diff --git a/TESTING/LIN/ctbt02.f b/TESTING/LIN/ctbt02.f index 359eb467f0..8c6a24b51e 100644 --- a/TESTING/LIN/ctbt02.f +++ b/TESTING/LIN/ctbt02.f @@ -29,13 +29,11 @@ *> \verbatim *> *> CTBT02 computes the residual for the computed solution to a -*> triangular system of linear equations A*x = b, A**T *x = b, or -*> A**H *x = b when A is a triangular band matrix. Here A**T denotes -*> the transpose of A, A**H denotes the conjugate transpose of A, and -*> x and b are N by NRHS matrices. The test ratio is the maximum over -*> the number of right hand sides of -*> norm(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. +*> triangular system of linear equations op(A)*X = B, when A is a +*> triangular band matrix. The test ratio is the maximum over the +*> number of right hand sides of +*> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ), +*> where op(A) = A, A**T, or A**H, and EPS is the machine epsilon. *> \endverbatim * * Arguments: @@ -142,7 +140,7 @@ *> \verbatim *> RESID is REAL *> The maximum over the number of right hand sides of -*> norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ). +*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). *> \endverbatim * * Authors: @@ -221,7 +219,7 @@ SUBROUTINE CTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X, END IF * * Compute the maximum over the number of right hand sides of -* norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ). +* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). * RESID = ZERO DO 10 J = 1, NRHS diff --git a/TESTING/LIN/ctpt02.f b/TESTING/LIN/ctpt02.f index 50acb05d36..12d8870c9d 100644 --- a/TESTING/LIN/ctpt02.f +++ b/TESTING/LIN/ctpt02.f @@ -28,14 +28,11 @@ *> \verbatim *> *> CTPT02 computes the residual for the computed solution to a -*> triangular system of linear equations A*x = b, A**T *x = b, or -*> A**H *x = 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, and x and b are N by NRHS matrices. The test ratio -*> is the maximum over the number of right hand sides of +*> triangular system of linear equations op(A)*X = B, when the +*> triangular matrix A is stored in packed format. The test ratio is *> the maximum over the number of right hand sides of -*> norm(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. +*> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ), +*> where op(A) = A, A**T, or A**H, and EPS is the machine epsilon. *> \endverbatim * * Arguments: @@ -53,9 +50,9 @@ *> \verbatim *> TRANS is CHARACTER*1 *> Specifies the operation applied to A. -*> = 'N': A *x = b (No transpose) -*> = 'T': A**T *x = b (Transpose) -*> = 'C': A**H *x = b (Conjugate transpose) +*> = 'N': A * X = B (No transpose) +*> = 'T': A**T * X = B (Transpose) +*> = 'C': A**H * X = B (Conjugate transpose) *> \endverbatim *> *> \param[in] DIAG @@ -130,7 +127,7 @@ *> \verbatim *> RESID is REAL *> The maximum over the number of right hand sides of -*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). +*> norm(op(A)*B - B) / ( norm(op(A)) * norm(X) * EPS ). *> \endverbatim * * Authors: @@ -191,7 +188,7 @@ SUBROUTINE CTPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, RETURN END IF * -* Compute the 1-norm of A or A**H. +* Compute the 1-norm of op(A). * IF( LSAME( TRANS, 'N' ) ) THEN ANORM = CLANTP( '1', UPLO, DIAG, N, AP, RWORK ) @@ -208,7 +205,7 @@ SUBROUTINE CTPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, END IF * * Compute the maximum over the number of right hand sides of -* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). +* norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ). * RESID = ZERO DO 10 J = 1, NRHS diff --git a/TESTING/LIN/ctrt02.f b/TESTING/LIN/ctrt02.f index f93cd77ac0..1addc5881c 100644 --- a/TESTING/LIN/ctrt02.f +++ b/TESTING/LIN/ctrt02.f @@ -29,13 +29,11 @@ *> \verbatim *> *> CTRT02 computes the residual for the computed solution to a -*> triangular system of linear equations A*x = b, A**T *x = b, -*> or A**H *x = b. Here A is a triangular matrix, A**T is the transpose -*> of A, A**H is the conjugate transpose of A, and x and b are N by NRHS -*> matrices. The test ratio is the maximum over the number of right -*> hand sides of -*> norm(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. +*> triangular system of linear equations op(A)*X = B, where A is a +*> triangular matrix. The test ratio is the maximum over the number of +*> right hand sides of +*> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ), +*> where op(A) = A, A**T, or A**H, and EPS is the machine epsilon. *> \endverbatim * * Arguments: @@ -53,9 +51,9 @@ *> \verbatim *> TRANS is CHARACTER*1 *> Specifies the operation applied to A. -*> = 'N': A *x = b (No transpose) -*> = 'T': A**T *x = b (Transpose) -*> = 'C': A**H *x = b (Conjugate transpose) +*> = 'N': A * X = B (No transpose) +*> = 'T': A**T * X = B (Transpose) +*> = 'C': A**H * X = B (Conjugate transpose) *> \endverbatim *> *> \param[in] DIAG @@ -138,7 +136,7 @@ *> \verbatim *> RESID is REAL *> The maximum over the number of right hand sides of -*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). +*> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ). *> \endverbatim * * Authors: @@ -200,7 +198,7 @@ SUBROUTINE CTRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, RETURN END IF * -* Compute the 1-norm of A or A**H. +* Compute the 1-norm of op(A). * IF( LSAME( TRANS, 'N' ) ) THEN ANORM = CLANTR( '1', UPLO, DIAG, N, N, A, LDA, RWORK ) @@ -217,7 +215,7 @@ SUBROUTINE CTRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, END IF * * Compute the maximum over the number of right hand sides of -* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ) +* norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ) * RESID = ZERO DO 10 J = 1, NRHS diff --git a/TESTING/LIN/dtbt02.f b/TESTING/LIN/dtbt02.f index 68b2f0ac5f..5f5192a003 100644 --- a/TESTING/LIN/dtbt02.f +++ b/TESTING/LIN/dtbt02.f @@ -28,12 +28,11 @@ *> \verbatim *> *> DTBT02 computes the residual for the computed solution to a -*> triangular system of linear equations A*x = b or A' *x = b when -*> A is a triangular band matrix. Here A' is the transpose of A and -*> x and b are N by NRHS matrices. The test ratio is the maximum over -*> the number of right hand sides of -*> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ), -*> where op(A) denotes A or A' and EPS is the machine epsilon. +*> triangular system of linear equations op(A)*X = B, when A is a +*> triangular band matrix. The test ratio is the maximum over the +*> number of right hand sides of +*> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ), +*> where op(A) = A, A**T, or A**H and EPS is the machine epsilon. *> The norm used is the 1-norm. *> \endverbatim * @@ -136,7 +135,7 @@ *> \verbatim *> RESID is DOUBLE PRECISION *> The maximum over the number of right hand sides of -*> norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ). +*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). *> \endverbatim * * Authors: @@ -214,7 +213,7 @@ SUBROUTINE DTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X, END IF * * Compute the maximum over the number of right hand sides of -* norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ). +* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). * RESID = ZERO DO 10 J = 1, NRHS diff --git a/TESTING/LIN/dtpt02.f b/TESTING/LIN/dtpt02.f index 1559f132f5..9506a1d195 100644 --- a/TESTING/LIN/dtpt02.f +++ b/TESTING/LIN/dtpt02.f @@ -27,12 +27,11 @@ *> \verbatim *> *> DTPT02 computes the residual for the computed solution to a -*> triangular system of linear equations A*x = b or A'*x = b when -*> the triangular matrix A is stored in packed format. Here A' is the -*> transpose of A and x and b are N by NRHS matrices. The test ratio is +*> triangular system of linear equations op(A)*X = B, when the +*> triangular matrix A is stored in packed format. The test ratio is *> the maximum over the number of right hand sides of -*> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ), -*> where op(A) denotes A or A' and EPS is the machine epsilon. +*> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ), +*> where op(A) = A or A**T, and EPS is the machine epsilon. *> The norm used is the 1-norm. *> \endverbatim * @@ -51,9 +50,9 @@ *> \verbatim *> TRANS is CHARACTER*1 *> Specifies the operation applied to A. -*> = 'N': A *x = b (No transpose) -*> = 'T': A'*x = b (Transpose) -*> = 'C': A'*x = b (Conjugate transpose = Transpose) +*> = 'N': A * X = B (No transpose) +*> = 'T': A**T * X = B (Transpose) +*> = 'C': A**H * X = B (Conjugate transpose = Transpose) *> \endverbatim *> *> \param[in] DIAG @@ -123,7 +122,7 @@ *> \verbatim *> RESID is DOUBLE PRECISION *> The maximum over the number of right hand sides of -*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). +*> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ). *> \endverbatim * * Authors: @@ -183,7 +182,7 @@ SUBROUTINE DTPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, RETURN END IF * -* Compute the 1-norm of A or A'. +* Compute the 1-norm of op(A). * IF( LSAME( TRANS, 'N' ) ) THEN ANORM = DLANTP( '1', UPLO, DIAG, N, AP, WORK ) @@ -200,7 +199,7 @@ SUBROUTINE DTPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, END IF * * Compute the maximum over the number of right hand sides of -* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). +* norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ). * RESID = ZERO DO 10 J = 1, NRHS diff --git a/TESTING/LIN/dtrt02.f b/TESTING/LIN/dtrt02.f index 378400081a..a7c95e136d 100644 --- a/TESTING/LIN/dtrt02.f +++ b/TESTING/LIN/dtrt02.f @@ -28,12 +28,11 @@ *> \verbatim *> *> DTRT02 computes the residual for the computed solution to a -*> triangular system of linear equations A*x = b or A'*x = b. -*> Here A is a triangular matrix, A' is the transpose of A, and x and b -*> are N by NRHS matrices. The test ratio is the maximum over the -*> number of right hand sides of -*> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ), -*> where op(A) denotes A or A' and EPS is the machine epsilon. +*> triangular system of linear equations op(A)*X = B, where A is a +*> triangular matrix. The test ratio is the maximum over the number of +*> right hand sides of +*> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ), +*> where op(A) = A or A**T, and EPS is the machine epsilon. *> The norm used is the 1-norm. *> \endverbatim * @@ -52,9 +51,9 @@ *> \verbatim *> TRANS is CHARACTER*1 *> Specifies the operation applied to A. -*> = 'N': A *x = b (No transpose) -*> = 'T': A'*x = b (Transpose) -*> = 'C': A'*x = b (Conjugate transpose = Transpose) +*> = 'N': A * X = B (No transpose) +*> = 'T': A**T * X = B (Transpose) +*> = 'C': A**H * X = B (Conjugate transpose = Transpose) *> \endverbatim *> *> \param[in] DIAG @@ -132,7 +131,7 @@ *> \verbatim *> RESID is DOUBLE PRECISION *> The maximum over the number of right hand sides of -*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). +*> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ). *> \endverbatim * * Authors: @@ -193,7 +192,7 @@ SUBROUTINE DTRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, RETURN END IF * -* Compute the 1-norm of A or A'. +* Compute the 1-norm of op(A). * IF( LSAME( TRANS, 'N' ) ) THEN ANORM = DLANTR( '1', UPLO, DIAG, N, N, A, LDA, WORK ) @@ -210,7 +209,7 @@ SUBROUTINE DTRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, END IF * * Compute the maximum over the number of right hand sides of -* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ) +* norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ) * RESID = ZERO DO 10 J = 1, NRHS diff --git a/TESTING/LIN/stbt02.f b/TESTING/LIN/stbt02.f index d25e93ef02..31fbf9262a 100644 --- a/TESTING/LIN/stbt02.f +++ b/TESTING/LIN/stbt02.f @@ -28,11 +28,11 @@ *> \verbatim *> *> STBT02 computes the residual for the computed solution to a -*> triangular system of linear equations op(A)*X = B when A is a -*> triangular band matrix. The test ratio is the maximum over the +*> triangular system of linear equations op(A)*X = B, when A is a +*> triangular band matrix. The test ratio is the maximum over the *> number of right hand sides of -*> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ), -*> where op(A) denotes A or A' and EPS is the machine epsilon. +*> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ), +*> where op(A) = A or A**T, and EPS is the machine epsilon. *> The norm used is the 1-norm. *> \endverbatim * @@ -135,7 +135,7 @@ *> \verbatim *> RESID is REAL *> The maximum over the number of right hand sides of -*> norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ). +*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). *> \endverbatim * * Authors: @@ -213,7 +213,7 @@ SUBROUTINE STBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X, END IF * * Compute the maximum over the number of right hand sides of -* norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ). +* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). * RESID = ZERO DO 10 J = 1, NRHS diff --git a/TESTING/LIN/stpt02.f b/TESTING/LIN/stpt02.f index a00755d5f4..72936dd044 100644 --- a/TESTING/LIN/stpt02.f +++ b/TESTING/LIN/stpt02.f @@ -27,12 +27,11 @@ *> \verbatim *> *> STPT02 computes the residual for the computed solution to a -*> triangular system of linear equations A*x = b or A'*x = b when -*> the triangular matrix A is stored in packed format. Here A' is the -*> transpose of A and x and b are N by NRHS matrices. The test ratio is +*> triangular system of linear equations op(A)*X = B, when the +*> triangular matrix A is stored in packed format. The test ratio is *> the maximum over the number of right hand sides of -*> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ), -*> where op(A) denotes A or A' and EPS is the machine epsilon. +*> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ), +*> where op(A) = A or A**T, and EPS is the machine epsilon. *> The norm used is the 1-norm. *> \endverbatim * @@ -51,9 +50,9 @@ *> \verbatim *> TRANS is CHARACTER*1 *> Specifies the operation applied to A. -*> = 'N': A *x = b (No transpose) -*> = 'T': A'*x = b (Transpose) -*> = 'C': A'*x = b (Conjugate transpose = Transpose) +*> = 'N': A * X = B (No transpose) +*> = 'T': A**T * X = B (Transpose) +*> = 'C': A**H * X = B (Conjugate transpose = Transpose) *> \endverbatim *> *> \param[in] DIAG @@ -123,7 +122,7 @@ *> \verbatim *> RESID is REAL *> The maximum over the number of right hand sides of -*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). +*> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ). *> \endverbatim * * Authors: @@ -183,7 +182,7 @@ SUBROUTINE STPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, RETURN END IF * -* Compute the 1-norm of A or A'. +* Compute the 1-norm of op(A). * IF( LSAME( TRANS, 'N' ) ) THEN ANORM = SLANTP( '1', UPLO, DIAG, N, AP, WORK ) @@ -200,7 +199,7 @@ SUBROUTINE STPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, END IF * * Compute the maximum over the number of right hand sides of -* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). +* norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ). * RESID = ZERO DO 10 J = 1, NRHS diff --git a/TESTING/LIN/strt02.f b/TESTING/LIN/strt02.f index 3ecb969fb3..df91501ded 100644 --- a/TESTING/LIN/strt02.f +++ b/TESTING/LIN/strt02.f @@ -28,12 +28,11 @@ *> \verbatim *> *> STRT02 computes the residual for the computed solution to a -*> triangular system of linear equations A*x = b or A'*x = b. -*> Here A is a triangular matrix, A' is the transpose of A, and x and b -*> are N by NRHS matrices. The test ratio is the maximum over the -*> number of right hand sides of -*> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ), -*> where op(A) denotes A or A' and EPS is the machine epsilon. +*> triangular system of linear equations op(A)*X = B, where A is a +*> triangular matrix. The test ratio is the maximum over the number of +*> right hand sides of +*> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ), +*> where op(A) = A or A**T, and EPS is the machine epsilon. *> The norm used is the 1-norm. *> \endverbatim * @@ -52,9 +51,9 @@ *> \verbatim *> TRANS is CHARACTER*1 *> Specifies the operation applied to A. -*> = 'N': A *x = b (No transpose) -*> = 'T': A'*x = b (Transpose) -*> = 'C': A'*x = b (Conjugate transpose = Transpose) +*> = 'N': A * X = B (No transpose) +*> = 'T': A**T * X = B (Transpose) +*> = 'C': A**H * X = B (Conjugate transpose = Transpose) *> \endverbatim *> *> \param[in] DIAG @@ -132,7 +131,7 @@ *> \verbatim *> RESID is REAL *> The maximum over the number of right hand sides of -*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). +*> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ). *> \endverbatim * * Authors: @@ -193,7 +192,7 @@ SUBROUTINE STRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, RETURN END IF * -* Compute the 1-norm of A or A'. +* Compute the 1-norm of op(A). * IF( LSAME( TRANS, 'N' ) ) THEN ANORM = SLANTR( '1', UPLO, DIAG, N, N, A, LDA, WORK ) @@ -210,7 +209,7 @@ SUBROUTINE STRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, END IF * * Compute the maximum over the number of right hand sides of -* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ) +* norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ) * RESID = ZERO DO 10 J = 1, NRHS diff --git a/TESTING/LIN/ztbt02.f b/TESTING/LIN/ztbt02.f index 9943d94672..3c9f119569 100644 --- a/TESTING/LIN/ztbt02.f +++ b/TESTING/LIN/ztbt02.f @@ -29,13 +29,11 @@ *> \verbatim *> *> ZTBT02 computes the residual for the computed solution to a -*> triangular system of linear equations A*x = b, A**T *x = b, or -*> A**H *x = b when A is a triangular band matrix. Here A**T denotes -*> the transpose of A, A**H denotes the conjugate transpose of A, and -*> x and b are N by NRHS matrices. The test ratio is the maximum over -*> the number of right hand sides of -*> norm(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. +*> triangular system of linear equations op(A)*X = B, when A is a +*> triangular band matrix. The test ratio is the maximum over the +*> number of right hand sides of +*> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ), +*> where op(A) = A, A**T, or A**H, and EPS is the machine epsilon. *> \endverbatim * * Arguments: @@ -142,7 +140,7 @@ *> \verbatim *> RESID is DOUBLE PRECISION *> The maximum over the number of right hand sides of -*> norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ). +*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). *> \endverbatim * * Authors: @@ -221,7 +219,7 @@ SUBROUTINE ZTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X, END IF * * Compute the maximum over the number of right hand sides of -* norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ). +* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). * RESID = ZERO DO 10 J = 1, NRHS diff --git a/TESTING/LIN/ztpt02.f b/TESTING/LIN/ztpt02.f index ca65a481ae..8555053d14 100644 --- a/TESTING/LIN/ztpt02.f +++ b/TESTING/LIN/ztpt02.f @@ -28,14 +28,11 @@ *> \verbatim *> *> ZTPT02 computes the residual for the computed solution to a -*> triangular system of linear equations A*x = b, A**T *x = b, or -*> A**H *x = 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, and x and b are N by NRHS matrices. The test ratio -*> is the maximum over the number of right hand sides of +*> triangular system of linear equations op(A)*X = B, when the +*> triangular matrix A is stored in packed format. The test ratio is *> the maximum over the number of right hand sides of -*> norm(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. +*> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ), +*> where op(A) = A, A**T, or A**H, and EPS is the machine epsilon. *> \endverbatim * * Arguments: @@ -53,9 +50,9 @@ *> \verbatim *> TRANS is CHARACTER*1 *> Specifies the operation applied to A. -*> = 'N': A *x = b (No transpose) -*> = 'T': A**T *x = b (Transpose) -*> = 'C': A**H *x = b (Conjugate transpose) +*> = 'N': A * X = B (No transpose) +*> = 'T': A**T * X = B (Transpose) +*> = 'C': A**H * X = B (Conjugate transpose) *> \endverbatim *> *> \param[in] DIAG @@ -130,7 +127,7 @@ *> \verbatim *> RESID is DOUBLE PRECISION *> The maximum over the number of right hand sides of -*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). +*> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ). *> \endverbatim * * Authors: @@ -191,7 +188,7 @@ SUBROUTINE ZTPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, RETURN END IF * -* Compute the 1-norm of A or A**H. +* Compute the 1-norm of op(A). * IF( LSAME( TRANS, 'N' ) ) THEN ANORM = ZLANTP( '1', UPLO, DIAG, N, AP, RWORK ) @@ -208,7 +205,7 @@ SUBROUTINE ZTPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, END IF * * Compute the maximum over the number of right hand sides of -* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). +* norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ). * RESID = ZERO DO 10 J = 1, NRHS diff --git a/TESTING/LIN/ztrt02.f b/TESTING/LIN/ztrt02.f index a23ce821f7..47e9f3463c 100644 --- a/TESTING/LIN/ztrt02.f +++ b/TESTING/LIN/ztrt02.f @@ -29,13 +29,11 @@ *> \verbatim *> *> ZTRT02 computes the residual for the computed solution to a -*> triangular system of linear equations A*x = b, A**T *x = b, -*> or A**H *x = b. Here A is a triangular matrix, A**T is the transpose -*> of A, A**H is the conjugate transpose of A, and x and b are N by NRHS -*> matrices. The test ratio is the maximum over the number of right -*> hand sides of -*> norm(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. +*> triangular system of linear equations op(A)*X = B, where A is a +*> triangular matrix. The test ratio is the maximum over the number of +*> right hand sides of +*> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ), +*> where op(A) = A, A**T, or A**H, and EPS is the machine epsilon. *> \endverbatim * * Arguments: @@ -53,9 +51,9 @@ *> \verbatim *> TRANS is CHARACTER*1 *> Specifies the operation applied to A. -*> = 'N': A *x = b (No transpose) -*> = 'T': A**T *x = b (Transpose) -*> = 'C': A**H *x = b (Conjugate transpose) +*> = 'N': A * X = B (No transpose) +*> = 'T': A**T * X = B (Transpose) +*> = 'C': A**H * X = B (Conjugate transpose) *> \endverbatim *> *> \param[in] DIAG @@ -138,7 +136,7 @@ *> \verbatim *> RESID is DOUBLE PRECISION *> The maximum over the number of right hand sides of -*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). +*> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ). *> \endverbatim * * Authors: @@ -200,7 +198,7 @@ SUBROUTINE ZTRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, RETURN END IF * -* Compute the 1-norm of A or A**H. +* Compute the 1-norm of op(A). * IF( LSAME( TRANS, 'N' ) ) THEN ANORM = ZLANTR( '1', UPLO, DIAG, N, N, A, LDA, RWORK ) @@ -217,7 +215,7 @@ SUBROUTINE ZTRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, END IF * * Compute the maximum over the number of right hand sides of -* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ) +* norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ) * RESID = ZERO DO 10 J = 1, NRHS