unbdb6(3) LAPACK unbdb6(3)

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


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

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. 'On the round-off error
   analysis of the Gram-Schmidt algorithm with reorthogonalization.'
   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.

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. 'On the round-off error
   analysis of the Gram-Schmidt algorithm with reorthogonalization.'
   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.

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. 'On the round-off error
   analysis of the Gram-Schmidt algorithm with reorthogonalization.'
   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.

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. 'On the round-off error
   analysis of the Gram-Schmidt algorithm with reorthogonalization.'
   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.

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