# hetrs2 - Man Page

{he,sy}trs2: solve using factor

## Synopsis

### Functions

subroutine **chetrs2** (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info)**CHETRS2**

subroutine **csytrs2** (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info)**CSYTRS2**

subroutine **dsytrs2** (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info)**DSYTRS2**

subroutine **ssytrs2** (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info)**SSYTRS2**

subroutine **zhetrs2** (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info)**ZHETRS2**

subroutine **zsytrs2** (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info)**ZSYTRS2**

## Detailed Description

## Function Documentation

### subroutine chetrs2 (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer info)

**CHETRS2**

**Purpose:**

CHETRS2 solves a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF and converted by CSYCONV.

**Parameters***UPLO*UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**H; = 'L': Lower triangular, form is A = L*D*L**H.

*N*N is INTEGER The order of the matrix A. N >= 0.

*NRHS*NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.

*A*A is COMPLEX array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CHETRF.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*IPIV*IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CHETRF.

*B*B is COMPLEX array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.

*LDB*LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).

*WORK*WORK is COMPLEX array, dimension (N)

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **125** of file **chetrs2.f**.

### subroutine csytrs2 (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer info)

**CSYTRS2**

**Purpose:**

CSYTRS2 solves a system of linear equations A*X = B with a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF and converted by CSYCONV.

**Parameters***UPLO*UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**T; = 'L': Lower triangular, form is A = L*D*L**T.

*N*N is INTEGER The order of the matrix A. N >= 0.

*NRHS*NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.

*A*A is COMPLEX array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSYTRF. Note that A is input / output. This might be counter-intuitive, and one may think that A is input only. A is input / output. This is because, at the start of the subroutine, we permute A in a 'better' form and then we permute A back to its original form at the end.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*IPIV*IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CSYTRF.

*B*B is COMPLEX array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.

*LDB*LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).

*WORK*WORK is COMPLEX array, dimension (N)

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **130** of file **csytrs2.f**.

### subroutine dsytrs2 (character uplo, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) work, integer info)

**DSYTRS2**

**Purpose:**

DSYTRS2 solves a system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF and converted by DSYCONV.

**Parameters***UPLO*UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**T; = 'L': Lower triangular, form is A = L*D*L**T.

*N*N is INTEGER The order of the matrix A. N >= 0.

*NRHS*NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.

*A*A is DOUBLE PRECISION array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSYTRF. Note that A is input / output. This might be counter-intuitive, and one may think that A is input only. A is input / output. This is because, at the start of the subroutine, we permute A in a 'better' form and then we permute A back to its original form at the end.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*IPIV*IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by DSYTRF.

*B*B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.

*LDB*LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).

*WORK*WORK is DOUBLE PRECISION array, dimension (N)

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **130** of file **dsytrs2.f**.

### subroutine ssytrs2 (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer info)

**SSYTRS2**

**Purpose:**

SSYTRS2 solves a system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF and converted by SSYCONV.

**Parameters***UPLO*UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**T; = 'L': Lower triangular, form is A = L*D*L**T.

*N*N is INTEGER The order of the matrix A. N >= 0.

*NRHS**A*A is REAL array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by SSYTRF. Note that A is input / output. This might be counter-intuitive, and one may think that A is input only. A is input / output. This is because, at the start of the subroutine, we permute A in a 'better' form and then we permute A back to its original form at the end.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*IPIV*IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by SSYTRF.

*B*B is REAL array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.

*LDB*LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).

*WORK*WORK is REAL array, dimension (N)

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **130** of file **ssytrs2.f**.

### subroutine zhetrs2 (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer info)

**ZHETRS2**

**Purpose:**

ZHETRS2 solves a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF and converted by ZSYCONV.

**Parameters***UPLO*UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**H; = 'L': Lower triangular, form is A = L*D*L**H.

*N*N is INTEGER The order of the matrix A. N >= 0.

*NRHS**A*A is COMPLEX*16 array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZHETRF.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*IPIV*IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZHETRF.

*B*B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.

*LDB*LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).

*WORK*WORK is COMPLEX*16 array, dimension (N)

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **125** of file **zhetrs2.f**.

### subroutine zsytrs2 (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer info)

**ZSYTRS2**

**Purpose:**

ZSYTRS2 solves a system of linear equations A*X = B with a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF and converted by ZSYCONV.

**Parameters***UPLO**N*N is INTEGER The order of the matrix A. N >= 0.

*NRHS**A*A is COMPLEX*16 array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZSYTRF. Note that A is input / output. This might be counter-intuitive, and one may think that A is input only. A is input / output. This is because, at the start of the subroutine, we permute A in a 'better' form and then we permute A back to its original form at the end.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*IPIV*IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZSYTRF.

*B*B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.

*LDB*LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).

*WORK*WORK is COMPLEX*16 array, dimension (N)

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **130** of file **zsytrs2.f**.

## Author

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