.TH "hesv_aa_2stage" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME hesv_aa_2stage \- {he,sy}sv_aa_2stage: Aasen, blocked 2-stage .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBchesv_aa_2stage\fP (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)" .br .RI "\fB CHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices\fP " .ti -1c .RI "subroutine \fBcsysv_aa_2stage\fP (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)" .br .RI "\fB CSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices\fP " .ti -1c .RI "subroutine \fBdsysv_aa_2stage\fP (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)" .br .RI "\fB DSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices\fP " .ti -1c .RI "subroutine \fBssysv_aa_2stage\fP (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)" .br .RI "\fB SSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices\fP " .ti -1c .RI "subroutine \fBzhesv_aa_2stage\fP (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)" .br .RI "\fB ZHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices\fP " .ti -1c .RI "subroutine \fBzsysv_aa_2stage\fP (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)" .br .RI "\fB ZSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine chesv_aa_2stage (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer info)" .PP \fB CHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> CHESV_AA_2STAGE computes the solution to a complex system of !> linear equations !> A * X = B, !> where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS !> matrices\&. !> !> Aasen's 2-stage algorithm is used to factor A as !> A = U**H * T * U, if UPLO = 'U', or !> A = L * T * L**H, if UPLO = 'L', !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and T is Hermitian and band\&. The matrix T is !> then LU-factored with partial pivoting\&. The factored form of A !> is then used to solve the system of equations A * X = B\&. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fINRHS\fP .PP .nf !> NRHS is INTEGER !> The number of right hand sides, i\&.e\&., the number of columns !> of the matrix B\&. NRHS >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX array, dimension (LDA,N) !> On entry, the hermitian matrix A\&. If UPLO = 'U', the leading !> N-by-N upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced\&. If UPLO = 'L', the !> leading N-by-N lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced\&. !> !> On exit, L is stored below (or above) the subdiagonal blocks, !> when UPLO is 'L' (or 'U')\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fITB\fP .PP .nf !> TB is COMPLEX array, dimension (MAX(1,LTB))\&. !> On exit, details of the LU factorization of the band matrix\&. !> .fi .PP .br \fILTB\fP .PP .nf !> LTB is INTEGER !> The size of the array TB\&. LTB >= MAX(1,4*N), internally !> used to select NB such that LTB >= (3*NB+1)*N\&. !> !> If LTB = -1, then a workspace query is assumed; the !> routine only calculates the optimal size of LTB, !> returns this value as the first entry of TB, and !> no error message related to LTB is issued by XERBLA\&. !> .fi .PP .br \fIIPIV\fP .PP .nf !> IPIV is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i\&.e\&., !> the row and column k of A were interchanged with the !> row and column IPIV(k)\&. !> .fi .PP .br \fIIPIV2\fP .PP .nf !> IPIV2 is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i\&.e\&., !> the row and column k of T were interchanged with the !> row and column IPIV(k)\&. !> .fi .PP .br \fIB\fP .PP .nf !> B is COMPLEX array, dimension (LDB,NRHS) !> On entry, the right hand side matrix B\&. !> On exit, the solution matrix X\&. !> .fi .PP .br \fILDB\fP .PP .nf !> LDB is INTEGER !> The leading dimension of the array B\&. LDB >= max(1,N)\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is COMPLEX workspace of size (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The size of WORK\&. LWORK >= MAX(1,N), internally used to !> select NB such that LWORK >= N*NB\&. !> !> If LWORK = -1, then a workspace query is assumed; the !> routine only calculates the optimal size of the WORK array, !> returns this value as the first entry of the WORK array, and !> no error message related to LWORK is issued by XERBLA\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value\&. !> > 0: if INFO = i, band LU factorization failed on i-th column !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .PP Definition at line \fB184\fP of file \fBchesv_aa_2stage\&.f\fP\&. .SS "subroutine csysv_aa_2stage (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer info)" .PP \fB CSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> CSYSV_AA_2STAGE computes the solution to a complex system of !> linear equations !> A * X = B, !> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS !> matrices\&. !> !> Aasen's 2-stage algorithm is used to factor A as !> A = U**T * T * U, if UPLO = 'U', or !> A = L * T * L**T, if UPLO = 'L', !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and T is symmetric and band\&. The matrix T is !> then LU-factored with partial pivoting\&. The factored form of A !> is then used to solve the system of equations A * X = B\&. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fINRHS\fP .PP .nf !> NRHS is INTEGER !> The number of right hand sides, i\&.e\&., the number of columns !> of the matrix B\&. NRHS >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX array, dimension (LDA,N) !> On entry, the symmetric matrix A\&. If UPLO = 'U', the leading !> N-by-N upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced\&. If UPLO = 'L', the !> leading N-by-N lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced\&. !> !> On exit, L is stored below (or above) the subdiagonal blocks, !> when UPLO is 'L' (or 'U')\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fITB\fP .PP .nf !> TB is COMPLEX array, dimension (LTB) !> On exit, details of the LU factorization of the band matrix\&. !> .fi .PP .br \fILTB\fP .PP .nf !> LTB is INTEGER !> The size of the array TB\&. LTB >= 4*N, internally !> used to select NB such that LTB >= (3*NB+1)*N\&. !> !> If LTB = -1, then a workspace query is assumed; the !> routine only calculates the optimal size of LTB, !> returns this value as the first entry of TB, and !> no error message related to LTB is issued by XERBLA\&. !> .fi .PP .br \fIIPIV\fP .PP .nf !> IPIV is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i\&.e\&., !> the row and column k of A were interchanged with the !> row and column IPIV(k)\&. !> .fi .PP .br \fIIPIV2\fP .PP .nf !> IPIV2 is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i\&.e\&., !> the row and column k of T were interchanged with the !> row and column IPIV(k)\&. !> .fi .PP .br \fIB\fP .PP .nf !> B is COMPLEX array, dimension (LDB,NRHS) !> On entry, the right hand side matrix B\&. !> On exit, the solution matrix X\&. !> .fi .PP .br \fILDB\fP .PP .nf !> LDB is INTEGER !> The leading dimension of the array B\&. LDB >= max(1,N)\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is COMPLEX workspace of size LWORK !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The size of WORK\&. LWORK >= N, internally used to select NB !> such that LWORK >= N*NB\&. !> !> If LWORK = -1, then a workspace query is assumed; the !> routine only calculates the optimal size of the WORK array, !> returns this value as the first entry of the WORK array, and !> no error message related to LWORK is issued by XERBLA\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value\&. !> > 0: if INFO = i, band LU factorization failed on i-th column !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .PP Definition at line \fB183\fP of file \fBcsysv_aa_2stage\&.f\fP\&. .SS "subroutine dsysv_aa_2stage (character uplo, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) work, integer lwork, integer info)" .PP \fB DSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> DSYSV_AA_2STAGE computes the solution to a real system of !> linear equations !> A * X = B, !> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS !> matrices\&. !> !> Aasen's 2-stage algorithm is used to factor A as !> A = U**T * T * U, if UPLO = 'U', or !> A = L * T * L**T, if UPLO = 'L', !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and T is symmetric and band\&. The matrix T is !> then LU-factored with partial pivoting\&. The factored form of A !> is then used to solve the system of equations A * X = B\&. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fINRHS\fP .PP .nf !> NRHS is INTEGER !> The number of right hand sides, i\&.e\&., the number of columns !> of the matrix B\&. NRHS >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is DOUBLE PRECISION array, dimension (LDA,N) !> On entry, the symmetric matrix A\&. If UPLO = 'U', the leading !> N-by-N upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced\&. If UPLO = 'L', the !> leading N-by-N lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced\&. !> !> On exit, L is stored below (or above) the subdiagonal blocks, !> when UPLO is 'L' (or 'U')\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fITB\fP .PP .nf !> TB is DOUBLE PRECISION array, dimension (MAX(1,LTB)) !> On exit, details of the LU factorization of the band matrix\&. !> .fi .PP .br \fILTB\fP .PP .nf !> LTB is INTEGER !> The size of the array TB\&. LTB >= MAX(1,4*N), internally !> used to select NB such that LTB >= (3*NB+1)*N\&. !> !> If LTB = -1, then a workspace query is assumed; the !> routine only calculates the optimal size of LTB, !> returns this value as the first entry of TB, and !> no error message related to LTB is issued by XERBLA\&. !> .fi .PP .br \fIIPIV\fP .PP .nf !> IPIV is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i\&.e\&., !> the row and column k of A were interchanged with the !> row and column IPIV(k)\&. !> .fi .PP .br \fIIPIV2\fP .PP .nf !> IPIV2 is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i\&.e\&., !> the row and column k of T were interchanged with the !> row and column IPIV(k)\&. !> .fi .PP .br \fIB\fP .PP .nf !> B is DOUBLE PRECISION array, dimension (LDB,NRHS) !> On entry, the right hand side matrix B\&. !> On exit, the solution matrix X\&. !> .fi .PP .br \fILDB\fP .PP .nf !> LDB is INTEGER !> The leading dimension of the array B\&. LDB >= max(1,N)\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is DOUBLE PRECISION workspace of size (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The size of WORK\&. LWORK >= MAX(1,N), internally used to !> select NB such that LWORK >= N*NB\&. !> !> If LWORK = -1, then a workspace query is assumed; the !> routine only calculates the optimal size of the WORK array, !> returns this value as the first entry of the WORK array, and !> no error message related to LWORK is issued by XERBLA\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value\&. !> > 0: if INFO = i, band LU factorization failed on i-th column !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .PP Definition at line \fB186\fP of file \fBdsysv_aa_2stage\&.f\fP\&. .SS "subroutine ssysv_aa_2stage (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer lwork, integer info)" .PP \fB SSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> SSYSV_AA_2STAGE computes the solution to a real system of !> linear equations !> A * X = B, !> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS !> matrices\&. !> !> Aasen's 2-stage algorithm is used to factor A as !> A = U**T * T * U, if UPLO = 'U', or !> A = L * T * L**T, if UPLO = 'L', !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and T is symmetric and band\&. The matrix T is !> then LU-factored with partial pivoting\&. The factored form of A !> is then used to solve the system of equations A * X = B\&. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fINRHS\fP .PP .nf !> NRHS is INTEGER !> The number of right hand sides, i\&.e\&., the number of columns !> of the matrix B\&. NRHS >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is REAL array, dimension (LDA,N) !> On entry, the symmetric matrix A\&. If UPLO = 'U', the leading !> N-by-N upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced\&. If UPLO = 'L', the !> leading N-by-N lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced\&. !> !> On exit, L is stored below (or above) the subdiagonal blocks, !> when UPLO is 'L' (or 'U')\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fITB\fP .PP .nf !> TB is REAL array, dimension (MAX(1,LTB)) !> On exit, details of the LU factorization of the band matrix\&. !> .fi .PP .br \fILTB\fP .PP .nf !> LTB is INTEGER !> The size of the array TB\&. LTB >= MAX(1,4*N), internally !> used to select NB such that LTB >= (3*NB+1)*N\&. !> !> If LTB = -1, then a workspace query is assumed; the !> routine only calculates the optimal size of LTB, !> returns this value as the first entry of TB, and !> no error message related to LTB is issued by XERBLA\&. !> .fi .PP .br \fIIPIV\fP .PP .nf !> IPIV is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i\&.e\&., !> the row and column k of A were interchanged with the !> row and column IPIV(k)\&. !> .fi .PP .br \fIIPIV2\fP .PP .nf !> IPIV2 is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i\&.e\&., !> the row and column k of T were interchanged with the !> row and column IPIV(k)\&. !> .fi .PP .br \fIB\fP .PP .nf !> B is REAL array, dimension (LDB,NRHS) !> On entry, the right hand side matrix B\&. !> On exit, the solution matrix X\&. !> .fi .PP .br \fILDB\fP .PP .nf !> LDB is INTEGER !> The leading dimension of the array B\&. LDB >= max(1,N)\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is REAL workspace of size (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The size of WORK\&. LWORK >= MAX(1,N), internally used to !> select NB such that LWORK >= N*NB\&. !> !> If LWORK = -1, then a workspace query is assumed; the !> routine only calculates the optimal size of the WORK array, !> returns this value as the first entry of the WORK array, and !> no error message related to LWORK is issued by XERBLA\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value\&. !> > 0: if INFO = i, band LU factorization failed on i-th column !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .PP Definition at line \fB185\fP of file \fBssysv_aa_2stage\&.f\fP\&. .SS "subroutine zhesv_aa_2stage (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer lwork, integer info)" .PP \fB ZHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> ZHESV_AA_2STAGE computes the solution to a complex system of !> linear equations !> A * X = B, !> where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS !> matrices\&. !> !> Aasen's 2-stage algorithm is used to factor A as !> A = U**H * T * U, if UPLO = 'U', or !> A = L * T * L**H, if UPLO = 'L', !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and T is Hermitian and band\&. The matrix T is !> then LU-factored with partial pivoting\&. The factored form of A !> is then used to solve the system of equations A * X = B\&. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fINRHS\fP .PP .nf !> NRHS is INTEGER !> The number of right hand sides, i\&.e\&., the number of columns !> of the matrix B\&. NRHS >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the hermitian matrix A\&. If UPLO = 'U', the leading !> N-by-N upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced\&. If UPLO = 'L', the !> leading N-by-N lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced\&. !> !> On exit, L is stored below (or above) the subdiagonal blocks, !> when UPLO is 'L' (or 'U')\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fITB\fP .PP .nf !> TB is COMPLEX*16 array, dimension (MAX(1,LTB))\&. !> On exit, details of the LU factorization of the band matrix\&. !> .fi .PP .br \fILTB\fP .PP .nf !> LTB is INTEGER !> The size of the array TB\&. LTB >= MAX(1,4*N), internally !> used to select NB such that LTB >= (3*NB+1)*N\&. !> !> If LTB = -1, then a workspace query is assumed; the !> routine only calculates the optimal size of LTB, !> returns this value as the first entry of TB, and !> no error message related to LTB is issued by XERBLA\&. !> .fi .PP .br \fIIPIV\fP .PP .nf !> IPIV is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i\&.e\&., !> the row and column k of A were interchanged with the !> row and column IPIV(k)\&. !> .fi .PP .br \fIIPIV2\fP .PP .nf !> IPIV2 is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i\&.e\&., !> the row and column k of T were interchanged with the !> row and column IPIV(k)\&. !> .fi .PP .br \fIB\fP .PP .nf !> B is COMPLEX*16 array, dimension (LDB,NRHS) !> On entry, the right hand side matrix B\&. !> On exit, the solution matrix X\&. !> .fi .PP .br \fILDB\fP .PP .nf !> LDB is INTEGER !> The leading dimension of the array B\&. LDB >= max(1,N)\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is COMPLEX*16 workspace of size (MAX(1,LWORK))\&. !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The size of WORK\&. LWORK >= MAX(1,N), internally used to !> select NB such that LWORK >= N*NB\&. !> !> If LWORK = -1, then a workspace query is assumed; the !> routine only calculates the optimal size of the WORK array, !> returns this value as the first entry of the WORK array, and !> no error message related to LWORK is issued by XERBLA\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value\&. !> > 0: if INFO = i, band LU factorization failed on i-th column !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .PP Definition at line \fB185\fP of file \fBzhesv_aa_2stage\&.f\fP\&. .SS "subroutine zsysv_aa_2stage (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer lwork, integer info)" .PP \fB ZSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> ZSYSV_AA_2STAGE computes the solution to a complex system of !> linear equations !> A * X = B, !> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS !> matrices\&. !> !> Aasen's 2-stage algorithm is used to factor A as !> A = U**T * T * U, if UPLO = 'U', or !> A = L * T * L**T, if UPLO = 'L', !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and T is symmetric and band\&. The matrix T is !> then LU-factored with partial pivoting\&. The factored form of A !> is then used to solve the system of equations A * X = B\&. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fINRHS\fP .PP .nf !> NRHS is INTEGER !> The number of right hand sides, i\&.e\&., the number of columns !> of the matrix B\&. NRHS >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the symmetric matrix A\&. If UPLO = 'U', the leading !> N-by-N upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced\&. If UPLO = 'L', the !> leading N-by-N lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced\&. !> !> On exit, L is stored below (or above) the subdiagonal blocks, !> when UPLO is 'L' (or 'U')\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fITB\fP .PP .nf !> TB is COMPLEX*16 array, dimension (LTB) !> On exit, details of the LU factorization of the band matrix\&. !> .fi .PP .br \fILTB\fP .PP .nf !> LTB is INTEGER !> The size of the array TB\&. LTB >= 4*N, internally !> used to select NB such that LTB >= (3*NB+1)*N\&. !> !> If LTB = -1, then a workspace query is assumed; the !> routine only calculates the optimal size of LTB, !> returns this value as the first entry of TB, and !> no error message related to LTB is issued by XERBLA\&. !> .fi .PP .br \fIIPIV\fP .PP .nf !> IPIV is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i\&.e\&., !> the row and column k of A were interchanged with the !> row and column IPIV(k)\&. !> .fi .PP .br \fIIPIV2\fP .PP .nf !> IPIV2 is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i\&.e\&., !> the row and column k of T were interchanged with the !> row and column IPIV(k)\&. !> .fi .PP .br \fIB\fP .PP .nf !> B is COMPLEX*16 array, dimension (LDB,NRHS) !> On entry, the right hand side matrix B\&. !> On exit, the solution matrix X\&. !> .fi .PP .br \fILDB\fP .PP .nf !> LDB is INTEGER !> The leading dimension of the array B\&. LDB >= max(1,N)\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is COMPLEX*16 workspace of size LWORK !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The size of WORK\&. LWORK >= N, internally used to select NB !> such that LWORK >= N*NB\&. !> !> If LWORK = -1, then a workspace query is assumed; the !> routine only calculates the optimal size of the WORK array, !> returns this value as the first entry of the WORK array, and !> no error message related to LWORK is issued by XERBLA\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value\&. !> > 0: if INFO = i, band LU factorization failed on i-th column !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .PP Definition at line \fB183\fP of file \fBzsysv_aa_2stage\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.