# rocsolver_ssytd2_batched Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_ssytd2_batched Interface Reference
hipfort_rocsolver::rocsolver_ssytd2_batched Interface Reference

SYTD2_BATCHED computes the tridiagonal form of a batch of real symmetric matrices A_j. More...

## Public Member Functions

integer(kind(rocblas_status_success)) function rocsolver_ssytd2_batched_ (handle, uplo, n, A, lda, D, strideD, E, strideE, tau, strideP, batch_count)

integer(kind(rocblas_status_success)) function rocsolver_ssytd2_batched_full_rank (handle, uplo, n, A, lda, D, strideD, E, strideE, tau, strideP, batch_count)

integer(kind(rocblas_status_success)) function rocsolver_ssytd2_batched_rank_0 (handle, uplo, n, A, lda, D, strideD, E, strideE, tau, strideP, batch_count)

integer(kind(rocblas_status_success)) function rocsolver_ssytd2_batched_rank_1 (handle, uplo, n, A, lda, D, strideD, E, strideE, tau, strideP, batch_count)

## Detailed Description

SYTD2_BATCHED computes the tridiagonal form of a batch of real symmetric matrices A_j.

(This is the unblocked version of the algorithm).

The tridiagonal form of $$A_j$$ is given by:

$T_j = Q_j' A_j Q_j$

where $$T_j$$ is symmetric tridiagonal and $$Q_j$$ is an orthogonal matrix represented as the product of Householder matrices

$\begin{array}{cl} Q_j = H_{j_1}H_{j_2}\cdots H_{j_{n-1}} & \: \text{if uplo indicates lower, or}\newline Q_j = H_{j_{n-1}}H_{j_{n-2}}\cdots H_{j_1} & \: \text{if uplo indicates upper.} \end{array}$

Each Householder matrix $$H_{j_i}$$ is given by

$H_{j_i} = I - \text{tau}_j[i] \cdot v_{j_i} v_{j_i}'$

where $$\text{tau}_j[i]$$ is the corresponding Householder scalar. When uplo indicates lower, the first i elements of the Householder vector $$v_{j_i}$$ are zero, and $$v_{j_i}[i+1] = 1$$. If uplo indicates upper, the last n-i elements of the Householder vector $$v_{j_i}$$ are zero, and $$v_{j_i}[i] = 1$$.

Parameters
 [in] handle rocblas_handle. [in] uplo rocblas_fill. Specifies whether the upper or lower part of the symmetric matrix A_j is stored. If uplo indicates lower (or upper), then the upper (or lower) part of A is not used. [in] n rocblas_int. n >= 0. The number of rows and columns of the matrices A_j. [in,out] A array of pointers to type. Each pointer points to an array on the GPU of dimension lda*n. On entry, the matrices A_j to be factored. On exit, if upper, then the elements on the diagonal and superdiagonal contain the tridiagonal form T_j; the elements above the superdiagonal contain the first i-1 elements of the Householder vectors v_(j_i) stored as columns. If lower, then the elements on the diagonal and subdiagonal contain the tridiagonal form T_j; the elements below the subdiagonal contain the last n-i-1 elements of the Householder vectors v_(j_i) stored as columns. [in] lda rocblas_int. lda >= n. The leading dimension of A_j. [out] D pointer to type. Array on the GPU (the size depends on the value of strideD). The diagonal elements of T_j. [in] strideD rocblas_stride. Stride from the start of one vector D_j to the next one D_(j+1). There is no restriction for the value of strideD. Normal use case is strideD >= n. [out] E pointer to type. Array on the GPU (the size depends on the value of strideE). The off-diagonal elements of T_j. [in] strideE rocblas_stride. Stride from the start of one vector E_j to the next one E_(j+1). There is no restriction for the value of strideE. Normal use case is strideE >= n-1. [out] tau pointer to type. Array on the GPU (the size depends on the value of strideP). Contains the vectors tau_j of corresponding Householder scalars. [in] strideP rocblas_stride. Stride from the start of one vector tau_j to the next one tau_(j+1). There is no restriction for the value of strideP. Normal use is strideP >= n-1. [in] batch_count rocblas_int. batch_count >= 0. Number of matrices in the batch.

## ◆ rocsolver_ssytd2_batched_()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_ssytd2_batched::rocsolver_ssytd2_batched_ ( type(c_ptr), value handle, integer(kind(rocblas_fill_upper)), value uplo, integer(c_int), value n, type(c_ptr) A, integer(c_int), value lda, type(c_ptr), value D, integer(c_int64_t), value strideD, type(c_ptr), value E, integer(c_int64_t), value strideE, real(c_float) tau, integer(c_int64_t), value strideP, integer(c_int), value batch_count )

## ◆ rocsolver_ssytd2_batched_full_rank()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_ssytd2_batched::rocsolver_ssytd2_batched_full_rank ( type(c_ptr) handle, integer(kind(rocblas_fill_upper)) uplo, integer(c_int) n, real(c_float), dimension(:,:,:), target A, integer(c_int) lda, real(c_float), dimension(:), target D, integer(c_int64_t) strideD, real(c_float), dimension(:), target E, integer(c_int64_t) strideE, real(c_float) tau, integer(c_int64_t) strideP, integer(c_int) batch_count )

## ◆ rocsolver_ssytd2_batched_rank_0()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_ssytd2_batched::rocsolver_ssytd2_batched_rank_0 ( type(c_ptr) handle, integer(kind(rocblas_fill_upper)) uplo, integer(c_int) n, real(c_float), target A, integer(c_int) lda, real(c_float), target D, integer(c_int64_t) strideD, real(c_float), target E, integer(c_int64_t) strideE, real(c_float) tau, integer(c_int64_t) strideP, integer(c_int) batch_count )

## ◆ rocsolver_ssytd2_batched_rank_1()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_ssytd2_batched::rocsolver_ssytd2_batched_rank_1 ( type(c_ptr) handle, integer(kind(rocblas_fill_upper)) uplo, integer(c_int) n, real(c_float), dimension(:), target A, integer(c_int) lda, real(c_float), dimension(:), target D, integer(c_int64_t) strideD, real(c_float), dimension(:), target E, integer(c_int64_t) strideE, real(c_float) tau, integer(c_int64_t) strideP, integer(c_int) batch_count )

The documentation for this interface was generated from the following file: