ZTPT03(3)

🌸 Welcome, bestie, to ztpt03.f(3) 🌸

This is a Library Functions Manual page, and the manual name is ztpt03.f(3). It's giving very specific LAPACK testing energy, and honestly? We're obsessed. 💅

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/ztpt03.f

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🎀 SYNOPSIS 🎀

🦋 Functions/Subroutines 🦋

subroutine ZTPT03 (uplo, trans, diag, n, nrhs, ap, scale, cnorm, tscal,
    x, ldx, b, ldb, work, resid)
    ZTPT03

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💖 Function/Subroutine Documentation 💖

Here's the full signature, exactly as it appears, no cap:

subroutine ZTPT03 (character uplo, character trans, character diag, integer
    n, integer nrhs, complex*16, dimension( * ) ap, double precision scale,
    double precision, dimension( * ) cnorm, double precision tscal,
    complex*16, dimension( ldx, * ) x, integer ldx, complex*16, dimension(
    ldb, * ) b, integer ldb, complex*16, dimension( * ) work, double
    precision resid)

ZTPT03

🌟 Purpose 🌟

Okay so listen: ZTPT03 computes the residual for the solution to a scaled triangular system of equations

A*x = s*b,  A**T *x = s*b,  or  A**H *x = s*b,

when the triangular matrix A is stored in packed format. Here A**T denotes the transpose of A, A**H denotes the conjugate transpose of A, s is a scalar, and x and b are N by NRHS matrices. The test ratio is the maximum over the number of right hand sides of

norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),

where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon. Iconic little residual check, honestly. 🫶

🌈 Parameters 🌈

• UPLO — UPLO is CHARACTER*1, and it specifies whether the matrix A is upper or lower triangular. The vibes are:

= 'U':  Upper triangular
= 'L':  Lower triangular

• TRANS — TRANS is CHARACTER*1, and it specifies the operation applied to A:

= 'N':  A *x = s*b     (No transpose)
= 'T':  A**T *x = s*b  (Transpose)
= 'C':  A**H *x = s*b  (Conjugate transpose)

• DIAG — DIAG is CHARACTER*1, and it specifies whether or not the matrix A is unit triangular:

= 'N':  Non-unit triangular
= 'U':  Unit triangular

• N — N is INTEGER. It's the order of the matrix A, and N >= 0.
• NRHS — NRHS is INTEGER. It's the number of right hand sides, i.e., the number of columns of the matrices X and B, and NRHS >= 0.
• AP — AP is COMPLEX*16 array, dimension (N*(N+1)/2). It's the upper or lower triangular 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((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
if UPLO = 'L',
   AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.

• SCALE — SCALE is DOUBLE PRECISION. It's the scaling factor s used in solving the triangular system.
• CNORM — CNORM is DOUBLE PRECISION array, dimension (N). It holds the 1-norms of the columns of A, not counting the diagonal.
• TSCAL — TSCAL is DOUBLE PRECISION. It's the scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A.
• X — X is COMPLEX*16 array, dimension (LDX,NRHS). It holds the computed solution vectors for the system of linear equations.
• LDX — LDX is INTEGER. It's the leading dimension of the array X, and LDX >= max(1,N).
• B — B is COMPLEX*16 array, dimension (LDB,NRHS). It holds the right hand side vectors for the system of linear equations.
• LDB — LDB is INTEGER. It's the leading dimension of the array B, and LDB >= max(1,N).
• WORK — WORK is COMPLEX*16 array, dimension (N).
• RESID — RESID is DOUBLE PRECISION. It's the maximum over the number of right hand sides of

norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 160 of file ztpt03.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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Final cute sign-off, bestie: this footer situation is LAPACK Version 3.12.0 and /home/abui...IN/ztpt03.f(3). Byeee, go compute those residuals responsibly 💅✨🎀