SRC/dppequ.f(3)

🌸 NAME 🌸

okay bestie, this page is SRC/dppequ.f(3) from the Library Functions Manual, and the name on the label is literally SRC/dppequ.f 💅.

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✨ SYNOPSIS ✨

💅 Functions/Subroutines 💅

subroutine dppequ (uplo, n, ap, s, scond, amax, info)
    DPPEQU

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💫 Function/Subroutine Documentation 💫

here’s the full signature, exactly as it’s giving:

   subroutine dppequ (character uplo, integer n, double precision, dimension( *
       ) ap, double precision, dimension( * ) s, double precision scond, double
       precision amax, integer info)
       DPPEQU

🎀 Purpose 🎀

okay so DPPEQU computes row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage 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 — UPLO is CHARACTER*1.
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — N is INTEGER. The order of the matrix A. N >= 0.
• AP — AP is DOUBLE PRECISION array, dimension (N*(N+1)/2). The upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:
  • if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
  • if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
• 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.

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👑 Author 👑

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

Definition at line 115 of file dppequ.f.

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🦋 Author 🦋 (Doxygen's version)

Generated automatically by Doxygen for LAPACK from the source code.

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xoxo bestie, this page is from LAPACK, Version 3.12.0, and its little tag is SRC/dppequ.f(3) 🫶💖✨