hbtrd(3)

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

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

    KD

              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

              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

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

    E

              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

              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.

Definition at line 161 of file chbtrd.f.

  subroutine dsbtrd (character vect, character uplo, integer n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, 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

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

    KD

              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

              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

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

    E

              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

              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.

Definition at line 161 of file dsbtrd.f.

  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

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

    KD

              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

              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

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

    E

              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

              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.

Definition at line 161 of file ssbtrd.f.

  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)

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

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

    KD

              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

              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

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

    E

              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

              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.

Definition at line 161 of file zhbtrd.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.