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man pages->IRIX man pages -> complib/spbtrs (3)
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### Contents

```
SPBTRS(3F)							    SPBTRS(3F)

```

### NAME[Toc][Back]

```     SPBTRS - solve a system of	linear equations A*X = B with a	symmetric
positive definite band matrix A using the Cholesky	factorization A	=
U**T*U or A = L*L**T computed by SPBTRF
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	SPBTRS(	UPLO, N, KD, NRHS, AB, LDAB, B,	LDB, INFO )

CHARACTER	UPLO

INTEGER	INFO, KD, LDAB,	LDB, N,	NRHS

REAL		AB( LDAB, * ), B( LDB, * )
```

### PURPOSE[Toc][Back]

```     SPBTRS solves a system of linear equations	A*X = B	with a symmetric
positive definite band matrix A using the Cholesky	factorization A	=
U**T*U or A = L*L**T computed by SPBTRF.

```

### ARGUMENTS[Toc][Back]

```     UPLO    (input) CHARACTER*1
= 'U':  Upper triangular factor stored in AB;
= 'L':  Lower triangular factor stored in AB.

N	     (input) INTEGER
The order of the matrix A.	 N >= 0.

KD	     (input) INTEGER
The number	of superdiagonals of the matrix	A if UPLO = 'U', or
the number	of subdiagonals	if UPLO	= 'L'.	KD >= 0.

NRHS    (input) INTEGER
The number	of right hand sides, i.e., the number of columns of
the matrix	B.  NRHS >= 0.

AB	     (input) REAL array, dimension (LDAB,N)
The triangular factor U or	L from the Cholesky factorization A =
U**T*U or A = L*L**T of the band matrix A,	stored in the first
KD+1 rows of the array.  The j-th column of U or L	is stored in
the j-th column of	the array AB as	follows:  if UPLO ='U',
AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L',
AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).

LDAB    (input) INTEGER
The leading dimension of the array	AB.  LDAB >= KD+1.

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

Page 1

SPBTRS(3F)							    SPBTRS(3F)

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

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
SPBTRS(3F)							    SPBTRS(3F)

```

### NAME[Toc][Back]

```     SPBTRS - solve a system of	linear equations A*X = B with a	symmetric
positive definite band matrix A using the Cholesky	factorization A	=
U**T*U or A = L*L**T computed by SPBTRF
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	SPBTRS(	UPLO, N, KD, NRHS, AB, LDAB, B,	LDB, INFO )

CHARACTER	UPLO

INTEGER	INFO, KD, LDAB,	LDB, N,	NRHS

REAL		AB( LDAB, * ), B( LDB, * )
```

### PURPOSE[Toc][Back]

```     SPBTRS solves a system of linear equations	A*X = B	with a symmetric
positive definite band matrix A using the Cholesky	factorization A	=
U**T*U or A = L*L**T computed by SPBTRF.

```

### ARGUMENTS[Toc][Back]

```     UPLO    (input) CHARACTER*1
= 'U':  Upper triangular factor stored in AB;
= 'L':  Lower triangular factor stored in AB.

N	     (input) INTEGER
The order of the matrix A.	 N >= 0.

KD	     (input) INTEGER
The number	of superdiagonals of the matrix	A if UPLO = 'U', or
the number	of subdiagonals	if UPLO	= 'L'.	KD >= 0.

NRHS    (input) INTEGER
The number	of right hand sides, i.e., the number of columns of
the matrix	B.  NRHS >= 0.

AB	     (input) REAL array, dimension (LDAB,N)
The triangular factor U or	L from the Cholesky factorization A =
U**T*U or A = L*L**T of the band matrix A,	stored in the first
KD+1 rows of the array.  The j-th column of U or L	is stored in
the j-th column of	the array AB as	follows:  if UPLO ='U',
AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L',
AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).

LDAB    (input) INTEGER
The leading dimension of the array	AB.  LDAB >= KD+1.

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

Page 1

SPBTRS(3F)							    SPBTRS(3F)

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

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

PPPPaaaaggggeeee 2222```
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