SRC/zupmtr.f(3)

🎀 NAME 🎀

okay so this is the SRC/zupmtr.f(3) page from the Library Functions Manual, and the NAME line is literally SRC/zupmtr.f — that's our main character. The routine living here is zupmtr, and she's about to get the full group-chat breakdown. 💖

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🌈 SYNOPSIS 🌈

🧚 Functions/Subroutines 🧚

• subroutine zupmtr (side, uplo, trans, m, n, ap, tau, c, ldc, work, info) — ZUPMTR

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🦋 Function/Subroutine Documentation 🦋

✨ subroutine zupmtr ✨

subroutine zupmtr (character side, character uplo, character trans, integer m, integer n, complex*16, dimension( * ) ap, complex*16, dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer info)

ZUPMTR is the name on the door, bestie.

💜 Purpose 💜

okay so here's the tea: ZUPMTR overwrites the general complex M-by-N matrix C with:

                SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'C':      Q**H * C       C * Q**H

where Q is a complex unitary matrix of order nq, with nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of nq-1 elementary reflectors, as returned by ZHPTRD using packed storage:

if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);

if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).

🍓 Parameters 🍓

• SIDE — SIDE is CHARACTER*1
  • = 'L': apply Q or Q**H from the Left;
  • = 'R': apply Q or Q**H from the Right.
• UPLO — UPLO is CHARACTER*1
  • = 'U': Upper triangular packed storage used in previous call to ZHPTRD;
  • = 'L': Lower triangular packed storage used in previous call to ZHPTRD.
• TRANS — TRANS is CHARACTER*1
  • = 'N': No transpose, apply Q;
  • = 'C': Conjugate transpose, apply Q**H.
• M — M is INTEGER. The number of rows of the matrix C. M >= 0.
• N — N is INTEGER. The number of columns of the matrix C. N >= 0.
• AP — AP is COMPLEX*16 array, dimension
  • (M*(M+1)/2) if SIDE = 'L'
  • (N*(N+1)/2) if SIDE = 'R'

The vectors which define the elementary reflectors, as returned by ZHPTRD. AP is modified by the routine but restored on exit.

• TAU — TAU is COMPLEX*16 array, dimension (M-1) if SIDE = 'L' or (N-1) if SIDE = 'R'. TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZHPTRD.
• C — C is COMPLEX*16 array, dimension (LDC,N). On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
• LDC — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,M).
• WORK — WORK is COMPLEX*16 array, dimension
  • (N) if SIDE = 'L'
  • (M) if SIDE = 'R'
• INFO — INFO is 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.

📍 Definition at line 148 of file zupmtr.f. 📍

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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that's the whole page, bestie! this one is LAPACK Version 3.12.0 on the SRC/zupmtr.f(3) page — mwah, and slay 💋✨