SRC/zgemlqt.f(3)

🎀 SRC/zgemlqt.f(3)

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💖 NAME

SRC/zgemlqt.f

✨ SYNOPSIS

Functions/Subroutines

subroutine zgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc,
     work, info)

That's the ZGEMLQT subroutine, no cap.

🌸 Function/Subroutine Documentation

subroutine zgemlqt (character side, character trans, integer m, integer n,
     integer k, integer mb, complex*16, dimension( ldv, * ) v, integer ldv,
     complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension(
     ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer info)

ZGEMLQT

💡 Purpose

ZGEMLQT 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 defined as the product of K elementary reflectors:

      Q = H(1) H(2) . . . H(K) = I - V T V**H

generated using the compact WY representation as returned by ZGELQT.

Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

📋 Parameters

• SIDE — CHARACTER*1
  • = 'L': apply Q or Q**H from the Left;
  • = 'R': apply Q or Q**H from the Right.
• TRANS — CHARACTER*1
  • = 'N': No transpose, apply Q;
  • = 'C': Conjugate transpose, apply Q**H.
• M — INTEGER The number of rows of the matrix C. M >= 0.
• N — INTEGER The number of columns of the matrix C. N >= 0.
• K — INTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.
• MB — INTEGER The block size used for the storage of T. K >= MB >= 1.

This must be the same value of MB used to generate T in ZGELQT.

• V — COMPLEX*16 array, dimension (LDV,M) if SIDE = 'L', (LDV,N) if SIDE = 'R'. The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGELQT in the first K rows of its array argument A.
• LDV — INTEGER The leading dimension of the array V. LDV >= max(1,K).
• T — COMPLEX*16 array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by ZGELQT, stored as a MB-by-K matrix.
• LDT — INTEGER The leading dimension of the array T. LDT >= MB.
• C — COMPLEX*16 array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q C, Q**H C, C Q**H or C Q.
• LDC — INTEGER The leading dimension of the array C. LDC >= max(1,M).
• WORK — COMPLEX*16 array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'.
• INFO — 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 166 of file zgemlqt.f.

🫶 Author

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