Visible to Intel only — GUID: GUID-4E76B45F-A4E9-4282-BA5E-463F6FD28B56
Visible to Intel only — GUID: GUID-4E76B45F-A4E9-4282-BA5E-463F6FD28B56
?tpqrt
Computes a blocked QR factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.
Syntax
call stpqrt(m, n, l, nb, a, lda, b, ldb, t, ldt, work, info)
call dtpqrt(m, n, l, nb, a, lda, b, ldb, t, ldt, work, info)
call ctpqrt(m, n, l, nb, a, lda, b, ldb, t, ldt, work, info)
call ztpqrt(m, n, l, nb, a, lda, b, ldb, t, ldt, work, info)
call tpqrt(a, b, t, nb[, info])
Include Files
- mkl.fi, lapack.f90
Description
The input matrix C is an (n+m)-by-n matrix
where A is an n-by-n upper triangular matrix, and B is an m-by-n pentagonal matrix consisting of an (m-l)-by-n rectangular matrix B1 on top of an l-by-n upper trapezoidal matrix B2:
The upper trapezoidal matrix B2 consists of the first l rows of an n-by-n upper triangular matrix, where 0 ≤ l ≤ min(m,n). If l=0, B is an m-by-n rectangular matrix. If m=l=n, B is upper triangular. The elementary reflectors H(i) are stored in the ith column below the diagonal in the (n+m)-by-n input matrix C. The structure of vectors defining the elementary reflectors is illustrated by:
The elements of the unit matrix I are not stored. Thus, V contains all of the necessary information, and is returned in array b.
Note that V has the same form as B:
The columns of V represent the vectors which define the H(i)s.
The number of blocks is k = ceiling(n/nb), where each block is of order nb except for the last block, which is of order ib = n - (k-1)*nb. For each of the k blocks, an upper triangular block reflector factor is computed: T1, T2, ..., Tk. The nb-by-nb (ib-by-ib for the last block) Tis are stored in the nb-by-n array t as
t = [T1T2 ... Tk] .
Input Parameters
- m
-
INTEGER. The total number of rows in the matrix B (m ≥ 0).
- n
-
INTEGER. The number of columns in B and the order of the triangular matrix A (n ≥ 0).
- l
-
INTEGER. The number of rows of the upper trapezoidal part of B (min(m, n) ≥ l ≥ 0).
- nb
-
INTEGER. The block size to use in the blocked QR factorization (n ≥ nb ≥ 1).
- a, b, work
-
REAL for stpqrt
DOUBLE PRECISION for dtpqrt
COMPLEX for ctpqrt
COMPLEX*16 for ztpqrt.
Arrays: a size (lda, n) contains the n-by-n upper triangular matrix A.
b size (ldb, n), the pentagonal m-by-n matrix B. The first (m-l) rows contain the rectangular B1 matrix, and the next l rows contain the upper trapezoidal B2 matrix.
work size (nb, n) is a workspace array.
- lda
-
INTEGER. The leading dimension of a; at least max(1, n).
- ldb
-
INTEGER. The leading dimension of b; at least max(1, m).
- ldt
-
INTEGER. The leading dimension of t; at least nb.
Output Parameters
- a
-
The elements on and above the diagonal of the array contain the upper triangular matrix R.
- b
-
The pentagonal matrix V.
- t
-
REAL for stpqrt
DOUBLE PRECISION for dtpqrt
COMPLEX for ctpqrt
COMPLEX*16 for ztpqrt.
Array, size (ldt, n).
The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks.
- info
-
INTEGER.
If info = 0, the execution is successful.
If info < 0 and info = -i, the ith argument had an illegal value.