/home/abui.../stpqrt2.f(3)

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📛 NAME 📛

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/stpqrt2.f

✨ SYNOPSIS ✨

Functions/Subroutines 🧩

subroutine STPQRT2 (m, n, l, a, lda, b, ldb, t, ldt, info)
    STPQRT2 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.

🧚 Function/Subroutine Documentation 🧚

subroutine STPQRT2 💖

subroutine STPQRT2 (integer m, integer n, integer l, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldt, * ) t, integer ldt, integer info)

STPQRT2 computes a QR factorization of a real or complex <mint>"triangular-pentagonal" matrix</mint>, which is composed of a triangular block and a pentagonal block, using the <hotpink>compact WY representation for Q</hotpink>. ✨

Purpose 🎯

Bestie, the purpose is literally this: STPQRT2 computes a QR factorization of a real matrix C, which is composed of a triangular block A and pentagonal block B, using the <hotpink>compact WY representation for Q</hotpink>. 💅

Parameters 🎛️

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

Author 👑

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

Further Details 🔍

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 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 the 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^H

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 stpqrt2.f. 📍

Author 🤖

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