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lapack.27793
Avoid-out-of-bounds-accesses-in-complex-EIG-tes...
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File Avoid-out-of-bounds-accesses-in-complex-EIG-tests.patch of Package lapack.27793
From ea2a102d3827a9de90fce729c9d7f132d4c96f4f Mon Sep 17 00:00:00 2001 From: Martin Kroeker <martin@ruby.chemie.uni-freiburg.de> Date: Sat, 27 Apr 2019 23:06:12 +0200 Subject: [PATCH 1/2] Avoid out-of-bounds accesses in complex EIG tests fixes #333 --- TESTING/EIG/chet21.f | 34 ++++++++++++++++------------------ TESTING/EIG/chpt21.f | 37 ++++++++++++++++--------------------- TESTING/EIG/zhet21.f | 34 ++++++++++++++++------------------ TESTING/EIG/zhpt21.f | 38 +++++++++++++++++--------------------- 4 files changed, 65 insertions(+), 78 deletions(-) diff --git a/TESTING/EIG/chet21.f b/TESTING/EIG/chet21.f index e5bf027c2..5aff64904 100644 --- a/TESTING/EIG/chet21.f +++ b/TESTING/EIG/chet21.f @@ -29,9 +29,8 @@ *> *> CHET21 generally checks a decomposition of the form *> -*> A = U S U**H -*> -*> where **H means conjugate transpose, A is hermitian, U is unitary, and +*> A = U S UC> +*> where * means conjugate transpose, A is hermitian, U is unitary, and *> S is diagonal (if KBAND=0) or (real) symmetric tridiagonal (if *> KBAND=1). *> @@ -43,19 +42,18 @@ *> *> Specifically, if ITYPE=1, then: *> -*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and -*> RESULT(2) = | I - U U**H | / ( n ulp ) +*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp ) *> *> If ITYPE=2, then: *> -*> RESULT(1) = | A - V S V**H | / ( |A| n ulp ) +*> RESULT(1) = | A - V S V* | / ( |A| n ulp ) *> *> If ITYPE=3, then: *> -*> RESULT(1) = | I - U V**H | / ( n ulp ) +*> RESULT(1) = | I - UV* | / ( n ulp ) *> *> For ITYPE > 1, the transformation U is expressed as a product -*> V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)**H and each +*> V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)C> and each *> vector v(j) has its first j elements 0 and the remaining n-j elements *> stored in V(j+1:n,j). *> \endverbatim @@ -68,15 +66,14 @@ *> ITYPE is INTEGER *> Specifies the type of tests to be performed. *> 1: U expressed as a dense unitary matrix: -*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and -*> RESULT(2) = | I - U U**H | / ( n ulp ) +*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp ) *> *> 2: U expressed as a product V of Housholder transformations: -*> RESULT(1) = | A - V S V**H | / ( |A| n ulp ) +*> RESULT(1) = | A - V S V* | / ( |A| n ulp ) *> *> 3: U expressed both as a dense unitary matrix and *> as a product of Housholder transformations: -*> RESULT(1) = | I - U V**H | / ( n ulp ) +*> RESULT(1) = | I - UV* | / ( n ulp ) *> \endverbatim *> *> \param[in] UPLO @@ -174,7 +171,7 @@ *> \verbatim *> TAU is COMPLEX array, dimension (N) *> If ITYPE >= 2, then TAU(j) is the scalar factor of -*> v(j) v(j)**H in the Householder transformation H(j) of +*> v(j) v(j)* in the Householder transformation H(j) of *> the product U = H(1)...H(n-2) *> If ITYPE < 2, then TAU is not referenced. *> \endverbatim @@ -297,7 +294,7 @@ SUBROUTINE CHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, * IF( ITYPE.EQ.1 ) THEN * -* ITYPE=1: error = A - U S U**H +* ITYPE=1: error = A - U S U* * CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N ) CALL CLACPY( CUPLO, N, N, A, LDA, WORK, N ) @@ -307,7 +304,8 @@ SUBROUTINE CHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, 10 CONTINUE * IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN - DO 20 J = 1, N - 1 +CMK DO 20 J = 1, N - 1 + DO 20 J = 2, N - 1 CALL CHER2( CUPLO, N, -CMPLX( E( J ) ), U( 1, J ), 1, $ U( 1, J-1 ), 1, WORK, N ) 20 CONTINUE @@ -316,7 +314,7 @@ SUBROUTINE CHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, * ELSE IF( ITYPE.EQ.2 ) THEN * -* ITYPE=2: error = V S V**H - A +* ITYPE=2: error = V S V* - A * CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N ) * @@ -373,7 +371,7 @@ SUBROUTINE CHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, * ELSE IF( ITYPE.EQ.3 ) THEN * -* ITYPE=3: error = U V**H - I +* ITYPE=3: error = U V* - I * IF( N.LT.2 ) $ RETURN @@ -409,7 +407,7 @@ SUBROUTINE CHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, * * Do Test 2 * -* Compute U U**H - I +* Compute UU* - I * IF( ITYPE.EQ.1 ) THEN CALL CGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO, diff --git a/TESTING/EIG/chpt21.f b/TESTING/EIG/chpt21.f index 458079614..e151a8bd8 100644 --- a/TESTING/EIG/chpt21.f +++ b/TESTING/EIG/chpt21.f @@ -29,9 +29,8 @@ *> *> CHPT21 generally checks a decomposition of the form *> -*> A = U S U**H -*> -*> where **H means conjugate transpose, A is hermitian, U is +*> A = U S UC> +*> where * means conjugate transpose, A is hermitian, U is *> unitary, and S is diagonal (if KBAND=0) or (real) symmetric *> tridiagonal (if KBAND=1). If ITYPE=1, then U is represented as *> a dense matrix, otherwise the U is expressed as a product of @@ -42,16 +41,15 @@ *> *> Specifically, if ITYPE=1, then: *> -*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and -*> RESULT(2) = | I - U U**H | / ( n ulp ) +*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp ) *> *> If ITYPE=2, then: *> -*> RESULT(1) = | A - V S V**H | / ( |A| n ulp ) +*> RESULT(1) = | A - V S V* | / ( |A| n ulp ) *> *> If ITYPE=3, then: *> -*> RESULT(1) = | I - U V**H | / ( n ulp ) +*> RESULT(1) = | I - UV* | / ( n ulp ) *> *> Packed storage means that, for example, if UPLO='U', then the columns *> of the upper triangle of A are stored one after another, so that @@ -72,16 +70,14 @@ *> *> If UPLO='U', then V = H(n-1)...H(1), where *> -*> H(j) = I - tau(j) v(j) v(j)**H -*> +*> H(j) = I - tau(j) v(j) v(j)C> *> and the first j-1 elements of v(j) are stored in V(1:j-1,j+1), *> (i.e., VP( j*(j+1)/2 + 1 : j*(j+1)/2 + j-1 ) ), *> the j-th element is 1, and the last n-j elements are 0. *> *> If UPLO='L', then V = H(1)...H(n-1), where *> -*> H(j) = I - tau(j) v(j) v(j)**H -*> +*> H(j) = I - tau(j) v(j) v(j)C> *> and the first j elements of v(j) are 0, the (j+1)-st is 1, and the *> (j+2)-nd through n-th elements are stored in V(j+2:n,j) (i.e., *> in VP( (2*n-j)*(j-1)/2 + j+2 : (2*n-j)*(j-1)/2 + n ) .) @@ -95,15 +91,14 @@ *> ITYPE is INTEGER *> Specifies the type of tests to be performed. *> 1: U expressed as a dense unitary matrix: -*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and -*> RESULT(2) = | I - U U**H | / ( n ulp ) +*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp ) *> *> 2: U expressed as a product V of Housholder transformations: -*> RESULT(1) = | A - V S V**H | / ( |A| n ulp ) +*> RESULT(1) = | A - V S V* | / ( |A| n ulp ) *> *> 3: U expressed both as a dense unitary matrix and *> as a product of Housholder transformations: -*> RESULT(1) = | I - U V**H | / ( n ulp ) +*> RESULT(1) = | I - UV* | / ( n ulp ) *> \endverbatim *> *> \param[in] UPLO @@ -186,7 +181,7 @@ *> \verbatim *> TAU is COMPLEX array, dimension (N) *> If ITYPE >= 2, then TAU(j) is the scalar factor of -*> v(j) v(j)**H in the Householder transformation H(j) of +*> v(j) v(j)* in the Householder transformation H(j) of *> the product U = H(1)...H(n-2) *> If ITYPE < 2, then TAU is not referenced. *> \endverbatim @@ -318,7 +313,7 @@ SUBROUTINE CHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP, * IF( ITYPE.EQ.1 ) THEN * -* ITYPE=1: error = A - U S U**H +* ITYPE=1: error = A - U S U* * CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N ) CALL CCOPY( LAP, AP, 1, WORK, 1 ) @@ -328,7 +323,7 @@ SUBROUTINE CHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP, 10 CONTINUE * IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN - DO 20 J = 1, N - 1 + DO 20 J = 2, N - 1 CALL CHPR2( CUPLO, N, -CMPLX( E( J ) ), U( 1, J ), 1, $ U( 1, J-1 ), 1, WORK ) 20 CONTINUE @@ -337,7 +332,7 @@ SUBROUTINE CHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP, * ELSE IF( ITYPE.EQ.2 ) THEN * -* ITYPE=2: error = V S V**H - A +* ITYPE=2: error = V S V* - A * CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N ) * @@ -405,7 +400,7 @@ SUBROUTINE CHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP, * ELSE IF( ITYPE.EQ.3 ) THEN * -* ITYPE=3: error = U V**H - I +* ITYPE=3: error = U V* - I * IF( N.LT.2 ) $ RETURN @@ -436,7 +431,7 @@ SUBROUTINE CHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP, * * Do Test 2 * -* Compute U U**H - I +* Compute UU* - I * IF( ITYPE.EQ.1 ) THEN CALL CGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO, diff --git a/TESTING/EIG/zhet21.f b/TESTING/EIG/zhet21.f index 11f94c63b..f6cb2d70a 100644 --- a/TESTING/EIG/zhet21.f +++ b/TESTING/EIG/zhet21.f @@ -29,9 +29,8 @@ *> *> ZHET21 generally checks a decomposition of the form *> -*> A = U S U**H -*> -*> where **H means conjugate transpose, A is hermitian, U is unitary, and +*> A = U S UC> +*> where * means conjugate transpose, A is hermitian, U is unitary, and *> S is diagonal (if KBAND=0) or (real) symmetric tridiagonal (if *> KBAND=1). *> @@ -43,19 +42,18 @@ *> *> Specifically, if ITYPE=1, then: *> -*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and -*> RESULT(2) = | I - U U**H | / ( n ulp ) +*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp ) *> *> If ITYPE=2, then: *> -*> RESULT(1) = | A - V S V**H | / ( |A| n ulp ) +*> RESULT(1) = | A - V S V* | / ( |A| n ulp ) *> *> If ITYPE=3, then: *> -*> RESULT(1) = | I - U V**H | / ( n ulp ) +*> RESULT(1) = | I - UV* | / ( n ulp ) *> *> For ITYPE > 1, the transformation U is expressed as a product -*> V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)**H and each +*> V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)C> and each *> vector v(j) has its first j elements 0 and the remaining n-j elements *> stored in V(j+1:n,j). *> \endverbatim @@ -68,15 +66,14 @@ *> ITYPE is INTEGER *> Specifies the type of tests to be performed. *> 1: U expressed as a dense unitary matrix: -*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and -*> RESULT(2) = | I - U U**H | / ( n ulp ) +*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp ) *> *> 2: U expressed as a product V of Housholder transformations: -*> RESULT(1) = | A - V S V**H | / ( |A| n ulp ) +*> RESULT(1) = | A - V S V* | / ( |A| n ulp ) *> *> 3: U expressed both as a dense unitary matrix and *> as a product of Housholder transformations: -*> RESULT(1) = | I - U V**H | / ( n ulp ) +*> RESULT(1) = | I - UV* | / ( n ulp ) *> \endverbatim *> *> \param[in] UPLO @@ -174,7 +171,7 @@ *> \verbatim *> TAU is COMPLEX*16 array, dimension (N) *> If ITYPE >= 2, then TAU(j) is the scalar factor of -*> v(j) v(j)**H in the Householder transformation H(j) of +*> v(j) v(j)* in the Householder transformation H(j) of *> the product U = H(1)...H(n-2) *> If ITYPE < 2, then TAU is not referenced. *> \endverbatim @@ -297,7 +294,7 @@ SUBROUTINE ZHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, * IF( ITYPE.EQ.1 ) THEN * -* ITYPE=1: error = A - U S U**H +* ITYPE=1: error = A - U S U* * CALL ZLASET( 'Full', N, N, CZERO, CZERO, WORK, N ) CALL ZLACPY( CUPLO, N, N, A, LDA, WORK, N ) @@ -307,7 +304,8 @@ SUBROUTINE ZHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, 10 CONTINUE * IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN - DO 20 J = 1, N - 1 +CMK DO 20 J = 1, N - 1 + DO 20 J = 2, N - 1 CALL ZHER2( CUPLO, N, -DCMPLX( E( J ) ), U( 1, J ), 1, $ U( 1, J-1 ), 1, WORK, N ) 20 CONTINUE @@ -316,7 +314,7 @@ SUBROUTINE ZHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, * ELSE IF( ITYPE.EQ.2 ) THEN * -* ITYPE=2: error = V S V**H - A +* ITYPE=2: error = V S V* - A * CALL ZLASET( 'Full', N, N, CZERO, CZERO, WORK, N ) * @@ -373,7 +371,7 @@ SUBROUTINE ZHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, * ELSE IF( ITYPE.EQ.3 ) THEN * -* ITYPE=3: error = U V**H - I +* ITYPE=3: error = U V* - I * IF( N.LT.2 ) $ RETURN @@ -409,7 +407,7 @@ SUBROUTINE ZHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, * * Do Test 2 * -* Compute U U**H - I +* Compute UU* - I * IF( ITYPE.EQ.1 ) THEN CALL ZGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO, diff --git a/TESTING/EIG/zhpt21.f b/TESTING/EIG/zhpt21.f index 909ec8a02..ef9e4418d 100644 --- a/TESTING/EIG/zhpt21.f +++ b/TESTING/EIG/zhpt21.f @@ -29,9 +29,8 @@ *> *> ZHPT21 generally checks a decomposition of the form *> -*> A = U S U**H -*> -*> where **H means conjugate transpose, A is hermitian, U is +*> A = U S UC> +*> where * means conjugate transpose, A is hermitian, U is *> unitary, and S is diagonal (if KBAND=0) or (real) symmetric *> tridiagonal (if KBAND=1). If ITYPE=1, then U is represented as *> a dense matrix, otherwise the U is expressed as a product of @@ -42,16 +41,15 @@ *> *> Specifically, if ITYPE=1, then: *> -*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and -*> RESULT(2) = | I - U U**H | / ( n ulp ) +*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp ) *> *> If ITYPE=2, then: *> -*> RESULT(1) = | A - V S V**H | / ( |A| n ulp ) +*> RESULT(1) = | A - V S V* | / ( |A| n ulp ) *> *> If ITYPE=3, then: *> -*> RESULT(1) = | I - U V**H | / ( n ulp ) +*> RESULT(1) = | I - UV* | / ( n ulp ) *> *> Packed storage means that, for example, if UPLO='U', then the columns *> of the upper triangle of A are stored one after another, so that @@ -72,16 +70,14 @@ *> *> If UPLO='U', then V = H(n-1)...H(1), where *> -*> H(j) = I - tau(j) v(j) v(j)**H -*> +*> H(j) = I - tau(j) v(j) v(j)C> *> and the first j-1 elements of v(j) are stored in V(1:j-1,j+1), *> (i.e., VP( j*(j+1)/2 + 1 : j*(j+1)/2 + j-1 ) ), *> the j-th element is 1, and the last n-j elements are 0. *> *> If UPLO='L', then V = H(1)...H(n-1), where *> -*> H(j) = I - tau(j) v(j) v(j)**H -*> +*> H(j) = I - tau(j) v(j) v(j)C> *> and the first j elements of v(j) are 0, the (j+1)-st is 1, and the *> (j+2)-nd through n-th elements are stored in V(j+2:n,j) (i.e., *> in VP( (2*n-j)*(j-1)/2 + j+2 : (2*n-j)*(j-1)/2 + n ) .) @@ -95,15 +91,14 @@ *> ITYPE is INTEGER *> Specifies the type of tests to be performed. *> 1: U expressed as a dense unitary matrix: -*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and -*> RESULT(2) = | I - U U**H | / ( n ulp ) +*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp ) *> *> 2: U expressed as a product V of Housholder transformations: -*> RESULT(1) = | A - V S V**H | / ( |A| n ulp ) +*> RESULT(1) = | A - V S V* | / ( |A| n ulp ) *> *> 3: U expressed both as a dense unitary matrix and *> as a product of Housholder transformations: -*> RESULT(1) = | I - U V**H | / ( n ulp ) +*> RESULT(1) = | I - UV* | / ( n ulp ) *> \endverbatim *> *> \param[in] UPLO @@ -186,7 +181,7 @@ *> \verbatim *> TAU is COMPLEX*16 array, dimension (N) *> If ITYPE >= 2, then TAU(j) is the scalar factor of -*> v(j) v(j)**H in the Householder transformation H(j) of +*> v(j) v(j)* in the Householder transformation H(j) of *> the product U = H(1)...H(n-2) *> If ITYPE < 2, then TAU is not referenced. *> \endverbatim @@ -318,7 +313,7 @@ SUBROUTINE ZHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP, * IF( ITYPE.EQ.1 ) THEN * -* ITYPE=1: error = A - U S U**H +* ITYPE=1: error = A - U S U* * CALL ZLASET( 'Full', N, N, CZERO, CZERO, WORK, N ) CALL ZCOPY( LAP, AP, 1, WORK, 1 ) @@ -328,7 +323,8 @@ SUBROUTINE ZHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP, 10 CONTINUE * IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN - DO 20 J = 1, N - 1 +CMK DO 20 J = 1, N - 1 + DO 20 J = 2, N - 1 CALL ZHPR2( CUPLO, N, -DCMPLX( E( J ) ), U( 1, J ), 1, $ U( 1, J-1 ), 1, WORK ) 20 CONTINUE @@ -337,7 +333,7 @@ SUBROUTINE ZHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP, * ELSE IF( ITYPE.EQ.2 ) THEN * -* ITYPE=2: error = V S V**H - A +* ITYPE=2: error = V S V* - A * CALL ZLASET( 'Full', N, N, CZERO, CZERO, WORK, N ) * @@ -405,7 +401,7 @@ SUBROUTINE ZHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP, * ELSE IF( ITYPE.EQ.3 ) THEN * -* ITYPE=3: error = U V**H - I +* ITYPE=3: error = U V* - I * IF( N.LT.2 ) $ RETURN @@ -436,7 +432,7 @@ SUBROUTINE ZHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP, * * Do Test 2 * -* Compute U U**H - I +* Compute UU* - I * IF( ITYPE.EQ.1 ) THEN CALL ZGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO, From d7be8c7220273c827813e9394f5e681b1e32d7a8 Mon Sep 17 00:00:00 2001 From: Martin Kroeker <martin@ruby.chemie.uni-freiburg.de> Date: Tue, 31 Dec 2019 13:40:06 +0100 Subject: [PATCH 2/2] Rebase on 3.9.0 --- TESTING/EIG/chet21.f | 32 +++++++++++++++++--------------- TESTING/EIG/chpt21.f | 35 ++++++++++++++++++++--------------- TESTING/EIG/zhet21.f | 32 +++++++++++++++++--------------- TESTING/EIG/zhpt21.f | 36 ++++++++++++++++++++---------------- 4 files changed, 74 insertions(+), 61 deletions(-) diff --git a/TESTING/EIG/chet21.f b/TESTING/EIG/chet21.f index 5aff64904..d5c4f1348 100644 --- a/TESTING/EIG/chet21.f +++ b/TESTING/EIG/chet21.f @@ -29,8 +29,9 @@ *> *> CHET21 generally checks a decomposition of the form *> -*> A = U S UC> -*> where * means conjugate transpose, A is hermitian, U is unitary, and +*> A = U S U**H +*> +*> where **H means conjugate transpose, A is hermitian, U is unitary, and *> S is diagonal (if KBAND=0) or (real) symmetric tridiagonal (if *> KBAND=1). *> @@ -42,18 +43,19 @@ *> *> Specifically, if ITYPE=1, then: *> -*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp ) +*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and +*> RESULT(2) = | I - U U**H | / ( n ulp ) *> *> If ITYPE=2, then: *> -*> RESULT(1) = | A - V S V* | / ( |A| n ulp ) +*> RESULT(1) = | A - V S V**H | / ( |A| n ulp ) *> *> If ITYPE=3, then: *> -*> RESULT(1) = | I - UV* | / ( n ulp ) +*> RESULT(1) = | I - U V**H | / ( n ulp ) *> *> For ITYPE > 1, the transformation U is expressed as a product -*> V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)C> and each +*> V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)**H and each *> vector v(j) has its first j elements 0 and the remaining n-j elements *> stored in V(j+1:n,j). *> \endverbatim @@ -66,14 +68,15 @@ *> ITYPE is INTEGER *> Specifies the type of tests to be performed. *> 1: U expressed as a dense unitary matrix: -*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp ) +*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and +*> RESULT(2) = | I - U U**H | / ( n ulp ) *> *> 2: U expressed as a product V of Housholder transformations: -*> RESULT(1) = | A - V S V* | / ( |A| n ulp ) +*> RESULT(1) = | A - V S V**H | / ( |A| n ulp ) *> *> 3: U expressed both as a dense unitary matrix and *> as a product of Housholder transformations: -*> RESULT(1) = | I - UV* | / ( n ulp ) +*> RESULT(1) = | I - U V**H | / ( n ulp ) *> \endverbatim *> *> \param[in] UPLO @@ -171,7 +174,7 @@ *> \verbatim *> TAU is COMPLEX array, dimension (N) *> If ITYPE >= 2, then TAU(j) is the scalar factor of -*> v(j) v(j)* in the Householder transformation H(j) of +*> v(j) v(j)**H in the Householder transformation H(j) of *> the product U = H(1)...H(n-2) *> If ITYPE < 2, then TAU is not referenced. *> \endverbatim @@ -294,7 +297,7 @@ SUBROUTINE CHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, * IF( ITYPE.EQ.1 ) THEN * -* ITYPE=1: error = A - U S U* +* ITYPE=1: error = A - U S U**H * CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N ) CALL CLACPY( CUPLO, N, N, A, LDA, WORK, N ) @@ -304,7 +307,6 @@ SUBROUTINE CHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, 10 CONTINUE * IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN -CMK DO 20 J = 1, N - 1 DO 20 J = 2, N - 1 CALL CHER2( CUPLO, N, -CMPLX( E( J ) ), U( 1, J ), 1, $ U( 1, J-1 ), 1, WORK, N ) @@ -314,7 +316,7 @@ SUBROUTINE CHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, * ELSE IF( ITYPE.EQ.2 ) THEN * -* ITYPE=2: error = V S V* - A +* ITYPE=2: error = V S V**H - A * CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N ) * @@ -371,7 +373,7 @@ SUBROUTINE CHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, * ELSE IF( ITYPE.EQ.3 ) THEN * -* ITYPE=3: error = U V* - I +* ITYPE=3: error = U V**H - I * IF( N.LT.2 ) $ RETURN @@ -407,7 +409,7 @@ SUBROUTINE CHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, * * Do Test 2 * -* Compute UU* - I +* Compute U U**H - I * IF( ITYPE.EQ.1 ) THEN CALL CGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO, diff --git a/TESTING/EIG/chpt21.f b/TESTING/EIG/chpt21.f index e151a8bd8..f20921bd9 100644 --- a/TESTING/EIG/chpt21.f +++ b/TESTING/EIG/chpt21.f @@ -29,8 +29,9 @@ *> *> CHPT21 generally checks a decomposition of the form *> -*> A = U S UC> -*> where * means conjugate transpose, A is hermitian, U is +*> A = U S U**H +*> +*> where **H means conjugate transpose, A is hermitian, U is *> unitary, and S is diagonal (if KBAND=0) or (real) symmetric *> tridiagonal (if KBAND=1). If ITYPE=1, then U is represented as *> a dense matrix, otherwise the U is expressed as a product of @@ -41,15 +42,16 @@ *> *> Specifically, if ITYPE=1, then: *> -*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp ) +*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and +*> RESULT(2) = | I - U U**H | / ( n ulp ) *> *> If ITYPE=2, then: *> -*> RESULT(1) = | A - V S V* | / ( |A| n ulp ) +*> RESULT(1) = | A - V S V**H | / ( |A| n ulp ) *> *> If ITYPE=3, then: *> -*> RESULT(1) = | I - UV* | / ( n ulp ) +*> RESULT(1) = | I - U V**H | / ( n ulp ) *> *> Packed storage means that, for example, if UPLO='U', then the columns *> of the upper triangle of A are stored one after another, so that @@ -70,14 +72,16 @@ *> *> If UPLO='U', then V = H(n-1)...H(1), where *> -*> H(j) = I - tau(j) v(j) v(j)C> +*> H(j) = I - tau(j) v(j) v(j)**H +*> *> and the first j-1 elements of v(j) are stored in V(1:j-1,j+1), *> (i.e., VP( j*(j+1)/2 + 1 : j*(j+1)/2 + j-1 ) ), *> the j-th element is 1, and the last n-j elements are 0. *> *> If UPLO='L', then V = H(1)...H(n-1), where *> -*> H(j) = I - tau(j) v(j) v(j)C> +*> H(j) = I - tau(j) v(j) v(j)**H +*> *> and the first j elements of v(j) are 0, the (j+1)-st is 1, and the *> (j+2)-nd through n-th elements are stored in V(j+2:n,j) (i.e., *> in VP( (2*n-j)*(j-1)/2 + j+2 : (2*n-j)*(j-1)/2 + n ) .) @@ -91,14 +95,15 @@ *> ITYPE is INTEGER *> Specifies the type of tests to be performed. *> 1: U expressed as a dense unitary matrix: -*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp ) +*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and +*> RESULT(2) = | I - U U**H | / ( n ulp ) *> *> 2: U expressed as a product V of Housholder transformations: -*> RESULT(1) = | A - V S V* | / ( |A| n ulp ) +*> RESULT(1) = | A - V S V**H | / ( |A| n ulp ) *> *> 3: U expressed both as a dense unitary matrix and *> as a product of Housholder transformations: -*> RESULT(1) = | I - UV* | / ( n ulp ) +*> RESULT(1) = | I - U V**H | / ( n ulp ) *> \endverbatim *> *> \param[in] UPLO @@ -181,7 +186,7 @@ *> \verbatim *> TAU is COMPLEX array, dimension (N) *> If ITYPE >= 2, then TAU(j) is the scalar factor of -*> v(j) v(j)* in the Householder transformation H(j) of +*> v(j) v(j)**H in the Householder transformation H(j) of *> the product U = H(1)...H(n-2) *> If ITYPE < 2, then TAU is not referenced. *> \endverbatim @@ -313,7 +318,7 @@ SUBROUTINE CHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP, * IF( ITYPE.EQ.1 ) THEN * -* ITYPE=1: error = A - U S U* +* ITYPE=1: error = A - U S U**H * CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N ) CALL CCOPY( LAP, AP, 1, WORK, 1 ) @@ -332,7 +337,7 @@ SUBROUTINE CHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP, * ELSE IF( ITYPE.EQ.2 ) THEN * -* ITYPE=2: error = V S V* - A +* ITYPE=2: error = V S V**H - A * CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N ) * @@ -400,7 +405,7 @@ SUBROUTINE CHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP, * ELSE IF( ITYPE.EQ.3 ) THEN * -* ITYPE=3: error = U V* - I +* ITYPE=3: error = U V**H - I * IF( N.LT.2 ) $ RETURN @@ -431,7 +436,7 @@ SUBROUTINE CHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP, * * Do Test 2 * -* Compute UU* - I +* Compute U U**H - I * IF( ITYPE.EQ.1 ) THEN CALL CGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO, diff --git a/TESTING/EIG/zhet21.f b/TESTING/EIG/zhet21.f index f6cb2d70a..cb854a850 100644 --- a/TESTING/EIG/zhet21.f +++ b/TESTING/EIG/zhet21.f @@ -29,8 +29,9 @@ *> *> ZHET21 generally checks a decomposition of the form *> -*> A = U S UC> -*> where * means conjugate transpose, A is hermitian, U is unitary, and +*> A = U S U**H +*> +*> where **H means conjugate transpose, A is hermitian, U is unitary, and *> S is diagonal (if KBAND=0) or (real) symmetric tridiagonal (if *> KBAND=1). *> @@ -42,18 +43,19 @@ *> *> Specifically, if ITYPE=1, then: *> -*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp ) +*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and +*> RESULT(2) = | I - U U**H | / ( n ulp ) *> *> If ITYPE=2, then: *> -*> RESULT(1) = | A - V S V* | / ( |A| n ulp ) +*> RESULT(1) = | A - V S V**H | / ( |A| n ulp ) *> *> If ITYPE=3, then: *> -*> RESULT(1) = | I - UV* | / ( n ulp ) +*> RESULT(1) = | I - U V**H | / ( n ulp ) *> *> For ITYPE > 1, the transformation U is expressed as a product -*> V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)C> and each +*> V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)**H and each *> vector v(j) has its first j elements 0 and the remaining n-j elements *> stored in V(j+1:n,j). *> \endverbatim @@ -66,14 +68,15 @@ *> ITYPE is INTEGER *> Specifies the type of tests to be performed. *> 1: U expressed as a dense unitary matrix: -*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp ) +*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and +*> RESULT(2) = | I - U U**H | / ( n ulp ) *> *> 2: U expressed as a product V of Housholder transformations: -*> RESULT(1) = | A - V S V* | / ( |A| n ulp ) +*> RESULT(1) = | A - V S V**H | / ( |A| n ulp ) *> *> 3: U expressed both as a dense unitary matrix and *> as a product of Housholder transformations: -*> RESULT(1) = | I - UV* | / ( n ulp ) +*> RESULT(1) = | I - U V**H | / ( n ulp ) *> \endverbatim *> *> \param[in] UPLO @@ -171,7 +174,7 @@ *> \verbatim *> TAU is COMPLEX*16 array, dimension (N) *> If ITYPE >= 2, then TAU(j) is the scalar factor of -*> v(j) v(j)* in the Householder transformation H(j) of +*> v(j) v(j)**H in the Householder transformation H(j) of *> the product U = H(1)...H(n-2) *> If ITYPE < 2, then TAU is not referenced. *> \endverbatim @@ -294,7 +297,7 @@ SUBROUTINE ZHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, * IF( ITYPE.EQ.1 ) THEN * -* ITYPE=1: error = A - U S U* +* ITYPE=1: error = A - U S U**H * CALL ZLASET( 'Full', N, N, CZERO, CZERO, WORK, N ) CALL ZLACPY( CUPLO, N, N, A, LDA, WORK, N ) @@ -304,7 +307,6 @@ SUBROUTINE ZHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, 10 CONTINUE * IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN -CMK DO 20 J = 1, N - 1 DO 20 J = 2, N - 1 CALL ZHER2( CUPLO, N, -DCMPLX( E( J ) ), U( 1, J ), 1, $ U( 1, J-1 ), 1, WORK, N ) @@ -314,7 +316,7 @@ SUBROUTINE ZHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, * ELSE IF( ITYPE.EQ.2 ) THEN * -* ITYPE=2: error = V S V* - A +* ITYPE=2: error = V S V**H - A * CALL ZLASET( 'Full', N, N, CZERO, CZERO, WORK, N ) * @@ -371,7 +373,7 @@ SUBROUTINE ZHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, * ELSE IF( ITYPE.EQ.3 ) THEN * -* ITYPE=3: error = U V* - I +* ITYPE=3: error = U V**H - I * IF( N.LT.2 ) $ RETURN @@ -407,7 +409,7 @@ SUBROUTINE ZHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, * * Do Test 2 * -* Compute UU* - I +* Compute U U**H - I * IF( ITYPE.EQ.1 ) THEN CALL ZGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO, diff --git a/TESTING/EIG/zhpt21.f b/TESTING/EIG/zhpt21.f index ef9e4418d..825d387c7 100644 --- a/TESTING/EIG/zhpt21.f +++ b/TESTING/EIG/zhpt21.f @@ -29,8 +29,9 @@ *> *> ZHPT21 generally checks a decomposition of the form *> -*> A = U S UC> -*> where * means conjugate transpose, A is hermitian, U is +*> A = U S U**H +*> +*> where **H means conjugate transpose, A is hermitian, U is *> unitary, and S is diagonal (if KBAND=0) or (real) symmetric *> tridiagonal (if KBAND=1). If ITYPE=1, then U is represented as *> a dense matrix, otherwise the U is expressed as a product of @@ -41,15 +42,16 @@ *> *> Specifically, if ITYPE=1, then: *> -*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp ) +*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and +*> RESULT(2) = | I - U U**H | / ( n ulp ) *> *> If ITYPE=2, then: *> -*> RESULT(1) = | A - V S V* | / ( |A| n ulp ) +*> RESULT(1) = | A - V S V**H | / ( |A| n ulp ) *> *> If ITYPE=3, then: *> -*> RESULT(1) = | I - UV* | / ( n ulp ) +*> RESULT(1) = | I - U V**H | / ( n ulp ) *> *> Packed storage means that, for example, if UPLO='U', then the columns *> of the upper triangle of A are stored one after another, so that @@ -70,14 +72,16 @@ *> *> If UPLO='U', then V = H(n-1)...H(1), where *> -*> H(j) = I - tau(j) v(j) v(j)C> +*> H(j) = I - tau(j) v(j) v(j)**H +*> *> and the first j-1 elements of v(j) are stored in V(1:j-1,j+1), *> (i.e., VP( j*(j+1)/2 + 1 : j*(j+1)/2 + j-1 ) ), *> the j-th element is 1, and the last n-j elements are 0. *> *> If UPLO='L', then V = H(1)...H(n-1), where *> -*> H(j) = I - tau(j) v(j) v(j)C> +*> H(j) = I - tau(j) v(j) v(j)**H +*> *> and the first j elements of v(j) are 0, the (j+1)-st is 1, and the *> (j+2)-nd through n-th elements are stored in V(j+2:n,j) (i.e., *> in VP( (2*n-j)*(j-1)/2 + j+2 : (2*n-j)*(j-1)/2 + n ) .) @@ -91,14 +95,15 @@ *> ITYPE is INTEGER *> Specifies the type of tests to be performed. *> 1: U expressed as a dense unitary matrix: -*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp ) +*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and +*> RESULT(2) = | I - U U**H | / ( n ulp ) *> *> 2: U expressed as a product V of Housholder transformations: -*> RESULT(1) = | A - V S V* | / ( |A| n ulp ) +*> RESULT(1) = | A - V S V**H | / ( |A| n ulp ) *> *> 3: U expressed both as a dense unitary matrix and *> as a product of Housholder transformations: -*> RESULT(1) = | I - UV* | / ( n ulp ) +*> RESULT(1) = | I - U V**H | / ( n ulp ) *> \endverbatim *> *> \param[in] UPLO @@ -181,7 +186,7 @@ *> \verbatim *> TAU is COMPLEX*16 array, dimension (N) *> If ITYPE >= 2, then TAU(j) is the scalar factor of -*> v(j) v(j)* in the Householder transformation H(j) of +*> v(j) v(j)**H in the Householder transformation H(j) of *> the product U = H(1)...H(n-2) *> If ITYPE < 2, then TAU is not referenced. *> \endverbatim @@ -313,7 +318,7 @@ SUBROUTINE ZHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP, * IF( ITYPE.EQ.1 ) THEN * -* ITYPE=1: error = A - U S U* +* ITYPE=1: error = A - U S U**H * CALL ZLASET( 'Full', N, N, CZERO, CZERO, WORK, N ) CALL ZCOPY( LAP, AP, 1, WORK, 1 ) @@ -323,7 +328,6 @@ SUBROUTINE ZHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP, 10 CONTINUE * IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN -CMK DO 20 J = 1, N - 1 DO 20 J = 2, N - 1 CALL ZHPR2( CUPLO, N, -DCMPLX( E( J ) ), U( 1, J ), 1, $ U( 1, J-1 ), 1, WORK ) @@ -333,7 +337,7 @@ SUBROUTINE ZHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP, * ELSE IF( ITYPE.EQ.2 ) THEN * -* ITYPE=2: error = V S V* - A +* ITYPE=2: error = V S V**H - A * CALL ZLASET( 'Full', N, N, CZERO, CZERO, WORK, N ) * @@ -401,7 +405,7 @@ SUBROUTINE ZHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP, * ELSE IF( ITYPE.EQ.3 ) THEN * -* ITYPE=3: error = U V* - I +* ITYPE=3: error = U V**H - I * IF( N.LT.2 ) $ RETURN @@ -432,7 +436,7 @@ SUBROUTINE ZHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP, * * Do Test 2 * -* Compute UU* - I +* Compute U U**H - I * IF( ITYPE.EQ.1 ) THEN CALL ZGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO,
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