SRC/cppequ.f(3)

🎀 SRC/cppequ.f(3) 🎀

okay so this is the Library Functions Manual page for SRC/cppequ.f, and bestie we are about to make this packed Hermitian scaling situation make sense. 💅 No cap, it’s giving LAPACK realness. 🦋

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✨ NAME ✨

SRC/cppequ.f

Short, iconic, to the point. 🎀

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🌈 SYNOPSIS 🌈

🫶 Functions/Subroutines 🫶

subroutine cppequ (uplo, n, ap, s, scond, amax, info)
    CPPEQU

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💖 Function/Subroutine Documentation 💖

Here’s the full signature, exactly as printed:

subroutine cppequ (character uplo, integer n, complex, dimension( * ) ap,
    real, dimension( * ) s, real scond, real amax, integer info)
    CPPEQU

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🌸 Purpose 🌸

CPPEQU computes row and column scalings intended to equilibrate a Hermitian 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. 💅

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💅 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 COMPLEX array, dimension (N*(N+1)/2)

The upper or lower triangle of the Hermitian 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 REAL array, dimension (N)

If INFO = 0, S contains the scale factors for A.

💜 SCOND 💜

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 🌈

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 💀

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 116 of file cppequ.f.

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that’s the whole page — signing off from the source/version footer: LAPACK Version 3.12.0, page SRC/cppequ.f(3). 💜✨