LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
stpqrt.f File Reference

Go to the source code of this file.

## Functions/Subroutines

subroutine stpqrt (M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO)
STPQRT

## Function/Subroutine Documentation

 subroutine stpqrt ( integer M, integer N, integer L, integer NB, real, dimension( lda, * ) A, integer LDA, real, dimension( ldb, * ) B, integer LDB, real, dimension( ldt, * ) T, integer LDT, real, dimension( * ) WORK, integer INFO )

STPQRT

Purpose:
``` STPQRT computes a blocked QR factorization of a real
"triangular-pentagonal" matrix C, which is composed of a
triangular block A and pentagonal block B, using the compact
WY representation for Q.```
Parameters:
 [in] M ``` M is INTEGER The number of rows of the matrix B. M >= 0.``` [in] N ``` N is INTEGER The number of columns of the matrix B, and the order of the triangular matrix A. N >= 0.``` [in] L ``` L is INTEGER The number of rows of the upper trapezoidal part of B. MIN(M,N) >= L >= 0. See Further Details.``` [in] NB ``` NB is INTEGER The block size to be used in the blocked QR. N >= NB >= 1.``` [in,out] A ``` A is REAL array, dimension (LDA,N) On entry, the upper triangular N-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the upper triangular matrix R.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in,out] B ``` B is REAL array, dimension (LDB,N) On entry, the pentagonal M-by-N matrix B. The first M-L rows are rectangular, and the last L rows are upper trapezoidal. On exit, B contains the pentagonal matrix V. See Further Details.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M).``` [out] T ``` T is REAL array, dimension (LDT,N) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See Further Details.``` [in] LDT ``` LDT is INTEGER The leading dimension of the array T. LDT >= NB.``` [out] WORK ` WORK is REAL array, dimension (NB*N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```
Date:
April 2012
Further Details:
```  The input matrix C is a (N+M)-by-N matrix

C = [ A ]
[ B ]

where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal
matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N
upper trapezoidal matrix B2:

B = [ B1 ]  <- (M-L)-by-N rectangular
[ B2 ]  <-     L-by-N upper trapezoidal.

The upper trapezoidal matrix B2 consists of the first L rows of a
N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
B is rectangular M-by-N; if M=L=N, B is upper triangular.

The matrix W stores the elementary reflectors H(i) in the i-th column
below the diagonal (of A) in the (N+M)-by-N input matrix C

C = [ A ]  <- upper triangular N-by-N
[ B ]  <- M-by-N pentagonal

so that W can be represented as

W = [ I ]  <- identity, N-by-N
[ V ]  <- M-by-N, same form as B.

Thus, all of information needed for W is contained on exit in B, which
we call V above.  Note that V has the same form as B; that is,

V = [ V1 ] <- (M-L)-by-N rectangular
[ V2 ] <-     L-by-N upper trapezoidal.

The columns of V represent the vectors which define the H(i)'s.

The number of blocks is B = ceiling(N/NB), where each
block is of order NB except for the last block, which is of order
IB = N - (B-1)*NB.  For each of the B blocks, a upper triangular block
reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
for the last block) T's are stored in the NB-by-N matrix T as

T = [T1 T2 ... TB].```

Definition at line 189 of file stpqrt.f.

Here is the call graph for this function:

Here is the caller graph for this function: