CPBSTF(3)

Hey bestie!! 💖 Welcome to the cpbstf.f(3) page from the Library Functions Manual — yes, we’re doing LAPACK Fortran realness today, and honestly? It’s giving iconic linear algebra energy. ✨

🌸 NAME 🌸

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

✨ SYNOPSIS ✨

Under Functions/Subroutines:

subroutine CPBSTF (uplo, n, kd, ab, ldab, info)
    CPBSTF

🧚 FUNCTION/SUBROUTINE DOCUMENTATION 🧚

   subroutine CPBSTF (character uplo, integer n, integer kd, complex,
       dimension( ldab, * ) ab, integer ldab, integer info)
       CPBSTF

🎀 PURPOSE 🎀

Okay so CPBSTF computes a split Cholesky factorization of a complex Hermitian positive definite band matrix A. 💅

This routine is designed to be used in conjunction with CHBGST. 🫶

The factorization has the form A = S**H*S, where S is a band matrix of the same bandwidth as A and the following structure:

S = ( U    )
    ( M  L )

where U is upper triangular of order m = (n+kd)/2, and L is lower triangular of order n-m. 🦋

🍓 PARAMETERS 🍓

• UPLO — CHARACTER*1. = 'U': the upper triangle of A is stored; = 'L': the lower triangle of A is stored. Pick your triangle, bestie. 💜
• N — INTEGER. The order of the matrix A. N >= 0.
• KD — INTEGER. The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.
• AB — COMPLEX array, dimension (LDAB,N). On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:
  • if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
  • if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, if INFO = 0, the factor S from the split Cholesky factorization A = S**H*S. See Further Details. ✨

• LDAB — INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
• INFO — INTEGER. = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value; > 0: if INFO = i, the factorization could not be completed, because the updated element a(i,i) was negative; the matrix A is not positive definite. 😭

👑 AUTHOR 👑

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

🔥 FURTHER DETAILS 🔥

The band storage scheme is illustrated by the following example, when N = 7, KD = 2:

S = ( s11  s12  s13                     )
    (      s22  s23  s24                )
    (           s33  s34                )
    (                s44                )
    (           s53  s54  s55           )
    (                s64  s65  s66      )
    (                     s75  s76  s77 )

If UPLO = 'U', the array AB holds:

on entry:                          on exit:

 *    *   a13  a24  a35  a46  a57   *    *   s13  s24  s53**H s64**H s75**H
 *   a12  a23  a34  a45  a56  a67   *   s12  s23  s34  s54**H s65**H s76**H
a11  a22  a33  a44  a55  a66  a77  s11  s22  s33  s44  s55    s66    s77

If UPLO = 'L', the array AB holds:

on entry:                          on exit:

a11  a22  a33  a44  a55  a66  a77  s11    s22    s33    s44  s55  s66  s77
a21  a32  a43  a54  a65  a76   *   s12**H s23**H s34**H s54  s65  s76   *
a31  a42  a53  a64  a64   *    *   s13**H s24**H s53    s64  s75   *    *

Array elements marked * are not used by the routine; s12**H denotes conjg(s12); the diagonal elements of S are real. 💀✨

Definition at line 152 of file cpbstf.f.

👑 AUTHOR 👑

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Mwah 😘 — this page is from LAPACK Version 3.12.0, and the footer path is /home/abui...RC/cpbstf.f(3). That’s the whole sign-off, bestie — slay and stay positive definite. 💖🌈