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test: factor out check_heev; use tests from LAWN 41 and LAPACK testers.
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| // Copyright (c) 2017-2023, University of Tennessee. All rights reserved. | ||
| // SPDX-License-Identifier: BSD-3-Clause | ||
| // This program is free software: you can redistribute it and/or modify it under | ||
| // the terms of the BSD 3-Clause license. See the accompanying LICENSE file. | ||
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| #include "blas.hh" | ||
| #include "lapack.hh" | ||
| #include "error.hh" | ||
| #include "check_ortho.hh" | ||
| #include "scale.hh" | ||
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| #include <vector> | ||
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| //------------------------------------------------------------------------------ | ||
| // Computes error measures: | ||
| // If jobz != NoVec: | ||
| // result[ 0 ] = || A - Z Lambda Z^H || / (n ||A||) if nfound == n; | ||
| // result[ 0 ] = || Z^H A Z - Lambda || / (n ||A||) otherwise. | ||
| // result[ 1 ] = || I - Z^H Z || / n, if jobz != NoVec. | ||
| // result[ 2 ] = 0 if Lambda is in non-decreasing order, else >= 1. | ||
| template< typename scalar_t > | ||
| void check_heev( | ||
| lapack::Job jobz, | ||
| lapack::Uplo uplo, int64_t n, | ||
| scalar_t const* A, int64_t lda, | ||
| int64_t nfound, | ||
| blas::real_type< scalar_t > const* Lambda, | ||
| scalar_t const* Z, int64_t ldz, | ||
| blas::real_type< scalar_t > result[ 3 ] ) | ||
| { | ||
| using namespace blas; | ||
| using namespace lapack; | ||
| using real_t = blas::real_type< scalar_t >; | ||
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| // Constants | ||
| const scalar_t one = 1; | ||
| const scalar_t zero = 0; | ||
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| if (jobz == Job::Vec) { | ||
| real_t Anorm = lapack::lanhe( Norm::One, uplo, n, A, lda ); | ||
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| // R is nfound-by-nfound, whether n == nfound or not. | ||
| int64_t ldr = nfound; | ||
| std::vector< scalar_t > R_( ldr*nfound ); | ||
| scalar_t* R = &R_[ 0 ]; | ||
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| if (n == nfound) { | ||
| // || A - Z Lambda Z^H || | ||
| std::vector< scalar_t > ZLambda_( ldz*n ); | ||
| scalar_t* ZLambda = &ZLambda_[ 0 ]; | ||
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| // ZLambda = Z Lambda is n-by-n. | ||
| lapack::lacpy( MatrixType::General, n, n, | ||
| Z, ldz, | ||
| ZLambda, ldz ); | ||
| col_scale( n, n, ZLambda, ldz, Lambda ); | ||
| // R = A - (Z Lambda) Z^H; could use gemmtr instead of gemm. | ||
| lapack::lacpy( MatrixType::General, n, n, | ||
| A, lda, | ||
| R, ldr ); | ||
| blas::gemm( Layout::ColMajor, Op::NoTrans, Op::ConjTrans, n, n, n, | ||
| -one, ZLambda, ldz, | ||
| Z, ldz, | ||
| one, R, ldr ); | ||
| } | ||
| else { | ||
| // || Z^H A Z - Lambda || | ||
| std::vector< scalar_t > AZ_( lda*nfound ); | ||
| scalar_t* AZ = &AZ_[ 0 ]; | ||
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| // AZ = A Z is n-by-nfound. | ||
| blas::hemm( Layout::ColMajor, Side::Left, uplo, n, nfound, | ||
| one, A, lda, | ||
| Z, ldz, | ||
| zero, AZ, lda ); | ||
| // R = Z^H (A Z); could use gemmtr instead of gemm. | ||
| blas::gemm( Layout::ColMajor, Op::ConjTrans, Op::NoTrans, | ||
| nfound, nfound, n, | ||
| one, Z, ldz, | ||
| AZ, lda, | ||
| zero, R, ldr ); | ||
| // R -= Lambda, along diagonal. | ||
| blas::axpy( nfound, -one, Lambda, 1, R, ldr + 1 ); | ||
| } | ||
| result[ 0 ] = lapack::lanhe( Norm::One, uplo, nfound, R, ldr ) | ||
| / (n * Anorm); | ||
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| result[ 1 ] = check_orthogonality( RowCol::Col, n, nfound, Z, ldz ); | ||
| } | ||
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| // Check that Lambda is non-decreasing. | ||
| result[ 2 ] = 0; | ||
| for (int64_t i = 0; i < nfound - 1; ++i) { | ||
| if (Lambda[ i ] > Lambda[ i+1 ]) | ||
| result[ 2 ] += 1; | ||
| } | ||
| } |
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