SRC/zunbdb6.f(3)

🎀 SRC/zunbdb6.f 🎀

okay so bestie, welcome to this Library Functions Manual page for SRC/zunbdb6.f. It’s a whole LAPACK situation and the details are literally everything, so let’s get into it 💅

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✨ NAME ✨

SRC/zunbdb6.f

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🌈 SYNOPSIS 🌈

💖 Functions/Subroutines 💖

   subroutine zunbdb6 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2,
           work, lwork, info)

ZUNBDB6

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🧚 Function/Subroutine Documentation 🧚

✨ subroutine zunbdb6 ✨

   subroutine zunbdb6 (integer m1, integer m2, integer n, complex*16,
       dimension(*) x1, integer incx1, complex*16, dimension(*) x2, integer
       incx2, complex*16, dimension(ldq1,*) q1, integer ldq1, complex*16,
       dimension(ldq2,*) q2, integer ldq2, complex*16, dimension(*) work,
       integer lwork, integer info)
       ZUNBDB6

🦋 Purpose 🦋

okay so ZUNBDB6 orthogonalizes the column vector

X = [ X1 ]
    [ X2 ]

with respect to the columns of

Q = [ Q1 ] .
    [ Q2 ]

The columns of Q must be orthonormal. The orthogonalized vector will be zero if and only if it lies entirely in the range of Q.

The projection is computed with at most two iterations of the classical Gram-Schmidt algorithm, see

• L. Giraud, J. Langou, M. Rozložník. 2002. CERFACS Technical Report No. TR/PA/02/33. URL: https://www.cerfacs.fr/algor/reports/2002/TR_PA_02_33.pdf

💜 Parameters 💜

• M1 — M1 is INTEGER; the dimension of X1 and the number of rows in Q1. 0 <= M1.
• M2 — M2 is INTEGER; the dimension of X2 and the number of rows in Q2. 0 <= M2.
• N — N is INTEGER; the number of columns in Q1 and Q2. 0 <= N.
• X1 — X1 is COMPLEX*16 array, dimension (M1). On entry, the top part of the vector to be orthogonalized. On exit, the top part of the projected vector.
• INCX1 — INCX1 is INTEGER; increment for entries of X1.
• X2 — X2 is COMPLEX*16 array, dimension (M2). On entry, the bottom part of the vector to be orthogonalized. On exit, the bottom part of the projected vector.
• INCX2 — INCX2 is INTEGER; increment for entries of X2.
• Q1 — Q1 is COMPLEX*16 array, dimension (LDQ1, N); the top part of the orthonormal basis matrix.
• LDQ1 — LDQ1 is INTEGER; the leading dimension of Q1. LDQ1 >= M1.
• Q2 — Q2 is COMPLEX*16 array, dimension (LDQ2, N); the bottom part of the orthonormal basis matrix.
• LDQ2 — LDQ2 is INTEGER; the leading dimension of Q2. LDQ2 >= M2.
• WORK — WORK is COMPLEX*16 array, dimension (LWORK).
• LWORK — LWORK is INTEGER; the dimension of the array WORK. LWORK >= N.
• 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 157 of file zunbdb6.f.

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🌟 Author 🌟

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