TESTING/LIN/ztpt03.f(3)

💖 NAME 💖

Okay bestie, this page is the manual for TESTING/LIN/ztpt03.f — and the manual name is literally TESTING/LIN/ztpt03.f(3), so we're folding that in right at the top like a little name tag. This is the ZTPT03 function/subroutine doc, and yes it's giving iconic LAPACK testing energy. 🦋

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

subroutine ztpt03 (uplo, trans, diag, n, nrhs, ap, scale, cnorm, tscal,
           x, ldx, b, ldb, work, resid)
           ZTPT03

💅 Function/Subroutine Documentation 💅

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 🦋

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. Literally the whole vibe check is: how big is the residual compared to the scale of the problem? 💜

🎀 Parameters 🎀

UPLO

UPLO is CHARACTER*1 — Specifies whether the matrix A is upper or lower triangular.

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

TRANS

TRANS is CHARACTER*1 — 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 — Specifies whether or not the matrix A is unit triangular.

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

N

N is INTEGER — The order of the matrix A. N >= 0.

NRHS

NRHS is INTEGER — The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.

AP

AP is COMPLEX*16 array, dimension (N*(N+1)/2) — 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 — The scaling factor s used in solving the triangular system.

CNORM

CNORM is DOUBLE PRECISION array, dimension (N) — The 1-norms of the columns of A, not counting the diagonal.

TSCAL

TSCAL is DOUBLE PRECISION — 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) — The computed solution vectors for the system of linear equations.

LDX

LDX is INTEGER — The leading dimension of the array X. LDX >= max(1,N).

B

B is COMPLEX*16 array, dimension (LDB,NRHS) — The right hand side vectors for the system of linear equations.

LDB

LDB is INTEGER — The leading dimension of the array B. LDB >= max(1,N).

WORK

WORK is COMPLEX*16 array, dimension (N).

RESID

RESID is DOUBLE PRECISION — 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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