LAPACK
3.8.0
LAPACK: Linear Algebra PACKage

subroutine stplqt  (  integer  M, 
integer  N,  
integer  L,  
integer  MB,  
real, dimension( lda, * )  A,  
integer  LDA,  
real, dimension( ldb, * )  B,  
integer  LDB,  
real, dimension( ldt, * )  T,  
integer  LDT,  
real, dimension( * )  WORK,  
integer  INFO  
) 
STPLQT
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DTPLQT computes a blocked LQ 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 number of rows of the matrix B, and the order of the triangular matrix A. M >= 0. 
[in]  N  N is INTEGER The number of columns of the matrix B. N >= 0. 
[in]  L  L is INTEGER The number of rows of the lower trapezoidal part of B. MIN(M,N) >= L >= 0. See Further Details. 
[in]  MB  MB is INTEGER The block size to be used in the blocked QR. M >= MB >= 1. 
[in,out]  A  A is REAL array, dimension (LDA,M) On entry, the lower triangular MbyM matrix A. On exit, the elements on and below the diagonal of the array contain the lower triangular matrix L. 
[in]  LDA  LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). 
[in,out]  B  B is REAL array, dimension (LDB,N) On entry, the pentagonal MbyN matrix B. The first NL columns are rectangular, and the last L columns are lower 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 lower 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 >= MB. 
[out]  WORK  WORK is REAL array, dimension (MB*M) 
[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 Mby(M+N) matrix C = [ A ] [ B ] where A is an lower triangular MbyM matrix, and B is MbyN pentagonal matrix consisting of a Mby(NL) rectangular matrix B1 on left of a MbyL upper trapezoidal matrix B2: [ B ] = [ B1 ] [ B2 ] [ B1 ] < Mby(NL) rectangular [ B2 ] < MbyL lower trapezoidal. The lower trapezoidal matrix B2 consists of the first L columns of a MbyM lower triangular matrix, where 0 <= L <= MIN(M,N). If L=0, B is rectangular MbyN; if M=L=N, B is lower triangular. The matrix W stores the elementary reflectors H(i) in the ith row above the diagonal (of A) in the Mby(M+N) input matrix C [ C ] = [ A ] [ B ] [ A ] < lower triangular MbyM [ B ] < MbyN pentagonal so that W can be represented as [ W ] = [ I ] [ V ] [ I ] < identity, MbyM [ 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 ] [ V2 ] [ V1 ] < Mby(NL) rectangular [ V2 ] < MbyL lower trapezoidal. The rows of V represent the vectors which define the H(i)'s. The number of blocks is B = ceiling(M/MB), where each block is of order MB except for the last block, which is of order IB = M  (M1)*MB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The MBbyMB (and IBbyIB for the last block) T's are stored in the MBbyN matrix T as T = [T1 T2 ... TB].
STPLQT computes a blocked LQ 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 number of rows of the matrix B, and the order of the triangular matrix A. M >= 0. 
[in]  N  N is INTEGER The number of columns of the matrix B. N >= 0. 
[in]  L  L is INTEGER The number of rows of the lower trapezoidal part of B. MIN(M,N) >= L >= 0. See Further Details. 
[in]  MB  MB is INTEGER The block size to be used in the blocked QR. M >= MB >= 1. 
[in,out]  A  A is REAL array, dimension (LDA,N) On entry, the lower triangular NbyN matrix A. On exit, the elements on and below the diagonal of the array contain the lower triangular matrix L. 
[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 MbyN matrix B. The first NL columns are rectangular, and the last L columns are lower 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 lower 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 >= MB. 
[out]  WORK  WORK is REAL array, dimension (MB*M) 
[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 Mby(M+N) matrix
C = [ A ] [ B ]
where A is an lower triangular NbyN matrix, and B is MbyN pentagonal matrix consisting of a Mby(NL) rectangular matrix B1 on left of a MbyL upper trapezoidal matrix B2: [ B ] = [ B1 ] [ B2 ] [ B1 ] < Mby(NL) rectangular [ B2 ] < MbyL upper trapezoidal.
The lower trapezoidal matrix B2 consists of the first L columns of a NbyN lower triangular matrix, where 0 <= L <= MIN(M,N). If L=0, B is rectangular MbyN; if M=L=N, B is lower triangular.
The matrix W stores the elementary reflectors H(i) in the ith row above the diagonal (of A) in the Mby(M+N) input matrix C [ C ] = [ A ] [ B ] [ A ] < lower triangular NbyN [ B ] < MbyN pentagonal
so that W can be represented as [ W ] = [ I ] [ V ] [ 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 ] [ V2 ] [ V1 ] < Mby(NL) rectangular [ V2 ] < MbyL lower trapezoidal.
The rows of V represent the vectors which define the H(i)'s.
The number of blocks is B = ceiling(M/MB), where each block is of order MB except for the last block, which is of order IB = M  (M1)*MB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The MBbyMB (and IBbyIB for the last block) T's are stored in the MBbyN matrix T as
T = [T1 T2 ... TB].
Definition at line 191 of file stplqt.f.