LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  dtpqrt2 (M, N, L, A, LDA, B, LDB, T, LDT, INFO) 
DTPQRT2 computes a QR factorization of a real or complex "triangularpentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q. 
subroutine dtpqrt2  (  integer  M, 
integer  N,  
integer  L,  
double precision, dimension( lda, * )  A,  
integer  LDA,  
double precision, dimension( ldb, * )  B,  
integer  LDB,  
double precision, dimension( ldt, * )  T,  
integer  LDT,  
integer  INFO  
) 
DTPQRT2 computes a QR factorization of a real or complex "triangularpentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.
Download DTPQRT2 + dependencies [TGZ] [ZIP] [TXT]DTPQRT2 computes a QR factorization of a real "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 total 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,out]  A  A is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDT,N) The NbyN upper triangular factor T of the block reflector. See Further Details. 
[in]  LDT  LDT is INTEGER The leading dimension of the array T. LDT >= max(1,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 (M+N)by(M+N) block reflector H is then given by H = I  W * T * W**T where W^H is the conjugate transpose of W and T is the upper triangular factor of the block reflector.
Definition at line 174 of file dtpqrt2.f.