LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  ztpqrt2 (M, N, L, A, LDA, B, LDB, T, LDT, INFO) 
ZTPQRT2 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 ztpqrt2  (  integer  M, 
integer  N,  
integer  L,  
complex*16, dimension( lda, * )  A,  
integer  LDA,  
complex*16, dimension( ldb, * )  B,  
integer  LDB,  
complex*16, dimension( ldt, * )  T,  
integer  LDT,  
integer  INFO  
) 
ZTPQRT2 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 ZTPQRT2 + dependencies [TGZ] [ZIP] [TXT]ZTPQRT2 computes a 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 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 COMPLEX*16 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*16 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*16 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**H 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 ztpqrt2.f.