Man page - hetrs_3(3)

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Manual

hetrs_3

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine chetrs_3 (character uplo, integer n, integer nrhs, complex,dimension( lda, * ) a, integer lda, complex, dimension( * ) e, integer,dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb,integer info)
subroutine csytrs_3 (character uplo, integer n, integer nrhs, complex,dimension( lda, * ) a, integer lda, complex, dimension( * ) e, integer,dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb,integer info)
subroutine dsytrs_3 (character uplo, integer n, integer nrhs, doubleprecision, dimension( lda, * ) a, integer lda, double precision,dimension( * ) e, integer, dimension( * ) ipiv, double precision,dimension( ldb, * ) b, integer ldb, integer info)
subroutine ssytrs_3 (character uplo, integer n, integer nrhs, real,dimension( lda, * ) a, integer lda, real, dimension( * ) e, integer,dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, integerinfo)
subroutine zhetrs_3 (character uplo, integer n, integer nrhs, complex*16,dimension( lda, * ) a, integer lda, complex*16, dimension( * ) e,integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b,integer ldb, integer info)
subroutine zsytrs_3 (character uplo, integer n, integer nrhs, complex*16,dimension( lda, * ) a, integer lda, complex*16, dimension( * ) e,integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b,integer ldb, integer info)
Author

NAME

hetrs_3 - {he,sy}trs_3: solve using factor

SYNOPSIS

Functions

subroutine chetrs_3 (uplo, n, nrhs, a, lda, e, ipiv, b, ldb, info)
CHETRS_3
subroutine csytrs_3 (uplo, n, nrhs, a, lda, e, ipiv, b, ldb, info)
CSYTRS_3
subroutine dsytrs_3 (uplo, n, nrhs, a, lda, e, ipiv, b, ldb, info)
DSYTRS_3
subroutine ssytrs_3 (uplo, n, nrhs, a, lda, e, ipiv, b, ldb, info)
SSYTRS_3
subroutine zhetrs_3 (uplo, n, nrhs, a, lda, e, ipiv, b, ldb, info)
ZHETRS_3
subroutine zsytrs_3 (uplo, n, nrhs, a, lda, e, ipiv, b, ldb, info)
ZSYTRS_3

Detailed Description

Function Documentation

subroutine chetrs_3 (character uplo, integer n, integer nrhs, complex,dimension( lda, * ) a, integer lda, complex, dimension( * ) e, integer,dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb,integer info)

CHETRS_3

Purpose:

CHETRS_3 solves a system of linear equations A * X = B with a complex
Hermitian matrix A using the factorization computed
by CHETRF_RK or CHETRF_BK:

A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix,
U**H (or L**H) is the conjugate of U (or L), P is a permutation
matrix, P**T is the transpose of P, and D is Hermitian and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This algorithm is using Level 3 BLAS.

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are
stored as an upper or lower triangular matrix:
= ā€™Uā€™: Upper triangular, form is A = P*U*D*(U**H)*(P**T);
= ā€™Lā€™: Lower triangular, form is A = P*L*D*(L**H)*(P**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)
Diagonal of the block diagonal matrix D and factors U or L
as computed by CHETRF_RK and CHETRF_BK:
a) ONLY diagonal elements of the Hermitian block diagonal
matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
(superdiagonal (or subdiagonal) elements of D
should be provided on entry in array E), and
b) If UPLO = ā€™Uā€™: factor U in the superdiagonal part of A.
If UPLO = ā€™Lā€™: factor L in the subdiagonal part of A.

LDA

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

E

E is COMPLEX array, dimension (N)
On entry, contains the superdiagonal (or subdiagonal)
elements of the Hermitian block diagonal matrix D
with 1-by-1 or 2-by-2 diagonal blocks, where
If UPLO = ā€™Uā€™: E(i) = D(i-1,i),i=2:N, E(1) not referenced;
If UPLO = ā€™Lā€™: E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

NOTE: For 1-by-1 diagonal block D(k), where
1 <= k <= N, the element E(k) is not referenced in both
UPLO = ā€™Uā€™ or UPLO = ā€™Lā€™ cases.

IPIV

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

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).

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.

Contributors:

June 2017, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

subroutine csytrs_3 (character uplo, integer n, integer nrhs, complex,dimension( lda, * ) a, integer lda, complex, dimension( * ) e, integer,dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb,integer info)

CSYTRS_3

Purpose:

CSYTRS_3 solves a system of linear equations A * X = B with a complex
symmetric matrix A using the factorization computed
by CSYTRF_RK or CSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix,
U**T (or L**T) is the transpose of U (or L), P is a permutation
matrix, P**T is the transpose of P, and D is symmetric and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This algorithm is using Level 3 BLAS.

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are
stored as an upper or lower triangular matrix:
= ā€™Uā€™: Upper triangular, form is A = P*U*D*(U**T)*(P**T);
= ā€™Lā€™: Lower triangular, form is A = P*L*D*(L**T)*(P**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)
Diagonal of the block diagonal matrix D and factors U or L
as computed by CSYTRF_RK and CSYTRF_BK:
a) ONLY diagonal elements of the symmetric block diagonal
matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
(superdiagonal (or subdiagonal) elements of D
should be provided on entry in array E), and
b) If UPLO = ā€™Uā€™: factor U in the superdiagonal part of A.
If UPLO = ā€™Lā€™: factor L in the subdiagonal part of A.

LDA

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

E

E is COMPLEX array, dimension (N)
On entry, contains the superdiagonal (or subdiagonal)
elements of the symmetric block diagonal matrix D
with 1-by-1 or 2-by-2 diagonal blocks, where
If UPLO = ā€™Uā€™: E(i) = D(i-1,i),i=2:N, E(1) not referenced;
If UPLO = ā€™Lā€™: E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

NOTE: For 1-by-1 diagonal block D(k), where
1 <= k <= N, the element E(k) is not referenced in both
UPLO = ā€™Uā€™ or UPLO = ā€™Lā€™ cases.

IPIV

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

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).

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.

Contributors:

June 2017, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

subroutine dsytrs_3 (character uplo, integer n, integer nrhs, doubleprecision, dimension( lda, * ) a, integer lda, double precision,dimension( * ) e, integer, dimension( * ) ipiv, double precision,dimension( ldb, * ) b, integer ldb, integer info)

DSYTRS_3

Purpose:

DSYTRS_3 solves a system of linear equations A * X = B with a real
symmetric matrix A using the factorization computed
by DSYTRF_RK or DSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix,
U**T (or L**T) is the transpose of U (or L), P is a permutation
matrix, P**T is the transpose of P, and D is symmetric and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This algorithm is using Level 3 BLAS.

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are
stored as an upper or lower triangular matrix:
= ā€™Uā€™: Upper triangular, form is A = P*U*D*(U**T)*(P**T);
= ā€™Lā€™: Lower triangular, form is A = P*L*D*(L**T)*(P**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)
Diagonal of the block diagonal matrix D and factors U or L
as computed by DSYTRF_RK and DSYTRF_BK:
a) ONLY diagonal elements of the symmetric block diagonal
matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
(superdiagonal (or subdiagonal) elements of D
should be provided on entry in array E), and
b) If UPLO = ā€™Uā€™: factor U in the superdiagonal part of A.
If UPLO = ā€™Lā€™: factor L in the subdiagonal part of A.

LDA

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

E

E is DOUBLE PRECISION array, dimension (N)
On entry, contains the superdiagonal (or subdiagonal)
elements of the symmetric block diagonal matrix D
with 1-by-1 or 2-by-2 diagonal blocks, where
If UPLO = ā€™Uā€™: E(i) = D(i-1,i),i=2:N, E(1) not referenced;
If UPLO = ā€™Lā€™: E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

NOTE: For 1-by-1 diagonal block D(k), where
1 <= k <= N, the element E(k) is not referenced in both
UPLO = ā€™Uā€™ or UPLO = ā€™Lā€™ cases.

IPIV

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

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).

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.

Contributors:

June 2017, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

subroutine ssytrs_3 (character uplo, integer n, integer nrhs, real,dimension( lda, * ) a, integer lda, real, dimension( * ) e, integer,dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, integerinfo)

SSYTRS_3

Purpose:

SSYTRS_3 solves a system of linear equations A * X = B with a real
symmetric matrix A using the factorization computed
by SSYTRF_RK or SSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix,
U**T (or L**T) is the transpose of U (or L), P is a permutation
matrix, P**T is the transpose of P, and D is symmetric and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This algorithm is using Level 3 BLAS.

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are
stored as an upper or lower triangular matrix:
= ā€™Uā€™: Upper triangular, form is A = P*U*D*(U**T)*(P**T);
= ā€™Lā€™: Lower triangular, form is A = P*L*D*(L**T)*(P**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 REAL array, dimension (LDA,N)
Diagonal of the block diagonal matrix D and factors U or L
as computed by SSYTRF_RK and SSYTRF_BK:
a) ONLY diagonal elements of the symmetric block diagonal
matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
(superdiagonal (or subdiagonal) elements of D
should be provided on entry in array E), and
b) If UPLO = ā€™Uā€™: factor U in the superdiagonal part of A.
If UPLO = ā€™Lā€™: factor L in the subdiagonal part of A.

LDA

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

E

E is REAL array, dimension (N)
On entry, contains the superdiagonal (or subdiagonal)
elements of the symmetric block diagonal matrix D
with 1-by-1 or 2-by-2 diagonal blocks, where
If UPLO = ā€™Uā€™: E(i) = D(i-1,i),i=2:N, E(1) not referenced;
If UPLO = ā€™Lā€™: E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

NOTE: For 1-by-1 diagonal block D(k), where
1 <= k <= N, the element E(k) is not referenced in both
UPLO = ā€™Uā€™ or UPLO = ā€™Lā€™ cases.

IPIV

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

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).

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.

Contributors:

June 2017, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

subroutine zhetrs_3 (character uplo, integer n, integer nrhs, complex*16,dimension( lda, * ) a, integer lda, complex*16, dimension( * ) e,integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b,integer ldb, integer info)

ZHETRS_3

Purpose:

ZHETRS_3 solves a system of linear equations A * X = B with a complex
Hermitian matrix A using the factorization computed
by ZHETRF_RK or ZHETRF_BK:

A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix,
U**H (or L**H) is the conjugate of U (or L), P is a permutation
matrix, P**T is the transpose of P, and D is Hermitian and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This algorithm is using Level 3 BLAS.

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are
stored as an upper or lower triangular matrix:
= ā€™Uā€™: Upper triangular, form is A = P*U*D*(U**H)*(P**T);
= ā€™Lā€™: Lower triangular, form is A = P*L*D*(L**H)*(P**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*16 array, dimension (LDA,N)
Diagonal of the block diagonal matrix D and factors U or L
as computed by ZHETRF_RK and ZHETRF_BK:
a) ONLY diagonal elements of the Hermitian block diagonal
matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
(superdiagonal (or subdiagonal) elements of D
should be provided on entry in array E), and
b) If UPLO = ā€™Uā€™: factor U in the superdiagonal part of A.
If UPLO = ā€™Lā€™: factor L in the subdiagonal part of A.

LDA

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

E

E is COMPLEX*16 array, dimension (N)
On entry, contains the superdiagonal (or subdiagonal)
elements of the Hermitian block diagonal matrix D
with 1-by-1 or 2-by-2 diagonal blocks, where
If UPLO = ā€™Uā€™: E(i) = D(i-1,i),i=2:N, E(1) not referenced;
If UPLO = ā€™Lā€™: E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

NOTE: For 1-by-1 diagonal block D(k), where
1 <= k <= N, the element E(k) is not referenced in both
UPLO = ā€™Uā€™ or UPLO = ā€™Lā€™ cases.

IPIV

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

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).

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.

Contributors:

June 2017, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

subroutine zsytrs_3 (character uplo, integer n, integer nrhs, complex*16,dimension( lda, * ) a, integer lda, complex*16, dimension( * ) e,integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b,integer ldb, integer info)

ZSYTRS_3

Purpose:

ZSYTRS_3 solves a system of linear equations A * X = B with a complex
symmetric matrix A using the factorization computed
by ZSYTRF_RK or ZSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix,
U**T (or L**T) is the transpose of U (or L), P is a permutation
matrix, P**T is the transpose of P, and D is symmetric and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This algorithm is using Level 3 BLAS.

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are
stored as an upper or lower triangular matrix:
= ā€™Uā€™: Upper triangular, form is A = P*U*D*(U**T)*(P**T);
= ā€™Lā€™: Lower triangular, form is A = P*L*D*(L**T)*(P**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*16 array, dimension (LDA,N)
Diagonal of the block diagonal matrix D and factors U or L
as computed by ZSYTRF_RK and ZSYTRF_BK:
a) ONLY diagonal elements of the symmetric block diagonal
matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
(superdiagonal (or subdiagonal) elements of D
should be provided on entry in array E), and
b) If UPLO = ā€™Uā€™: factor U in the superdiagonal part of A.
If UPLO = ā€™Lā€™: factor L in the subdiagonal part of A.

LDA

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

E

E is COMPLEX*16 array, dimension (N)
On entry, contains the superdiagonal (or subdiagonal)
elements of the symmetric block diagonal matrix D
with 1-by-1 or 2-by-2 diagonal blocks, where
If UPLO = ā€™Uā€™: E(i) = D(i-1,i),i=2:N, E(1) not referenced;
If UPLO = ā€™Lā€™: E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

NOTE: For 1-by-1 diagonal block D(k), where
1 <= k <= N, the element E(k) is not referenced in both
UPLO = ā€™Uā€™ or UPLO = ā€™Lā€™ cases.

IPIV

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

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).

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.

Contributors:

June 2017, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

Author

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