stbsv.f −

**Functions/Subroutines**

subroutine **stbsv** (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)

STBSV

**subroutine stbsv (characterUPLO, characterTRANS, characterDIAG, integerN, integerK, real, dimension(lda,*)A, integerLDA, real, dimension(*)X, integerINCX)
STBSV Purpose:**

STBSV solves one of the systems of equations

A*x = b, or A**T*x = b,

where b and x are n element vectors and A is an n by n unit, or

non-unit, upper or lower triangular band matrix, with ( k + 1 )

diagonals.

No test for singularity or near-singularity is included in this

routine. Such tests must be performed before calling this routine.

**Parameters:**

*UPLO*

UPLO is CHARACTER*1

On entry, UPLO specifies whether the matrix is an upper or

lower triangular matrix as follows:

UPLO = ’U’ or ’u’ A is an upper triangular matrix.

UPLO = ’L’ or ’l’ A is a lower triangular matrix.

*TRANS*

TRANS is CHARACTER*1

On entry, TRANS specifies the equations to be solved as

follows:

TRANS = ’N’ or ’n’ A*x = b.

TRANS = ’T’ or ’t’ A**T*x = b.

TRANS = ’C’ or ’c’ A**T*x = b.

*DIAG*

DIAG is CHARACTER*1

On entry, DIAG specifies whether or not A is unit

triangular as follows:

DIAG = ’U’ or ’u’ A is assumed to be unit triangular.

DIAG = ’N’ or ’n’ A is not assumed to be unit

triangular.

*N*

N is INTEGER

On entry, N specifies the order of the matrix A.

N must be at least zero.

*K*

K is INTEGER

On entry with UPLO = ’U’ or ’u’, K specifies the number of

super-diagonals of the matrix A.

On entry with UPLO = ’L’ or ’l’, K specifies the number of

sub-diagonals of the matrix A.

K must satisfy 0 .le. K.

*A*

A is REAL array of DIMENSION ( LDA, n ).

Before entry with UPLO = ’U’ or ’u’, the leading ( k + 1 )

by n part of the array A must contain the upper triangular

band part of the matrix of coefficients, supplied column by

column, with the leading diagonal of the matrix in row

( k + 1 ) of the array, the first super-diagonal starting at

position 2 in row k, and so on. The top left k by k triangle

of the array A is not referenced.

The following program segment will transfer an upper

triangular band matrix from conventional full matrix storage

to band storage:

DO 20, J = 1, N

M = K + 1 - J

DO 10, I = MAX( 1, J - K ), J

A( M + I, J ) = matrix( I, J )

10 CONTINUE

20 CONTINUE

Before entry with UPLO = ’L’ or ’l’, the leading ( k + 1 )

by n part of the array A must contain the lower triangular

band part of the matrix of coefficients, supplied column by

column, with the leading diagonal of the matrix in row 1 of

the array, the first sub-diagonal starting at position 1 in

row 2, and so on. The bottom right k by k triangle of the

array A is not referenced.

The following program segment will transfer a lower

triangular band matrix from conventional full matrix storage

to band storage:

DO 20, J = 1, N

M = 1 - J

DO 10, I = J, MIN( N, J + K )

A( M + I, J ) = matrix( I, J )

10 CONTINUE

20 CONTINUE

Note that when DIAG = ’U’ or ’u’ the elements of the array A

corresponding to the diagonal elements of the matrix are not

referenced, but are assumed to be unity.

*LDA*

LDA is INTEGER

On entry, LDA specifies the first dimension of A as declared

in the calling (sub) program. LDA must be at least

( k + 1 ).

*X*

X is REAL array of dimension at least

( 1 + ( n - 1 )*abs( INCX ) ).

Before entry, the incremented array X must contain the n

element right-hand side vector b. On exit, X is overwritten

with the solution vector x.

*INCX*

INCX is INTEGER

On entry, INCX specifies the increment for the elements of

X. INCX must not be zero.

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

**Further Details:**

Level 2 Blas routine.

-- Written on 22-October-1986.

Jack Dongarra, Argonne National Lab.

Jeremy Du Croz, Nag Central Office.

Sven Hammarling, Nag Central Office.

Richard Hanson, Sandia National Labs.

Definition at line 190 of file stbsv.f.

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