/home/abui.../dtpqrt2.f(3)

🎀 NAME 🎀

Okay bestie, the official name on this page is this whole file path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dtpqrt2.f

This is the /home/abui.../dtpqrt2.f(3) page, and it comes from the Library Functions Manual. Very demure, very LAPACK. ✨

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

       subroutine DTPQRT2 (m, n, l, a, lda, b, ldb, t, ldt, info)
           DTPQRT2 computes a QR factorization of a real or complex triangular-
           pentagonal"matrix,whichiscomposedofatriangularblockandapentagonalblock,usingthecompactWYrepresentationforQ.

💅 Function/Subroutine Documentation 💅

Here’s the full signature, no crumbs:

   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 "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.

🌸 Purpose 🌸

DTPQRT2 computes a QR factorization of a real matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q.

🍓 Parameters 🍓

• M — M is INTEGER. The total number of rows of the matrix B. M >= 0.
• N — N is INTEGER. The number of columns of the matrix B, and the order of the triangular matrix A. N >= 0.
• L — L is INTEGER. The number of rows of the upper trapezoidal part of B. MIN(M,N) >= L >= 0. See Further Details.
• A — A is DOUBLE PRECISION 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.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• B — B is DOUBLE PRECISION 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.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,M).
• T — T is DOUBLE PRECISION array, dimension (LDT,N). The N-by-N upper triangular factor T of the block reflector. See Further Details.
• LDT — LDT is INTEGER. The leading dimension of the array T. LDT >= max(1,N).
• INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.

👑 Author 👑

Shoutout to the author besties:

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

🧚 Further Details 🧚

Okay so 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 an 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 (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 172 of file dtpqrt2.f.

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📝 Author 📝

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