latrs3(3)

NAME
latrs3 - latrs3: triangular solve with robust scaling, level 3

SYNOPSIS

  Functions

subroutine clatrs3 (uplo, trans, diag, normin, n, nrhs, a, lda, x, ldx, scale, cnorm, work, lwork, info)
CLATRS3 solves a triangular system of equations with the scale factors set to prevent overflow.
subroutine dlatrs3 (uplo, trans, diag, normin, n, nrhs, a, lda, x, ldx, scale, cnorm, work, lwork, info)
DLATRS3 solves a triangular system of equations with the scale factors set to prevent overflow.
subroutine slatrs3 (uplo, trans, diag, normin, n, nrhs, a, lda, x, ldx, scale, cnorm, work, lwork, info)
SLATRS3 solves a triangular system of equations with the scale factors set to prevent overflow.
subroutine zlatrs3 (uplo, trans, diag, normin, n, nrhs, a, lda, x, ldx, scale, cnorm, work, lwork, info)
ZLATRS3 solves a triangular system of equations with the scale factors set to prevent overflow.

Detailed Description

Function Documentation

  subroutine clatrs3 (character uplo, character trans, character diag, character normin, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldx, * ) x, integer ldx, real, dimension( * ) scale, real, dimension( * ) cnorm, real, dimension( * ) work, integer lwork, integer info)

CLATRS3 solves a triangular system of equations with the scale factors set to prevent overflow.

Purpose:

    !>
    !> CLATRS3 solves one of the triangular systems
    !>
    !>    A * X = B * diag(scale),  A**T * X = B * diag(scale), or
    !>    A**H * X = B * diag(scale)
    !>
    !> 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
    !> conjugate transpose of A. X and B are n-by-nrhs matrices and scale
    !> is an nrhs-element vector of scaling factors. A scaling factor scale(j)
    !> is usually less than or equal to 1, chosen such that X(:,j) is less
    !> than the overflow threshold. If the matrix A is singular (A(j,j) = 0
    !> for some j), then a non-trivial solution to A*X = 0 is returned. If
    !> the system is so badly scaled that the solution cannot be represented
    !> as (1/scale(k))*X(:,k), then x(:,k) = 0 and scale(k) is returned.
    !>
    !> This is a BLAS-3 version of LATRS for solving several right
    !> hand sides simultaneously.
    !>
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the matrix A is upper or lower triangular.
    !>          = 'U':  Upper triangular
    !>          = 'L':  Lower triangular
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          Specifies the operation applied to A.
    !>          = 'N':  Solve A * x = s*b  (No transpose)
    !>          = 'T':  Solve A**T* x = s*b  (Transpose)
    !>          = 'C':  Solve A**T* x = s*b  (Conjugate transpose)
    !>

    DIAG

    !>          DIAG is CHARACTER*1
    !>          Specifies whether or not the matrix A is unit triangular.
    !>          = 'N':  Non-unit triangular
    !>          = 'U':  Unit triangular
    !>

    NORMIN

    !>          NORMIN is CHARACTER*1
    !>          Specifies whether CNORM has been set or not.
    !>          = 'Y':  CNORM contains the column norms on entry
    !>          = 'N':  CNORM is not set on entry.  On exit, the norms will
    !>                  be computed and stored in CNORM.
    !>

    N

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

    NRHS

    !>          NRHS is INTEGER
    !>          The number of columns of X.  NRHS >= 0.
    !>

    A

    !>          A is COMPLEX array, dimension (LDA,N)
    !>          The triangular matrix A.  If UPLO = 'U', the leading n by n
    !>          upper triangular part of the array A contains the upper
    !>          triangular matrix, and the strictly lower triangular part of
    !>          A is not referenced.  If UPLO = 'L', the leading n by n lower
    !>          triangular part of the array A contains the lower triangular
    !>          matrix, and the strictly upper triangular part of A is not
    !>          referenced.  If DIAG = 'U', the diagonal elements of A are
    !>          also not referenced and are assumed to be 1.
    !>

    LDA

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

    X

    !>          X is COMPLEX array, dimension (LDX,NRHS)
    !>          On entry, the right hand side B of the triangular system.
    !>          On exit, X is overwritten by the solution matrix X.
    !>

    LDX

    !>          LDX is INTEGER
    !>          The leading dimension of the array X.  LDX >= max (1,N).
    !>

    SCALE

    !>          SCALE is REAL array, dimension (NRHS)
    !>          The scaling factor s(k) is for the triangular system
    !>          A * x(:,k) = s(k)*b(:,k)  or  A**T* x(:,k) = s(k)*b(:,k).
    !>          If SCALE = 0, the matrix A is singular or badly scaled.
    !>          If A(j,j) = 0 is encountered, a non-trivial vector x(:,k)
    !>          that is an exact or approximate solution to A*x(:,k) = 0
    !>          is returned. If the system so badly scaled that solution
    !>          cannot be presented as x(:,k) * 1/s(k), then x(:,k) = 0
    !>          is returned.
    !>

    CNORM

    !>          CNORM is REAL array, dimension (N)
    !>
    !>          If NORMIN = 'Y', CNORM is an input argument and CNORM(j)
    !>          contains the norm of the off-diagonal part of the j-th column
    !>          of A.  If TRANS = 'N', CNORM(j) must be greater than or equal
    !>          to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j)
    !>          must be greater than or equal to the 1-norm.
    !>
    !>          If NORMIN = 'N', CNORM is an output argument and CNORM(j)
    !>          returns the 1-norm of the offdiagonal part of the j-th column
    !>          of A.
    !>

    WORK

    !>          WORK is REAL array, dimension (MAX(1,LWORK)).
    !>          On exit, if INFO = 0, WORK(1) returns the optimal size of
    !>          WORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK.
    !>
    !>          If MIN(N,NRHS) = 0, LWORK >= 1, else
    !>          LWORK >= MAX(1, 2*NBA * MAX(NBA, MIN(NRHS, 32)), where
    !>          NBA = (N + NB - 1)/NB and NB is the optimal block size.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the optimal dimensions 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.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -k, the k-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

  subroutine dlatrs3 (character uplo, character trans, character diag, character normin, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldx, * ) x, integer ldx, double precision, dimension( * ) scale, double precision, dimension( * ) cnorm, double precision, dimension( * ) work, integer lwork, integer info)

DLATRS3 solves a triangular system of equations with the scale factors set to prevent overflow.

Purpose:

    !>
    !> DLATRS3 solves one of the triangular systems
    !>
    !>    A * X = B * diag(scale)  or  A**T * X = B * diag(scale)
    !>
    !> with scaling to prevent overflow.  Here A is an upper or lower
    !> triangular matrix, A**T denotes the transpose of A. X and B are
    !> n by nrhs matrices and scale is an nrhs element vector of scaling
    !> factors. A scaling factor scale(j) is usually less than or equal
    !> to 1, chosen such that X(:,j) is less than the overflow threshold.
    !> If the matrix A is singular (A(j,j) = 0 for some j), then
    !> a non-trivial solution to A*X = 0 is returned. If the system is
    !> so badly scaled that the solution cannot be represented as
    !> (1/scale(k))*X(:,k), then x(:,k) = 0 and scale(k) is returned.
    !>
    !> This is a BLAS-3 version of LATRS for solving several right
    !> hand sides simultaneously.
    !>
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the matrix A is upper or lower triangular.
    !>          = 'U':  Upper triangular
    !>          = 'L':  Lower triangular
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          Specifies the operation applied to A.
    !>          = 'N':  Solve A * x = s*b  (No transpose)
    !>          = 'T':  Solve A**T* x = s*b  (Transpose)
    !>          = 'C':  Solve A**T* x = s*b  (Conjugate transpose = Transpose)
    !>

    DIAG

    !>          DIAG is CHARACTER*1
    !>          Specifies whether or not the matrix A is unit triangular.
    !>          = 'N':  Non-unit triangular
    !>          = 'U':  Unit triangular
    !>

    NORMIN

    !>          NORMIN is CHARACTER*1
    !>          Specifies whether CNORM has been set or not.
    !>          = 'Y':  CNORM contains the column norms on entry
    !>          = 'N':  CNORM is not set on entry.  On exit, the norms will
    !>                  be computed and stored in CNORM.
    !>

    N

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

    NRHS

    !>          NRHS is INTEGER
    !>          The number of columns of X.  NRHS >= 0.
    !>

    A

    !>          A is DOUBLE PRECISION array, dimension (LDA,N)
    !>          The triangular matrix A.  If UPLO = 'U', the leading n by n
    !>          upper triangular part of the array A contains the upper
    !>          triangular matrix, and the strictly lower triangular part of
    !>          A is not referenced.  If UPLO = 'L', the leading n by n lower
    !>          triangular part of the array A contains the lower triangular
    !>          matrix, and the strictly upper triangular part of A is not
    !>          referenced.  If DIAG = 'U', the diagonal elements of A are
    !>          also not referenced and are assumed to be 1.
    !>

    LDA

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

    X

    !>          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
    !>          On entry, the right hand side B of the triangular system.
    !>          On exit, X is overwritten by the solution matrix X.
    !>

    LDX

    !>          LDX is INTEGER
    !>          The leading dimension of the array X.  LDX >= max (1,N).
    !>

    SCALE

    !>          SCALE is DOUBLE PRECISION array, dimension (NRHS)
    !>          The scaling factor s(k) is for the triangular system
    !>          A * x(:,k) = s(k)*b(:,k)  or  A**T* x(:,k) = s(k)*b(:,k).
    !>          If SCALE = 0, the matrix A is singular or badly scaled.
    !>          If A(j,j) = 0 is encountered, a non-trivial vector x(:,k)
    !>          that is an exact or approximate solution to A*x(:,k) = 0
    !>          is returned. If the system so badly scaled that solution
    !>          cannot be presented as x(:,k) * 1/s(k), then x(:,k) = 0
    !>          is returned.
    !>

    CNORM

    !>          CNORM is DOUBLE PRECISION array, dimension (N)
    !>
    !>          If NORMIN = 'Y', CNORM is an input argument and CNORM(j)
    !>          contains the norm of the off-diagonal part of the j-th column
    !>          of A.  If TRANS = 'N', CNORM(j) must be greater than or equal
    !>          to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j)
    !>          must be greater than or equal to the 1-norm.
    !>
    !>          If NORMIN = 'N', CNORM is an output argument and CNORM(j)
    !>          returns the 1-norm of the offdiagonal part of the j-th column
    !>          of A.
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)).
    !>          On exit, if INFO = 0, WORK(1) returns the optimal size of
    !>          WORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK.
    !>
    !>          If MIN(N,NRHS) = 0, LWORK >= 1, else
    !>          LWORK >= MAX(1, 2*NBA * MAX(NBA, MIN(NRHS, 32)), where
    !>          NBA = (N + NB - 1)/NB and NB is the optimal block size.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the optimal dimensions 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.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -k, the k-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

  subroutine slatrs3 (character uplo, character trans, character diag, character normin, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( ldx, * ) x, integer ldx, real, dimension( * ) scale, real, dimension( * ) cnorm, real, dimension( * ) work, integer lwork, integer info)

SLATRS3 solves a triangular system of equations with the scale factors set to prevent overflow.

Purpose:

    !>
    !> SLATRS3 solves one of the triangular systems
    !>
    !>    A * X = B * diag(scale)  or  A**T * X = B * diag(scale)
    !>
    !> with scaling to prevent overflow.  Here A is an upper or lower
    !> triangular matrix, A**T denotes the transpose of A. X and B are
    !> n by nrhs matrices and scale is an nrhs element vector of scaling
    !> factors. A scaling factor scale(j) is usually less than or equal
    !> to 1, chosen such that X(:,j) is less than the overflow threshold.
    !> If the matrix A is singular (A(j,j) = 0 for some j), then
    !> a non-trivial solution to A*X = 0 is returned. If the system is
    !> so badly scaled that the solution cannot be represented as
    !> (1/scale(k))*X(:,k), then x(:,k) = 0 and scale(k) is returned.
    !>
    !> This is a BLAS-3 version of LATRS for solving several right
    !> hand sides simultaneously.
    !>
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the matrix A is upper or lower triangular.
    !>          = 'U':  Upper triangular
    !>          = 'L':  Lower triangular
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          Specifies the operation applied to A.
    !>          = 'N':  Solve A * x = s*b  (No transpose)
    !>          = 'T':  Solve A**T* x = s*b  (Transpose)
    !>          = 'C':  Solve A**T* x = s*b  (Conjugate transpose = Transpose)
    !>

    DIAG

    !>          DIAG is CHARACTER*1
    !>          Specifies whether or not the matrix A is unit triangular.
    !>          = 'N':  Non-unit triangular
    !>          = 'U':  Unit triangular
    !>

    NORMIN

    !>          NORMIN is CHARACTER*1
    !>          Specifies whether CNORM has been set or not.
    !>          = 'Y':  CNORM contains the column norms on entry
    !>          = 'N':  CNORM is not set on entry.  On exit, the norms will
    !>                  be computed and stored in CNORM.
    !>

    N

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

    NRHS

    !>          NRHS is INTEGER
    !>          The number of columns of X.  NRHS >= 0.
    !>

    A

    !>          A is REAL array, dimension (LDA,N)
    !>          The triangular matrix A.  If UPLO = 'U', the leading n by n
    !>          upper triangular part of the array A contains the upper
    !>          triangular matrix, and the strictly lower triangular part of
    !>          A is not referenced.  If UPLO = 'L', the leading n by n lower
    !>          triangular part of the array A contains the lower triangular
    !>          matrix, and the strictly upper triangular part of A is not
    !>          referenced.  If DIAG = 'U', the diagonal elements of A are
    !>          also not referenced and are assumed to be 1.
    !>

    LDA

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

    X

    !>          X is REAL array, dimension (LDX,NRHS)
    !>          On entry, the right hand side B of the triangular system.
    !>          On exit, X is overwritten by the solution matrix X.
    !>

    LDX

    !>          LDX is INTEGER
    !>          The leading dimension of the array X.  LDX >= max (1,N).
    !>

    SCALE

    !>          SCALE is REAL array, dimension (NRHS)
    !>          The scaling factor s(k) is for the triangular system
    !>          A * x(:,k) = s(k)*b(:,k)  or  A**T* x(:,k) = s(k)*b(:,k).
    !>          If SCALE = 0, the matrix A is singular or badly scaled.
    !>          If A(j,j) = 0 is encountered, a non-trivial vector x(:,k)
    !>          that is an exact or approximate solution to A*x(:,k) = 0
    !>          is returned. If the system so badly scaled that solution
    !>          cannot be presented as x(:,k) * 1/s(k), then x(:,k) = 0
    !>          is returned.
    !>

    CNORM

    !>          CNORM is REAL array, dimension (N)
    !>
    !>          If NORMIN = 'Y', CNORM is an input argument and CNORM(j)
    !>          contains the norm of the off-diagonal part of the j-th column
    !>          of A.  If TRANS = 'N', CNORM(j) must be greater than or equal
    !>          to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j)
    !>          must be greater than or equal to the 1-norm.
    !>
    !>          If NORMIN = 'N', CNORM is an output argument and CNORM(j)
    !>          returns the 1-norm of the offdiagonal part of the j-th column
    !>          of A.
    !>

    WORK

    !>          WORK is REAL array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK.
    !>
    !>          If MIN(N,NRHS) = 0, LWORK >= 1, else
    !>          LWORK >= MAX(1, 2*NBA * MAX(NBA, MIN(NRHS, 32)), where
    !>          NBA = (N + NB - 1)/NB and NB is the optimal block size.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the optimal dimensions 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.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -k, the k-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

  subroutine zlatrs3 (character uplo, character trans, character diag, character normin, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldx, * ) x, integer ldx, double precision, dimension( * ) scale, double precision, dimension( * ) cnorm, double precision, dimension( * ) work, integer lwork, integer info)

ZLATRS3 solves a triangular system of equations with the scale factors set to prevent overflow.

Purpose:

    !>
    !> ZLATRS3 solves one of the triangular systems
    !>
    !>    A * X = B * diag(scale),  A**T * X = B * diag(scale), or
    !>    A**H * X = B * diag(scale)
    !>
    !> 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
    !> conjugate transpose of A. X and B are n-by-nrhs matrices and scale
    !> is an nrhs-element vector of scaling factors. A scaling factor scale(j)
    !> is usually less than or equal to 1, chosen such that X(:,j) is less
    !> than the overflow threshold. If the matrix A is singular (A(j,j) = 0
    !> for some j), then a non-trivial solution to A*X = 0 is returned. If
    !> the system is so badly scaled that the solution cannot be represented
    !> as (1/scale(k))*X(:,k), then x(:,k) = 0 and scale(k) is returned.
    !>
    !> This is a BLAS-3 version of LATRS for solving several right
    !> hand sides simultaneously.
    !>
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the matrix A is upper or lower triangular.
    !>          = 'U':  Upper triangular
    !>          = 'L':  Lower triangular
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          Specifies the operation applied to A.
    !>          = 'N':  Solve A * x = s*b  (No transpose)
    !>          = 'T':  Solve A**T* x = s*b  (Transpose)
    !>          = 'C':  Solve A**T* x = s*b  (Conjugate transpose)
    !>

    DIAG

    !>          DIAG is CHARACTER*1
    !>          Specifies whether or not the matrix A is unit triangular.
    !>          = 'N':  Non-unit triangular
    !>          = 'U':  Unit triangular
    !>

    NORMIN

    !>          NORMIN is CHARACTER*1
    !>          Specifies whether CNORM has been set or not.
    !>          = 'Y':  CNORM contains the column norms on entry
    !>          = 'N':  CNORM is not set on entry.  On exit, the norms will
    !>                  be computed and stored in CNORM.
    !>

    N

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

    NRHS

    !>          NRHS is INTEGER
    !>          The number of columns of X.  NRHS >= 0.
    !>

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          The triangular matrix A.  If UPLO = 'U', the leading n by n
    !>          upper triangular part of the array A contains the upper
    !>          triangular matrix, and the strictly lower triangular part of
    !>          A is not referenced.  If UPLO = 'L', the leading n by n lower
    !>          triangular part of the array A contains the lower triangular
    !>          matrix, and the strictly upper triangular part of A is not
    !>          referenced.  If DIAG = 'U', the diagonal elements of A are
    !>          also not referenced and are assumed to be 1.
    !>

    LDA

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

    X

    !>          X is COMPLEX*16 array, dimension (LDX,NRHS)
    !>          On entry, the right hand side B of the triangular system.
    !>          On exit, X is overwritten by the solution matrix X.
    !>

    LDX

    !>          LDX is INTEGER
    !>          The leading dimension of the array X.  LDX >= max (1,N).
    !>

    SCALE

    !>          SCALE is DOUBLE PRECISION array, dimension (NRHS)
    !>          The scaling factor s(k) is for the triangular system
    !>          A * x(:,k) = s(k)*b(:,k)  or  A**T* x(:,k) = s(k)*b(:,k).
    !>          If SCALE = 0, the matrix A is singular or badly scaled.
    !>          If A(j,j) = 0 is encountered, a non-trivial vector x(:,k)
    !>          that is an exact or approximate solution to A*x(:,k) = 0
    !>          is returned. If the system so badly scaled that solution
    !>          cannot be presented as x(:,k) * 1/s(k), then x(:,k) = 0
    !>          is returned.
    !>

    CNORM

    !>          CNORM is DOUBLE PRECISION array, dimension (N)
    !>
    !>          If NORMIN = 'Y', CNORM is an input argument and CNORM(j)
    !>          contains the norm of the off-diagonal part of the j-th column
    !>          of A.  If TRANS = 'N', CNORM(j) must be greater than or equal
    !>          to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j)
    !>          must be greater than or equal to the 1-norm.
    !>
    !>          If NORMIN = 'N', CNORM is an output argument and CNORM(j)
    !>          returns the 1-norm of the offdiagonal part of the j-th column
    !>          of A.
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (LWORK).
    !>          On exit, if INFO = 0, WORK(1) returns the optimal size of
    !>          WORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK.
    !>
    !>          If MIN(N,NRHS) = 0, LWORK >= 1, else
    !>          LWORK >= MAX(1, 2*NBA * MAX(NBA, MIN(NRHS, 32)), where
    !>          NBA = (N + NB - 1)/NB and NB is the optimal block size.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the optimal dimensions 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.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -k, the k-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

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