          On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK\&.
.fi
.PP
.br
\fILIWORK\fP 
.PP
.nf
          LIWORK is INTEGER
          The dimension of the array IWORK\&.
          If JOBZ  = 'N' or N <= 1, LIWORK >= 1\&.
          If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N\&.

          If LIWORK = -1, then a workspace query is assumed; the
          routine only calculates the optimal sizes of the WORK and
          IWORK arrays, returns these values as the first entries of
          the WORK and IWORK arrays, and no error message related to
          LWORK or LIWORK is issued by XERBLA\&.
.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, and i is:
             <= N:  the algorithm failed to converge:
                    i off-diagonal elements of an intermediate
                    tridiagonal form did not converge to zero;
             > N:   if INFO = N + i, for 1 <= i <= N, then SPBSTF
                    returned INFO = i: B is not positive definite\&.
                    The factorization of B could not be completed and
                    no eigenvalues or eigenvectors were computed\&.
.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
\fBContributors:\fP
.RS 4
Mark Fahey, Department of Mathematics, Univ\&. of Kentucky, USA 
.RE
.PP

.SS "subroutine zhbgvd (character jobz, character uplo, integer n, integer ka, integer kb, complex*16, dimension( ldab, * ) ab, integer ldab, complex*16, dimension( ldbb, * ) bb, integer ldbb, double precision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info)"

.PP
\fBZHBGVD\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZHBGVD computes all the eigenvalues, and optionally, the eigenvectors
 of a complex generalized Hermitian-definite banded eigenproblem, of
 the form A*x=(lambda)*B*x\&. Here A and B are assumed to be Hermitian
 and banded, and B is also positive definite\&.  If eigenvectors are
 desired, it uses a divide and conquer algorithm\&.
.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 triangles of A and B are stored;
          = 'L':  Lower triangles of A and B are stored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrices A and B\&.  N >= 0\&.
.fi
.PP
.br
\fIKA\fP 
.PP
.nf
          KA is INTEGER
          The number of superdiagonals of the matrix A if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'\&. KA >= 0\&.
.fi
.PP
.br
\fIKB\fP 
.PP
.nf
          KB is INTEGER
          The number of superdiagonals of the matrix B if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'\&. KB >= 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 ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka)\&.

          On exit, the contents of AB are destroyed\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array AB\&.  LDAB >= KA+1\&.
.fi
.PP
.br
\fIBB\fP 
.PP
.nf
          BB is COMPLEX*16 array, dimension (LDBB, N)
          On entry, the upper or lower triangle of the Hermitian band
          matrix B, stored in the first kb+1 rows of the array\&.  The
          j-th column of B is stored in the j-th column of the array BB
          as follows:
          if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
          if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb)\&.

          On exit, the factor S from the split Cholesky factorization
          B = S**H*S, as returned by ZPBSTF\&.
.fi
.PP
.br
\fILDBB\fP 
.PP
.nf
          LDBB is INTEGER
          The leading dimension of the array BB\&.  LDBB >= KB+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 matrix Z of
          eigenvectors, with the i-th column of Z holding the
          eigenvector associated with W(i)\&. The eigenvectors are
          normalized so that Z**H*B*Z = 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 >= N\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
          On exit, if INFO=0, WORK(1) returns the optimal LWORK\&.
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          LWORK is INTEGER
          The dimension of the array WORK\&.
          If N <= 1,               LWORK >= 1\&.
          If JOBZ = 'N' and N > 1, LWORK >= N\&.
          If JOBZ = 'V' and N > 1, LWORK >= 2*N**2\&.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal sizes of the WORK, RWORK and
          IWORK arrays, returns these values as the first entries of
          the WORK, RWORK and IWORK arrays, and no error message
          related to LWORK or LRWORK or LIWORK is issued by XERBLA\&.
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
          RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
          On exit, if INFO=0, RWORK(1) returns the optimal LRWORK\&.
.fi
.PP
.br
\fILRWORK\fP 
.PP
.nf
          LRWORK is INTEGER
          The dimension of array RWORK\&.
          If N <= 1,               LRWORK >= 1\&.
          If JOBZ = 'N' and N > 1, LRWORK >= N\&.
          If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2\&.

          If LRWORK = -1, then a workspace query is assumed; the
          routine only calculates the optimal sizes of the WORK, RWORK
          and IWORK arrays, returns these values as the first entries
          of the WORK, RWORK and IWORK arrays, and no error message
          related to LWORK or LRWORK or LIWORK is issued by XERBLA\&.
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
          On exit, if INFO=0, IWORK(1) returns the optimal LIWORK\&.
.fi
.PP
.br
\fILIWORK\fP 
.PP
.nf
          LIWORK is INTEGER
          The dimension of array IWORK\&.
          If JOBZ = 'N' or N <= 1, LIWORK >= 1\&.
          If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N\&.

          If LIWORK = -1, then a workspace query is assumed; the
          routine only calculates the optimal sizes of the WORK, RWORK
          and IWORK arrays, returns these values as the first entries
          of the WORK, RWORK and IWORK arrays, and no error message
          related to LWORK or LRWORK or LIWORK is issued by XERBLA\&.
.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, and i is:
             <= N:  the algorithm failed to converge:
                    i off-diagonal elements of an intermediate
                    tridiagonal form did not converge to zero;
             > N:   if INFO = N + i, for 1 <= i <= N, then ZPBSTF
                    returned INFO = i: B is not positive definite\&.
                    The factorization of B could not be completed and
                    no eigenvalues or eigenvectors were computed\&.
.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
\fBContributors:\fP
.RS 4
Mark Fahey, Department of Mathematics, Univ\&. of Kentucky, USA 
.RE
.PP

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.