SRC/spbequ.f(3)

🦋 SRC/spbequ.f 🦋

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✨ NAME ✨

SRC/spbequ.f — literally the name, no cap.

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🎀 SYNOPSIS 🎀

🌟 Functions/Subroutines 🌟

• subroutine spbequ (uplo, n, kd, ab, ldab, s, scond, amax, info) — SPBEQU

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🌸 Function/Subroutine Documentation 🌸

subroutine spbequ (character uplo, integer n, integer kd, real, dimension(
     ldab, * ) ab, integer ldab, real, dimension( * ) s, real scond, real
     amax, integer info)

SPBEQU — main character subroutine energy, fr fr. 👑

💖 Purpose 💖

SPBEQU computes row and column scalings intended to equilibrate a symmetric 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. slay. ✨

🌈 Parameters 🌈

• UPLO — is CHARACTER*1:
  • = 'U': Upper triangular of A is stored;
  • = 'L': Lower triangular of A is stored.
• N — is INTEGER. The order of the matrix A. N >= 0.
• 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 — is REAL array, dimension (LDAB,N). The upper or lower triangle of the symmetric 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 — is INTEGER. The leading dimension of the array A. LDAB >= KD+1.
• S — is REAL array, dimension (N). If INFO = 0, S contains the scale factors for A.
• SCOND — is REAL. 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 — is REAL. Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.
• 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 🫶

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

Definition at line 128 of file spbequ.f.

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💜 Author 💜

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