unbdb5(3)

NAME
unbdb5 - {un,or}bdb5: step in uncsd2by1

SYNOPSIS

  Functions

subroutine cunbdb5 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)
CUNBDB5
subroutine dorbdb5 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)
DORBDB5
subroutine sorbdb5 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)
SORBDB5
subroutine zunbdb5 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)
ZUNBDB5

Detailed Description

Function Documentation

  subroutine cunbdb5 (integer m1, integer m2, integer n, complex, dimension(*) x1, integer incx1, complex, dimension(*) x2, integer incx2, complex, dimension(ldq1,*) q1, integer ldq1, complex, dimension(ldq2,*) q2, integer ldq2, complex, dimension(*) work, integer lwork, integer info)

CUNBDB5

Purpose:

    !>
    !> CUNBDB5 orthogonalizes the column vector
    !>      X = [ X1 ]
    !>          [ X2 ]
    !> with respect to the columns of
    !>      Q = [ Q1 ] .
    !>          [ Q2 ]
    !> The columns of Q must be orthonormal.
    !>
    !> If the projection is zero according to Kahan's
    !> criterion, then some other vector from the orthogonal complement
    !> is returned. This vector is chosen in an arbitrary but deterministic
    !> way.
    !>
    !>

Parameters
    M1

    !>          M1 is INTEGER
    !>           The dimension of X1 and the number of rows in Q1. 0 <= M1.
    !>

    M2

    !>          M2 is INTEGER
    !>           The dimension of X2 and the number of rows in Q2. 0 <= M2.
    !>

    N

    !>          N is INTEGER
    !>           The number of columns in Q1 and Q2. 0 <= N.
    !>

    X1

    !>          X1 is COMPLEX array, dimension (M1)
    !>           On entry, the top part of the vector to be orthogonalized.
    !>           On exit, the top part of the projected vector.
    !>

    INCX1

    !>          INCX1 is INTEGER
    !>           Increment for entries of X1.
    !>

    X2

    !>          X2 is COMPLEX array, dimension (M2)
    !>           On entry, the bottom part of the vector to be
    !>           orthogonalized. On exit, the bottom part of the projected
    !>           vector.
    !>

    INCX2

    !>          INCX2 is INTEGER
    !>           Increment for entries of X2.
    !>

    Q1

    !>          Q1 is COMPLEX array, dimension (LDQ1, N)
    !>           The top part of the orthonormal basis matrix.
    !>

    LDQ1

    !>          LDQ1 is INTEGER
    !>           The leading dimension of Q1. LDQ1 >= M1.
    !>

    Q2

    !>          Q2 is COMPLEX array, dimension (LDQ2, N)
    !>           The bottom part of the orthonormal basis matrix.
    !>

    LDQ2

    !>          LDQ2 is INTEGER
    !>           The leading dimension of Q2. LDQ2 >= M2.
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (LWORK)
    !>

    LWORK

    !>          LWORK is INTEGER
    !>           The dimension of the array WORK. LWORK >= 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.

  subroutine dorbdb5 (integer m1, integer m2, integer n, double precision, dimension(*) x1, integer incx1, double precision, dimension(*) x2, integer incx2, double precision, dimension(ldq1,*) q1, integer ldq1, double precision, dimension(ldq2,*) q2, integer ldq2, double precision, dimension(*) work, integer lwork, integer info)

DORBDB5

Purpose:

    !>
    !> DORBDB5 orthogonalizes the column vector
    !>      X = [ X1 ]
    !>          [ X2 ]
    !> with respect to the columns of
    !>      Q = [ Q1 ] .
    !>          [ Q2 ]
    !> The columns of Q must be orthonormal.
    !>
    !> If the projection is zero according to Kahan's
    !> criterion, then some other vector from the orthogonal complement
    !> is returned. This vector is chosen in an arbitrary but deterministic
    !> way.
    !>
    !>

Parameters
    M1

    !>          M1 is INTEGER
    !>           The dimension of X1 and the number of rows in Q1. 0 <= M1.
    !>

    M2

    !>          M2 is INTEGER
    !>           The dimension of X2 and the number of rows in Q2. 0 <= M2.
    !>

    N

    !>          N is INTEGER
    !>           The number of columns in Q1 and Q2. 0 <= N.
    !>

    X1

    !>          X1 is DOUBLE PRECISION array, dimension (M1)
    !>           On entry, the top part of the vector to be orthogonalized.
    !>           On exit, the top part of the projected vector.
    !>

    INCX1

    !>          INCX1 is INTEGER
    !>           Increment for entries of X1.
    !>

    X2

    !>          X2 is DOUBLE PRECISION array, dimension (M2)
    !>           On entry, the bottom part of the vector to be
    !>           orthogonalized. On exit, the bottom part of the projected
    !>           vector.
    !>

    INCX2

    !>          INCX2 is INTEGER
    !>           Increment for entries of X2.
    !>

    Q1

    !>          Q1 is DOUBLE PRECISION array, dimension (LDQ1, N)
    !>           The top part of the orthonormal basis matrix.
    !>

    LDQ1

    !>          LDQ1 is INTEGER
    !>           The leading dimension of Q1. LDQ1 >= M1.
    !>

    Q2

    !>          Q2 is DOUBLE PRECISION array, dimension (LDQ2, N)
    !>           The bottom part of the orthonormal basis matrix.
    !>

    LDQ2

    !>          LDQ2 is INTEGER
    !>           The leading dimension of Q2. LDQ2 >= M2.
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (LWORK)
    !>

    LWORK

    !>          LWORK is INTEGER
    !>           The dimension of the array WORK. LWORK >= 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.

  subroutine sorbdb5 (integer m1, integer m2, integer n, real, dimension(*) x1, integer incx1, real, dimension(*) x2, integer incx2, real, dimension(ldq1,*) q1, integer ldq1, real, dimension(ldq2,*) q2, integer ldq2, real, dimension(*) work, integer lwork, integer info)

SORBDB5

Purpose:

    !>
    !> SORBDB5 orthogonalizes the column vector
    !>      X = [ X1 ]
    !>          [ X2 ]
    !> with respect to the columns of
    !>      Q = [ Q1 ] .
    !>          [ Q2 ]
    !> The columns of Q must be orthonormal.
    !>
    !> If the projection is zero according to Kahan's
    !> criterion, then some other vector from the orthogonal complement
    !> is returned. This vector is chosen in an arbitrary but deterministic
    !> way.
    !>
    !>

Parameters
    M1

    !>          M1 is INTEGER
    !>           The dimension of X1 and the number of rows in Q1. 0 <= M1.
    !>

    M2

    !>          M2 is INTEGER
    !>           The dimension of X2 and the number of rows in Q2. 0 <= M2.
    !>

    N

    !>          N is INTEGER
    !>           The number of columns in Q1 and Q2. 0 <= N.
    !>

    X1

    !>          X1 is REAL array, dimension (M1)
    !>           On entry, the top part of the vector to be orthogonalized.
    !>           On exit, the top part of the projected vector.
    !>

    INCX1

    !>          INCX1 is INTEGER
    !>           Increment for entries of X1.
    !>

    X2

    !>          X2 is REAL array, dimension (M2)
    !>           On entry, the bottom part of the vector to be
    !>           orthogonalized. On exit, the bottom part of the projected
    !>           vector.
    !>

    INCX2

    !>          INCX2 is INTEGER
    !>           Increment for entries of X2.
    !>

    Q1

    !>          Q1 is REAL array, dimension (LDQ1, N)
    !>           The top part of the orthonormal basis matrix.
    !>

    LDQ1

    !>          LDQ1 is INTEGER
    !>           The leading dimension of Q1. LDQ1 >= M1.
    !>

    Q2

    !>          Q2 is REAL array, dimension (LDQ2, N)
    !>           The bottom part of the orthonormal basis matrix.
    !>

    LDQ2

    !>          LDQ2 is INTEGER
    !>           The leading dimension of Q2. LDQ2 >= M2.
    !>

    WORK

    !>          WORK is REAL array, dimension (LWORK)
    !>

    LWORK

    !>          LWORK is INTEGER
    !>           The dimension of the array WORK. LWORK >= 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.

  subroutine zunbdb5 (integer m1, integer m2, integer n, complex*16, dimension(*) x1, integer incx1, complex*16, dimension(*) x2, integer incx2, complex*16, dimension(ldq1,*) q1, integer ldq1, complex*16, dimension(ldq2,*) q2, integer ldq2, complex*16, dimension(*) work, integer lwork, integer info)

ZUNBDB5

Purpose:

    !>
    !> ZUNBDB5 orthogonalizes the column vector
    !>      X = [ X1 ]
    !>          [ X2 ]
    !> with respect to the columns of
    !>      Q = [ Q1 ] .
    !>          [ Q2 ]
    !> The columns of Q must be orthonormal.
    !>
    !> If the projection is zero according to Kahan's
    !> criterion, then some other vector from the orthogonal complement
    !> is returned. This vector is chosen in an arbitrary but deterministic
    !> way.
    !>
    !>

Parameters
    M1

    !>          M1 is INTEGER
    !>           The dimension of X1 and the number of rows in Q1. 0 <= M1.
    !>

    M2

    !>          M2 is INTEGER
    !>           The dimension of X2 and the number of rows in Q2. 0 <= M2.
    !>

    N

    !>          N is INTEGER
    !>           The number of columns in Q1 and Q2. 0 <= N.
    !>

    X1

    !>          X1 is COMPLEX*16 array, dimension (M1)
    !>           On entry, the top part of the vector to be orthogonalized.
    !>           On exit, the top part of the projected vector.
    !>

    INCX1

    !>          INCX1 is INTEGER
    !>           Increment for entries of X1.
    !>

    X2

    !>          X2 is COMPLEX*16 array, dimension (M2)
    !>           On entry, the bottom part of the vector to be
    !>           orthogonalized. On exit, the bottom part of the projected
    !>           vector.
    !>

    INCX2

    !>          INCX2 is INTEGER
    !>           Increment for entries of X2.
    !>

    Q1

    !>          Q1 is COMPLEX*16 array, dimension (LDQ1, N)
    !>           The top part of the orthonormal basis matrix.
    !>

    LDQ1

    !>          LDQ1 is INTEGER
    !>           The leading dimension of Q1. LDQ1 >= M1.
    !>

    Q2

    !>          Q2 is COMPLEX*16 array, dimension (LDQ2, N)
    !>           The bottom part of the orthonormal basis matrix.
    !>

    LDQ2

    !>          LDQ2 is INTEGER
    !>           The leading dimension of Q2. LDQ2 >= M2.
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (LWORK)
    !>

    LWORK

    !>          LWORK is INTEGER
    !>           The dimension of the array WORK. LWORK >= 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.

Author

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