From 0e40ab207de16ae133cc97d2d6b3a29d0f4f009b Mon Sep 17 00:00:00 2001 From: Mathieu Faverge <mathieu.faverge@inria.fr> Date: Thu, 11 Apr 2019 18:51:37 +0200 Subject: [PATCH] Update **T as **H --- compute/zgesvd.c | 2 +- compute/zgetrs_incpiv.c | 2 +- compute/zgetrs_nopiv.c | 2 +- compute/zsysv.c | 4 ++-- compute/zsytrf.c | 2 +- compute/zsytrs.c | 4 ++-- coreblas/compute/core_zherfb.c | 4 ++-- coreblas/compute/core_zpamm.c | 2 +- coreblas/compute/core_zpemv.c | 4 ++-- coreblas/compute/core_zunmlq.c | 2 +- coreblas/compute/core_zunmqr.c | 2 +- runtime/openmp/codelets/codelet_zunmlq.c | 2 +- runtime/openmp/codelets/codelet_zunmqr.c | 2 +- runtime/quark/codelets/codelet_zunmlq.c | 2 +- runtime/quark/codelets/codelet_zunmqr.c | 2 +- runtime/starpu/codelets/codelet_zunmlq.c | 2 +- runtime/starpu/codelets/codelet_zunmqr.c | 2 +- testing/lin/clagsy.f | 2 +- testing/lin/clarhs.f | 4 ++-- testing/lin/clatrs.f | 16 ++++++++-------- testing/lin/dpocon.f | 4 ++-- testing/lin/dporfs.f | 2 +- testing/lin/dposvx.f | 12 ++++++------ testing/lin/dpotri.f | 4 ++-- testing/lin/spocon.f | 4 ++-- testing/lin/sporfs.f | 2 +- testing/lin/sposvx.f | 12 ++++++------ testing/lin/spotri.f | 4 ++-- testing/lin/zlagsy.f | 2 +- testing/lin/zlarhs.f | 4 ++-- testing/lin/zlatrs.f | 16 ++++++++-------- 31 files changed, 65 insertions(+), 65 deletions(-) diff --git a/compute/zgesvd.c b/compute/zgesvd.c index 65954ded7..7d12a10ba 100644 --- a/compute/zgesvd.c +++ b/compute/zgesvd.c @@ -44,7 +44,7 @@ * are returned in descending order. The first min(m,n) columns of * U and V are the left and right singular vectors of A. * - * Note that the routine returns V**T, not V. + * Note that the routine returns V^T, not V. ******************************************************************************* * * @param[in] jobu diff --git a/compute/zgetrs_incpiv.c b/compute/zgetrs_incpiv.c index 092066b6e..225cb125f 100644 --- a/compute/zgetrs_incpiv.c +++ b/compute/zgetrs_incpiv.c @@ -37,7 +37,7 @@ * @param[in] trans * Intended to specify the the form of the system of equations: * = ChamNoTrans: A * X = B (No transpose) - * = ChamTrans: A**T * X = B (Transpose) + * = ChamTrans: A^T * X = B (Transpose) * = ChamConjTrans: A^H * X = B (Conjugate transpose) * Currently only ChamNoTrans is supported. * diff --git a/compute/zgetrs_nopiv.c b/compute/zgetrs_nopiv.c index 9392d31a1..3a3dfe360 100644 --- a/compute/zgetrs_nopiv.c +++ b/compute/zgetrs_nopiv.c @@ -38,7 +38,7 @@ * @param[in] trans * Intended to specify the the form of the system of equations: * = ChamNoTrans: A * X = B (No transpose) - * = ChamTrans: A**T * X = B (Transpose) + * = ChamTrans: A^T * X = B (Transpose) * = ChamConjTrans: A^H * X = B (Conjugate transpose) * Currently only ChamNoTrans is supported. * diff --git a/compute/zsysv.c b/compute/zsysv.c index 256e27de9..ebee2c6f1 100644 --- a/compute/zsysv.c +++ b/compute/zsysv.c @@ -62,7 +62,7 @@ * triangular part of the matrix A, and the strictly upper triangular part of A is not * referenced. * On exit, if return value = 0, the factor U or L from the Cholesky factorization - * A = U**T*U or A = L*L**T. + * A = U^T*U or A = L*L^T. * * @param[in] LDA * The leading dimension of the array A. LDA >= max(1,N). @@ -194,7 +194,7 @@ int CHAMELEON_zsysv( cham_uplo_t uplo, int N, int NRHS, * triangular part of the matrix A, and the strictly upper triangular part of A is not * referenced. * On exit, if return value = 0, the factor U or L from the Cholesky factorization - * A = U**T*U or A = L*L**T. + * A = U^T*U or A = L*L^T. * * @param[in,out] B * On entry, the N-by-NRHS right hand side matrix B. diff --git a/compute/zsytrf.c b/compute/zsytrf.c index 3f13655ce..b603ddde5 100644 --- a/compute/zsytrf.c +++ b/compute/zsytrf.c @@ -164,7 +164,7 @@ int CHAMELEON_zsytrf( cham_uplo_t uplo, int N, * triangular part of the matrix A, and the strictly upper triangular part of A is not * referenced. * On exit, if return value = 0, the factor U or L from the Cholesky factorization - * A = U**T*U or A = L*L**T. + * A = U^T*U or A = L*L^T. * ******************************************************************************* * diff --git a/compute/zsytrs.c b/compute/zsytrs.c index 7cf60f28e..84a2c778f 100644 --- a/compute/zsytrs.c +++ b/compute/zsytrs.c @@ -48,7 +48,7 @@ * The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. * * @param[in] A - * The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, + * The triangular factor U or L from the Cholesky factorization A = U^T*U or A = L*L^T, * computed by CHAMELEON_zsytrf. * * @param[in] LDA @@ -172,7 +172,7 @@ int CHAMELEON_zsytrs( cham_uplo_t uplo, int N, int NRHS, * = ChamLower: Lower triangle of A is stored. * * @param[in] A - * The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, + * The triangular factor U or L from the Cholesky factorization A = U^T*U or A = L*L^T, * computed by CHAMELEON_zsytrf. * * @param[in,out] B diff --git a/coreblas/compute/core_zherfb.c b/coreblas/compute/core_zherfb.c index d71c18028..a54de4a5a 100644 --- a/coreblas/compute/core_zherfb.c +++ b/coreblas/compute/core_zherfb.c @@ -27,7 +27,7 @@ * * CORE_zherfb overwrites the symmetric complex N-by-N tile C with * - * Q**T*C*Q + * Q^T*C*Q * * where Q is a complex unitary matrix defined as the product of k * elementary reflectors @@ -72,7 +72,7 @@ * * @param[in,out] C * On entry, the symmetric N-by-N tile C. - * On exit, C is overwritten by Q**T*C*Q. + * On exit, C is overwritten by Q^T*C*Q. * * @param[in] ldc * The leading dimension of the array C. LDC >= max(1,M). diff --git a/coreblas/compute/core_zpamm.c b/coreblas/compute/core_zpamm.c index 438737436..01a25ea55 100644 --- a/coreblas/compute/core_zpamm.c +++ b/coreblas/compute/core_zpamm.c @@ -52,7 +52,7 @@ static inline int CORE_zpamm_w(cham_side_t side, cham_trans_t trans, cham_uplo_t * * where op( V ) is one of * - * op( V ) = V or op( V ) = V**T or op( V ) = V^H, + * op( V ) = V or op( V ) = V^T or op( V ) = V^H, * * A1, A2 and W are general matrices, and V is: * diff --git a/coreblas/compute/core_zpemv.c b/coreblas/compute/core_zpemv.c index 846c26950..0144020a7 100644 --- a/coreblas/compute/core_zpemv.c +++ b/coreblas/compute/core_zpemv.c @@ -36,7 +36,7 @@ * * where op( A ) is one of * - * op( A ) = A or op( A ) = A**T or op( A ) = A^H, + * op( A ) = A or op( A ) = A^T or op( A ) = A^H, * * alpha and beta are scalars, x and y are vectors and A is a * pentagonal matrix (see further details). @@ -52,7 +52,7 @@ * @param[in] trans * * @arg ChamNoTrans : y := alpha*A*x + beta*y. - * @arg ChamTrans : y := alpha*A**T*x + beta*y. + * @arg ChamTrans : y := alpha*A^T*x + beta*y. * @arg ChamConjTrans : y := alpha*A^H*x + beta*y. * * @param[in] M diff --git a/coreblas/compute/core_zunmlq.c b/coreblas/compute/core_zunmlq.c index b1b98c485..6a310b859 100644 --- a/coreblas/compute/core_zunmlq.c +++ b/coreblas/compute/core_zunmlq.c @@ -90,7 +90,7 @@ * * @param[in,out] C * On entry, the M-by-N tile C. - * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. + * On exit, C is overwritten by Q*C or Q^T*C or C*Q^T or C*Q. * * @param[in] LDC * The leading dimension of the array C. LDC >= max(1,M). diff --git a/coreblas/compute/core_zunmqr.c b/coreblas/compute/core_zunmqr.c index 068a5f40c..712da7e6c 100644 --- a/coreblas/compute/core_zunmqr.c +++ b/coreblas/compute/core_zunmqr.c @@ -91,7 +91,7 @@ * * @param[in,out] C * On entry, the M-by-N tile C. - * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. + * On exit, C is overwritten by Q*C or Q^T*C or C*Q^T or C*Q. * * @param[in] LDC * The leading dimension of the array C. LDC >= max(1,M). diff --git a/runtime/openmp/codelets/codelet_zunmlq.c b/runtime/openmp/codelets/codelet_zunmlq.c index 6a4f7bdac..92d6e71f8 100644 --- a/runtime/openmp/codelets/codelet_zunmlq.c +++ b/runtime/openmp/codelets/codelet_zunmlq.c @@ -90,7 +90,7 @@ * * @param[in,out] C * On entry, the M-by-N tile C. - * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. + * On exit, C is overwritten by Q*C or Q^T*C or C*Q^T or C*Q. * * @param[in] LDC * The leading dimension of the array C. LDC >= max(1,M). diff --git a/runtime/openmp/codelets/codelet_zunmqr.c b/runtime/openmp/codelets/codelet_zunmqr.c index 2e796545f..66aa62b5d 100644 --- a/runtime/openmp/codelets/codelet_zunmqr.c +++ b/runtime/openmp/codelets/codelet_zunmqr.c @@ -90,7 +90,7 @@ * * @param[in,out] C * On entry, the M-by-N tile C. - * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. + * On exit, C is overwritten by Q*C or Q^T*C or C*Q^T or C*Q. * * @param[in] LDC * The leading dimension of the array C. LDC >= max(1,M). diff --git a/runtime/quark/codelets/codelet_zunmlq.c b/runtime/quark/codelets/codelet_zunmlq.c index bed3fa03f..5b8687571 100644 --- a/runtime/quark/codelets/codelet_zunmlq.c +++ b/runtime/quark/codelets/codelet_zunmlq.c @@ -114,7 +114,7 @@ void CORE_zunmlq_quark(Quark *quark) * * @param[in,out] C * On entry, the M-by-N tile C. - * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. + * On exit, C is overwritten by Q*C or Q^T*C or C*Q^T or C*Q. * * @param[in] LDC * The leading dimension of the array C. LDC >= max(1,M). diff --git a/runtime/quark/codelets/codelet_zunmqr.c b/runtime/quark/codelets/codelet_zunmqr.c index 34ca5fdce..f03746016 100644 --- a/runtime/quark/codelets/codelet_zunmqr.c +++ b/runtime/quark/codelets/codelet_zunmqr.c @@ -114,7 +114,7 @@ void CORE_zunmqr_quark(Quark *quark) * * @param[in,out] C * On entry, the M-by-N tile C. - * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. + * On exit, C is overwritten by Q*C or Q^T*C or C*Q^T or C*Q. * * @param[in] LDC * The leading dimension of the array C. LDC >= max(1,M). diff --git a/runtime/starpu/codelets/codelet_zunmlq.c b/runtime/starpu/codelets/codelet_zunmlq.c index 28d4c5095..be36f957d 100644 --- a/runtime/starpu/codelets/codelet_zunmlq.c +++ b/runtime/starpu/codelets/codelet_zunmlq.c @@ -159,7 +159,7 @@ CODELETS(zunmlq, 4, cl_zunmlq_cpu_func, cl_zunmlq_cuda_func, STARPU_CUDA_ASYNC) * * @param[in,out] C * On entry, the M-by-N tile C. - * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. + * On exit, C is overwritten by Q*C or Q^T*C or C*Q^T or C*Q. * * @param[in] LDC * The leading dimension of the array C. LDC >= max(1,M). diff --git a/runtime/starpu/codelets/codelet_zunmqr.c b/runtime/starpu/codelets/codelet_zunmqr.c index 6681a39f7..8ff98bc79 100644 --- a/runtime/starpu/codelets/codelet_zunmqr.c +++ b/runtime/starpu/codelets/codelet_zunmqr.c @@ -159,7 +159,7 @@ CODELETS(zunmqr, 4, cl_zunmqr_cpu_func, cl_zunmqr_cuda_func, STARPU_CUDA_ASYNC) * * @param[in,out] C * On entry, the M-by-N tile C. - * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. + * On exit, C is overwritten by Q*C or Q^T*C or C*Q^T or C*Q. * * @param[in] LDC * The leading dimension of the array C. LDC >= max(1,M). diff --git a/testing/lin/clagsy.f b/testing/lin/clagsy.f index c5fea1b7d..0522d0600 100644 --- a/testing/lin/clagsy.f +++ b/testing/lin/clagsy.f @@ -55,7 +55,7 @@ * * CLAGSY generates a complex symmetric matrix A, by pre- and post- * multiplying a real diagonal matrix D with a random unitary matrix: -* A = U*D*U**T. The semi-bandwidth may then be reduced to k by +* A = U*D*U^T. The semi-bandwidth may then be reduced to k by * additional unitary transformations. * * Arguments diff --git a/testing/lin/clarhs.f b/testing/lin/clarhs.f index 4a683f6a7..22165f3a3 100644 --- a/testing/lin/clarhs.f +++ b/testing/lin/clarhs.f @@ -58,7 +58,7 @@ * CLARHS chooses a set of NRHS random solution vectors and sets * up the right hand sides for the linear system * op( A ) * X = B, -* where op( A ) may be A, A**T (transpose of A), or A^H (conjugate +* where op( A ) may be A, A^T (transpose of A), or A^H (conjugate * transpose of A). * * Arguments @@ -102,7 +102,7 @@ * Used only if A is nonsymmetric; specifies the operation * applied to the matrix A. * = 'N': B := A * X -* = 'T': B := A**T * X +* = 'T': B := A^T * X * = 'C': B := A^H * X * * M (input) INTEGER diff --git a/testing/lin/clatrs.f b/testing/lin/clatrs.f index 0510829d6..38cc5a2a2 100644 --- a/testing/lin/clatrs.f +++ b/testing/lin/clatrs.f @@ -57,10 +57,10 @@ * * CLATRS solves one of the triangular systems * -* A * x = s*b, A**T * x = s*b, or A^H * x = s*b, +* A * x = s*b, A^T * x = s*b, or A^H * x = s*b, * * with scaling to prevent overflow. Here A is an upper or lower -* triangular matrix, A**T denotes the transpose of A, A^H denotes the +* triangular matrix, A^T denotes the transpose of A, A^H denotes the * conjugate transpose of A, x and b are n-element vectors, and s is a * scaling factor, usually less than or equal to 1, chosen so that the * components of x will be less than the overflow threshold. If the @@ -79,7 +79,7 @@ * TRANS (input) CHARACTER*1 * Specifies the operation applied to A. * = 'N': Solve A * x = s*b (No transpose) -* = 'T': Solve A**T * x = s*b (Transpose) +* = 'T': Solve A^T * x = s*b (Transpose) * = 'C': Solve A^H * x = s*b (Conjugate transpose) * * DIAG (input) CHARACTER*1 @@ -115,7 +115,7 @@ * * SCALE (output) REAL * The scaling factor s for the triangular system -* A * x = s*b, A**T * x = s*b, or A^H * x = s*b. +* A * x = s*b, A^T * x = s*b, or A^H * x = s*b. * If SCALE = 0, the matrix A is singular or badly scaled, and * the vector x is an exact or approximate solution to A*x = 0. * @@ -181,7 +181,7 @@ * prevent overflow, but if the bound overflows, x is set to 0, x(j) to * 1, and scale to 0, and a non-trivial solution to A*x = 0 is found. * -* Similarly, a row-wise scheme is used to solve A**T *x = b or +* Similarly, a row-wise scheme is used to solve A^T *x = b or * A^H *x = b. The basic algorithm for A upper triangular is * * for j = 1, ..., n @@ -412,7 +412,7 @@ * ELSE * -* Compute the growth in A**T * x = b or A^H * x = b. +* Compute the growth in A^T * x = b or A^H * x = b. * IF( UPPER ) THEN JFIRST = 1 @@ -632,7 +632,7 @@ * ELSE IF( LSAME( TRANS, 'T' ) ) THEN * -* Solve A**T * x = b +* Solve A^T * x = b * DO 150 J = JFIRST, JLAST, JINC * @@ -744,7 +744,7 @@ ELSE * * A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and -* scale = 0 and compute a solution to A**T *x = 0. +* scale = 0 and compute a solution to A^T *x = 0. * DO 140 I = 1, N X( I ) = ZERO diff --git a/testing/lin/dpocon.f b/testing/lin/dpocon.f index 43c957d38..1a4c1b67a 100644 --- a/testing/lin/dpocon.f +++ b/testing/lin/dpocon.f @@ -59,7 +59,7 @@ * * DPOCON estimates the reciprocal of the condition number (in the * 1-norm) of a real symmetric positive definite matrix using the -* Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF. +* Cholesky factorization A = U^T*U or A = L*L^T computed by DPOTRF. * * An estimate is obtained for norm(inv(A)), and the reciprocal of the * condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). @@ -76,7 +76,7 @@ * * A (input) DOUBLE PRECISION array, dimension (LDA,N) * The triangular factor U or L from the Cholesky factorization -* A = U**T*U or A = L*L**T, as computed by DPOTRF. +* A = U^T*U or A = L*L^T, as computed by DPOTRF. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). diff --git a/testing/lin/dporfs.f b/testing/lin/dporfs.f index 3a1496638..c93d5793a 100644 --- a/testing/lin/dporfs.f +++ b/testing/lin/dporfs.f @@ -92,7 +92,7 @@ * * AF (input) DOUBLE PRECISION array, dimension (LDAF,N) * The triangular factor U or L from the Cholesky factorization -* A = U**T*U or A = L*L**T, as computed by DPOTRF. +* A = U^T*U or A = L*L^T, as computed by DPOTRF. * * LDAF (input) INTEGER * The leading dimension of the array AF. LDAF >= max(1,N). diff --git a/testing/lin/dposvx.f b/testing/lin/dposvx.f index aeca6aee0..79d723a27 100644 --- a/testing/lin/dposvx.f +++ b/testing/lin/dposvx.f @@ -61,7 +61,7 @@ * Purpose * ======= * -* DPOSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to +* DPOSVX uses the Cholesky factorization A = U^T*U or A = L*L^T to * compute the solution to a real system of linear equations * A * X = B, * where A is an N-by-N symmetric positive definite matrix and X and B @@ -84,8 +84,8 @@ * * 2. If FACT = 'N' or 'E', the Cholesky decomposition is used to * factor the matrix A (after equilibration if FACT = 'E') as -* A = U**T* U, if UPLO = 'U', or -* A = L * L**T, if UPLO = 'L', +* A = U^T* U, if UPLO = 'U', or +* A = L * L^T, if UPLO = 'L', * where U is an upper triangular matrix and L is a lower triangular * matrix. * @@ -156,18 +156,18 @@ * AF (input or output) DOUBLE PRECISION array, dimension (LDAF,N) * If FACT = 'F', then AF is an input argument and on entry * contains the triangular factor U or L from the Cholesky -* factorization A = U**T*U or A = L*L**T, in the same storage +* factorization A = U^T*U or A = L*L^T, in the same storage * format as A. If EQUED .ne. 'N', then AF is the factored form * of the equilibrated matrix diag(S)*A*diag(S). * * If FACT = 'N', then AF is an output argument and on exit * returns the triangular factor U or L from the Cholesky -* factorization A = U**T*U or A = L*L**T of the original +* factorization A = U^T*U or A = L*L^T of the original * matrix A. * * If FACT = 'E', then AF is an output argument and on exit * returns the triangular factor U or L from the Cholesky -* factorization A = U**T*U or A = L*L**T of the equilibrated +* factorization A = U^T*U or A = L*L^T of the equilibrated * matrix A (see the description of A for the form of the * equilibrated matrix). * diff --git a/testing/lin/dpotri.f b/testing/lin/dpotri.f index f8585b348..2a5f4c2dd 100644 --- a/testing/lin/dpotri.f +++ b/testing/lin/dpotri.f @@ -53,7 +53,7 @@ * ======= * * DPOTRI computes the inverse of a real symmetric positive definite -* matrix A using the Cholesky factorization A = U**T*U or A = L*L**T +* matrix A using the Cholesky factorization A = U^T*U or A = L*L^T * computed by DPOTRF. * * Arguments @@ -68,7 +68,7 @@ * * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) * On entry, the triangular factor U or L from the Cholesky -* factorization A = U**T*U or A = L*L**T, as computed by +* factorization A = U^T*U or A = L*L^T, as computed by * DPOTRF. * On exit, the upper or lower triangle of the (symmetric) * inverse of A, overwriting the input factor U or L. diff --git a/testing/lin/spocon.f b/testing/lin/spocon.f index 02392607f..380896480 100644 --- a/testing/lin/spocon.f +++ b/testing/lin/spocon.f @@ -59,7 +59,7 @@ * * SPOCON estimates the reciprocal of the condition number (in the * 1-norm) of a real symmetric positive definite matrix using the -* Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF. +* Cholesky factorization A = U^T*U or A = L*L^T computed by SPOTRF. * * An estimate is obtained for norm(inv(A)), and the reciprocal of the * condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). @@ -76,7 +76,7 @@ * * A (input) REAL array, dimension (LDA,N) * The triangular factor U or L from the Cholesky factorization -* A = U**T*U or A = L*L**T, as computed by SPOTRF. +* A = U^T*U or A = L*L^T, as computed by SPOTRF. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). diff --git a/testing/lin/sporfs.f b/testing/lin/sporfs.f index 8dcdea760..e633b0978 100644 --- a/testing/lin/sporfs.f +++ b/testing/lin/sporfs.f @@ -92,7 +92,7 @@ * * AF (input) REAL array, dimension (LDAF,N) * The triangular factor U or L from the Cholesky factorization -* A = U**T*U or A = L*L**T, as computed by SPOTRF. +* A = U^T*U or A = L*L^T, as computed by SPOTRF. * * LDAF (input) INTEGER * The leading dimension of the array AF. LDAF >= max(1,N). diff --git a/testing/lin/sposvx.f b/testing/lin/sposvx.f index b8a94475a..8a8f53564 100644 --- a/testing/lin/sposvx.f +++ b/testing/lin/sposvx.f @@ -61,7 +61,7 @@ * Purpose * ======= * -* SPOSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to +* SPOSVX uses the Cholesky factorization A = U^T*U or A = L*L^T to * compute the solution to a real system of linear equations * A * X = B, * where A is an N-by-N symmetric positive definite matrix and X and B @@ -84,8 +84,8 @@ * * 2. If FACT = 'N' or 'E', the Cholesky decomposition is used to * factor the matrix A (after equilibration if FACT = 'E') as -* A = U**T* U, if UPLO = 'U', or -* A = L * L**T, if UPLO = 'L', +* A = U^T* U, if UPLO = 'U', or +* A = L * L^T, if UPLO = 'L', * where U is an upper triangular matrix and L is a lower triangular * matrix. * @@ -156,18 +156,18 @@ * AF (input or output) REAL array, dimension (LDAF,N) * If FACT = 'F', then AF is an input argument and on entry * contains the triangular factor U or L from the Cholesky -* factorization A = U**T*U or A = L*L**T, in the same storage +* factorization A = U^T*U or A = L*L^T, in the same storage * format as A. If EQUED .ne. 'N', then AF is the factored form * of the equilibrated matrix diag(S)*A*diag(S). * * If FACT = 'N', then AF is an output argument and on exit * returns the triangular factor U or L from the Cholesky -* factorization A = U**T*U or A = L*L**T of the original +* factorization A = U^T*U or A = L*L^T of the original * matrix A. * * If FACT = 'E', then AF is an output argument and on exit * returns the triangular factor U or L from the Cholesky -* factorization A = U**T*U or A = L*L**T of the equilibrated +* factorization A = U^T*U or A = L*L^T of the equilibrated * matrix A (see the description of A for the form of the * equilibrated matrix). * diff --git a/testing/lin/spotri.f b/testing/lin/spotri.f index 13885e2fd..d52f05699 100644 --- a/testing/lin/spotri.f +++ b/testing/lin/spotri.f @@ -53,7 +53,7 @@ * ======= * * SPOTRI computes the inverse of a real symmetric positive definite -* matrix A using the Cholesky factorization A = U**T*U or A = L*L**T +* matrix A using the Cholesky factorization A = U^T*U or A = L*L^T * computed by SPOTRF. * * Arguments @@ -68,7 +68,7 @@ * * A (input/output) REAL array, dimension (LDA,N) * On entry, the triangular factor U or L from the Cholesky -* factorization A = U**T*U or A = L*L**T, as computed by +* factorization A = U^T*U or A = L*L^T, as computed by * SPOTRF. * On exit, the upper or lower triangle of the (symmetric) * inverse of A, overwriting the input factor U or L. diff --git a/testing/lin/zlagsy.f b/testing/lin/zlagsy.f index d2a05500d..a9366c90c 100644 --- a/testing/lin/zlagsy.f +++ b/testing/lin/zlagsy.f @@ -55,7 +55,7 @@ * * ZLAGSY generates a complex symmetric matrix A, by pre- and post- * multiplying a real diagonal matrix D with a random unitary matrix: -* A = U*D*U**T. The semi-bandwidth may then be reduced to k by +* A = U*D*U^T. The semi-bandwidth may then be reduced to k by * additional unitary transformations. * * Arguments diff --git a/testing/lin/zlarhs.f b/testing/lin/zlarhs.f index 9ace77805..333feeb71 100644 --- a/testing/lin/zlarhs.f +++ b/testing/lin/zlarhs.f @@ -58,7 +58,7 @@ * ZLARHS chooses a set of NRHS random solution vectors and sets * up the right hand sides for the linear system * op( A ) * X = B, -* where op( A ) may be A, A**T (transpose of A), or A^H (conjugate +* where op( A ) may be A, A^T (transpose of A), or A^H (conjugate * transpose of A). * * Arguments @@ -102,7 +102,7 @@ * Used only if A is nonsymmetric; specifies the operation * applied to the matrix A. * = 'N': B := A * X -* = 'T': B := A**T * X +* = 'T': B := A^T * X * = 'C': B := A^H * X * * M (input) INTEGER diff --git a/testing/lin/zlatrs.f b/testing/lin/zlatrs.f index 6447bee9a..ba7f497ef 100644 --- a/testing/lin/zlatrs.f +++ b/testing/lin/zlatrs.f @@ -57,10 +57,10 @@ * * ZLATRS solves one of the triangular systems * -* A * x = s*b, A**T * x = s*b, or A^H * x = s*b, +* A * x = s*b, A^T * x = s*b, or A^H * x = s*b, * * with scaling to prevent overflow. Here A is an upper or lower -* triangular matrix, A**T denotes the transpose of A, A^H denotes the +* triangular matrix, A^T denotes the transpose of A, A^H denotes the * conjugate transpose of A, x and b are n-element vectors, and s is a * scaling factor, usually less than or equal to 1, chosen so that the * components of x will be less than the overflow threshold. If the @@ -79,7 +79,7 @@ * TRANS (input) CHARACTER*1 * Specifies the operation applied to A. * = 'N': Solve A * x = s*b (No transpose) -* = 'T': Solve A**T * x = s*b (Transpose) +* = 'T': Solve A^T * x = s*b (Transpose) * = 'C': Solve A^H * x = s*b (Conjugate transpose) * * DIAG (input) CHARACTER*1 @@ -115,7 +115,7 @@ * * SCALE (output) DOUBLE PRECISION * The scaling factor s for the triangular system -* A * x = s*b, A**T * x = s*b, or A^H * x = s*b. +* A * x = s*b, A^T * x = s*b, or A^H * x = s*b. * If SCALE = 0, the matrix A is singular or badly scaled, and * the vector x is an exact or approximate solution to A*x = 0. * @@ -181,7 +181,7 @@ * prevent overflow, but if the bound overflows, x is set to 0, x(j) to * 1, and scale to 0, and a non-trivial solution to A*x = 0 is found. * -* Similarly, a row-wise scheme is used to solve A**T *x = b or +* Similarly, a row-wise scheme is used to solve A^T *x = b or * A^H *x = b. The basic algorithm for A upper triangular is * * for j = 1, ..., n @@ -412,7 +412,7 @@ * ELSE * -* Compute the growth in A**T * x = b or A^H * x = b. +* Compute the growth in A^T * x = b or A^H * x = b. * IF( UPPER ) THEN JFIRST = 1 @@ -632,7 +632,7 @@ * ELSE IF( LSAME( TRANS, 'T' ) ) THEN * -* Solve A**T * x = b +* Solve A^T * x = b * DO 170 J = JFIRST, JLAST, JINC * @@ -744,7 +744,7 @@ ELSE * * A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and -* scale = 0 and compute a solution to A**T *x = 0. +* scale = 0 and compute a solution to A^T *x = 0. * DO 150 I = 1, N X( I ) = ZERO -- GitLab