ZPBEQU(3)

Okay bestie, welcome to ZPBEQU(3) — from the Library Functions Manual — where we compute scalings for a Hermitian positive definite band matrix and make it behave. No cap, she’s giving linear algebra main character energy. 💅

💖 NAME 💖

The source file for this routine is literally:

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

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✨ SYNOPSIS ✨

Functions/Subroutines

       subroutine ZPBEQU (uplo, n, kd, ab, ldab, s, scond, amax, info)
           ZPBEQU

🫶 Function/Subroutine Documentation 🫶

Full signature, character-for-character:

   subroutine ZPBEQU (character uplo, integer n, integer kd, complex*16,
       dimension( ldab, * ) ab, integer ldab, double precision, dimension( * )
       s, double precision scond, double precision amax, integer info)
       ZPBEQU

🎯 Purpose 🎯

ZPBEQU computes row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the two-norm). S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings. Obsessed with a diagonal of ones, honestly. ✨

🌈 Parameters 🌈

• UPLO — UPLO is CHARACTER*1.
  • = 'U': Upper triangular of A is stored;
  • = 'L': Lower triangular of A is stored.
• N — N is INTEGER. The order of the matrix A. N >= 0.
• KD — KD is INTEGER. The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.
• AB — AB is COMPLEX*16 array, dimension (LDAB,N). 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).
• LDAB — LDAB is INTEGER. The leading dimension of the array A. LDAB >= KD+1.
• S — S is DOUBLE PRECISION array, dimension (N). If INFO = 0, S contains the scale factors for A.
• SCOND — SCOND is DOUBLE PRECISION. If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S.
• AMAX — AMAX is DOUBLE PRECISION. Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.
• INFO — INFO is INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value.
  • > 0: if INFO = i, the i-th diagonal element is nonpositive.

👑 Author 👑

Respect, respect:

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

Definition at line 129 of file zpbequ.f.

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code.

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