LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  ctpqrt (M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO) 
CTPQRT 
subroutine ctpqrt  (  integer  M, 
integer  N,  
integer  L,  
integer  NB,  
complex, dimension( lda, * )  A,  
integer  LDA,  
complex, dimension( ldb, * )  B,  
integer  LDB,  
complex, dimension( ldt, * )  T,  
integer  LDT,  
complex, dimension( * )  WORK,  
integer  INFO  
) 
CTPQRT
Download CTPQRT + dependencies [TGZ] [ZIP] [TXT]CTPQRT computes a blocked QR factorization of a complex "triangularpentagonal" matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q.
[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 COMPLEX array, dimension (LDA,N) On entry, the upper triangular NbyN 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 COMPLEX array, dimension (LDB,N) On entry, the pentagonal MbyN matrix B. The first ML 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 COMPLEX 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 COMPLEX array, dimension (NB*N) 
[out]  INFO  INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value 
The input matrix C is a (N+M)byN matrix C = [ A ] [ B ] where A is an upper triangular NbyN matrix, and B is MbyN pentagonal matrix consisting of a (ML)byN rectangular matrix B1 on top of a LbyN upper trapezoidal matrix B2: B = [ B1 ] < (ML)byN rectangular [ B2 ] < LbyN upper trapezoidal. The upper trapezoidal matrix B2 consists of the first L rows of a NbyN upper triangular matrix, where 0 <= L <= MIN(M,N). If L=0, B is rectangular MbyN; if M=L=N, B is upper triangular. The matrix W stores the elementary reflectors H(i) in the ith column below the diagonal (of A) in the (N+M)byN input matrix C C = [ A ] < upper triangular NbyN [ B ] < MbyN pentagonal so that W can be represented as W = [ I ] < identity, NbyN [ V ] < MbyN, 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 ] < (ML)byN rectangular [ V2 ] < LbyN 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  (B1)*NB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The NBbyNB (and IBbyIB for the last block) T's are stored in the NBbyN matrix T as T = [T1 T2 ... TB].
Definition at line 189 of file ctpqrt.f.