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- A
- (
*input/output*) **REAL** or **COMPLEX**
array, shape .

On entry, the matrix .

On exit, has been overwritten by details of its
complete orthogonal factorization.

- B
- (
*input/output*) **REAL** or **COMPLEX** array,
shape with (**B**,1) (**A**,1),
(**A**,2)) or shape with =
(**A**,1), (**A**,2)).

On entry, the matrix .

On exit, rows to contain the solution matrix .

If
and
, the residual sum-of-squares for
the solution vector in a column of **B** is given by the sum of
squares of elements in rows
of that column.

- RANK
*Optional* (*output*) **INTEGER**.

The effective rank of , i.e., the order of the submatrix
. This is the same as the order of the submatrix
in the complete orthogonal factorization of .

- JPVT
*Optional* (*input/output*) **INTEGER** array,
shape with (**JPVT**) (**A**,2).

On entry, if
, the column of
is an initial column, otherwise it is a free column. Before
the factorization of , all initial columns are
permuted to the leading positions; only the remaining
free columns are moved as a result of column pivoting
during the factorization.

On exit, if
, then the column of
the matrix product was the column of .

- RCOND
*Optional* (*input*) **REAL**.

is used to determine the effective rank of .
This is defined as the order of the largest leading triangular
submatrix in the factorization of , with
pivoting, whose estimated condition number
.

Default value:
where *wp* is the working precision.

- INFO
*Optional* (*output*) **INTEGER**.

If is not present and an error occurs, then the program is
terminated with an error message.

**References**: [1] and [17,9,20,35].

** Next:** Example (from Program LA_GELSY_EXAMPLE)
** Up:** Linear Least Squares Problems
** Previous:** Purpose
** Contents**
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Susan Blackford
2001-08-19