71 lines
2.3 KiB
Markdown
71 lines
2.3 KiB
Markdown
# CondNumReciprocalTriangular
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Estimates the reciprocal of the condition number of a upper or lower triangular matrix A in either the one-norm or infinity-norm. LAPACK function [TRCON](https://www.intel.com/content/www/us/en/docs/onemkl/developer-reference-fortran/2025-2/trcon.html).
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Computing for type matrix<double>
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```
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bool matrix::CondNumReciprocalTriangular(
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ENUM_BLAS_NORM norm // matrix norm
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double& rcond // condition number reciprocal
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);
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```
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Computing for type matrix<float>
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```
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bool matrixf::CondNumReciprocalTriangular(
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ENUM_BLAS_NORM norm // matrix norm
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float& rcond // condition number reciprocal
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);
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```
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Computing for type matrix<complex>
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```
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bool matrixc::CondNumReciprocalTriangular(
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ENUM_BLAS_NORM norm // matrix norm
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double& rcond // condition number reciprocal
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);
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```
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Computing for type matrix<complexf>
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```
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bool matrixcf::CondNumReciprocalTriangular(
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ENUM_BLAS_NORM norm // matrix norm
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float& rcond // condition number reciprocal
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);
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```
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Parameters
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norm
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[in] Value from the ENUM_BLAS_NORM enumeration, which defines estimation the reciprocal of the condition number.
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rcond
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[out] An estimate of the reciprocal of the condition number. The routine sets rcond=0 if the estimate underflows; in this case the matrix is singular (to working precision). However, anytime rcond is small compared to 1.0, for the working precision, the matrix may be poorly conditioned or even singular.
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Return Value
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Return true if successful, otherwise false in case of an [error](/en/docs/constants/errorswarnings/errorcodes).
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Note
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The computed rcond is never less than r (the reciprocal of the true condition number) and in practice is nearly always less than 10r. A call to this routine involves solving a number of systems of linear equations A*x = b; the number is usually 4 or 5 and never more than 11
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ENUM_BLAS_NORM
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An enumeration defining the matrix norm.
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| ID | Description |
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| --- | --- |
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| BLASNORM_O | 'O': One-norm |
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| BLASNORM_I | 'I': Infinity-norm |
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