unbdb6(3)

NAME
unbdb6 - {un,or}bdb6: step in uncsd2by1

SYNOPSIS

  Functions

subroutine cunbdb6 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)
CUNBDB6
subroutine dorbdb6 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)
DORBDB6
subroutine sorbdb6 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)
SORBDB6
subroutine zunbdb6 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)
ZUNBDB6

Detailed Description

Function Documentation

  subroutine cunbdb6 (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)

CUNBDB6

Purpose:

    !>
    !> CUNBDB6 orthogonalizes the column vector
    !>      X = [ X1 ]
    !>          [ X2 ]
    !> with respect to the columns of
    !>      Q = [ Q1 ] .
    !>          [ Q2 ]
    !> The columns of Q must be orthonormal. The orthogonalized vector will
    !> be zero if and only if it lies entirely in the range of Q.
    !>
    !> The projection is computed with at most two iterations of the
    !> classical Gram-Schmidt algorithm, see
    !> * L. Giraud, J. Langou, M. Rozložník.
    !>   2002. CERFACS Technical Report No. TR/PA/02/33. URL:
    !>   https://www.cerfacs.fr/algor/reports/2002/TR_PA_02_33.pdf
    !>
    !>

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 dorbdb6 (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)

DORBDB6

Purpose:

    !>
    !> DORBDB6 orthogonalizes the column vector
    !>      X = [ X1 ]
    !>          [ X2 ]
    !> with respect to the columns of
    !>      Q = [ Q1 ] .
    !>          [ Q2 ]
    !> The columns of Q must be orthonormal. The orthogonalized vector will
    !> be zero if and only if it lies entirely in the range of Q.
    !>
    !> The projection is computed with at most two iterations of the
    !> classical Gram-Schmidt algorithm, see
    !> * L. Giraud, J. Langou, M. Rozložník.
    !>   2002. CERFACS Technical Report No. TR/PA/02/33. URL:
    !>   https://www.cerfacs.fr/algor/reports/2002/TR_PA_02_33.pdf
    !>
    !>

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 sorbdb6 (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)

SORBDB6

Purpose:

    !>
    !> SORBDB6 orthogonalizes the column vector
    !>      X = [ X1 ]
    !>          [ X2 ]
    !> with respect to the columns of
    !>      Q = [ Q1 ] .
    !>          [ Q2 ]
    !> The columns of Q must be orthonormal. The orthogonalized vector will
    !> be zero if and only if it lies entirely in the range of Q.
    !>
    !> The projection is computed with at most two iterations of the
    !> classical Gram-Schmidt algorithm, see
    !> * L. Giraud, J. Langou, M. Rozložník.
    !>   2002. CERFACS Technical Report No. TR/PA/02/33. URL:
    !>   https://www.cerfacs.fr/algor/reports/2002/TR_PA_02_33.pdf
    !>
    !>

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 zunbdb6 (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)

ZUNBDB6

Purpose:

    !>
    !> ZUNBDB6 orthogonalizes the column vector
    !>      X = [ X1 ]
    !>          [ X2 ]
    !> with respect to the columns of
    !>      Q = [ Q1 ] .
    !>          [ Q2 ]
    !> The columns of Q must be orthonormal. The orthogonalized vector will
    !> be zero if and only if it lies entirely in the range of Q.
    !>
    !> The projection is computed with at most two iterations of the
    !> classical Gram-Schmidt algorithm, see
    !> * L. Giraud, J. Langou, M. Rozložník.
    !>   2002. CERFACS Technical Report No. TR/PA/02/33. URL:
    !>   https://www.cerfacs.fr/algor/reports/2002/TR_PA_02_33.pdf
    !>
    !>

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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