hbgst - Man Page

subroutine chbgst (vect, uplo, n, ka, kb, ab, ldab, bb, ldbb, x, ldx, work, rwork, info)
CHBGST
subroutine dsbgst (vect, uplo, n, ka, kb, ab, ldab, bb, ldbb, x, ldx, work, info)
DSBGST
subroutine ssbgst (vect, uplo, n, ka, kb, ab, ldab, bb, ldbb, x, ldx, work, info)
SSBGST
subroutine zhbgst (vect, uplo, n, ka, kb, ab, ldab, bb, ldbb, x, ldx, work, rwork, info)
ZHBGST

CHBGST  

Purpose:

 CHBGST reduces a complex Hermitian-definite banded generalized
 eigenproblem  A*x = lambda*B*x  to standard form  C*y = lambda*y,
 such that C has the same bandwidth as A.

 B must have been previously factorized as S**H*S by CPBSTF, using a
 split Cholesky factorization. A is overwritten by C = X**H*A*X, where
 X = S**(-1)*Q and Q is a unitary matrix chosen to preserve the
 bandwidth of A.

Parameters

VECT

          VECT is CHARACTER*1
          = 'N':  do not form the transformation matrix X;
          = 'V':  form X.

UPLO

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

N

          N is INTEGER
          The order of the matrices A and B.  N >= 0.

KA

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

KB

          KB is INTEGER
          The number of superdiagonals of the matrix B if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'.  KA >= KB >= 0.

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 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 transformed matrix X**H*A*X, stored in the same
          format as A.

LDAB

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

BB

          BB is COMPLEX array, dimension (LDBB,N)
          The banded factor S from the split Cholesky factorization of
          B, as returned by CPBSTF, stored in the first kb+1 rows of
          the array.

LDBB

          LDBB is INTEGER
          The leading dimension of the array BB.  LDBB >= KB+1.

X

          X is COMPLEX array, dimension (LDX,N)
          If VECT = 'V', the n-by-n matrix X.
          If VECT = 'N', the array X is not referenced.

LDX

          LDX is INTEGER
          The leading dimension of the array X.
          LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.

WORK

          WORK is COMPLEX array, dimension (N)

RWORK

          RWORK 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.

Definition at line 163 of file chbgst.f.

DSBGST  

Purpose:

 DSBGST reduces a real symmetric-definite banded generalized
 eigenproblem  A*x = lambda*B*x  to standard form  C*y = lambda*y,
 such that C has the same bandwidth as A.

 B must have been previously factorized as S**T*S by DPBSTF, using a
 split Cholesky factorization. A is overwritten by C = X**T*A*X, where
 X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the
 bandwidth of A.

Parameters

VECT

          VECT is CHARACTER*1
          = 'N':  do not form the transformation matrix X;
          = 'V':  form X.

UPLO

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

N

          N is INTEGER
          The order of the matrices A and B.  N >= 0.

KA

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

KB

          KB is INTEGER
          The number of superdiagonals of the matrix B if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'.  KA >= KB >= 0.

AB

          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 transformed matrix X**T*A*X, stored in the same
          format as A.

LDAB

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

BB

          BB is DOUBLE PRECISION array, dimension (LDBB,N)
          The banded factor S from the split Cholesky factorization of
          B, as returned by DPBSTF, stored in the first KB+1 rows of
          the array.

LDBB

          LDBB is INTEGER
          The leading dimension of the array BB.  LDBB >= KB+1.

X

          X is DOUBLE PRECISION array, dimension (LDX,N)
          If VECT = 'V', the n-by-n matrix X.
          If VECT = 'N', the array X is not referenced.

LDX

          LDX is INTEGER
          The leading dimension of the array X.
          LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.

WORK

          WORK is DOUBLE PRECISION array, dimension (2*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.

Definition at line 157 of file dsbgst.f.

SSBGST  

Purpose:

 SSBGST reduces a real symmetric-definite banded generalized
 eigenproblem  A*x = lambda*B*x  to standard form  C*y = lambda*y,
 such that C has the same bandwidth as A.

 B must have been previously factorized as S**T*S by SPBSTF, using a
 split Cholesky factorization. A is overwritten by C = X**T*A*X, where
 X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the
 bandwidth of A.

Parameters

VECT

          VECT is CHARACTER*1
          = 'N':  do not form the transformation matrix X;
          = 'V':  form X.

UPLO

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

N

          N is INTEGER
          The order of the matrices A and B.  N >= 0.

KA

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

KB

          KB is INTEGER
          The number of superdiagonals of the matrix B if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'.  KA >= KB >= 0.

AB

          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 transformed matrix X**T*A*X, stored in the same
          format as A.

LDAB

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

BB

          BB is REAL array, dimension (LDBB,N)
          The banded factor S from the split Cholesky factorization of
          B, as returned by SPBSTF, stored in the first KB+1 rows of
          the array.

LDBB

          LDBB is INTEGER
          The leading dimension of the array BB.  LDBB >= KB+1.

X

          X is REAL array, dimension (LDX,N)
          If VECT = 'V', the n-by-n matrix X.
          If VECT = 'N', the array X is not referenced.

LDX

          LDX is INTEGER
          The leading dimension of the array X.
          LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.

WORK

          WORK is REAL array, dimension (2*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.

Definition at line 157 of file ssbgst.f.

ZHBGST  

Purpose:

 ZHBGST reduces a complex Hermitian-definite banded generalized
 eigenproblem  A*x = lambda*B*x  to standard form  C*y = lambda*y,
 such that C has the same bandwidth as A.

 B must have been previously factorized as S**H*S by ZPBSTF, using a
 split Cholesky factorization. A is overwritten by C = X**H*A*X, where
 X = S**(-1)*Q and Q is a unitary matrix chosen to preserve the
 bandwidth of A.

Parameters

VECT

          VECT is CHARACTER*1
          = 'N':  do not form the transformation matrix X;
          = 'V':  form X.

UPLO

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

N

          N is INTEGER
          The order of the matrices A and B.  N >= 0.

KA

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

KB

          KB is INTEGER
          The number of superdiagonals of the matrix B if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'.  KA >= KB >= 0.

AB

          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 transformed matrix X**H*A*X, stored in the same
          format as A.

LDAB

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

BB

          BB is COMPLEX*16 array, dimension (LDBB,N)
          The banded factor S from the split Cholesky factorization of
          B, as returned by ZPBSTF, stored in the first kb+1 rows of
          the array.

LDBB

          LDBB is INTEGER
          The leading dimension of the array BB.  LDBB >= KB+1.

X

          X is COMPLEX*16 array, dimension (LDX,N)
          If VECT = 'V', the n-by-n matrix X.
          If VECT = 'N', the array X is not referenced.

LDX

          LDX is INTEGER
          The leading dimension of the array X.
          LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.

WORK

          WORK is COMPLEX*16 array, dimension (N)

RWORK

          RWORK 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.

Definition at line 163 of file zhbgst.f.